FORECASTING AND ON THE INFLUENCE OF CLIMATIC FACTORS ON RISING DENGUE INCIDENCE IN BAGUIO CITY, PHILIPPINES

Dengue fever or dengue has been a concern for individuals living in Baguio City, Philippines. Every year, incidence counts rise during rainy seasons experienced from June to October. Several researches suggest that meteorological factors have great influence on the life, growth, and reproduction of dengue-carrying mosquitoes, resulting in higher dengue incidence in the area. With the continuing rise of dengue incidence in Baguio City, we aim to forecast dengue incidence in the area for the year 2019, starting from January until the end of the outbreak period in the area. Here, we use the projections package of R as it involves the serial interval distribution and 𝑅𝑡 value of dengue incidence. We also aim to use multiple linear regression analysis to determine if meteorological factors have significant effects in the rise of dengue incidence in the city. With the inclusion of time-varying reproduction number and serial interval distribution of dengue, we projected that dengue incidence may reach up to 101 cases by June 16, 2021, and without further actions, cases may rise up to 529 cases by August 29, 2021. Based on the average two-year period, such increase is attributed to relative humidity and average temperature as these are the most significant factors associated with dengue incidence based on the MLR analysis. The highest and mean maximum temperatures remain as key meteorological variables that influence dengue incidence in the city. As early as possible, local officials are recommended to uphold proper safety and health procedures in preventing the spread of dengue in Baguio City.


INTRODUCTION
Dengue fever (or dengue) is a mosquito-borne viral infection commonly spread by female Aedes aegypti mosquitoes in tropical and subtropical regions, especially urban environments (Cogan, 2021). In Baguio City, where rainy seasons are felt on June to October and dry seasons on the rest of the months in a year, dengue is a common illness among locals, where reported spikes in local dengue cases in the area from January to May 2016 compared to other months from 2010 to 2018 (Polonio, 2016). As a result, several protective measures and clean-up drives were conducted to destroy potential breeding sites of dengue-carrying mosquitoes and larvae.
Several notable researches were conducted to determine the effects of meteorological factors -humidity, precipitation, and temperature -to the growth of dengue incidence in a certain area. According to the study at Jakarta in Indonesia, the strong correlation between the population density of Aedes aegypti mosquitoes, temperature, and relative humidity indicated that the weather factors influence the growth and population of mosquitoes in the area (Sintorini, 2018). In another study in Thailand, the combination of humidity and temperature has become beneficial in the development, survival, length of the extrinsic incubation period, and competence of denguecarrying mosquitoes (Campbell et al., 2013). Similar studies were also conducted within the Philippines. In Metro Manila, a simple linear regression (SLR) analysis on the monthly climatic factors (temperature and rainfall) and dengue incidence data from 1996 to 2005 concluded that the dengue incidence is likely affected by changes in the amount of rainfall affecting mosquito populations as breeding grounds increase (Sia Su, 2008). Another correlation on the effect of climatic factors on laboratory-confirmed dengue and leptospirosis infections in the Philippines suggests that dengue fever and leptospirosis correlate with rainfall, relative humidity, and temperature (Sumi et al., 2016).
In another case study at Iligan City in Mindanao, researchers used multiple linear regression (MLR) analysis, Poisson regression, and random forest in developing a best-fitting model for dengue incidence in the area. Considering the monthly climatic factors -relative rainfall maximum temperature and average (relative humidity -together with the monthly time period from 2008 to 2017 (Olmoguez et al., 2019), results show that the MLR model, having 18% accuracy percentage and 67.14% error result, has the form (1) However, they further conclude that the Random Forest performed better with a 73% accuracy percentage and 33.58% error result.
Several researches also involve forecasting using regression methods. In Pakistan, Sabir et al. (2018) applied SLR analysis to forecast the possible cumulative incidence of dengue in 2017 and 2018, utilising the yearly period as the independent variable. On the other hand, a case study in China by Guo et al. (2017) applied multiple regression algorithms to develop a dengue forecast model in the area.
In Baguio City, several other forecasting methods were also employed considering local dengue incidence data. Addawe et al. (2016) used Differential Evolution -Simulated Annealing (DESA) algorithm in acquiring the best-fitting forecasting models for young and adult populations. Another study by Magsakay et. al (2017) applied winsorization, square root, and logarithmic transformations to treat the outliers on age groups (ages 0 to 8 years old and 45 years old and above) who are not eligible for the dengue vaccine. Through [2] ermine the effects of meteorological factorshumidity, engue incidence in a certain area. According to the study een the population density of Aedes aegypti mosquitoes, e weather factors influence the growth and population of er study in Thailand, the combination of humidity and ment, survival, length of the extrinsic incubation period, ampbell et al., 2013).
ippines. In Metro Manila, a simple linear regression (SLR) ure and rainfall) and dengue incidence data from 1996 to y affected by changes in the amount of rainfall affecting se (Sia Su, 2008). Another correlation on the effect of d leptospirosis infections in the Philippines suggests that ll, relative humidity, and temperature (Sumi et al., 2016). searchers used multiple linear regression (MLR) analysis, ng a best-fitting model for dengue incidence in the area. lative rainfall ( 1 ), maximum temperature ( 2 ), and monthly time period ( 4 ) from 2008 to 2017 (Olmoguez aving 18% accuracy percentage and 67.14% error result, .83 2 − 6.20 3 + 0.72 4 + 815. 98 (1) Forest performed better with a 73% accuracy percentage gression methods. In Pakistan, Sabir et al. (2018) applied cidence of dengue in 2017 and 2018, utilising the yearly and, a case study in China by Guo et al. (2017) applied forecast model in the area.
were also employed considering local dengue incidence ion -Simulated Annealing (DESA) algorithm in acquiring ult populations. Another study by Magsakay et. al (2017) transformations to treat the outliers on age groups (ages o are not eligible for the dengue vaccine. Through the [2] rmine the effects of meteorological factorshumidity, ngue incidence in a certain area. According to the study en the population density of Aedes aegypti mosquitoes, weather factors influence the growth and population of r study in Thailand, the combination of humidity and ent, survival, length of the extrinsic incubation period, mpbell et al., 2013).
pines. In Metro Manila, a simple linear regression (SLR) re and rainfall) and dengue incidence data from 1996 to affected by changes in the amount of rainfall affecting e (Sia Su, 2008). Another correlation on the effect of leptospirosis infections in the Philippines suggests that l, relative humidity, and temperature (Sumi et al., 2016). earchers used multiple linear regression (MLR) analysis, g a best-fitting model for dengue incidence in the area. tive rainfall ( 1 ), maximum temperature ( 2 ), and monthly time period ( 4 ) from 2008 to 2017 (Olmoguez ing 18% accuracy percentage and 67.14% error result, 3 2 − 6.20 3 + 0.72 4 + 815.98 (1) orest performed better with a 73% accuracy percentage ression methods. In Pakistan, Sabir et al. (2018) applied idence of dengue in 2017 and 2018, utilising the yearly nd, a case study in China by Guo et al. (2017) applied forecast model in the area.
ere also employed considering local dengue incidence n -Simulated Annealing (DESA) algorithm in acquiring lt populations. Another study by Magsakay et. al (2017) transformations to treat the outliers on age groups (ages are not eligible for the dengue vaccine. Through the [2] and larvae. able researches were conducted to determine the effects of meteorological factorshumidity, , and temperatureto the growth of dengue incidence in a certain area. According to the study Indonesia, the strong correlation between the population density of Aedes aegypti mosquitoes, , and relative humidity indicated that the weather factors influence the growth and population of in the area (Sintorini, 2018). In another study in Thailand, the combination of humidity and has become beneficial in the development, survival, length of the extrinsic incubation period, ence of dengue-carrying mosquitoes (Campbell et al., 2013).
ies were also conducted within the Philippines. In Metro Manila, a simple linear regression (SLR) the monthly climatic factors (temperature and rainfall) and dengue incidence data from 1996 to ded that the dengue incidence is likely affected by changes in the amount of rainfall affecting opulations as breeding grounds increase (Sia Su, 2008). Another correlation on the effect of tors on laboratory-confirmed dengue and leptospirosis infections in the Philippines suggests that r and leptospirosis correlate with rainfall, relative humidity, and temperature (Sumi et al., 2016).
ase study at Iligan City in Mindanao, researchers used multiple linear regression (MLR) analysis, ression, and random forest in developing a best-fitting model for dengue incidence in the area. the monthly climatic factors -relative rainfall ( 1 ), maximum temperature ( 2 ), and lative humidity ( 3 ) -together with the monthly time period ( 4 ) from 2008 to 2017 (Olmoguez , results show that the MLR model, having 18% accuracy percentage and 67.14% error result, dengue cases = 0.10 1 − 9.83 2 − 6.20 3 + 0.72 4 + 815. 98 (1) ey further conclude that the Random Forest performed better with a 73% accuracy percentage error result.
arches also involve forecasting using regression methods. In Pakistan, Sabir et al. (2018) applied is to forecast the possible cumulative incidence of dengue in 2017 and 2018, utilising the yearly e independent variable. On the other hand, a case study in China by Guo et al. (2017) applied ression algorithms to develop a dengue forecast model in the area.
ity, several other forecasting methods were also employed considering local dengue incidence e et al. (2016) used Differential Evolution -Simulated Annealing (DESA) algorithm in acquiring ng forecasting models for young and adult populations. Another study by Magsakay et. al (2017) sorization, square root, and logarithmic transformations to treat the outliers on age groups (ages s old and 45 years old and above) who are not eligible for the dengue vaccine. Through the [2] osquitoes and larvae.
everal notable researches were conducted to determine the effects of meteorological factorsrecipitation, and temperatureto the growth of dengue incidence in a certain area. According to t Jakarta in Indonesia, the strong correlation between the population density of Aedes aegypti mo emperature, and relative humidity indicated that the weather factors influence the growth and pop osquitoes in the area (Sintorini, 2018). In another study in Thailand, the combination of hum emperature has become beneficial in the development, survival, length of the extrinsic incubatio nd competence of dengue-carrying mosquitoes (Campbell et al., 2013). imilar studies were also conducted within the Philippines. In Metro Manila, a simple linear regressi nalysis on the monthly climatic factors (temperature and rainfall) and dengue incidence data from 005 concluded that the dengue incidence is likely affected by changes in the amount of rainfall osquito populations as breeding grounds increase (Sia Su, 2008). Another correlation on the limatic factors on laboratory-confirmed dengue and leptospirosis infections in the Philippines sug engue fever and leptospirosis correlate with rainfall, relative humidity, and temperature (Sumi et a n another case study at Iligan City in Mindanao, researchers used multiple linear regression (MLR) oisson regression, and random forest in developing a best-fitting model for dengue incidence in onsidering the monthly climatic factors -relative rainfall ( 1 ), maximum temperature ( verage (relative humidity ( 3 ) -together with the monthly time period ( 4 ) from 2008 to 2017 (O t al., 2019), results show that the MLR model, having 18% accuracy percentage and 67.14% err as the form dengue cases = 0.10 1 − 9.83 2 − 6.20 3 + 0.72 4 + 815.98 owever, they further conclude that the Random Forest performed better with a 73% accuracy p nd 33.58% error result. everal researches also involve forecasting using regression methods. In Pakistan, Sabir et al. (2018 LR analysis to forecast the possible cumulative incidence of dengue in 2017 and 2018, utilising t eriod as the independent variable. On the other hand, a case study in China by Guo et al. (2017 ultiple regression algorithms to develop a dengue forecast model in the area. n Baguio City, several other forecasting methods were also employed considering local dengue ata. Addawe et al. (2016) used Differential Evolution -Simulated Annealing (DESA) algorithm in he best-fitting forecasting models for young and adult populations. Another study by Magsakay et. pplied winsorization, square root, and logarithmic transformations to treat the outliers on age gro to 8 years old and 45 years old and above) who are not eligible for the dengue vaccine. Thr [2] a common illness among locals, where reported spikes in local dengue cases in the area from January to ay 2016 compared to other months from 2010 to 2018 (Polonio, 2016). As a result, several protective easures and clean-up drives were conducted to destroy potential breeding sites of dengue-carrying osquitoes and larvae.
everal notable researches were conducted to determine the effects of meteorological factorshumidity, recipitation, and temperatureto the growth of dengue incidence in a certain area. According to the study t Jakarta in Indonesia, the strong correlation between the population density of Aedes aegypti mosquitoes, mperature, and relative humidity indicated that the weather factors influence the growth and population of osquitoes in the area (Sintorini, 2018). In another study in Thailand, the combination of humidity and mperature has become beneficial in the development, survival, length of the extrinsic incubation period, nd competence of dengue-carrying mosquitoes (Campbell et al., 2013).
imilar studies were also conducted within the Philippines. In Metro Manila, a simple linear regression (SLR) nalysis on the monthly climatic factors (temperature and rainfall) and dengue incidence data from 1996 to 005 concluded that the dengue incidence is likely affected by changes in the amount of rainfall affecting osquito populations as breeding grounds increase (Sia Su, 2008). Another correlation on the effect of limatic factors on laboratory-confirmed dengue and leptospirosis infections in the Philippines suggests that engue fever and leptospirosis correlate with rainfall, relative humidity, and temperature (Sumi et al., 2016).
another case study at Iligan City in Mindanao, researchers used multiple linear regression (MLR) analysis, oisson regression, and random forest in developing a best-fitting model for dengue incidence in the area. onsidering the monthly climatic factors -relative rainfall ( 1 ), maximum temperature ( 2 ), and verage (relative humidity ( 3 ) -together with the monthly time period ( 4 ) from 2008 to 2017 (Olmoguez t al., 2019), results show that the MLR model, having 18% accuracy percentage and 67.14% error result, as the form dengue cases = 0.10 1 − 9.83 2 − 6.20 3 + 0.72 4 + 815.98 (1) owever, they further conclude that the Random Forest performed better with a 73% accuracy percentage nd 33.58% error result.
everal researches also involve forecasting using regression methods. In Pakistan, Sabir et al. (2018) applied LR analysis to forecast the possible cumulative incidence of dengue in 2017 and 2018, utilising the yearly eriod as the independent variable. On the other hand, a case study in China by Guo et al. (2017) applied ultiple regression algorithms to develop a dengue forecast model in the area.
Baguio City, several other forecasting methods were also employed considering local dengue incidence ata. Addawe et al. (2016) used Differential Evolution -Simulated Annealing (DESA) algorithm in acquiring e best-fitting forecasting models for young and adult populations. Another study by Magsakay et. al (2017) pplied winsorization, square root, and logarithmic transformations to treat the outliers on age groups (ages to 8 years old and 45 years old and above) who are not eligible for the dengue vaccine. Through the acquired the best-fitting forecasting models for each age group.
Another notable characteristic to consider is the time-dependent reproduction number Compared to the basic reproduction number incorporates the time-dependent variations in the transmission of diseases to the secondary cases from the corresponding primary case (Nishiura & Chowell, 2009). In the work of Nouvellet et al. (2017), they included the effect of and the serial interval of some pathogens as factors to acquire an accurate forecast. As defined in Du et al. (2020), a serial interval is the time interval between the primary infected patient and its secondary infected patient. The corresponding probability density function is called the serial interval distribution w. With the influence of temperature, the serial interval of dengue is a combination of intrinsic incubation period (IIP), human-to-mosquito transmission period (HMTP), extrinsic incubation period (EIP), and mosquito-to-human transmission period (MHTP) (Siraj et al., 2017). To differentiate, IIP is the time difference between the patient's date of infection and the date of symptom onset; HMTP is the time between the conclusion of IIP and the date when the susceptible mosquito becomes infected; EIP is the time from ingesting the virus by the susceptible mosquito until it becomes infected; and MHTP is the time between the infected mosquito transfers the virus to a new host (Cogan, 2021;Siraj et al., 2017). In the study of Aldstadt et al. (2012) in Thailand, they concluded that the serial interval for dengue infection is most likely 15-17 days with a significant excess risk of illness that persists for 32-34 days.
In our previous studies, we conducted SLR analysis in determining the climatological factors affecting the dengue incidence in Baguio City within the two -year average period (Marigmen et al., 2021). Results showed that humidity is the main factor affecting the dengue incidence, followed by precipitation. Despite relatively high adjusted R-squared values, their difference from a perfect adjusted R-squared value (adjusted R-squared value is 1) indicates that there are other possible factors that affect the growth of dengue incidence in the area.
In this paper, we extend our previous study by conducting an MLR analysis on the dengue incidence from 2011 to 2018 to determine the said possible variables. odel, they acquired the best-fitting forecasting models -dependent reproduction number . Compared to the e-dependent variations in the transmission of diseases ary case (Nishiura & Chowell, 2009). In the work of and the serial interval of some pathogens as factors to 2020), a serial interval is the time interval between the atient. The corresponding probability density function fluence of temperature, the serial interval of dengue is an-to-mosquito transmission period (HMTP), extrinsic ransmission period (MHTP) (Siraj et al., 2017). To tient's date of infection and the date of symptom onset; nd the date when the susceptible mosquito becomes he susceptible mosquito until it becomes infected; and sfers the virus to a new host (Cogan, 2021;Siraj et al., and, they concluded that the serial interval for dengue excess risk of illness that persists for 32-34 days.
in determining the climatological factors affecting the year average period (Marigmen et al., 2021). Results dengue incidence, followed by precipitation. Despite ence from a perfect adjusted R-squared value (adjusted sible factors that affect the growth of dengue incidence cting an MLR analysis on the dengue incidence from . aim to conduct a dengue forecast using the projections res the dengue serial interval distribution and computed rial interval distribution, we then forecast the dengue responding outbreak period. Further discussions on the ethodology. this paper. We only considered the available monthly lysis. As for the forecast, due to the lack of published ippines, we incorporated the findings of Aldstadt et al. g one forecasting method as part of our study.
ting are provided in the Theoretical Framework.

FRAMEWORK
x-Jenkins (UBJ-ARIMA) time series model, they acquired the best-fitting forecasting models oup.
le characteristic to consider is the time-dependent reproduction number . Compared to the tion number 0 , incorporates the time-dependent variations in the transmission of diseases ry cases from the corresponding primary case (Nishiura & Chowell, 2009). In the work of . (2017), they included the effect of and the serial interval of some pathogens as factors to urate forecast. As defined in Du et al. (2020), a serial interval is the time interval between the ed patient and its secondary infected patient. The corresponding probability density function rial interval distribution w. With the influence of temperature, the serial interval of dengue is of intrinsic incubation period (IIP), human-to-mosquito transmission period (HMTP), extrinsic riod (EIP), and mosquito-to-human transmission period (MHTP) (Siraj et al., 2017). To IP is the time difference between the patient's date of infection and the date of symptom onset; time between the conclusion of IIP and the date when the susceptible mosquito becomes s the time from ingesting the virus by the susceptible mosquito until it becomes infected; and ime between the infected mosquito transfers the virus to a new host (Cogan, 2021;Siraj et al., tudy of Aldstadt et al. (2012) in Thailand, they concluded that the serial interval for dengue st likely 15-17 days with a significant excess risk of illness that persists for 32-34 days.
s studies, we conducted SLR analysis in determining the climatological factors affecting the nce in Baguio City within the twoyear average period (Marigmen et al., 2021). Results umidity is the main factor affecting the dengue incidence, followed by precipitation. Despite adjusted R-squared values, their difference from a perfect adjusted R-squared value (adjusted e is 1) indicates that there are other possible factors that affect the growth of dengue incidence e extend our previous study by conducting an MLR analysis on the dengue incidence from o determine the said possible variables. ase of dengue cases in the area, we also aim to conduct a dengue forecast using the projections statistical software. The package requires the dengue serial interval distribution and computed g the computed values and the serial interval distribution, we then forecast the dengue 19, starting from January until the corresponding outbreak period. Further discussions on the ethods are documented as part of the Methodology. and, some limitations are discussed in this paper. We only considered the available monthly s from 2011 to 2018 in our MLR analysis. As for the forecast, due to the lack of published the serial interval of dengue in the Philippines, we incorporated the findings of Aldstadt et al. nalysis. In this paper, we are only using one forecasting method as part of our study.
sions on the MLR analysis and forecasting are provided in the Theoretical Framework.

THEORETICAL FRAMEWORK
ivariate Box-Jenkins (UBJ-ARIMA) time series model, they acquired the best-fitting forecasting each age group.
other notable characteristic to consider is the time-dependent reproduction number . Compared ic reproduction number 0 , incorporates the time-dependent variations in the transmission of d the secondary cases from the corresponding primary case (Nishiura & Chowell, 2009). In the w uvellet et al. (2017), they included the effect of and the serial interval of some pathogens as fac uire an accurate forecast. As defined in Du et al. (2020), a serial interval is the time interval betw mary infected patient and its secondary infected patient. The corresponding probability density fu alled the serial interval distribution w. With the influence of temperature, the serial interval of den ombination of intrinsic incubation period (IIP), human-to-mosquito transmission period (HMTP), ex ubation period (EIP), and mosquito-to-human transmission period (MHTP) (Siraj et al.,201 ferentiate, IIP is the time difference between the patient's date of infection and the date of symptom TP is the time between the conclusion of IIP and the date when the susceptible mosquito be ected; EIP is the time from ingesting the virus by the susceptible mosquito until it becomes infecte TP is the time between the infected mosquito transfers the virus to a new host (Cogan, 2021;Sira 7). In the study of Aldstadt et al. (2012) in Thailand, they concluded that the serial interval for d ection is most likely 15-17 days with a significant excess risk of illness that persists for 32-34 days our previous studies, we conducted SLR analysis in determining the climatological factors affect gue incidence in Baguio City within the twoyear average period (Marigmen et al., 2021). R wed that humidity is the main factor affecting the dengue incidence, followed by precipitation. D atively high adjusted R-squared values, their difference from a perfect adjusted R-squared value (a quared value is 1) indicates that there are other possible factors that affect the growth of dengue inc the area. this paper, we extend our previous study by conducting an MLR analysis on the dengue incidenc 1 to 2018 to determine the said possible variables. th the increase of dengue cases in the area, we also aim to conduct a dengue forecast using the proj kage in R, a statistical software. The package requires the dengue serial interval distribution and com value. Using the computed values and the serial interval distribution, we then forecast the idence in 2019, starting from January until the corresponding outbreak period. Further discussions kage and methods are documented as part of the Methodology. the other hand, some limitations are discussed in this paper. We only considered the available m matic factors from 2011 to 2018 in our MLR analysis. As for the forecast, due to the lack of pub uments on the serial interval of dengue in the Philippines, we incorporated the findings of Aldstad 12) in our analysis. In this paper, we are only using one forecasting method as part of our study. rther discussions on the MLR analysis and forecasting are provided in the Theoretical Framework.
With the increase of dengue cases in the area, we also aim to conduct a dengue forecast using the projections package in R, a statistical software. The package requires the dengue serial interval distribution and computed value. Using the computed values and the serial interval distribution, we then forecast the dengue incidence in 2019, starting from January until the corresponding outbreak period. Further discussions on the package and methods are documented as part of the Methodology.
On the other hand, some limitations are discussed in this paper. We only considered the available monthly climatic factors from 2011 to 2018 in our MLR analysis. As for the forecast, due to the lack of published documents on the serial interval of dengue in the Philippines, we incorporated the findings of Aldstadt et al. (2012) in our analysis. In this paper, we are only using one forecasting method as part of our study.
Further discussions on the MLR analysis and forecasting are provided in the Theoretical Framework.

THEORETICAL FRAMEWORK
In this section, we discuss the theoretical framework behind forecasting and MLR analysis.
Given the daily incidence I, w, and Rt, we apply the renewal equation (2) in generating a branching process model and use it in our forecast (Nouvellet et al., 2017). In determining its accuracy to our available data, the renewal equation is applied to available historical data, where we estimate the trend of dengue incidence from previous years. Error analysis is also applied to determine the accuracy of the calculated estimates from the said data. Here, we apply the Root Mean Square Error (RMSE) to check the accuracy of the estimates. We emphasize here that the RMSE values must be low enough for the model to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality of residuals. The residual is the difference between the estimated value from the equation and the actual value from the data.
[3] -squared value is 1) indicates that there are other possible factors that affect the growth of dengue i the area.
n this paper, we extend our previous study by conducting an MLR analysis on the dengue inciden 011 to 2018 to determine the said possible variables.
ith the increase of dengue cases in the area, we also aim to conduct a dengue forecast using the pr ackage in R, a statistical software. The package requires the dengue serial interval distribution and c value. Using the computed values and the serial interval distribution, we then forecast the cidence in 2019, starting from January until the corresponding outbreak period. Further discussio ackage and methods are documented as part of the Methodology. n the other hand, some limitations are discussed in this paper. We only considered the available limatic factors from 2011 to 2018 in our MLR analysis. As for the forecast, due to the lack of p ocuments on the serial interval of dengue in the Philippines, we incorporated the findings of Aldst 2012) in our analysis. In this paper, we are only using one forecasting method as part of our study.
urther discussions on the MLR analysis and forecasting are provided in the Theoretical Framewor

THEORETICAL FRAMEWORK
n this section, we discuss the theoretical framework behind forecasting and MLR analysis.
iven the daily incidence I, w, and Rt, we apply the renewal equation R-squared value is 1) indicates that there are other possible factors tha in the area.
In this paper, we extend our previous study by conducting an MLR 2011 to 2018 to determine the said possible variables.
With the increase of dengue cases in the area, we also aim to conduct package in R, a statistical software. The package requires the dengue s value. Using the computed values and the serial interval dis incidence in 2019, starting from January until the corresponding outb package and methods are documented as part of the Methodology.
On the other hand, some limitations are discussed in this paper. We climatic factors from 2011 to 2018 in our MLR analysis. As for the documents on the serial interval of dengue in the Philippines, we inc (2012) in our analysis. In this paper, we are only using one forecastin Further discussions on the MLR analysis and forecasting are provide

THEORETICAL FRAMEWO
In this section, we discuss the theoretical framework behind forecast Given the daily incidence I, w, and Rt, we apply the renewal equatio in generating a branching process model and use it in our forecast (Nouvellet et al., 2017). In accuracy to our available data, the renewal equation is applied to available historical data, whe the trend of dengue incidence from previous years. Error analysis is also applied to determin of the calculated estimates from the said data. Here, we apply the Root Mean Square Error (R the accuracy of the estimates. We emphasize here that the RMSE values must be low enough to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality of residual is the difference between the estimated value from the equation and the actual value from the To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the varian distribution based on a random sample of n observations (Royston, 1995; Gonzalez -Estra 2019). The residuals are normally distributed if the resulting p-value is greater than 0.05 (p Otherwise, the residuals are not normal. To attain the normality of residuals, we use the co statistic. Given the residuals i, the W statistic is defined as To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the variance of a normal distribution based on a random sample of n observations (Royston, 1995;Gonzalez -Estrada & Cosmes, 2019). The residuals are normally distributed if the resulting p-value is greater than 0.05 (p-value > 0.05). Otherwise, the residuals are not normal. To attain the normality of residuals, we use the corresponding W statistic. Given the residuals i, the W statistic is defined as (3) where is the sample mean of the residuals, and are the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal distribution, and is the covariance matrix of the order statistics (Razali & Yap, 2011). The statistic value lies between zero and one, and the larger the value indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, we proceed with dengue forecasting in Baguio City for 2019, starting from January until the end of the outbreak period.
On the other hand, MLR is an extension of SLR where we consider more than one independent variable and has the form (4) where are the coefficients that need to determine and is the dependent variable (Pearson, 2018).
As part of constructing best-fitting MLR models, we first conduct correlation analysis to determine the strength of relationship between two variables. In computing the correlation coefficient, we apply Pearson's Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, we consider r to be strong if its absolute value is at least 0.70 (Schober et al., 2018). We also use the correlation results to check for collinearity or having high correlation between two independent variables to acquire a better fitting MLR model (Chatterjee & Simonoff, 2013).
[4] the trend of dengue incidence from previous years. Error analysis is also applied to determine the of the calculated estimates from the said data. Here, we apply the Root Mean Square Error (RMSE the accuracy of the estimates. We emphasize here that the RMSE values must be low enough for t to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality of residuals. Th is the difference between the estimated value from the equation and the actual value from the data.
To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the variance of distribution based on a random sample of n observations (Royston, 1995;Gonzalez -Estrada & 2019). The residuals are normally distributed if the resulting p-value is greater than 0.05 (p-valu Otherwise, the residuals are not normal. To attain the normality of residuals, we use the corresp statistic. Given the residuals i, the W statistic is defined as where is the sample mean of the residuals, = ( 1 , 2 , … , ) = −1 ( −1 −1 ) 1/2 a ( 1 , 2 , … , ) are the expected values of the order statistics of independent and identically d random variables sampled from the standard normal distribution, and is the covariance matrix of statistics (Razali & Yap, 2011). The statistic value lies between zero and one, and the larger indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, we proceed wit forecasting in Baguio City for 2019, starting from January until the end of the outbreak period.
On the other hand, MLR is an extension of SLR where we consider more than one independent v and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is the dependent variable (Pearson,20 As part of constructing best-fitting MLR models, we first conduct correlation analysis to dete strength of relationship between two variables. In computing the correlation coefficient, we apply Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, we consider r to be str absolute value is at least 0.70 (Schober et al., 2018). We also use the correlation results to collinearity or having high correlation between two independent variables 's to acquire a better fit model (Chatterjee & Simonoff, 2013).
[4] the trend of dengue incidence from previous years. Error analysis is also applied to de of the calculated estimates from the said data. Here, we apply the Root Mean Square Er the accuracy of the estimates. We emphasize here that the RMSE values must be low e to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality of re is the difference between the estimated value from the equation and the actual value fro To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the distribution based on a random sample of n observations (Royston, 1995;Gonzalez -2019). The residuals are normally distributed if the resulting p-value is greater than 0 Otherwise, the residuals are not normal. To attain the normality of residuals, we use t statistic. Given the residuals i, the W statistic is defined as where is the sample mean of the residuals, = ( 1 , 2 , … , ) = ( −1 ( 1 , 2 , … , ) are the expected values of the order statistics of independent and id random variables sampled from the standard normal distribution, and is the covarianc statistics (Razali & Yap, 2011). The statistic value lies between zero and one, and indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, we p forecasting in Baguio City for 2019, starting from January until the end of the outbreak On the other hand, MLR is an extension of SLR where we consider more than one ind and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is the dependent variable (P As part of constructing best-fitting MLR models, we first conduct correlation analy strength of relationship between two variables. In computing the correlation coefficient Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, we consider absolute value is at least 0.70 (Schober et al., 2018). We also use the correlation collinearity or having high correlation between two independent variables 's to acquire model (Chatterjee & Simonoff, 2013).
in generating a branching process model and use it in our forecast (Nouvellet et al., 2017). In determining its accuracy to our available data, the renewal equation is applied to available historical data, where we estimate the trend of dengue incidence from previous years. Error analysis is also applied to determine the accuracy of the calculated estimates from the said data. Here, we apply the Root Mean Square Error (RMSE) to check the accuracy of the estimates. We emphasize here that the RMSE values must be low enough for the model to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality of residuals. The residual is the difference between the estimated value from the equation and the actual value from the data.
To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the variance of a normal distribution based on a random sample of n observations (Royston, 1995;Gonzalez -Estrada & Cosmes, 2019). The residuals are normally distributed if the resulting p-value is greater than 0.05 (p-value > 0.05). Otherwise, the residuals are not normal. To attain the normality of residuals, we use the corresponding W statistic. Given the residuals i, the W statistic is defined as ( 3) where is the sample mean of the residuals, = ( 1 , 2 , … , ) = −1 ( −1 −1 ) 1/2 and = ( 1 , 2 , … , ) are the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal distribution, and is the covariance matrix of the order statistics (Razali & Yap, 2011). The statistic value lies between zero and one, and the larger the value indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, we proceed with dengue forecasting in Baguio City for 2019, starting from January until the end of the outbreak period.
On the other hand, MLR is an extension of SLR where we consider more than one independent variable and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is the dependent variable (Pearson, 2018).
As part of constructing best-fitting MLR models, we first conduct correlation analysis to determine the strength of relationship between two variables. In computing the correlation coefficient, we apply Pearson's Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, we consider r to be strong if its absolute value is at least 0.70 (Schober et al., 2018). We also use the correlation results to check for collinearity or having high correlation between two independent variables 's to acquire a better fitting MLR model (Chatterjee & Simonoff, 2013).
[4] the trend of dengue incidence from previous years. Error analysis is also ap of the calculated estimates from the said data. Here, we apply the Root Mean the accuracy of the estimates. We emphasize here that the RMSE values mu to fit with the data. We also apply the Shapiro-Wilk W Test to check the nor is the difference between the estimated value from the equation and the actu To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estima distribution based on a random sample of n observations (Royston, 1995;2019). The residuals are normally distributed if the resulting p-value is gre Otherwise, the residuals are not normal. To attain the normality of residua statistic. Given the residuals i, the W statistic is defined as where is the sample mean of the residuals, = ( 1 , 2 , … , ( 1 , 2 , … , ) are the expected values of the order statistics of indepen random variables sampled from the standard normal distribution, and is th statistics (Razali & Yap, 2011). The statistic value lies between zero an indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satis forecasting in Baguio City for 2019, starting from January until the end of th On the other hand, MLR is an extension of SLR where we consider more th and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is the dependen As part of constructing best-fitting MLR models, we first conduct correl strength of relationship between two variables. In computing the correlation Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, w absolute value is at least 0.70 (Schober et al., 2018). We also use the c collinearity or having high correlation between two independent variables ' model (Chatterjee & Simonoff, 2013 cy to our available data, the renewal equation is applied to available historical data, where we estim nd of dengue incidence from previous years. Error analysis is also applied to determine the accur calculated estimates from the said data. Here, we apply the Root Mean Square Error (RMSE) to ch uracy of the estimates. We emphasize here that the RMSE values must be low enough for the mo ith the data. We also apply the Shapiro-Wilk W Test to check the normality of residuals. The resid ifference between the estimated value from the equation and the actual value from the data.
borate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the variance of a norm ution based on a random sample of n observations (Royston, 1995;Gonzalez -Estrada & Cosm The residuals are normally distributed if the resulting p-value is greater than 0.05 (p-value > 0.0 ise, the residuals are not normal. To attain the normality of residuals, we use the corresponding c. Given the residuals i, the W statistic is defined as ( is the sample mean of the residuals, = ( 1 , 2 , … , ) = −1 ( −1 −1 ) 1/2 and 2 , … , ) are the expected values of the order statistics of independent and identically distribu variables sampled from the standard normal distribution, and is the covariance matrix of the or cs (Razali & Yap, 2011). The statistic value lies between zero and one, and the larger the va es that the residuals are normally distributed.
the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, we proceed with deng sting in Baguio City for 2019, starting from January until the end of the outbreak period. other hand, MLR is an extension of SLR where we consider more than one independent variable s the form = 0 + 1 1 + 2 2 + ⋯ + ( 's are the coefficients that need to determine and is the dependent variable (Pearson, 2018).
t of constructing best-fitting MLR models, we first conduct correlation analysis to determine h of relationship between two variables. In computing the correlation coefficient, we apply Pearso t Moment Correlation Coefficient r (Walpole et al., 2012). Here, we consider r to be strong if te value is at least 0.70 (Schober et al., 2018). We also use the correlation results to check arity or having high correlation between two independent variables 's to acquire a better fitting M (Chatterjee & Simonoff, 2013). [4] in generating a branching process model and use it in our forecast (Nouvellet et al., 2017). In deter accuracy to our available data, the renewal equation is applied to available historical data, where w the trend of dengue incidence from previous years. Error analysis is also applied to determine the of the calculated estimates from the said data. Here, we apply the Root Mean Square Error (RMSE the accuracy of the estimates. We emphasize here that the RMSE values must be low enough for to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality of residuals. Th is the difference between the estimated value from the equation and the actual value from the data To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the variance of distribution based on a random sample of n observations (Royston, 1995;Gonzalez -Estrada & 2019). The residuals are normally distributed if the resulting p-value is greater than 0.05 (p-valu Otherwise, the residuals are not normal. To attain the normality of residuals, we use the corresp statistic. Given the residuals i, the W statistic is defined as where is the sample mean of the residuals, ) are the expected values of the order statistics of independent and identically d random variables sampled from the standard normal distribution, and is the covariance matrix of statistics (Razali & Yap, 2011). The statistic value lies between zero and one, and the larger indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, we proceed wit forecasting in Baguio City for 2019, starting from January until the end of the outbreak period.
On the other hand, MLR is an extension of SLR where we consider more than one independent v and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is the dependent variable (Pearson,20 As part of constructing best-fitting MLR models, we first conduct correlation analysis to dete strength of relationship between two variables. In computing the correlation coefficient, we apply Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, we consider r to be st absolute value is at least 0.70 (Schober et al., 2018). We also use the correlation results to collinearity or having high correlation between two independent variables 's to acquire a better fit model (Chatterjee & Simonoff, 2013).
[4] the trend of dengue incidence from previous years. Error analysis is also applied to d of the calculated estimates from the said data. Here, we apply the Root Mean Square E the accuracy of the estimates. We emphasize here that the RMSE values must be low to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality of r is the difference between the estimated value from the equation and the actual value fr To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of the distribution based on a random sample of n observations (Royston, 1995;Gonzalez 2019). The residuals are normally distributed if the resulting p-value is greater than Otherwise, the residuals are not normal. To attain the normality of residuals, we use statistic. Given the residuals i, the W statistic is defined as where is the sample mean of the residuals, = ( 1 , 2 , … , ) = ( − ( 1 , 2 , … , ) are the expected values of the order statistics of independent and random variables sampled from the standard normal distribution, and is the covarian statistics (Razali & Yap, 2011). The statistic value lies between zero and one, an indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, we forecasting in Baguio City for 2019, starting from January until the end of the outbrea On the other hand, MLR is an extension of SLR where we consider more than one in and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is the dependent variable As part of constructing best-fitting MLR models, we first conduct correlation anal strength of relationship between two variables. In computing the correlation coefficien Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, we conside absolute value is at least 0.70 (Schober et al., 2018). We also use the correlation collinearity or having high correlation between two independent variables 's to acqui model (Chatterjee & Simonoff, 2013).
[4] the trend of dengue incidence from previous years. Error analysis is also applied t of the calculated estimates from the said data. Here, we apply the Root Mean Squar the accuracy of the estimates. We emphasize here that the RMSE values must be l to fit with the data. We also apply the Shapiro-Wilk W Test to check the normality is the difference between the estimated value from the equation and the actual valu To elaborate, the Shapiro-Wilk W Test is defined as the ratio of two estimates of distribution based on a random sample of n observations (Royston, 1995;Gonza 2019). The residuals are normally distributed if the resulting p-value is greater th Otherwise, the residuals are not normal. To attain the normality of residuals, we statistic. Given the residuals i, the W statistic is defined as where is the sample mean of the residuals, = ( 1 , 2 , … , ) = ( ( 1 , 2 , … , ) are the expected values of the order statistics of independent a random variables sampled from the standard normal distribution, and is the cova statistics (Razali & Yap, 2011). The statistic value lies between zero and one indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Test are satisfied, w forecasting in Baguio City for 2019, starting from January until the end of the outb On the other hand, MLR is an extension of SLR where we consider more than on and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is the dependent variab As part of constructing best-fitting MLR models, we first conduct correlation a strength of relationship between two variables. In computing the correlation coeffi Product Moment Correlation Coefficient r (Walpole et al., 2012). Here, we cons absolute value is at least 0.70 (Schober et al., 2018). We also use the correla collinearity or having high correlation between two independent variables 's to ac model (Chatterjee & Simonoff, 2013).
[4] accuracy to our available data, the renewal equation is applied to the trend of dengue incidence from previous years. Error analysi of the calculated estimates from the said data. Here, we apply the the accuracy of the estimates. We emphasize here that the RMSE to fit with the data. We also apply the Shapiro-Wilk W Test to ch is the difference between the estimated value from the equation a To elaborate, the Shapiro-Wilk W Test is defined as the ratio of distribution based on a random sample of n observations (Roys 2019). The residuals are normally distributed if the resulting p-v Otherwise, the residuals are not normal. To attain the normality statistic. Given the residuals i, the W statistic is defined as where is the sample mean of the residuals, = ( ( 1 , 2 , … , ) are the expected values of the order statistics random variables sampled from the standard normal distribution, statistics (Razali & Yap, 2011). The statistic value lies betw indicates that the residuals are normally distributed.
Once the conditions for RMSE and the Shapiro-Wilk W Te forecasting in Baguio City for 2019, starting from January until t On the other hand, MLR is an extension of SLR where we consi and has the form = 0 + 1 1 + 2 2 + ⋯ + where 's are the coefficients that need to determine and is th As part of constructing best-fitting MLR models, we first con strength of relationship between two variables. In computing the Product Moment Correlation Coefficient r (Walpole et al.,201 absolute value is at least 0.70 (Schober et al., 2018). We als collinearity or having high correlation between two independent v model (Chatterjee & Simonoff, 2013).
forecast (Nouvellet et al., 2017). In determining its plied to available historical data, where we estimate analysis is also applied to determine the accuracy pply the Root Mean Square Error (RMSE) to check e RMSE values must be low enough for the model st to check the normality of residuals. The residual uation and the actual value from the data. ratio of two estimates of the variance of a normal s (Royston, 1995; Gonzalez -Estrada & Cosmes, lting p-value is greater than 0.05 (p-value > 0.05). rmality of residuals, we use the corresponding W s tatistics of independent and identically distributed ibution, and is the covariance matrix of the order es between zero and one, and the larger the value W Test are satisfied, we proceed with dengue y until the end of the outbreak period. e consider more than one independent variable (4) is the dependent variable (Pearson, 2018).
irst conduct correlation analysis to determine the ting the correlation coefficient, we apply Pearson's al., 2012). Here, we consider r to be strong if its We also use the correlation results to check for endent variables 's to acquire a better fitting MLR [4] in our forecast (Nouvellet et al., 2017). In determining its is applied to available historical data, where we estimate Error analysis is also applied to determine the accuracy we apply the Root Mean Square Error (RMSE) to check hat the RMSE values must be low enough for the model W Test to check the normality of residuals. The residual the equation and the actual value from the data. s the ratio of two estimates of the variance of a normal vations (Royston, 1995;Gonzalez -Estrada & Cosmes, resulting p-value is greater than 0.05 (p-value > 0.05). the normality of residuals, we use the corresponding W ined as rder statistics of independent and identically distributed l distribution, and is the covariance matrix of the order lue lies between zero and one, and the larger the value .
-Wilk W Test are satisfied, we proceed with dengue anuary until the end of the outbreak period.
here we consider more than one independent variable ne and is the dependent variable (Pearson, 2018).
we first conduct correlation analysis to determine the omputing the correlation coefficient, we apply Pearson's le et al., 2012). Here, we consider r to be strong if its 018). We also use the correlation results to check for independent variables 's to acquire a better fitting MLR In constructing an MLR model, we consider the following assumptions as discussed in Kleinbaum et al. (1988): (a) Existence of the MLR model such that for a combination of values of the independent variables the dependent variable y is a random variable with a probability distribution having a finite mean and variance; (b) The y observations must be statistically independent of one another; (c) The mean value of y for each specific combination of is a linear function of ; that is, or (6) where is the error component between the observed value and the theoretical value Here, must be normally distributed with a zero mean and variance For an acceptable estimate of we apply the residual where (7) and are estimates of (d) Homoscedasticity or the variance of must be the same for any fixed combination of that is,  (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W Test, the MLR model is homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heteroscedastic.
In addition to the aforementioned conditions, we also conduct additional error analysis on every MLR model. Here, we check the residual standard error, the multiple and adjusted R-squared, the F statistic and its p-value, and the p-value of each coefficient. Note that the coefficient is significant in the model if its corresponding p-value In constructing an MLR model, we consider the following assumption (1988): (a) Existence of the MLR model such that for a combination of v 's, the dependent variable y is a random variable with a probability di variance; (b) The y observations must be statistically independent of on for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the the must be normally distributed with a zero mean and variance 2 . For an the residual ̂ where and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of combination of 's, that is, The variable is normally distributed for any fixed combination of To elaborate, we use the Least Square Method in solving ̂' s on each mod , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of White's Test compares the estimated variances of regression coefficien ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapi homoscedastic if its p-value is greater than 0.05. Otherwise, the model is In addition to the aforementioned conditions, we also conduct additional e Here, we check the residual standard error, the multiple and adjusted R value, and the p-value of each coefficient. Note that the coefficient corresponding p-value is less than 0.05. Since the multiple R-squared va we instead consider the adjusted R-squared value as it considers the issu (Pearson, 2018).
In constructing an MLR model, we consider the following assum (1988): (a) Existence of the MLR model such that for a combinatio 's, the dependent variable y is a random variable with a probabil variance; (b) The y observations must be statistically independent for each specific combination of is a linear function of ; that is | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and t must be normally distributed with a zero mean and variance 2 . F the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the varian combination of 's, that is,  (Jeong & Lee, 1999). Similar to the homoscedastic if its p-value is greater than 0.05. Otherwise, the mo In addition to the aforementioned conditions, we also conduct additi Here, we check the residual standard error, the multiple and adju value, and the p-value of each coefficient. Note that the coeff corresponding p-value is less than 0.05. Since the multiple R-squar we instead consider the adjusted R-squared value as it considers th (Pearson, 2018). g an MLR model, we consider the following assumptions as discussed in Kleinbaum et al. istence of the MLR model such that for a combination of values of the independent variables dent variable y is a random variable with a probability distribution having a finite mean and he y observations must be statistically independent of one another; (c) The mean value of y ic combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + (5) error component between the observed value and the theoretical value | 1 , 2 ,…, . Here, lly distributed with a zero mean and variance 2 . For an acceptable estimate of , we apply where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) stimates of 's; (d) Homoscedasticity or the variance of must be the same for any fixed f 's, that is, he aforementioned conditions, we also conduct additional error analysis on every MLR model. k the residual standard error, the multiple and adjusted R-squared, the F statistic and its pp-value of each coefficient. Note that the coefficient is significant in the model if its p-value is less than 0.05. Since the multiple R-squared value ignores the issue of overfitting, sider the adjusted R-squared value as it considers the issue of overfitting in the MLR model In constructing an MLR model, we consider the following assumptions as discussed in Klei (1988): (a) Existence of the MLR model such that for a combination of values of the independ 's, the dependent variable y is a random variable with a probability distribution having a fin variance; (b) The y observations must be statistically independent of one another; (c) The mea for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical value | 1 , 2 must be normally distributed with a zero mean and variance 2 . For an acceptable estimate of the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must be the same f combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.  (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W Test, the M homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heteroscedastic.
In addition to the aforementioned conditions, we also conduct additional error analysis on every Here, we check the residual standard error, the multiple and adjusted R-squared, the F statis value, and the p-value of each coefficient. Note that the coefficient is significant in the corresponding p-value is less than 0.05. Since the multiple R-squared value ignores the issue o we instead consider the adjusted R-squared value as it considers the issue of overfitting in the In constructing an MLR model, we consider the following assumptions as discussed in Kle (1988): (a) Existence of the MLR model such that for a combination of values of the independ 's, the dependent variable y is a random variable with a probability distribution having a fin variance; (b) The y observations must be statistically independent of one another; (c) The me for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical value | 1 , must be normally distributed with a zero mean and variance 2 . For an acceptable estimate o the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must be the same combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For the normality o , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the model, we apply White's Test compares the estimated variances of regression coefficients under homoscedast ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W Test, the M homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heteroscedastic.
In addition to the aforementioned conditions, we also conduct additional error analysis on every Here, we check the residual standard error, the multiple and adjusted R-squared, the F statis value, and the p-value of each coefficient. Note that the coefficient is significant in the corresponding p-value is less than 0.05. Since the multiple R-squared value ignores the issue we instead consider the adjusted R-squared value as it considers the issue of overfitting in the (Pearson, 2018).
In constructing an MLR model, we consider the following assumptions as discu (1988): (a) Existence of the MLR model such that for a combination of values of 's, the dependent variable y is a random variable with a probability distribution variance; (b) The y observations must be statistically independent of one another for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical v must be normally distributed with a zero mean and variance 2 . For an acceptabl the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must b combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For th , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the mode White's Test compares the estimated variances of regression coefficients under h ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heterosce In addition to the aforementioned conditions, we also conduct additional error analy Here, we check the residual standard error, the multiple and adjusted R-squared value, and the p-value of each coefficient. Note that the coefficient is signifi corresponding p-value is less than 0.05. Since the multiple R-squared value ignore we instead consider the adjusted R-squared value as it considers the issue of over (Pearson, 2018).
The details and procedures for the application of these methods will be discussed i In constructing an MLR model, we consider the following assumptions as discu (1988): (a) Existence of the MLR model such that for a combination of values of t 's, the dependent variable y is a random variable with a probability distribution variance; (b) The y observations must be statistically independent of one another; for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical v must be normally distributed with a zero mean and variance 2 . For an acceptable the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must b combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For the , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the mode White's Test compares the estimated variances of regression coefficients under h ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heterosce In addition to the aforementioned conditions, we also conduct additional error analy Here, we check the residual standard error, the multiple and adjusted R-squared, value, and the p-value of each coefficient. Note that the coefficient is signifi corresponding p-value is less than 0.05. Since the multiple R-squared value ignore we instead consider the adjusted R-squared value as it considers the issue of overf (Pearson, 2018).
The details and procedures for the application of these methods will be discussed in owing assumptions as discussed in Kleinbaum et al. a combination of values of the independent variables ith a probability distribution having a finite mean and independent of one another; (c) The mean value of y of ; that is, value and the theoretical value | 1 , 2 ,…, . Here, ariance 2 . For an acceptable estimate of , we apply ⋯ +̂) or the variance of must be the same for any fixed | 1 , 2 , … , ) ≡ 2 ; onduct additional error analysis on every MLR model. ple and adjusted R-squared, the F statistic and its pat the coefficient is significant in the model if its ltiple R-squared value ignores the issue of overfitting, t considers the issue of overfitting in the MLR model an MLR model, we consider the following assumptions as discussed in Kleinbaum et al. stence of the MLR model such that for a combination of values of the independent variables dent variable y is a random variable with a probability distribution having a finite mean and he y observations must be statistically independent of one another; (c) The mean value of y ic combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + = 0 + 1 1 + 2 2 + ⋯ + + error component between the observed value and the theoretical value | 1 , 2 ,…, . Here, lly distributed with a zero mean and variance 2 . For an acceptable estimate of , we apply here ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) timates of 's; (d) Homoscedasticity or the variance of must be the same for any fixed 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; e aforementioned conditions, we also conduct additional error analysis on every MLR model. k the residual standard error, the multiple and adjusted R-squared, the F statistic and its pp-value of each coefficient. Note that the coefficient is significant in the model if its p-value is less than 0.05. Since the multiple R-squared value ignores the issue of overfitting, sider the adjusted R-squared value as it considers the issue of overfitting in the MLR model ).
llowing assumptions as discussed in Kleinbaum et al. r a combination of values of the independent variables ith a probability distribution having a finite mean and independent of one another; (c) The mean value of y n of ; that is, value and the theoretical value | 1 , 2 ,…, . Here, ariance 2 . For an acceptable estimate of , we apply or the variance of must be the same for any fixed | 1 , 2 , … , ) ≡ 2 ;  Kleinbaum et al. tence of the MLR model such that for a combination of values of the independent variables ent variable y is a random variable with a probability distribution having a finite mean and e y observations must be statistically independent of one another; (c) The mean value of y combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + (5) = 0 + 1 1 + 2 2 + ⋯ + + ror component between the observed value and the theoretical value | 1 , 2 ,…, . Here, y distributed with a zero mean and variance 2 . For an acceptable estimate of , we apply here ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) imates of 's; (d) Homoscedasticity or the variance of must be the same for any fixed 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; aforementioned conditions, we also conduct additional error analysis on every MLR model. the residual standard error, the multiple and adjusted R-squared, the F statistic and its pp-value of each coefficient. Note that the coefficient is significant in the model if its -value is less than 0.05. Since the multiple R-squared value ignores the issue of overfitting, ider the adjusted R-squared value as it considers the issue of overfitting in the MLR model In constructing an MLR model, we consider the following assumptions as discussed in Klei (1988): (a) Existence of the MLR model such that for a combination of values of the independ 's, the dependent variable y is a random variable with a probability distribution having a fin variance; (b) The y observations must be statistically independent of one another; (c) The me for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical value | 1 , 2 must be normally distributed with a zero mean and variance 2 . For an acceptable estimate o the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must be the same combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For the normality o , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the model, we apply W White's Test compares the estimated variances of regression coefficients under homoscedasti ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W Test, the M homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heteroscedastic.
In addition to the aforementioned conditions, we also conduct additional error analysis on every Here, we check the residual standard error, the multiple and adjusted R-squared, the F statis value, and the p-value of each coefficient. Note that the coefficient is significant in the corresponding p-value is less than 0.05. Since the multiple R-squared value ignores the issue o we instead consider the adjusted R-squared value as it considers the issue of overfitting in the (Pearson, 2018).
The details and procedures for the application of these methods will be discussed in the method In constructing an MLR model, we consider the following assumptions as discu (1988): (a) Existence of the MLR model such that for a combination of values of t 's, the dependent variable y is a random variable with a probability distribution variance; (b) The y observations must be statistically independent of one another; for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical v must be normally distributed with a zero mean and variance 2 . For an acceptabl the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must b combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For the , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the mode White's Test compares the estimated variances of regression coefficients under h ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heterosce In addition to the aforementioned conditions, we also conduct additional error analy Here, we check the residual standard error, the multiple and adjusted R-squared, value, and the p-value of each coefficient. Note that the coefficient is signifi corresponding p-value is less than 0.05. Since the multiple R-squared value ignore we instead consider the adjusted R-squared value as it considers the issue of overf (Pearson, 2018).
The details and procedures for the application of these methods will be discussed in In constructing an MLR model, we consider the following assumptions as discus (1988): (a) Existence of the MLR model such that for a combination of values of th 's, the dependent variable y is a random variable with a probability distribution h variance; (b) The y observations must be statistically independent of one another; for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical va must be normally distributed with a zero mean and variance 2 . For an acceptable the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must be combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For the , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the model, White's Test compares the estimated variances of regression coefficients under ho ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heterosced In addition to the aforementioned conditions, we also conduct additional error analys Here, we check the residual standard error, the multiple and adjusted R-squared, value, and the p-value of each coefficient. Note that the coefficient is signific corresponding p-value is less than 0.05. Since the multiple R-squared value ignores we instead consider the adjusted R-squared value as it considers the issue of overfi (Pearson, 2018).
The details and procedures for the application of these methods will be discussed in ing assumptions as discussed in Kleinbaum et al. ombination of values of the independent variables a probability distribution having a finite mean and ependent of one another; (c) The mean value of y ; that is, ue and the theoretical value | 1 , 2 ,…, . Here, nce 2 . For an acceptable estimate of , we apply +̂) the variance of must be the same for any fixed , 2 , … , ) ≡ 2 ; uct additional error analysis on every MLR model. and adjusted R-squared, the F statistic and its pthe coefficient is significant in the model if its le R-squared value ignores the issue of overfitting, nsiders the issue of overfitting in the MLR model thods will be discussed in the methodology.
In constructing an MLR model, we consider th (1988): (a) Existence of the MLR model such th 's, the dependent variable y is a random varia variance; (b) The y observations must be statist for each specific combination of is a linear fu | 1 , 2 ,…, = 0 + 1 1 or = 0 + 1 1 + 2 2 where is the error component between the obs must be normally distributed with a zero mean the residual ̂ where ̂= − (̂0 +̂1 1 + and ̂' s are estimates of 's; (d) Homoscedas combination of 's, that is, | 1 , 2 ,…, 2 = (e) The variable is normally distributed for any To elaborate, we use the Least Square Method in , we apply the Shapiro-Wilk W Test. While for White's Test compares the estimated variances ones under heteroscedasticity (Jeong & Lee,199 homoscedastic if its p-value is greater than 0.05. In addition to the aforementioned conditions, we Here, we check the residual standard error, the value, and the p-value of each coefficient. N corresponding p-value is less than 0.05. Since th we instead consider the adjusted R-squared valu (Pearson, 2018).
The details and procedures for the application of structing an MLR model, we consider the following assumptions as discussed in Kleinbaum et : (a) Existence of the MLR model such that for a combination of values of the independent variab e dependent variable y is a random variable with a probability distribution having a finite mean ce; (b) The y observations must be statistically independent of one another; (c) The mean value o h specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + (  (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W Test, the MLR mode cedastic if its p-value is greater than 0.05. Otherwise, the model is heteroscedastic.
ition to the aforementioned conditions, we also conduct additional error analysis on every MLR mo we check the residual standard error, the multiple and adjusted R-squared, the F statistic and its and the p-value of each coefficient. Note that the coefficient is significant in the model if ponding p-value is less than 0.05. Since the multiple R-squared value ignores the issue of overfitti tead consider the adjusted R-squared value as it considers the issue of overfitting in the MLR mo on, 2018). tails and procedures for the application of these methods will be discussed in the methodology.
In constructing an MLR model, we consider the following assumptions as discu (1988): (a) Existence of the MLR model such that for a combination of values of t 's, the dependent variable y is a random variable with a probability distribution variance; (b) The y observations must be statistically independent of one another; for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical v must be normally distributed with a zero mean and variance 2 . For an acceptable the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must b combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For the , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the mode White's Test compares the estimated variances of regression coefficients under h ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heterosce In addition to the aforementioned conditions, we also conduct additional error analy Here, we check the residual standard error, the multiple and adjusted R-squared, value, and the p-value of each coefficient. Note that the coefficient is signifi corresponding p-value is less than 0.05. Since the multiple R-squared value ignore we instead consider the adjusted R-squared value as it considers the issue of overf (Pearson, 2018).
The details and procedures for the application of these methods will be discussed in wing assumptions as discussed in Kleinbaum et al. combination of values of the independent variables h a probability distribution having a finite mean and ndependent of one another; (c) The mean value of y of ; that is, alue and the theoretical value | 1 , 2 ,…, . Here, iance 2 . For an acceptable estimate of , we apply ⋯ +̂) r the variance of must be the same for any fixed 1 , 2 , … , ) ≡ 2 ; nduct additional error analysis on every MLR model. le and adjusted R-squared, the F statistic and its pt the coefficient is significant in the model if its iple R-squared value ignores the issue of overfitting, considers the issue of overfitting in the MLR model methods will be discussed in the methodology.
In constructing an MLR model, we consider the following assumptions as disc (1988): (a) Existence of the MLR model such that for a combination of values of 's, the dependent variable y is a random variable with a probability distribution variance; (b) The y observations must be statistically independent of one anothe for each specific combination of is a linear function of ; that is, | 1 , 2 ,…, = 0 + 1 1 + 2 2 + ⋯ + or = 0 + 1 1 + 2 2 + ⋯ + + where is the error component between the observed value and the theoretical must be normally distributed with a zero mean and variance 2 . For an acceptab the residual ̂ where ̂= − (̂0 +̂1 1 +̂2 2 + ⋯ +̂) and ̂' s are estimates of 's; (d) Homoscedasticity or the variance of must combination of 's, that is, | 1 , 2 ,…, 2 = ( | 1 , 2 , … , ) ≡ 2 ; (e) The variable is normally distributed for any fixed combination of 's.
To elaborate, we use the Least Square Method in solving ̂' s on each model. For th , we apply the Shapiro-Wilk W Test. While for the homoscedasticity of the mod White's Test compares the estimated variances of regression coefficients under ones under heteroscedasticity (Jeong & Lee, 1999). Similar to the Shapiro-Wilk W homoscedastic if its p-value is greater than 0.05. Otherwise, the model is heterosc In addition to the aforementioned conditions, we also conduct additional error anal Here, we check the residual standard error, the multiple and adjusted R-squared value, and the p-value of each coefficient. Note that the coefficient is signif corresponding p-value is less than 0.05. Since the multiple R-squared value ignor we instead consider the adjusted R-squared value as it considers the issue of ove (Pearson, 2018).
The details and procedures for the application of these methods will be discussed In constructing an MLR model, we co (1988): (a) Existence of the MLR mode 's, the dependent variable y is a rand variance; (b) The y observations must for each specific combination of is a In addition to the aforementioned condi Here, we check the residual standard e value, and the p-value of each coeff corresponding p-value is less than 0.05 we instead consider the adjusted R-squ (Pearson, 2018).
The details and procedures for the appl is less than 0.05. Since the multiple R-squared value ignores the issue of overfitting, we instead consider the adjusted R-squared value as it considers the issue of overfitting in the MLR model (Pearson, 2018).
The details and procedures for the application of these methods will be discussed in the methodology.

METHODOLOGY
For this paper, we use the daily dengue incidence data and the monthly climatic factors from 2011 -2018 acquired from Baguio City Health Service Office and the Regional Department of Science and Technology -Philippine Atmospheric Geophysical and Astronomical Services Administration (DOST-PAGASA), respectively. We use the daily incidence data in conducting our forecast, whereas we use the monthly incidence data and the monthly climatic factors in conducting MLR analysis. For easier computation, we utilize various packages and functions from the statistical software R (Verzani, 2014).
Given the daily dengue incidence data from 2011 -2018, we first determine the outbreak periods in Baguio City. The months having the highest monthly tallies of daily incidence in each year serve as the outbreak periods in the city.
Next, we determine the values for each month until the outbreak period of each year. In computing we incorporate the EpiEstim package, a tool used to quantify transmissibility throughout an epidemic from the analysis of time series of incidence (Cori et al., 2013;Cori, 2020). From the package, we use the estimate_R function to calculate the given the time series of incidence and the serial interval distribution. As mentioned earlier, we use the mean and median values of 16 days and 1.64 days, respectively (Siraj et al., 2017) for our serial interval distribution.
Once the outbreak periods and are determined, we proceed with model fitting using the renewal equation. For convenience, we use the projections package in R (Jombart & Nouvellet, 2021). Within the package, we incorporate the project function to acquire the estimated model. In checking the model's normality of residuals, we apply the shapiro.test function to calculate the statistic and the resulting

METHODOLOGY
For this paper, we use the daily dengue incidence data and the monthly climatic fac acquired from Baguio City Health Service Office and the Regional Department of Sc -Philippine Atmospheric Geophysical and Astronomical Services Administratio respectively. We use the daily incidence data in conducting our forecast, wherea incidence data and the monthly climatic factors in conducting MLR analysis. For e utilize various packages and functions from the statistical software R (Verzani, 2014) Given the daily dengue incidence data from 2011 -2018, we first determine the outb City. The months having the highest monthly tallies of daily incidence in each year periods in the city.
Next, we determine the values for each month until the outbreak period of each y we incorporate the EpiEstim package, a tool used to quantify transmissibility through the analysis of time series of incidence (Cori et al., 2013;Cori, 2020). From the estimate_R function to calculate the given the time series of incidence and the seri As mentioned earlier, we use the mean and median values of 16 days and 1.64 days, re 2017) for our serial interval distribution.
Once the outbreak periods and are determined, we proceed with model fitting using For convenience, we use the projections package in R (Jombart & Nouvellet, 2021). W incorporate the project function to acquire the estimated model. In checking the residuals, we apply the shapiro.test function to calculate the statistic and the resul model fits well with the data, we then proceed with forecasting dengue incidence in B In forecasting February to September 2019, the values will be taken from aver representing each month. In some cases, we will also treat the outlying values by re calculated average of eight values for that month. After conducting the forecast, analysis to determine the main factors that influence the growth of dengue incidence i Aside from time in months, we consider three monthly climatic factors, namely relati LOGY and the monthly climatic factors from 2011 -2018 e Regional Department of Science and Technology ical Services Administration (DOST-PAGASA), ucting our forecast, whereas we use the monthly ducting MLR analysis. For easier computation, we l software R (Verzani, 2014).
, we first determine the outbreak periods in Baguio daily incidence in each year serve as the outbreak the outbreak period of each year. In computing , antify transmissibility throughout an epidemic from 013; Cori, 2020). From the package, we use the ries of incidence and the serial interval distribution. s of 16 days and 1.64 days, respectively (Siraj et al., oceed with model fitting using the renewal equation. ombart & Nouvellet, 2021). Within the package, we ted model. In checking the model's normality of the statistic and the resulting -value. Once the casting dengue incidence in Baguio City. lues will be taken from averaging the eight values reat the outlying values by replacing them with the fter conducting the forecast, we proceed with MLR growth of dengue incidence in Baguio City.

METHODOLOGY
paper, we use the daily dengue incidence data and the monthly climatic factors from 2011 -20 d from Baguio City Health Service Office and the Regional Department of Science and Technolo pine Atmospheric Geophysical and Astronomical Services Administration (DOST-PAGASA ively. We use the daily incidence data in conducting our forecast, whereas we use the month ce data and the monthly climatic factors in conducting MLR analysis. For easier computation, w arious packages and functions from the statistical software R (Verzani, 2014). he daily dengue incidence data from 2011 -2018, we first determine the outbreak periods in Bagu he months having the highest monthly tallies of daily incidence in each year serve as the outbre in the city. e determine the values for each month until the outbreak period of each year. In computing rporate the EpiEstim package, a tool used to quantify transmissibility throughout an epidemic fro lysis of time series of incidence (Cori et al., 2013;Cori, 2020). From the package, we use t e_R function to calculate the given the time series of incidence and the serial interval distributio tioned earlier, we use the mean and median values of 16 days and 1.64 days, respectively (Siraj et a or our serial interval distribution. e outbreak periods and are determined, we proceed with model fitting using the renewal equatio venience, we use the projections package in R (Jombart & Nouvellet, 2021). Within the package, w rate the project function to acquire the estimated model. In checking the model's normality ls, we apply the shapiro.test function to calculate the statistic and the resulting -value. Once t its well with the data, we then proceed with forecasting dengue incidence in Baguio City.
asting February to September 2019, the values will be taken from averaging the eight valu nting each month. In some cases, we will also treat the outlying values by replacing them with t ted average of eight values for that month. After conducting the forecast, we proceed with ML s to determine the main factors that influence the growth of dengue incidence in Baguio City.

METHODOLOGY
For this paper, we use the daily dengue incidence data and the monthly climatic fa acquired from Baguio City Health Service Office and the Regional Department of S -Philippine Atmospheric Geophysical and Astronomical Services Administrati respectively. We use the daily incidence data in conducting our forecast, where incidence data and the monthly climatic factors in conducting MLR analysis. For utilize various packages and functions from the statistical software R (Verzani, 2014 Given the daily dengue incidence data from 2011 -2018, we first determine the outb City. The months having the highest monthly tallies of daily incidence in each yea periods in the city. Next, we determine the values for each month until the outbreak period of each we incorporate the EpiEstim package, a tool used to quantify transmissibility throug the analysis of time series of incidence (Cori et al., 2013;Cori, 2020). From th estimate_R function to calculate the given the time series of incidence and the ser As mentioned earlier, we use the mean and median values of 16 days and 1.64 days, r 2017) for our serial interval distribution.
Once the outbreak periods and are determined, we proceed with model fitting usin For convenience, we use the projections package in R (Jombart & Nouvellet, 2021). incorporate the project function to acquire the estimated model. In checking the residuals, we apply the shapiro.test function to calculate the statistic and the resu model fits well with the data, we then proceed with forecasting dengue incidence in In forecasting February to September 2019, the values will be taken from ave representing each month. In some cases, we will also treat the outlying values by r calculated average of eight values for that month. After conducting the forecast,

METHODOLOGY
aper, we use the daily dengue incidence data and the monthly climatic factors from 2011 -2018 from Baguio City Health Service Office and the Regional Department of Science and Technology ine Atmospheric Geophysical and Astronomical Services Administration (DOST-PAGASA), ly. We use the daily incidence data in conducting our forecast, whereas we use the monthly data and the monthly climatic factors in conducting MLR analysis. For easier computation, we ious packages and functions from the statistical software R (Verzani, 2014).
daily dengue incidence data from 2011 -2018, we first determine the outbreak periods in Baguio months having the highest monthly tallies of daily incidence in each year serve as the outbreak the city.
determine the values for each month until the outbreak period of each year. In computing , orate the EpiEstim package, a tool used to quantify transmissibility throughout an epidemic from sis of time series of incidence (Cori et al., 2013;Cori, 2020). From the package, we use the R function to calculate the given the time series of incidence and the serial interval distribution. ned earlier, we use the mean and median values of 16 days and 1.64 days, respectively (Siraj et al., our serial interval distribution. outbreak periods and are determined, we proceed with model fitting using the renewal equation. nience, we use the projections package in R (Jombart & Nouvellet, 2021). Within the package, we te the project function to acquire the estimated model. In checking the model's normality of we apply the shapiro.test function to calculate the statistic and the resulting -value. Once the well with the data, we then proceed with forecasting dengue incidence in Baguio City.
ting February to September 2019, the values will be taken from averaging the eight values ng each month. In some cases, we will also treat the outlying values by replacing them with the Once the model fits well with the data, we then proceed with forecasting dengue incidence in Baguio City.
In forecasting February to September 2019, the values will be taken from averaging the eight values representing each month. In some cases, we will also treat the outlying values by replacing them with the calculated average of eight values for that month. After conducting the forecast, we proceed with MLR analysis to determine the main factors that influence the growth of dengue incidence in Baguio City.
Aside from time in months, we consider three monthly climatic factors, namely relative humidity (RelHum) (unitless variable written in decimal form), precipitation (Prec) (measured in mm), and temperature (measured in o C), as the independent variables for our MLR model. We also emphasize that the temperature data has seven types, namely total maximum (TotalMaxTemp), mean maximum (MeanMaxTemp), total minimum (TotalMinTemp), mean minimum (MeanMinTemp), average (AveTemp), highest (HighTemp), and lowest (LowTemp). Note that the average temperature is computed as the average between the mean maximum and the mean minimum temperatures. Furthermore, each variable has ninety-six data points and are independent with one another. To avoid the issue of generating MLR models consisting mainly of different monthly temperature types, we restrict our MLR model to have one temperature type as the independent variable.
For an efficient statistical analysis, we utilize the lm function and the summary function to calculate the and the residuals of each MLR model, and to calculate the necessary parts of our error analysis. The normality of residuals will be checked through the use of shapiro.test function, and the homoscedasticity will be determined through the use of the bptest function from the lmtest package in calculating the resulting p-value (Zeileis & Hothorn, 2002).

RESULTS AND DISCUSSION
In this section, we discuss the results acquired from the model fitting and forecast using the branching process model and the MLR fitting using the renewal equation. let, 2021). Within the package, we ecking the model's normality of nd the resulting -value. Once the cidence in Baguio City.
from averaging the eight values alues by replacing them with the e forecast, we proceed with MLR incidence in Baguio City. mely relative humidity (RelHum) sured in mm), and temperature so emphasize that the temperature aximum (MeanMaxTemp), total (AveTemp), highest (HighTemp), as the average between the mean ble has ninety-six data points and LR models consisting mainly of ave one temperature type as the mary function to calculate the ̂' s f our error analysis. The normality and the homoscedasticity will be in calculating the resulting p-value Once the outbreak periods and are determined, we proceed with model fitting u For convenience, we use the projections package in R (Jombart & Nouvellet, 2021 incorporate the project function to acquire the estimated model. In checking residuals, we apply the shapiro.test function to calculate the statistic and the re model fits well with the data, we then proceed with forecasting dengue incidence In forecasting February to September 2019, the values will be taken from a representing each month. In some cases, we will also treat the outlying values b calculated average of eight values for that month. After conducting the foreca analysis to determine the main factors that influence the growth of dengue inciden Aside from time in months, we consider three monthly climatic factors, namely re (unitless variable written in decimal form), precipitation (Prec) (measured i (measured in o C), as the independent variables for our MLR model. We also emph data has seven types, namely total maximum (TotalMaxTemp), mean maximum minimum (TotalMinTemp), mean minimum (MeanMinTemp), average (AveTem and lowest (LowTemp). Note that the average temperature is computed as the a maximum and the mean minimum temperatures. Furthermore, each variable has are independent with one another. To avoid the issue of generating MLR mod different monthly temperature types, we restrict our MLR model to have one independent variable.
For an efficient statistical analysis, we utilize the lm function and the summary fun and the residuals of each MLR model, and to calculate the necessary parts of our err of residuals will be checked through the use of shapiro.test function, and the determined through the use of the bptest function from the lmtest package in calcul (Zeileis & Hothorn, 2002).
[6] estimate_R function to calculate the given the time series of incidence and the serial interval As mentioned earlier, we use the mean and median values of 16 days and 1.64 days, respectively 2017) for our serial interval distribution.
Once the outbreak periods and are determined, we proceed with model fitting using the renew For convenience, we use the projections package in R (Jombart & Nouvellet, 2021). Within the incorporate the project function to acquire the estimated model. In checking the model's n residuals, we apply the shapiro.test function to calculate the statistic and the resulting -val model fits well with the data, we then proceed with forecasting dengue incidence in Baguio Cit In forecasting February to September 2019, the values will be taken from averaging the representing each month. In some cases, we will also treat the outlying values by replacing th calculated average of eight values for that month. After conducting the forecast, we procee analysis to determine the main factors that influence the growth of dengue incidence in Baguio Aside from time in months, we consider three monthly climatic factors, namely relative humidi (unitless variable written in decimal form), precipitation (Prec) (measured in mm), and (measured in o C), as the independent variables for our MLR model. We also emphasize that the data has seven types, namely total maximum (TotalMaxTemp), mean maximum (MeanMax minimum (TotalMinTemp), mean minimum (MeanMinTemp), average (AveTemp), highest ( and lowest (LowTemp). Note that the average temperature is computed as the average betwe maximum and the mean minimum temperatures. Furthermore, each variable has ninety-six dat are independent with one another. To avoid the issue of generating MLR models consistin different monthly temperature types, we restrict our MLR model to have one temperature independent variable.
For an efficient statistical analysis, we utilize the lm function and the summary function to calcu and the residuals of each MLR model, and to calculate the necessary parts of our error analysis. T of residuals will be checked through the use of shapiro.test function, and the homoscedast determined through the use of the bptest function from the lmtest package in calculating the resu (Zeileis & Hothorn, 2002).

6]
of daily incidence in each year serve as the outbreak il the outbreak period of each year. In computing , uantify transmissibility throughout an epidemic from , 2013; Cori, 2020). From the package, we use the series of incidence and the serial interval distribution. ues of 16 days and 1.64 days, respectively (Siraj et al., proceed with model fitting using the renewal equation. (Jombart & Nouvellet, 2021). Within the package, we ated model. In checking the model's normality of ate the statistic and the resulting -value. Once the recasting dengue incidence in Baguio City.
values will be taken from averaging the eight values treat the outlying values by replacing them with the After conducting the forecast, we proceed with MLR he growth of dengue incidence in Baguio City.
climatic factors, namely relative humidity (RelHum) itation (Prec) (measured in mm), and temperature MLR model. We also emphasize that the temperature MaxTemp), mean maximum (MeanMaxTemp), total inTemp), average (AveTemp), highest (HighTemp), rature is computed as the average between the mean hermore, each variable has ninety-six data points and ue of generating MLR models consisting mainly of r MLR model to have one temperature type as the nction and the summary function to calculate the ̂' s the necessary parts of our error analysis. The normality piro.test function, and the homoscedasticity will be the lmtest package in calculating the resulting p-value analysis. We also include an Exploratory Data Analysis (EDA) in MLR to explain the distribution and possible association of variables in our data frame. The accompanying results from EDA will be used in constructing our MLR model. Figure 1 shows the monthly dengue incidence in Baguio City from 2011 -2018. It can be observed that most of the monthly cases are recorded highest from July to September every year. Thus, we consider the third quarter of the year -the months of July, August, and September -as the dengue outbreak period in Baguio City.

Figure 1
Monthly total dengue incidence in Baguio City from 2011 -2018 Next, we calculate the latest value for 2018. Figure 2 shows the result. It can be observed that the mean value for the last week of 2018 is 1.71 having a 95% confidence interval of [0.63,3.32] and a standard deviation (SD) of 0.70. The mean value implies that dengue incidence may still increase by almost 1.71 times in the succeeding weeks. [7]

RESULTS AND DISCUSSION
In this section, we discuss the results acquired from the model fitting and forecast using the branching process model and the MLR analysis. We also include an Exploratory Data Analysis (EDA) in MLR to explain the distribution and possible association of variables in our data frame. The accompanying results from EDA will be used in constructing our MLR model. Figure 1 shows the monthly dengue incidence in Baguio City from 2011 -2018. It can be observed that most of the monthly cases are recorded highest from July to September every year. Thus, we consider the third quarter of the yearthe months of July, August, and Septemberas the dengue outbreak period in Baguio City.

Figure 1
Monthly total dengue incidence in Baguio City from 2011 -2018.
Next, we calculate the latest value for 2018. Figure 2 shows the result. It can be observed that the mean value for the last week of 2018 is 1.71 having a 95% confidence interval of [0.63,3.32] and a standard deviation (SD) of 0.70. The mean value implies that dengue incidence may still increase by almost 1.71 times in the succeeding weeks.

Figure 2
Epidemic curve, estimated , and explored SI distribution of dengue incidence for 2018.
[7] model and the MLR analysis. We also include an Exploratory Data Analysis (EDA) distribution and possible association of variables in our data frame. The accompan will be used in constructing our MLR model. Figure 1 shows the monthly dengue incidence in Baguio City from 2011 -2018. It ca of the monthly cases are recorded highest from July to September every year. Thus quarter of the yearthe months of July, August, and Septemberas the dengue ou City.

Figure 1
Monthly total dengue incidence in Baguio City from 2011 -2018.
Next, we calculate the latest value for 2018. Figure 2 shows the result. It can be value for the last week of 2018 is 1.71 having a 95% confidence interval of [0. deviation (SD) of 0.70. The mean value implies that dengue incidence may still times in the succeeding weeks.

Figure 2
Epidemic curve, estimated , and explored SI distribution of dengue incidence for 2 model and the MLR analysis. We also incl distribution and possible association of var will be used in constructing our MLR mode Forecasting Figure 1 shows the monthly dengue inciden of the monthly cases are recorded highest quarter of the yearthe months of July, Au City.

Figure 1
Monthly total dengue incidence in Baguio C Next, we calculate the latest value for 2 value for the last week of 2018 is 1.71 deviation (SD) of 0.70. The mean value times in the succeeding weeks.

Figure 2
Epidemic curve, estimated , and explored In this section, we discuss the results acquired from the model fitting model and the MLR analysis. We also include an Exploratory Data distribution and possible association of variables in our data frame will be used in constructing our MLR model. Figure 1 shows the monthly dengue incidence in Baguio City from 2 of the monthly cases are recorded highest from July to September quarter of the yearthe months of July, August, and Septembera City.

Figure 1
Monthly total dengue incidence in Baguio City from 2011 -2018.
Next, we calculate the latest value for 2018. Figure 2 shows the value for the last week of 2018 is 1.71 having a 95% confidenc deviation (SD) of 0.70. The mean value implies that dengue inci times in the succeeding weeks.

Figure 2
Epidemic curve, estimated , and explored SI distribution of dengu

Figure 2
Epidemic curve, estimated and explored SI distribution of dengue incidence for 2018 Using the projections package in estimating the monthly dengue incidence for 2011 to 2018, Table 1 summarizes the results. All months, except for June and July, show high accuracy such that their absolute mean residuals range from 0-3 cases. On the other hand, the average mean residual for June shows that the estimated incidence is 9 cases larger compared to actual data. In addition, the average mean residual for July shows that the estimated incidence is around 16 cases larger compared to actual data. Meanwhile, normality pvalues of February, April, June, July, August, and September show that the mean residual of the majority of the months are normally distributed. In addition, RMSE values are mostly low, indicating that the estimation on the dengue incidence in 2019 is accurate.
[7] value for the last week of 2018 is 1.71 having a 95% confidence interval of [ deviation (SD) of 0.70. The mean value implies that dengue incidence may sti times in the succeeding weeks.

Figure 2
Epidemic curve, estimated , and explored SI distribution of dengue incidence fo [8] Using the projections package in estimating the monthly dengue incidence for 2011 to 2018, Table 1 summarizes the results. All months, except for June and July, show high accuracy such that their absolute mean residuals range from 0-3 cases. On the other hand, the average mean residual for June shows that the estimated incidence is 9 cases larger compared to actual data. In addition, the average mean residual for July shows that the estimated incidence is around 16 cases larger compared to actual data. Meanwhile, normality pvalues of February, April, June, July, August, and September show that the mean residual of the majority of the months are normally distributed. In addition, RMSE values are mostly low, indicating that the estimation on the dengue incidence in 2019 is accurate.

Table 1
Error analysis on the model estimation using projections package for January to September from 2011 to 2018 Year January Estimate We incorporate the residual values as part of our 2019 forecasting. Table 2 tabulates the forecasting results for January to September 2019.

Table 2
Forecasted dengue incidence in Baguio City for January -September 2019.
29, 2021. It is also observed that dengue incidence is projected to dramatically increase starting from mid-June 2019 as dengue-carrying mosquitoes may start to infect at least 100 individuals in a day. Such values imply that a possible dengue outbreak may resurface in the city.
In a report by Agoot (2019), dengue cases in Baguio City show a downward trend as there are 210 reported cases from January 1 -July 13, 2019 compared to the same period last 2018. This resulted from the continued efforts of the locals in preventing the spread of the disease within their locality, and is further intensified with the cooperation of the local government in promoting and preventing the spread of dengue.
Once new data is available, the forecasting will be updated based from the newly -calculated values.
To fully understand the possible influences that further affect the current dengue incidence, we proceed with MLR analysis. Figure 3 shows the average yearly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018. In Figure  3a, the trends show that precipitation has an inverse influence on the incidence. Observe that in 2016, the incidence reached its peak despite low precipitation. It can be seen from Figures 3b and 3c that Baguio City experiences high temperatures relative to other years, more evidently in terms of Total Minimum and Total Maximum. This has been noted in Polonio (2016) that the hot temperature gives an advantage to the lifespan and reproduction of dengue-carrying mosquitoes.

Multiple Linear Regression Analysis
ease within their locality, and is further intensified with and preventing the spread of dengue.
dated based from the newlycalculated values.
r affect the current dengue incidence, we proceed with idence and meteorological factors in Baguio City from ecipitation has an inverse influence on the incidence. despite low precipitation. It can be seen from Figures tures relative to other years, more evidently in terms of noted in Polonio (2016) that the hot temperature gives ue-carrying mosquitoes.
orological factors in Baguio City from 2011 to 2018.

Figure 4
Two-year average monthly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018.
In Figures 4a and 4c, trends show that high incidence is recorded on the 8th and 20th months, both in August, in a two-year period along with precipitation and relative humidity. Furthermore, in Figures 4a and  4b, average temperature, mean maximum temperature, highest temperature, and total maximum

Figure 3
Average yearly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018 In Figure 3d, relative humidity follows a generally increasing pattern in Baguio City for every two years. We use this pattern to analyze the influences of the period and the environmental factors on the incidence. As a result, we modify our monthly data into a twoyear average monthly, resulting in twenty-four data points for each variable. Figure 4 shows the resulting two-year average monthly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018.

Figure 4
Two-year average monthly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018 [12] Figure 3 shows the average yearly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018. In Figure 3a, the trends show that precipitation has an inverse influence on the incidence. Observe that in 2016, the incidence reached its peak despite low precipitation. It can be seen from Figures  3b and 3c that Baguio City experiences high temperatures relative to other years, more evidently in terms of Total Minimum and Total Maximum. This has been noted in Polonio (2016) that the hot temperature gives an advantage to the lifespan and reproduction of dengue-carrying mosquitoes.

Figure 3
Average yearly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018.
In Figure 3d, relative humidity follows a generally increasing pattern in Baguio City for every two years.
We use this pattern to analyze the influences of the period and the environmental factors on the incidence. As a result, we modify our monthly data into a two-year average monthly, resulting in twenty-four data points for each variable. Figure 4 shows the resulting two-year average monthly trend of dengue incidence and meteorological factors in Baguio City from 2011 to 2018.
In Figures 4a and 4c, trends show that high incidence is recorded on the 8th and 20th months, both in August, in a two-year period along with precipitation and relative humidity. Furthermore, in Figures 4a and 4b, average temperature, mean maximum temperature, highest temperature, and total maximum temperature show a decline in those months. We use this information as we construct our MLR models. For the normality distribution, Figure 5 shows the boxplot for each data.
In Figures 5a -5d, the data distributions are shown to be not normally distributed.

Figure 5
Two-year average monthly boxplots of dengue incidence and meteorological factors in Baguio City from 2011 to 2018 However, according to Li et al. (2012), it is more accurate to check the normality of the residuals or the conditional normality of the dependent variable rather than the dependent variable itself is normally distributed. Hence, despite the non-normality of the dependent variable, we can still proceed with our experiment on MLR models. Table 3 shows the correlation coefficient matrix using Pearson's correlation. Strong correlations are indicated in green cells. Cells with NA entries indicate that the corresponding correlation coefficient is not applicable in our study.
It can be observed that Relative Humidity and Precipitation have high correlation with Incidence. This means that one of the two climatic factors has a high influence on the incidence. However, by collinearity, Relative Humidity and Precipitation cannot be both independent variables in one model. [14]

Figure 5
Two-year average monthly boxplots of dengue incidence and meteorological factors in Baguio City from 2011 to 2018 However, according to Li et al. (2012), it is more accurate to check the normality of the residuals or the conditional normality of the dependent variable rather than the dependent variable itself is normally distributed. Hence, despite the non-normality of the dependent variable, we can still proceed with our experiment on MLR models. Table 3 shows the correlation coefficient matrix using Pearson's correlation. Strong correlations are indicated in green cells. Cells with NA entries indicate that the corresponding correlation coefficient is not applicable in our study.
It can be observed that Relative Humidity and Precipitation have high correlation with Incidence. This means that one of the two climatic factors has a high influence on the incidence. However, by collinearity, Relative Humidity and Precipitation cannot be both independent variables in one model.  Establishing the possible MLR models given the correlation table and applying the necessary error analysis, we acquire four models -Incidence vs. RelHum + AveTemp (Model 1), Incidence vs. RelHum + HighTemp (Model 2), Incidence vs. RelHum + MeanMaxTemp (Model 3), Incidence vs. Prec + MeanMaxTemp (Model 4).
All models exhibit relatively high R-squared values and small p-values, indicating that they are highly correlated with dengue incidence. There are other models that have high R-squared values like Incidence vs. RelHum + TotalMaxTemp and Incidence vs. RelHum + MeanMaxTemp + Time, but the p-value of one of their coefficients are greater than 0.05, thus making it insignificant for the model.
Model 3 shows to be the best-fitting model as it exhibits the highest adjusted R-squared value, indicating that the model shows a very strong correlation with 83.83%.    Next, we look at the normality of the residuals and the homoscedasticity of the four models. Table 8 summarizes the results. Model 4 is heteroscedastic since its p-value is less than 0.05. This model does not qualify as a good model. Each of the three remaining has at least 81% accuracy based on their adjusted R-squared values. Each model has a significant correlation coefficient value of at least 0.90. Their respective W statistic is at least 0.970, satisfying the assumptions of normality of model residuals. Model 1 has the largest W statistic, normality p-value, and homoscedastic p-value among the three models. These p-values demonstrate that Model 1 is homoscedastic, with normally distributed residuals with a mean of 0.
From the three models, relative humidity is the most significant independent variable. Following the assumptions of MLR analysis, Model 1 is the best MLR model, implying that relative humidity and average temperature largely influence dengue incidence in Baguio City.
Despite that, Model 2 and Model 3 may still be utilized. Variables such as highest temperature and mean maximum temperature are considered significant alternatives to average temperature since according to Sintorini (2017) and Campbell, et al. (2013), the temperature influences the incidence regardless its type. Henceforth, these three models are relevant in describing the influence of dengue cases in Baguio City.

CONCLUSION
Dengue incidence in Baguio City continues to infect more individuals as possible breeding sites for dengue-carrying mosquitoes develop with time. These have been brought about by continuous fluctuation of climatic factors -precipitation, relative humidity, and temperature -in the area. Using MLR analysis, relative humidity and temperature, either average, highest, or mean maximum temperature, are shown to be significant factors in the occurrence of dengue cases in Baguio City within a two-year average timespan. In particular, relative humidity and average temperature are the variables that show the strongest influence on dengue incidence in Baguio City.
Without proper protocols in preventing the spread of dengue, it is forecasted that by June 16, 2019, dengue incidences are projected to reach 101 cases in a day. And if the current situation continues without providing certain local actions, dengue incidence may rise to 529 cases by August 29, 2019. It is recommended to alert the local officials regarding this projection so that proper safety and health protocols must be established in the locality to prevent the further spread of the disease. Once we have acquired new data for 2019, the projection will be updated based on the newly -calculated values.
Since we only consider weather-related factors, we recommend considering other possible factors such as geographic or population factors in the MLR model. Dengue cases and weather factors may be analyzed together as a time series to determine the trend in the area. We also recommend conducting other forecasting methods and regression algorithms to generate a more accurate dengue forecast in the area.