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ModelBuilding_HomeAudio.R
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ModelBuilding_HomeAudio.R
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################################################################################################################################################################
# :::::::: Model Building [HomeAudio] ::::::::
################################################################################################################################################################
#********************************************************[Linear Regression Model]
### Preparing dataset
## Removing lag variables and Moving averages variables
## Also removing "list_price" and "promotional_offer" column as those are on dependent variable (i.e. gmv)
## Retaining those is not good idea as 'gmv' won't present in unseen data
LR_HA_data <- HomeAudio_final[,-c(21:22,63:77)]
## Scaling the variables
LR_HA_data[,2:ncol(LR_HA_data)] <- scale(LR_HA_data[,2:ncol(LR_HA_data)])
### Stepwise Regression to remove insignificant and correlated variables
LR_HA_base.mod <- lm(gmv ~ 1 , data= LR_HA_data) # base intercept only model
LR_HA_all.mod <- lm(gmv ~ . , data= LR_HA_data) # full model with all predictors
LR_HA_stepMod <- step(LR_HA_base.mod, scope = list(lower = LR_HA_base.mod, upper = LR_HA_all.mod), direction = "both", trace = 1, steps = 1000) # perform step-wise algorithm
LR_HA_shortlistedVars <- names(unlist(LR_HA_stepMod[[1]])) # get the shortlisted variable.
LR_HA_shortlistedVars <- LR_HA_shortlistedVars[!LR_HA_shortlistedVars %in% "(Intercept)"] # remove intercept
### Model Building::
## Building First model after short listing the variables [using LR_HA_stepMod]
LR_HA_model_1 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + product_analytic_vertical.xDockingStation +
Digital_adstock + sla + price_tag.xMass_Product + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + deliverybdays +
TV_adstock + product_analytic_vertical.xDJController + Content_Marketing +
TV, data = LR_HA_data)
summary(LR_HA_model_1)
vif(LR_HA_model_1)
## High VIF and Insignificant p-value columns: price_tag.xMass_Product, TV
## Insignificant p-value columns: special_sale_day.xEid...Rathayatra
LR_HA_model_2 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + product_analytic_vertical.xDockingStation +
Digital_adstock + sla + product_analytic_vertical.xKaraokePlayer +
week + deliverybdays + TV_adstock + product_analytic_vertical.xDJController +
Content_Marketing, data = LR_HA_data)
summary(LR_HA_model_2)
vif(LR_HA_model_2)
## Slightly High VIF and Insignificant p-value columns: Content_Marketing
## Less significant p-value columns: sla
LR_HA_model_3 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + product_analytic_vertical.xDockingStation +
Digital_adstock + product_analytic_vertical.xKaraokePlayer + week + deliverybdays +
TV_adstock + product_analytic_vertical.xDJController , data = LR_HA_data)
summary(LR_HA_model_3)
vif(LR_HA_model_3)
## Less significant p-value columns: TV_adstock
LR_HA_model_4 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + product_analytic_vertical.xDockingStation +
Digital_adstock + product_analytic_vertical.xKaraokePlayer + week + deliverybdays +
product_analytic_vertical.xDJController , data = LR_HA_data)
summary(LR_HA_model_4)
vif(LR_HA_model_4)
## Slightly higher VIF and less significant p-value columns: deliverybdays
LR_HA_model_5 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + product_analytic_vertical.xDockingStation +
Digital_adstock + product_analytic_vertical.xKaraokePlayer + week +
product_analytic_vertical.xDJController , data = LR_HA_data)
summary(LR_HA_model_5)
vif(LR_HA_model_5)
## Insignificant p-value columns: week, product_analytic_vertical.xDJController
LR_HA_model_6 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + product_analytic_vertical.xDockingStation +
Digital_adstock + product_analytic_vertical.xKaraokePlayer, data = LR_HA_data)
summary(LR_HA_model_6)
vif(LR_HA_model_6)
## Insignificant p-value columns: product_analytic_vertical.xKaraokePlayer
LR_HA_model_7 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + product_analytic_vertical.xDockingStation +
Digital_adstock, data = LR_HA_data)
summary(LR_HA_model_7)
vif(LR_HA_model_7)
## Less significant p-value columns: Digital_adstock, product_analytic_vertical.xDockingStation
LR_HA_model_8 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates, data = LR_HA_data)
summary(LR_HA_model_8)
vif(LR_HA_model_8)
## Trying to remove "product_mrp" [as it is having high VIF] and then see the change in Adjusted R-squared
LR_HA_model_9 <- lm(formula = gmv ~ units + special_sale_day.xDaussera +
product_procurement_sla + Affiliates, data = LR_HA_data)
summary(LR_HA_model_9) # Adjusted R-squared value is changed at 3rd place of decimal, we're good to remove the variable
# We also tried to remove "units" variable but change in Adjusted R-squared value was more
vif(LR_HA_model_9)
## Insignificant p-value columns: Affiliates, product_procurement_sla
LR_HA_model_10 <- lm(formula = gmv ~ units + special_sale_day.xDaussera, data = LR_HA_data)
summary(LR_HA_model_10)
vif(LR_HA_model_10)
### Cross-validation
cv.lm(data = LR_HA_data, form.lm = LR_HA_model_10, m=5, dots = FALSE, seed=29, plotit=TRUE, printit=TRUE)
### Estimating the elasticity coefficients
elasticity_2 <- function(var){
LR_HA_elasticity <-as.numeric(LR_HA_model_10$coefficients[var]*mean(LR_HA_data[,var])/mean(LR_HA_data$gmv))
return(LR_HA_elasticity)
}
LR_HA_var_list <- list()
for(i in 2:length(LR_HA_model_10$coefficients)){
LR_HA_var_list[i-1] <-elasticity_2(names(LR_HA_model_10$coefficients)[i])
}
LR_HA_elasticity.outputs <- data.frame(names(LR_HA_model_10$coefficients[2:length(LR_HA_model_10$coefficients)]))
LR_HA_elasticity.outputs <- cbind(LR_HA_elasticity.outputs,do.call(rbind.data.frame, LR_HA_var_list))
colnames(LR_HA_elasticity.outputs) <- c("Variable","Elasticity")
LR_HA_elasticity.outputs$Direction <- ifelse(LR_HA_elasticity.outputs$Elasticity > 0, "Positive", "Negative")
# Plotting the elasticity
ggplot(LR_HA_elasticity.outputs, aes(x=reorder(Variable,Elasticity),y=Elasticity, fill = Direction)) +
geom_bar(position="dodge",stat="identity", width = 0.9) + theme_base() + coord_flip() +
scale_fill_manual(values=c(Positive="green3",Negative="red")) + geom_text(aes(label=Variable, y= 0.5),hjust = 1, color="black", size=5) +
theme(plot.title = element_text(hjust = 0.5), axis.title.y=element_blank(),axis.text.y=element_blank()) +
ggtitle("HomeAudio - Linear Regression Model") +xlab("Variables")
#********************************************************[Multiplicative Model]
### Preparing dataset
## Removing lag variables and Moving averages variables
## Also removing "list_price" and "promotional_offer" column as those are on dependent variable (i.e. gmv)
## Retaining those is not good idea as 'gmv' won't present in unseen data
MM_HA_data <- HomeAudio_final[,-c(21:22,63:77)]
## Replacing 0 value in column with '0.00001' as log(0) is undefined
MM_HA_data[MM_HA_data == 0] <- 0.00001
## Taking log of all the variable to buils to Multiplicative model
MM_HA_data <- log(MM_HA_data)
## Checking the variables for linear relationship or multicollinearity
MM_HA_model <- lm(gmv~.,MM_HA_data)
alias(MM_HA_model)
## Removing the variables which were showing linear relationship or multicollinearity
MM_HA_data <- MM_HA_data[, -c(51:58)]
### Stepwise Regression to remove insignificant and correlated variables
MM_HA_base.mod <- lm(gmv ~ 1 , data= MM_HA_data) # base intercept only model
MM_HA_all.mod <- lm(gmv ~ . , data= MM_HA_data) # full model with all predictors
MM_HA_stepMod <- step(MM_HA_base.mod, scope = list(lower = MM_HA_base.mod, upper = MM_HA_all.mod), direction = "both", trace = 1, steps = 1000) # perform step-wise algorithm
MM_HA_shortlistedVars <- names(unlist(MM_HA_stepMod[[1]])) # get the shortlisted variable.
MM_HA_shortlistedVars <- MM_HA_shortlistedVars[!MM_HA_shortlistedVars %in% "(Intercept)"] # remove intercept
### Model Building::
## Building First model after short listing the variables [using MM_HA_stepMod]
MM_HA_model_1 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
SEM_adtock + deliverybdays + wday.xTuesday + price_tag.xPremium_Product +
TV_adstock + wday.xSunday + product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
product_analytic_vertical.xSlingBox + sla + wday.xWednesday +
Content_Marketing_adstock + Sponsorship + product_analytic_vertical.xDJController +
wday.xMonday + product_analytic_vertical.xSoundMixer + is_special_sale_day +
special_sale_day.xChristmas...New.Year + Online_Marketing +
units + Total_Investment, data = MM_HA_data)
summary(MM_HA_model_1)
vif(MM_HA_model_1)
## High VIF and insignificant p-value columns: Total_Investment, units
MM_HA_model_2 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
SEM_adtock + deliverybdays + wday.xTuesday + price_tag.xPremium_Product +
TV_adstock + wday.xSunday + product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
product_analytic_vertical.xSlingBox + sla + wday.xWednesday +
Content_Marketing_adstock + Sponsorship + product_analytic_vertical.xDJController +
wday.xMonday + product_analytic_vertical.xSoundMixer + is_special_sale_day +
special_sale_day.xChristmas...New.Year + Online_Marketing, data = MM_HA_data)
summary(MM_HA_model_2)
vif(MM_HA_model_2)
## Insignificant p-value columns: product_analytic_vertical.xSoundMixer
## Less significant p-value columns: is_special_sale_day
MM_HA_model_3 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
SEM_adtock + deliverybdays + wday.xTuesday + price_tag.xPremium_Product +
TV_adstock + wday.xSunday + product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
product_analytic_vertical.xSlingBox + sla + wday.xWednesday +
Content_Marketing_adstock + Sponsorship + product_analytic_vertical.xDJController +
wday.xMonday + special_sale_day.xChristmas...New.Year + Online_Marketing, data = MM_HA_data)
summary(MM_HA_model_3)
vif(MM_HA_model_3)
## Slightly high VIF and Insignificant p-value columns: special_sale_day.xChristmas...New.Year
## High VIF and Insignificant p-value columns: Online_Marketing
## Insignificant p-value columns: wday.xMonday
MM_HA_model_4 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
SEM_adtock + deliverybdays + wday.xTuesday + price_tag.xPremium_Product +
TV_adstock + wday.xSunday + product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
product_analytic_vertical.xSlingBox + sla + wday.xWednesday +
Content_Marketing_adstock + Sponsorship + product_analytic_vertical.xDJController, data = MM_HA_data)
summary(MM_HA_model_4)
vif(MM_HA_model_4)
##High VIF and Insignificant p-value columns: product_analytic_vertical.xDJController
MM_HA_model_5 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
SEM_adtock + deliverybdays + wday.xTuesday + price_tag.xPremium_Product +
TV_adstock + wday.xSunday + product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
product_analytic_vertical.xSlingBox + sla + wday.xWednesday +
Content_Marketing_adstock + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_5)
vif(MM_HA_model_5)
## High VIF and Insignificant p-value columns: SEM_adtock
## Less significant p-value columns: price_tag.xPremium_Product
MM_HA_model_6 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
deliverybdays + wday.xTuesday + TV_adstock + wday.xSunday +
product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
product_analytic_vertical.xSlingBox + sla + wday.xWednesday +
Content_Marketing_adstock + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_6)
vif(MM_HA_model_6)
## Less significant p-value columns: product_analytic_vertical.xSlingBox
## High VIF and less significant p-value columns: wday.xWednesday
MM_HA_model_7 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
deliverybdays + wday.xTuesday + TV_adstock + wday.xSunday +
product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
sla + Content_Marketing_adstock + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_7)
vif(MM_HA_model_7)
## High VIF and Insignificant p-value columns: Content_Marketing_adstock
MM_HA_model_8 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + Content_Marketing +
deliverybdays + wday.xTuesday + TV_adstock + wday.xSunday +
product_procurement_sla + product_analytic_vertical.xKaraokePlayer +
sla + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_8)
vif(MM_HA_model_8)
## Insignificant p-value columns: Content_Marketing
## Less significant p-value columns: wday.xSunday, product_procurement_sla, wday.xTuesday
MM_HA_model_9 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + deliverybdays +
TV_adstock + product_analytic_vertical.xKaraokePlayer +
sla + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_9)
vif(MM_HA_model_9)
## Less significant p-value columns: product_analytic_vertical.xKaraokePlayer
MM_HA_model_10 <- lm(formula = gmv ~ price_tag.xMass_Product + product_mrp + deliverybdays +
TV_adstock + sla + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_10)
vif(MM_HA_model_10)
## Removing "price_tag.xMass_Product" [as it's having high VIF]
MM_HA_model_11 <- lm(formula = gmv ~ product_mrp + deliverybdays +
TV_adstock + sla + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_11) # Adjusted R-squared is changed at 3rd place of decimal, we're good to remove that variable
vif(MM_HA_model_11)
## Less significant p-value columns: TV_adstock
MM_HA_model_12 <- lm(formula = gmv ~ product_mrp + deliverybdays + sla + Sponsorship, data = MM_HA_data)
summary(MM_HA_model_12)
vif(MM_HA_model_12)
## Insignificant p-value columns: Sponsorship
MM_HA_model_13 <- lm(formula = gmv ~ product_mrp + deliverybdays + sla, data = MM_HA_data)
summary(MM_HA_model_13)
vif(MM_HA_model_13)
### Cross-validation
cv.lm(data = MM_HA_data, form.lm = MM_HA_model_13, m=5, dots = FALSE, seed=29, plotit=TRUE, printit=TRUE)
### Estimating the elasticity coefficients
elasticity_5 <- function(var){
MM_HA_elasticity <- as.numeric(MM_HA_model_13$coefficients[var]*mean(MM_HA_data[,var])/mean(MM_HA_data$gmv))
return(MM_HA_elasticity)
}
MM_HA_var_list <- list()
for(i in 2:length(MM_HA_model_13$coefficients)){
MM_HA_var_list[i-1] <- elasticity_5(names(MM_HA_model_13$coefficients)[i])
}
MM_HA_elasticity.outputs <- data.frame(names(MM_HA_model_13$coefficients[2:length(MM_HA_model_13$coefficients)]))
MM_HA_elasticity.outputs <- cbind(MM_HA_elasticity.outputs,do.call(rbind.data.frame, MM_HA_var_list))
colnames(MM_HA_elasticity.outputs) <- c("Variable","Elasticity")
MM_HA_elasticity.outputs$Direction <- ifelse(MM_HA_elasticity.outputs$Elasticity > 0, "Positive", "Negative")
# Plotting the elasticity
ggplot(MM_HA_elasticity.outputs, aes(x=reorder(Variable,Elasticity),y=Elasticity, fill = Direction)) +
geom_bar(position="dodge",stat="identity") + theme_base() + coord_flip() +
scale_fill_manual(values=c(Positive="green3",Negative="red")) + geom_text(aes(label=Variable, y=-0.5),hjust=0.1, color="black", size=5) +
theme(plot.title = element_text(hjust = 0.5), axis.title.y=element_blank(),axis.text.y=element_blank(),axis.ticks.y=element_blank()) +
ggtitle("HomeAudio - Multiplicative Model") +xlab("Variables")
#********************************************************[Koyck Model]
### Preparing dataset
## Removing lag variables and Moving averages variables but considering the 1 week lag value of 'gmv'
## Also removing "list_price" and "promotional_offer" column as those are on dependent variable (i.e. gmv)
## Retaining those is not good idea as 'gmv' won't present in unseen data
KM_HA_data <- HomeAudio_final[,-c(21:22,63:74,76:77)]
## Scaling the variables
KM_HA_data[,2:ncol(KM_HA_data)] <- scale(KM_HA_data[,2:ncol(KM_HA_data)])
### Stepwise Regression to remove insignificant and correlated variables
KM_HA_base.mod <- lm(gmv ~ 1 , data= KM_HA_data) # base intercept only model
KM_HA_all.mod <- lm(gmv ~ . , data= KM_HA_data) # full model with all predictors
KM_HA_stepMod <- step(KM_HA_base.mod, scope = list(lower = KM_HA_base.mod, upper = KM_HA_all.mod), direction = "both", trace = 1, steps = 1000) # perform step-wise algorithm
KM_HA_shortlistedVars <- names(unlist(KM_HA_stepMod[[1]])) # get the shortlisted variable.
KM_HA_shortlistedVars <- KM_HA_shortlistedVars[!KM_HA_shortlistedVars %in% "(Intercept)"] # remove intercept
### Model Building::
## Building First model after short listing the variables [using KM_HA_stepMod]
KM_HA_model_1 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + Digital_adstock +
sla + product_analytic_vertical.xKaraokePlayer + special_sale_day.xEid...Rathayatra +
week + GMV_lag_1_per + deliverybdays + TV_adstock + Digital +
wday.xSaturday + special_sale_day.xBSD + product_analytic_vertical.xHomeAudioSpeaker +
wday.xSunday + product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day + Online_Marketing_adstock +
Other_adstock + price_tag.xMass_Product + Sponsorship + Content_Marketing_adstock +
product_analytic_vertical.xSlingBox, data = KM_HA_data)
summary(KM_HA_model_1)
vif(KM_HA_model_1)
## Insignificant p-value columns: product_analytic_vertical.xSlingBox
## High VIF and Insignificant p-value columns: product_analytic_vertical.xHomeAudioSpeaker, wday.xSunday
## Slightly High VIF and Insignificant p-value columns: sla
KM_HA_model_2 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Affiliates + Digital_adstock +
product_analytic_vertical.xKaraokePlayer + special_sale_day.xEid...Rathayatra +
week + GMV_lag_1_per + deliverybdays + TV_adstock + Digital + wday.xSaturday +
special_sale_day.xBSD + product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day + Online_Marketing_adstock + Other_adstock +
price_tag.xMass_Product + Sponsorship + Content_Marketing_adstock, data = KM_HA_data)
summary(KM_HA_model_2)
vif(KM_HA_model_2)
## Slightly High VIF and Insignificant p-value columns: wday.xSaturday
## Insignificant p-value columns: special_sale_day.xBSD
## Slightly High VIF and less significant p-value columns: Affiliates
KM_HA_model_3 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + GMV_lag_1_per + deliverybdays +
TV_adstock + Digital + product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day + Online_Marketing_adstock + Other_adstock +
price_tag.xMass_Product + Sponsorship + Content_Marketing_adstock, data = KM_HA_data)
summary(KM_HA_model_3)
vif(KM_HA_model_3)
## High VIF and Insignificant p-value columns: Online_Marketing_adstock
KM_HA_model_4 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + GMV_lag_1_per + deliverybdays +
TV_adstock + Digital + product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day + Other_adstock + price_tag.xMass_Product + Sponsorship +
Content_Marketing_adstock, data = KM_HA_data)
summary(KM_HA_model_4)
vif(KM_HA_model_4)
## Slightly High VIF and less significant p-value columns: Sponsorship
## High VIF and less significant p-value columns: Content_Marketing_adstock
KM_HA_model_5 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + GMV_lag_1_per + deliverybdays +
TV_adstock + Digital + product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day + Other_adstock + price_tag.xMass_Product, data = KM_HA_data)
summary(KM_HA_model_5)
vif(KM_HA_model_5)
## Insignificant p-value columns: Other_adstock
##Less significant p-value columns: deliverybdays
KM_HA_model_6 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + GMV_lag_1_per + TV_adstock +
Digital + product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day + price_tag.xMass_Product, data = KM_HA_data)
summary(KM_HA_model_6)
vif(KM_HA_model_6)
## Insignificant p-value columns: special_sale_day.xRepublic.Day
KM_HA_model_7 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + GMV_lag_1_per + TV_adstock +
Digital + product_analytic_vertical.xFMRadio +
special_sale_day.xValentine.Day + price_tag.xMass_Product, data = KM_HA_data)
summary(KM_HA_model_7)
vif(KM_HA_model_7)
## High VIF and Insignificant p-value columns: price_tag.xMass_Product
## Insignificant p-value columns: special_sale_day.xValentine.Day
KM_HA_model_8 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + GMV_lag_1_per + TV_adstock +
Digital + product_analytic_vertical.xFMRadio, data = KM_HA_data)
summary(KM_HA_model_8)
vif(KM_HA_model_8)
## High VIF and Insignificant p-vaue value columns: product_analytic_vertical.xFMRadio
KM_HA_model_9 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + product_analytic_vertical.xKaraokePlayer +
special_sale_day.xEid...Rathayatra + week + GMV_lag_1_per + TV_adstock +
Digital, data = KM_HA_data)
summary(KM_HA_model_9)
vif(KM_HA_model_9)
## Slightly hogh VIF and Insignificant p-value columns: Digital
## Less significant p-value columns: product_analytic_vertical.xKaraokePlayer
KM_HA_model_10 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + special_sale_day.xEid...Rathayatra +
week + GMV_lag_1_per + TV_adstock, data = KM_HA_data)
summary(KM_HA_model_10)
vif(KM_HA_model_10)
## Less significant p-va;ue columns: TV_adstock, Digital_adstock
KM_HA_model_11 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + special_sale_day.xEid...Rathayatra +
week + GMV_lag_1_per, data = KM_HA_data)
summary(KM_HA_model_11)
vif(KM_HA_model_11)
## Insignificant p-value columns: week
## Less significant p-value columns: GMV_lag_1_per, special_sale_day.xEid...Rathayatra
KM_HA_model_12 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla, data = KM_HA_data)
summary(KM_HA_model_12)
vif(KM_HA_model_12)
## Less significant p-value columns: product_procurement_sla
KM_HA_model_13 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera, data = KM_HA_data)
summary(KM_HA_model_13)
vif(KM_HA_model_13)
## Removing "product_mrp" variable [as it' is's having high VIF] and will check the change in Adjusted R-squared value
KM_HA_model_14 <- lm(formula = gmv ~ units + special_sale_day.xDaussera, data = KM_HA_data)
summary(KM_HA_model_14) # Slight change in Adjusted R-squared value at 3rd place of decimal
vif(KM_HA_model_14)
### Cross-validation
cv.lm(data = KM_HA_data, form.lm = KM_HA_model_14, m=5, dots = FALSE, seed=29, plotit=TRUE, printit=TRUE)
### Estimating the elasticity coefficients
elasticity_8 <- function(var){
KM_HA_elasticity <- as.numeric(KM_HA_model_14$coefficients[var]*mean(KM_HA_data[,var])/mean(KM_HA_data$gmv))
return(KM_HA_elasticity)
}
KM_HA_var_list <- list()
for(i in 2:length(KM_HA_model_14$coefficients)){
KM_HA_var_list[i-1] <- elasticity_8(names(KM_HA_model_14$coefficients)[i])
}
KM_HA_elasticity.outputs <- data.frame(names(KM_HA_model_14$coefficients[2:length(KM_HA_model_14$coefficients)]))
KM_HA_elasticity.outputs <- cbind(KM_HA_elasticity.outputs,do.call(rbind.data.frame, KM_HA_var_list))
colnames(KM_HA_elasticity.outputs) <- c("Variable","Elasticity")
KM_HA_elasticity.outputs$Direction <- ifelse(KM_HA_elasticity.outputs$Elasticity > 0, "Positive", "Negative")
# Plotting the elasticity
ggplot(KM_HA_elasticity.outputs, aes(x=reorder(Variable,Elasticity),y=Elasticity, fill = Direction)) +
geom_bar(position="dodge",stat="identity") + theme_base() + coord_flip() +
scale_fill_manual(values=c(Positive="green3",Negative="red")) + geom_text(aes(label=Variable, y=-0.1),hjust = 1, color="black", size=5) +
theme(plot.title = element_text(hjust = 0.5), axis.title.y=element_blank(),axis.text.y=element_blank(),axis.ticks.y=element_blank()) +
ggtitle("HomeAudio - Koyck Model") +xlab("Variables")
#********************************************************[Distributive Lag Model]
### Preparing dataset
## Removing lag variables and Moving averages variables but considering the 1, 2 and 3 weeks lag value of 'gmv'
## Also removing "list_price" and "promotional_offer" column as those are on dependent variable (i.e. gmv)
## Retaining those is not good idea as 'gmv' won't present in unseen data
DL_HA_data <- HomeAudio_final[,-c(21:22,63:74)]
## Scaling the variables
DL_HA_data[,2:ncol(DL_HA_data)] <- scale(DL_HA_data[,2:ncol(DL_HA_data)])
### Stepwise Regression to remove insignificant and correlated variables
DL_HA_base.mod <- lm(gmv ~ 1 , data= DL_HA_data) # base intercept only model
DL_HA_all.mod <- lm(gmv ~ . , data= DL_HA_data) # full model with all predictors
DL_HA_stepMod <- step(DL_HA_base.mod, scope = list(lower = DL_HA_base.mod, upper = DL_HA_all.mod), direction = "both", trace = 1, steps = 1000) # perform step-wise algorithm
DL_HA_shortlistedVars <- names(unlist(DL_HA_stepMod[[1]])) # get the shortlisted variable.
DL_HA_shortlistedVars <- DL_HA_shortlistedVars[!DL_HA_shortlistedVars %in% "(Intercept)"] # remove intercept
### Model Building::
## Building First model after short listing the variables [using DL_HA_stepMod]
DL_HA_model_1 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + product_analytic_vertical.xDockingStation +
Digital_adstock + sla + price_tag.xMass_Product + product_analytic_vertical.xKaraokePlayer +
GMV_lag_2_per + week + deliverybdays + GMV_lag_1_per + TV_adstock +
Digital + wday.xSaturday + special_sale_day.xBSD + GMV_lag_3_per +
product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day + Other_adstock + Radio +
special_sale_day.xFHSD + product_analytic_vertical.xSlingBox +
product_analytic_vertical.xHiFiSystem + Sponsorship + deliverycdays +
wday.xWednesday, data = DL_HA_data)
summary(DL_HA_model_1)
vif(DL_HA_model_1)
## Slightly High VIF and Insignificant p-value columns: wday.xWednesday, product_analytic_vertical.xHiFiSystem, sla
## High VIF and Insignificant p-value columns: deliverybdays
## Insignificant p-value columns: special_sale_day.xFHSD, Sponsorship, product_analytic_vertical.xSlingBox
DL_HA_model_2 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + product_analytic_vertical.xDockingStation +
Digital_adstock + price_tag.xMass_Product + product_analytic_vertical.xKaraokePlayer +
GMV_lag_2_per + week + GMV_lag_1_per + TV_adstock + Digital + wday.xSaturday +
special_sale_day.xBSD + GMV_lag_3_per + product_analytic_vertical.xFMRadio +
special_sale_day.xRepublic.Day + special_sale_day.xValentine.Day +
Other_adstock + Radio + deliverycdays, data = DL_HA_data)
summary(DL_HA_model_2)
vif(DL_HA_model_2)
## Slightly high VIF and Insignificant p-value columns: wday.xSaturday, product_analytic_vertical.xDockingStation
DL_HA_model_3 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + price_tag.xMass_Product +
product_analytic_vertical.xKaraokePlayer + GMV_lag_2_per + week +
GMV_lag_1_per + TV_adstock + Digital + special_sale_day.xBSD +
GMV_lag_3_per + product_analytic_vertical.xFMRadio +
special_sale_day.xRepublic.Day + special_sale_day.xValentine.Day +
Other_adstock + Radio + deliverycdays, data = DL_HA_data)
summary(DL_HA_model_3)
vif(DL_HA_model_3)
## Less significant p-value columns: GMV_lag_3_per, deliverycdays, Other_adstock
## Slightly high VIF and less significant p-value columns: Radio
DL_HA_model_4 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + price_tag.xMass_Product +
product_analytic_vertical.xKaraokePlayer + GMV_lag_2_per + week +
GMV_lag_1_per + TV_adstock + Digital + special_sale_day.xBSD +
product_analytic_vertical.xFMRadio + special_sale_day.xRepublic.Day +
special_sale_day.xValentine.Day, data = DL_HA_data)
summary(DL_HA_model_4)
vif(DL_HA_model_4)
## Insignificant p-value columns: special_sale_day.xRepublic.Day
DL_HA_model_5 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + price_tag.xMass_Product +
product_analytic_vertical.xKaraokePlayer + GMV_lag_2_per + week +
GMV_lag_1_per + TV_adstock + Digital + special_sale_day.xBSD +
product_analytic_vertical.xFMRadio + special_sale_day.xValentine.Day, data = DL_HA_data)
summary(DL_HA_model_5)
vif(DL_HA_model_5)
## High VIF and Insignificant p-value columns: price_tag.xMass_Product
## Insignificant p-value columns: special_sale_day.xValentine.Day
DL_HA_model_6 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock +
product_analytic_vertical.xKaraokePlayer + GMV_lag_2_per + week +
GMV_lag_1_per + TV_adstock + Digital + special_sale_day.xBSD +
product_analytic_vertical.xFMRadio, data = DL_HA_data)
summary(DL_HA_model_6)
vif(DL_HA_model_6)
## High VIF and Insignificant p-value columns: product_analytic_vertical.xFMRadio
## Slightly High VIF and less significant p-value columns: Digital
## Less significant p-value columns: special_sale_day.xBSD, product_analytic_vertical.xKaraokePlayer
DL_HA_model_7 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + GMV_lag_2_per + week +
GMV_lag_1_per + TV_adstock, data = DL_HA_data)
summary(DL_HA_model_7)
vif(DL_HA_model_7)
## Less significant p-value columns: TV_adstock, week
DL_HA_model_8 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla + Digital_adstock + GMV_lag_2_per +
GMV_lag_1_per, data = DL_HA_data)
summary(DL_HA_model_8)
vif(DL_HA_model_8)
## Insignificant p-value columns: Digital_adstock
## Less significant p-value columns: GMV_lag_1_per, GMV_lag_2_per
DL_HA_model_9 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera +
product_procurement_sla, data = DL_HA_data)
summary(DL_HA_model_9)
vif(DL_HA_model_9)
## Removing "product_procurement_sla" value and will check the Adjusted R-squared value
DL_HA_model_10 <- lm(formula = gmv ~ units + product_mrp + special_sale_day.xDaussera, data = DL_HA_data)
summary(DL_HA_model_10) # Slight change in Adjusted R-squared value at 3rd place of decimal
vif(DL_HA_model_10)
## Removing "product_mrp" value and will check the Adjusted R-squared value
DL_HA_model_11 <- lm(formula = gmv ~ units + special_sale_day.xDaussera, data = DL_HA_data)
summary(DL_HA_model_11) # Slight change in Adjusted R-squared value at 3rd place of decimal
vif(DL_HA_model_11)
### Cross-validation
cv.lm(data = DL_HA_data, form.lm = DL_HA_model_11, m=5, dots = FALSE, seed=29, plotit=TRUE, printit=TRUE)
### Estimating the elasticity coefficients
elasticity_11 <- function(var){
DL_HA_elasticity <- as.numeric(DL_HA_model_11$coefficients[var]*mean(DL_HA_data[,var])/mean(DL_HA_data$gmv))
return(DL_HA_elasticity)
}
DL_HA_var_list <- list()
for(i in 2:length(DL_HA_model_11$coefficients)){
DL_HA_var_list[i-1] <- elasticity_11(names(DL_HA_model_11$coefficients)[i])
}
DL_HA_elasticity.outputs <- data.frame(names(DL_HA_model_11$coefficients[2:length(DL_HA_model_11$coefficients)]))
DL_HA_elasticity.outputs <- cbind(DL_HA_elasticity.outputs,do.call(rbind.data.frame, DL_HA_var_list))
colnames(DL_HA_elasticity.outputs) <- c("Variable","Elasticity")
DL_HA_elasticity.outputs$Direction <- ifelse(DL_HA_elasticity.outputs$Elasticity > 0, "Positive", "Negative")
# Plotting the elasticity
ggplot(DL_HA_elasticity.outputs, aes(x=reorder(Variable,Elasticity),y=Elasticity, fill = Direction)) +
geom_bar(position="dodge",stat="identity") + theme_base() + coord_flip() +
scale_fill_manual(values=c(Positive="green3",Negative="red")) + geom_text(aes(label=Variable, y=-0.1),hjust = 1, color="black", size=5) +
theme(plot.title = element_text(hjust = 0.5), axis.title.y=element_blank(),axis.text.y=element_blank(),axis.ticks.y=element_blank()) +
ggtitle("HomeAudio - Distributive Lag Model") +xlab("Variables")
#********************************************************[Multiplicative + Distributive Lag Model]
### Preparing dataset
## Removing lag variables and Moving averages variables but considering the 1, 2 and 3 weeks lag value of 'gmv'
## Also removing "list_price" and "promotional_offer" column as those are on dependent variable (i.e. gmv)
## Retaining those is not good idea as 'gmv' won't present in unseen data
MD_HA_data <- HomeAudio_final[,-c(21:22,63:74)]
## Replacing 0 value in column with '0.00001' as log(0) is undefined
MD_HA_data[MD_HA_data == 0] <- 0.00001
## Tranforming the negative values
MD_HA_data$GMV_lag_1_per <- 1 + MD_HA_data$GMV_lag_1_per - min(MD_HA_data$GMV_lag_1_per)
MD_HA_data$GMV_lag_2_per <- 1 + MD_HA_data$GMV_lag_2_per - min(MD_HA_data$GMV_lag_2_per)
MD_HA_data$GMV_lag_3_per <- 1 + MD_HA_data$GMV_lag_3_per - min(MD_HA_data$GMV_lag_3_per)
## Taking log of all the variable to buils to Multiplicative model
MD_HA_data <- log(MD_HA_data)
## Checking the variables for linear relationship or multicollinearity
MD_HA_model <- lm(gmv~.,MD_HA_data)
alias(MD_HA_model)
## Removing the variables which were showing linear relationship or multicollinearity
MD_HA_data <- MD_HA_data[, -c(51:63)]
### Stepwise Regression to remove insignificant and correlated variables
MD_HA_base.mod <- lm(gmv ~ 1 , data= MD_HA_data) # base intercept only model
MD_HA_all.mod <- lm(gmv ~ . , data= MD_HA_data) # full model with all predictors
MD_HA_stepMod <- step(MD_HA_base.mod, scope = list(lower = MD_HA_base.mod, upper = MD_HA_all.mod), direction = "both", trace = 1, steps = 1000) # perform step-wise algorithm
MD_HA_shortlistedVars <- names(unlist(MD_HA_stepMod[[1]])) # get the shortlisted variable.
MD_HA_shortlistedVars <- MD_HA_shortlistedVars[!MD_HA_shortlistedVars %in% "(Intercept)"] # remove intercept
### Model Building::
## Building First model after short listing the variables [using MD_HA_stepMod]
MD_HA_model_1 <- lm(formula = gmv ~ units + product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + TV_adstock + Digital +
product_analytic_vertical.xDockingStation + sla + product_analytic_vertical.xKaraokePlayer +
product_analytic_vertical.xSlingBox + wday.xTuesday + product_analytic_vertical.xFMRadio +
product_analytic_vertical.xDJController + wday.xWednesday +
product_analytic_vertical.xHiFiSystem + Sponsorship + holiday_count +
week + Affiliates + product_analytic_vertical.xVoiceRecorder +
Sponsorship_adstock + Content_Marketing_adstock + special_sale_day.xChristmas...New.Year +
Radio + Online_Marketing_adstock + Other + product_analytic_vertical.xSoundMixer,
data = MD_HA_data)
summary(MD_HA_model_1)
vif(MD_HA_model_1)
## Insignificant p-value columns: product_analytic_vertical.xSoundMixer, product_analytic_vertical.xSlingBox
## High VIF and insignifiacnt p-value columns: units, product_analytic_vertical.xFMRadio, product_analytic_vertical.xHiFiSystem
MD_HA_model_2 <- lm(formula = gmv ~ product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + TV_adstock + Digital +
product_analytic_vertical.xDockingStation + sla + product_analytic_vertical.xKaraokePlayer +
wday.xTuesday + product_analytic_vertical.xDJController + wday.xWednesday +
Sponsorship + holiday_count + week + Affiliates + product_analytic_vertical.xVoiceRecorder +
Sponsorship_adstock + Content_Marketing_adstock + special_sale_day.xChristmas...New.Year +
Radio + Online_Marketing_adstock + Other, data = MD_HA_data)
summary(MD_HA_model_2)
vif(MD_HA_model_2)
## High VIF and Insignificant p-value columns: wday.xTuesday
## Less significant p-value columns: week, product_analytic_vertical.xDJController
## High VIF value columns: Online_Marketing_adstock
MD_HA_model_3 <- lm(formula = gmv ~ product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + TV_adstock + Digital +
product_analytic_vertical.xDockingStation + sla + product_analytic_vertical.xKaraokePlayer +
wday.xWednesday + Sponsorship + holiday_count + Affiliates +
product_analytic_vertical.xVoiceRecorder + Sponsorship_adstock + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year + Radio + Other, data = MD_HA_data)
summary(MD_HA_model_3)
vif(MD_HA_model_3)
## High VIF and Insignificant p-value columns: product_analytic_vertical.xVoiceRecorder
MD_HA_model_4 <- lm(formula = gmv ~ product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + TV_adstock + Digital +
product_analytic_vertical.xDockingStation + sla + product_analytic_vertical.xKaraokePlayer +
wday.xWednesday + Sponsorship + holiday_count + Affiliates +
Sponsorship_adstock + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year + Radio + Other, data = MD_HA_data)
summary(MD_HA_model_4)
vif(MD_HA_model_4)
## Insignificant p-value columns: holiday_count
## High VIF value columns: Other
MD_HA_model_5 <- lm(formula = gmv ~ product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + TV_adstock + Digital +
product_analytic_vertical.xDockingStation + sla + product_analytic_vertical.xKaraokePlayer +
wday.xWednesday + Sponsorship + Affiliates + Sponsorship_adstock + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year + Radio , data = MD_HA_data)
summary(MD_HA_model_5)
vif(MD_HA_model_5)
## Insignificant p-value columns: Radio
MD_HA_model_6 <- lm(formula = gmv ~ product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + TV_adstock + Digital +
product_analytic_vertical.xDockingStation + sla + product_analytic_vertical.xKaraokePlayer +
wday.xWednesday + Sponsorship + Affiliates + Sponsorship_adstock + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year, data = MD_HA_data)
summary(MD_HA_model_6)
vif(MD_HA_model_6)
## Less significant p-value columns: product_analytic_vertical.xKaraokePlayer
## Slightly High VIF and Less significant p-value columns: TV_adstock
MD_HA_model_7 <- lm(formula = gmv ~ product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + Digital +
product_analytic_vertical.xDockingStation + sla + wday.xWednesday +
Sponsorship + Affiliates + Sponsorship_adstock + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year, data = MD_HA_data)
summary(MD_HA_model_7)
vif(MD_HA_model_7)
## Less significant p-value columns: product_analytic_vertical.xDockingStation
## High VIF value columns: Sponsorship_adstock
MD_HA_model_8 <- lm(formula = gmv ~ product_mrp + deliverybdays + Digital_adstock +
product_procurement_sla + wday.xSunday + Digital + sla +
wday.xWednesday + Sponsorship + Affiliates + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year, data = MD_HA_data)
summary(MD_HA_model_8)
vif(MD_HA_model_8)
## Slightly High VIF and Insignificant p-value columns: Digital_adstock
## Less significant p-value columns: Digital, Sponsorship
MD_HA_model_9 <- lm(formula = gmv ~ product_mrp + deliverybdays +
product_procurement_sla + wday.xSunday + sla +
wday.xWednesday + Affiliates + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year, data = MD_HA_data)
summary(MD_HA_model_9)
vif(MD_HA_model_9)
## High VIF value columns: wday.xWednesday
MD_HA_model_10 <- lm(formula = gmv ~ product_mrp + deliverybdays + product_procurement_sla +
wday.xSunday + sla + Affiliates + Content_Marketing_adstock +
special_sale_day.xChristmas...New.Year, data = MD_HA_data)
summary(MD_HA_model_10)
vif(MD_HA_model_10)
## Insignificant p-value columns: Content_Marketing_adstock
MD_HA_model_11 <- lm(formula = gmv ~ product_mrp + deliverybdays + product_procurement_sla +
wday.xSunday + sla + Affiliates + special_sale_day.xChristmas...New.Year, data = MD_HA_data)
summary(MD_HA_model_11)
vif(MD_HA_model_11)
## Insignificant p-value columns: special_sale_day.xChristmas...New.Year
MD_HA_model_12 <- lm(formula = gmv ~ product_mrp + deliverybdays + product_procurement_sla +
wday.xSunday + sla + Affiliates, data = MD_HA_data)
summary(MD_HA_model_12)
vif(MD_HA_model_12)
## Insignificant p-value columns: wday.xSunday
MD_HA_model_13 <- lm(formula = gmv ~ product_mrp + deliverybdays + product_procurement_sla +
sla + Affiliates, data = MD_HA_data)
summary(MD_HA_model_13)