setwd("G:/My Drive/Term V/DAM 2018/2018-10-27")
dat = read.csv("PricePromoData.csv")
View(dat)
attach(dat)#1.X Own elasticity
xelast = lm(log(oz_X) ~ log(pX))
summary(xelast)##
## Call:
## lm(formula = log(oz_X) ~ log(pX))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6564 -0.2395 -0.0788 0.1190 1.2732
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -16.5304 0.3840 -43.05 <2e-16 ***
## log(pX) -6.9446 0.1074 -64.63 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3671 on 726 degrees of freedom
## Multiple R-squared: 0.8519, Adjusted R-squared: 0.8517
## F-statistic: 4177 on 1 and 726 DF, p-value: < 2.2e-16#2.Y own elasticity
yelast = lm(log(oz_Y) ~ log(pY))
summary(yelast)##
## Call:
## lm(formula = log(oz_Y) ~ log(pY))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9059 -0.6063 0.0550 0.6057 3.4900
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -15.5981 0.8990 -17.35 <2e-16 ***
## log(pY) -6.6942 0.2519 -26.57 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9671 on 726 degrees of freedom
## Multiple R-squared: 0.4931, Adjusted R-squared: 0.4924
## F-statistic: 706.1 on 1 and 726 DF, p-value: < 2.2e-16The results show that Coke is more price elastic than Pepsi, therefore discounts on Coke will have a higher effect on sales than on Pepsi.
#Cross Elasticities
#4.Demand of X wrt price of Y
xyelast = lm(log(oz_X) ~ log(pY))
summary(xyelast)##
## Call:
## lm(formula = log(oz_X) ~ log(pY))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3777 -0.5510 -0.4059 -0.1456 2.5414
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.4395 0.8857 10.658 <2e-16 ***
## log(pY) 0.3268 0.2482 1.317 0.188
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9528 on 726 degrees of freedom
## Multiple R-squared: 0.002383, Adjusted R-squared: 0.001008
## F-statistic: 1.734 on 1 and 726 DF, p-value: 0.1883#5.Demand of Y wrt price of X
yxelast = lm(log(oz_Y) ~ log(pX))
summary(yxelast)##
## Call:
## lm(formula = log(oz_Y) ~ log(pX))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3541 -0.9954 -0.0906 0.9914 3.6652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.1712 1.4169 7.884 1.16e-14 ***
## log(pX) 0.8120 0.3965 2.048 0.0409 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.354 on 726 degrees of freedom
## Multiple R-squared: 0.005745, Adjusted R-squared: 0.004376
## F-statistic: 4.195 on 1 and 726 DF, p-value: 0.0409The cross elasticities are different. The price of Coke has a higher effect on the sales on Pepsi than vice versa.
#7.X regular vs promotion
xdeal = lm(log(oz_X) ~ log(pX) + deal_X + log(pX)*deal_X)
summary(xdeal)##
## Call:
## lm(formula = log(oz_X) ~ log(pX) + deal_X + log(pX) * deal_X)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.47804 -0.11484 -0.01953 0.06748 1.28798
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.4229 0.5048 -4.800 1.93e-06 ***
## log(pX) -2.9133 0.1435 -20.302 < 2e-16 ***
## deal_XYes -3.9397 1.3448 -2.930 0.0035 **
## log(pX):deal_XYes -1.4255 0.3588 -3.973 7.80e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2288 on 724 degrees of freedom
## Multiple R-squared: 0.9426, Adjusted R-squared: 0.9424
## F-statistic: 3966 on 3 and 724 DF, p-value: < 2.2e-16#9.Y regular vs promotion
ydeal = lm(log(oz_Y) ~ log(pY) + deal_Y + log(pY)*deal_Y)
summary(ydeal)##
## Call:
## lm(formula = log(oz_Y) ~ log(pY) + deal_Y + log(pY) * deal_Y)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.83238 -0.61046 0.02982 0.60163 3.06752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.5422 1.7345 -2.042 0.0415 *
## log(pY) -3.2352 0.4947 -6.539 1.17e-10 ***
## deal_YYes -7.0003 6.7669 -1.034 0.3013
## log(pY):deal_YYes -2.2084 1.7845 -1.238 0.2163
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.927 on 724 degrees of freedom
## Multiple R-squared: 0.5355, Adjusted R-squared: 0.5335
## F-statistic: 278.2 on 3 and 724 DF, p-value: < 2.2e-16The price elasticities change for both Coke and Pepsi when promotion is offered. However in the case of Pepsi, there is no significant difference between sales with and without promotion. Promotions are effective only in the sales of Coke.