PricePromoData<-read.csv("PricePromoData.csv")
m_coke=lm(log(PricePromoData$oz_X)~log(PricePromoData$pX))
m_pepsi=lm(log(PricePromoData$oz_Y)~log(PricePromoData$pY))
summary(m_coke)##
## Call:
## lm(formula = log(PricePromoData$oz_X) ~ log(PricePromoData$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(PricePromoData$pX) -6.9446 0.1074 -64.63 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3671 on 726 degrees of freedom
## Multiple R-squared: 0.8519, Adjusted R-squared: 0.8517
## F-statistic: 4177 on 1 and 726 DF, p-value: < 2.2e-16summary(m_pepsi)##
## Call:
## lm(formula = log(PricePromoData$oz_Y) ~ log(PricePromoData$pY))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9059 -0.6063 0.0550 0.6057 3.4900
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -15.5981 0.8990 -17.35 <2e-16 ***
## log(PricePromoData$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-16Price elasticity is always negative
Following are the price elasticities of:
coke = -6.9446
pepsi = -6.6942
Thus we can conclude that coke is more price elastic than pepsi.
m_cross_xy=lm(log(PricePromoData$oz_X)~log(PricePromoData$pY))
summary(m_cross_xy)##
## Call:
## lm(formula = log(PricePromoData$oz_X) ~ log(PricePromoData$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(PricePromoData$pY) 0.3268 0.2482 1.317 0.188
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9528 on 726 degrees of freedom
## Multiple R-squared: 0.002383, Adjusted R-squared: 0.001008
## F-statistic: 1.734 on 1 and 726 DF, p-value: 0.1883m_cross_yx=lm(log(PricePromoData$oz_Y)~log(PricePromoData$pX))
summary(m_cross_yx)##
## Call:
## lm(formula = log(PricePromoData$oz_Y) ~ log(PricePromoData$pX))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3541 -0.9954 -0.0906 0.9914 3.6652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.1712 1.4169 7.884 1.16e-14 ***
## log(PricePromoData$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: 0.0409For 1 unit of % increase in Price of Pepsi, the demand of Coke increases by 0.3268
For 1 unit of % increase in Price of Coke, the demand of Pepsi increases by 0.8120
Therefore, cross elasticity of coke is more than the cross elasticity of pepsi.
We do not subset the data as there would be no relation between deal and no deal samples
m_coke_deal=lm(log(PricePromoData$oz_X)~log(PricePromoData$pX)+PricePromoData$deal_X+log(PricePromoData$pX)*PricePromoData$deal_X)
summary(m_coke_deal)##
## Call:
## lm(formula = log(PricePromoData$oz_X) ~ log(PricePromoData$pX) +
## PricePromoData$deal_X + log(PricePromoData$pX) * PricePromoData$deal_X)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.47804 -0.11484 -0.01953 0.06748 1.28798
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -2.4229 0.5048
## log(PricePromoData$pX) -2.9133 0.1435
## PricePromoData$deal_XYes -3.9397 1.3448
## log(PricePromoData$pX):PricePromoData$deal_XYes -1.4255 0.3588
## t value Pr(>|t|)
## (Intercept) -4.800 1.93e-06 ***
## log(PricePromoData$pX) -20.302 < 2e-16 ***
## PricePromoData$deal_XYes -2.930 0.0035 **
## log(PricePromoData$pX):PricePromoData$deal_XYes -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-16The elasticity of coke when a deal is not offered is -2.9133
The elasticity of coke when a deal is offered is -4.3388
Thus demand is affected more by price when a deal is offered by coke
m_pepsi_deal=lm(log(PricePromoData$oz_Y)~log(PricePromoData$pY)+PricePromoData$deal_Y+log(PricePromoData$pY)*PricePromoData$deal_Y)
summary(m_pepsi_deal)##
## Call:
## lm(formula = log(PricePromoData$oz_Y) ~ log(PricePromoData$pY) +
## PricePromoData$deal_Y + log(PricePromoData$pY) * PricePromoData$deal_Y)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.83238 -0.61046 0.02982 0.60163 3.06752
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -3.5422 1.7345
## log(PricePromoData$pY) -3.2352 0.4947
## PricePromoData$deal_YYes -7.0003 6.7669
## log(PricePromoData$pY):PricePromoData$deal_YYes -2.2084 1.7845
## t value Pr(>|t|)
## (Intercept) -2.042 0.0415 *
## log(PricePromoData$pY) -6.539 1.17e-10 ***
## PricePromoData$deal_YYes -1.034 0.3013
## log(PricePromoData$pY):PricePromoData$deal_YYes -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 elasticity of pepsi when a deal is not offered is -3.2352
The elasticity of pepsi when a deal is offered is -5.4436
Thus demand is affected more by price when a deal is offered by pepsi
To conclude, pepsi offering a deal affects the price more than coke offering a deal