Reading the data

pricepromdata = read.csv(paste("PricePromoData.csv"))
attach(pricepromdata)

Self-price elasticity of Coke

xfit = lm(log(oz_X)~log(pX), data = pricepromdata)
summary(xfit)
## 
## Call:
## lm(formula = log(oz_X) ~ log(pX), data = pricepromdata)
## 
## 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

Self-price elasticity of Pepsi

yfit = lm(log(oz_Y)~log(pY), data = pricepromdata)
summary(yfit)
## 
## Call:
## lm(formula = log(oz_Y) ~ log(pY), data = pricepromdata)
## 
## 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-16

Inference

# For every 1% rise in the price of Coke, the demand falls by 6.94%
# For every 1% rise in the price of Pepsi, the demand falls by 6.69%
# (The p-value for both Coke and Pepsi are significant)

# Inference : The demand of Coke is more price elastic compared to Pepsi

Cross-price elasticity of Coke

xcrossfit = lm(log(oz_X)~log(pY), data = pricepromdata)
summary(xcrossfit)
## 
## Call:
## lm(formula = log(oz_X) ~ log(pY), data = pricepromdata)
## 
## 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

Cross-price elasticity of Pepsi

ycrossfit = lm(log(oz_Y)~log(pX), data = pricepromdata)
summary(ycrossfit)
## 
## Call:
## lm(formula = log(oz_Y) ~ log(pX), data = pricepromdata)
## 
## 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: 0.0409

Inference

# For every 1% rise in the price of Pepsi, the demand for Coke rises by 0.33%, but the p-value is not significant.
# For every 1% rise in the price of Coke, the demand for Pepsi rises by 0.81%. 

# Inference : The cross-price elasticities are not same. Assuming that only these two brands exist in market, we can say that the consumers of Coke are more price sensitive as compared to that of Pepsi. However, we cannot say this conclusively as the p-value for cross-price elasticity of Coke is insignificant.

Self-price elasticity of Coke with price as well as promotion(Deal)

xfit1=lm(log(oz_X)~log(pX)+deal_X+deal_X*log(pX), data = pricepromdata)
summary(xfit1)
## 
## Call:
## lm(formula = log(oz_X) ~ log(pX) + deal_X + deal_X * log(pX), 
##     data = pricepromdata)
## 
## 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

Inference

# Price elasticity of Coke when no deal is being offered is -2.91, whereas it increases by 1.4 to equal -4.33 when a deal is being offered.
# Inference : Promotions have a significant impact on the price elasticity of Coke.

Self-price elasticity of Pepsi with price as well as promotion(Deal)

yfit1=lm(log(oz_Y)~log(pY)+deal_Y+deal_Y*log(pY), data = pricepromdata)
summary(yfit1)
## 
## Call:
## lm(formula = log(oz_Y) ~ log(pY) + deal_Y + deal_Y * log(pY), 
##     data = pricepromdata)
## 
## 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-16

Inference

# Price elasticity of Pepsi when no deal is being offered is -3.23, whereas it increases by 2.2 to equal -5.43 when a deal is being offered.
# Inference : Since the p-values are insignificant we cannot conclude that promotions have a significant impact on the price elasticity of Pepsi.