To compare the effectiveness of advertising campaigns A , B , and C , we define

Question

     To compare the effectiveness of advertising campaigns A, B, and C, we define two dummy variables. Specifically, we define the dummy variable DB to equal 1 if campaign B is used in a sales period and 0 otherwise. Furthermore, we define the dummy variable DC to equal 1 if campaign C is used in a sales period and 0 otherwise. The table presents the Excel and Excel add-in (MegaStat) output of a regression analysis of the Fresh demand data by using the model

9.29

Historical Data Concerning Demand for Fresh Detergent Sales
Period Price for
Fresh, x1 Average Industry
Price, x2 Advertising
Expenditure
for Fresh, x3 Demand
for Fresh, y 1       3.85 3.87 5.59 7.39 2       3.72 4.07 6.72 8.52 3       3.77 4.39 7.22 9.21 4       3.74 3.77 5.57 7.55 5       3.68 3.85 7.02 9.33 6       3.65 3.87 6.57 8.23 7       3.62 3.73 6.79 8.78 8       3.82 3.83 5.20 7.81 9       3.89 3.60 5.27 7.14 10       3.84 4.03 6.08 8.05 11       3.97 4.13 6.57 7.85 12       3.92 4.05 6.23 8.16 13       3.75 4.18 7.08 9.15 14       3.75 4.20 6.90 8.84 15       3.78 4.14 6.82 8.94 16       3.86 4.11 6.84 8.87 17       3.72 4.20 7.11 9.29 18       3.86 4.38 7.04 9.06 19       3.73 4.17 6.82 8.75 20       3.83 3.77 6.54 7.98 21       3.80 3.78 6.26 7.66 22       3.79 3.65 6.02 7.26 23       3.75 3.97 6.57 8.05 24       3.54 3.68 7.08 8.55 25       3.64 4.16 6.82 8.78 26       3.64 4.21 6.84 9.22 27       3.71 3.68 6.55 8.25 28       3.70 3.73 5.70 7.60 29       3.82 3.87 5.85 7.95 30       3.79 4.25 6.84

9.29

Explanation / Answer

The regression is built through R:

> tt <- read.csv("clipboard",header=TRUE,sep=" ")
> head(tt)
Time Price Average_Industry_Price Advertisement Demand Campaign
1 1 3.85 3.87 5.59 7.39 B
2 2 3.72 4.07 6.72 8.52 B
3 3 3.77 4.39 7.22 9.21 B
4 4 3.74 3.77 5.57 7.55 A
5 5 3.68 3.85 7.02 9.33 C
6 6 3.65 3.87 6.57 8.23 A
> tt$Campaign <- as.character(tt$Campaign)
> ttlm <- lm(Demand~.,data=tt[,-1]
+ )
> summary(ttlm)

Call:
lm(formula = Demand ~ ., data = tt[, -1])

Residuals:
Min 1Q Median 3Q Max
-0.44873 -0.12693 -0.02959 0.14872 0.43023

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.62996 1.99491 3.323 0.002844 **
Price -2.09917 0.52951 -3.964 0.000577 ***
Average_Industry_Price 1.42502 0.26034 5.474 1.26e-05 ***
Advertisement 0.57814 0.10899 5.304 1.93e-05 ***
Campaign B 0.24397 0.09595 2.543 0.017870 *
Campaign C 0.44986 0.09843 4.570 0.000124 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2108 on 24 degrees of freedom
Multiple R-squared: 0.9188, Adjusted R-squared: 0.9018
F-statistic: 54.28 on 5 and 24 DF, p-value: 2.67e-12

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