3) A consumer packaged goods company puts out several advertisements every month

ID: 3181931 • Letter: 3

Question

3) A consumer packaged goods company puts out several advertisements every month in the local news paper and includes a discount coupon with the advertisements. The company has collected data on the number of advertisements it ran for the last 12 months as well as the dollar value of the coupon offered in each of the last 12 months. The sales (in thousands of dollars) is also recorded. The company wishes to investigate the impact of advertising and coupon value on sales. The company suspects that advertising and coupon value have a positive impact on sales. Express the regression model that the company must use, state the null and alternate hypothesis, estimate the model and provide interpretation. Given the results of your estimation, what are the expected sales in a month where 8 advertisements were put out using a $3 coupon. The data is in coupon.sav. and below.

Sales Ads Coupon Value 58 2.5 4.17 87 12.5 1.67 145 12.5 3.33 58 12.5 0.83 72.5 7.5 2.5 203 12.5 4.17 101.5 15 0.83 43.5 2.5 2.5 29 2.5 1.67 116 15 2.5 43.5 7.5 0.83 87 15 1.67

Explanation / Answer

Solution:

Here, we have to find the regression equation for the prediction of the dependent variable or response variable as the sales based on the independent variables or predictors such as advertisements and coupon value. The regression model (by using excel) for the prediction of the sales is given as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.920374554

R Square

0.84708932

Adjusted R Square

0.813109169

Standard Error

21.3830988

Observations

ANOVA

Significance F

Regression

22796.86777

11398.434

24.928945

0.000213782

Residual

4115.132227

457.23691

Total

26912

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-52.02936652

20.66052304

-2.518299

0.03286026

-98.76671659

-5.292016438

Ads

7.644673824

1.311440785

5.8292177

0.00025016

4.677988665

10.61135898

Coupon Value

28.87526149

5.532146356

5.2195404

0.00054953

16.36067701

41.38984597

The multiple correlation coefficient between the dependent variable or response variable sales and the independent variables or predictors such as ads and coupon value is given as R = 0.9204 approximately. This means there is a strong positive correlation or association exists between the dependent variable or response variable sales and the independent variables or predictors such as ads and coupon value. The value of the R square or coefficient of determination is given as 0.8471 which means about 84.71% of the variation in the dependent variable sales is explained by the independent variables ads and coupon value. The p-value for this regression model is given as 0.00 approximately, this means the given regression model is statistically significant. The required regression equation is given as below:

Sales = -52.03 + 7.64*Ads + 28.88*Coupon value

Now, we have to find the predicted value for sales for ads = 8 and coupon value = $3

Sales = -52.03 + 7.64*8 + 28.88*3

Sales = $95.73