Topic 10 Multiple Regression Complete Solution

Question: #1875

Exercise:
The marketing manager of a chain of stores needed more information about the effectiveness of the three types of advertising that the chain used: television advertising, direct mailing and newspaper advertising. The manager collected data from 25 randomly selected stores. For each store, the following variables were recorded per week: store sales, TV advertising, Direct mailing and Newspaper advertising. All variables are recorded in thousands of euros (i.e. 1 unit=€1000).
You enter all the independent variables. You can see PART of the data below. The SPSS output follows.

Sales TV Direct Newspaper
17.49 0.86 1.62 1.97
22.53 0.78 2.2 1.61
23.98 1.20 1.77 1.13
18.96 0.83 1.17 1.77
24.64 1.91 1.76 2.04
19.52 1.34 1.81 1.63
…………………….
19.97 0.55 2.25 1.93
18.86 1.06 1.98 1.63
22.79 0.90 1.54 2.27
20.38 1.88 1.15 1.45
16.51 0.51 1.19 1.93
18.32 0.53 1.75 1.44
Notes written by Dr. Haritini Tsangari for MBA-603

Model R R Square Adjusted R Square
Std. Error of the
Estimate
1 .618 .382 .294 2.26713
ANOVA
Model Sum of Squares df Mean Square F Sig.
1 Regression 66.726 3 22.242 4.327 .016
Residual 107.937 21 5.140
Total 174.663 24
Coefficients
Model
Unstandardized Coefficients
Standardized
Coefficients
B Std. Error Beta t Sig.
(Constant) 10.629 3.623 2.934 .008
Television 2.869 1.126 .439 2.548 .019
Direct 3.012 1.342 .390 2.244 .036
Newspaper .522 1.707 .053 .306 .763

Answer the following questions:
(1) Do an overall F test and write your conclusions.
(2) According to your result of part (1) continue further to test individually which variables are significant for the model.
(3) Write down the final estimated model and interpret the coefficients.
(4) Is the final model better than the model which included only television advertising as an independent variable? Explain.
(5) Using your model estimate the weekly sales for a store that spends €1200 on TV advertising, €1770 on direct mailing and €1130 on newspaper advertising.

Solution: #1862

Topic 10 Multiple Regression Complete Solution

Using a F test in regression we test for the overall significance of the model. Here we test, H_0:None of the independent variables are significant and H_a:...