The owner of Showtime Movie Theaters, Inc. would like to estimate weekly gross r
ID: 3314404 • Letter: T
Question
The owner of Showtime Movie Theaters, Inc. would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.
Weekly Gross
Television
Newspaper
Radio
Revenue
Advertising
Advertising
Advertising
($1000s)
($1000s)
($1000s)
($1000s)
96
5
1.5
0.3
90
2
2
0.2
95
4
1.5
0.3
92
2.5
2.5
0.1
95
3
3.3
0.4
94
3.5
2.3
0.4
94
2.5
4.2
0.3
94
3
2.5
0.3
a) Obtain and compare the multiple coefficient of determination and the adjusted multiple coefficient of determination for parts a), b) and c). How does the coefficient of determination changes as a result of adding more independent variables in the equation?
Weekly Gross
Television
Newspaper
Radio
Revenue
Advertising
Advertising
Advertising
($1000s)
($1000s)
($1000s)
($1000s)
96
5
1.5
0.3
90
2
2
0.2
95
4
1.5
0.3
92
2.5
2.5
0.1
95
3
3.3
0.4
94
3.5
2.3
0.4
94
2.5
4.2
0.3
94
3
2.5
0.3
Explanation / Answer
The different Regression models along with there R-Sq and Adj-R are given below
Regression Analysis: Weekly Gross Revenue Versus Television Advertising
The regression equation is
Weekly Gross Revenue = 88.6 + 1.60 Television Advertising and its corresponding
R-Sq = 65.3% R-Sq(adj) = 59.5%
Regression Analysis: Weekly Gross Revenue Versus Newspaper Advertising
The regression equation is
Weekly Gross Revenue = 93.9 - 0.043 Newspaper Advertising and its corresponding
R-Sq = 0.0% R-Sq(adj) = 0.0%
Regression Analysis: Weekly Gross Revenue Versus Radio Advertising
The regression equation is
Weekly Gross Revenue = 90.1 + 12.7 Radio Advertising and its corresponding
R-Sq = 43.7% R-Sq(adj) = 34.3%
Regression Analysis: Weekly Gross Revenue Versus Television Advertising , Newspaper Advertising
The regression equation is
Weekly Gross Revenue = 83.2 + 2.29 Television Advertising + 1.30 Newspaper Advertising and its corresponding
R-Sq = 91.9% R-Sq(adj) = 88.7%
Regression Analysis: Weekly Gross Revenue Versus Television Advertising , Radio Advertising
The regression equation is
Weekly Gross Revenue = 87.4 + 1.28 Television Advertising + 7.71 Radio Advertising and its corresponding
R-Sq = 78.7% R-Sq(adj) = 70.1%
Regression Analysis: Weekly Gross Revenue Versus Newspaper Advertising , Radio Advertising
The regression equation is
Weekly Gross Revenue = 90.7 - 0.287 Newspaper Advertising + 13.2 Radio Advertising and its corresponding
R-Sq = 45.5% R-Sq(adj) = 23.7%
Regression Analysis: Weekly Gross Revenue Versus Television Advertising , Newspaper Advertising , Radio Advertising
The regression equation is
Weekly Gross Revenue = 83.5 + 2.08 Television Advertising + 1.12 Newspaper Advertising + 2.84 Radio Advertising and its corresponding 8
R-Sq = 93.2% R-Sq(adj) = 88.2%
Explaination
R-Sq is commonly called as the coefficient of determination. Both R-Sq and the adjusted R-Sq give us an idea of how many data points fall within the line of the regression equation or how well the data points are well presented with the line of regression. However, there is one main difference between R-Sq and the adjusted R-Sq: R-Sq assumes that every single variable explains the variation in the dependent variable so only R-Sq enhance or enlarging as a result of adding more independent variables. The adjusted R-Sq tells you the percentage of variation explained by only the independent variables that actually affect the dependent variable. The adjusted R-Sq will penalize you for adding independent variables (K in the equation) that do not fit the model. Adjusted R-Sq did not take in to the consideration the redenent varaibles.
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