Question

The owner of Showtime Movie Theaters would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks are as below:

Week	Weekly gross revenue ($1000s)	TV Advertising ($1000s)	Newspaper Advertising ($1000s)
1	96	5.0	1.5
2	90	2.0	2.0
3	95	4.0	1.5
4	92	2.5	2.5
5	95	3.0	3.3
6	94	3.5	2.3
7	94	2.5	4.2
8	94	3.0	2.5

Following are the regression results for the data using Excel. In this problem, you will be interpreting the regression results.

Use this table to answer the following questions:

1) yˆ=83.23+2.29*Newspaper Advertising+1.30*TV Advertisingy^=83.23+2.29*Newspaper Advertising+1.30*TV Advertising

2) Interpret the coefficient of TV Advertising.

3) Interpret the coefficient of Newspaper Advertising.

4) What is the estimate of the weekly gross revenue for a week when $3500 is spent on TV advertising and $1800 is spent on newspaper advertising?

5) Which variables have a statistically significant relationship with the dependent variable at the 1% level? (Use three decimals on the p value)

6) What is the 99% confidence interval estimate for the coefficient of TV Advertising?

7) What would be average weekly gross revenues if nothing is spent on TV and newspaper advertising?

8) At what level (probability) would the relationship between the dependent variable and the Newspaper Advertising will NOT be statistically significant? (Hint: think of the p value)

Answer 1

using excel>data>data annalysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.958663444
R Square	0.9190356
Adjusted R Square	0.88664984
Standard Error	0.642587303
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	23.43540779	11.7177039	28.37776839	0.001865242
Residual	5	2.064592208	0.412918442
Total	7	25.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	83.23009169	1.573868952	52.88247894	4.57175E-08	79.18433275	87.27585063	76.88403	89.57616
TV Advertising ($1000s)	2.290183621	0.304064556	7.531899313	0.000653232	1.508560796	3.071806446	1.064152	3.516215
Newspaper Advertising ($1000s)	1.300989098	0.320701597	4.056696662	0.009760798	0.476599398	2.125378798	0.007874	2.594104

1) yˆ=83.23+2.29*Newspaper Advertising+1.30*TV Advertising

2) Interpret the coefficient of TV Advertising.: for every 1000 $ increase in TV Ads weekly gross revenue increase by 2.29*1000$

3) the coefficient of Newspaper Advertising.: for every 1000 $ increase in TV Ads weekly gross revenue increase by 1.30*1000$

4) the estimate of the weekly gross revenue for a week when $3500 is spent on TV advertising and $1800 is spent on newspaper advertising

yˆ=83.23+2.29*3.5+1.30*1.8 =93.585 ( in 1000$)

5) both the variables are statistically significant

6) the 99% confidence interval estimate for the coefficient of TV Advertising is 1.0642,3.5162

7) the average weekly gross revenues, if nothing is spent on TV and newspaper advertising, is 83.23

8) at 0.002 , the relationship between the dependent variable and the Newspaper Advertising will NOT be statistically significant