Question

Market	Revenue	Paper Ads	TV Ads
Augusta	99.3	3.1	4.1
Baton Rouge	198.0	6.9	5.8
Biloxi	120.2	3.5	2.3
Birmingham	166.4	4.3	4.3
Jackson	74.8	4.0	1.5
Little Rock	137.8	3.6	4.0
Mobile	90.8	5.0	1.5
New Orleans	237.8	5.0	8.4
Savannah	147.0	4.4	2.7
Shreveport	56.5	3.0	3.0
Tunica	78.8	1.9	4.4

Specifically only need help with f-h.

1. Refer to the Excel “Dixie” data posted on eLearning: (18)
   1. Develop an estimated regression equation with the Revenue serving as the dependent variable and Paper Ads and TV Ads serving as explanatory variables. Write out this estimated equation (use the estimate values!) to explain Revenue.
   2. Show the residual plots where residuals are plotted against each explanatory variable separately. Comment on whether you can proceed with statistical inference based on what you see in the plots. (Hint: Don’t go looking for trouble!)
   3. Provide an interpretation for the three coefficient estimates that you calculated in part “a”. (don’t forget the intercept).
   4. What would your regression model predict the revenue amount to be in a market with 0 TV Ads and 0 Paper Ads? Is this a meaningful prediction? Answer, in a sentence, why or why not.
   5. Provide a 90% confidence interval for your estimate of the Paper Ads Coefficient. Interpret exactly what this 90% confidence interval means.
   6. What statistic and p-value would you use to test the specific null hypothesis that:

Ho: b _{Paper Ads} = b _{TV Ads} = 0

      Do you reject or fail to reject this null hypothesis?

1. g. If I asked you to consider a “backward selection” approach which only included predictors to the model that were significant at a 99% level, then would your answer to part “a” change? If so, what would it change to?
2. h. What percentage of the variation in Revenue can be explained by the model you developed on part “a”? How much more variation does this model explain than a model which uses only TV Ads to help predict Revenue?

Answer 1

(f) since the p-value of the regression model is 0.000917 is less than typical level of significance alpha=0.1 (90% confidence),

so we reject the null hypothesis H0: Ho: b _{Paper Ads} = b _{TV Ads} = 0

(g) since the p-value of the paper=0.013747 is less than alpha=0.01 ( or 99% confidence level), so first we remove variable paper in case of backward elimination method

(h) 82.596 percentage of the variation in Revenue can be explained by the model you developed on part “a”

since R²=0.82596 which is amount of variation explained in dependent variable by the independent variables

when only use TV Ads as dependent variable then the R²=0.61108 ( 61.108%)

so increase is 82.596-61.108=21.488%

21.488 %  more variation does this model explain than a model which uses only TV Ads to help predict Revenue

following regression analysis information has been generated using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.908824
R Square	0.82596
Adjusted R Square	0.78245
Standard Error	26.18582
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	2	26033.53	13016.76	18.98326	0.000917
Residual	8	5485.577	685.6972
Total	10	31519.11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%
Intercept	-24.3672	28.15079	-0.8656	0.411917	-89.283	40.54864	-89.283
paper	20.72377	6.594005	3.14282	0.013747	5.51797	35.92957	5.51797
TV	17.83539	4.298827	4.148897	0.003214	7.92228	27.74851	7.92228