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Regression Analysis: SSR, F-Value, Partial F-Test, VIF, and CI

A large consumer product company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, two types of advertising media are to be considered: radio/TV advertising and newspaper advertising (including the cost of discount coupons). The sales of product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded in ADRADTV.XLS (from the CD). Let X1 and X2 be the dollar amount of radio/TV ads and newspaper ads, respectively. Using EXCEL or PHStat2, answer the following:

1. What is SSR(X1 and X2)?
a) 2028032.69
b) 632259.45
c) 1395773.24

2. What is the F-value for X1 when used the partial F test criterion for determining the contribution of X1?
a) 55.28
b) 32.12
c) 43.81

3. What is the F-value for X2 when used the partial F test criterion for determining the contribution of X2?
a) 55.28
b) 32.12
c) 43.81

4. Determine which explanatory variable has a significant relationship with sales (Y) using the 5% significance level.
a) Radio/TV only
b) Newspaper only
c) Both Radio/TV and Newspaper

5. Set up a 95% confidence interval estimate of the population slope between sales and radio/TV ads.
a) (9.399, 16.763)
b) (10.593, 22.998)
c) (6.320, 18.005)

6. Set up a 95% confidence interval estimate for the average sales that have 10 radio/TV ads and 20 newspaper ads.
a) (464.393, 781.893)
b) (254.608, 991.678)
c) (158.750, 464.393)

7. Compute the VIF (Variance Inflationary Factor) for Newspaper Ads.
a) 0.008464
b) 0.991536
c) 1.008560

8. Using the result of Question 7, is there reason to suspect the existence of collinearity?
a) Yes, there is reason to suspect the existence of collinearity.
b) No, there is no reason to suspect the existence of collinearity.
c) There is not enough information to determine such a situation.

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This solution is comprised of detailed step-by-step calculations and analysis of the given problems based on Regression Analysis and provides students with a clear perspective of the underlying concepts.

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