Suppose you study the impact of advertising on sales of a soft drink company. Yo

Question

Suppose you study the impact of advertising on sales of a soft drink company. You build and estimate the following model (standard errors in parentheses):

St

=

3080

75,000Pt

+

4.23At

1.04Bt

(25,000)

(1.06)

(0.51)

N = 28   R2adj = 0.825

where St is the company's sales, Pt is the price of the product, At is the company's expenditures on advertising, and Bt is the expenditures on advertising by the company's main competitor (the subscript t stands for the time period when the observation was made).

Assume that there are no omitted variables. All variables are measured in real dollars; that is, the nominal values are divided, or deflated, by a price index. Suppose that according to other studies, advertising in the soft drink industry is cut-throat, and firms tend to match their main competitor’s advertising expenditures. Further, suppose that the simple correlation coefficient between the two advertising variables is 0.974 and that their respective VIFs are 14 and 12.

Which of the following conclusions from your analysis are correct? (Check all that apply.)

a. Multicollinearity in this equation is likely to cause bias in the coefficient of Pt.

b. Multicollinearity in this equation is likely to cause biased coefficients of Atand Bt.

c. Severe multicollinearity is likely to be present in the equation.

d. Bt should be dropped from the equation.

e. At should be dropped from the equation.

f. All estimated coefficients are statistically significant in the expected direction at the 5% level.

Part 2

In the previous question's scenario, suppose you’ve dropped Bt from the equation and estimated the following equation (standard errors in parentheses):

St

=

2586

78,000Pt

+

0.52At

(24,000)

(4.32)

N = 28   R2adj = 0.531

Given this result, which of the following conclusions should you make? (Check all that apply.)

a. The expected bias of the coefficient of At is negative.

b. Correcting for multicollinearity in the new equation leads to more reliable coefficient estimates.

c. The coefficient of Atis statistically insignificant due to omitted variable bias.

d. At should have been dropped instead of Bt.

e. Neither At nor Bt should have been dropped from the equation.

f. In the new equation, the coefficient of At is statistically insignificant due to multicollinearity.

St

=

3080

75,000Pt

+

4.23At

1.04Bt

(25,000)

(1.06)

(0.51)

Explanation / Answer

Answers to the questions:

We see high VIF and correlation between two Advertising variables

So, there is multicollinearity in the linear regression' variables
of At and Bt

Advertising in the soft drink industry is cut-throat, and firms tend to match their main competitor’s advertising expenditures

The right option is :
a, b , c, d are to be removed

part 2)

a. - False, it is positive, you can see in the regression equation
b. - True. Treating for collinearity solves the case
c. - True t-value is within the critical range
d - False. Its not neccessary we drop Bt or At
e - False. There is a multicollinearity
f - False. Although At is statistically insiginificant, there is no multicollinearity in new equation

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