REGRESSION MODELS QUESTION 1. You are estimating the relationship between a firm
ID: 3150638 • Letter: R
Question
REGRESSION MODELS QUESTION
1. You are estimating the relationship between a firm’s sales and advertising expenditures in an industry. It becomes apparent to you that half the firms in the industry are large relative to the other half, and you are concerned about the proper estimation technique in such a situation. Assume that the error variances associated with the large firms are twice the error variances associated with the small firms.
a) if you used ordinary least squares to estimate the regression of sales on advertising (assuming that advertising expenditure is an independent variable and uncorrelated with the error term), would your estimated parameters be unbiased? Consistent? Efficient?
b) how mightt you revise the estimation procedure to elminate or resolve your difficulties?
c) can you test whether the original error-variance assumption is valid?
Explanation / Answer
You are estimating the relationship between a firm’s sales and advertising expenditures in an industry. It becomes apparent to you that half the firms in the industry are large relative to the other half, and you are concerned about the proper estimation technique in such a situation. Assume that the error variances associated with the large firms are twice the error variances associated with the small firms.
a) if you used ordinary least squares to estimate the regression of sales on advertising (assuming that advertising expenditure is an independent variable and uncorrelated with the error term), would your estimated parameters be unbiased? Consistent? Efficient?
Using ordinary least squares, we will have heteroscedasticity problem. The parameters areunbiased but inefficient.
b) how mightt you revise the estimation procedure to elminate or resolve your difficulties?
We shoud divide all the variables by the variable which most likely causes the problem.
c) can you test whether the original error-variance assumption is valid?
Yes, the Goldfeld-Quandt test of heteroscedasicity can be applied.
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