Question

A multiple regression was run to explain CEO compensation (in $ per year) of major Northwest firms using three explanatory variables: the number of Employees, MarketCap (market capitalization in $thousands), and NetIncome (in $thousands). The prediction equation was

CEOComp = 6,260,416 + 29.167*Employees - 0.06309*MarketCap + 2.5617*NetIncome

         Furthermore, the F-test had F = 7.32 with a p-value of 0.000333, the t-test for Employees had a p-value of 0.208, the t-test for MarketCap had a p-value of 0.040, and the t-test for NetIncome had a p-value of 0.00158. The R² was 28.9%, the standard error of estimate was $9,618,328, with sample size n = 58. The standard deviation of CEOComp was $11,102,997.

a.   Overall, is CEOComp significantly related to these explanatory variables taken as a group? How do you know?

Yes			Reason:
No

b.   Name, and give numeric values for, two measures of the overall quality of this regression analysis: One that indicates variability explained, the other that summarizes how closely the predictions match actual CEOComp

                        Variability Explained

Name:

Value:

                        Closeness of Predictions

Name:

Value:

c.   If we look only at CEOComp and MktCap without the other variables, we find a significant positive relationship with regression correlation 0.0200 (this analysis is not shown above). However, in the multiple regression, the coefficient for MktCap is significant and negative. Please explain how this change from positive to negative is possible by describing and contrasting the meanings of these two regression coefficients.

Explanation:

Answer 1

a) Yes, as the p value for the overall model is given by 0.000333 and this is very very less which implies that not all the estimates of the coefficients are zero and hence it can be said that model is significant.

b) Variability explained

Name-R^2

Value=28.9%

Closeness of predictions

Name- Standard error of estimate

Value = $9,618,328

c) This is possible in case of multiple regression and this is a multiple regression model.

this happens due to the fact that the estimated coefficients are some kind of partial correlations which are different to usual correlations and hence we can't compare both of them directly.

Thank you !!!