10. ls a company\'s reputation, a subjective assessment, related to objective me

Question

10. ls a company's reputation, a subjective assessment, related to objective measures of corporate performance such as its profitability? One study of this relationship examined the records of 154 Fortune 500 firms. Corporate reputation was measured on a scale of 1 to 10 by a Fortune magazine survey. Profitability was defined as the rate of return on invested capital. Figure 10.19, below, contains SAS output for the regression of profitability (PROFIT) on reputation score (REPUTAT). The format is very similar to the Excel and Minitab output we have seen, with minor differences in labels. You can take it as given that examination of the data shows no serious violations of the conditions required for regression inference. SAS Dependent Variable: PROFIT Analysis of variance Sum of DF Squares Square P value Prob>F Model 0.18957 0.18957 36.492 0.0001 152 0.78963 0.00519 Error C Total 153 0.97920 Root MSE 0.07208 R-Square 0.1936 0.1883 0.10000 Adj R-sq Dep Mean 72.07575 C.V Parameter Rstimates Parameter Standard T for H0: Variable DF Estimate Error Parameter-0 Prob IT P 1. 0.147573 0.04139259 3.565 0.0005 REPUTAT 1 0.039111 0.00647442 6.041 0.0001 SAS labels the regression standard error s as Root MSE. How can we obtain s from the ANOVA table?

Explanation / Answer

Residual is another name for error

Se = sqrt(Se^2) = sqrt( Sum of squares of errors or residuals)

This term can be got from ANOVA table by:

>> Square root of sumof squares of residuals (errors) divided by the degrees of freedom

Hence, option A = sqrt( SSres/Df) is the right answer.

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