Practice Example 1 14. From a sample of 209 firms, Wooldridge obtained the follo

Question

Practice Example 1 14. From a sample of 209 firms, Wooldridge obtained the following regres- sion results: log (salary) = 4.32 + 0.280 log (sales) + 0.0174 roe+ 0.00024 ros se = (032) (0.035) (0.0041) (0.00054) R2 = 0.283 where salary = salary of CEO sales = annual firm sales roe= return on equity in percent ros = return on firms stock and where figures in the parentheses are the estimated standard errors. a. Interpret the preceding regression taking into account any prior expec- tations that you may have about the signs of the various coefficients. b. Which of the coefficients are individually statistically significant at the c. What is the overall significance of the regression? Which test do you d. Can you interpret the coefficients of roe and ros as elasticity coeffi- 5 percent level? use? And why? cients? Why or why not?

Explanation / Answer

A) &D)

Coefficients of above regression Line can be interpreted as follows i

Parameter of log sample tells us about the elasticity of percentage change in salary with respect to percent change in sales.

Parameters of roe and ros tells us about the percentagr change in sells with respect to salary.

For parameter of log sales elasticity between sales and salary is 0.28 when other things considered constant

Similarly 0.17 % change in salary if roe Moves up or down in 1 unit similar interpretation goes with ros.

Sample size is more than 100 here we are using t test and this is general rule if sample size is more than 30 and critical t is 2

Then any t value which overshoots above 2 hints the rejection of hypothesis.

For all the parameters except ros t value is greater than 2 hence they are statistically significant than zero but in case of ros t value is 24/54= .44 which is less than 2 hence not significant that is we can't reject the hypothesis that parameter of ros is 0

Test for goodness that is R^2 is 0.28 which tells us the only 28 % of dependant variable that is salary explained by this model

As ros parameter turns out to be insignificant we can reduce the model by removing ros and can check for R^2 and adjusted R^2

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