From a sample of 209 firms, Wooldridge obtained the following regression results
ID: 3251186 • Letter: F
Question
From a sample of 209 firms, Wooldridge obtained the following regression results:* log (salary)= 4.32 4- 0.280 log (sales) + 0.0174 roe + 0.00024 ros R^2 = 0.283 where salary = salary of CEO sales = annual firm sales roe = return on equity in percent ros = return on firm's stock and where figures in the parentheses are the estimated standard errors. a. Interpret the preceding regression taking into account any prior expectations that you may have about the signs of the various coefficients. b. Which of the coefficients are individually statistically significant at the 5 percent level? c. What is the overall significance of the regression? Which test do you use? And why? d. Can you interpret the coefficients of roe and ros as elasticity coefficients? Why or why not?Explanation / Answer
This seems like a logit function that we use in logistic regression. Sometimes we use log form of dependent variable to counter heteroscedasticity.
Lets proceed further with the given problem
t statistic = (Value/ SE) ; apply this with every coefficient in the equation to check their individual significance. Remember we are checking against the hypothesis that this coefficient is zero. If it is not zero then we need to subtract that value from the numerator.
Intercept = 4.32/0.32 = 13.5 , p-value ~ 0
ln(sales) = 0.28/0.035 = 8, p-value ~ 0
roe = 0.0174/0.0041 = 4.24, p-value ~ 0
ros = 0.00024/0.00054 = 0.45, p-value = 0.6736
Sample size is > 30 so we can assume normal distribution and use z table to find the p values against each parameter.
Lower the p value more significant is our variable. Only ros variables fails its significance at 5% level since its p value is more than 0.05.
R^2 gives us an understanding as how much independent variables are capable of explaining dependent variable.
Overall significance of a model is tested by F test. If you are comparing 2-3 models then use anova function in various softwares and even in excel too.
F = (SS1 / df1) / (SS2 / df2) [ explained variance / unexplained variance ]
SS1 = Sum of squares regression = (y' - y'')^2 where y' is the predicted value and y'' is the average original values
SS2 = Sum of squares residuall = (y -y')^2 where y is the original value
df = degrees of freedom
df1 = 4-1 = 3
df2 = 209 - 4 - 1 = 204
By calculating this and finding its p value will help us to determine the significance of this model.
R^2 = explained variance / total variance : This always increases if we increase the number of predictors. So Adjusted R^2 is a better approach which considers the number of predictors into consideration too.
F test helps us in understanding the overall significance by calculating the ratio of explained and unexplained variance present in the data. As the F values becoming more and more greater than 1. your model become more significant.
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