ECO 5350-701 T. Fomby
Purpose: We are going to be focusing on (1) interpreting the coefficients in level-level, log-level, level-log, and log-log regression models, (2) conducting a Chow Test of the difference in the regression functions of two groups, (3) the analysis of a regression equation with a quadratic part of the model, and (4) interpreting the coefficients of a standardized regression. This exercise is to be handed in on Tuesday, March 9 at 5:00 pm CT on Canvas. The Lecture Notes 9.pdf should contain all the information your need to complete this exercise.
When I refer to reporting a regression model in standard form I mean something like:
(0.257) (0.039) (0.050) (0.0053)
where the standard errors of the coefficient estimates are placed in parentheses below the coefficient estimates.
Use the Hitters data set that we have analyzed in class that is part of the ISLR library in R. Do all of your work in this exercise using R and RStudio.
(a) Using Salary as the dependent variable and CHits as the sole independent variable, report the following regressions in standard form and for each model interpret the coefficient on the sole independent variable, CHits.
(i) level-level regression
(ii) log-level regression
(iii) level-log regression
(iv) log-log regression
(b) Here we are going to compare the level-level salary equations of the National League versus the American League using the Chow Test applied to the Additive/Multiplicative Dummy variable model. The sole independent variable we are going to be using is CHits while the Dummy variable is the variable “League” in the Hitters data set. Report your estimated Additive/Multiplicative Dummy variable model in standard form. Separately, write out the fitted equation of the National League salaries and the fitted equation of the American League salaries (no standard errors needed). Using the F-statistic, test the null hypothesis that the regression model of the National League is the same as the regression model of the American League. Report your calculated F-statistic and its p-value. In EXCEL you can use the “F.DIST.RT()” function to get the p-value of your calculated F statistic. What is your conclusion?
(c) Now add to your original level-level equation the quadratic terms involving the explanatory variable “Years.” Write out your estimated model in standard form. At what year do major league baseball salaries reach a peak, on average. Show your work. Suppose that you are a player with 7 years of experience. How would expect your salary to change in the transition to the eighth year, other factors held constant? Show your work.
(d) Run a standardized regression of Salary on CHits. Be sure and drop the intercept of your regression in this case as in lm(scale(y) ~ -1 + scale(x)). Report your regression in standard form. Interpret the coefficient on the standardized CHits variable. Compare the t-ratio on the standardized CHits variable with the CHits variable in your first level-level regression. What do you conclude from this?
(e) Report the R program that you used to complete this exercise.