Below is the population regression model that explain salaries of players of Chicago Cubs: ln (wages) = B0 +B1yrs + B2 avegames + B3 battingave + B4 homerunsperyear + B5 totalrunsperyear + u
The regressors are yrs (no of years in the team), avegames ( average games played), battingave (batting average of the player), home runs per year and total runs per year of the player. Assume the errors are homoskedastic. The table below presents the OLS estimates for different regression models for the dependent variable ln (wages). The numbers in the brackets denote the OLS standard errors of the coefficient.
regressor Model 1 Model 2
yrs .0689(.0121) .0713(.0125)
avegames .0136(.0026) .0202(.0013)
battingave .00089(.00110)
homerunsperyear .0145 (.0161)
totalrunsperyear .0109(.0072)
Intercept 11.19(.29) 11.22(.11)
R^2 ( R squared) .5349 .3528
N 45 45
I. Compute R2 (bar on top) for Model 2.
II. Test whether the regression coefficients of battingave, homerunsperyear and totalrunsperyear individually statistically significantly different from zero at 5% level?
III. Test whether the variables battingave, homerunsperyear and totalrunsperyear together belong to the model at 5% level, that is, are they jointly significant?
IV. The correlation coefficient between homerunsperyear and totalrunsperyear is .87. Comparing the results of individual hypothesis testing and joint hypothesis testing, explain your observations briefly and suggest ways to improve the regression, if need be.