Fit a linear regression model.
(1) Fit a linear regression model with salary as the response and the other 16 variables (excluding names) as the independent variables.
(2) What percentage of the variation in salaries is explained by the linear model?
(3) Comment on the coefficient of the independent variable “hits.” Is this coefficient consistent with what your intuition says should be the relationship between number of hits and salary? Why or why not?
(4) Test the null hypothesis (using level of significance 0.05) that none of the 16 independent variables is related to salary. What is the proper conclusion about the linear model?
(5) Test the null hypothesis (using level of significance 0.05) that the variables batting average, on base percentage, hits, doubles and triples are not needed in the same model with the other 11 independent variables. Is the result surprising? Give a possible explanation for the result.
(6) What percentage of the variation in salaries is explained by the linear model containing the 11 variables not named in problem (5)?