The following estimated equations use the data in MLB1, which contains information on major league baseball salaries. The dependent variable, lsalary, is the log of salary. The two explanatory variables are years in the major leagues (years) and runs batted in per year (rbisyr):

lsalary 5 12.373 1 .1770 years 1.0982 1.01322 n 5 353, SSR 5 326.196, SER 5 .964, R2 5 .337 lsalary 5 11.861 1 .0904 years 1 .0302 rbisyr 1.0842 1.01182 1.00202 n 5 353, SSR 5 198.475, SER 5 .753, R2 5 .597

(i) How many degrees of freedom are in each regression? How come the SER is smaller in the second regression than the first?

(ii) The sample correlation coefficient between years and rbisyr is about 0.487. Does this make sense?

What is the variance inflation factor (there is only one) for the slope coefficients in the multiple regression? Would you say there is little, moderate, or strong collinearity between years and rbisyr?

(iii) How come the standard error for the coefficient on years in the multiple regression is lower than its counterpart in the simple regression?