Question

1. The following models estimate the salary of professional baseball players, based on the number of years they have been playing, and their runs batted in per year (rbisyr). N = 353 for all models.

(1)  ^log(salary) = 11.978 + 0.186 years

R² = 0.337

(2) ^log(salary) = 11.731 + 0.096 years + 0.031 rbisyr

R² = 0.597

a. How many degrees of freedom are in model (1)? How many are in model (2)?

You estimate two alternative specifications:

(3) ^log(salary) = 10.492 + 0.091 years + 0.687 log(rbisyr)

R² = 0.573

(4) ^salary = -1512939 + 92723 years + 698845 log(rbisyr)

R² = 0.390

Separately for each of the models (2), (3), and (4), describe the estimated relationship between runs batted in per year and player salary in one sentence.

Answer 1

a)

For Model 1,

Residual Degrees of freedom = n-2 = 353 – 2 = 351

For Model 2,

Residual Degrees of freedom = n-k-1 = 353 - 2 -1 = 350

b)

For Model 2,

For 1 unit increase in rbisyr, log(salary) increases by 0.031 units

For Model 3,

For 1 unit increase in log(rbisyr), log(salary) increases by 0.687 units

For Model 4,

For 1 unit increase in log(rbisyr), salary increases by 698845 units