We estimate the following model for wages for major league baseball players: ln(salary)= β0 +β1years + β2gamesyr + β3frstbase + β4scndbase + β5shrtstop + β6thrdbase + β7outfield + u where ln(salary) = the natural log of a player’s salary years = the player’s years in the major league gamesyr = the player’s average number of games played per year and frstbase, scndbase, shrtstop, thrdbase and outfield are each a dummy variable equal to 1 if the player plays that position on the field (when their team is fielding) and 0 otherwise. These are mutually exclusive dummy variables and there is one omitted fielding position, catcher. We find: *Regress lsalary years gamesyr frstbase scndbase shrtstop thrdbase outfield Source SS df MS Model Residual 300.454626 191.720909 7 345 42.9220894 0.55571278 Total 492.175535 352 1.39822595 lsalary coef. std. err. t P > |t| [95% Conf. Interval] years 0.0672574 0.0125509 5.36 0.000 0.0425716 0.0919433 gamesyr 0.0210952 0.0014124 14.94 0.000 0.0183171 0.0238732 frstbase -0.1900736 0.1574503 -1.21 0.228 -0.4997569 0.1196098 scndbase -0.4703525 0.1678491 -2.80 0.005 -0.8004888 -0.1402161 shrtstop -0.362002 0.1505844 -2.40 0.017 -0.6581811 -0.0658229 thrdbase -0.1268056 0.1682518 -0.75 0.452 -0.4577339 0.2041228 outfield -0.1296679 0.1264578 -1.03 0.306 -0.3783931 0.1190574 _cons 11.35251 0.1298462 87.43 0.000 11.09712 11.6079 Number of obs = 353 F (7, 345) = 77.24 Prob > F = 0.0000 R-squared = 0.6105 Adj R-squared = 0.6026 Root MSE = 0.74546 We test whether the set of dummies for the fielding position of the player are jointly significant in the log salary model. We obtain the following results for the restricted model: *Regress lsalary years gamesyr Source SS df MS Model Residual 293.864058 198.311477 2 350 146.932029 0.566604221 Total 492.175535 352 1.39822595 lsalary coef. std. err. t P > |t| [95% Conf. Interval] years 0.071318 0.012505 5.70 0.000 0.0467236 0.0959124 gamesyr 0.0201745 0.0013429 15.02 0.000 0.0175334 0.0228156 _cons 11.2238 0.108312 103.62 0.000 11.01078 11.43683 Number of obs = 353 F (2, 350) = 259.32 Prob > F = 0.0000 R-squared = 0.5971 Adj R-squared = 0.5948 Root MSE = 0.75273 What is the F-statistic for this test? a) 259.32 b) 5.93 c) 2.37 d) 77.24
We estimate the following model for wages for major league baseball players:
ln(salary)= β0 +β1years + β2gamesyr + β3frstbase + β4scndbase + β5shrtstop + β6thrdbase + β7outfield + u
where
- ln(salary) = the natural log of a player’s salary
- years = the player’s years in the major league
- gamesyr = the player’s average number of games played per year
and frstbase, scndbase, shrtstop, thrdbase and outfield are each a dummy variable equal to 1 if the player plays that position on the field (when their team is fielding) and 0 otherwise. These are mutually exclusive dummy variables and there is one omitted fielding position, catcher.
We find:
*Regress lsalary years gamesyr frstbase scndbase shrtstop thrdbase outfield
|
Source |
SS |
df |
MS |
|
Model Residual |
300.454626 191.720909 |
7 345 |
42.9220894 0.55571278 |
|
Total |
492.175535 |
352 |
1.39822595 |
|
lsalary |
coef. |
std. err. |
t |
P > |t| |
[95% Conf. Interval] |
|
|
years |
0.0672574 |
0.0125509 |
5.36 |
0.000 |
0.0425716 |
0.0919433 |
|
gamesyr |
0.0210952 |
0.0014124 |
14.94 |
0.000 |
0.0183171 |
0.0238732 |
|
frstbase |
-0.1900736 |
0.1574503 |
-1.21 |
0.228 |
-0.4997569 |
0.1196098 |
|
scndbase |
-0.4703525 |
0.1678491 |
-2.80 |
0.005 |
-0.8004888 |
-0.1402161 |
|
shrtstop |
-0.362002 |
0.1505844 |
-2.40 |
0.017 |
-0.6581811 |
-0.0658229 |
|
thrdbase |
-0.1268056 |
0.1682518 |
-0.75 |
0.452 |
-0.4577339 |
0.2041228 |
|
outfield |
-0.1296679 |
0.1264578 |
-1.03 |
0.306 |
-0.3783931 |
0.1190574 |
|
_cons |
11.35251 |
0.1298462 |
87.43 |
0.000 |
11.09712 |
11.6079 |
Number of obs = 353
F (7, 345) = 77.24
Prob > F = 0.0000
R-squared = 0.6105
Adj R-squared = 0.6026
Root MSE = 0.74546
We test whether the set of dummies for the fielding position of the player are jointly significant in the log salary model. We obtain the following results for the restricted model:
*Regress lsalary years gamesyr
|
Source |
SS |
df |
MS |
|
Model Residual |
293.864058 198.311477 |
2 350 |
146.932029 0.566604221 |
|
Total |
492.175535 |
352 |
1.39822595 |
|
lsalary |
coef. |
std. err. |
t |
P > |t| |
[95% Conf. Interval] |
|
|
years |
0.071318 |
0.012505 |
5.70 |
0.000 |
0.0467236 |
0.0959124 |
|
gamesyr |
0.0201745 |
0.0013429 |
15.02 |
0.000 |
0.0175334 |
0.0228156 |
|
_cons |
11.2238 |
0.108312 |
103.62 |
0.000 |
11.01078 |
11.43683 |
Number of obs = 353
F (2, 350) = 259.32
Prob > F = 0.0000
R-squared = 0.5971
Adj R-squared = 0.5948
Root MSE = 0.75273
What is the F-statistic for this test?
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