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? a) 259.32 b) 5.93 c) 2.37 d) 77.24

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

Model

Residual

300.454626

191.720909

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

Model

Residual

293.864058

198.311477

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