Fixed-effects estimator
This is a panel data, t is 17, i is 5, the variables in the dataset are avgsalry, Allstars, attend, wins and teamed, the dataset contains 25 teams, 17 years are covered, the variable was measured in millions.
Wins have a positive effect on attendance and it is linear (upward linear trend)
There is homogeneity across wins.
Transformation in the attached R script.
The coefficient on wins is 20550 using the lm () function.
The coefficient on wins is 20550.3 using plm () function, the results are the same.
lm(formula = attend ~ wins + factor(teamid) - 1, data = panel)
Residuals:
Min 1Q Median 3Q Max
-701531 -237900 -17908 206587 989027
+
Coefficients:
Estimate Std. Error t value Pr(>|t|)
wins 18941 1493 12.684 < 2e-16 ***
factor(teamid)1 739134 149966 4.929 1.22e-06 ***
factor(teamid)2 1064265 139783 7.614 1.95e-13 ***
factor(teamid)3 743807 147562 5.041 7.05e-07 ***
factor(teamid)4 448318 144802 3.096 0.002099 **
factor(teamid)5 896821 138176 6.490 2.54e-10 ***
factor(teamid)6 597614 145993 4.093 5.15e-05 ***
factor(teamid)7 669337 144653 4.627 5.02e-06 ***
factor(teamid)8 540935 136722 3.956 9.00e-05 ***
factor(teamid)9 417589 147338 2.834 0.004827 **
factor(teamid)10 541477 139344 3.886 0.000119 ***
factor(teamid)11 1143475 145769 7.844 4.02e-14 ***
factor(teamid)12 574438 137884 4.166 3.80e-05 ***
factor(teamid)13 369900 138832 2.664 0.008026 **
factor(teamid)14 239706 142136 1.686 0.092489 .
factor(teamid)15 800743 152913 5.237 2.65e-07 ***
factor(teamid)16 705246 148987 4.734 3.07e-06 ***
factor(teamid)17 463995 147113 3.154 0.001732 **
factor(teamid)18 605697 136287 4.444 1.14e-05 ***
factor(teamid)19 413927 137157 3.018 0.002709 **
factor(teamid)20 573882 139783 4.106 4.89e-05 ***
factor(teamid)21 599319 141841 4.225 2.96e-05 ***
factor(teamid)22 570085 146142 3.901 0.000112 ***
factor(teamid)23 966598 145173 6.658 9.20e-11 ***
factor(teamid)24 721152 141399 5.100 5.26e-07 ***
factor(teamid)25 902227 148387 6.080 2.81e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 318100 on 399 degrees of freedom
Multiple R-squared: 0.9809, Adjusted R-squared: 0.9796
F-statistic: 786.7 on 26 and 399 DF, p-value: < 2.2e-16
plm(formula = attend ~ wins + factor(teamid) - 1, data = panel)
Balanced Panel: n = 25, T = 17, N = 425
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-701531 -237900 -17908 206587 989027
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
wins 18940.7 1493.3 12.684 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 5.6651e+13
Residual sum of Squares: 4.0373e+13
R-Squared: 0.28735
Adj. R-Squared: 0.2427
F-statistic: 160.881 on 1 and 399 DF, p-value: < 2.22e-16
There is no much difference in their results.
Estimate Std. Error t-value Pr(>|t|)
1 86746 149966 0.5784 0.563293
2 411878 139783 2.9466 0.003402 **
3 91419 147562 0.6195 0.535921
4 -204069 144802 -1.4093 0.159525
5 244434 138176 1.7690 0.077656 .
6 -54774 145993 -0.3752 0.707726
7 16950 144653 0.1172 0.906780
8 -111453 136722 -0.8152 0.415455
9 -234799 147338 -1.5936 0.111815
10 -110910 139344 -0.7959 0.426537
11 491088 145769 3.3689 0.000828 ***
12 -77949 137884 -0.5653 0.572171
13 -282488 138832 -2.0347 0.042537 *
14 -412682 142136 -2.9034 0.003896 **
15 148356 152913 0.9702 0.332537
16 52859 148987 0.3548 0.722936
17 -188393 147113 -1.2806 0.201079
18 -46691 136287 -0.3426 0.732085
19 -238461 137157 -1.7386 0.082877 .
20 -78506 139783 -0.5616 0.574688
21 -53069 141841 -0.3741 0.708496
22 -82303 146142 -0.5632 0.573637
23 314211 145173 2.1644 0.031028 *
24 68765 141399 0.4863 0.627008
25 249840 148387 1.6837 0.093020 .
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The graphs show that the relationships seem heteroskedastic, linearity exists between attend and avrsalry while non-linear relationship exists between attend and Allstars
Regression of attendance on variables
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 820348 117997 6.952 1.38e-11 ***
wins 10875 1653 6.578 1.42e-10 ***
avgsalry 331558 22118 14.991 < 2e-16 ***
allstars 66749 13125 5.086 5.52e-07 ***
the expected value of attendance is 820348 if all the
independent variables are held constant. The expected value of attendance increases by 10875 when wins increase by one unit. The expected value of attendance increases by 1331558 when avgsalry increases by one unit the expected value of attendance increases by 66749 when Allstars increases by one unit it is actually easy to tell which variables have the largest impact reason been that the higher the magnitude of the coefficient the more the impact. In this case, avgsalry has the largest impact.
The relationships seem heteroskedastic, linearity exists between attending and the log of avrsalry while a non-linear relationship exists between attend and the log of Allstars
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1521621 555133 -2.741 0.00639 **
log(wins) 837102 128833 6.498 2.31e-10 ***
log(avgsalry) 377530 23260 16.231 < 2e-16 ***
log(allstars) 166452 30316 5.491 6.94e-08 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 290500 on 421 degrees of freedom
Multiple R-squared: 0.5648, Adjusted R-squared: 0.5617
F-statistic: 182.1 on 3 and 421 DF, p-value: < 2.2e-16
the expected value of attendance increases by 837102 when the log of wins increases by one unit.
the expected value of attendance increases by 377530 when logging of avgsalry increases by one unit
the expected value of attendance increases by 166452 when the log of Allstars increases by one unit.
Studentized Breusch-Pagan test
data: olsmodel
BP = 1.8949, df = 3, p-value = 0.5945
Since the p-value is greater than the significance value, we do not reject the null hypothesis and conclude that there is homoscedasticity, hence, there is no need to correct our standard errors.
Home advantage, Population
Estimate Std. Error t-value Pr(>|t|)
log(wins)&nbasp; 930936 115273 8.0760 8.098e-15 ***
log(avgsalry) 326092 20840 15.6472 < 2.2e-16 ***
log(allstars) 123676 27468 4.5026 8.835e-06 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 5.6651e+13
Residual sum of Squares: 2.4522e+13
R-Squared: 0.56714
Adj. R-Squared: 0.5377
F-statistic: 173.383 on 3 and 397 DF, p-value: < 2.22e-16
The coefficient for the log of wins increases, however, there is a decrease in the coefficients of the log of avgsalry and log of Allstars.
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
log(wins) 904804 103933 8.7057 < 2.2e-16 ***
log(avgsalry) 305295 40274 7.5805 2.648e-13 ***
log(allstars) 126114 25081 5.0283 7.632e-07 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 3.7492e+13
Residual sum of Squares: 1.8645e+13
R-Squared: 0.50268
Adj. R-Squared: 0.44655
F-statistic: 128.368 on 3 and 381 DF, p-value: < 2.22e-16
The fixed effect did not change the result in much difference.
