Speed Distance Effect On Salary
Speed Distance Effect On Salary
Table of Contents
TOC o “1-3” h z u HYPERLINK l “_Toc372731266” Cover page PAGEREF _Toc372731266 h 1
HYPERLINK l “_Toc372731267” Executive Summary PAGEREF _Toc372731267 h 6
HYPERLINK l “_Toc372731268” Introduction PAGEREF _Toc372731268 h 7
HYPERLINK l “_Toc372731269” Data description PAGEREF _Toc372731269 h 7
HYPERLINK l “_Toc372731270” Methodology PAGEREF _Toc372731270 h 8
HYPERLINK l “_Toc372731271” Model results. PAGEREF _Toc372731271 h 9
HYPERLINK l “_Toc372731272” Conclusion PAGEREF _Toc372731272 h 10
HYPERLINK l “_Toc372731273” Appendices PAGEREF _Toc372731273 h 11
HYPERLINK l “_Toc372731274” Appendix 1. PAGEREF _Toc372731274 h 11
HYPERLINK l “_Toc372731275” Appendix 2 PAGEREF _Toc372731275 h 12
HYPERLINK l “_Toc372731276” Appendix 3. PAGEREF _Toc372731276 h 12
HYPERLINK l “_Toc372731277” Appendix 4 PAGEREF _Toc372731277 h 13
HYPERLINK l “_Toc372731278” References PAGEREF _Toc372731278 h 14
Executive SummaryThe aim of this research paper is to find out whether there is a relationship between the salary an NBA player receives the amount of games a player has played(GP), the amount of minutes he has played(minutes), the total distance travelled calculated in miles(distance travelled), the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court(average speed), the distance the player covered while he was on the game(distance travelled per game) and distance the player covered while he was on the court calculated per 48 minutes(distance travelled per 48 min(miles)).
The data used was got from two NBA performance tracking companies. The data on salaries can be downloaded from basketball-refence.com while data on players can be got from NBA stats. The results did not give a significant association between salaries and the variables mentioned above. This was against the hypothesis, which expected salary to be affected by these factors.
IntroductionBasketball is a game that started in America. It was started by a group called the American association group. It gained popularity at a very high rate. Best players started coming up. It is a game that was considered lively; it excited the players very much, competing to estimate the one who scored most goals. Balls were introduced, with various colors like blue, white and red. At this time the game was not very popular. The salaries rewarded to the players were also not very pleasing. The first International match was held in Euro in 1909. It was held in Saint Petersburg, this was the first march and being an international match the players received a good reward. Since then the game has continued expanding in other countries and there are players who depend on it. The players, just like in other games are known of their rich living from the rewards they get.
In most real life cases those who are smart always get the bet. This has been proven in various cases including jobs, schools, politics and other areas. This theory is not left out in the field of games. The benefits that accompany the best players include huge salaries and fame. This research project concentrates its interest on NBA among the games that are popular in the current era. The objectives of the paper will therefore be:-
Determining the factors that affect the salaries of the players most
Getting the factor that influences salaries most
Data descriptionThe equation that represents the data above has one dependent variable, salary and various independent variable, the amount of games a player has played(GP), the amount of minutes he has played(minutes), the total distance travelled calculated in miles(distance travelled), the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court(average speed), the distance the player covered while he was on the game(distance travelled per game) and distance the player covered while he was on the court calculated per 48 minutes(distance travelled per 48 min(miles)).
The variables can be represented by;
Y for salary
X1 for GP
X2 for amount of minutes he has played(minutes)
X3 for total distance travelled calculated in miles(distance travelled)
X4 for average speed of the player in miles per hour
X5 for the distance the player covered while he was on the game(distance travelled per game)
X6 for distance the player covered while he was on the court calculated per 48 minutes
The initial regression equation will therefore be:-
Y = a + b0X1 + b2X2 + b3X3 + b4X4 +b5X5 + b6X6 + ε
The model for appendix 4 was:
Y = a + b0X1 + b2X2 + b3X3 + b4X4 +b5X5 + ε
The model for appendix 5 was:
Y = a + b2X2 + b3X3 + b4X4 +b5X5 + b6X6 + ε
The model for appendix 6 was:
Y = a + b1X1 + b3X3 + b4X4 +b5X5 + b6X6 +ε
The model for appendix 7 was:
Y = a + b1X1 + b2X2 + b4X4 +b5X5 + b6X6 + ε
The model for appendix 6 was:
Y = a + b1X1 + b2X2 + b3X3 +b5X5 + b6X6 + ε
The other appendices, 1 and 2 were just meant to find out whether there was a certain variable that had an influence individually. Backward elimination on this data could not be used since none of the tested had a significant effect.
MethodologyThe hypothesis of this research was that the salary one receives is affected by the factors; the amount of games a player has played(GP), the amount of minutes he has played(minutes), the total distance travelled calculated in miles(distance travelled), the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court(average speed), the distance the player covered while he was on the game(distance travelled per game) and distance the player covered while he was on the court calculated per 48 minutes(distance travelled per 48 min(miles)).This data is readily available on the websites of the NBA companies given above.
Regression analysis was used to test the above hypothesis. Various factors were also considered each at a time to find out whether it would explain salary on its own. Log of the dependent variable is used to make the coefficients in the regression more meaningful. Various tests are carried out (Achen 1982).Model results.Appendix 1
This appendix shows the initial model regression model results. This is the model that has combined all the factors together. The results do not show a very good relationship. The goodness of fit of this model showed that just 25.737% of the salary was explained by the factors combined. All the coefficients had a p-value that was less than 0.05. This indicated that the combination of the amount of games a player has played, the amount of minutes he has played, the total distance travelled calculated in miles, the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court, the distance the player covered while he was on the game and distance the player covered while he was on the court calculated per 48 minutes did not have a significant effect on salary. These were not the expected results. It was against the hypothesis. Further analysis was therefore needed to determine whether individual factors have an effect on salary (Lewis-Beck 1980).
Appendix 4
It combined the amount of games a player has played, the amount of minutes he has played, the total distance travelled calculated in miles, the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court, the distance the player covered while he was on the game. This did not work well also as just 23.98& of the variation is salary was caused by these factors. The p-values were also very large and they did not make significant change on salary. The coefficients on GP, Min per game average speed and distance travelled per game were all negative. This meant that the relationship that existed was negative.
Appendix 5
This appendix combined the amount of minutes he has played, the total distance travelled calculated in miles, the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court, the distance the player covered while he was on the game and backwards while a player is on the court, the distance the player covered while he was on the game. This did not work well also as just 25.53% of the variation is salary was caused by these factors. The p-values were also very large and they did not make significant change on salary. Some of the coefficients of the variables were negative. This meant that the relationship that existed was negative.
Appendix 6
This appendix combined the amount of the total distance travelled calculated in miles, the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court, the distance the player covered while he was on the game and backwards while a player is on the court, the distance the player covered while he was on the game and the amount of games the player has played. This did not work well also as just 25.48% of the variation is salary was caused by these factors. The p-values were also very large and they did not make significant change on salary. Some of the coefficients of the variables were negative.This meant that the relationship that existed was negative.
Appendix 7
This appendix combined the amount of the average speed of the player in miles per hour. This includes jogging, sprinting, walking, standing, forwards and backwards while a player is on the court, the distance the player covered while he was on the game and backwards while a player is on the court, the distance the player covered while he was on the game and the amount of games the player has played. This did not work well also as just 25.63% of the variation is salary was caused by these factors. The p-values were also very large and they did not make significant change on salary. Some of the coefficients of the variables were negative. This meant that the relationship that existed was negative.
Appendix 8
This appendix combined the amount of the distance the player covered while he was on the game and backwards while a player is on the court, the distance the player covered while he was on the game, the amount of games the player has played and the distance travelled by a player in miles. This did not work well also as just 23.66% of the variation is salary was caused by these factors. The p-values were also very large and they did not make significant change on salary. Some of the coefficients of the variables were negative. This meant that the relationship that existed was negative.
Appendix 2
Shows the results of the amount of games played on salary. The output of this was also against what was expected. The goodness of fit of this model was around 9.5% of the salary was influenced by the amount of games a player has played. This is not a very good fit. The p-value however shows that it has some significant influence on the salary. The coefficient is negative which shows that the influence could be negative.
Appendix 3
The output of these three factors tried to go with the hypothesis. The goodness of fit of this model was 48.657% .The p-value of Average Speed (mph) and Distance Traveled Per Game (miles) was 0.00645 and 0.0096626 which means that there could be a significant relationship between them and salary. Average Speed (mph) however gave a negative coefficient which showed that the relationship was negative. Distance travelled is the only factor that had a significant effect in this combination.
ConclusionThe above results were not expected. It was expected that there could be an association between the salary the players received and the activities they had in the court. This was proven wrong from the data used. It was found that the activities of a player did not affect his salary. This information would be important, if shared out with the government and the sponsors who support these games. They should try to reward the players according to how they play. However, the salary could be explained by other factors like businesses.
AppendicesAppendix 1.Initial regression result
SUMMARY OUTPUT Regression Statistics Multiple R 0.507315 R Square 0.257369 Adjusted R Square 0.209457 Standard Error 0.761889 Observations 100 ANOVA df SS MS F Significance F Regression 6 18.70892 3.11813 5.37173 8.43E-05 Residual 93 53.98415 0.58045 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 19.63743 13.14199 1.49425 0.13846 -6.45997 45.73482 -6.45997 45.73482
X Variable 1 -0.33728 0.663356 0.50844 0.61235 -1.65457 0.980018 -1.65457 0.980018
X Variable 2 0.13077 0.229791 0.56902 0.57062 -0.32555 0.587089 -0.32555 0.587089
X Variable 3 0.100743 0.285148 0.3533 0.72463 -0.4655 0.66699 -0.4655 0.66699
X Variable 4 -3.25962 2.021706 1.61231 0.11023 -7.27433 0.755086 -7.27433 0.755086
X Variable 5 -2.06709 2.385136 0.86666 0.38832 -6.8035 2.669316 -6.8035 2.669316
X Variable 6 3.272762 2.206541 1.48329 0.1414 -1.10899 7.654514 -1.10899 7.654514
Appendix 2SUMMARY OUTPUT Regression Statistics Multiple R 0.308258 R Square 0.095023 Adjusted R Square 0.085788 Standard Error 0.819318 Observations 100 ANOVA df SS MS F Significance F Regression 1 6.907494 6.907494 10.29001 0.001807 Residual 98 65.78557 0.671281 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 18.57952 0.939401 19.77806 5.48E-36 16.71531 20.44373 16.71531 20.44373
X Variable 1 -0.32559 0.101499 -3.2078 0.001807 -0.52701 -0.12417 -0.52701 -0.12417
Appendix 3.SUMMARY OUTPUT Regression Statistics Multiple R 0.486868 R Square 0.23704 Adjusted R Square 0.213198 Standard Error 0.760084 Observations 100 ANOVA df SS MS F Significance F Regression 3 17.23118 5.74376 9.94192056 9.07E-06 Residual 96 55.46189 0.57778 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 21.33732 1.742628 12.2443 2.54067E-21 17.87823 24.79641 17.87823 24.79641
X Variable 1 -4.54379 1.631644 -2.78479 0.00645298 -7.78258 -1.30501 -7.78258 -1.30501
X Variable 2 0.788131 0.298475 2.64056 0.00966262 0.195663 1.380599 0.195663 1.380599
X Variable 3 3.406 1.952369 1.74458 0.08426405 -0.46942 7.281421 -0.46942 7.281421
Appendix 4SUMMARY OUTPUT Regression Statistics Multiple R 0.489696 R Square 0.239802 Adjusted R Square 0.199366 Standard Error 0.766736 Observations 100 ANOVA df SS MS F Significance F Regression 5 17.43193 3.486386 5.930393 8.26E-05 Residual 94 55.26114 0.587884 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 28.18385 11.88658 2.371064 0.019778 4.582759 51.78493 4.582759 51.78493
X Variable 1 -0.75346 0.604911 -1.24557 0.216016 -1.95453 0.447603 -1.95453 0.447603
X Variable 2 -0.01025 0.21053 -0.04868 0.961274 -0.42826 0.407763 -0.42826 0.407763
X Variable 3 0.272701 0.262172 1.040159 0.300934 -0.24785 0.79325 -0.24785 0.79325
X Variable 4 -1.72081 1.746238 -0.98544 0.326939 -5.18801 1.746387 -5.18801 1.746387
X Variable 5 -1.7073 2.387864 -0.71499 0.476388 -6.44846 3.033862 -6.44846 3.033862
Appendix 5
SUMMARY OUTPUT Regression Statistics Multiple R 0.505277 R Square 0.255304 Adjusted R Square 0.215693 Standard Error 0.758878 Observations 100 ANOVA df SS MS F Significance F Regression 5 18.55886 3.711772 6.445215 3.42E-05 Residual 94 54.13421 0.575896 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 13.73621 6.14002 2.23716 0.027639 1.545052 25.92736
X Variable 1 0.210266 0.167731 1.253592 0.213099 -0.12277 0.5433
X Variable 2 -0.04224 0.046935 -0.90004 0.370397 -0.13544 0.050947
X Variable 3 -3.00975 1.953312 -1.54084 0.126715 -6.88809 0.868601
X Variable 4 -1.82695 2.328665 -0.78455 0.434691 -6.45057 2.796669
X Variable 5 3.747319 1.991512 1.881646 0.062978 -0.20687 7.701512
Appendix 6
SUMMARY OUTPUT Regression Statistics Multiple R 0.50476 R Square 0.254783 Adjusted R Square 0.215143 Standard Error 0.759144 Observations 100 ANOVA df SS MS F Significance F Regression 5 18.52093 3.704186 6.427539 3.53E-05 Residual 94 54.17214 0.576299 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 26.59455 4.805176 5.534564 2.81E-07 17.05376 36.13534
X Variable 1 0.210326 0.209551 1.003697 0.318101 -0.20574 0.626393
X Variable 2 -3.88783 1.687624 -2.30373 0.023441 -7.23864 -0.53701
X Variable 3 -1.29111 1.949882 -0.66215 0.509495 -5.16265 2.580422
X Variable 4 2.753208 2.001571 1.375524 0.172238 -1.22096 6.727373
X Variable 5 -0.59414 0.484372 -1.22661 0.223033 -1.55587 0.367596
Appendix 7
SUMMARY OUTPUT Regression Statistics Multiple R 0.506332 R Square 0.256372 Adjusted R Square 0.216817 Standard Error 0.758334 Observations 100 ANOVA df SS MS F Significance F Regression 5 18.63646 3.727293 6.481457 3.22E-05 Residual 94 54.0566 0.57507 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 15.56561 6.285957 2.476252 0.015066 3.084698 28.04653
X Variable 1 -3.07099 1.940831 -1.58231 0.116939 -6.92455 0.782578
X Variable 2 -1.88972 2.320823 -0.81425 0.417562 -6.49777 2.718325
X Variable 3 3.589723 2.006519 1.78903 0.076831 -0.39427 7.573713
X Variable 4 -0.10613 0.10911 -0.97272 0.333188 -0.32277 0.110507
X Variable 5 0.185594 0.16869 1.100211 0.27405 -0.14934 0.520532
SUMMARY OUTPUT Regression Statistics Multiple R 0.486426 R Square 0.236611 Adjusted R Square 0.196005 Standard Error 0.768344 Observations 100 ANOVA df SS MS F Significance F Regression 5 17.19995 3.439989 5.82701 9.88E-05 Residual 94 55.49312 0.590352 Total 99 72.69307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 9.378201 11.59627 0.808725 0.420715 -13.6465 32.40287
X Variable 1 -3.71385 2.173646 -1.70858 0.090829 -8.02968 0.601975
X Variable 2 1.447075 1.909884 0.757677 0.45054 -2.34505 5.239195
X Variable 3 -0.07728 0.648909 -0.11909 0.905455 -1.36571 1.211143
X Variable 4 0.333068 0.194143 1.71558 0.089533 -0.05241 0.718544
X Variable 5 -0.02067 0.277354 -0.07454 0.940742 -0.57137 0.530021
ReferencesTop of Form
Achen, C. H. (1982). Interpreting and using regression. Beverly Hills, Calif: Sage Publications.
Bottom of Form
Top of Form
Lewis-Beck, M. S. (1980). Applied regression: An introduction. Beverly Hills, Calif: Sage Publications.
Bottom of Form
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