Relationship between sporting talent and the body sizes 3
Data collection and description 3
Data analysis 3
The model 3
The hypothesis statements 4
The model assumption 4
Regression Analysis: Wins versus Salary 4
Analysis of Correlation salaries of the players and the number of wins the clubs register 4
Checking the adequacy of the modeling 5
Residual analysis 5
Summary of Results 5
Discussion and Conclusions 5
Introduction
There is usually a very close relationship between salaries of players in every club and the number of wins the club register every season. According to Mullins (2006), the salaries of players are directly related to the number of wins a club registers every season. The salary refers to the appreciation given by the club to its players for the work they have done to support the club in every season. The relation that can take these variables is the simple regression. In simple regression we will attempt to predict the dependent variable or response variable y (wins) on the basis of assumed linear relationship with predictor or independent variable (salaries).
In additional to constructing the model we will access the relationship between the dependent variable y and the independent variables x’s. In the project the independent variable is a continuous random variable and the x variables are fixed constant (either discrete or continuous) and that are controlled by the experimenter.
Significance of the study
Different researchers had successfully shown the correlation between salaries proportions of the players and the number of wins registered by all the teama (e.g., Dintiman & Ward, 2003; Haubenstricker & Sapp, 1980). However, there is a lack of studies focusing on the model and the nature of the relationship. This study provides data on the topic and helps to understand the the model and the nature of the relationship between the players’ salaries and the number of wins the club register every season. Besides, the relationship between the salaries of players and the number of wins the club registered, we will look at the correlation between the two variables of interest in this project.
Once the correlation between the salaries of the players and number of wins have been established, it allows the management and players know more about the investment in the players’ salaries , the players value in the team and review their rewards schemes in their teams and related sports they are potentially good at. On the other hand, the information is useful for the management and coaches to form different groups based on players’ sporting abilities. It served as references for them, to know more about the specific body proportions and the relative potential sporting ability.
Relationship between sporting talent and the body sizes
Several of the researches have shown that salaries of the players were correlated with the number of wins registered by individuals clubs (e.g., Loovis et al., 2003; Dintiman & Ward, 2003). However, there was an exception. Through 20 seasons performance by 10 basketball clubs from USA (Kinnunen et al. (2001) indicated that the correlations between salaries measurements and number of wins registered by different club were higher.
Other variables that correlate with the number of wins the clubs register every season
Above-mentioned, age of the players and the time the players invest in training greatly influence the performance of the team every season. However, many other variables correlated to the clubs performance as well they range from the players attitude to the coach, the coach handling of the players, the general feeding of the players, the family relationship in the players and the popularity of the players and the clubs. Most of the above variables have successfully shown correlation with sporting performance; however, Steigelman & Gwen (1981) found the role of sporting performance in the social status of preschool children differed among age groups.
Data collection and description
The data in this study include a collection of 40 subjects (clubs). Data was obtained from the following site http://www.statcan.gc.ca. The performance of 40 clubs was first evaluated on the bases of wins registered in the period of 1993 to 2012.Then, the salaries of the players was also determined. The salaries and the number of wins were recorded in the table
Data analysis
The purpose of this investigation was to examine the relationship between salaries the player receive from their clubs and the performance of the clubs every season. Also, the researcher attempted to perform two regression equations between the salaries and the club number of wins in the last 20seasons.
The model
The model yi=β0+β1x1i+εi is a simple linear regression model. The parameter βj j=1,2 are called the regression coefficient. Such model describes the hyper plane in the 2-dimensional space of the regression variablexi. The parameters βj represent the expected change in the response variable y per a change inxi, while all the repressor remains constants. The regression equation is
The hypothesis statements
- Ho:β1=0 vs
That is, the null hypothesis, the salary cannot be used to predict the salary
The alternative hypothesis
H1:β1≠0
That is, the salary can be used to predict the salary
The model assumption
1 Eε=0
Or equivalently EY=β0+β1xi
2. covε=σ2 or equivalently covY=σ2
Analysis
Regression Analysis: Wins versus Salary
The regression equation is
Wins = 69.8 + 0.000000 Salary
Predictor Coef SE Coef T P
Constant 69.810 4.220 16.54 0.000
Salary 0.00000015 0.00000005 2.92 0.007
S = 9.65487 R-Sq = 23.3% R-Sq(adj) = 20.6%
Analysis of Variance
Source DF SS MS F P
Regression 1 793.94 793.94 8.52 0.007
Residual Error 28 2610.06 93.22
Total 29 3404.00
Analysis of Correlation salaries of the players and the number of wins the clubs register
A Bivariate correlational method, the Pearson product moment coefficient of correlation (r) was used to determine the relationships between the salaries of the players and the club performance in the last 20 seasons. The Pearson correlation coefficient and the coefficient of determination were shown. The salaries the players receive were correlated with the number of wins the club received every season. A significant positive 0.4796 correlation was found between salaries of the players and the number of wins the clubs were registering every season: (r=0.4796, t= 16.54 and p-value = 0.000) Hence the null hypothesis that there was no relationship between salaries the players receive from the clubs and the club performance that season was rejected.
Checking the adequacy of the modeling
Fitting a regression model requires several assumptions. Estimation of model parameters require the assumption that the error are uncorrelated with mean zero and variance constant σ2 . in addition we need to consider the regression between y and x as a straight line. In our project we consider all these assumptions doubtful and conduct the analysis to determine the adequacy of the model
Residual analysis
Analysis of the residual is frequently helpful in checking that the errors are approximately normally fitted with constant values. To check the normality we construct the histogram
Summary of Results
This study was designed to examine the relationship between the salaries of the players and the clubs performance for 30 clubs in the basketball league in USA for the last 20 seasons. Regression equations between the salaries of the players and the number of win every club register. A total of 30clubs participated in the study with all the players of the clubs interviewed.. The number of trophies and awards the players and the club received every season was used to measure the performance of the club that season. Collected data were analyzed by the minitab statistical package for window 16.0 version computer programs. Pearson Product Moment Coefficient of Correlation and multiple regression method were used with the alpha level being set at 0.05.
Discussion and Conclusions
References
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