Analyzing Data Dissertation Sample

Introduction

In this paper I would like to investigate whether the salary of basketball players is associated with their successful playing. I believe that those, who show better result, are being paid more. For this purpose I have collected a data set of basketball most famous players and their salary.

Body

There are 99 observations in the data set. The following variables are characterizing these observations:
Rank – the rank of the player in the sample
Player – a full name of a basketball player
Position, Team – A position and a team played
Salary – player’s annual salary, in $
Points per game – an average of points earned per game
As a first step of the analysis, I begin with visual representation of the data. The understanding of distribution of the variables is one of the most important steps in statistical analysis. The frequency histograms represent distribution of the quantitative variables of the data: Salary and Points per game. The distribution of both variables is seems to be normal. The distribution of salary is positively skewed; the distribution of Points per game is approximately symmetric. Thus, the assumption of normality is met and I can proceed with a scatterplot to explore whether these variables are related. The scatterplot displays a set of points which are not situated closely to the straight line. That’s why I don’t think that the relationship between the variables is linearly strong. However, the overall trend is positive: greater values of salary correspond to greater values of points per game.
The next step of the analysis is a descriptive statistics. Descriptive statistics consists of measures of central tendency and measures of variability. This information helps to understand the distribution characteristics of the variables. The average salary among the players is $10,357,398 with a standard deviation of $6,008,582 (the data is quite dispersed). The median salary is $9,500,000; the most typical is $8,000,000. The minimum salary is $926,500, the maximum is $30,453,805. The average points per game is 0.468515 points with a standard deviation of 0,053161 (the data is not very dispersed). The median score is 0.457, the most typical is 0.438. The minimum result is 0.354 and the maximum is 0.623.
The final step of the report is to develop a linear regression between salary and points per game and check whether the relationship is strong or not. I constructed a scatterplot of the data and added a trend line. The relationship between salary and points per game is the following:
Salary=1264066+19408832*PointsPerGame
This equation describes how to predict salary level of the player by the given average points per game. However, this relationship is not strong. The coefficient of determination of this model is only 0.029487 which means that approximately 2.95% of Salary’s variance is explained by this model. Also, the ANOVA output shows that the model is not significant at 5%.

Conclusion

In this research I have explored the association between the average result of famous basketball players and their salary. As a result of the research, the hypothesis about linear association between the variables was not supported. There is no significant linear relationship between the variables. I may assume that there are some other factors exist, which have a significant impact on players’ salaries. For example, such factors may be the position of the player in a team, the popularity in media, affiliation to a certain team, and so on. To improve this study it is better to avoid the difference in other factors. For example, it’s better to take a sample among players with the same position.
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