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Created: Dec 3, 2019
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KBulley project 3

Kevin Bulley

Math 125

Project 3

Introduction

Statcrunch provided data on a study 2015 study that measured the correlation of base salary vs guaranteed salary of Major League Soccer players. The study of Major League Soccer players' salaries had a sample size of 570 players. The soccer players' base salary was the independent variable. The soccer players guaranteed compensation/salary was noted as the dependent variable.

Analysis

The regression equation in table two is 2015 Guaranteed Compensation = 3006.9887 + 1.0928 2015 Base Salary. The correlation coefficient (variable R) is 0.9933. The coefficient of determination (R^2) is 0.9867. The coefficient determination suggest that 98.67% of the change in 2015 guaranteed compensation to based salary can be explained by the regression equation in the independent variable.

Conclusion

In summary, the independent variable was the soccer player’s base salary. The dependent variable was the guaranteed compensation and the sample size is 570 players. The results of the simple linear regression graph shows that there is a strong positive correlation between guaranteed salary and based salary. With the cluster points within the graph falling closely by the regression line. The strong positive correlation coefficient, 0.9933 indicates that it is an appropriate way of determining the data’s regression.

Result 1: Simple Linear Regression graph   [Info]

Result 2: Simple Linear Regression Data   [Info]

### Simple linear regression results:

Dependent Variable: 2015 Guaranteed Compensation
Independent Variable: 2015 Base Salary
2015 Guaranteed Compensation = 3006.9887 + 1.0928344 2015 Base Salary
Sample size: 570
R (correlation coefficient) = 0.99332467
R-sq = 0.9866939
Estimate of error standard deviation: 92788.37

### Parameter estimates:

ParameterEstimateStd. Err.AlternativeDFT-StatP-value
Intercept3006.98874135.3833 ≠ 05680.727136640.4674
Slope1.09283440.0053249359 ≠ 0568205.22959<0.0001

### Analysis of variance table for regression model:

SourceDFSSMSF-statP-value
Model13.6263276e143.6263276e1442119.184<0.0001
Error5684.8902991e128.6096816e9
Total5693.6752306e14

Data set 1. 2015 Major League Soccer Players Salaries   [Info]