How to Score a Pay Day

How To Score a Payday

Football Fanatics

Alex Ifrim

Executive Summary

Sports have risen to astronomical levels in the past decade in the United States. Athletes are getting mind-blowing contracts that would put the G8 summit to shame. Millions of people watch football yearly and with all the revenue the NFL brings in, the salaries are easily covered. Football Fanatics decided to analyze what it takes to earn a high salary as an NFL quarterback with pass completion percentage being the dependent variable.

In this research paper, several tests were performed in order to validate the data. The regression equation of NFL Quarterback salaries was $ 4,443,755.85 + 244,351.32(Pass Completion %). By using regression analysis, about 15.5% of the variation in the salaries of quarterbacks is explained by the straight-line relationship between their total pass completion % and their final salaries. All three assumptions were tested showing normal distribution, slight homoscedasticity and no auto correlation. Football Fanatics believes it has some evidence to support this correlation, but it believes there are other variables that contribute to it.  

Introduction

Football Fanatics is a non-profit organization formed by three students at Oakland University in June of 2014. The main focus of this trio is providing statistical evidence to companies, scouts, teams, and the public on the salaries quarterbacks makes based upon their performance on the field. There are many possible independent variables that can attribute to their salaries, but for this study, pass completion % is assumed to have some correlation on how much money these quarterbacks make. A simple regression, a residual test, and unusual residuals will show if a real relationship exists between pass completion % and the salaries of these quarterbacks.

Figure 1

Quarterback Salaries ŷ =  4,443,755.85 + 244,351.32(Pass Completion %) 

Simple Regression Summary

The simple regression in Figure 2 shows the relationship between salaries of quarterbacks and their pass completion %.

Figure 2

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Regression Statistics

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Multiple R 0.3940

R Square 0.1553

Standard Error 847745.5958

Observations 30

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ANOVA

Source SS df MS F p-value

Regression 1491153883895247.2 1 1491153883895247.2 82.14 0.0005

Residual 526472882567217.75 28 18154237329904.06

Total 2017626766462464.95 29

Coefficients Standard Error t-stat p-value Lower 95 Upper

Intercept  4,443,755.85 1.7741 2.2477 0.0005

Total Pass

Completion % 244,351.32 1,100,129.10 1.7741 0.0143

in 2009-2010

This regression analysis produces the equation:

Fitted Regression= ŷ =  4,443,755.85 + 244,351.32x

The y hat variable represents the predicted salary of quarterbacks in dollars while the x variable represents the Pass completion %.

Interpretation of Slope

If you increase x (pass completion %) by 1, the quarterback’s salary is predicted to increase by $244,351.32. A quarterback needs to be more accurate with his throws to get more money.

Interpretation of the Intercept

If the quarterback gets a rating of 0.0, he would make $4,443,755.85. That sounds about right as a backup quarterback who barely makes any throws a season.

Interpretation of R and R^2

Correlation