American football is the highest paying sport on a per-game basis. The quarterback, considered the most important player on the team, is appropriately compensated. A sports statistician wants to use 2009 data to estimate a multiple linear regression model that links the quarterback’s salary (in $ millions) with his pass completion percentage (PCT), total touchdowns scored (TD), and his age. A portion of the data is shown in the accompanying table.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
All but B please
American football is the highest paying sport on a per-game basis. The quarterback, considered the most important player on the team, is appropriately compensated. A sports statistician wants to use 2009 data to estimate a multiple linear regression model that links the quarterback’s salary (in $ millions) with his pass completion percentage (PCT), total touchdowns scored (TD), and his age. A portion of the data is shown in the accompanying table.
| Name | Salary | PCT | TD | Age |
| Philip Rivers | 25.5566 | 65.2 | 28 | 27 |
| Jay Cutler | 22.0441 | 60.5 | 27 | 26 |
| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
| Tony Romo | 0.6260 | 63.1 | 26 | 29 |
SOURCE: USA Today database for salaries; http://NFL.com for other data.
Click here for the Excel Data File
a. Estimate the model defined as Salary = β0 + β1PCT + β2TD + β3Age + ε. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)
| Salaryˆ=Salary^= + PCT + TD + Age. |
b. Are you surprised by the estimated coefficient for PCT?
multiple choice
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Yes Correct
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No
c. Drew Brees earned 12.9895 million dollars in 2009. What is his predicted salary if PCT = 70.6, TD = 34, and Age = 30? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)
| SalaryˆSalary^ |
d. Tom Brady earned 8.0073 million dollars in 2009. According to the model, what is his predicted salary if PCT = 65.7, TD = 28, and Age = 32? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)
| SalaryˆSalary^ |
e-1. Compute the residual salary for Drew Brees and Tom Brady. (Negative values should be indicated by a minus sign. Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)
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