A sports analyst for Major League Baseball wonders whether there is a relationship between a pitcher’s salary (in $ millions) and his earned run average (ERA). The accompanying table lists a portion of the data that she collected for 10 pitchers.
Pitcher Salary ERA
1 11.0 2.52
2 3.0 2.38
⋮ ⋮ ⋮
10 0.2 2.96
a-1. Estimate the model: Salary = β0 + β1ERA + ε. (Negative values should be indicated by a minus sign. Enter your answers, in millions, rounded to 2 decimal places.)
a-2. Interpret the coefficient of ERA.
multiple choice
A one-unit increase in ERA, predicted salary decreases by $3.31 million.
A one-unit increase in ERA, predicted salary increases by $3.31 million.
A one-unit increase in ERA, predicted salary decreases by $11.32 million.
A one-unit increase in ERA, predicted salary increases by $11.32 million.
b. Use the estimated model to predict salary for each player, given his ERA. For example, use the sample regression equation to predict the salary for J. Santana with ERA = 2.52. (Do not round intermediate calculations. Round your final answers (in millions) to 2 decimal places.)
c. Derive the corresponding residuals. (Negative values should be indicated by a minus sign. Round your final answers (in millions) to 2 decimal places.)
Pitcher Salary ERA
1 11 2.52
2 3 2.38
3 0.4 2.23
4 9 2.15
5 10 2.02
6 5 2.68
7 8.3 2.68
8 6.1 2.56
9 10.9 2.68
10 0.2 2.96