Question 1

Given the regression equation $$\hat{y} = -0.21x + 6.77$$ for the relationship between number of wins ($$x) $$and earned run average ($$y) $$for baseball pitchers, what does the slope of the regression line represent in this context?

Accepted Answer

For each additional win, the earned run average decreases by 0.21.

Question 2

Using the regression equation $$\hat{y} = -0.21x + 6.77$$, what is the predicted earned run average for a pitcher with 15 wins?

Accepted Answer

$$\hat{y} = -0.21(15) + 6.77 = 3.66$$

Question 3

Which of the following best describes the correlation between wins and earned run average based on the regression equation $$\hat{y} = -0.21x + 6.77$$?

Accepted Answer

There is a negative correlation: as wins increase, ERA decreases.

Question 4

If a pitcher has 5 wins, what is the predicted earned run average using the regression equation $$\hat{y} = -0.21x + 6.77$$?

Accepted Answer

$$\hat{y} = -0.21(5) + 6.77 = 5.72$$

Question 5

Why might it not be meaningful to use the regression equation to predict the earned run average for a pitcher with 25 wins?

Accepted Answer

Because 25 wins is outside the range of the observed data (extrapolation).

Question 6

Given the data: Wins (x): 20, 18, 17, 16, 14, 12, 11, 9 and ERA (y): 2.78, 3.32, 2.55, 3.83, 3.93, 4.31, 3.77, 5.01, which point is likely to be the most influential in determining the regression line?

Accepted Answer

(9, 5.01)

Question 7

If the correlation coefficient $$r$$ for the data is calculated to be $$-0.85$$, what does this indicate about the relationship between wins and ERA?

Accepted Answer

There is a strong negative linear relationship.

Question 8

Suppose a new pitcher has 10 wins. Using the regression equation $$\hat{y} = -0.21x + 6.77$$, what is the predicted ERA?

Accepted Answer

$$\hat{y} = -0.21(10) + 6.77 = 4.67$$

Question 9

Which of the following is NOT an assumption of linear regression?

Accepted Answer

The dependent variable must be categorical.

Question 10

If the regression equation is $$\hat{y} = -0.21x + 6.77$$, what is the y-intercept and what does it represent in this context?

Accepted Answer

The y-intercept is 6.77, representing the predicted ERA for a pitcher with 0 wins.

Question 11

If a pitcher has 19 wins, is it meaningful to use the regression equation to predict their ERA? Why or why not?

Accepted Answer

Yes, because 19 is within the range of observed wins.

Question 12

Which of the following best describes extrapolation in the context of regression analysis?

Accepted Answer

Predicting values of the dependent variable for independent variable values outside the observed range.

Regression Line, Scatter Plot, and Prediction for Baseball Pitchers

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