Question

The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values. If meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins (b) x=10 wins (c) x=21 wins (d) x=15 wins

The equation of the regression line is y= ? x+? (Round to two decimal places as needed.)

a. Predict the ERA for 5 wins, if it is meaningful.Select the correct choice below and ,if necessary, fill in the answer box within your choice.

A. ^y= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=5 is well outside the range of the original data.

C. It is not meaningful to predict this value of y because x=5 is not an x-value in the original data.

(b) Predict the ERA for 10 wins, if it is meaningful.Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=10 is not an x-value in the original data.

C. it is not meaningful to predict this value of y because x=10 is inside the range of the orginal data.

(c) Predict the ERA for 21 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your

choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=21 is not x-value in the original data.

C. it is not meaningful to predict this value of y because x=21 is well outside the range of the original data.

(d) Predict the ERA for 15 wins, if it meaningful. Select the correct choice below and,if necessary,fill in the box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=15 is inside the range of the original data.

C. It is not meaningful to predict this value of y because x=15 is not an x-value in the original data.

Wins, x Earned run average, y

20, 2.82

18, 3.24

17, 2.56

16, 3.65

14, 3.79

12, 4.34

11, 3.78

9, 5.07

Answer 1

The regression line that we want to estimate is

where is the intercept, is the slope of the regression line and is a random error

We calculate the following

The sum of squares are

An estimate of the slope is

an estimate of the intercept is

ans: the equation of the regression line is

construct a scatter plot of the data and draw the regression line.

First we get the predicted value of y for each x in the data

Wins, x	Earned run average, Y	Predicted Y
20	2.82	-0.19*20+6.41=2.64
18	3.24	-0.19*18+6.41=3.02
17	2.56	-0.19*17+6.41=3.21
16	3.65	-0.19*16+6.41=3.4
14	3.79	-0.19*14+6.41=3.77
12	4.34	-0.19*12+6.41=4.15
11	3.78	-0.19*11+6.41=4.34
9	5.07	-0.19*9+6.41=4.71

Next draw the scatter plot with Y and add the predicted Y to the same plot.

The minimum value of wins in the sample is 9 and the maximum value is 20. The linear model holds good only between 9 and 20. Outside this range we are not sure if the estimated model holds good. We will use the estimated equation to predict the ERA if and only if the wins are with in the range 9 to 20.

a) Predict the ERA for 5 wins, if it is meaningful.Select the correct choice below and ,if necessary, fill in the answer box within your choice.

x=5 is outside the range 9 to 20.

ans: B. it is not meaningful to predict this value of y because x=5 is well outside the range of the original data.

(b) Predict the ERA for 10 wins, if it is meaningful.Select the correct choice below and, if necessary, fill in the answer box within your choice.

x=10 is within the range 9 to 20

ans: A. (Round to two decimal places as needed.)

(c) Predict the ERA for 21 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice.

x=21 is outside the range 9 to 20. But it is not well outside the range. Hence we will predict y hoping that the model holds good.

ans: A.

(d) Predict the ERA for 15 wins, if it meaningful. Select the correct choice below and,if necessary,fill in the box within your choice.

x=15 is within the range 9 to 20

A. (Round to two decimal places as needed.)