A baseball analyst would like to study various team statistics for a recent season to determine which variables might be useful in predicting the number of wins achieved by teams during the season. He begins by using a team's earned run average (ERA), a measure of pitching performance, to predict the number of wins. He collects the team ERA and team wins for each of the 30 teams in a two-league organization, with the accompanying results. Complete parts (a) through (I) below. c. Use the prediction line developed in (a) to predict the mean number of wins for a team with an ERA of 4.00. (Round to one decimal place as needed.) d. Compute the coefficient of determination, r´, and interpret its meaning. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) O A. The coefficient of determination is r This value is the probability that the slope of the regression line is statistically significant. O B. The coefficient of determination is r´ = 2. This value is the proportion of variation in team ERA that is explained by the variation in wins. OC. The coefficient of determination is This value is the proportion of variation in wins that is explained by the variation in team ERA. O D. The coefficient of determination is r: This value is the probability that the correlation between the variables is %3D statistically significant. e. At the 0.05 level of significance, is there evidence of a linear relationship between the number of wins and the ERA? State the null and alternative hypotheses. Ho:
A baseball analyst would like to study various team statistics for a recent season to determine which variables might be useful in predicting the number of wins achieved by teams during the season. He begins by using a team's earned run average (ERA), a measure of pitching performance, to predict the number of wins. He collects the team ERA and team wins for each of the 30 teams in a two-league organization, with the accompanying results. Complete parts (a) through (I) below. c. Use the prediction line developed in (a) to predict the mean number of wins for a team with an ERA of 4.00. (Round to one decimal place as needed.) d. Compute the coefficient of determination, r´, and interpret its meaning. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) O A. The coefficient of determination is r This value is the probability that the slope of the regression line is statistically significant. O B. The coefficient of determination is r´ = 2. This value is the proportion of variation in team ERA that is explained by the variation in wins. OC. The coefficient of determination is This value is the proportion of variation in wins that is explained by the variation in team ERA. O D. The coefficient of determination is r: This value is the probability that the correlation between the variables is %3D statistically significant. e. At the 0.05 level of significance, is there evidence of a linear relationship between the number of wins and the ERA? State the null and alternative hypotheses. Ho:
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 21PPS
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Transcribed Image Text:Team
E.R.A.
Wins
1.
Team 1
3.65
99
4.45
71
Team 2
4.72
73
4 Team 3
5 Team 4
4.01
85
4.37
89
6 Team 5
7 Team 6
4.47
71
8.
Team 7
3.84
88
9.
Team 8
3.92
98
70
10 Team 9
11 Team 10
4.81
4.09
85
12 Team 11
13 Team 12
3.54
87
3.43
86
14 Team 13
3.87
78
15 Team 14
4.77
66
16 Team 15
4.22
83
17 Team 16
4.57
65
18 Team 17
3.68
80
19 Team 18
4.36
73
20 Team 19
3.78
77
21 Team 20
5.05
66
22 Team 21
3.83
94
23 Team 22
4.15
77
24 Team 23
4.04
82
25 Team 24
3.82
78
26 Team 25
4.24
73
27 Team 26
3.89
87
28 Team 27
3.55
78
29 Team 28
3.77
87
30 Team 29
3.73
91
31 Team 30
3.43
32
96
33
34
35
36
23
Transcribed Image Text:A baseball analyst would like to study various team statistics for a recent season to determine which variables might be
useful in predicting the number of wins achieved by teams during the season. He begins by using a team's earned run
average (ERA), a measure of pitching performance, to predict the number of wins. He collects the team ERA and team wins
for each of the 30 teams in a two-league organization, with the accompanying results. Complete parts (a) through (I) below.
c. Use the prediction line developed in (a) to predict the mean number of wins for a team with an ERA of 4.00.
(Round to one decimal place as needed.)
d. Compute the coefficient of determination, r, and interpret its meaning. Select the correct choice below and fill in the
answer box within your choice.
(Round to three decimal places as needed.)
O A. The coefficient of determination is r
This value is the probability that the slope of the regression line is
%3D
statistically significant.
O B.
The coefficient of determination is
. This value is the proportion of variation in team ERA that is explained by
the variation in wins.
O C. The coefficient of determination is r´ =
This value is the proportion of variation in wins that is explained by the
variation in team ERA.
O D.
The coefficient of determination is
This value is the probability that the correlation between the variables is
%3D
statistically significant.
e. At the 0.05 level of significance, is there evidence of a linear relationship between the number of wins and the ERA?
State the null and alternative hypotheses.
Ho:
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