Regression. A coach wants to see the relationship between the statistics of practice games and official games of a local
Posted: Sun Jul 10, 2022 10:12 am
Regression. A coach wants to see therelationship between the statistics of practice games and officialgames of a local soccer
team.
A sample of
18
players was used and the resulting (partial) Excel outputis shown below. Assume both x and y form normaldistributions.
Regression
Statistics
Multiple R
***
R Square
0.70524
Adjusted R Square
0.668395
Standard Error
8.703633
Observations
18
Coefficients
Standard
Error
t Stat
P-value
Lower
95%
Upper
95%
Intercept
40.27213
8.506861
4.794266
0.001366
21.1673
60.40101
mimi
0.760062
0.178063
4.378708
0.002365
0.362046
1.169078
Question contentarea bottom
Part 1
(a) The slope of the regression line is
A.
0.76
B.
40.272
C.
4.379
D.
0.178
(b) The correlation coefficient is
A.
0.8398
B.
None of the other answers
C.
0.705
D.
-0.8398
A hypothesis test is done to determine whether the correlationcoefficient is significantly different from zero.
(c) The alternate hypothesis is
A.
H1 : β ≠ 0
B.
H1 : ρ ≠ 0
C.
H1 : μ = 0
D.
H1 : ρ = 0
(d) The test statistic is
A.
4.794
B.
0.362
C.
None of the other answers
D.
40.78
(e) The degrees of freedom are:
A.
17
B.
18
C.
16
D.
15
(f) At the 5% significance level it can be concluded thatthere is evidence to suggest the correlation coefficient is
A.
positive
B.
not zero
C.
zero
D.
negative
team.
A sample of
18
players was used and the resulting (partial) Excel outputis shown below. Assume both x and y form normaldistributions.
Regression
Statistics
Multiple R
***
R Square
0.70524
Adjusted R Square
0.668395
Standard Error
8.703633
Observations
18
Coefficients
Standard
Error
t Stat
P-value
Lower
95%
Upper
95%
Intercept
40.27213
8.506861
4.794266
0.001366
21.1673
60.40101
mimi
0.760062
0.178063
4.378708
0.002365
0.362046
1.169078
Question contentarea bottom
Part 1
(a) The slope of the regression line is
A.
0.76
B.
40.272
C.
4.379
D.
0.178
(b) The correlation coefficient is
A.
0.8398
B.
None of the other answers
C.
0.705
D.
-0.8398
A hypothesis test is done to determine whether the correlationcoefficient is significantly different from zero.
(c) The alternate hypothesis is
A.
H1 : β ≠ 0
B.
H1 : ρ ≠ 0
C.
H1 : μ = 0
D.
H1 : ρ = 0
(d) The test statistic is
A.
4.794
B.
0.362
C.
None of the other answers
D.
40.78
(e) The degrees of freedom are:
A.
17
B.
18
C.
16
D.
15
(f) At the 5% significance level it can be concluded thatthere is evidence to suggest the correlation coefficient is
A.
positive
B.
not zero
C.
zero
D.
negative