Regression. A coach wants to see the relationship between the statistics of practice games and official games of a local

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Regression. A coach wants to see the relationship between thestatistics of practice games and official games of a localsoccer
team.
A sample of
25
players was used and the resulting​ (partial) Excel outputis shown below. Assume both x and y form normal distributions.
Regression
Statistics
Multiple R
​***
R Square
0.70524
Adjusted R Square
0.668395
Standard Error
8.703633
Observations
25
Coefficients
Standard
Error
t Stat
​P-value
Lower
​95%
Upper
​95%
Intercept
40.87873
8.506861
4.794266
0.001366
21.1673
60.40101
Mid-term
0.731553
0.175459
4.3748
0.002365
0.362046
1.169078
​(a) The slope of the regression line is
A.
40.879
B.
0.732
C.
0.175
D.
4.375
​(b) The correlation coefficient is
A.
None of the other answers
B.
0.8398
C.
​-0.8398
D.
0.705
A hypothesis test is done to determine whether the correlationcoefficient is significantly different from zero.
​(c) The alternate hypothesis is
A.
H1 : μ = 0
B.
H1 : ρ ≠ 0
C.
H1 : ρ = 0
D.
H1 : β ≠ 0
​(d) The test statistic is
A.
40.78
B.
0.362
C.
None of the other answers
D.
4.794
​(e) The degrees of freedom​ are:
A.
25
B.
24
C.
22
D.
23
​(f) At the​ 5% significance level it can be concluded thatthere is evidence to suggest the correlation coefficient is
A.
not zero
B.
positive
C.
negative
D.
zero