It is believed that GPA (grade point average, based on a four point scale) shoul
ID: 3436038 • Letter: I
Question
It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big-Ten university.
Regressing GPA on ACT
Regression Statistics
Multiple R
0.7598
R Square
0.5774
Adjusted R Square
0.5069
Standard Error
0.2691
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
0.5940
0.5940
8.1986
0.0286
Residual
6
0.4347
0.0724
Total
7
1.0287
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
0.5681
0.9284
0.6119
0.5630
-1.7036
2.8398
ACT
0.1021
0.0356
2.8633
0.0286
0.0148
0.1895
1) The interpretation of the coefficient of determination in this regression is
A) 57.74% of the total variation of ACT scores can be explained by GPA.
B) ACT scores account for 57.74% of the total fluctuation in GPA.
C) GPA accounts for 57.74% of the variability of ACT scores.
D) None of the above.
2) What is the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT?
3) What is the predicted average value of GPA when ACT = 20? Show how you obtain your answer.
4) What are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores? Explain your answer.
Regressing GPA on ACT
Regression Statistics
Multiple R
0.7598
R Square
0.5774
Adjusted R Square
0.5069
Standard Error
0.2691
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
0.5940
0.5940
8.1986
0.0286
Residual
6
0.4347
0.0724
Total
7
1.0287
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
0.5681
0.9284
0.6119
0.5630
-1.7036
2.8398
ACT
0.1021
0.0356
2.8633
0.0286
0.0148
0.1895
Explanation / Answer
1) Answer is B.
2) F=8.1986
3) The model is
GPA= 0.5681+0.1021*ACT=0.5681+0.1021*20=2.6101
4) The p value is 0.0286. Since this is > 0.01, we accept the null hypothesis nd conclude that there is no linear relatonship between the two variables.
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