26- 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 for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university. The interpretation of the coefficient of determination in this regression is Regressing GPA on ACT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.7598 0.5774 0.5069 0.2691 Observations ANOVA df SS Significance F 0 0286 MS F Regression Residual 0.5940 0.5940 8.1986 0.4347 0.0724 Total 1.0287 Coefficients Standard Error 0.5681 t Stat P-value Upper 95% 2.8398 Lower 95% Intercept 0.9284 0.6119 0.5630 -1.7036 ACT 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 a) GPA accounts for 57.74% of the variability of ACT scores. b) 57.74% of the total variation of ACT scores can be explained by GPA. C) None of the given statements. d) ACT Scores account for 57.74% of the total fluctuation in GPA. 167

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26 - 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 for predicting GPA using ACT scores based a data set of 8 randomly
chosen students from a Big-Ten university.
The interpretation of the coefficient of determination in this regression is
Regressing GPA on ACT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
0.7598
0.5774
0.5069
0.2691
Observations
ANOVA
df
SS
Significance F
0 0286
MS
F
Regression
Residual
0.5940
0.5940
8.1986
6.
0.4347
0.0724
Total
1.0287
Coefficients Standard Error
t Stat
Upper 95%
2.8398
P-value
Lower 95%
Intercept
0.5681
0.9284
0.6119
0.5630
-1.7036
ACT
0.1021
0.0356
2.8633
0.0286
0.0148
0.1895
a)
GPA accounts for 57.74% of the variability of ACT scores.
b)
57.74% of the total variation of ACT scores can be explained by GPA.
C)
None of the given statements.
d) ACT Scores account for 57.74% of the total fluctuation in GPA.
Transcribed Image Text:26 - 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 for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university. The interpretation of the coefficient of determination in this regression is Regressing GPA on ACT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.7598 0.5774 0.5069 0.2691 Observations ANOVA df SS Significance F 0 0286 MS F Regression Residual 0.5940 0.5940 8.1986 6. 0.4347 0.0724 Total 1.0287 Coefficients Standard Error t Stat Upper 95% 2.8398 P-value Lower 95% Intercept 0.5681 0.9284 0.6119 0.5630 -1.7036 ACT 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 a) GPA accounts for 57.74% of the variability of ACT scores. b) 57.74% of the total variation of ACT scores can be explained by GPA. C) None of the given statements. d) ACT Scores account for 57.74% of the total fluctuation in GPA.
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