It is believed that GPA grade point average based on a four

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

Solution

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.