Question

The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1 x 1 ) is the number of hours spent studying, and the second independent variable (x2 x 2 ) is the student's GPA.

Study Hours   GPA   ACT Score
1   2   18
5   2   27
5   3   29
6   3   31
6   3   31

Step 1 of 2:

Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

Step 2 of 2:

Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.050.05 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.999835
R Square	0.999671
Adjusted R Square	0.999341
Standard Error	0.138675
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	2	116.7615	58.38077	3035.8	0.000329
Residual	2	0.038462	0.019231
Total	4	116.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	12.03846	0.352506	34.1511	0.000856	10.52175	13.55517	10.52175	13.55517
x1	2.230769	0.047106	47.3568	0.000446	2.02809	2.433448	2.02809	2.433448
x2	1.884615	0.178339	10.56761	0.008836	1.117285	2.651945	1.117285	2.651945

.

a) p value = 0.0003

2) yes,  a statistically significant linear relationship exists between the independent and dependent variables at the 0.05

Y^ = 12.038 + 2.231*x1 + 1.885*x2