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 (x1x1) is the number of hours spent studying, and the second independent variable (x2x2) is the student's GPA.

Effects on ACT Scores

Study Hours	GPA	ACT Score
00	22	1616
33	22	2121
55	33	2323
55	44	2323
66	44	2424

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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.

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Answer 1

The statistical software output for this problem is:

Multiple linear regression results:
Dependent Variable: ACT Score
Independent Variable(s): Study Hours, GPA
ACT Score = 17.264706 + 1.5294118 Study Hours + -0.55882353 GPA

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	17.264706	0.68188371	? 0	2	25.319135	0.0016
Study Hours	1.5294118	0.14705882	? 0	2	10.4	0.0091
GPA	-0.55882353	0.35109813	? 0	2	-1.5916449	0.2525

Analysis of variance table for multiple regression model:

Source	DF	SS	MS	F-stat	P-value
Model	2	40.905882	20.452941	139.08	0.0071
Error	2	0.29411765	0.14705882
Total	4	41.2

Summary of fit:
Root MSE: 0.38348249
R-squared: 0.9929
R-squared (adjusted): 0.9857

Hence,

Multiple regression equation:

= 17.265 + (1.529) x1 + (-0.559) x2