Question

# The following data was collected to explore how the average number of hours a student studies...

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.

Selecting a checkbox will replace the entered answer value(s) with the checkbox value. If the checkbox is not selected, the entered answer is used.

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

Hence,

Multiple regression equation:

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

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