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.
|Study Hours||GPA||ACT Score|
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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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
|Study Hours||1.5294118||0.14705882||? 0||2||10.4||0.0091|
Analysis of variance table for multiple regression model:
Summary of fit:
Root MSE: 0.38348249
R-squared (adjusted): 0.9857
Multiple regression equation:
= 17.265 + (1.529) x1 + (-0.559) x2
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