Question

In: Statistics and Probability

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 (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.

Solutions

Expert Solution

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


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