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) is the number of hours spent studying, and the second independent variable (x2) is the student's GPA.

Effects on ACT Scores

Study Hours	GPA	ACT Score
1	2	17
2	3	18
3	4	20
5	4	31
5	4	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 0.01 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

P-value for the regression equation= 0.0008<0.01 (from ANOVA Table), hence regression of ACT score (y) on the number of hours spent studying (x1) and the student's GPA (x2) is significant.

Since R square 0.9992 i.e. 99.92% of total variation in y is explained by linear regression. Hence the linear regression equation is highly significant and good fit for this data. Moreover adjusted R square 0.9983 which is also high hence all to independent variables have significant effect on y.

Now the fitted reggression equation:

and intercept term and the regression coefficients are all significantly present since their p-value<0.01 (see second portion of ANOVA table).