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

4 3 31

4 3 30

3 3 18

2 2 17

2 2 17

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.

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.

yˆ=___+ _____ x1+ _____ x2 () There is not enough evidence.

Answer 1

Applying regression on above data:

	df	SS	MS	F	Significance F
Regression	2	208.7	104.35	417.4	0.00239
Residual	2	0.5	0.25
Total	4	209.2
	Coefficients	Standard Error	t Stat	P-value
Intercept	15	1.457738	10.28992	0.009313
x1	12.5	0.612372	20.41241	0.002391
x2	-11.5	1.118034	-10.2859	0.00932

Step 1 of 2:

p-value for the regression equation =0.0024

Step 2 of 2:

y^ =15.000+12.500x1+(-11.500)*x