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.

ACT Score Study Data

Study Hours GPA ACT Score 1 2 19.91 1 2 19.69 2 2 25.52 2 3 29.67 2 4 29.77

A regression Analysis has been performed to estimate the model and the output is given.

Regression Statistics

Multiple R 0.99993 R Square 0.99813 Adjusted R Square 0.9865 Standard Error 0.414 Observations 5

ANOVA

	df	SS	MS	F	Significance F
Regression	2	90.525	31.776	59.41	0.01297
Residual	2	0.055	0.344
Total	4	87.138

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	10.28	0.87	21.713	0.00022	-2.66	22.36
Study Hours	7.2	1.06	31.573	0.00745	3.69	9.34
Student's GPA	2.45	0.305	31.038	0.00144	1.41

Step 1 of 4:

What is the intercept of the estimated regression equation?

Step 2 of 4:

What is the standard deviation of the error term?

Step 3 of 4:

What is the predicted value of an ACT Score if the student studies 1.5 hours per night, and has a GPA of 3.5?

Step 4 of 4:

If you were testing with a significance level of 0.05, would you recommend removing "GPA" as an explanatory variable for predicting ACT scores?

Answer 1