Question

Conduct a study in a statistics class to measure the effect of solving problems at home on the performance on the final exam. She collected data at random for 10 students from a class on the number of hours spent in a week doing problem sets at home (X) and their score on the final exam (Y), as shown in the following table

X = number of hours per week	Y = score on the final exam
10	80
15	85
24	95
5	80
8	90
4	80
20	95
24	100
30	85
18	70

What are the regression slope and vertical intercept? Write the equation for the line.

Predict the final score of a student who studies for 12 hours every week.

Find the coefficients of determination and non-determination. What do they mean

Perform an F-test for the significance of the regression at 0.05 level of significance. What does it mean

Answer 1

X	Y		SUMMARY OUTPUT
10	80
15	85		Regression Statistics
24	95		Multiple R	0.876000225
5	80		R Square	0.767376394
8	90		Adjusted R Square	0.728605793
4	80		Standard Error	4.162404636
20	95		Observations	8
24	100
			ANOVA
				df	SS	MS	F	Significance F
			Regression	1	342.9213259	342.9213	19.79274	0.004334241
			Residual	6	103.9536741	17.32561
			Total	7	446.875
				Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
			Intercept	76.37380192	3.023662612	25.2587	2.54E-07	68.97516604	83.7724378
			X	0.854632588	0.192099617	4.448903	0.004334	0.384581759	1.324683417

The regression slope=0.8546 and vertical intercept=76.3738 and the regression equation is:

Predicted final score of a student who studies for 12 hours every week=76.3738+0.8546*12=86.63.

The coefficients of determination=R²=0.7674

The coefficients of non-determination=1-R²=1-0.7674=0.2326.

76.74% of total variation in score on the final exam in the sample is explained by this regression equation and 23.26% of total variation in score on the final exam in the sample is not explained by this regression equation.

From ANOVA table, value of F-test=19.7927 and corresponding P-value=0.0043<0.05 so the regression equation is significant at 0.05 level of significance.