Question

9. Researchers record the age and life satisfaction score (rated from 1 to 10, with higher scores indicating greater life satisfaction) among a sample of college students. They hypothesize that age will predict life satisfaction among college students. Compute an analysis of regression.

X (Age in Years)	Y (Life Satisfaction)
18	6
18	8
26	7
28	5
32	9
19	8
21	5
20	6
25	7
42	9

F-statistic                             ______

Decision                               ______

10. Suppose that a computer glitch inflated each life satisfaction score by two. Subtract 2 points from each life satisfaction score to correct this. Compute an analysis of regression.

F-statistic                             ______

Decision                               ______

11. Instead, suppose that the computer glitch divided each life satisfaction score by half. Multiply each life satisfaction score by 2 to correct this. Compute an analysis of regression.

F-statistic                             ______

Decision                               ______

12. Does the F-statistic or the decision change from Question 1 to 3? Explain why.

Answer 1

The regression output is:

	r²	0.230
	r	0.479
	Std. Error	1.388
	n	10
	k	1
	Dep. Var.	Y (Life Satisfaction)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	4.5917	1	4.5917	2.38	.1612
Residual	15.4083	8	1.9260
Total	20.0000	9
Regression output					confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	4.6667
X (Age in Years)	0.0937	0.0607	1.544	.1612	-0.0462	0.2337

F-statistic = 2.38

Decision:

Since the p-value (0.1612) is greater than the significance level (0.05), we cannot reject the null hypothesis.

The regression output is:

	r²	0.230
	r	0.479
	Std. Error	1.388
	n	10
	k	1
	Dep. Var.	Y (Life Satisfaction)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	4.5917	1	4.5917	2.38	.1612
Residual	15.4083	8	1.9260
Total	20.0000	9
Regression output					confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	2.6667
X (Age in Years)	0.0937	0.0607	1.544	.1612	-0.0462	0.2337

F-statistic = 2.38

Decision:

Since the p-value (0.1612) is greater than the significance level (0.05), we cannot reject the null hypothesis.

No, the decision did not change.