Question

The manufacturer of a type of exercise equipment wants to study the relationship between the number of months (Months) since the type of equipment was purchased and the length of time (Hours) the equipment was used last week. The data is below. Person Fred Bob Joe Tina Lisa Jen Karl Hank Leah Anna Months 12 2 6 9 7 2 8 4 10 5 Hours 4 10 8 5 5 8 3 8 2 5

Following the style of the worksheet illustrated in Table 12.2 in your textbook, use the data provided above and create an analogous worksheet. Computer Deliverable d. Using the answers developed in the worksheet, what is the estimated regression equation? Use the labels Months and Hours appropriately in your equation. e. Predict the number of hours of usage for someone who bought the equipment 8 months ago? (4 pts) f. If there is a person who bought the equipment 8 months ago, what is the residual for that particular person?

Answer 1

x	y	x-xbar	y-ybar	(x-xbar)(y-ybar)	(x-xbar)^2
12	4	5.5	-1.8	-9.9	30.25
2	10	-4.5	4.2	-18.9	20.25
6	8	-0.5	2.2	-1.1	0.25
9	5	2.5	-0.8	-2	6.25
7	5	0.5	-0.8	-0.4	0.25
2	8	-4.5	2.2	-9.9	20.25
8	3	1.5	-2.8	-4.2	2.25
4	8	-2.5	2.2	-5.5	6.25
10	2	3.5	-3.8	-13.3	12.25
5	5	-1.5	-0.8	1.2	2.25
65	58	0	0	-64	100.5
6.5	5.8
mean xbar	ybar			SS_xy	SS_xx

xbar and ybar are average .

e)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.826939645
R Square	0.683829176
Adjusted R Square	0.644307823
Standard Error	1.534754911
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	40.75622	40.75622	17.30278	0.003167
Residual	8	18.84378	2.355473
Total	9	59.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	9.939303483	1.107151	8.97737	1.89E-05	7.386209
months	-0.63681592	0.153093	-4.15966	0.003167	-0.98985

y^ = 9.9393 - 0.6368* months

f)

y^ = 9.9393 - 0.6368 * 8

= 4.8449

residual = yi - y^

= 4 - 4.8449

= -0.8449