Question

Carlson Mining, Inc. has 12 large pumps that pump water from the mines it operates.
Management has been concerned lately about the amount of money required to
repair malfunctioning pumps. These costs are sums over and above the amounts
spent for routine maintenance. When asked what factors they thought might affect
the mean monthly repair costs, employees suggested the age of the pumps and the
number of hours of operation. The following information was collected.
Choose the relevant Summary Output to answer the questions. Note that the
mean monthly repair costs are in dollars, so when questions ask about repair
costs, make sure that your answers reflect that.
Mean Weekly Hours of Operation over Past Year	Age of Pump at First of Year (months)	Mean Monthly Repair Costs over Past Year
28	80	$1,049
26	48	$1,095
15	27	$882
12	2	$447
16	13	$715
21	55	$542
13	30	$415
21	35	$454
16	36	$495
12	13	$370
18	28	$448
18	49	$509

What is the estimate for the mean monthly repair costs if the pump is 40 months old
at the first of the year and the pump is typically in operation for 20 hours per week?
Is there a significant relationship overall between the mean monthly repair costs and
the age of the pumps and the mean weekly hours of operations the .10 level of
significance? Yes   No Defend your answer.

Answer 1

Excel:

Data --> Data analysis --> Regression

ANOVA
	df	SS	MS	F	Significance F
Regression	2	363822.3883	181911.2	4.689688	0.040234891
Residual	9	349106.5283	38789.61
Total	11	712928.9167
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-87.70037103	261.5249413	-0.33534	0.745051	-679.3108903	503.9101
Mean Weekly Hours of Operation over Past Year	45.09732343	21.8704701	2.062019	0.069253	-4.377117167	94.57176
Age of Pump at First of Year (months)	-3.047157232	5.329493207	-0.57175	0.581485	-15.10330846	9.008994

estimate for the mean monthly repair costs = -87.7004+(45.0973*20)-(3.047157*40) =692.35932

Is there a significant relationship overall between the mean monthly repair costs and

the age of the pumps and the mean weekly hours of operations the .10 level of

significance? Yes   No Defend your answer.

Ans : Yes, because significance F = 0.040234891 <0.10