Question

One of the questions most frequently asked by prospective home buyers along the east coast of the United States is:
If we purchase this home, how much can we expect to pay to heat it during the winter? The research department
at Herrington Real Estate has collected the following information. Temperature = Mean Outside Temperature (F);
Attic = Attic insulation (in inches).
Home	Mean Outside Temperature (degrees)	Attic Insulation (inches)	Monthly Heating Costs ($)
1	18	3	188
2	34	2	256
3	36	7	127
4	60	6	239
5	65	5	190
6	20	5	180
7	10	6	210
8	7	9	260
9	21	4	255
10	35	6	160
11	54	12	100
12	26	8	105
13	25	3	375
14	39	4	250

According to your equation, for every one inch increase in the number of inches of attic insulation, monthly heating
costs (increase / do not change / decrease) by _____________. Round appropriately. Include the units! (8 pts.)
According to your equation, if you want your house's monthly heating costs to be $200/month, how many inches of
attic insulation do you need to have? (4 pts.) Round correctly and include the units.
Are monthly heating costs statistically related to the number of inches of attic insulation? Test at the .05 level of significance:
State H0 and H1.
Obtain the appropriate output.

Answer 1

According to your equation, for every one inch increase in the number of inches of attic insulation, monthly heating costs decrease by $16.68. Round appropriately. Include the units! (8 pts.)

According to your equation, if you want your house's monthly heating costs to be $200/month, how many inches of attic insulation do you need to have? (4 pts.) Round correctly and include the units.

6.12 inches

Are monthly heating costs statistically related to the number of inches of attic insulation? Test at the .05 level of significance:

The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value is 0.0217.

Since the p-value (0.0217) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that monthly heating costs is statistically related to the number of inches of attic insulation.

	r²	0.367
	r	-0.606
	Std. Error	60.982
	n	14
	k	1
	Dep. Var.	Monthly Heating Costs ($)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	25,834.9371	1	25,834.9371	6.95	.0217
Residual	44,625.4200	12	3,718.7850
Total	70,460.3571	13
Regression output				confidence interval
variables	coefficients	std. error	t (df=12)	p-value	95% lower	95% upper
Intercept	302.1000
Attic Insulation (inches)	-16.6800	6.3284	-2.636	.0217	-30.4684	-2.8916

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