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

What is the estimate for monthly heating costs with a mean outside temperature of 45 degrees and 4 inches of attic
insulation? ( WATCH YOUR UNITS!
According to your equation, holding the amount of attic insulation constant, for each one degree increase in the
mean outside temperature, monthly heating costs (increase/ do not change / decrease) by __________________.
Round Correctly and include the units!
According to your equation, holding the mean outside temperature size constant, for every one inch increase in the
amount of insulation, monthly heating costs (increase / do not change / decrease) by __________________________.
Round like the original data and include the units.
How much of the variability in monthly heating costs is explained by the estimated regression equation?

Answer 1

What is the estimate for monthly heating costs with a mean outside temperature of 45 degrees and 4 inches of attic insulation?

y = 226.482

According to your equation, holding the amount of attic insulation constant, for each one degree increase in the mean outside temperature, monthly heating costs decrease by 0.6116.

According to your equation, holding the mean outside temperature size constant, for every one inch increase in the amount of insulation, monthly heating costs decrease by 16.0768.

How much of the variability in monthly heating costs is explained by the estimated regression equation?

38.8%

	R²	0.388
	Adjusted R²	0.277
	R	0.623
	Std. Error	62.617
	n	14
	k	2
	Dep. Var.	Monthly Heating Costs ($)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	27,331.0822	2	13,665.5411	3.49	.0672
Residual	43,129.2749	11	3,920.8432
Total	70,460.3571	13
Regression output				confidence interval
variables	coefficients	std. error	t (df=11)	p-value	95% lower	95% upper
Intercept	318.3129
Mean Outside Temperature (degre	-0.6116	0.9901	-0.618	.5493	-2.7909	1.5676
Attic Insulation (inches)	-16.0768	6.5710	-2.447	.0324	-30.5395	-1.6142
Predicted values for: Monthly Heating Costs ($)
			95% Confidence Interval	95% Prediction Interval
Mean Outside Temperature (degre	Attic Insulation (inches)	Predicted	lower	upper	lower	upper
45	4	226.482	172.049	280.915	78.304	374.660

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