Question

Q1-

Salsberry Realty sells homes along the East Coast of the United States. One of the questions most frequently asked by prospective buyers is: If we purchase this home, how much can we expect to pay to heat it during the winter? The research department at Salsberry has been asked to develop some guidelines regarding heating costs for single-family homes. Three variables are thought to relate to the heating costs: (1) the mean daily outside temperature, (2) the number of inches of insulation in the attic (roof), and (3) the age in years of the furnace. To investigate, Salsberry’s research department selected a random sample of 20 recently sold homes. It determined the cost to heat each home last January, as well as the January outside temperature in the region, the number of inches of insulation in the attic, and the age of the furnace.

FACTORS IN JANUARY HEATING COST FOR A SAMPLE OF 20 HOMES

Home	Heating Cost	Mean Outside	Attic Insulation	Age of Furnace
	($)	Temperature (°F)	(inches)	(Years)
1	250	35	3	6
2	360	29	4	10
3	165	36	7	3
4	43	60	6	9
5	92	65	5	6
6	200	30	5	5
7	355	10	6	7
8	290	7	10	10
9	230	21	9	11
10	120	55	2	5
11	73	54	12	4
12	205	48	5	1
13	400	20	5	15
14	320	39	4	7
15	72	60	8	6
16	272	20	5	8
17	94	58	7	3
18	190	40	8	11
19	235	27	9	8
20	139	30	7	5

1. Develop an estimated regression equation that relates heating cost to mean outside temperature.

2. Develop an estimated regression equation that relates heating cost to age of furnace.

Answer 1

Sol:

Excel : Data --> Data analysis --> Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.811508835
R Square	0.65854659
Adjusted R Square	0.639576956
Standard Error	63.55260676
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	140214.9411	140214.9	34.71583	1.40701E-05
Residual	18	72700.80886	4038.934
Total	19	212915.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	388.8019517	34.24084305	11.35492	1.22E-09	316.8646098	460.7392935
Mean Outside	-4.934192249	0.837437277	-5.89201	1.41E-05	-6.693582681	-3.174801817

yhat = 318.3129-0.6116(Mean Outside Temperature)-16.0768(Attic Insulation)