Question

You are studying the market value of home in Houston. You collect data from the recent sale of 30 single family homes. The data is organized and stored in an Excel file. The dataset includes the fair market value (in $thousands), land area of the property in acres, and age, in years of the 30 homes. Develop a multilinear regression model to predict the fair market value based on land area of the property (in acres) and age, in years.

The name of the Excel data file is HoustonHomes.xlsx. Import the data into SPSS and complete the assignment using SPSS.

1. State the multiple regression equation.

2. Interpret the meaning of the slopes, b1 and b2 , in this problem?

3. Explain why the regression coefficient, b0, has no practical meaning in the context of this problem.

4. Predict the mean fair market value for a house that has a land area of 0.25 acre and is 55 years old?

5. Construct a 95% prediction interval estimate for the fair market value for an individual house that has a land area of 0.25 acre and is 55 years old.

Address	Fair Market Value ($000)	Property Size (acres)	Age	House Size (square feet)	Rooms	Baths	Garage
9 Sycamore Road	522.9	0.2297	56	2448	7	3.5	2
21 Jefferson St	425.0	0.2192	61	1942	7	2.5	1
38 Hitching Post Lane	539.2	0.1630	39	2073	5	3	2
4 Poppy Lane	628.2	0.4608	28	2707	8	2.5	1
5 Daniel Drive	490.4	0.2549	56	2042	7	1.5	1
15 Francis Terrace	487.7	0.2290	98	2089	7	2	0
23 Guilfoy Street	370.3	0.1808	58	1433	7	2	0
17 Carlyle Drive	777.9	0.5015	17	2991	9	2.5	1
8 Craft Avenue	347.1	0.2229	62	1008	5	1	0
22 Beechwood Ct.	756.8	0.1300	25	3202	8	2.5	2
14 Fox Street	389.0	0.1763	64	2230	8	2	0
1 Raynham Road	889.0	1.3100	62	1848	7	2	1
2 Jerome Drive	452.2	0.2520	56	2100	6	2	0
7 Valentine Street	412.4	0.1148	22	1846	5	3	1
38 Jefferson Street	338.3	0.1693	74	1331	5	1	1
15 Inwood Road	334.3	0.1714	62	1344	8	1	0
29 Meadowfield Lane	437.4	0.3849	54	1822	6	2	1
13 Westland Drive	644.0	0.6545	56	2479	6	2.5	2
79 Valentine Street	387.8	0.1722	62	1605	6	3	0
13 Fairmont Place	399.8	0.1435	88	2080	11	2	0
1 Prestwick Terrace	356.4	0.2755	81	2410	6	1	1
11 Clement Street	346.9	0.1148	107	1753	8	2	0
7 Woodland Road	541.8	0.3636	55	1884	7	2	2
36 Elm Avenue	388.0	0.1474	51	2050	10	2	2
17 Duke Place	564.0	0.2281	50	2978	6	2.5	2
12 Prospect Avenue	454.4	0.4626	92	2132	7	1	0
1 Buckeye Road	417.3	0.1889	64	1551	6	2	0
30 Ann Street	318.8	0.1228	54	1129	5	1	0
26 Broadfield Place	519.8	0.1492	44	1674	7	2	1
16 Jackson Street	310.2	0.0852	104	1184	5	1	0

Answer 1

a) Let the multiple linear regression equation be y = b₀ + b₁x₁ +b₂x₂

b)

Regression Analysis: Fair Market Value ($000) versus ... ize (acres), Age

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	2	422043	211021	31.32	0.000
Property Size (acres)	1	265946	265946	39.47	0.000
Age	1	115900	115900	17.20	0.000
Error	27	181915	6738
Total	29	603958

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
82.0829	69.88%	67.65%	62.19%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	532.3	48.7	10.94	0.000
Property Size (acres)	407.1	64.8	6.28	0.000	1.01
Age	-2.826	0.681	-4.15	0.000	1.01

Regression Equation

Fair Market Value ($000)

=

532.3 + 407.1 Property Size (acres) - 2.826 Age

Interpretation of b₁ :- The slope coefficient of Property size is 407.1 which says that with increase in 1 acre of property size there will be an increase of 407.1 thousand dollars in Fair market value by keeping the others constant.

Interpretation of b₂ :- The slope coefficient of Age is -2.826 which says that with increase in 1 year of age there will be a decrease 2.826 thousand dollars in Fair market value by keeping the others constant.

Interpretation of b₀ :- The intercept 532.3 thousand dollars does not have any meaning in this case because if there is no land area and at zero age there wont be any fair market value.

Given a land area of 0.25 acre and is 55 years old

Fair Market Value ($000) = 532.3 + 407.1 Property Size (acres) - 2.826 Age = 532.3 + 407.1*0.25 - 2.826*55 = 478.658

Prediction for Fair Market Value ($000) = 478.658 thousand dollars.

Regression Equation

Fair Market Value ($000)

=

532.3 + 407.1 Property Size (acres) - 2.826 Age

Settings

Variable	Setting
Property Size (acres)	0.25
Age	55

95% Prediction interval

Fit	SE Fit	95% CI	95% PI
478.658	15.5086	(446.837, 510.479)	(307.258, 650.058)