Question

Sales price, y (thousands)	Square feet, x1	Rooms, x2	Bedrooms, x3	Age, x4
53.5	1008	5	2	35
49	1290	6	3	36
50.5	860	8	2	36
49.9	912	5	3	41
52	1204	6	3	40
55	1204	5	3	10
80.5	1764	8	4	64
86	1600	7	3	19
69	1255	5	3	16
149	3600	10	5	17
46	864	5	3	37
38	720	4	2	41
49.5	1008	6	3	35
103	1950	8	3	52
152.5	2086	7	3	12
85	2011	9	4	76
60	1465	6	3	102
58.5	1232	5	2	69
101	1736	7	3	67
79.4	1296	6	3	11
125	1996	7	3	9
87.9	1874	5	2	14
80	1580	5	3	11
94	1920	5	3	14
74	1430	9	3	16
69	1486	6	3	27
63	1008	5	2	35
67.5	1282	5	3	20
35	1134	5	2	74
142.5	2400	9	4	15
92.2	1701	5	3	15
56	1020	6	3	16
63	1053	5	2	24
60	1728	6	3	26
34	416	3	1	42
52	1040	5	2	9
75	1496	6	3	30
93	1936	8	4	39
60	1904	7	4	32
73	1080	5	2	24
71	1768	8	4	74
83	1503	6	3	14
90	1736	7	3	16
83	1695	6	3	12
115	2186	8	4	12
50	888	5	2	34
55.2	1120	6	3	29
61	1400	5	3	33
147	2165	7	3	2
210	2353	8	4	15
60	1536	6	3	36
100	1972	8	3	37
44.5	1120	5	3	27
55	1664	7	3	79
53.4	925	5	3	20
65	1288	5	3	2
73	1400	5	3	2
40	1376	6	3	103
141	2038	12	4	62
68	1572	6	3	29
139	1545	6	3	9
140	1993	6	3	4
55	1130	5	2	21

The excel data file named “Family-Residences Data” (posted in the content area under Week IX) presents the sale price y (thousands), square footage (x₁), number of rooms (x₂), number of bedrooms (x₃), and age (x₄) for each of 63 single-family residences sold in Oxford, Ohio. Use any software of your choice to conduct a multiple regression analysis for this data set. Use the result of this analysis to answer the questions below.

1. Write a regression model that relates the dependent variable to the independent variables.

2. Interpret the error term in this model. What does it represent?

3. Identify the least squares point estimates of b₀, b₁, b₂, b₃, and b₄ from your software output. Approximate these to four decimal places when necessary.

4. Write a multiple regression equation that relates sale price to square footage, number of rooms, number of bedrooms, and age.

5. Does the model explain a substantial portion of the variability in sale prices? Explain.

6. Do the signs and magnitudes of the estimated coefficients appear to be reasonable? Explain.

7. Write the multiple regression hypotheses to be tested.

8. Use F test to test the adequacy of the model with a = .05. Interpret the result of this test.

9. Use the p-value from your software output to test the importance of each of the independent variables x₁, x₂, x₃, and x₄ at a= .05. Which variables are not important? Explain.

10. Use the residential sales estimated equation to predict sales price of a residence that has 1700 square feet, seven rooms, and three bedrooms and is 15 years old.

Answer 1

Sol:

install analysis tool pack excel.

Go to data>data analysis>Regression>Select y as sales price and remaining variables as x.you get the below output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.851737
R Square	0.725456
Adjusted R Square	0.706522
Standard Error	18.95903
Observations	63
ANOVA
	df	SS	MS	F	Significance F
Regression	4	55088.34	13772.08	38.31488	1.16E-15
Residual	58	20847.8	359.4448
Total	62	75936.13
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	10.4041	11.49694	0.904945	0.369238	-12.6095	33.41773
Square feet, x1	0.049911	0.008103	6.159486	7.43E-08	0.033691	0.066131
Rooms, x2	6.292436	2.527656	2.489436	0.015684	1.232783	11.35209
Bedrooms, x3	-11.0008	5.867606	-1.87483	0.065854	-22.7461	0.744511
Age, x4	-0.43301	0.109692	-3.94755	0.000216	-0.65258	-0.21344

The rgression eq is

sale price=10.4041+0.049911*squarefeet+6.292436*rooms-11.0008bedrroms-0.43301*age

Solution2:

Error term is standad error of estimate

=18.95903

Solution3:

he least squares point estimates of b0, b1, b2, b3, and b4 from output are:

b0=10.4041

b1=0.0499

b2=6.2924

b3=-11.0008

b4=-0.4330

Solution4:

sale price=10.4041+0.049911*squarefeet+6.292436*rooms-11.0008bedrroms-0.43301*age