Download RegHousePrice.xlsx from the course Blackboard site. The first variable measures the price of the house,...

Download RegHousePrice.xlsx from the course Blackboard site. The first variable measures the price of the house, and this is followed by the number of bedrooms, the size of the house (in sq. ft.), and the size of the lot (i.e. yard; also in sq. ft.). a. Build and estimate a regression model to predict the selling price of a house. b. Evaluate the model: be sure to mention the goodness of fit, the sign of the coefficients, the statistical significance of the coefficients, and the economic plausibility of the results. c. Suppose your house is 1,600 sq. ft., there are four bedrooms, and the lot size is 5,000 sq. ft. According to your model, what should its price be?

Price	Bedrooms	House Size	Lot Size
124100	3	1290	3900
218300	4	2080	6600
117800	3	1250	3750
168300	3	1550	4650
120400	3	1360	4050
159200	3	1450	4200
158000	4	2110	6600
73800	2	1270	4200
142500	4	1940	6300
160100	3	1290	4050
199200	4	2190	6900
179200	4	2030	6300
153800	3	1310	4350
150900	4	2300	7200
180100	4	1870	5700
132600	4	1920	6000
147200	4	1530	4500
149800	3	1350	4200
151500	3	1590	5100
132800	4	1680	5100
115300	3	1370	4200
196600	4	2130	6450
217400	4	1840	5700
106100	3	1600	4950
220900	4	2330	7200
162000	4	2290	6900
179000	4	2270	6900
107700	4	1910	5550
136900	4	2150	6450
115400	3	1230	3600
118500	3	1410	4500
208600	5	2360	7200
186700	4	2320	7050
131800	4	1530	4950
149400	3	1280	3900
155600	4	1690	5250
160300	3	1560	4800
131200	4	1810	5550
107300	3	1240	4050
109700	3	1320	4200
203100	4	1870	5700
144800	4	1920	6000
150400	3	1520	4800
96400	2	1070	3450
153500	3	1570	4800
139900	4	2260	7050
146900	4	1970	6000
136800	3	1360	4200
96400	3	1290	4050
148400	3	1550	5100
143100	2	1220	3750
191800	5	2330	7350
102000	3	1460	4500
147500	3	1410	4350
184300	4	2300	7050
178100	4	2220	6750
267800	5	2980	9150
245700	5	2950	9000
107000	3	1550	4800
137700	4	2010	6150
88900	3	1570	4800
98700	4	1660	5100
181200	4	2310	7350
199500	4	2200	6750
162400	4	1590	4950
125500	3	1360	4350
165400	4	2310	7350
209400	5	2790	8400
129800	4	1540	4950
192000	4	1780	5400
124700	3	1320	4350
147300	4	1780	5250
154700	4	1980	6000
122200	4	1590	5100
125000	4	1830	5850
253200	5	2340	7500
157800	3	1540	4800
123700	3	1200	3750
125500	4	1560	4650
130000	4	1520	4650
179800	4	2070	6150
150200	4	1840	5700
160900	4	1950	5850
153200	3	1280	4050
204200	4	2310	7050
215800	4	2380	7200
159700	3	1580	4800
180800	4	2140	6600
178800	5	2300	7050
120200	3	1370	4500
134200	4	1590	5100
134800	3	1480	4650
161500	4	1870	5700
155400	3	1520	4500
113200	3	1250	3750
180500	3	1320	3900
218100	5	2980	9000
117500	3	1570	4950
157400	3	1560	5100
155900	4	1620	4800

Expert Solution

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.748329963
R Square	0.559997733
Adjusted R Square	0.546247662
Standard Error	25022.70761
Observations	100

ANOVA
	df	SS	MS	F	Significance F
Regression	3	76501718347.31	25500572782.44	40.73	0.00
Residual	96	60109046052.69	626135896.38
Total	99	136610764400.00

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	37718	14177	3	0	9577	65858	9577	65858
Bedrooms	2306	6994	0	1	-11577	16189	-11577	16189
House Size	74	53	1	0	-31	179	-31	179
Lot Size	-4	17	0	1	-38	29	-38	29



RESIDUAL OUTPUT

Observation	Predicted Price	Residuals
1	123459.9635	640.0364917
2	172678.3073	45621.69269
3	121142.6587	-3342.658699
4	139504.2959	28795.70409
5	128006.1725	-7606.172498
6	134038.3176	25161.68239
7	174907.2115	-16907.21149
8	118358.8117	-44558.8117
9	163585.8893	-21085.88933
10	122805.3961	37294.60392
11	179541.8211	19658.17889
12	170272.6019	8927.398125
13	122982.1973	30817.80267
14	186405.3349	-35505.33491
15	161003.3826	19096.61736
16	163409.0881	-30809.08808
17	140979.008	6220.991953
18	126608.637	23191.36299
19	140512.4659	10987.53414
20	149505.2592	-16705.25922
21	128094.5731	-12794.57313
22	177047.715	19552.28495
23	158774.4785	58625.52154
24	141910.0014	-35810.00135
25	188634.2391	32265.76091
26	186971.5017	-24971.50171
27	185485.5656	-6485.565592
28	164629.8223	-56929.82231
29	178533.6512	-41633.65117
30	120311.29	-4911.290011
31	129757.3105	-11257.3105
32	193169.2241	15430.77591
33	188545.8385	-1845.838462
34	139015.3058	-7215.305751
35	122716.9954	26683.00455
36	149593.6599	6006.340149
37	139592.6965	20707.30346
38	157200.1417	-26000.14171
39	119090.5558	-11790.55578
40	124379.7328	-14679.73282
41	161003.3826	42096.61736
42	163409.0881	-18609.08808
43	136620.8243	13779.1757
44	106772.2877	-10372.28766
45	140335.6646	13164.3354
46	184088.0301	-44188.0301
47	167123.9284	-20223.92838
48	127351.6051	9448.394934
49	122805.3961	-26405.39608
50	137540.5936	10859.40638
51	116607.6737	26492.3263
52	190285.7525	1514.247521
53	133472.1508	-31472.1508
54	130411.8779	17088.12206
55	187059.9023	-2759.902341
56	182425.2927	-4325.292723
57	230723.8672	37076.13279
58	229149.5305	16550.46954
59	138849.7285	-31849.72848
60	169441.2332	-31741.23319
61	140335.6646	-51435.6646
62	148019.3231	-49319.3231
63	186493.7355	-5293.735537
64	180939.3566	18560.6434
65	143473.1141	18926.88589
66	126697.0376	-1197.037634
67	186493.7355	-21093.73554
68	219880.3112	-10480.31123
69	139758.2738	-9958.273811
70	155625.805	36374.19504
71	123725.1654	974.8346071
72	156280.3724	-8980.372393
73	167866.8964	-13166.89644
74	142818.5467	-20618.54668
75	157376.943	-32376.94297
76	190374.1531	62825.84689
77	138106.7604	19693.23958
78	117427.8184	6272.181602
79	142553.3448	-17053.3448
80	139581.4726	-9581.472555
81	173899.0415	5900.958452
82	158774.4785	-8574.478458
83	166292.5597	-5392.559689
84	122062.428	31137.57198
85	187802.8704	16397.1296
86	192349.0794	23450.92061
87	141078.6327	18621.36734
88	177136.1157	3663.884327
89	189365.9832	-10565.98316
90	126785.4383	-6585.438262
91	142818.5467	-8618.54668
92	134303.5195	496.4805072
93	161003.3826	496.6173611
94	137929.9592	17470.04083
95	121142.6587	-7942.658699
96	125688.8677	54811.13231
97	231378.4346	-13278.43464
98	139681.0972	-22181.09717
99	138283.5617	19116.43832
100	146356.5857	9543.414275

a. Price = 37718 + 2306 * bedroom + 74*housesize - 4*lotsize

b. R2 = 0.56

p-value > alpha, hence insignificant

Coefficient has correct sign for bedroom and housesize but not lotsize

Hence, it is not a very good fit.

c. Suppose your house is 1,600 sq. ft., there are four bedrooms, and the lot size is 5,000 sq. ft.

Price = 37718 + 2306 * bedroom + 74*housesize - 4*lotsize

= 37718 + 2306 * 4 + 74*1600 - 4*5000

= 37718 + 9224 + 118400 - 20000

=145342

Rahul Sunny answered 2 years ago

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