Question

In: Math

Sales of single-family houses have been brisk in Mid City this year. This has especially been...

Sales of single-family houses have been brisk in Mid City this year. This has especially been true in older, more established neighborhoods, where housing is relatively inexpensive compared to the new homes being built in the newer neighborhoods. Nevertheless, there are also many families who are willing to pay a higher price for the prestige of living in one of the newer neighborhoods. The file C10_02. Xls contains data on 128 recent sales in Mid City. For each sales the file shows the neighborhood(1,2, or3) in which the house is located, the number of offers made on the house, the square footage, whether the house is made primarily of brick, the number of bathrooms, the number of bedrooms, and the selling price. Neighborhoods 1 and 2 are more traditional neighborhoods, whereas neighborhood 3 is a newer more prestigious neighborhood. Use regression to estimate and interprets the pricing structure of houses in Mid City. Here are some considerations.

Use regression to estimate and interpret the pricing structure of houses in Mid City. Here are some considerations.

1. Do buyers pay a premium for a brick house, all else being equal?

2. Is there a premium for a house in neighborhood 3, all else being equal?

3. Is there an extra premium for a brick house in neighborhood 3, in addition to the usual premium for a brick house?

4. For purposes of estimation and prediction, could neighborhoods 1 and 2 be collapsed into a single “older” neighborhood?

Home Nbhd Offers Sq Ft Brick Bedrooms Bathrooms Price
1 2 2 1790 No 2 2 228600
2 2 3 2030 No 4 2 228400
3 2 1 1740 No 3 2 229600
4 2 3 1980 No 3 2 189400
5 2 3 2130 No 3 3 239600
6 1 2 1780 No 3 2 229200
7 3 3 1830 Yes 3 3 303200
8 3 2 2160 No 4 2 301400
9 2 3 2110 No 4 2 238400
10 2 3 1730 No 3 3 208000
11 2 3 2030 Yes 3 2 265000
12 2 2 1870 Yes 2 2 246000
13 1 4 1910 No 3 2 205200
14 1 5 2150 Yes 3 3 252600
15 3 4 2590 No 4 3 353600
16 3 1 1780 No 4 2 291600
17 2 4 2190 Yes 3 3 294200
18 1 4 1990 No 3 3 167200
19 2 1 1700 Yes 2 2 222800
20 3 2 1920 Yes 3 3 334400
21 2 3 1790 No 3 2 232400
22 1 4 2000 No 3 2 227600
23 1 3 1690 No 3 2 183400
24 1 3 1820 Yes 3 2 212200
25 2 2 2210 Yes 4 3 312800
26 1 3 2290 No 4 3 298600
27 3 3 2000 No 4 2 274000
28 2 2 1700 No 3 2 198600
29 1 3 1600 No 2 2 138200
30 3 1 2040 Yes 4 3 376000
31 3 3 2250 Yes 4 3 364000
32 1 2 1930 Yes 2 2 224600
33 2 3 2250 Yes 3 3 270000
34 2 4 2280 Yes 5 3 279200
35 1 3 2000 No 2 2 235600
36 1 3 2080 No 3 3 234200
37 1 2 1880 No 2 2 235000
38 3 4 2420 No 4 3 294000
39 3 1 1720 No 3 2 262600
40 1 2 1740 No 3 2 216400
41 2 1 1560 No 2 2 213200
42 3 2 1840 No 4 3 267200
43 2 3 1990 No 2 2 211200
44 2 1 1920 Yes 3 2 308000
45 3 2 1940 Yes 3 3 333000
46 2 3 1810 No 3 2 206400
47 1 2 1990 No 2 3 259600
48 1 6 2050 No 3 2 180600
49 2 2 1980 No 2 2 231800
50 1 3 1700 Yes 3 2 215000
51 2 3 2100 Yes 3 2 302200
52 1 3 1860 No 2 2 182200
53 1 4 2150 No 2 3 234800
54 1 3 2100 No 3 2 261600
55 1 3 1650 No 3 2 162600
56 2 2 1720 Yes 2 2 251400
57 2 3 2190 Yes 3 2 281800
58 3 3 2240 No 4 3 304600
59 3 1 1840 No 3 3 276200
60 3 1 2090 No 4 2 310800
61 3 1 2200 No 3 3 361800
62 1 2 1610 No 2 2 201800
63 3 2 2220 No 4 3 322600
64 2 2 1910 No 2 3 241000
65 3 2 1860 No 3 2 260600
66 1 1 1450 Yes 2 2 222200
67 1 4 2210 No 3 3 252400
68 2 3 2040 No 4 3 303800
69 1 4 2140 No 3 2 187200
70 3 3 2080 No 4 3 331200
71 3 3 1950 Yes 3 3 333400
72 3 1 2160 No 4 2 315200
73 1 3 1650 No 3 2 214600
74 2 2 2040 No 3 3 251400
75 3 3 2140 No 3 3 288400
76 1 2 1900 No 2 2 213800
77 3 2 1930 No 3 2 259600
78 3 3 2280 Yes 4 3 353000
79 1 3 2130 No 3 2 242600
80 3 1 1780 No 4 2 287200
81 2 4 2190 Yes 3 3 286800
82 3 2 2140 Yes 4 3 368600
83 3 1 2050 Yes 2 2 329600
84 2 2 2410 No 3 3 295400
85 1 3 1520 No 2 2 181000
86 3 2 2250 Yes 4 3 376600
87 1 4 1900 No 4 2 205400
88 3 1 1880 Yes 3 3 345000
89 1 2 1930 No 3 3 255400
90 1 4 2010 No 2 2 195600
91 3 2 1920 No 4 2 286200
92 2 2 2150 No 3 2 233000
93 3 2 2110 No 3 2 285200
94 2 2 2080 No 3 3 314200
95 3 3 2150 Yes 4 3 321200
96 3 1 1970 Yes 2 2 305000
97 2 3 2440 No 3 3 266600
98 2 1 2000 Yes 2 2 253600
99 3 1 2060 No 3 2 291000
100 3 2 2080 Yes 3 3 342000
101 1 5 2010 No 3 2 206400
102 2 5 2260 No 3 3 246200
103 2 4 2410 No 3 3 273600
104 3 3 2440 Yes 4 3 422400
105 2 4 1910 No 3 2 164600
106 3 4 2530 No 4 3 293800
107 1 4 2130 No 3 2 217000
108 2 1 1890 Yes 3 2 268000
109 2 3 1990 Yes 3 3 234000
110 2 3 2110 No 3 2 217400
111 1 1 1710 No 2 2 223200
112 1 2 1740 No 2 2 229800
113 2 2 1940 Yes 2 2 247200
114 1 3 2000 Yes 3 2 231400
115 2 2 2010 No 4 3 249000
116 1 3 1900 No 3 3 205000
117 3 1 2290 Yes 5 4 399000
118 1 2 1920 No 3 2 235600
119 1 3 1950 Yes 3 2 300400
120 1 4 1920 No 2 2 219400
121 1 3 1930 No 2 3 220800
122 2 3 1930 No 3 3 211200
123 2 1 2060 Yes 2 2 289600
124 2 3 1900 Yes 3 3 239400
125 2 3 2160 Yes 4 3 295800
126 1 2 2070 No 2 2 227000
127 3 1 2020 No 3 3 299800
128 1 4 2250 No 3 3 249200

Please provide step by step answer

Solutions

Expert Solution

ANSWER:

The number of offers made on the house, the square footage, whether the house is made primarily of bricks.

Since there are two categorical variable (Nbhd and Brick) with different classes, dummy variables must be introduced.

Neighborhood #3

Nbhd_3 = 1 = Yes

0 = No

Neighborhood #2

Nbhd_2 = 1= Yes

0=no

So obviously if both are zero then its Nbdh_1 (we don’t introduce this dummy variable into the model).

Brick_Y = 1 =yes

0= No (non brick)

Therefore, 3 dummy variables will be introduced.

The sample of the data is give below:

The model will be given by:

Price= constant + b1(offers) + b2 (sq ft) + b3(Bedrroms) + b4(bathroom)+ b5(Nbhd_2) +b6 (Nbhd_3) + b7(Brick_Y)

Using excel, data tools, fit the linear regression model and the output is given below:

Price = 4318.996375 - 16534.97664*offers + 105.9874816*Sq ft + 8493.587783*Bedrooms + 15766.55699*Bathrooms -3121.158239*Nbhd_2 + 41362.0747*Nbhd_3 + 34594.69906*Brick_Y

1)Since the p-value of Brick_Y (1.7829E-14) < 0.05, the brick_Y variable is significant and buyers pay a premium of 34594.69906 when other variables are held constant.

2) Since the p-value of Nbhd_3 (1.378E-09)< 0.05, the Nbhd_3 variable is significant and there is a premium of 41362.0747 for a house in neighborhood 3.


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