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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