Question
In: Statistics and Probability
The data below id from 128 recent sales in Mid City. For each sale, it shows...
The data below id from 128 recent sales in Mid City. For each sale, it shows the neighborhood (1, 2, or 3) of the house, # of offers made on the house, sq. footage, whether house is primarily made of brick, # of bathrooms, # of bedrooms, & selling price. Â Neghborhoods 1 & 2 are traditional, 3 is newer/more prestigious. Use regression to estimate & interpret the pricing structure of houses in Mid City.
Q2. Predict Price using SqFt as the independent variable. Is the relationship between these variables statistically significant? YES or NO
| 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 |
Solutions
Expert Solution
using excel>data analysis>regression
independent variable =sq ft
dependent varible = Price
| Regression Statistics | ||||||
| Multiple R | 0.5530 | |||||
| R Square | 0.3058 | |||||
| Adjusted R Square | 0.3003 | |||||
| Standard Error | 44951.0673 | |||||
| Observations | 128 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 112145452218.5470 | 112145452218.5470 | 55.5011 | 0.0000 | |
| Residual | 126 | 254595404968.9530 | 2020598452.1346 | |||
| Total | 127 | 366740857187.5000 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | -20182.2598 | 37932.2080 | -0.5321 | 0.5956 | -95248.9843 | 54884.4647 |
| Sq Ft | 140.4526 | 18.8529 | 7.4499 | 0.0000 | 103.1432 | 177.7620 |
for every one unit increase in sq ft there is a $140.4526 increase in price.
since the p-value of f statistic is less than 0.05 so the relationship between these variables statistically significant
orchestra answered 2 years agoRelated Solutions
The data below id from 128 recent sales in Mid City. For each sale, it shows...
The data below id from 128 recent sales in Mid City. For each
sale, it shows the neighborhood (1, 2, or 3) of the house, # of
offers made on the house, sq. footage, whether house is primarily
made of brick, # of bathrooms, # of bedrooms, & selling price.
Neghborhoods 1 & 2 are traditional, 3 is newer/more
prestigious. Use regression to estimate & interpret the
pricing structure of houses in Mid City.
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offers made on the house, sq. footage, whether house is primarily
made of brick, # of bathrooms, # of bedrooms, & selling price.
 Neghborhoods 1 & 2 are traditional, 3 is newer/more
prestigious. Use regression to estimate & interpret the
pricing structure of houses in Mid City.
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The data below id from 128 recent sales in Mid City. For each sale, it shows...
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sale, it shows the neighborhood (1, 2, or 3) of the house, # of
offers made on the house, sq. footage, whether house is primarily
made of brick, # of bathrooms, # of bedrooms, & selling price.
 Neghborhoods 1 & 2 are traditional, 3 is newer/more
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offers made on the house, sq. footage, whether house is primarily
made of brick, # of bathrooms, # of bedrooms, & selling price.
 Neghborhoods 1 & 2 are traditional, 3 is newer/more
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