In: Statistics and Probability
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.
Q3. Based on the regression of SqFt on Price, the total amount of variation in price that is explained by SqFt is about __________.
0.31% |
||
0.55 |
||
30.6% |
||
69.4% |
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 |
Solution:
We can use the excel regression on (Price and Sq Ft) data analysis to find the coefficient of determination (R-square), which will explain the amount of variation in price that is explained by SqFt. The excel output is given below:
SUMMARY OUTPUT | ||||||
Regression Statistics | ||||||
Multiple R | 0.553 | |||||
R Square | 30.6% | |||||
Adjusted R Square | 0.300 | |||||
Standard Error | 44951.067 | |||||
Observations | 128 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 112145452218.547 | 112145452218.547 | 55.501 | 0.000 | |
Residual | 126 | 254595404968.953 | 2020598452.135 | |||
Total | 127 | 366740857187.500 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | -20182.2598 | 37932.2080 | -0.5321 | 0.5956 | -95248.9833 | 54884.4637 |
Sq Ft | 140.4526 | 18.8529 | 7.4499 | 0.0000 | 103.1432 | 177.7620 |
Therefore, the option 30.6% is correct
Q3. Based on the regression of SqFt on Price, the total amount of variation in price that is explained by SqFt is about 30.6%.