Download RegHousePrice.xlsx fr
Download RegHousePrice.xlsx from the course Blackboard site. Thefirst variable measures the price of the house, and this isfollowed 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 priceof a house. b. Evaluate the model: be sure to mention the goodnessof fit, the sign of the coefficients, the statistical significanceof 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, whatshould 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 |
Answer:
| SUMMARYOUTPUT | ||||||||
| 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 notlotsize
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
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