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

 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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