A real estate agent wishes to determine the selling price of residences using th

Question

A real estate agent wishes to determine the selling price of residences using the size (square feet), and whether the residence is a condominium or a single-family home. A sample of 20 residences was obtained with the following results:

Price ($) Type Square Feet

199,700 F 1,500

211,800 C 2,085

197,100 F 1,450

228,400 F 1,836

215,800 F 1,730

190,900 C 1,726

312,200 F 2,300

313,600 C 1,650

239,000 F 1,950

184,400 C 1,545

200,600 C 1,375

208,000 C 1,825

210,500 F 1,650

233,300 F 1,960

187,200 C 1,360

185,200 C 1,200

284,100 F 2,000

207,200 F 1,755

258,200 F 1,850

203,100 F 1,630

F: Single-Family Home

C: Condomnium Residence

a. Produce a regression equation to predict the selling price for residences using a model of the following form: (2 marks)

b. Interpret the parameters 1, and 2 in the model given in part a. (2 marks)

c. Produce an equation that describes the relationship between the selling price and the square footage of (1) condominiums and (2) single-family homes. (3 marks)

d. Conduct a test of hypothesis to determine if the relationship between the selling price and the square footage is different between condominiums and single-family homes. (3 marks)

Explanation / Answer

n= 20 X Y X^2 XY Type Area Selling Price($) F 1500 199700 2250000 299550000 C 2085 211800 4347225 441603000 F 1450 197100 2102500 285795000 F 1836 228400 3370896 419342400 F 1730 215800 2992900 373334000 C 1726 190900 2979076 329493400 F 2300 312200 5290000 718060000 C 1650 313600 2722500 517440000 F 1950 239000 3802500 466050000 C 1545 184400 2387025 284898000 C 1375 200600 1890625 275825000 C 1825 208000 3330625 379600000 F 1650 210500 2722500 347325000 F 1960 233300 3841600 457268000 C 1360 187200 1849600 254592000 C 1200 185200 1440000 222240000 F 2000 284100 4000000 568200000 F 1755 207200 3080025 363636000 F 1850 258200 3422500 477670000 F 1630 203100 2656900 331053000 Sum 25942 3332500 60478997 7812974800 a = 64976.02 b = 92.35 Y = a+ bX r= 0.572705233 SUMMARY OUTPUT Regression Statistics Multiple R 0.626822775 R Square 0.392906791 Adjusted R Square 0.357195426 Standard Error 32223.71761 Observations 19 ANOVA df SS MS F Significance F Regression 1 11424425448 11424425448 11.00228985 0.004077897 Residual 17 17652255604 1038367977 Total 18 29076681053 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 64976.01651 48738.13029 1.333165965 0.200068561 -37852.45001 167804.483 -37852.45001 167804.483 1500 92.34588577 27.84043459 3.31696998 0.004077897 33.60770317 151.0840684 33.60770317 151.0840684

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