Question

A realtor in Arlington, Massachusetts, is analyzing the relationship between the sale price of a home (Price), its square footage (Sqft), the number of bedrooms (Beds), and the number of bathrooms (Baths). She collects data on 36 recent sales in Arlington in the first quarter of 2009 for the analysis. The data is shown in the accompanying table Price 840,000 2,768 822,000 2,500 713,000 2,400 689,000 2,200 685,000 2,716 645,000 2,524 625,000 2,732 620,000 2,436 587,500 2,100 585,000 1,947 583,000 2,224 569,000 3,26.2 546,000 1,79.2 540,000 1,488 537,000 2,907 516,000 1,951 511,000 1,752 510,000 1,727 495,000 1,692 463,000 1,714 457,000 1,650 451,000 1,685 435,000 1,500 431,700 1,896 414,000 1,182 401,500 1,152 399,000 1,383 380,000 1,344 380,000 1,27'2 375,900 2,275 372,000 1,005 367,500 1,272 356,500 1,431 Sqft Beds Baths 3.5 2.5 3.0 2.5 3.5 2.0 2.5 3.5 2.5 2.0 2.0 2.5 2.0 2.0 2.0 2.0 2.0 2.0 2 2.0 2.0 330,000 1,362 330,000 1,465 307,500 3 850 SOURCE: http://Newenglandmoves.com lic a. Estimate the model Price-β0 + β1 Sqft + β2Beds+ ßgBaths + ε Coefficients Intercept Sqft Beds Baths b-1. Interpret the coefficient of sqft. For every additional square foot, the predicted price of a home increases by $95.86, holding number of bedrooms and bathrooms constant. For every additional square foot, the predicted price of a home increases by $95.86, holdingg square foot, number of bedrooms and bathrooms constant. For every additional square foot, the predicted price of a home increases by $95.86 b-2. Interpret the coefficient of beds For every additional bedroom, the predicted price of a home increases by $556.89 For every additional bedroom, the predicted price of a home increases by $556.89, holding number of square feet and bathrooms constant. For every additional bedroom, the predicted price of a home increases by $556.89, holding square foot, number of bedrooms and bathrooms constant. b-3. Interpret the coefficient of baths For every additional bathroom, the predicted price of a home increases by $92,022.91. For every additional bathroom, the predicted price of a home increases by $92,022.91, holding number of square feet and bedrooms constant. For every additional bathroom, the predicted price of a home increases by $92,022.91, holding square foot, number of bedrooms and bathrooms constant. c. Predict the price of a 2,500 square-foot home with three bedrooms and two bathrooms. (Round intermediate coefficient values to 2 decimal places. Round your answer to 2 decimal places.) Price

Answer 1

EXCEL (Mega Stat) output:

Regression Analysis R 0.724 Adjusted R2 0.698 R 0.851 Std. Error 74984.984 Dep. Var. Price ANOVA table Source Regesson 471270.518.47509017.07172.825 0807sed MS 3 157,070,172,825.0300 27.93 4.59E-09 Residual 179,927.931,247 1320 Total 651,138,449,722 2220 32 5,622,747,851.4729 35 confidence interval ssion out variables Intercept Sqft Beds Baths coefficients std. error 153,348.2664 57.141.7937 35.3997 556.8907 20,280.3128 92,022.9126 25.012 2976 t (df-32)-p-value-95% lower 2.684 0114 36,954.2419 269,742.2909 2.708 0108 23.7490 0.027 9783 -40,752.7544 41,866.5358 3.679 0009 41,074.5299 142,971.2953 95% upper std coeff 0.000 0.416 0.003 0.500 95.8559 167.9629 Intercept 153348.27 Sqft 95.86 Beds 556.89 Baths 92022.91 (b-1) For every additional square foot, the predicted price of a home increases by S95.86, holding number ofbedrooms and bathrooms constant

(b-2) For every additional bedroom, the predicted price of a home increases by S556.89, holding number of square feet and bathrooms constant. (b-3) For every additional bathroom, the predicted price of a home increases by S92022.91, holding number of sqaure feet and bedrooms constant Pricê 153348.27+95.86 Saft +556.89 Beds+92022.91Baths 153348.27+95.86(2500)+556.89(3)+92022.91(2) - 153348.27+239650 +1670.67 +184045.82 $578714.76