A realtor in Arlington, Massachusetts, is analyzing the relationship between the

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 Sqft Beds Baths 672,000 2,214 5 1.0 569,077 1,731 3 1.5 831,833 2,800 5 2.0 814,273 2,600 4 2.5 685,000 2,716 3 3.5 645,000 2,524 3 2.0 625,000 2,732 4 2.5 620,000 2,436 4 3.5 783,333 2,800 4 2.0 585,000 1,947 3 1.5 583,000 2,224 3 2.5 379,333 2,175 3 1.0 546,000 1,792 3 2.0 780,000 2,149 4 2.5 732,273 3,964 4 3.5 344,000 1,301 3 1.0 511,000 1,752 3 1.5 714,000 2,418 4 3.0 693,000 2,369 4 3.0 648,200 2,400 4 3.0 639,800 2,310 4 3.0 451,000 1,685 3 2.0 628,333 2,167 4 2.5 431,700 1,896 2 1.5 414,000 1,182 2 1.5 602,250 1,728 4 2.0 478,800 1,660 4 2.0 380,000 1,344 4 2.0 475,000 1,590 3 2.0 375,900 2,275 5 1.0 372,000 1,005 2 1.0 459,375 1,590 3 2.0 356,500 1,431 2 2.0 412,500 1,703 3 2.0 412,500 1,831 3 2.0 307,500 850 1 1.0 SOURCE: http://Newenglandmoves.com. Picture Click here for the Excel Data File a. Estimate the model Price = 0 + 1Sqft + 2Beds + 3Baths + . (Round Coefficients and Standard Error answers to 2 decimal places. Round t Stat and p-value answers to 4 decimal places.) 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 $117.44. For every additional square foot, the predicted price of a home increases by $117.44, holding number of bedrooms and bathrooms constant. For every additional square foot, the predicted price of a home increases by $117.44, holding square foot, number of bedrooms and bathrooms constant. b-2. Interpret the coefficient of Beds. For every additional bedroom, the predicted price of a home increases by $41,233.60. For every additional bedroom, the predicted price of a home increases by $41,233.60, holding number of square feet and bathrooms constant. For every additional bedroom, the predicted price of a home increases by $41,233.60, 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 $45,886.41. For every additional bathroom, the predicted price of a home increases by $45,886.41, holding number of square feet and bedrooms constant. For every additional bathroom, the predicted price of a home increases by $45,886.41, holding square foot, number of bedrooms and bathrooms constant. c. Predict the price of a 2,041-square-foot home with two bedrooms and one bathrooms. (Round intermediate coefficient values to 2 decimal places. Round your answer to 2 decimal places.) 21formula563.mml $ rev: 11_14_2015_QC_CS-31836, 10_19_2016_QC_CS-66482 eBook & Resources eBook: Estimate the multiple linear regression model and interpret the coefficients.

Explanation / Answer

a. After running the regression in R, we get the below equation.

Price = 80619.8 + 117.44 Sqft + 41233.6 Beds + 45886.41 Baths

Coefficients of Intercept = 80619.8

Coefficients of Sqft = 117.44

Coefficients of Beds = 41233.6

Coefficients of Baths = 45886.41

Standard error of Intercept = 64052.2

Standard error of Sqft = 38.7

Standard error of Beds = 21480.7

Standard error of Baths = 26603.1

t-stat of Intercept = 1.259

t-stat of Sqft = 3.035

t-stat of Beds = 1.920

t-stat of Baths = 1.725

p-value of Intercept = 0.21726

p-value of Sqft = 0.00475

p-value of Beds = 0.06387

p-value of Baths = 0.09420

b-1 . The answer is For every additional square foot, the predicted price of a home increases by $117.44, holding number of bedrooms and bathrooms constant.

b-2 The answer is For every additional bedroom, the predicted price of a home increases by $41,233.60, holding number of square feet and bathrooms constant.

b-3 The answer is For every additional bathroom, the predicted price of a home increases by $45,886.41, holding number of square feet and bedrooms constant.

c. Predict the price of a 2,041-square-foot home with two bedrooms and one bathrooms.

The regression equation is Price = 80619.8 + 117.44 Sqft + 41233.6 Beds + 45886.41 Baths

Sqft = 2041, Beds = 2 , Baths = 1

Price = 80619.8 + 117.44 * 2041 + 41233.6 * 2 + 45886.41 * 1

= 448668.5

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