A realtor in Arlington, Massachusetts, is analyzing the relationship between the
ID: 3314508 • Letter: A
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
728,000
2,399
4
2.5
822,000
2,500
4
2.5
713,000
2,400
3
3.0
689,000
2,200
3
2.5
685,000
2,716
3
3.5
838,500
3,281
4
2.5
432,692
1,891
3
1.5
620,000
2,436
4
3.5
718,056
2,567
3
2.5
585,000
1,947
3
1.5
795,000
3,033
4
3.5
569,000
3,262
4
2.0
546,000
1,792
3
2.0
540,000
1,488
3
1.5
537,000
2,907
3
2.5
344,000
1,301
3
1.0
738,111
2,531
4
2.5
714,000
2,418
4
3.0
693,000
2,369
4
3.0
463,000
1,714
3
2.0
457,000
1,650
3
2.0
631,400
2,359
4
3.0
435,000
1,500
3
1.5
431,700
1,896
2
1.5
414,000
1,182
2
1.5
401,500
1,152
3
1.0
319,200
1,106
3
1.0
253,333
896
3
1.0
475,000
1,590
3
2.0
375,900
2,275
5
1.0
620,000
1,675
3
2.0
459,375
1,590
3
2.0
534,750
2,147
3
3.0
247,500
1,022
2
1.0
247,500
1,099
2
1.0
307,500
850
1
1.0
SOURCE: http://Newenglandmoves.com.
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.)
Predict the price of a 2,188-square-foot home with four bedrooms and three bathrooms. (Round intermediate coefficient values to 2 decimal places. Round your answer to 2 decimal places.)
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.
Explanation / Answer
The statistical software output for this problem is:
Multiple linear regression results:
Dependent Variable: Price
Independent Variable(s): Sqft, Beds, Baths
Price = 72968.876 + 102.73901 Sqft + 17808.677 Beds + 100202.6 Baths
Parameter estimates:
Analysis of variance table for multiple regression model:
Summary of fit:
Root MSE: 82740.336
R-squared: 0.782
R-squared (adjusted): 0.7616
Hence,
a) Coefficients:
Intercept = 72968.88
sqft = 102.74
Beds = 17808.68
Baths = 100202.60
b - 1) For every additional square foot, the predicted price of a home increases by $102.74, holding number of bedrooms and bathrooms constant.
b - 2) For every additional bedroom, the predicted price of a home increases by $17,808.68, holding number of square feet and bathrooms constant.
b - 3) For every additional bathroom, the predicted price of a home increases by $100,202.60, holding number of square feet and bedrooms constant.
c) For sqft = 2188, Bedrooms = 4 and Bathrooms = 3,
Price = $ 669604.34
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 72968.876 59610.039 0 32 1.2241038 0.2298 Sqft 102.73901 38.772397 0 32 2.6497979 0.0124 Beds 17808.677 24707.26 0 32 0.7207872 0.4763 Baths 100202.6 26991.817 0 32 3.7123323 0.0008Related Questions
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