A realtor in Arlington, Massachusetts, is analyzing the relationship between the
ID: 3051512 • 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
840,000
2,768
4
3.5
569,077
1,731
3
1.5
831,833
2,800
5
2.0
689,000
2,200
3
2.5
685,000
2,716
3
3.5
774,000
3,029
4
2.0
625,000
2,732
4
2.5
454,667
1,786
3
2.5
587,500
2,100
3
1.5
585,000
1,947
3
1.5
583,000
2,224
3
2.5
569,000
3,262
4
2.0
764,400
2,509
4
3.0
780,000
2,149
4
2.5
537,000
2,907
3
2.5
516,000
1,951
4
2.0
511,000
1,752
3
1.5
510,000
1,727
3
2.0
495,000
1,692
3
2.0
463,000
1,714
3
2.0
457,000
1,650
3
2.0
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
253,333
896
3
1.0
285,000
954
2
1.0
375,900
2,275
5
1.0
372,000
1,005
2
1.0
275,625
954
2
1.0
534,750
2,147
3
3.0
412,500
1,703
3
2.0
330,000
1,465
3
1.0
461,250
1,275
2
1.0
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.)
Predict the price of a 1,930-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
Sqft
Beds
Baths
840,000
2,768
4
3.5
569,077
1,731
3
1.5
831,833
2,800
5
2.0
689,000
2,200
3
2.5
685,000
2,716
3
3.5
774,000
3,029
4
2.0
625,000
2,732
4
2.5
454,667
1,786
3
2.5
587,500
2,100
3
1.5
585,000
1,947
3
1.5
583,000
2,224
3
2.5
569,000
3,262
4
2.0
764,400
2,509
4
3.0
780,000
2,149
4
2.5
537,000
2,907
3
2.5
516,000
1,951
4
2.0
511,000
1,752
3
1.5
510,000
1,727
3
2.0
495,000
1,692
3
2.0
463,000
1,714
3
2.0
457,000
1,650
3
2.0
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
253,333
896
3
1.0
285,000
954
2
1.0
375,900
2,275
5
1.0
372,000
1,005
2
1.0
275,625
954
2
1.0
534,750
2,147
3
3.0
412,500
1,703
3
2.0
330,000
1,465
3
1.0
461,250
1,275
2
1.0
Explanation / Answer
SUMMARY OUTPUT Regression Statistics Multiple R 0.833401 R Square 0.694557 Adjusted R Square 0.665921 Standard Error 87807.56 Observations 36 ANOVA df SS MS F Significance F Regression 3 5.61E+11 1.87E+11 24.25524 2.23742E-08 Residual 32 2.47E+11 7.71E+09 Total 35 8.08E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 60885.55 65221.04 0.93 0.36 -71965.37 193736.47 -71965.37 193736.47 Sqft 103.51 40.19 2.58 0.01 21.64 185.39 21.64 185.39 Beds 33169.79 24897.43 1.33 0.19 -17544.60 83884.19 -17544.60 83884.19 Baths 82447.17 28856.18 2.86 0.01 23669.05 141225.29 23669.05 141225.29 Price = 60885.55 + 103.51 Sqft + 33169.79 Beds + 82447.17 Baths Price of 1930 sqft home with 3 beds and 2 baths is 525063.56
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