A realtor in Arlington, Massachusetts, is analyzing the relationship between the
ID: 3221964 • 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
784,000
2,583
4
3.0
632,308
1,923
3
2.0
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
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 2,490-square-foot home with two bedrooms and one 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.
PriceExplanation / Answer
Answer:
Regression Analysis
R²
0.684
Adjusted R²
0.655
n
36
R
0.827
k
3
Std. Error
87996.674
Dep. Var.
Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
537,305,216,227.6880
3
179,101,738,742.5630
23.13
3.75E-08
Residual
247,789,270,033.9510
32
7,743,414,688.5610
Total
785,094,486,261.6390
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
59,080.2916
66,283.2400
0.891
.3794
-75,934.2502
194,094.8334
Sqft
103.3549
40.3182
2.563
.0153
21.2293
185.4805
Beds
32,865.3281
24,863.0249
1.322
.1956
-17,778.9963
83,509.6526
Baths
84,118.8784
29,956.8213
2.808
.0084
23,098.8303
145,138.9265
Predicted values for: Price
95% Confidence Interval
95% Prediction Interval
Sqft
Beds
Baths
Predicted
lower
upper
lower
upper
2,490
2
1
466,283.495
335,876.137
596,690.852
244,621.001
687,945.988
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
59,080.2916
Sqft
103.3549
Beds
32,865.3281
Baths
84,118.8784
b-1.
Interpret the coefficient of Sqft.
For every additional square foot, the predicted price of a home increases by $103.35.
Answer: For every additional square foot, the predicted price of a home increases by $103.35, holding number of bedrooms and bathrooms constant.
For every additional square foot, the predicted price of a home increases by $103.35, 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 $32,865.33.
Answer: For every additional bedroom, the predicted price of a home increases by $32,865.33, holding number of square feet and bathrooms constant.
For every additional bedroom, the predicted price of a home increases by $32,865.33, 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 $84,118.88.
Answer: For every additional bathroom, the predicted price of a home increases by $84,118.88, holding number of square feet and bedrooms constant.
For every additional bathroom, the predicted price of a home increases by $84,118.88, holding square foot, number of bedrooms and bathrooms constant.
c.
Predict the price of a 2,490-square-foot home with two bedrooms and one bathrooms. (Round intermediate coefficient values to 2 decimal places. Round your answer to 2 decimal places.)
$ 466,283.50
Regression Analysis
R²
0.684
Adjusted R²
0.655
n
36
R
0.827
k
3
Std. Error
87996.674
Dep. Var.
Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
537,305,216,227.6880
3
179,101,738,742.5630
23.13
3.75E-08
Residual
247,789,270,033.9510
32
7,743,414,688.5610
Total
785,094,486,261.6390
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
59,080.2916
66,283.2400
0.891
.3794
-75,934.2502
194,094.8334
Sqft
103.3549
40.3182
2.563
.0153
21.2293
185.4805
Beds
32,865.3281
24,863.0249
1.322
.1956
-17,778.9963
83,509.6526
Baths
84,118.8784
29,956.8213
2.808
.0084
23,098.8303
145,138.9265
Predicted values for: Price
95% Confidence Interval
95% Prediction Interval
Sqft
Beds
Baths
Predicted
lower
upper
lower
upper
2,490
2
1
466,283.495
335,876.137
596,690.852
244,621.001
687,945.988
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