A realtor in Arlington, Massachusetts, is analyzing the relationship between the
ID: 3221952 • 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
569,077
1,731
3
1.5
713,000
2,400
3
3.0
689,000
2,200
3
2.5
737,692
2,925
5
2.0
580,500
2,272
3
1.5
432,692
1,891
3
1.5
454,667
1,786
3
2.5
718,056
2,567
3
2.5
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
537,000
2,907
3
2.5
344,000
1,301
3
1.0
511,000
1,752
3
1.5
714,000
2,418
4
3.0
495,000
1,692
3
2.0
463,000
1,714
3
2.0
639,800
2,310
4
3.0
631,400
2,359
4
3.0
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
620,000
1,675
3
2.0
275,625
954
2
1.0
534,750
2,147
3
3.0
247,500
1,022
2
1.0
412,500
1,831
3
2.0
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 2,417-square-foot home with two bedrooms and two 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
Answer:
Regression Analysis
R²
0.694
Adjusted R²
0.665
n
36
R
0.833
k
3
Std. Error
81258.406
Dep. Var.
Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
478,339,473,029.1640
3
159,446,491,009.7210
24.15
2.35E-08
Residual
211,293,711,621.8080
32
6,602,928,488.1815
Total
689,633,184,650.9720
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
59,457.1434
61,782.6633
0.962
.3431
-66,390.0236
185,304.3103
Sqft
117.2983
39.8542
2.943
.0060
36.1180
198.4786
Beds
15,394.4024
21,070.4143
0.731
.4703
-27,524.6271
58,313.4320
Baths
97,670.8822
26,674.7568
3.662
.0009
43,336.1807
152,005.5837
Predicted values for: Price
95% Confidence Interval
95% Prediction Interval
Sqft
Beds
Baths
Predicted
lower
upper
lower
upper
2,417
2
2
569,097.619
485,368.325
652,826.913
383,606.950
754,588.288
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
59,457.1434
Sqft
117.2983
Beds
15,394.4024
Baths
97,670.8822
b-1.
Interpret the coefficient of Sqft.
For every additional square foot, the predicted price of a home increases by $117.30.
Answer: For every additional square foot, the predicted price of a home increases by $117.30, holding number of bedrooms and bathrooms constant.
For every additional square foot, the predicted price of a home increases by $117.30, 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 $15,394.40.
Answer: For every additional bedroom, the predicted price of a home increases by $15,394.40, holding number of square feet and bathrooms constant.
For every additional bedroom, the predicted price of a home increases by $15,394.40, 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 $97,670.88.
Answer: For every additional bathroom, the predicted price of a home increases by $97,670.88, holding number of square feet and bedrooms constant.
For every additional bathroom, the predicted price of a home increases by $97,670.88, holding square foot, number of bedrooms and bathrooms constant.
c.
Predict the price of a 2,417-square-foot home with two bedrooms and two bathrooms. (Round intermediate coefficient values to 2 decimal places. Round your answer to 2 decimal places.)
Predicted price = $569,097.62
Regression Analysis
R²
0.694
Adjusted R²
0.665
n
36
R
0.833
k
3
Std. Error
81258.406
Dep. Var.
Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
478,339,473,029.1640
3
159,446,491,009.7210
24.15
2.35E-08
Residual
211,293,711,621.8080
32
6,602,928,488.1815
Total
689,633,184,650.9720
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
59,457.1434
61,782.6633
0.962
.3431
-66,390.0236
185,304.3103
Sqft
117.2983
39.8542
2.943
.0060
36.1180
198.4786
Beds
15,394.4024
21,070.4143
0.731
.4703
-27,524.6271
58,313.4320
Baths
97,670.8822
26,674.7568
3.662
.0009
43,336.1807
152,005.5837
Predicted values for: Price
95% Confidence Interval
95% Prediction Interval
Sqft
Beds
Baths
Predicted
lower
upper
lower
upper
2,417
2
2
569,097.619
485,368.325
652,826.913
383,606.950
754,588.288
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