A realtor in Arlington, Massachusetts, is analyzing the relationship between the
ID: 3313114 • 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
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
645,000
2,524
3
2.0
625,000
2,732
4
2.5
620,000
2,436
4
3.5
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
546,000
1,792
3
2.0
540,000
1,488
3
1.5
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
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
399,000
1,383
4
1.0
380,000
1,344
4
2.0
380,000
1,272
3
1.0
375,900
2,275
5
1.0
372,000
1,005
2
1.0
367,500
1,272
3
1.0
356,500
1,431
2
2.0
330,000
1,362
3
1.0
330,000
1,465
3
1.0
307,500
850
1
1.0
Estimate the model Price = 0 + 1Sqft + 2Beds + 3Baths + .
Predict the price of a 2,500 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
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
645,000
2,524
3
2.0
625,000
2,732
4
2.5
620,000
2,436
4
3.5
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
546,000
1,792
3
2.0
Explanation / Answer
Solution:
First of all we have to find the multiple regression model for the prediction of the prices for homes based on independent variables or explanatory variables such as square foot area of the home, number of bedrooms, and number of bathrooms. Required regression output by using excel is given as below:
Regression Statistics
Multiple R
0.850689001
R Square
0.723671776
Adjusted R Square
0.697766005
Standard Error
74984.98417
Observations
36
ANOVA
df
SS
MS
F
Significance F
Regression
3
4.71211E+11
1.5707E+11
27.9347709
4.59052E-09
Residual
32
1.79928E+11
5622747851
Total
35
6.51138E+11
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
153348.2664
57141.79374
2.6836446
0.01143313
36954.24193
269742.2909
Sqft
95.85594255
35.39974687
2.70781435
0.0107794
23.74901811
167.962867
Beds
556.8906656
20280.31276
0.02745967
0.97826365
-40752.75444
41866.53577
Baths
92022.91259
25012.29756
3.67910674
0.00085465
41074.52992
142971.2953
Part a
The estimated model for dependent variable price is given as below:
Price = 153348.2664 + 95.85594255*Sqft + 556.8906656*Beds + 92022.91259*Baths
Table for coefficients is given as below:
Coefficients
Intercept
153348.2664
Sqft
95.85594255
Beds
556.8906656
Baths
92022.91259
Part c
Here, we have to predict the value for price for a given values as below:
Square foot = Sqft = 2500
Beds = 3
Baths = 2
Price = 153348.2664 + 95.85594255*Sqft + 556.8906656*Beds + 92022.91259*Baths
Price = 153348.2664 + 95.85594255*2500 + 556.8906656*3 + 92022.91259*2
Price = 578704.62
Predicted price = $578704.62
Regression Statistics
Multiple R
0.850689001
R Square
0.723671776
Adjusted R Square
0.697766005
Standard Error
74984.98417
Observations
36
ANOVA
df
SS
MS
F
Significance F
Regression
3
4.71211E+11
1.5707E+11
27.9347709
4.59052E-09
Residual
32
1.79928E+11
5622747851
Total
35
6.51138E+11
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
153348.2664
57141.79374
2.6836446
0.01143313
36954.24193
269742.2909
Sqft
95.85594255
35.39974687
2.70781435
0.0107794
23.74901811
167.962867
Beds
556.8906656
20280.31276
0.02745967
0.97826365
-40752.75444
41866.53577
Baths
92022.91259
25012.29756
3.67910674
0.00085465
41074.52992
142971.2953
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