The following data give the selling price, sqare footage, number of bedrooms, an
ID: 3301554 • Letter: T
Question
The following data give the selling price, sqare footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months.
Develop three regression models to predict the selling price based upon each of the other factors individually. Which of these is best?
Use the data from the chart and develop a regression model to predict selling price based on the square footage and number of bedrooms. use this to predict the selling price of 2000 square foot house with 3 bedrroms and compare this model wth the models in the above problem . should the nuber of bedrooms be included in the model? why or why not?
SELLING PRICE SQUARE FOOTAGE BEDROOMS AGE 84000 1670 2 30 79000 1339 2 25 91500 1712 3 30 120000 1840 3 40 127500 2300 3 18 132500 2234 3 30 145000 2311 3 19 164000 2377 3 7 155000 2736 4 10 168000 2500 3 1 172500 2500 4 3 174000 2479 3 3 175000 2400 3 1 177500 3124 4 0 184000 2500 3 2 195500 4062 4 10 195000 2854 3 3Explanation / Answer
Answer:
The following data give the selling price, sqare footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months.
Develop three regression models to predict the selling price based upon each of the other factors individually. Which of these is best?
Predict the selling price from square footage.
Regression Analysis
r²
0.700
n
17
r
0.837
k
1
Std. Error
21360.304
Dep. Var.
SELLING PRICE
ANOVA table
Source
SS
df
MS
F
p-value
Regression
15,966,678,628.6376
1
15,966,678,628.6376
34.99
2.83E-05
Residual
6,843,939,018.4213
15
456,262,601.2281
Total
22,810,617,647.0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
26,532.2361
21,408.3553
1.239
.2343
-19,098.5930
72,163.0653
SQUARE FOOTAGE
51.0272
8.6259
5.916
2.83E-05
32.6416
69.4128
The regression line is
Selling price = 26,532.2361+51.0272*square footage.
The percentage variance explained by the model is 70%.
predict the selling price from bedrooms.
Regression Analysis
r²
0.433
n
17
r
0.658
k
1
Std. Error
29358.339
Dep. Var.
SELLING PRICE
ANOVA table
Source
SS
df
MS
F
p-value
Regression
9,881,936,524.6098
1
9,881,936,524.6098
11.47
.0041
Residual
12,928,681,122.4490
15
861,912,074.8299
Total
22,810,617,647.0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
20,331.6327
38,780.7764
0.524
.6078
-62,327.6356
102,990.9009
BEDROOMS
41,403.0612
12,227.6474
3.386
.0041
15,340.4478
67,465.6746
Selling price = 20,331.6327 +41,403.0612 *bedrooms.
The percentage variance explained by the model is 43.3%.
predict the selling price from age.
Regression Analysis
r²
0.703
n
17
r
-0.838
k
1
Std. Error
21263.218
Dep. Var.
SELLING PRICE
ANOVA table
Source
SS
df
MS
F
p-value
Regression
16,028,750,755.6044
1
16,028,750,755.6044
35.45
2.64E-05
Residual
6,781,866,891.4545
15
452,124,459.4303
Total
22,810,617,647.0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
182,504.7044
7,581.9751
24.071
2.12E-13
166,344.1069
198,665.3018
AGE
-2,424.9137
407.2635
-5.954
2.64E-05
-3,292.9752
-1,556.8522
Selling price = 182,504.7044 -2,424.9137 *age.
The percentage variance explained by the model is 70.3%.
The models by square footage or age are better because the variances explained by the two are almost same.
Use the data from the chart and develop a regression model to predict selling price based on the square footage and number of bedrooms. use this to predict the selling price of 2000 square foot house with 3 bedrroms and compare this model wth the models in the above problem . should the number of bedrooms be included in the model? why or why not?
Regression Analysis
R²
0.700
Adjusted R²
0.657
n
17
R
0.837
k
2
Std. Error
22098.209
Dep. Var.
SELLING PRICE
ANOVA table
Source
SS
df
MS
F
p-value
Regression
15,973,985,883.9289
2
7,986,992,941.9644
16.36
.0002
Residual
6,836,631,763.1300
14
488,330,840.2236
Total
22,810,617,647.0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
24,202.3825
29,211.1020
0.829
.4213
-38,449.2002
86,853.9652
SQUARE FOOTAGE
49.6965
14.0702
3.532
.0033
19.5189
79.8742
BEDROOMS
1,775.1630
14,511.6959
0.122
.9044
-29,349.3291
32,899.6551
Predicted values for: SELLING PRICE
95% Confidence Interval
95% Prediction Interval
SQUARE FOOTAGE
BEDROOMS
Predicted
lower
upper
lower
upper
2,000
3
128,920.898
113,837.835
144,003.961
79,182.841
178,658.955
Selling price = 24,202.3825 +49.6965*square footage +1,775.1630 *bedrooms.
The predicted the selling price of 2000 square foot house with 3 bedrroms = $128920.898.
The percentage variance explained by the model is 70.0%.
The number of bedrooms should not be included in the model because there is no improvement in the percentage of variance explained.
Regression Analysis
r²
0.700
n
17
r
0.837
k
1
Std. Error
21360.304
Dep. Var.
SELLING PRICE
ANOVA table
Source
SS
df
MS
F
p-value
Regression
15,966,678,628.6376
1
15,966,678,628.6376
34.99
2.83E-05
Residual
6,843,939,018.4213
15
456,262,601.2281
Total
22,810,617,647.0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
26,532.2361
21,408.3553
1.239
.2343
-19,098.5930
72,163.0653
SQUARE FOOTAGE
51.0272
8.6259
5.916
2.83E-05
32.6416
69.4128
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