A real estate developer wishes to study the relationship between the size of hom
ID: 2923020 • Letter: A
Question
A real estate developer wishes to study the relationship between the size of home a client will purchase (in square feet) and other variables. Possible independent variables include the family income, family size, whether there is a senior adult parent living with the family (1 for yes, 0 for no), and the total years of education beyond high school for the husband and wife. The sample information is reported below. Family Square Feet Income (000s) Family Size Senior Parent Education 1 2,790 68.4 3 0 4 2 2,380 68.4 2 1 6 3 3,576 104.5 3 0 7 4 3,154 53.5 3 1 0 5 3,195 94.1 5 0 2 6 3,142 114 3 1 10 7 4,480 125.4 6 0 6 8 2,520 83.6 3 0 8 9 4,200 133 5 0 2 10 2,800 95 3 0 6 Picture Click here for the Excel Data File a. Develop an appropriate multiple regression equation using stepwise method. (Use excel data analysis and enter number of family members first, then their income and delete any insignificant variables. Round P-value to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Round the Constant, Income values to 1 decimal place and T-value, R2, R2(adj) to 2 decimal places.) Step 1 2 Constant Family T-Value P-Value Income T-Value P-Value S R2 % % R2(adj) % %
Explanation / Answer
1)
We first run keeping just the family_size
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.833
R Square
0.693
Adjusted R Square
0.655
Standard Error
403.344
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
2941073.669
2941073.669
18.078
0.003
Residual
8
1301490.431
162686.304
Total
9
4242564.100
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1596.750
403.344
3.959
0.004
666.637
2526.863
Family Size
451.931
106.290
4.252
0.003
206.824
697.037
2)
Now we run keeping the family size and income
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.876
R Square
0.767
Adjusted R Square
0.701
Standard Error
375.420
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
2
3255984.258
1627992.129
11.551
0.006
Residual
7
986579.842
140939.977
Total
9
4242564.100
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1165.747
473.370
2.463
0.043
46.405
2285.090
Income (000s)
9.691
6.483
1.495
0.179
-5.639
25.021
Family Size
318.640
133.187
2.392
0.048
3.702
633.579
3)
Now we run keeping family size, income and senior
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.886
R Square
0.786
Adjusted R Square
0.678
Standard Error
389.415
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
3
3332699.861
1110899.954
7.326
0.020
Residual
6
909864.239
151644.040
Total
9
4242564.100
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
920.061
600.346
1.533
0.176
-548.933
2389.055
Income (000s)
10.194
6.762
1.508
0.182
-6.352
26.740
Family Size
355.137
147.374
2.410
0.053
-5.474
715.748
Senior
223.301
313.951
0.711
0.504
-544.909
991.510
4)
Finally, we run keeping all the variables: -
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.905
R Square
0.820
Adjusted R Square
0.675
Standard Error
391.299
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
4
3476988.767
869247.192
5.677
0.042
Residual
5
765575.333
153115.067
Total
9
4242564.100
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1129.252
640.585
1.763
0.138
-517.425
2775.930
Income (000s)
16.496
9.397
1.755
0.140
-7.660
40.652
Family Size
219.775
203.405
1.080
0.329
-303.095
742.644
Senior
201.159
316.293
0.636
0.553
-611.899
1014.216
Parent Education
-60.298
62.114
-0.971
0.376
-219.968
99.373
Here, we can see that the p-value of all the other variables except Family Size go above 0.05 and hence those models are not significant. Only Family Size turns out to be significant
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.833
R Square
0.693
Adjusted R Square
0.655
Standard Error
403.344
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
2941073.669
2941073.669
18.078
0.003
Residual
8
1301490.431
162686.304
Total
9
4242564.100
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1596.750
403.344
3.959
0.004
666.637
2526.863
Family Size
451.931
106.290
4.252
0.003
206.824
697.037