12. A real estate developer wishes to study the relationship between the size of
ID: 3134695 • Letter: 1
Question
12. 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.
Develop an appropriate multiple regression equation. Which independent variables would you include in the final regression equation? Use the stepwise method.
FAMILY SQUARE FEET INCOME (000s) Family Size Senior Parent Education 1 2240 60.8 2 0 4 2 2380 68.4 2 1 6 3 3640 104.5 3 0 7 4 3360 89.3 4 1 0 5 3080 72.2 4 0 2 6 2940 114 3 1 10 7 4480 125.4 6 0 6 8 2520 83.6 3 0 8 9 4200 133 5 0 2 10 2800 95 3 0 6Explanation / Answer
We are give that 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 amd square feet is depecdent variable.
Mulitple regression using MINITAB.
steps :
Input all the data in MINITAB sheet --> Stat --> Regression --> Regression --> Response : square feet --> And predictors : select all the remaining variables --> Result : select second option --> ok --> ok
The regression equation is
SQUARE FEET = 879 + 16.3 INCOME (000s) + 275 Family Size - 83 Senior Parent
- 38.6 Education
Predictor Coef SE Coef T P
Constant 879.4 439.1 2.00 0.102
INCOME (000s) 16.329 7.398 2.21 0.078
Family Size 274.7 153.7 1.79 0.134
Senior Parent -83.0 217.8 -0.38 0.719
Education -38.60 42.88 -0.90 0.409
S = 298.412 R-Sq = 91.3% R-Sq(adj) = 84.4%
Analysis of Variance
Source DF SS MS F P
Regression 4 4697791 1174448 13.19 0.007
Residual Error 5 445249 89050
Total 9 5143040
Multiple regression equation is,
SQUARE FEET = 879 + 16.3 INCOME (000s) + 275 Family Size - 83 Senior Parent
- 38.6 Education
The test of hypothesis is,
H0 : Bj = 0 Vs H1 : Bj 0
Where Bj is Population regression coefficient.
Test statistic F = 13.19
P-value = 0.007
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : Population regression coefficient is differ than 0.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.