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 Square Income Family Senior Family Feet (000s) Size Parent Education 60.8 2,380 68.4 3,640 104.5 3,360 89.3 3,080 2,940 72.2 10 4,480 1254 83.6 133 2,520 4.200 10 2,800 95 a. Develop an appropriate mutiple regression equation using stopwise method. (Use Excel data analysis and enter number of family members first, then their income and delete any insignificant variables. Leave no cells blank be certain to enter "0" wherever required. Round your answers to 2 decimal places.) Step Family T-Value P-Value b. Select all independent variables that should be in the final model. (Select all that apply.) Senior parent Square feet Family size Income Education

Answer 1

a)

family	square feet	income	family size	senior parent	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	1	1	0
5	3080	72.2	4	0	2
6	2940	114.3	1	1	10
7	4480	125.4	6	0	6
8	2520	83.6	3	0	8
9	4200	133.5	5	0	2
10	2800	95.3	3	0	6

Regression Analysis: square feet versus income family ....nt, Education

Stepwise selection of terms

α to enter = 0.15, α to remove = 0.15

Analysis of Variance

Source DF Adj SS Adj MS F-value P-value

Regression 2 4619699 2309849 30.90 0.000

income 1 380692 380692 5.09 0.059

family size 1 962595 962595 12.88 0.009

Error 7 523341 74763

Total 9 5143040

Model Summary

S R-sq R-sq(adj) R-sq(pred)

273.428 89.82% 86.92% 82.48%

Coefficients

Term Coef SE Coef T-value p-value VIF

Constant 713 363 1.96 0.091

income 12.15 5.38 2.26 0.0059 2.08

family size 372 104 3.59 0.009 2.08

Regression Equation

Square feet = 713 + 12.15 income + 372 family size

Fits and Diagnostics for Unusual Observations

Obs Square feet fit Resid Std Resid   

3 3640 3098 542 2.25 R

R large residual

From the above output, the multiple linear regression equation is,

Y = 713 + 12.15 (income, X1) + 372 (Family size, X2)

b)

Family size and income are independent variables. That should be in the final model.