A local real estate developer wishes to study the relationship between the size

Question

A local 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 contained in the file RealEstateChapter14. Mr. Robert Bostick is a real estate broker who asked you to produce a model to predict the square footage a potential buyer would purchase. Based on the data in the file RealEstateChapter14, is the overall regression model significant if = 0.05? Write a memorandum to Mr. Bostick explaining if the model is significant and if so, which variables make a difference in the size of home a client might purchase Family Square Feet Income (000s)

****Please use stepwise regression and fully explain how and why you got the answer.

Family Square Feet Income (000s) Family Size Senior Parent Education 1 2,771 46.9 3 0 4 2 2,380 68.4 2 1 6 3 3,283 104.5 3 0 7 4 3,119 94.1 3 1 0 5 3,217 50.6 3 0 2 6 2,595 114 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

Explanation / Answer

The Regression equation is

y=a+bx1+cx2+dx3+ex4

From Excel

The fitted Regression is

y= 1650.1 +4.46 x1 +431.3 x2 -156.1 x3 -67.1 x4

Now we test whether the model is best or not

Here P=0.0037 and alpha=0.05

P<alpha we reject the null hypothesis. Hence results are not significant

SUMMARY OUTPUT Regression Statistics Multiple R 0.96655 R Square 0.93422 Adjusted R Square 0.881595 Standard Error 242.1416 Observations 10 ANOVA df SS MS F Significance F Regression 4 4163520 1040880 17.7526 0.003702 Residual 5 293162.7 58632.55 Total 9 4456683 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1650.146 342.2616 4.821301 0.004793 770.3347 2529.957 Income (000s) 4.46485 4.564738 0.978118 0.372937 -7.26918 16.19888 Family Size 431.3283 125.6296 3.433333 0.018569 108.3871 754.2696 Senior Parent -156.136 212.3397 -0.73531 0.495171 -701.973 389.7004 Education -67.0742 29.46766 -2.2762 0.071879 -142.823 8.674819

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