A real estate developer wishes to study the relationship between the size of hom
ID: 3064611 • 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 Size Income Parent Education 60.8 68.4 104.5 89.3 72.2 2,380 3,640 3,360 3,080 2,940 4,480 2,520 4,200 2,800 114 10 125.4 83.6 133 10 95 Develop an estimated regression equation with size of a home as a dependent variable and the others as the independent variables. a. b. Does the overall model a good fit for the data? Explain your reasoning. c. Is the overall relationship significant? Why or why not? d. How would you interpret the coefficient involving senior parent? e. Which of the independent variables are significant? What would you do if some variables are found to be not significant? Are there any outliers? Why or why not? What will be the predicted size for a household whose income is $100,000, family size is 3 with no senior parent and an education level of 6? f. &.Explanation / Answer
We have given dependent variable is square feet and independent variables are family size , income, senior parent and education.
This is the problem of multiple regression.
We can do multiple regression in EXCEL.
steps :
ENTER data into EXCEL sheet --> Data --> Data Analysis --> Regression --> ok -->Input Y Range : Select family size range --> Input X Range : select all the variables --> Click on labels --> Output Range : Select one empty cell --> ok
a) The regression equation is,
family size = 879.39 + 16.33*square feet + -83.05*income - 38.60*senior parent + 274.68*education
c) Here we have to test ,
H0 : Bj = 0 Vs H1 : Bj not= 0
where Bj is population slope for jth independent variable.
Assume alpha = level of significance = 0.05
Here test statistic follows F-distribution .
F = 13.19
P-value = 0.007
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : Atleast one of the slope is differ than 0.
i.e. Overall model is significant.
d) Interpretation of coefficient of senior parent.
Coefficient of senior parent = -83.05
If we fix square feet, income and education then one unit change in senior parent will be 83.05 unit decrease in family size.
e) Here we have to test the hypothesis that,
H0 : B = 0 Vs H1 : B not= 0
where B is population slope for independent variable.
Assume alpha = 0.05
The test statistic follows t-distribution.
We say that the independent variable is significant iff P-value for independent variable is less than alpha.
We can say that the variable all the variables are insignificant because P-value for each variable is greator than alpha.
Therefore all the variables are insignificant.
We drop insignificant variables from the model and add significant variables.
g) Here we have to find family size when
income = 100
family size= 3
senior parent = 0
and education level = 6
This we can find using regression equation.
family size = 879.39 + 16.33*income -83.05*senior parent - 38.60*education + 274.68*family size
= 879.39+16.33*100-83.05*0 -38.60*6 + 274.68*3 = 3104.68
SUMMARY OUTPUT Regression Statistics Multiple R 0.955733725 R Square 0.913426953 Adjusted R Square 0.844168515 Standard Error 298.412012 Observations 10 ANOVA df SS MS F Significance F Regression 4 4697791 1174448 13.18867394 0.007241069 Residual 5 445248.6 89049.73 Total 9 5143040 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 879.3937802 439.1037 2.002702 0.101588361 -249.3581037 2008.145664 -249.3581037 2008.145664 income 16.32862748 7.39776 2.207239 0.078376292 -2.687919854 35.34517481 -2.687919854 35.34517481 senior parent -83.04632698 217.7626 -0.38136 0.718602689 -642.8227954 476.7301415 -642.8227954 476.7301415 education -38.60445866 42.87598 -0.90038 0.409189755 -148.820664 71.61174671 -148.820664 71.61174671 family size 274.6823214 153.6518 1.787693 0.133862071 -120.2922893 669.6569322 -120.2922893 669.6569322