A real estate developer wishes to study the relationship between the size of hom
ID: 3021265 • 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.
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.)
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.
Explanation / Answer
For stepwise method, we first need to model all the independent variables against the dependent variable as shown below -
1)
The first regression output considering all the independent variables from excel is as shown below -
2)
Now, note that the p-value for the variable 'Senior Parent' is much greater than the required level of significance i.e. 0.05. Hence, we need to remove this variable from the model as our first step. And then we run the regression model agian with the remaining variables to get the following output -
3)
Again, note that the p-value corresponding to the variable "Education" is greater than the significance level of 0.05 and hence this variable is insignificant for the multiple regression model. Hence, we would remove it from the model as our second step. But as we are asked to make an approximate model, so the p-value of 0.061 can be accepted as it is not much higher than 0.05.
Also the R-square value decreases if we remove the variable "Education" and it leads to the higher p-value of the variable "Income" as shown below -
So, it would be better if we accept the p-value of 0.061 for the variable "Education" so that we get a better approximate model.
Hence, we can fill the required values in the table as shown -
SUMMARY OUTPUT Regression Statistics Multiple R 0.943910301 R Square 0.890966657 Adjusted R Square 0.803739982 Standard Error 314.4888704 Observations 10 ANOVA df SS MS F Significance F Regression 4 4040942.652 1010235.663 10.21438291 0.012669322 Residual 5 494516.2481 98903.24962 Total 9 4535458.9 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1519.778359 539.5202219 2.816907129 0.037243978 132.897477 2906.659242 Income (000s) 12.32901134 5.179368317 2.380408302 0.063133015 -0.984978773 25.64300146 Family Size 295.8881934 145.1557789 2.038418282 0.097064182 -77.24661514 669.0230018 Senior Parent -44.88879217 264.1648583 -0.16992719 0.871728921 -723.9461786 634.1685943 Education -98.64102621 46.82217508 -2.106716017 0.088991758 -219.001259 21.71920656Related Questions
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