In 2011 home prices and mortgage rates dropped so low that in a number of cities

Question

In 2011 home prices and mortgage rates dropped so low that in a number of cities the monthly cost of owning a home was less expensive than renting. The following data show the average asking rent for 10 markets and the monthly mortgage on the median priced home (including taxes and insurance) for 10 cities where the average monthly mortgage payment was less than the average asking rent (The Wall Street Journal, November 26–27, 2011)

1. Test the significant of the regression coefficient at an alpha level of .05.

2.Test the overall significant of the regression model.

3. Interpret the coefficient of determination.

4. Are there any indications of violations of the general linear model?

City Atlanta Chicago Detroit Jacksonville, Fla. Las Vegas Miami Minneapolis Orlando, Fla. Phoenix St. Louis Rent 840 1062 823 779 796 1071 953 851 762 723 Mortgage 539 1002 626 655 977 776 695 651 654

Explanation / Answer

Here Rent is independent variable ( x) and Mortage is dependent variable ( y).

We can solve this question using excel.

First enter data into excel.

Click on Data -------> Data Analysis --------> Regression ------->

Input

Input Y Range : select y values

Input X Range :select values of x.

Output Range : select any empty cell

---------> ok

We get

1) p-value corresponding to intercept is 0.322379 which is greater than 0.05 so intercept is insignificant.

p-value corresponding to rent is 0.001079 which is less than 0.05 so rent is significant.

2) In ANOVA ther is F statistic = 24.81

and critical value = 0.0011

F statistic > critical value so overall regression model is significant.

3) Coefficient of determination = R^2 = 0.7561

Interpretation: 75.61% variability explained in Mortgage by a model using regressor rent.

4) There is no violation because correlation coefficient is 0.8696 there is a strong relation between rent and mortgage.

SUMMARY OUTPUT Regression Statistics Multiple R 0.869565 R Square 0.756143 Adjusted R Square 0.725661 Standard Error 78.78191 Observations 10 ANOVA df SS MS F Significance F Regression 1 153961.7 153961.7 24.80616 0.001079 Residual 8 49652.72 6206.59 Total 9 203614.4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -197.958 187.695 -1.05468 0.322379 -630.784 234.8671 -630.784 234.8671 Rent 1.069929 0.21482 4.980579 0.001079 0.574553 1.565305 0.574553 1.565305

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