## Question

###### One would suspect that new home construction and sales depend on mortgage interest rates. If interest...

One would suspect that new home construction and sales depend on mortgage interest rates. If interest rates are high, fewer people will be able to afford to borrow the funds necessary to finance the purchase of a new home. Builders are aware of this fact, therefore when interest rates are high, they will be less inclined to build new homes. A question of interest is “If interest rates go up by 1% by how much does home construction fall?”. Data on the 30 year fixed mortgage rate, housing starts (thousands), and houses sold (thousands) are contained in the file house starts.csv. There are 184 monthly observations from January 1990 to April 2005. Answer the following questions using R & Rstudio.

(a) Estimate a linear relationship of STARTS on the FIXED RATE. Interpret the intercept and slope.

(b) Obtain a scatter plot of STARTS against the FIXED RATE. Plot the fitted regression line along with the scatter plot.

(c) Construct a 95% interval estimates for the slope. Interpret the CI for the slope. What does it mean that we are “95% confident”?

(d) Is there evidence to suggest that there is a significant relationship between the 30 year fixed rate (FIXED RATE) and the house starts (STARTS)? Use a level of significance of 5%.

i. set up the null and alternative hypothesis

ii. show a sketch of the rejection region

iii. state your conclusion

iv. calculate the p-value for this test and perform the test using the p-value approach.

(e) Test that if the interest rate increases by 1%, then house starts will fall by 150,000. Use a level of significance of 5%.

(f) Comment on the goodness of fit of your model. Make sure to discuss both R2 and adjusted R2.