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 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.

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