Question

One would expect 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 well aware of this fact and, when mortgage rates are high, they will be less inclined to build new homes. Based upon a sample of 184 monthly observations from January, 1990 to April, 2005, you have estimated the following regression: STARTS = B1 + B FIXED_RATE: + Es Where STARTS is defined as the number of housing starts in time periodi measures in '000, and FIXED_RATE is defined as the fixed mortgage interest rate measured as a percentage. Given the following regression output, answer the following questions: (26 points) Pay attention to the unit of measurement in your analysis. Model 1: OLS, using observations 1-184 Dependent variable: STARTS Coeficient 2992.74 -194.233 Std. Error 78.9515 10.2061 t-ratio 37.9061 -19.0312 p-value <0.00001 *** <0.00001 *** const FIXED_RATE Mean dependent var Sum squared resid R-squared F(1,182) Log-likelihood Schwarz criterion 1506.696 4558359 0.665556 362.1861 -1191.898 2394.226 S.D. dependent var S.E. of regression Adjusted R-squared P-value(F) Akaike criterion Hanran-Quinn 272.9083 158.2590 0.663718 3.73e-45 2387.796 2390.402

Answer 1

SOLUTION A: The estimated regression equation from the given table is

$\mathbf{\widehat{y}= 2992.74-194.233*Fixed rate}$

(78.9515) (10.2061)

Where number in brackets are Standard error

SOLUTION B: Economic Interpretation of Slope: Here slope is 194.233 which means that for a percentage increased in fixed mortgage interest rate then housing starts will decrease by 194233  in given time period.

c: From the given statement we need to TEST

NULL HYPOTHESIS H0:
82 = 0

ALTERNATIVE HYPOTHESIS Ha:$\beta 2< 0$

Level of significance= 0.05

Test statistic= b2 coefficient /S.E

= -194.233/10.2061

t = -19.0311

P value= 0.0000

Since P value smaller than the level of significance 0.05 therefore SIGNIFICANT.

DECISION: REJECT NULL HYPOTHESIS H0.

Conclusion: We have sufficient evidence to show that if the 30 year old fixed mortgage rate increase by 1% then housing rate will start decreasing by 150,000.

SOLUTION D: 95% confidence interval of $\beta 2$

$\widehat{\beta2}\pm tc*s.e$

degrees of freedom= 182-2=180

t critical value = 1.97

$-194.233\pm 1.97*10.2061$

$-194.233\pm 20.106$

is 95% confidence interval of $\beta 2$

We are 95% confident that population $\beta 2$ is within this confidence interval.

e) The estimated regression equation from the given table is

$\mathbf{\widehat{y}= 2992.74-194.233*Fixed rate}$

Fixed rate=6%

$\mathbf{\widehat{y}= 2992.74-194.233*6}$

$\mathbf{1827.342}$ thousand dollars.