Housing industry analyst Elaine Smith has been assigned the task of forecasting housing foreclosures. Specifically, Smith is asked to forecast the percentage of outstanding mortgages that will be foreclosed upon in the coming quarter. Smith decides to employ multiple linear regression and time series analysis.
Besides constructing a forecast for the foreclosure percentage, Smith wants to address the following two questions:
Research Question 1:  Is the foreclosure percentage significantly affected by shortterm interest rates?  Research Question 2:  Is the foreclosure percentage significantly affected by government intervention policies? 
Smith contends that adjustable rate mortgages often are used by higher risk borrowers and that their homes are at higher risk of foreclosure. Therefore, Smith decides to use shortterm interest rates as one of the independent variables to test Research Question 1.
To measure the effects of government intervention in Research Question 2, Smith uses a dummy variable that equals 1 whenever the Federal government intervened with a fiscal policy stimulus package that exceeded 2% of the annual Gross Domestic Product. Smith sets the dummy variable equal to 1 for four quarters starting with the quarter in which the policy is enacted and extending through the following 3 quarters. Otherwise, the dummy variable equals zero.
Smith uses quarterly data over the past 5 years to derive her regression. Smith’s regression equation is provided in Exhibit 1:
Exhibit 1: Foreclosure Share Regression Equationforeclosure share = b0 + b1(ΔINT) + b2(STIM) + b3(CRISIS) + ε
where:  <P td > [td=1,1,700]<P td > [/td]  Foreclosure share  =  the percentage of all outstanding mortgages foreclosed upon during the quarter  ΔINT  =  the quarterly change in the 1year Treasury bill rate (e.g., ΔINT = 2 for a two percentage point increase in interest rates)  STIM  =  1 for quarters in which a Federal fiscal stimulus package was in place  CRISIS  =  1 for quarters in which the median house price is one standard deviation below its 5year moving average 
The results of Smith’s regression are provided in Exhibit 2:Exhibit 2: Foreclosure Share Regression Results Variable  Coefficient  tstatistic 
Intercept  3.00  2.40 
ΔINT  1.00  2.22 
STIM  2.50  2.10 
CRISIS  4.00  2.35 
The ANOVA results from Smith’s regression are provided in Exhibit 3:Exhibit 3: Foreclosure Share Regression Equation ANOVA Table Source  Degrees of Freedom  Sum of Squares  Mean Sum of Squares 
Regression 
3 
15 
5.0000 
Error 
16 
5 
0.3125 
Total 
19 
20 

Smith expresses the following concerns about the test statistics derived in her regression:
Concern 1:  If my regression errors exhibit conditional heteroskedasticity, my tstatistics will be underestimated.  Concern 2:  If my independent variables are correlated with each other, my Fstatistic will be overestimated. 
Before completing her analysis, Smith runs a regression of the changes in foreclosure share on its lagged value. The following regression results and autocorrelations were derived using quarterly data over the past 5 years (Exhibits 4 and 5, respectively):
Exhibit 4. Lagged Regression Results
Δ foreclosure sharet = 0.05 + 0.25(Δ foreclosure sharet–1)Exhibit 5. Autocorrelation Analysis Lag  Autocorrelation  tstatistic  1  0.05  0.22  2  0.35  1.53  3  0.25  1.09  4  0.10  0.44 
Exhibit 6 provides critical values for the Student’s tDistributionExhibit 6: Critical Values for Student’s tDistribution
[td=4,1,237]Area in Both Tails Combined  Degrees of Freedom  20%  10%  5%  1%  16  1.337  1.746  2.120  2.921  17  1.333  1.740  2.110  2.898  18  1.330  1.734  2.101  2.878  19  1.328  1.729  2.093  2.861  20  1.325  1.725  2.086  2.845 
Using a 1% significance level, which of the following is closest to the lower bound of the lower confidence interval of the ΔINT slope coefficient?
The appropriate confidence interval associated with a 1% significance level is the 99% confidence level, which equals;
slope coefficient ± critical tstatistic (1% significance level) × coefficient standard error
The standard error is not explicitly provided in this question, but it can be derived by knowing the formula for the tstatistic:
From Exhibit 1, the ΔINT slope coefficient estimate equals 1.0, and its tstatistic equals 2.22. Therefore, solving for the standard error, we derive:
The critical value for the 1% significance level is found down the 1% column in the ttables provided in Exhibit 6. The appropriate degrees of freedom for the confidence interval equals n – k – 1 = 20 – 3 – 1 = 16 (k is the number of slope estimates = 3). Therefore, the critical value for the 99% confidence interval (or 1% significance level) equals 2.921.
So, the 99% confidence interval for the ΔINT slope coefficient is:
1.00 ± 2.921(0.450): lower bound equals 1 – 1.316 and upper bound 1 + 1.316
or (0.316, 2.316).
(Study Session 3, LOS 12.c)
Based on her regression results in Exhibit 2, using a 5% level of significance, Smith should conclude that: A)
 stimulus packages have significant effects on foreclosure percentages, but housing crises do not have significant effects on foreclosure percentages. 
 B)
 stimulus packages do not have significant effects on foreclosure percentages, but housing crises do have significant effects on foreclosure percentages. 
 C)
 both stimulus packages and housing crises have significant effects on foreclosure percentages. 

The appropriate test statistic for tests of significance on individual slope coefficient estimates is the tstatistic, which is provided in Exhibit 2 for each regression coefficient estimate. The reported tstatistic equals 2.10 for the STIM slope estimate and equals 2.35 for the CRISIS slope estimate. The critical tstatistic for the 5% significance level equals 2.12 (16 degrees of freedom, 5% level of significance).
Therefore, the slope estimate for STIM is not statistically significant (the reported tstatistic, 2.10, is not large enough). In contrast, the slope estimate for CRISIS is statistically significant (the reported tstatistic, 2.35, exceeds the 5% significance level critical value). (Study Session 3, LOS 12.a)
The standard error of estimate for Smith’s regression is closest to:
The formula for the Standard Error of the Estimate (SEE) is:
The SEE equals the standard deviation of the regression residuals. A low SEE implies a high R2. (Study Session 3, LOS 12.f)
Is Smith correct or incorrect regarding Concerns 1 and 2? A)
 Incorrect on both Concerns. 
 B)
 Only correct on one concern and incorrect on the other. 
 C)
 Correct on both Concerns. 

Smith’s Concern 1 is incorrect. Heteroskedasticity is a violation of a regression assumption, and refers to regression error variance that is not constant over all observations in the regression. Conditional heteroskedasticity is a case in which the error variance is related to the magnitudes of the independent variables (the error variance is “conditional” on the independent variables). The consequence of conditional heteroskedasticity is that the standard errors will be too low, which, in turn, causes the tstatistics to be too high. Smith’s Concern 2 also is not correct. Multicollinearity refers to independent variables that are correlated with each other. Multicollinearity causes standard errors for the regression coefficients to be too high, which, in turn, causes the tstatistics to be too low. However, contrary to Smith’s concern, multicollinearity has no effect on the Fstatistic. (Study Session 3, LOS 12.i)
The most recent change in foreclosure share was +1 percent. Smith decides to base her analysis on the data and methods provided in Exhibits 4 and 5, and determines that the twostep ahead forecast for the change in foreclosure share (in percent) is 0.125, and that the mean reverting value for the change in foreclosure share (in percent) is 0.071. Is Smith correct? A)
 Smith is correct on the twostep ahead forecast for change in foreclosure share only. 
 B)
 Smith is correct on the meanreverting level for forecast of change in foreclosure share only. 
 C)
 Smith is correct on both the forecast and the mean reverting level. 

Forecasts are derived by substituting the appropriate value for the period t1 lagged value.
So, the onestep ahead forecast equals 0.30%. The twostep ahead (%) forecast is derived by substituting 0.30 into the equation.
ΔForeclosure Sharet+1 = 0.05 + 0.25(0.30) = 0.125
Therefore, the twostep ahead forecast equals 0.125%.
(Study Session 3, LOS 13.d)
Assume for this question that Smith finds that the foreclosure share series has a unit root. Under these conditions, she can most reliably regress foreclosure share against the change in interest rates (ΔINT) if: A)
 ΔINT does not have unit root. 
 B)
 ΔINT has unit root and is not cointegrated with foreclosure share. 
 C)
 ΔINT has unit root and is cointegrated with foreclosure share. 

The error terms in the regressions for choices A, B, and C will be nonstationary. Therefore, some of the regression assumptions will be violated and the regression results are unreliable. If, however, both series are nonstationary (which will happen if each has unit root), but cointegrated, then the error term will be covariance stationary and the regression results are reliable. (Study Session 3, LOS 13.k) 