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The standard error of estimate for Smith’s regression is closest to:

 A) 0.53
 B) 0.16
 C) 0.56

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) Only correct on one concern and incorrect on the other.
 B) Correct on both Concerns.
 C) Incorrect 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 t-statistics 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 t-statistics to be too low. However, contrary to Smith’s concern, multicollinearity has no effect on the F-statistic. (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 two-step 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 two-step ahead forecast for change in foreclosure share only.
 B) Smith is correct on the mean-reverting 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 t-1 lagged value.

So, the one-step ahead forecast equals 0.30%. The two-step ahead (%) forecast is derived by substituting 0.30 into the equation.

ΔForeclosure Sharet+1 = 0.05 + 0.25(0.30) = 0.125

Therefore, the two-step 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)

Consider the following estimated regression equation, with calculated t-statistics of the estimates as indicated:

AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INSt

with a PI calculated t-statstic of 0.45, a TEEN calculated t-statstic of 2.2, and an INS calculated t-statstic of 0.63.

The equation was estimated over 40 companies. Using a 5% level of significance, which of the independent variables significantly different from zero?

 A) PI and INS only.
 B) PI only.
 C) TEEN only.

The critical t-values for 40-3-1 = 36 degrees of freedom and a 5% level of significance are ± 2.028. Therefore, only TEEN is statistically significant.

Jacob Warner, CFA, is evaluating a regression analysis recently published in a trade journal that hypothesizes that the annual performance of the S& 500 stock index can be explained by movements in the Federal Funds rate and the U.S. Producer Price Index (PPI). Which of the following statements regarding his analysis is most accurate?

 A) If the p-value of a variable is less than the significance level, the null hypothesis can be rejected.
 B) If the p-value of a variable is less than the significance level, the null hypothesis cannot be rejected.
 C) If the t-value of a variable is less than the significance level, the null hypothesis cannot be rejected.

The p-value is the smallest level of significance for which the null hypothesis can be rejected. Therefore, for any given variable, if the p-value of a variable is less than the significance level, the null hypothesis can be rejected and the variable is considered to be statistically significant.

Which of the following statements most accurately interprets the following regression results at the given significance level?

 Variable p-value Intercept 0.0201 X1 0.0284 X2 0.0310 X3 0.0143

 A) The variables X1 and X2 are statistically significantly different from zero at the 2% significance level.
 B) The variable X2 is statistically significantly different from zero at the 3% significance level.
 C) The variable X3 is statistically significantly different from zero at the 2% significance level.

The p-value is the smallest level of significance for which the null hypothesis can be rejected. An independent variable is significant if the p-value is less than the stated significance level. In this example, X3 is the variable that has a p-value less than the stated significance level.

When interpreting the results of a multiple regression analysis, which of the following terms represents the value of the dependent variable when the independent variables are all equal to zero?

 A) Slope coefficient.
 B) Intercept term.
 C) p-value.

The intercept term is the value of the dependent variable when the independent variables are set to zero.

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