Holding the inflation surprise variable constant, the coefficient on GDP growth of 1.85 is best interpreted as meaning that:
A. a one-unit increase in GDP growth is associated with an increase of 1.85 units in fund excess return, on average
B. GDP growth explains 1.85% of the variation in fund excess return
C. a one-unit increase in GDP growth causes fund excess return to increase by exactly 1.85 units
D. the correlation between GDP growth and fund excess return is 1.85
Show answer and reasoning
Correct answer: A. a one-unit increase in GDP growth is associated with an increase of 1.85 units in fund excess return, on average
- B: This describes what R-squared measures, not what a slope coefficient measures.
- C: Regression coefficients describe an average statistical association from the estimated model, not a proven causal effect, and this option overstates certainty with the word 'exactly.'
- D: A correlation coefficient is bounded between -1 and 1, so 1.85 cannot be a correlation; the coefficient is a slope, not a correlation.
Source: CFA Program Curriculum, Quantitative Methods, "Multiple Regression" -- Interpreting coefficients in a multiple regression model (https://www.cfainstitute.org/insights/professional-learning/refresher-readings)
Based on the regression output, is the coefficient on the inflation surprise variable statistically significant at the 5% level?
A. Yes, because its t-statistic of -1.90 is more extreme than the critical value of -2.00
B. No, because its t-statistic of -1.90 is less extreme in absolute value than the critical value of 2.00
C. Yes, because its coefficient is negative, which is always significant in a regression
D. No, because its standard error of 0.50 exceeds its coefficient of -0.95
Show answer and reasoning
Correct answer: B. No, because its t-statistic of -1.90 is less extreme in absolute value than the critical value of 2.00
t-statistic = coefficient / standard error = -0.95 / 0.50 = -1.90. |-1.90| < 2.00 (critical value), so fail to reject the null hypothesis that the coefficient equals zero.
- A: This reverses the comparison: |-1.90| = 1.90 is smaller than 2.00 in absolute value, so the coefficient fails the significance test rather than passing it.
- C: The sign of a coefficient has no bearing on statistical significance; significance depends on the ratio of the coefficient to its standard error relative to the critical value.
- D: Comparing the standard error to the coefficient directly is not the correct significance test; the correct test compares the t-statistic (coefficient divided by standard error) to the critical t-value.
Source: CFA Program Curriculum, Quantitative Methods, "Multiple Regression" -- Hypothesis testing of individual regression coefficients (https://www.cfainstitute.org/insights/professional-learning/refresher-readings)
Which of the following is closest to the F-statistic for testing the null hypothesis that all slope coefficients are jointly equal to zero, and what does it imply?
A. F = 20.64; reject the null hypothesis, so the regression has significant explanatory power overall
B. F = 2.98; fail to reject the null hypothesis
C. F = 0.42; reject the null hypothesis
D. F = 1.85; fail to reject the null hypothesis
Show answer and reasoning
Correct answer: A. F = 20.64; reject the null hypothesis, so the regression has significant explanatory power overall
F = (R^2/k) / [(1 - R^2)/(n - k - 1)] = (0.42/2) / [(0.58)/57] = 0.21 / 0.010175 = 20.64. Since 20.64 > the critical F-value of approximately 3.15 (2, 57 degrees of freedom, 5% significance), reject the null hypothesis that all slope coefficients are zero.
- B: 2.98 is the t-statistic on GDP growth, not the F-statistic for overall regression significance; it also does not use the correct F-test decision rule.
- C: 0.42 is the R-squared value, not the F-statistic; substituting R-squared directly for F conflates two different statistics.
- D: 1.85 is the GDP growth coefficient, not the F-statistic, and the computed F-statistic exceeds the critical value of 3.15, so the null should be rejected, not failed to be rejected.
Source: CFA Program Curriculum, Quantitative Methods, "Multiple Regression" -- F-test of overall regression significance (https://www.cfainstitute.org/insights/professional-learning/refresher-readings)
Shah is concerned that the regression residuals may exhibit heteroskedasticity. If present but left uncorrected, heteroskedasticity most directly causes which of the following problems?
A. Biased and inconsistent regression coefficients
B. Incorrect standard errors, which can lead to invalid t-statistics and hypothesis tests
C. An R-squared value that is always overstated
D. A violation of the assumption that the independent variables are measured without error
Show answer and reasoning
Correct answer: B. Incorrect standard errors, which can lead to invalid t-statistics and hypothesis tests
- A: Heteroskedasticity alone does not bias the coefficient estimates themselves; ordinary least squares coefficients remain unbiased and consistent, but the standard errors become unreliable.
- C: Heteroskedasticity does not have a predictable directional effect on R-squared; the coefficient of determination is not systematically overstated by unequal error variance.
- D: This describes a measurement error problem in the independent variables, which is a different violation of regression assumptions than heteroskedasticity, which concerns the variance of the error term.
Source: CFA Program Curriculum, Quantitative Methods, "Multiple Regression" -- Violations of regression assumptions: heteroskedasticity (https://www.cfainstitute.org/insights/professional-learning/refresher-readings)
Using the auxiliary regression R-squared of 0.81, the variance inflation factor (VIF) for the debt-to-EBITDA variable is closest to:
A. 0.81
B. 1.23
C. 5.26
D. 8.10
Show answer and reasoning
Correct answer: C. 5.26
VIF = 1 / (1 - R^2_j) = 1 / (1 - 0.81) = 1 / 0.19 = 5.26.
- A: This is simply the auxiliary regression's R-squared restated, not the VIF formula applied to that R-squared.
- B: This value results from computing 1/0.81 rather than the correct VIF formula of 1/(1 - R-squared).
- D: This results from multiplying the R-squared by 10 rather than applying the correct VIF formula.
Source: CFA Program Curriculum, Quantitative Methods, "Multiple Regression" -- Detecting multicollinearity using variance inflation factors (https://www.cfainstitute.org/insights/professional-learning/refresher-readings)
