FRM Quantitative Analysis 2 — Questions and Answers
Question 1: OLS (Ordinary Least Squares) regression minimizes which of the following?
- The sum of absolute residuals
- The sum of squared residuals (Correct answer)
- The maximum residual
- The variance of the dependent variable
Correct answer: The sum of squared residuals
OLS minimizes the sum of squared residuals (differences between observed and predicted values), making it sensitive to outliers but analytically tractable.
Question 2: An R-squared of 0.85 in a regression model indicates:
- The slope coefficient equals 0.85
- 85% of the variation in the dependent variable is explained by the model (Correct answer)
- The model has 85% predictive accuracy
- The correlation between variables is 0.85
Correct answer: 85% of the variation in the dependent variable is explained by the model
R-squared (coefficient of determination) represents the proportion of variance in the dependent variable explained by the independent variables — 0.85 means 85% is explained.
Question 3: Heteroskedasticity in regression analysis refers to:
- Non-normality of the dependent variable
- Correlation among independent variables
- Non-constant variance of the error terms across observations (Correct answer)
- Serial correlation in the residuals
Correct answer: Non-constant variance of the error terms across observations
Heteroskedasticity occurs when the variance of error terms is not constant across observations, violating an OLS assumption and affecting the efficiency of estimates.
Question 4: The Durbin-Watson statistic is primarily used to test for:
- Heteroskedasticity in residuals
- Multicollinearity among predictors
- First-order autocorrelation in residuals (Correct answer)
- Non-normality of error terms
Correct answer: First-order autocorrelation in residuals
The Durbin-Watson statistic tests for first-order serial correlation in regression residuals, with values near 2 indicating no autocorrelation.
Question 5: A GARCH(1,1) model is primarily designed to capture:
- Mean reversion in interest rates
- Volatility clustering in financial return series (Correct answer)
- Linear time trends in asset prices
- Jump discontinuities in equity prices
Correct answer: Volatility clustering in financial return series
GARCH(1,1) models capture volatility clustering — the well-documented tendency for high-volatility periods to be followed by high volatility and low by low.
Question 6: Multicollinearity among predictors in a regression model causes:
- Biased coefficient estimates
- Inflated standard errors of the affected coefficients (Correct answer)
- Heteroskedastic residuals
- A non-zero mean of the residuals
Correct answer: Inflated standard errors of the affected coefficients
Multicollinearity inflates the standard errors of correlated predictors' coefficients, making it hard to isolate individual effects, though OLS estimates remain unbiased.
Question 7: Which statistic is used to test the overall significance of a multiple regression model?
- t-statistic
- z-statistic
- F-statistic (Correct answer)
- Chi-square statistic
Correct answer: F-statistic
The F-statistic tests overall model significance by comparing explained variance to unexplained variance; a significant F indicates the model explains meaningful variation beyond the intercept.
FRM Quantitative Analysis 2
OLS (Ordinary Least Squares) regression minimizes which of the following?