Quantitative Methods

CFA® Level II, published weight 5–10%. Multiple regression, misspecification, time series, machine learning.

What the outline covers

Basics of Multiple Regression and Underlying Assumptions
Evaluating Regression Model Fit and Interpreting Model Results
Model Misspecification
Extensions of Multiple Regression
Time-Series Analysis
Machine Learning
Big Data Projects

Sample questions

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Question 1

A multiple regression reports a significant F-statistic but no individually significant t-statistics. This most likely indicates:

A. Heteroskedasticity
B. Serial correlation
C. Multicollinearity
D. A unit root

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C. Multicollinearity inflates the standard errors of individual coefficients while leaving the joint explanatory power intact — exactly this signature.

Reading: Quantitative Methods — Model Misspecification, LOS 3.b

Question 2

Adding a variable to a regression raises R² from 0.42 to 0.44 but lowers adjusted R² from 0.39 to 0.38. The analyst should conclude the variable:

R²: 0.42 → 0.44 · R̄²: 0.39 → 0.38

A. Improves the model and should be retained
B. Does not justify its loss of degrees of freedom
C. Introduces heteroskedasticity
D. Makes the model non-stationary

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B. R² always rises with an added regressor. A falling adjusted R² means the explanatory gain does not compensate for the lost degree of freedom.

Reading: Quantitative Methods — Evaluating Regression Model Fit, LOS 2.c

Question 3

An AR(1) model is estimated on a series with a unit root. The most appropriate remedy is to:

A. Add a lag to the model
B. First-difference the series
C. Use White-corrected standard errors
D. Apply a log transformation to the dependent variable

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B. A unit root violates covariance stationarity and produces spurious results. First differencing typically restores stationarity.

Reading: Quantitative Methods — Time-Series Analysis, LOS 5.f

Question 4

Conditional heteroskedasticity in a regression most directly causes:

A. Biased coefficient estimates
B. Unreliable standard errors and invalid t-tests
C. A spurious unit root
D. Perfect multicollinearity

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B. Coefficients remain unbiased and consistent, but the standard errors are wrong, so hypothesis tests based on them are invalid.

Reading: Quantitative Methods — Model Misspecification, LOS 3.a

Question 5

A machine learning model shows very low training error and substantially higher validation error. This is best described as:

A. Underfitting
B. Overfitting
C. Data leakage
D. Correct generalisation

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B. A large gap between training and validation performance means the model has fitted noise in the training sample rather than signal.

Reading: Quantitative Methods — Machine Learning, LOS 6.c

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