Free CFA Quantitative Methods Practice Questions & Answers
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Question 1
A dummy variable is typically used to represent:
Select an option first.
Correct answer: B — A categorical characteristic (e.g., industry, region)
Explanation: Right: Dummy variables encode categories as 0/1. Wrong: A/C/D: Not their role.
Question 2
If residuals show a clear pattern over time, this suggests:
Select an option first.
Correct answer: B — Possible serial correlation or misspecification
Explanation: Right: Patterns in residuals often indicate violations of assumptions. Wrong: A/C/D: Not correct.
Question 3
A common remedy for heteroskedasticity is to:
Select an option first.
Correct answer: A — Use robust (heteroskedasticity-consistent) standard errors
Explanation: Right: Robust standard errors adjust inference under heteroskedasticity. Wrong: B/C/D: Not valid fixes.
Question 4
A residual plot that shows a funnel shape (variance increasing with fitted values) suggests:
Select an option first.
Correct answer: B — Heteroskedasticity
Explanation: Right: Changing spread indicates heteroskedasticity. Wrong: A/C/D: Not consistent.
Question 5
If a model has a very high (R^2) but nonsensical coefficients, this may indicate:
Select an option first.
Correct answer: B — A data entry error or misspecification
Explanation: Right: Strange coefficients can signal issues despite high (R^2).Wrong:A/C/D: Ignore the warning sign.
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When comparing two models with the same dependent variable, a common approach is to:
Select an option first.
Correct answer: B — Choose the one with the higher adjusted (R^2)
Explanation: Right: Higher adjusted (R^2) usually indicates better fit, controlling for complexity.Wrong:A/C/D: Poor criteria.
Question 7
A p-value for a coefficient represents:
Select an option first.
Correct answer: B — The probability of observing such a coefficient if the true coefficient were zero
Explanation: Right: p-value is the probability of the observed (or more extreme) statistic under the null.Wrong:A/C/D: Misinterpretations.
Question 8
Adjusted (R^2) is used instead of (R^2) because:
Select an option first.
Correct answer: B — It penalizes adding variables that do not improve the model
Explanation: Right: Adjusted (R^2) accounts for the number of predictors.Wrong:A: Opposite.C: It can be smaller.D: It is slightly more complex
Question 9
A key limitation of K means is that it:
Select an option first.
Correct answer: A — Assumes spherical clusters
Explanation: Why A is right: K‑means assumes clusters are roughly spherical and similar in size.Why others are wrong:B: K‑means requires numeric data.C: It scales well.D: It does require initialization.
Question 10
A centroid in K means represents:
Select an option first.
Correct answer: A — The mean of all points in a cluster
Explanation: Correct: AWhy A is right: K‑means uses the mean to define cluster centers.Why others are wrong: B/C/D: Not used in K‑means
Question 11
What is the main purpose of multiple linear regression in an investment context?
Select an option first.
Correct answer: B — To explain or predict a variable using several explanatory variables
Explanation: Multiple regression is used to explain or predict a dependent variable using several independent variables. A: Averaging is not regression. C: Independence tests are different (e.g., chi-square). D: The median is a descriptive statistic, not a regression output.
Question 12
In a multiple regression model, the dependent variable is:
Select an option first.
Correct answer: A — The variable being explained or predicted
Explanation: Right: The dependent variable is the outcome we want to explain or forecast. Wrong: B: It can change. C: It is chosen deliberately, not randomly. D: Variance size is irrelevant to the role.
Question 13
The intercept in a multiple regression model represents:
Select an option first.
Correct answer: B — The expected value of the dependent variable when all independent variables are zero
Explanation: Right: The intercept is the predicted value of (Y) when all (X)’s are zero. Wrong: A: It is not an average of (X)’s. C/D: It does not represent extremes of (Y).
Question 14
A “partial regression coefficient” refers to:
Select an option first.
Correct answer: B — A slope that measures the effect of one variable while holding others constant
Explanation: Right: Partial regression coefficients measure the marginal effect of one independent variable, controlling for others. Wrong: A: Not about sample size. C/D: Significance or sign changes are separate issues.
Question 15
Which of the following is a typical use of multiple regression in finance?
Select an option first.
Correct answer: B — Explaining stock returns using several risk factors
Explanation: Right: Multiple regression is often used to relate returns to multiple risk factors. Wrong: A/C: Descriptive statistics, not regression. D: Not related to regression.
Question 16
In multiple regression, the error term captures:
Select an option first.
Correct answer: B — The part of the dependent variable not explained by the independent variables
Explanation: Right: The error term represents unexplained variation in (Y). Wrong: A: It is random. C/D: Not the role of the error term.
Question 17
Which of the following is a key decision when specifying a multiple regression model?
Select an option first.
Correct answer: B — Selecting the dependent and independent variables
Explanation: Right: Model specification requires choosing which variables to include. Wrong: A/C/D: Presentation choices, not model specification.
Question 18
If the dependent variable is a continuous return, a common model type is:
Select an option first.
Correct answer: A — Linear regression
Explanation: Right: Continuous outcomes are typically modeled with linear regression. Wrong: B: Used for binary outcomes. C: Used for count data. D: Not a model.
Question 19
If the dependent variable is a 0/1 indicator (e.g., default vs no default), a more appropriate model is:
Select an option first.
Correct answer: C — Logistic regression
Explanation: Right: Logistic regression is standard for binary outcomes. Wrong: A/B: Linear models are not ideal for binary dependent variables. D: A time-series smoothing method.
Question 20
In multiple regression, adding a relevant independent variable typically:
Select an option first.
Correct answer: B — Increases or maintains explanatory power
Explanation: Right: A relevant variable should not reduce explanatory power. Wrong: A: Usually false. C: It may or may not cause multicollinearity. D: Linearity depends on functional form, not number of variables.
Question 21
The number of observations in a regression should be:
Select an option first.
Correct answer: C — Larger than the number of independent variables
Explanation: Right: You need more observations than parameters to estimate. Wrong: A/B: Insufficient for estimation. D: Sample size clearly matters.
Question 22
A regression model is called “linear” because it is linear in:
Select an option first.
Correct answer: B — The parameters (coefficients)
Explanation: Right: Linearity refers to being linear in the coefficients. Wrong: A: Variables can appear in transformed form. C/D: Not the defining feature.
Question 23
In multiple regression, “holding other variables constant” means:
Select an option first.
Correct answer: C — Measuring the effect of one variable while controlling for the others
Explanation: Right: It refers to controlling for other variables in the model. Wrong: A/B/D: Misinterpret the idea of “holding constant.”
Question 24
A common goal of multiple regression in portfolio analysis is to:
Select an option first.
Correct answer: B — Explain returns using several risk factors
Explanation: Right: Factor models are a classic use of multiple regression. Wrong: A/C/D: Not regression goals.
Question 25
The error term in a regression model is assumed to have:
Select an option first.
Correct answer: A — Zero mean
Explanation: Right: One standard assumption is that the error term has mean zero. Wrong: B/C/D: Not standard assumptions.
Question 26
In a regression context, “prediction” refers to:
Select an option first.
Correct answer: B — Using the model to estimate future or unknown values of the dependent variable
Explanation: Right: Prediction uses the model to estimate future or unknown outcomes. Wrong: A/C/D: Not prediction.
Question 27
A regression model with one dependent variable and three independent variables is called:
Select an option first.
Correct answer: C — Multiple regression
Explanation: Right: More than one independent variable → multiple regression. Wrong: A: Only one independent variable. B: Not standard terminology. D: Linearity is separate.
Question 28
In multiple regression, the term “residual” refers to:
Select an option first.
Correct answer: B — The difference between the actual and predicted values
Explanation: Right: Residual = actual minus predicted. Wrong: A/C/D: Different components of the model.
Question 29
The coefficient of determination ((R^2)) measures:
Select an option first.
Correct answer: B — The proportion of variation in the dependent variable explained by the model
Explanation: Right: (R^2) shows how much of (Y)’s variation is explained by the model. Wrong: A/C/D: Not the definition of (R^2).
Question 30
A higher (R^2) generally indicates:
Select an option first.
Correct answer: A — Better in-sample fit
Explanation: Right: Higher (R^2) means more variation explained. Wrong: B/C/D: Incorrect interpretations.
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