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QUESTION 1

A dummy variable is typically used to represent:

A. A continuous variable
B. A categorical characteristic (e.g., industry, region)
C. The error term
D. The intercept

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:

A. Independence of errors
B. Possible serial correlation or misspecification
C. Perfect model fit
D. No need for further analysis

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:

A. Use robust (heteroskedasticity-consistent) standard errors
B. Delete all residuals
C. Force residuals to be zero
D. Remove the intercept

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:

A. Homoskedasticity
B. Heteroskedasticity
C. Perfect fit
D. No residuals

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:

A. A perfect model
B. A data entry error or misspecification
C. No problem at all
D. That the intercept must be removed

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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QUESTION 6

When comparing two models with the same dependent variable, a common approach is to:

A. Choose the one with the lower adjusted (R^2)
B. Choose the one with the higher adjusted (R^2)
C. Choose the one with more variables
D. Choose the one with the largest residuals

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:

A. The probability the model is correct
B. The probability of observing such a coefficient if the true coefficient were zero
C. The probability the coefficient is exactly zero
D. The probability the residuals are normal

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

A key limitation of K means is that it:

A. Assumes spherical clusters
B. Works only with categorical data
C. Cannot scale to large datasets
D. Does not require initialization

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 9

A centroid in K means represents:

A. The mean of all points in a cluster
B. The median of all points
C. The mode of all points
D. The farthest point from the cluster

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 10

What is the fair 9×12 forward rate?

A. 4.00%
B. 4.10%
C. 4.50%
D. 4.88%

Correct answer: D — 4.88%

Explanation: A. N(d1) B. e−qTN(d1) C. N(d2) D. e−rTN(d1)

QUESTION 11

What is the main purpose of multiple linear regression in an investment context?

A. To find the average of several variables
B. To explain or predict a variable using several explanatory variables
C. To test whether two variables are independent
D. To compute the median of a dataset

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:

A. The variable being explained or predicted
B. The variable that never changes
C. Any variable chosen at random
D. The variable with the largest variance

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

In the equation (Y = b_0 + b_1X_1 + b_2X_2 + \varepsilon), what does (b_1) represent?

A. The error term
B. The intercept
C. The change in (Y) for a one-unit change in (X_1), holding (X_2) constant
D. The change in (X_1) for a one-unit change in (Y)

Correct answer: C — The change in (Y) for a one-unit change in (X_1), holding (X_2) constant

Explanation: Right: (b_1) is the partial slope for (X_1), holding other variables constant. Wrong: A: (\varepsilon) is the error term. B: (b_0) is the intercept. D: Regression explains (Y) given (X), not the reverse.

QUESTION 14

The intercept in a multiple regression model represents:

A. The average of all independent variables
B. The expected value of the dependent variable when all independent variables are zero
C. The maximum value of the dependent variable
D. The minimum value of the dependent variable

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 15

A “partial regression coefficient” refers to:

A. A coefficient estimated using only half the data
B. A slope that measures the effect of one variable while holding others constant
C. A coefficient that is not statistically significant
D. A coefficient that changes sign frequently

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 16

Which of the following is a typical use of multiple regression in finance?

A. Estimating the mode of returns
B. Explaining stock returns using several risk factors
C. Computing the range of a dataset
D. Sorting stocks alphabetically

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 17

In multiple regression, the error term captures:

A. The exact prediction error with no randomness
B. The part of the dependent variable not explained by the independent variables
C. The average of the independent variables
D. The maximum possible value of the dependent variable

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 18

Which of the following is a key decision when specifying a multiple regression model?

A. Choosing the color of the chart
B. Selecting the dependent and independent variables
C. Deciding the font size in the report
D. Choosing the file format for saving results

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 19

If the dependent variable is a continuous return, a common model type is:

A. Linear regression
B. Logistic regression
C. Poisson regression
D. Random sorting

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 20

If the dependent variable is a 0/1 indicator (e.g., default vs no default), a more appropriate model is:

A. Simple linear regression
B. Multiple linear regression
C. Logistic regression
D. Moving average

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 21

In multiple regression, adding a relevant independent variable typically:

A. Reduces explanatory power
B. Increases or maintains explanatory power
C. Always causes multicollinearity
D. Makes the model non-linear

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 22

The number of observations in a regression should be:

A. Smaller than the number of independent variables
B. Equal to the number of independent variables
C. Larger than the number of independent variables
D. Irrelevant

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 23

A regression model is called “linear” because it is linear in:

A. The independent variables
B. The parameters (coefficients)
C. The error term
D. Time

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 24

Which of the following is an example of a multiple regression equation?

A. (Y = b_0 + b_1X)
B. (Y = b_0 + \varepsilon)
C. (Y = b_0 + b_1X_1 + b_2X_2)
D. (Y = X_1X_2)

Correct answer: C — (Y = b_0 + b_1X_1 + b_2X_2)

Explanation: Right: Multiple regression includes more than one independent variable. Wrong: A/B: Only one or no independent variable. D: No intercept or coefficients shown.

QUESTION 25

In multiple regression, “holding other variables constant” means: