Question 31
The F-test in multiple regression is used to test:
A. Whether each coefficient individually equals zero
B. Whether all slope coefficients are jointly equal to zero
C. Whether the intercept equals zero
D. Whether the residuals are normally distributed
Check answer
Select an option first.
Correct answer: B — Whether all slope coefficients are jointly equal to zero
Explanation: Right: The F-test checks joint significance of the regressors. Wrong: A: That’s for t-tests. C/D: Different tests.
Question 32
A statistically significant F-statistic suggests:
A. The model explains none of the variation in the dependent variable
B. At least one independent variable is useful in explaining the dependent variable
C. All independent variables are useless
D. The residuals are perfectly zero
Check answer
Select an option first.
Correct answer: B — At least one independent variable is useful in explaining the dependent variable
Explanation: Right: Significant F → at least one slope is non-zero. Wrong: A/C/D: Opposite or unrelated.
Question 33
A t-statistic for a slope coefficient tests:
A. Whether the coefficient equals zero
B. Whether the intercept equals one
C. Whether (R^2) equals zero
D. Whether residuals are independent
Check answer
Select an option first.
Correct answer: A — Whether the coefficient equals zero
Explanation: Right: t-tests check if a coefficient is significantly different from zero. Wrong: B/C/D: Different questions.
Question 34
A low p-value (e.g., below 0.05) for a slope coefficient typically indicates:
A. Strong evidence that the coefficient is zero
B. Weak evidence that the coefficient is zero
C. Strong evidence that the coefficient is not zero
D. No information about the coefficient
Check answer
Select an option first.
Correct answer: C — Strong evidence that the coefficient is not zero
Explanation: Right: Low p-value → reject the null of zero coefficient. Wrong: A/B/D: Incorrect.
Question 35
When using a regression model for forecasting, a key concern is:
A. Whether the residuals are sorted
B. Whether the model performs well on new data
C. Whether the intercept is exactly zero
D. Whether the independent variables are alphabetically ordered
Check answer
Select an option first.
Correct answer: B — Whether the model performs well on new data
Explanation: Right: Out-of-sample performance is crucial for forecasting. Wrong: A/C/D: Not central to forecasting quality.
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Question 36
Confidence intervals for regression coefficients provide:
A. A range of plausible values for the true coefficient
B. The exact value of the true coefficient
C. The range of the dependent variable
D. The range of the independent variables
Check answer
Select an option first.
Correct answer: A — A range of plausible values for the true coefficient
Explanation: Right: Confidence intervals give plausible ranges for parameters. Wrong: B/C/D: Not what they represent.
Question 37
A residual plot that shows no clear pattern suggests:
A. The model assumptions may be reasonable
B. The model is definitely wrong
C. The dependent variable is constant
D. The independent variables are perfectly correlated
Check answer
Select an option first.
Correct answer: A — The model assumptions may be reasonable
Explanation: Right: Random residuals support model assumptions. Wrong: B/C/D: Not implied by such a plot.
Question 38
Forecast intervals (prediction intervals) are generally:
A. Narrower than confidence intervals for the mean
B. Wider than confidence intervals for the mean
C. Exactly the same as confidence intervals
D. Unrelated to regression
Check answer
Select an option first.
Correct answer: B — Wider than confidence intervals for the mean
Explanation: Right: Prediction intervals include both parameter and error uncertainty. Wrong: A/C/D: Incorrect.
Question 39
The assumption of linearity in regression means:
A. The data must be plotted as a straight line
B. The relationship between the dependent variable and each independent variable is linear in parameters
C. Time must increase linearly
D. The residuals must form a straight line
Check answer
Select an option first.
Correct answer: B — The relationship between the dependent variable and each independent variable is linear in parameters
Explanation: Right: Linearity refers to the functional form in parameters. Wrong: A/C/D: Misinterpretations.
Question 40
Homoskedasticity means:
A. Residuals have constant variance across observations
B. Residuals have increasing variance over time
C. Residuals are always zero
D. Residuals are perfectly correlated
Check answer
Select an option first.
Correct answer: A — Residuals have constant variance across observations
Explanation: Right: Homoskedasticity = constant error variance. Wrong: B: Heteroskedasticity. C/D: Not correct.
Question 41
Heteroskedasticity is a problem because it:
A. Biases the estimated coefficients
B. Makes standard errors unreliable
C. Eliminates residuals
D. Forces (R^2) to be zero
Check answer
Select an option first.
Correct answer: B — Makes standard errors unreliable
Explanation: Right: It mainly affects standard errors and inference. Wrong: A: Coefficients can remain unbiased. C/D: Not true.
Question 42
A common visual way to detect heteroskedasticity is to:
A. Plot residuals against fitted values
B. Plot independent variables alphabetically
C. Plot the intercept over time
D. Plot the mean of the dependent variable
Check answer
Select an option first.
Correct answer: A — Plot residuals against fitted values
Explanation: Right: Residual vs fitted plots can reveal changing variance. Wrong: B/C/D: Not diagnostic for heteroskedasticity.
Question 43
Serial correlation (autocorrelation) in residuals is most often a concern in:
A. Cross-sectional data
B. Time-series data
C. Randomly permuted data
D. Categorical data only
Check answer
Select an option first.
Correct answer: B — Time-series data
Explanation: Right: Serial correlation is especially relevant in time series. Wrong: A/C/D: Less typical context.
Question 44
Serial correlation means:
A. Residuals are independent
B. Residuals are correlated across time
C. Residuals are always positive
D. Residuals are always negative
Check answer
Select an option first.
Correct answer: B — Residuals are correlated across time
Explanation: Right: Serial correlation = correlation of errors over time. Wrong: A/C/D: Incorrect.
Question 45
A consequence of positive serial correlation in residuals is that:
A. Standard errors may be underestimated
B. Coefficients become perfectly accurate
C. (R^2) must be zero
D. The intercept disappears
Check answer
Select an option first.
Correct answer: A — Standard errors may be underestimated
Explanation: Right: Serial correlation can distort standard errors and tests. Wrong: B/C/D: Not true.
Question 46
Multicollinearity refers to:
A. Correlation between residuals and the dependent variable
B. High correlation among independent variables
C. High correlation between the dependent variable and time
D. No correlation among any variables
Check answer
Select an option first.
Correct answer: B — High correlation among independent variables
Explanation: Right: Multicollinearity is about correlated predictors. Wrong: A/C/D: Different concepts.
Question 47
A symptom of multicollinearity is:
A. Very small standard errors for coefficients
B. Very large standard errors and unstable coefficient estimates
C. Residuals that are always zero
D. A negative (R^2)
Check answer
Select an option first.
Correct answer: B — Very large standard errors and unstable coefficient estimates
Explanation: Right: Multicollinearity inflates standard errors and makes coefficients unstable. Wrong: A/C/D: Not typical.
Question 48
One way to reduce multicollinearity is to:
A. Add more highly correlated variables
B. Remove or combine highly correlated variables
C. Increase the error variance
D. Ignore the problem
Check answer
Select an option first.
Correct answer: B — Remove or combine highly correlated variables
Explanation: Right: Dropping or combining correlated predictors can help. Wrong: A/C/D: Worsen or ignore the issue.
Question 49
A model is “misspecified” when:
A. It uses more than one independent variable
B. It omits important variables or uses an incorrect functional form
C. It has a non-zero intercept
D. It has a high (R^2)
Check answer
Select an option first.
Correct answer: B — It omits important variables or uses an incorrect functional form
Explanation: Right: Misspecification includes omitted variables, wrong form, etc. Wrong: A/C/D: Not definitions of misspecification.
Question 50
Omitting a relevant variable that is correlated with included variables can:
A. Have no effect
B. Bias the estimated coefficients
C. Reduce the sample size
D. Eliminate residuals
Check answer
Select an option first.
Correct answer: B — Bias the estimated coefficients
Explanation: Right: Omitted variable bias is a classic problem. Wrong: A/C/D: Incorrect.
Question 51
Including an irrelevant variable (one that has no real effect) typically:
A. Biases all coefficients
B. Increases variance of estimates without adding explanatory power
C. Eliminates heteroskedasticity
D. Eliminates serial correlation
Check answer
Select an option first.
Correct answer: B — Increases variance of estimates without adding explanatory power
Explanation: Right: Irrelevant variables add noise and reduce efficiency. Wrong: A/C/D: Not standard consequences.
Question 52
A non-linear relationship between (Y) and an independent variable can sometimes be handled by:
A. Deleting the variable
B. Transforming the variable (e.g., using a squared term or log)
C. Ignoring the non-linearity
D. Sorting the data
Check answer
Select an option first.
Correct answer: B — Transforming the variable (e.g., using a squared term or log)
Explanation: Right: Transformations can capture non-linear patterns. Wrong: A/C/D: Poor practice.
Question 53
Independence of errors means:
A. Errors are uncorrelated with each other
B. Errors are always positive
C. Errors are always negative
D. Errors are equal to the intercept
Check answer
Select an option first.
Correct answer: A — Errors are uncorrelated with each other
Explanation: Right: Independence means no correlation among errors. Wrong: B/C/D: Not assumptions.
Question 54
Normality of errors is mainly important for:
A. Estimating coefficients
B. Conducting hypothesis tests and building confidence intervals
C. Computing the mean of the dependent variable
D. Sorting the data
Check answer
Select an option first.
Correct answer: B — Conducting hypothesis tests and building confidence intervals
Explanation: Right: Normality supports standard inference procedures. Wrong: A/C/D: Not the main reason.
Question 55
A common test for serial correlation in residuals is:
A. A visual inspection of the intercept
B. A test statistic designed for autocorrelation (e.g., Durbin–Watson)
C. A test of the mean of the dependent variable
D. A test of the median of the independent variables
Check answer
Select an option first.
Correct answer: B — A test statistic designed for autocorrelation (e.g., Durbin–Watson)
Explanation: Right: Specific tests exist for autocorrelation. Wrong: A/C/D: Not appropriate.
Question 56
A dummy variable that equals 1 for “technology firms” and 0 otherwise allows the model to:
A. Ignore technology firms
B. Capture the average difference in the dependent variable for technology firms vs others
C. Force all technology firms to have the same dependent variable
D. Remove non-technology firms from the sample
Check answer
Select an option first.
Correct answer: B — Capture the average difference in the dependent variable for technology firms vs others
Explanation: Right: It measures the shift in the dependent variable for that group. Wrong: A/C/D: Misinterpretations.
Question 57
When using dummy variables for a category with (k) groups, a common rule is to:
A. Use (k) dummies
B. Use (k-1) dummies and one base group
C. Use only one dummy
D. Use no dummies
Check answer
Select an option first.
Correct answer: B — Use (k-1) dummies and one base group
Explanation: Right: (k-1) dummies avoid perfect multicollinearity. Wrong: A/C/D: Either cause problems or ignore categories.
Question 58
The “dummy variable trap” refers to:
A. Using too few dummy variables
B. Using a dummy variable as the dependent variable
C. Including a full set of dummies plus an intercept, causing perfect multicollinearity
D. Using dummies in time-series models
Check answer
Select an option first.
Correct answer: C — Including a full set of dummies plus an intercept, causing perfect multicollinearity
Explanation: Right: Full set + intercept → perfect collinearity. Wrong: A/B/D: Not the trap.
Question 59
In a regression with a dummy variable for “crisis period” (1 during crisis, 0 otherwise), the coefficient on the dummy measures:
A. The slope of the trend
B. The average change in the dependent variable during crisis vs non-crisis periods
C. The variance of the residuals
D. The correlation between crises and time
Check answer
Select an option first.
Correct answer: B — The average change in the dependent variable during crisis vs non-crisis periods
Explanation: Right: It captures the shift in the level of (Y) during crisis periods. Wrong: A/C/D: Not what the dummy coefficient means.
Question 60
Logistic regression is most appropriate when the dependent variable is:
A. A continuous return
B. A count of events
C. A binary outcome (e.g., default vs no default)
D. A nominal interest rate
Check answer
Select an option first.
Correct answer: C — A binary outcome (e.g., default vs no default)
Explanation: Right: Logistic regression models binary outcomes. Wrong: A/B/D: Different types of data.
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