Question 691
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 692
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.
Question 693
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 694
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 695
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
Check answer
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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Question 696
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
Check answer
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 697
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 698
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 699
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 700
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 701
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 702
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 703
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 704
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 705
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 706
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 707
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 708
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 709
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 710
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 711
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 712
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 713
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 714
A residual plot that shows a funnel shape (variance increasing with fitted values) suggests:
A. Homoskedasticity
B. Heteroskedasticity
C. Perfect fit
D. No residuals
Check answer
Select an option first.
Correct answer: B — Heteroskedasticity
Explanation: Right: Changing spread indicates heteroskedasticity. Wrong: A/C/D: Not consistent.
Question 715
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
Check answer
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 716
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 717
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
Check answer
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 718
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
Check answer
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 719
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 720
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.
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