CEA Data Analysis & Statistical Methods 5 — Questions and Answers
Question 1: Which of the following is an example of a non-parametric statistical test?
- Student's t-test
- One-way ANOVA
- Mann-Whitney U test (Correct answer)
- Pearson correlation test
Correct answer: Mann-Whitney U test
The Mann-Whitney U test compares two independent groups without assuming normality, making it a non-parametric alternative to the independent-samples t-test.
Question 2: In regression analysis, the Variance Inflation Factor (VIF) is used to:
- Measure heteroskedasticity in residuals
- Quantify the degree of multicollinearity for each predictor (Correct answer)
- Test whether coefficients are jointly significant
- Determine the optimal number of predictors
Correct answer: Quantify the degree of multicollinearity for each predictor
VIF for each predictor indicates how much its estimated variance is inflated due to correlation with other predictors; VIF > 10 is commonly considered problematic.
Question 3: The Law of Large Numbers (LLN) guarantees that as the number of observations increases, the sample mean:
- Becomes normally distributed
- Converges to the population mean in probability (Correct answer)
- Has declining skewness
- Has variance equal to one
Correct answer: Converges to the population mean in probability
The LLN states that the sample mean converges in probability (weak LLN) or almost surely (strong LLN) to the true population mean as n → ∞.
Question 4: A spurious regression in time-series analysis is most likely to occur when:
- Both variables are stationary and uncorrelated
- Both variables contain unit roots but are not cointegrated (Correct answer)
- The sample size is very large
- Lagged dependent variables are included as regressors
Correct answer: Both variables contain unit roots but are not cointegrated
Regressing two independent non-stationary (unit-root) series on each other typically produces high R² and significant t-statistics even though no true relationship exists.
Question 5: In Bayesian statistics, the posterior distribution is proportional to:
- The prior distribution alone
- The likelihood function alone
- The prior distribution times the likelihood function (Correct answer)
- The marginal distribution of the data
Correct answer: The prior distribution times the likelihood function
Bayes' theorem states that the posterior is proportional to the likelihood times the prior, combining new evidence with prior beliefs.
Question 6: An economic analyst uses k-fold cross-validation primarily to:
- Reduce multicollinearity in the model
- Estimate out-of-sample predictive performance using the available data (Correct answer)
- Test for structural breaks in the time series
- Identify influential observations in the dataset
Correct answer: Estimate out-of-sample predictive performance using the available data
K-fold cross-validation partitions data into k subsets, trains on k−1 folds and tests on the remaining fold repeatedly, yielding an unbiased estimate of model generalization error.
Question 7: The Chow test in econometrics is used to determine whether:
- Residuals follow a normal distribution
- A regression model has a structural break at a known point (Correct answer)
- Two variables are cointegrated
- The model suffers from multicollinearity
Correct answer: A regression model has a structural break at a known point
The Chow test compares regression coefficients estimated on two subsamples to detect if a structural change occurred at a specified breakpoint.
CEA Data Analysis & Statistical Methods 5
Which of the following is an example of a non-parametric statistical test?