CEA Data Analysis & Statistical Methods 2 — Questions and Answers
Question 1: In a multiple regression model, multicollinearity refers to:
- High correlation among independent variables (Correct answer)
- Correlation between residuals and fitted values
- Non-constant variance of residuals
- Omitted variable bias in the model
Correct answer: High correlation among independent variables
Multicollinearity occurs when two or more independent variables are highly correlated, making it difficult to isolate their individual effects.
Question 2: Which test is most appropriate for detecting autocorrelation in regression residuals?
- Breusch-Pagan test
- Durbin-Watson test (Correct answer)
- White test
- Jarque-Bera test
Correct answer: Durbin-Watson test
The Durbin-Watson test specifically tests for first-order autocorrelation (serial correlation) in OLS regression residuals.
Question 3: A Type II error in hypothesis testing occurs when:
- A true null hypothesis is rejected
- A false null hypothesis is not rejected (Correct answer)
- The p-value exceeds the significance level
- The sample size is too large
Correct answer: A false null hypothesis is not rejected
A Type II error (false negative) occurs when we fail to reject a null hypothesis that is actually false.
Question 4: In time-series analysis, a process is considered weakly stationary if:
- Its mean and variance are time-invariant and its autocovariance depends only on lag (Correct answer)
- Its distribution is identical at every time point
- It has no seasonal component
- Its autocorrelation function decays to zero immediately
Correct answer: Its mean and variance are time-invariant and its autocovariance depends only on lag
Weak (covariance) stationarity requires a constant mean, constant variance, and autocovariance that depends only on the lag, not on the specific time period.
Question 5: The interquartile range (IQR) is preferred over standard deviation as a measure of spread when:
- The data are normally distributed
- The dataset contains significant outliers (Correct answer)
- The sample size is very large
- All observations are positive
Correct answer: The dataset contains significant outliers
The IQR (Q3 − Q1) is robust to outliers because it focuses on the middle 50% of the data, unlike standard deviation which is sensitive to extreme values.
Question 6: In logistic regression, the output of the model before applying the sigmoid function is called:
- Probability estimate
- Log-odds (logit) (Correct answer)
- Odds ratio
- Likelihood ratio
Correct answer: Log-odds (logit)
Logistic regression models the log-odds (logit) of the probability of an event; the sigmoid function transforms this into a probability between 0 and 1.
Question 7: Which criterion penalizes model complexity more heavily than the Akaike Information Criterion (AIC)?
- Root Mean Square Error (RMSE)
- Bayesian Information Criterion (BIC) (Correct answer)
- Adjusted R-squared
- F-statistic
Correct answer: Bayesian Information Criterion (BIC)
The BIC applies a larger penalty for additional parameters than AIC, especially as sample size grows, leading to selection of more parsimonious models.
CEA Data Analysis & Statistical Methods 2
In a multiple regression model, multicollinearity refers to: