MS-DS Master of Data science FREE Master of Data Science: Statistical Inference & Regression Models Questions and Answers 2 — Questions and Answers
Question 1: In multiple linear regression, what does a Variance Inflation Factor (VIF) greater than 10 typically indicate?
- Heteroscedasticity in residuals
- Severe multicollinearity among predictors (Correct answer)
- Non-normality of the response variable
- Autocorrelation in the error terms
Correct answer: Severe multicollinearity among predictors
A VIF exceeding 10 signals that a predictor is highly correlated with other predictors, indicating severe multicollinearity.
Question 2: Which assumption is tested by the Breusch-Pagan test in a regression model?
- Normality of residuals
- Independence of errors
- Homoscedasticity of residuals (Correct answer)
- Linearity of the relationship
Correct answer: Homoscedasticity of residuals
The Breusch-Pagan test checks whether the variance of residuals is constant across levels of the fitted values (homoscedasticity).
Question 3: What is the primary purpose of a confidence interval for a regression coefficient?
- To predict individual future observations
- To estimate the range of plausible values for the true population parameter (Correct answer)
- To test whether the model has multicollinearity
- To determine the R-squared value of the model
Correct answer: To estimate the range of plausible values for the true population parameter
A confidence interval for a regression coefficient provides a range within which the true population parameter is likely to fall at a given confidence level.
Question 4: In logistic regression, what does the odds ratio represent when an independent variable increases by one unit?
- The change in probability of the outcome
- The multiplicative change in the odds of the outcome (Correct answer)
- The absolute change in the log-odds
- The change in the R-squared value
Correct answer: The multiplicative change in the odds of the outcome
The odds ratio in logistic regression represents how the odds of the outcome are multiplied for each one-unit increase in the predictor.
Question 5: When performing a likelihood ratio test comparing a full model to a reduced model, the test statistic follows which distribution under the null hypothesis?
- Normal distribution
- F-distribution
- Chi-squared distribution (Correct answer)
- t-distribution
Correct answer: Chi-squared distribution
The likelihood ratio test statistic, calculated as -2 times the log-likelihood difference, follows a chi-squared distribution with degrees of freedom equal to the difference in parameters.
Question 6: What does Cook's distance measure in regression diagnostics?
- The correlation between predictor variables
- The overall influence of a single observation on all fitted values (Correct answer)
- The normality of the residual distribution
- The degree of heteroscedasticity in the model
Correct answer: The overall influence of a single observation on all fitted values
Cook's distance quantifies how much all fitted values change when a single observation is removed, measuring that observation's overall influence on the model.
