Statistical Inference & Regression Models Flashcards
7 cards from real MS-DS Master of Data science practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Statistical Inference & Regression Models flashcards as text
A researcher fits a multiple linear regression model and finds that adding a 5th predictor increases R² from 0.82 to 0.83 but decreases adjusted R² from 0.81 to 0.80. What does this indicate?
Answer: The new predictor does not contribute enough to justify its inclusion
Adjusted R² penalizes unnecessary predictors, so a decrease indicates the added variable does not improve the model enough to offset the loss of a degree of freedom.
In hypothesis testing, a p-value of 0.03 is obtained with α = 0.05. Which conclusion is correct?
Answer: Reject H₀; there is sufficient evidence against it at the 5% level
Since p = 0.03 < α = 0.05, we reject the null hypothesis at the 5% significance level.
Which assumption of OLS regression is violated when the variance of residuals increases with fitted values?
Answer: Homoscedasticity
Heteroscedasticity is the violation of the homoscedasticity assumption, where error variance is not constant across levels of the predictors.
A 95% confidence interval for a population mean is (12.4, 18.6). What is the correct interpretation?
Answer: If repeated sampling is used, 95% of similarly constructed intervals will contain the true mean
Confidence intervals are interpreted in terms of long-run frequency: 95% of intervals constructed with this procedure will capture the true parameter.
In logistic regression, the logit function transforms the response variable to:
Answer: The log of the odds of the outcome
The logit transformation is log(p/(1-p)), the natural log of the odds, which maps probabilities from (0,1) to (-∞, +∞).
When performing a Durbin-Watson test, a statistic close to 2 indicates:
Answer: No significant autocorrelation in residuals
The Durbin-Watson statistic ranges from 0 to 4, with values near 2 indicating no autocorrelation in the residuals.
A Variance Inflation Factor (VIF) of 12 for a predictor in a multiple regression model suggests:
Answer: Severe multicollinearity affecting that predictor
VIF > 10 is a common threshold indicating severe multicollinearity, meaning the predictor is nearly linearly dependent on others in the model.