Regression Analysis Flashcards

Which plot is most useful for checking the normality assumption of regression residuals?

Answer: Normal Q-Q plot of residuals

A Q-Q plot compares the distribution of residuals to a theoretical normal distribution; points falling on the diagonal line indicate normality.

If two predictors X₁ and X₂ have a correlation of r = 0.97, a likely consequence in multiple regression is:

Answer: Inflated standard errors and unstable coefficient estimates

Near-perfect correlation (multicollinearity) makes it difficult to separate the effects of X₁ and X₂, inflating their standard errors.

The F-test in regression analysis tests the null hypothesis that:

Answer: All slope coefficients simultaneously equal zero

The omnibus F-test evaluates whether at least one predictor in the model explains a significant portion of variance in Y.

Cross-validation in regression is used primarily to:

Answer: Estimate how well the model generalizes to new, unseen data

Cross-validation splits data into training and test sets (or folds) to assess out-of-sample predictive performance and detect overfitting.

In logistic regression (as opposed to linear regression), the outcome variable is:

Answer: A binary or categorical variable

Logistic regression models the probability of a binary outcome (e.g., yes/no, 0/1) using the logistic (sigmoid) function.

A regression coefficient has a p-value of 0.002. Which conclusion is most appropriate?

Answer: There is strong evidence the coefficient differs from zero in the population

A small p-value (< 0.05) rejects the null that the coefficient = 0, indicating the predictor has a statistically significant relationship with Y.

When comparing two nested regression models, the appropriate statistical test is:

Answer: Partial F-test (likelihood ratio test)

The partial F-test compares SSE of the restricted and full models to determine whether the additional predictors in the full model significantly improve fit.