Regression Analysis Flashcards

A regression model has SSR = 400 and SSE = 100. What is the R² value?

Answer: 0.80

R² = SSR / SST = 400 / (400 + 100) = 400 / 500 = 0.80.

An interaction term (X₁ × X₂) is included in a regression model when:

Answer: The effect of X₁ on Y differs depending on the level of X₂

An interaction term captures moderation — when the slope of X₁ on Y changes at different values of X₂.

In stepwise regression, variables are selected based on:

Answer: Statistical criteria such as p-value or AIC at each step

Stepwise methods (forward, backward, or mixed) add or remove predictors using significance tests or information criteria at each iteration.

A dummy variable for a categorical predictor with four categories (A, B, C, D) requires how many dummy variables?

Answer: 3

For k categories, you create k–1 dummy variables; the omitted category serves as the reference group to avoid perfect multicollinearity.

The standard error of the estimate (SEE) in regression measures:

Answer: The average distance between observed and predicted Y values

SEE (also called RMSE) quantifies the typical prediction error — how far actual values tend to stray from the fitted line.

Lasso regression (L1 regularization) is preferred over Ridge when the goal is to:

Answer: Perform variable selection by shrinking some coefficients to exactly zero

Lasso's L1 penalty can drive coefficients to exactly zero, effectively removing irrelevant predictors from the model.

A researcher reports a 95% prediction interval of [42, 68] for a new observation. This means:

Answer: There is a 95% probability the new individual's value falls between 42 and 68

A prediction interval gives a range for a single new observation's outcome, accounting for both estimation uncertainty and individual variability.