What is the multiple linear regression model?
y = β0 + β1x1 + β2x2 + … + βkxk + ε
Where:
y = response variable
xj = predictor variables
βj = regression coefficients
ε = random error
Why is a prediction interval wider than a confidence interval?
Because it includes both:
variability of the mean estimate
variability of individual observations.
What are standardized regression coefficients?
Regression coefficients obtained after standardizing variables (converting them to z-scores)
What is the least squares estimator for regression coefficients in matrix form?
β̂ = (X’X)^(-1) X’y
What does rejecting the overall F-test mean?
At least one predictor variable significantly affects the response variable
What does βj represent in multiple regression?
The change in the mean response y for a one-unit increase in xj while holding all other predictors constant
What does rejecting H0: βj = 0 indicate?
Predictor xj significantly contributes to explaining variation in y.
What is hidden extrapolation?
Making predictions for combinations of predictor values that were not observed in the original dataset
