prediction from the linear model Flashcards
(12 cards)
What is the difference between interpolation and extrapolation in prediction?
Interpolation: Predicting
Y within the observed range of X (safe).
Extrapolation: Predicting Y outside the observed range of X (risky, assumes linearity holds).
How do you calculate a point estimate for a new observation in R?
Use predict():
How do you compute a confidence interval (CI) for the mean response?
y^p±tα/2,df×se(y^p)
What is the difference between a confidence interval and a prediction interval?
CI: Uncertainty in the mean response (narrower).
PI: Uncertainty in an individual response (wider, includes residual variance).
How do you calculate a prediction interval in R?
predict(model, newdata, interval = “prediction”, level = 0.99)
Why is the prediction interval wider than the confidence interval?
It accounts for:
Uncertainty in the estimated coefficients (same as CI).
Variability of individual observations around the mean (extra term).
What are the risks of extrapolation?
Assumes linearity continues beyond observed data (often untrue).
No data to validate predictions → high uncertainty.
How does multiple regression prediction differ from simple regression?
Requires values for all predictors in the model.
What is MSE and where do you find it in R output?
Mean Square Error: Average squared residual.
Sources:
ANOVA table: Mean Sq for Residuals.
summary(model)$sigma^2.
How do you interpret a 99% prediction interval of (106.7, 107.6) for IQ?
We are 99% confident that an individual with height=1.72m will have an IQ between 106.7 and 107.6.
Why is the CI narrowest at the mean of X?
Because
∑(xi−xˉ)2∑(xi−xˉ)2is minimized at xˉxˉ, reducing se(y^p)se(y^p).
What is the t-multiplier for a 95% CI with 98 degrees of freedom?
qt(0.975, df = 98) # ≈ 1.984
