Prediction

Can predict a new response value from our model by substituting in the values of the response variables. Prediction error is calculated from $\sqrt{Var(predictor) + \sigma^2}$ . We normally give a 95% confidence interval of $\pm ~2$ se’s. In R:

predict(model, data, se.fit=T, interval="prediction")

Can estimate average response similarly, but confidence intervals will be smaller because variance does not include sigma (ie. standard error = $\sqrt{Var(predictor)}$ .

predict(model, data, se.fit=T, interval="confidence")