Prediction

Prediction is the use of the model to predict the population mean or value of an individual future observation, at specific values of the predictors. Inverse prediction deals with the problem of predicting the value of a predictor for a given value of the response variable.

When making predictions, it is important that the data used to fit the model is similar to future populations to which you want to apply the prediction. You should be careful of making predictions outside the range of the observed data. Assumptions met for the observed data may not be met outside the range. Non-constant variance can cause confidence intervals for the predicted values to become unrealistically narrow or so large as to be useless. Alternatively, a different fit function may better describe the unobserved data outside the range.

When making multiple predictions of the population mean at different sets of predictor values the confidence intervals can be simultaneous or individual. A simultaneous interval ensures you achieve the confidence level simultaneously for all predictions, whereas individual intervals only ensure confidence for the individual prediction. With individual inferences, the chance of at least one interval not including the true value increases with the number of predictions.