You can use the PLS model to estimate response values for a new data set, which is often referred to as a test set. Minitab displays one predicted response table for each response.

Minitab calculates one predicted response for each new observation. You can interpret the predicted response value in two ways:

·      As the estimated mean response for all observations in a population with a given set of predictor values

·      As the predicted response for a new single observation with a given set of predictor values

The predicted response value for both interpretations is the same, but the variance or precision of the predictions differs. This difference is reflected in the confidence interval and the prediction interval, which are ranges in which the predicted value is expected to fall. The confidence interval corresponds to the estimated mean response and the prediction interval corresponds to predicted response of a single observation. The prediction interval is larger than the confidence interval because it contains the greater uncertainty. The prediction interval not only includes the uncertainty in the regression parameter estimates, but it also includes the uncertainty from the new measurements. The standard error of the fitted values (SE Fit) estimates the variation in the estimated mean response for a given set of predictor values. The smaller the standard error, the more precise the estimated response.

In this example, the new observations in the test set include 6 samples of soybean flour. Minitab predicts responses for these samples using the PLS model. The predicted response for moisture for the first flour sample is 14.5184. If 14.5184 is the estimated mean response, the scientists use the confidence interval. If 14.5184 is the predicted response for a single observation, the scientists use the prediction interval.