How Minitab handles center points in a 2-level factorial design

When center points are included in a two-level factorial design, Minitab fits a plane (all linear terms), using the corner points, and then fits the center point. If the center point is far away from the plane, you can conclude there is curvature in the model. However, this also means it is impossible to predict the value of the response for predictor values not included in the design, because there isn't one surface that fits all points in the model. In this case, you might want to add axial points and model the curvature with a response surface design.

By contrast, when center points are not included in the model, Minitab fits a plane using all points in the model, including the center point runs. This means you cannot test for curvature, but, since the model is a single surface, you can then predict responses for values not included in the model.