Ellipse, Prediction Interval (Area) and Range

Prediction Interval (Area) Ellipse: This type of ellipse is useful for establishing confidence intervals for the prediction of single new observations (prediction intervals). Such bivariate confidence or control limits are, for example, often used in the context of multivariate control charts for industrial quality control (see, for example, Montgomery, 1996; see also Hotelling T-square chart ).

The ellipse is determined based on the assumption that the two variables follow the bivariate normal distribution . The orientation of this ellipse is determined by the sign of the linear correlation between two variables (the longer axis of the ellipse is superimposed on the regression line). The probability that the values will fall within the area marked by the ellipse is determined by the value of the coefficient that defines the ellipse (e.g., 95%). For additional information see, for example, Tracy, Young, and Mason (1992), or Montgomery 1996); see also the description of the prediction interval ellipse .
Range Ellipse: This type of ellipse is a fixed size ellipse determined such that the length of its horizontal and vertical projection onto the X- and Y-axis (respectively) is equal to the mean (Range * I) where the mean and range refer to the X or Y variable, and I is the current value of the coefficient field.