Several writers have studied the problem of obtaining confidence bands for a straight line regression under the requirement that the bands be at a specified confidence level, (1 -a) say, for values of the independent variable restricted to a pre-specified closed interval. The bands studied by other writers have been either bands of equal width throughout the interval or trapezoidal bands. This p 11per studies confidence b:tnds of the class ical hyperbolic type under the restriction noted above. Relev:mt distribution results differ according to whether the pre-specified interval on the independent variable is symmetric or asymmetric about the mean of the independent variuble values in the experiment. In the former case the problem under study, is shown to he equivalent to a problem studied by Halperin et al (.J ASA, Sept. 1967) for which distribution theory and tables are already available. The symmetrical case is generalized to obtain confidence bands in multiple linear regression at level (1-a) for an ellipsoidal region on the independent variables centered at the point of means of the independent variable values used in the experiment.For straight line regression some numerical comparisons are made with bands of the other types mentioned above. These comparisons suggest that the bands proposed in this paper are uniformly superior to bunds of equal width in the sense of having smaller average width; the proposed bands appear to be superior to trapezoidal bands in the same sense for intervals of practical interest, i.e. within or reasonably close to the range on the independent variables used in the experiment.
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