Dear Colleagues: I found a somewhat unusual way of using the confidence interval (CI) & prediction interval (PI) in multiple linear regression (MLR) in practice and I'm wondering someone could help me
We have a multiple linear regression equation, let's say Y = b0 + b1*X1+b2*X2+b3*X4+b4*X4. The derived equation is a very good one after checking residual, p-values, multicollinearity, etc... I understand how to compute confidence interval estimation of the mean response and prediction interval for a new observation in MLR at a particular point (e.g., average values of independent variables) as usual from text books. However, I found that some people use the predicted-Y values calculated by using the above equation as an independent variable and the measured Y is regressed on the predicted-Y again (not independent variables!). Then CI or PI are computed at a nominal value of the Y-predicted (e.g. average of the predicted values). By doing that, they can draw CI and PI on a sheet where y-axis is actual Y values and x-axis is predicted Y values. I see their needs to show some errors in prediction: if we have more than 2 independent variables, it's very difficult to draw CI or PI on a sheet. And they said that the above equation has +/- 50 kg in errors. I believe that the current practice is not correct. If the above approach is not the right way, how can I say in more elaborate way not to use such an approach rather than say simply "It's wrong!"? Am I asking a wrong question that is impossible to answer? Or I have to have them/myself in a training course. Any thoughts or references are welcome. I read through a few books on MLR and the "Statistical Intervals" written by Gerald. Hahn but found no such practice. Thank you very much. Sangdon Lee, Ph.D., CQE, CRE Michigan . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
