The size of the error in prediction is smallest at the mean of the predictors and increases as the values for the predictors move toward the extremes. One woul need to take this into account. Any good regression book (like Draper and Smith) will have the formula, which is difficult to represent in text format. Var(mean Y hat) = X(0)'(X'X)inv X(0)sigma hat squared: where X(0) represents the vector of X's you are predicting from. Assuming normality, then a t could be determined that would give an approximate idea of how far the observation was from the prediction.
Paul R. Swank, Ph.D. Professor, Developmental Pediatrics Medical School UT Health Science Center at Houston -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Rajarshi Guha Sent: Saturday, March 27, 2004 8:55 PM To: [EMAIL PROTECTED] Subject: [edstat] classifying predictions from linear regression Hello, I'm considering a problem where I would like to classify the predictions made by a multiple linear regression model as 'good' or 'bad'. I have considered a number of ways to go about it - the most obvious being the use of outlier diagnostics and classifying outliers as 'bad' predictions. However I was also wondering whether it would make sense to use the standard deviation of the observations (or the predictions) as a criterion. That is, if a prediction lies outside, say, 1 standard deviation, it would be 'bad'. The problem is '1 standard deviation of *what* ?' I'm not sure that it seems to make sense to say 1 standard deviation beyond the mean of the observation. Is it possible to calculate confidence intervals for the predictions and then say that if an observation lies outside the calculated confidence interval it would be 'bad'? Or should I simply stick to outlier diagnostics? Thanks, -- ------------------------------------------------------------------- Rajarshi Guha <[EMAIL PROTECTED]> <http://jijo.cjb.net> GPG Fingerprint: 0CCA 8EE2 2EEB 25E2 AB04 06F7 1BB9 E634 9B87 56EE ------------------------------------------------------------------- Q: What's purple and commutes? A: An abelian grape. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
