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ms_x
2005 Jul 20
1
predict.lm - standard error of predicted means?
...5
predict.lm(model,newdata=data.frame(x=c(10,20)),se.fit=T,interval="prediction")$se.fit
1 2
0.2708064 0.7254615
I was surprised to find that the standard errors returned were in fact the
standard errors of the sampling distribution of Y_hat:
sqrt(MSE(1/n + (x-x_bar)^2/SS_x)),
not the standard errors of Y_new (predicted value):
sqrt(MSE(1 + 1/n + (x-x_bar)^2/SS_x)).
Is there a reason this quantity is called the "standard error of predicted
means" if it doesn't relate to the prediction distribution?
Turning to Neter et al.'s Applied Linear Statist...