Is there a statistics guru out there who can help me figure out the predistion interval equation.

I did a fitted line regression (using Minitab) which is a quadratic fit and applying a log10 transformation to the response (Y). There is an option to display the 95% prediction interval. By looking at it, the lines seem to fit the data quite well and in particular flare out as X increases, just like the data. The software does not give the actual values. The minitab support gave me the formula used which is the same as I have in a book: Yi(predicted) +/- t(1-alpha/2,n-3)*sqrt((sum(yi-y(predicted))^2/n-3)*(1+1/n+((Xk-Xbar)^2/sum(Xi-Xbar)^2)). The problem I am seeing is that the only variation to the +/- comes from the variation of x-xbar which is divided by a large number, so the variation is non-existant. What am I doing wrong?

Thanks,

Michel.

I believe you are closer than you think.

First of all, there seem to be two slight typos, highlighted below. They shouldn't much affect the basic question. (I also changed a couple parentheses to make them easier for me to follow.)

Yi(p) +/- t(1-alpha/2,n-3) * sqrt[ (sum(yi-y(p))^2/n-3) * (1+1/n+{(Xi-Xbar)^2/sum(Xi-Xbar)^2}) ]


As to the size of the prediction interval, the equation above does still lead to some variation. It may seem that (Xi-Xbar)^2 would be much smaller than sum(Xi-Xbar)^2, but the data points near the ends of the curve contribute the most to sum(Xi-Xbar)^2.

For example, for nine data points at x = -4, -3, ... 4, sum(Xi-Xbar)^2 = 60. At the center, { (Xi-Xbar)^2/sum(Xi-Xbar)^2 } = 0 but at the ends, it is 0.27. This sort of effect is (presumably) enough to account for the spreading you see.

You may just have to grind through the numbers to convince yourself!

Tim F

I few comments for you to consider. Since you did a transformation of the data, you need to back transform the prediction interval to get it back into the native units.

Secondly, if you have very small MSE from the model, then any interval is going to be small. The variation comes from the model (MSE) and the future observation (xo-xbar).

Hope this helps

Steven