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After the regression coefficients have been calculated, projections may be made based on the curve fit. I'm disappointed that you may only key in an x value to see an estimated y value. How about keying in a known y value? I thought about adding this feature to the CFIT program, similar to the Curve Fitting program originally published in the HP-67 Standard Pac. Are there any issues with running a tweaked program from main memory, with the advantage pac still installed?

Projecting Y onto X may seem harmless from a mathematical point of view. However, some statistician may frown upon that, because (the way I understand it) the measurement in variable X have no error in its measurement while those of variable Y has normally distributed errors. For some reason statisticians frown on calculating X^ ... and the really get into a hissy fit (pun intended) if you calculate the confidence interval of X^.


Edited: 21 June 2011, 8:17 p.m.

Well, suppose you measure the gross weight of a UPS truck (y) with various numbers of packages (x) in it, and you get the regression equation ˆy = 2.17x+2463. The slope, 2.17, is the average weight per package, and the y intercept, 2463, is the weight of the empty truck. The value of ˆy when x is 0 isn't always meaningful, but in this case, it has physical meaning!

Edited: 21 June 2011, 10:36 p.m.

From what I've read it's not the same if you just invert the resulting regression equation as opposed to swapping x and y in the data set and do a new regression to predict x from y. So in order to do it correctly, you need to accumulate the reverse statistic in parallel for this kind of calculation.

You were asking about supplying a value for Y and calculating X. Some statisticians will cry foul because the relation of the regression line is to correlated Y with X and not X with Y.

The point I was trying to make is that a least squares fit has applications other than statistics. For instance, I use it to iterate between finite element analyses results, when determining the starting point for the next iteration. The relation between X and Y is not statistical, but is based on geometry and material properties used in the model. If the material(s) have a linear stress-strain relationship, then the straight line fit would represent the combined spring rate (for complex models this would be difficult to calculate directly). And geometry can introduce non-linear behavior (e.g. belleville spring). For such uses, it would be nice to have the option to calculate estimates in either direction, where Y=load and X=deflection.

Edited: 22 June 2011, 8:48 a.m.

Makes sense to me.

The HP 20s has (IMHO) both!

Just to bad it hasn't RPN.

I modified the CFIT program over the weekend to include Y predictions. One thing I noticed is that if you call the subroutines (e.g. "A~", BFIT, etc.) from the module and get an error, a R/S will continue execution from within the unmodified CFIT program.

The HP-33s and HP-35s provide the capability you want and have rpn.