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Can the HP15C interpolate? - Printable Version

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Can the HP15C interpolate? - Daniel Cook - 01-15-2001

I still have my trusty old HP15C, although I can't find the manual any longer. I'd like to use it in the field for doing photography calcs. I have graphs of exposure time vs. adjusted exposure time for pinhole cameras. I'd like to enter a series of X,Y data points from those graphs and ask the 15C do an interpolation (i.e. expected value) of a value of Y for a known value of X. Does anybody know if the 15C can be programmed for this type of operation and, if so, whether my best bet for doing learning the trick is to spring for the manuals on CD? Thanks.

Re: Can the HP15C interpolate? - Thibaut.be - 01-15-2001

Yes, irt can, by doing a linear regression.

First, clear your stat reg (f <GSB>
Key in your Y,X values by doing Y1 <ENTER> Y2 <ENTER>
Then key f <L.R.>
A linear regression calculates a straight line that best fits with your series, equation Y=aX + b
you get 2 values : in X register is the b value stored, and in Y register the a value.

So all you have to do is with your new X value multiply it with your Y register value and add the X register value.

Should you wish to get other kind of regression, the following formulas are appliccable :

Power regression (Dx/x = C; Dy/y = C) : y = ab^x
Exp. regression : (Dx=C, Dy/y=c) : y : kax^b

just write down all X & Y values, calculate Dx, Dy, and Dx/x, Dy/y, and check what best fits. Then with 2 samples (preferably the most far of each other) calculate the 2 variables system of equation. Remeber your logs formulas :
loag a/b = log a-log b
loag ab : log a+log b
loag a^b = loag a . log b

Good luck

Re: Can the HP15C interpolate? - Bill Smith - 01-16-2001

yes, it can. in fact there is a built-in function on the bottom row of keys, y^, r (the linear estimation key). which operates on the data stored in the statistics registers.

providing your curves can be linearized with respect to the coefficients, probably you would like to calculate these coefficients once, and then create a program to use them. that way the statistics registers can be used for other purposes.

alternatively, the 15C manual describes an interpolation technique using tabulated values which involves entering the bracketing table values and calculating the intermediate one of interest. this served me well in my thermodynamics courses, but may not be too handy for your field work.

finally, i have a pretty nice one page summary of straight-line functions of certain equations. i'd be glad to mail you a copy if your interested.