## Sunday, November 29, 2020

### HP Prime: Linear Exponential Combination Fit

HP Prime:  Linear Exponential Combination Fit

The program LINEXPREG attempts to fit bivariate data to the curve:

y = a + b * x + c * e^x

The LSQ (least square) function is used.  The output is a list of three matrices:

*  A matrix of coefficients:  [ [ a ] [ b ] [ c ] ]

*  A matrix of y values entered

*  A matrix of predicted y values

HP Prime Program LINEXPREG

EXPORT LINEXPREG(lx,ly)

BEGIN

// 2020-11-17 EWS

// x list, y list

LOCAL n,lx2,lx3,mx,my,k,mr,mq;

n:=SIZE(lx);

lx2:=e^(lx);

lx3:={};

FOR k FROM 1 TO n DO

lx3:=CONCAT(lx3,{1,lx(k),lx2(k)});

END;

mx:=list2mat(lx3,3);

my:=list2mat(ly,1);

mq:=LSQ(mx,my);

mr:=mq(1,1)+mq(2,1)*lx+

mq(3,1)*e^(lx);

mr:=list2mat(mr,1);

RETURN {mq,my,mr};

END;

Example

x list:  {0, 1, 2, 3, 4, 5}

y list:  {2, 7, 13, 18, 26, 34}

LINEXPREG({0, 1, 2, 3, 4, 5},{2, 7, 13, 18, 26, 34})

Results:  {coefficients, y values, predicted y values}

coefficients:

[ [ 1.74935499143 ]

[ 5.39455446221 ]

[ 3.66584105034E-2 ] ]

y values:

[ [ 2 ]

[ 7 ]

[ 13 ]

[ 18 ]

[ 26 ]

[ 34 ] ]

predicted y values:

[ [  1.78601340193 ]

[ 7.24355734477 ]

[ 12.8093349675 ]

[ 18.6693222357 ]

[ 25.3290542368 ]

[ 34.1627178129 ] ]

Equation:

y = 1.74935499143 + 5.39455446221 * x + 3.66584105034E-2 * e^x

On to the last month of 2020...

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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