Re: [Gnuplot-info] Gnuplot Linear Regression Problem

[Hans-Bernhard B. <br...@ph...>]

Maurice Al-Khaliedy wrote:
> i have a problem with gnuplot 4.0 and Linear Regression. 

gnuplot doesn't do linear regression.  It does non-linear least-squares 
fitting, which encloses linear fits to a simple straight line as a 
special case.

> I got different values between MS excel and gnuplot.

I'm not as sure as you that this difference must mean it's gnuplot that 
is wrong ;-)

> Excel Funcion: f(x) = -6.64*x+ 256915
> Gnuplot Function: f(x) = 7.9214e-06*x + 1

This suggests you were *way* off with the startup values you gave 
gnuplot --- that's why the value for 'b' never moved at all.

There are a lot of things wrong with your example case:

* your 'x' is a date+time.  You don't seem to have used gnuplot's
date/time parsing capabilities in the fragment of gnuplot command script 
you show

* gnuplot and Excel use wildly different internal scales for date/time 
values, so the expectation of getting numerically equal results is flawed.

* you wrote 'using 1:2' --- that will plot and fit the hour against the 
date.  Almost certainly not what you wanted.

* the model function (linear dependance of y on time) doesn't fit the 
data at all, neither for 'using 1:2', nor for 'using 1:3'.

* the form a*x+b is spectacularly mismatched to a dataset that sits this 
far away from the point x=0 (new year 2000 for gnuplot, some thing like 
newyear 1900 for Excel, IIRC).

* the fit, once it's been forced to work by fixing most of the above 
problems, would have hugely different sizes for parameters a and b:

gnuplot> show func

         User-Defined Functions:
         f(x)=a*(x-17e7)+1e8*b


gnuplot> a=1 ; b=1; fit f(x) 'date.dat' u 1:3 via a, b
[...]
Final set of parameters            Asymptotic Standard Error
=======================            ==========================

a               = -7.70491e-005    +/- 0.0001626    (211.1%)
b               = 1.19202e-005     +/- 2.862e-006   (24.01%)


correlation matrix of the fit parameters:

                a      b
a               1.000
b               0.996  1.000

Translated to the original form, this fitted function is:

	f(x) = (-7+/-16)*1e-5*(x-17e7) + 1e8*(1.2+/-0.3)*1e-5
	     = (-7e-5 +/- 16e-5) * x + (14000 +/- 27000)

That's nine orders of magnitudes of difference between a and b.  This 
causes severe numerical problems for the fit.


gnuplot is at least honest with you.  It's telling you right away that 
this didn't work:

> a               = 7.9214e-06       +/- 0.0001624    (2050%)
> b               = 1                +/- 2.732e+04    (2.732e+06%)

Errors of 2000 percent and more should be sufficient warning that 
something's not right here.