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Multiple linear regression 1.05

Ramine

7/8/2015 8:12:00 PM

Hello,


Multiple linear regression was updated to version 1.05, i have
updated the cmatrix DLLs for win32 and win64 to the newer versions,
and i have used the tbbmalloc memory manager that is better...


Authors: Amine Moulay Ramdane

Email: aminer@videotron.ca

Description:

Multiple linear regression that uses SIMD SSE2 instructions and that
implements the following mathematical theorem:

If A is an m x n rank n matrix, then the least-squares solutions to the
system A*vector(X) = vector(C) are the solutions to the system:

A*vector(X)=

A*inverse(transpose(A)*A))*transpose(A)*vector(C).

This system has the following unique solution:

vector(X) = inverse(transpose(A)*A)*transpose(A)*vector(C)

I have updated my multiple linear regression program to support
SSE (Standard Error of the Estimate), the "SSE" is important in quality
control, the interpretation of SSE is similar to standard deviation's
"68-95-99 rule", that is, 68% of the time the predicted score will fall
plus-or-minus 1 x SSE of the actual score based on the regression
equation, 95% of the time the predicted score will fall plus-or-minus 2
x SSE , and 99% of the time the predicted score will fall plus-or-minus
3 x SSE.

So my Multiple linear regression program does show the multiple
regression equation that approximate the statistical data and it
calculates and shows the Coefficient of determination R2 and it
calculates and shows the Standard Error of the Estimate.

I have also included a Matrix library called LinMath that uses SIMD SSE2
instructions and that is multithreaded, LinMath was derived fom mrmath
Matrix library by Rabatscher Michael and modified to become compatible
with both FreePascal and Delphi.

LinMath is offered under the licence agreement described on:

http://www.m...

Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freep...

Operating Systems: Windows.

Required FPC switches: -O3 -Sd

-Sd for delphi mode....

Required Delphi switches: -$H+


You can download my Multiple linear regression version 1.05 from:

https://sites.google.com/site/aminer68/multiple-linear-...



Thank you,
Amine Moulay Ramdane.
1 Answer

Ramine

7/8/2015 8:42:00 PM

0


Hello..


Please note that the example inside the "test.pas" inside the zip file
have a mathematical function of 4 variables as:

a5:=f(a1,a2,a3,a4)

but notice that if you are using a mathematical function of 4 variables
as in my example inside the test.pas source code, the 5th variable
inside the mat2 matrix must be always 1, this is how my solver works,
but i you have a mathematical function of 2 variables the 3th variable
inside the mat2 matrix must be always 1 , please take a look at the
source code inside the "test.pas" example and you will understand , it's
really easy to work with my multiple linear regression solver.


Thank you,
Amine Moulay Ramdane.