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Multiple linear regression 1.01

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  Multiple linear regression 1.01 Ramine <ramine@1.1> - 2014-08-29 15:53 -0700

#2588 — Multiple linear regression 1.01

Hello,


Multiple linear regression 1.01


Author: Amine Moulay Ramdane


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.mrsoft.org/


You can downloawd my Multiple linear regression 1.01 from:

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


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

Operating Systems: Windows.

Required FPC switches: -O3 -Sd

-Sd for delphi mode....

Required Delphi switches:  -$H+




Amine Moulay Ramdane.

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