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rajeshj
29th January 2005, 12:53 PM
hello,
can anyone give a suggestion or reference regarding how a system of multiple regression equations are solved?
rajesh

sharief77
29th January 2005, 05:52 PM
You should be able to use SPSS. There are some other techniques like Neural networks and Evolutionary Algorithms to solve/predict Multi variable problems.

rocksea
30th January 2005, 10:56 AM
Here I have tried to have a simple look into solving multiple regression.
Any misunderstandings, please notify.

Assumptions:
1. Two independent variables SST (S) and Wind (W) and dependent variable
Precipitation (P). Suppose we can say P=aS + bW
'a' represents an estimate of the change in P corresponding to a one-unit
change in S when all other independent variables(here W) are held constant.
Similarily, 'b'.

2. We have some values of P, S and W. With that, we want to make a
predictor model which gives the relationship. i.e. the constants a and b.

The "best" combination of a and b values is the combination that minimizes
the sum of squares of the difference between the dependent variable and
the dependent variable predicted by the model.

This sum square of differences:
SSD= E(Pi - Ppi)2
SSD= E(Pi - (a * Si + b * Wi)) 2

where Pi, Si and Wi [i=1 to N], known
Ppi = Pp[i=1 to N], unknown

note that the sequences Pi, Si, and Wi are deviations from mean.
i.e. Pi=Pi(original)-P(average)

A partial derivative of the above equation (w.r.to a and b) set to zero
will give two equations for a and b in which a and b gives the least sum of
differences.

dSSD/da = 0
dSSD/db = 0

This will be:

a = [E(SiPi) * E(Wi2) - E(SiWi) * E(WiPi)] / [E(Si2) * E(Wi2 ) - E(SiWi) * E(SiWi)]

b = [E(SiPi) * E(SiWi) - E(Si2) * E(WiPi)] / [E(SiWi) * E(SiWi) - E(Si2) * E(Wi2 )]

thus you will get a perdictor model:
P = aS + bW in which you can put S, W and get P.

'a' and 'b' can be found out by giving Si,Wi and Pi as input to a software
which does regression. You will also get the error-intercept values as well.
Maybe fortran functions can be used for it. In MatLab, there are a lot
of regression functions starting from regress(). Just type in >> lookfor regress.
Also a toolbox in MatLab, glmlab is referred for analysis including multiple regressions.
http://www.sci.usq.edu.au/staff/dunn/glmlab/glmlab.html

I think someone else can add on to this and give a developed version of this.

rajeshj
30th January 2005, 11:16 AM
hello roxy,
thanks for assistance. i will look into that.
rajesh

rajeshj
30th January 2005, 11:40 AM
hello all,
i installed glmlab in matlab, but when typing glmlab i get this error message.

>> glmlab
??? Undefined function or variable 'dllist'.

Error in ==> D:\programs\toolbox\matlab\glmlab\glmlab.m
On line 85 ==> L1=dllist(which('llist'),'l'); %load link functions

why is it so? is anybody familiar?

rajesh

rocksea
30th January 2005, 03:47 PM
hi, I just downloaded it and checked.
Maybe you missed to Set Path of glmlab with subfolders.

File-> Set Path -> Add with subfolders-> Select the folder where
you unzipped glmlab. Save and Close.

Then, I havent used glmlab though I saw many references to it.
If it is useful, do tell. Try the built-in functions with matlab too.

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