
multiple regression equations
hello,
can anyone give a suggestion or reference regarding how a system of multiple regression equations are solved?
rajesh


You should be able to use SPSS. There are some other techniques like Neural networks and Evolutionary Algorithms to solve/predict Multi variable problems.


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 oneunit
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= ∑(Pi  P_{p}i)^{2}
SSD= ∑(Pi  (a * Si + b * Wi)) ^{2}
where Pi, Si and Wi [i=1 to N], known
P_{p}i = P_{p}[i=1 to N], unknown
note that the sequences Pi, Si, and Wi are deviations from mean.
i.e. Pi=P_{i}(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.
δSSD/δa = 0
δSSD/δb = 0
This will be:
a = [∑(SiPi) * ∑(Wi^{2})  ∑(SiWi) * ∑(WiPi)] / [∑(Si^{2}) * ∑(Wi^{2} )  ∑(SiWi) * ∑(SiWi)]
b = [∑(SiPi) * ∑(SiWi)  ∑(Si^{2}) * ∑(WiPi)] / [∑(SiWi) * ∑(SiWi)  ∑(Si^{2}) * ∑(Wi^{2} )]
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 errorintercept 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.


hello roxy,
thanks for assistance. i will look into that.
rajesh


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


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 builtin functions with matlab too.

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