In article <91715h$sbv$[EMAIL PROTECTED]>,
"junk" <[EMAIL PROTECTED]> writes:
snip
|> Why I am trying to do is come up with a simple method of doing a
|> multivariable (multidimensional ?) least squares approximation.
|>
|> How could I easily create:
|> Y = (a1*A^4 + b1*A^3 . e1*A + f1) + (a2*B^4 .. + f2) + (a3*C^4 +.+f3)
the model is wrong! replace f1+f2+f3 by _one- f
snip
I hope EXCEL has a linear system solver which works correctly.
(Off limits for MS here)
In this case set up a matrix "M" with 13 columns and
with rows
[ A^4 A^3 A^2 A B^4 B^3 B^2 B C^4 C^3 C^2 C 1 ]
inserting the values of A,B and C from one row of your data file
also set up a vector "n" of all Y's,
In your case "M" has 18 rows (not that much for 13 parameters !)
Now solve
M'M [x] = M'n
this is a linear system of equations with 13 equations and 13 unknowns [x]
M' means transposition . e.g. element (13,13) of M'M is 18.
solve the system. then
[x]=(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3,f)
If your data points are not properly distributed in space, then it may turn out
that the matrix is singular (for example you must not have all data points with
A=B=C). In that case you need more points resp. better distributed points.
just for curiosity: with the meaning of A=paint, B=engine, C=amenities
Y=price, why do you assume this linear behaviour with respect to the
influences of A,B,C but such a strange behaviour in powers of A,B,C alone?
shouldn't the influence of "C" show some saturation effect?
hope that helps
peter
|> A B C Y
|> paint engine amenities price
|> 0.1 1 6 $1000
|> 0.11 2 5 1200
|> 0.14 1 3 1150
|> 0.16 2 5 1200
|> 0.2 1 4 3000
|> 0.201 4 5 2700
|> 0.3 2 3 4000
|> 0.33 4 7 3500
|> 0.35 1 4 6000
|> 0.4 2 6 4650
|> 0.41 3 4 4400
|> 0.42 4 3 4750
|> 0.44 1 5 5360
|> 0.45 1 3 7500
|> 0.6 3 3 7400
|> 0.8 2 5 7700
|> 0.87 2 6 8500
|> 0.88 3 5 9000
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