MaplePrimes - comments on Post, Least squares documentation

MaplePrimes - comments on Post, Least squares documentation http://www.mapleprimes.com/posts/38243-Least-Squares-Documentation en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 21:25:46 GMT Wed, 10 Jun 2026 21:25:46 GMT The latest comments added to the Post, Least squares documentation http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, Least squares documentation http://www.mapleprimes.com/posts/38243-Least-Squares-Documentation Linearity http://www.mapleprimes.com/posts/38243-Least-Squares-Documentation?ref=Feed:MaplePrimes:Least squares documentation:Comments#comment68541 Linearity in this context means that the derivative over a parameter doesn't depend on this or other parameters. Non-linear models also can be fit in Maple. In particular, using Statistics:-NonlinearFit. The help page for it has an example of a non-linear model. Alec The latest comments added to the Post, Least squares documentation 68541 Sat, 06 Dec 2008 23:33:43 Z alec alec Appearing linearly http://www.mapleprimes.com/posts/38243-Least-Squares-Documentation?ref=Feed:MaplePrimes:Least squares documentation:Comments#comment68535 For example, linear least squares could fit the curve y = a*x^2 + b*y + c where the unknown parameters are a,b,c, because this is a linear function of a,b and c, even though it is nonlinear in x.   But y = a*x^p + c would be nonlinear in the parameter p, so fitting it would be a nonlinear least-squares problem. The latest comments added to the Post, Least squares documentation 68535 Sun, 07 Dec 2008 09:49:33 Z Robert Israel Robert Israel An example might be choosing http://www.mapleprimes.com/posts/38243-Least-Squares-Documentation?ref=Feed:MaplePrimes:Least squares documentation:Comments#comment68515 An example might be choosing the the vertex of a parabola as parameters. Least squares can't fit to a and b directly: y = (x-a)^2 + b since the fitting equations will depend on a non-linearly. For each point on the parabola e.g. (x,y)=(-1,1) you get a quadratic equation like 1 = (a+1)^2+b.  Least squares only works on a set of linear equations. The latest comments added to the Post, Least squares documentation 68515 Mon, 08 Dec 2008 19:35:15 Z jpmay jpmay Making it linear http://www.mapleprimes.com/posts/38243-Least-Squares-Documentation?ref=Feed:MaplePrimes:Least squares documentation:Comments#comment68499 Another way of saying it is to say that a linear model is a linear combination of some functions of independent variables (sometimes called "test" functions.) It looks like a*f(x,y)+b*g(x,y)+c*h(x,y)+k(x,y) for a model with 3 parameters, 2 independent variables, and 4 test functions, one of which can not be changed. Sometimes non-linear models can be rewritten in another form as linear. For example, model a*cos(x-b) with independent variable x and 2 parameters a and b is non-linear, but it can be written in form A*cos(x)+B*sin(x), which is linear in parameters A and B. Similarly, a non-linear model in jpmay example above can be written as a linear model x^2+A*x+B. That is not always possible though. Alec The latest comments added to the Post, Least squares documentation 68499 Tue, 09 Dec 2008 04:11:52 Z alec alec