Matlab fit to three dimensions function

6 次查看（过去 30 天）
standy
standy 2019-8-28
评论： the cyclist 2019-8-28
Hi
I got three input vectors: x1, x2, x3 and output vectory y. How do i fit to my custom function?
y=a0+a1*x1+a2*x2+a3*x3+a11*x1^2+a22*x2^2+a33*x3^2+a12*x1*x2+a13*x1*x3+a23*x2*x3
Obviously I want to get parameters a1, a2, ...
For two variables (x1, x2) i can do it like:
f = fit([x1, x2], y, 'poly33');
But I'm struggling to do that for the function above.
Any help appreciated.
  2 个评论
the cyclist
the cyclist 2019-8-28
Do you also have the Statistics and Machine Learning Toolbox available, or only the Curve Fitting Toolbox?

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

Bruno Luong
Bruno Luong 2019-8-28
编辑：Bruno Luong 2019-8-28
n = length(y);
A = [ones(n,1) x1(:) x2(:) x3(:) x1(:).^2 x2(:).^2 x3(:).^2 x1(:).*x2(:) x1(:).*x3(:) x2(:).*x3(:)] \ y(:)
the cyclist
the cyclist 2019-8-28
编辑：the cyclist 2019-8-28
I would do it like this:
% Set the random number generator seed, for reproducibility
rng default
% Create some random data
N = 1000;
x1 = randn(N,1);
x2 = randn(N,1);
x3 = randn(N,1);
% Create a response variable with known coefficients, and some noise
y = 2 + 3*x1 + 5*x2 + 7*x3 ...
+ 11*x1.^2 + 13*x2.^2 + 17*x3.^2 ...
+ 19*x1.*x2 + 23*x1.*x3 + 29*x2.*x3 ...
+ 31*randn(N,1);
% Fit a quadratic model
mdl = fitlm([x1 x2 x3],y,'quadratic')
% % The above is equivalent to the following model, written out in full Wilkinson notation
% mdl = fitlm([x1,x2,x3],y,'y ~ x1 + x2 + x3 + x1^2 + x2^2 + x3^2 + x1:x2 + x1:x3 + x2:x3');
Almost all of this code is me creating the data, to illustrate everything. Since you have the data already, you should only need
mdl = fitlm([x1 x2 x3],y,'quadratic')
The resulting model object, mdl, has methods for lots of information about the model fit.
  4 个评论
显示 2更早的评论
standy
standy 2019-8-28
Ahhh
Makes sense now. I got the output like:
Linear regression model:
y ~ 1 + x1*x2 + x1*x3 + x2*x3 + x1^2 + x2^2 + x3^2
Estimated Coefficients:
Estimate SE tStat pValue
__________ __________ ________ _______
(Intercept) 1.4267 1.1233 1.2701 0.23281
x1 -0.015338 0.024769 -0.61922 0.54962
x2 -0.90665 3.3137 -0.27361 0.78995
x3 0 0 NaN NaN
x1:x2 0.0031125 0.012077 0.25772 0.80185
x1:x3 0 0 NaN NaN
x2:x3 0.765 3.0553 0.25038 0.80736
x1^2 6.8008e-05 0.00011935 0.56982 0.58137
x2^2 0 0 NaN NaN
x3^2 0 0 NaN NaN
Does it mean that a0=1, a1=-0.015338 etc?

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Linear and Nonlinear Regression 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by