Matlab 偏最小二乘 PLSregress

　　[XLOADINGS,YLOADINGS] = plsregress(X,Y,NCOMP)

　　//　　Ncomp:主成分个数

　　// XLOADING : X 的线性组合系数矩阵

　　//YLOADING : y 

　　// XSCORES is an N-by-NCOMP orthonormal matrix with rows corresponding to observations, columns to components.

　　// YSCORES is an N-by-NCOMP matrix with rows corresponding to observations,columns to components. 　　YSCORES is neither orthogonal nor normalized.

　　//BETA is a (P+1)-by-M matrix, containing intercept terms(截距项) in the first row, i.e., Y = [ONES(N,1) X]*BETA + Yresiduals, and Y0 = X0*BETA(2:END,:) + Yresiduals.

　　// PCTVAR containing the percentage of variance explained by the model.

　　// MSE containing estimated mean squared errors for PLS models with 0:NCOMP components.

[XL2,YL2,XS2,YS2,BETA2,PCTVAR2,MSE2,stats2] =plsregress(a,b,ncomp)

beta3(1,:)=mu(n+1:end)-mu(1:n)./sig(1:n)*BETA2([2:end],:).*sig(n+1:end) %原始数据回归方程的常数项

beta3([2:n+1],:)=(1./sig(1:n))'*sig(n+1:end).*BETA2([2:end],:) %计算原始变量x1,...,xn的系数，每一列是一个回归方程

sig = std(data)

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Χ₁^{' = -4.1306 * u_1+0.0558 *u}2t

XL2 =

-4.1306 0.0558
-4.1933 1.0239
2.2264 3.4441

YL2 =

2.1191 -0.9714
2.5809 -0.8398
0.8869 -0.1877

XSCORES is an N-by-NCOMP orthonormal matrix with rows    corresponding to observations, columns to components.