variable selection using covsel, then multiple linear regression (MLR)
model=covsel_mlr(x,y,split,lv,(centred))
the calibration dataset; dimensions (n x q) and (n x k) or Div structures
warning: when x is not square and of full rank, the MLR is computed with the Moore-Penrose pseudo-inverse of xx'
parameter for the cross-validation:
- an integer: number of random blocs
- two integers [a b]: a random blocks ; b repetitions of the cross-validation
- a vector of dimension n attributing each observation to a block (numbers 1,2,...k for k blocks): blocks given by the vector
- a matrix (n x b ) of column-vectors of dimension n attributing each observation to a block (numbers 1,2,...k for k blocs): blocks given by each vector, b repetitions of the cross-validation
- 'vnbxx': venitian blinds, xx blocks; ex: 'vnb10' for 10 blocks
- 'jckxx': Jack knife, xx blocks; ex: 'jck8' for 8 blocks
the number of x-variables to be selected
1=centred (by default); 0=not centred
the standard errors of calibration aand cross-validation
model.err.d is a matrix (2 x lv x k); the lines are the rmsec and the rmsecv respectively
the predicted values of y after cross-validation
model.ypredcv.d is a matrix of dimensions (n x q x k)
the b-vector or vector of the regression coefficients
model.b.d is a matrix of dimensions (q x lv x k)
means of x and y , a vector (q x 1) and a vector (k x 1)
centering option applied; 1=centred; 0=not centred
the method name; here: 'covsel_mlr'
the selected x-variables determined with all the y-variables, line (k+1), then ordered for each of the k y-variables, (lines 1 to k)
model.var_selected.d is of dimensions ((k+1) x lv )