Hi Hamid,
I understand that you are interested in understanding how the "plsregress" function in MATLAB calculates the variance explained by each Partial Least Squares (PLS) component, specifically focusing on the "PCTVAR" output.
1. The "plsregress" function in MATLAB performs Partial Least Squares Regression, which is a method used to model relationships between input variables (predictors) and output variables (responses) by extracting latent variables (components).
2. The "PCTVAR" output from "plsregress" provides the percentage of variance explained by each PLS component for both the predictors and responses. This is crucial for understanding how well the components capture the original data variance.
3. The variance explained by each component is calculated by comparing the variance of the data explained by the PLS components to the total variance. This involves computing the sum of squared deviations from the mean for both the original data and the data reconstructed from the components.
4. Specifically, for each component, the explained variance for the predictors is calculated as follows:
- Calculate the sum of squared deviations of the original predictor data.
- Calculate the sum of squared deviations of the predictor data reconstructed using the PLS components.
- The ratio of the explained variance to the total variance gives the percentage of variance explained by that component.
5. The same procedure is applied to the response variables to compute the variance explained by each component for the responses.
Refer to the documentation of "plsregress" for more details on PLS regression: https://www.mathworks.com/help/stats/plsregress.html
Hope this helps!
