Partial Least Square Regression Result - Question

Hi, I am wondering why when I use PLS to find the coefficient for the independent variable, I get R^2 for each of the independent variable?

For instance, if my equation is Y=m1X1+m2X2+c

Minitab gives me the value of m1,m2, and c. It also gives me the R^2 value for each of the X1 and X2. I am wondering why do they give 2 R^2 value? What does each R^2 suppose to mean? Why doesnt it gives only one R^2? (R^2 for the independent value together with the dependent value)

Thank you!

Can any of you folks who are math wizards help with this one?

You may want to read this link on partial least squares regression for some background.

Minitab is doing something akin to a best subsets regression. It tries as many combinations of the x factors as you specify. You then select the number of components with the highest R-Sq value. This tells you the number of components in your model.

Components are combinations of related or correlated factors. Use the Loading Plot to determine what these are.

• Load values between -0.4 and 0.4 are not significant.
• Load values between -0.7 and -0.4 or between 0.4 and 0.7 are moderately significant.
• Load values < -0.7 or > 0.7 are highly significant.

I recommend that you open the Partial Least Squares Regression dialog box, click on the Help button, then click on the Examples link. Minitab will walk you through an example data set and explain how to interpret the graphs.

Thanks alot!! I think I got the general overview of it now.