I'm attempting to validate a PLS-regression model using sklearn.

 From the documentation it states that the score function "returns the R^2 of self.predict(X) wrt.y". R2 is calculated as:

$$ R^2 = 1 - RSS/TSS $$ $$ RSS =\sum(y-\hat{\mathbf{y}})^2 $$ $$ \ TSS = \sum(y - \bar{\mathbf{y}})^2 $$ Additionally from my understanding I need to validate the model using a test set on which I can then calculate the Predictive performance (Q2) of the model. Q2 is calculated as: 1-PRESS/Total Sum of Squares.

$$ \ Q2 = 1 - PRESS/TSS $$ $$ \ PRESS = \sum(y-\hat{\mathbf{y}})^2 $$

The Calculation for R2 and Q2 seem practically identical. In this case could I calculate R2 as on the training set and Q2 on the test set? In that case could I simply call:

r2 = pls.score(x_train,y_train) q2 = pls.score(x_test,y_test) 

to compute r2 and q2?

Additionally a side question: Is it good practice to scale Y in the same manner as X in PLS regression?

I'm attempting to validate my Partial Least Squares (PLS) -regression model. From documentation and other readings regarding PLS regression I've come to understand that there are generally two metrics used to evaluate the performance of the algorithm. $R^2$ is calculated as 1 - residual sum of squares(RSS) and the total sum of squares(TSS):

$$ R^2 = 1 - RSS/TSS $$ $$ RSS =\sum(y-\hat{\mathbf{y}})^2 $$ $$ \ TSS = \sum(y - \bar{\mathbf{y}})^2 $$ While $Q^2$ is calculated as 1  - Predictive residual Error sum of squares(PRESS)/ TSS: $$ \ Q^2 = 1 - PRESS/TSS $$ $$ \ PRESS = \sum(y-\hat{\mathbf{y}})^2 $$

The Calculation for $R^2$ and $Q^2$ are almost identical, with the only difference being that RSS is calculated from the data on which the algorithm is trained and PRESS is calculated from held out data.

My question:

In the view of training/test splits of data, is it appropriate to call $R^2$ a metric of how the algorithm fits the training data and $Q^2$ a metric of algorithm performance on test data?

Side question: Is it good practice to scale Y in the same manner as X in PLS regression?