We see that the total sum of squares is preserved. This is because V is orthogonal. Now to start understanding how Y V is useful, plot ss_y against the column number and then do the same for ss_yv....

We see that the total sum of squares is preserved. This is because V is orthogonal. Now to start understanding how Y V is useful, plot ss_y against the column number and then do the same for ss_yv. What do you observe?

From the above we know that the sum of squares of the columns of Y (the total sum of squares) add up to the sum of s$dˆ2 and that the transformation Y V gives us columns with sums of squares equal to s$dˆ2. Now compute what percent of the total variability is explained by just the first three columns of Y V .