We know that U 1 d 1 , 1 , the first column of UD, has the most variability of all the columns of UD. Earlier we saw an image of Y : in which we can see that the student to student variability is...

We know that U₁d₁,₁, the first column of UD, has the most variability of all the columns of UD. Earlier we saw an image of Y :

in which we can see that the student to student variability is quite large and that it appears that students that are good in one subject are good in all. This implies that the average (across all subjects) for each student should explain a lot of the variability. Compute the average score for each student and plot it against U₁d₁,₁
and describe what you find.