Normalized residual squared

[Nick Bornschein]

Hello Stata user,

I was working on a special leverage plot I wanted to create with "twoway scatter". Therefor I was calculating the "normalized residual squared" the lvr2plot is using. But I have some problems. I have found the equation in the Stata help:

As far as I can see that correctly, e_i_hat is the residual (difference between my y variable and the predicted y value). But which residual is e_j ?

Thanks
Nick

[Andrew Musau]

It's the \(j\;^{th}\) residual that you want to normalize. Obviously, it will be confusing to index it as \(i\) given that you also define \(i\) as an arbitrary index of all other residuals that you are summing in the denominator.

[Nick Bornschein]

What I wanted to do ist the following:

clear
sysuse auto
reg price weight
lvr2plot

I wanted to create this plot for my own by using:

predict lev, leverage
predict resid, resid
gen resid2 = resid*resid
qui: su resid2
gen e_nj = resid / sqrt(`r(sum)')
twoway scatter lev e_nj // not the same x-axis like lvr2plot

But my normalized squared residuals aren't the same as in lvr2plot. So what's wrong calculating e_nj in my code?

Thanks again
Nick

PS. Didn't know I can use Latex Code here. How did you write j_th in your post?

[Andrew Musau]

You almost have it right, but the x-axis is the square of the normalized residuals.

gen e2_nj = e_nj^2
twoway scatter lev e2_nj

PS. Didn't know I can use Latex Code here. How did you write j_th in your post?

\[ LATEX CODE \]

where you change the square brackets to parentheses.

[Nick Bornschein]

Ahhh! Thank you! I was totally blind to "squared"! Thank you so much, also for the Latex.