Correlation/Regression

• Partial to You

Music and lyrics ©2010-2013 by Lawrence Mark Lesser

I feel young when you're near me:
I regress easily!
My age held constant by all you do -
I'm partial to you.

My old "(e)x", I sent back 'cause
We were unstable from too much overlap.
Then you brought so much new -
I'm partial to you.

Love explained can't be denied:
Our fit makes R-square high.
We're homoskedastic and normal too -
I'm partial to you . . . partial to you.

• The Line

Lyrics copyright by Kyle White
May be sung to the tune of "The Middle" (Jimmy Eat World)

Data, a scattered n by p set.
It's only in your points you feel spread out, and without trend.
You want to test if your set's a scam
and you worry when they tell your points, "you're unexplained!"

It just takes a line,
X prime X beta equals X prime Y!
Everything, everything will fit just fine.
Everything everything will fit alright, alright.

Beta, you define that plane.
That hat you're wearing makes you look pretty BLUE, but no, not sad.
You fit great, the data need a friend.
It doesn't matter if it's up or down, go find some trends!

It just takes a line, X prime X beta equals X prime Y!
Everything, everything will fit just fine.
Everything everything will fit alright, alright.

It just takes a line,
Gauss and Markov they were pretty fly guys!
Everything, everything will fit just fine.
Everything everything will fit alright, alright.

Data, a scattered n by p set.
It's only in your points; they feel spread out, and without trend.
Just do your test, with beta hat's great plane,
and hope that every x in your set... remains!

It just takes a line,
X prime X beta equals X prime Y!
Everything, everything will fit just fine.
Everything, everything will fit alright, alright.

It just takes a line,
minimize the sum of squares and it's a sign!
Everything, everything will fit just fine.
Everything, everything will fit alright, alright.

Watch the video

• Shrink It

Lyrics copyright by Bradley Turnbull, Joe Usset, Sidd Roy, and Kyle White
May be sung to the tune of "Shake It" (Metro Station)

I got a beta hat and great I get a zero score.
Least squares works, but prediction's so poor.
And I was thinking of ways that I could penalize.
I need some zero values!
LASSO is what I choose!

You tune that baby up;
just the best will come back.
If prediction's all you want, OLS is on crack.
Just shrink those betas down,
then you loop it right back.
(Thank you,)
Tib-Tib Tib-Tib-shir-a-ni!!

Your betas tremble because your Xs are collinear,
and without a lambda you feel so singular.
So I was thinking of ways that I could penalize.
Makes no sense to select!
Ridge regression perfect!

Now you leave one out, then you find a Y-hat.
Then you sum them all up, yeah pick lambda like that.
Now beta's pretty small, but you like it like that.
(Come on!)

Shrink shrink, shrink shrink, shrink it!!

My beta's biased but
I kissed some variance goodbye.
My MSE is not so mean,
I guess this was worth my time?

The path ahead is sparse,
so I will look up and pray:
Oracle, please!
I can adapt and you can show me the way (way).

Now we're penalizing beta with a norm in L1
and a fan of Thomas Bayes isn't missing any fun
'cause a double exponential
and the mode can get it done, c'mon!

Tib-Tib Tib-Tib-shir-a-ni!!
Shrink shrink, shrink shrink, shrink it!!

Watch the video