# Correlation/Regression

• ### Banana Peel

I tried to fit a line to estimate how many people fall per banana peel, but it was a slippery slope.

Larry Lesser and Dennis Pearl

• ### You're My Null

Lyrics & Music © 2014 Greg Crowther

If every gal I’ve met is a hypothesis
Who might turn out to be the mate I’ve sought,
And if I were to yield
To the conventions of my field,
Then you would be referred to as H-naught...

CHORUS:
You’re my null, after all; you’re a theory in the making,
So robust to every test -- my hypothesis of choice.
You account for the past; you’re a vision of the future;
And when I feel confused, you’re my signal through the noise.

My life has been an uncontrolled experiment --
A source of all too many scattered plots.
But you provide a line
With an R-squared of point-nine;
Yes, you and you alone connect my dots...

CHORUS

One can never prove a null
In a finite length of time;
Each finding simply strengthens it or not.
But if I see trends emerge --
And let’s just say I do --
I’d be crazy not to publish what I’ve got...

CHORUS [twice]

• ### Regression Rumba

Lyric © 2015 Lawrence M. Lesser; Music by Dominic Dousa

Before you do regression,
Check out the scatterplot
Make sure a linear relationship
Is good for what you've got!

We try to predict weight
Using height as the predictor
If the correlation is really strong,
We will be a victor!

For a unit increase of height
The expected weight will go
Up by five units:
That's the meaning of the slope!

If r equals 0.9
then 0.81 is r square:
The part of variation
In Y that X does share!

X and Y
Have a relationship
And our well-fit line
Gives us a good model to predict!

• ### Correlation Illustration

Lyric © 2015 by Lawrence Mark Lesser
may sing to tune of "Twinkle, Twinkle, Little Star"

How do shoe length values go
When height is high or when it's low?
Like horses on a merry-go-round
When they're both up or they're both down,
This provides an illustration of a positive correlation!

How do used car prices go
When mileage is high or low?
Like horses on a merry-go-round
Where one is up when the other's down,
This provides an illustration of a negative correlation!

How do weights of people go
When IQ score is high or low?
Wild horses on a merry-go-round:
No pattern to the up or down.
This is an illustration of zero correlation!

• ### Correlation Does Not Imply Causation

Music and Lyrics © 2016 Monty Harper

OPENING CHORUS:
Correlation does not imply causation
Correlation does not imply causation

People who own goggles are often getting fit
We seem to see that happen quite a lot
May we conclude that getting fit is caused by owning goggles?
Clearly, we may not!
If we take into account how many people swim,
It's a factor that confounds the implication,
For people who swim own goggles and get fit
And that that explains our wacky correlation!

[REPEAT OPENING CHORUS]

I've found that when I'm happy, I often seem to giggle
Knowing that may really serve me well.
Or maybe when I giggle, it tends to make me happy?
How am I supposed to tell?
The arrow of causation may point left or right or both,
So here's what I suspect to be the scoop:
I giggle and I feel happy so I giggle and feel more happy
So I giggle because I'm in a causal loop!

[REPEAT OPENING CHORUS]

The yearly rate of poverty and the length of my own hair
Correlate with an r of .99
I discovered this by accident and I don't know what to do
With this amazing hair of mine!
Is there some hidden mystic power built into my hair?
My professor says it's nothing of the kind.
It's coincidence my hair length predicts the yearly rate of poverty,
The universe is just messing with my mind.

[REPEAT OPENING CHORUS]

Post hoc ergo propter hoc is just a fallacy
You expect a certain melody here, but - that's up to me

[REPEAT OPENING CHORUS 2X]
• ### The viral cat picture

Last year, my goofy cat picture went viral - but now it barely gets more hits than my other posts.  Must be regression to the meme.

Larry Lesser and Dennis Pearl

• ### Slip Slidin' to the Mean

Lyric © 2017 Lawrence M. Lesser
may be sung to the tune of “Slip Slidin’ Away” by Paul Simon

CHORUS: Slip slidin’ to the mean, slip slidin’ to the mean,
You know the less your correlation, the more you’re slip slidin’ to the mean.

Well parents have daughter or son—
Their heights were all observed by England’s Francis Galton:
Extreme parents he did see
Had kids that regressed toward mediocrity!

(Repeat Chorus)

And I know a teacher who gave high praise
To the students whose midterms were the highest As;
Those failing badly received rebuke—
But the next test showed those extremes were a partial fluke!

(Repeat Chorus)

And I know a rookie who made the All-Star team
And the cover of Sports Illustrated magazine.
You can imagine what the coach thinks
When the star has sophomore slump as if there was a jinx!

(Repeat Chorus)

Watch the video

• ### Standard Deviation of the Slope

Lyrics © Mary McLellan
may sing to the tune of Adele's "Hello"

Slope.Varies.
It’s the standard deviation of the slope
You need to know

Slope.Varies.
It’s the standard deviation of the slope
You need to know

If you sample many times
I’d expect the slope you find
Of the relation between X and Y
To vary this much
On average over time.

If you sample many times
I’d expect the slope you find
Of the relation between X and Y
To vary this much
On average over time.