Pearson Coefficient

  

Categories: Metrics

Not to be confused with the production possibilities curve, the Pearson correlation coefficient (the other “PPC”) is a measurement in statistics of the linear correlation between X and Y.

Imagine a bunch of dots on a graph, spread out everywhere pretty evenly. That’s a pretty weak correlation of the two variables, which means the Pearson coefficient is close to zero. Now imagine those dots practically creating an upward-sloping line...that’s a positive correlation, which means it’s close to one.

If the dots make up the line pretty well, but it’s downward-sloping instead of upward-sloping, we’ve got just as good of a correlation, but it’s negative instead (close to negative one).

Since the Pearson coefficient is only measuring linear correlation, it’s pretty straightforward...no crazy curves to deal with, as would be the case with a logistic function. Yet it means that, for some X and Y relationships, a linear correlation might be the wrong tool to use. For many relationships though, it fits the statistical bill. There are some tests you can do, like T-tests, to see if you should be using another statistical tool or not.

The Pearson coefficient has a lot of (good) baggage attached to it: it’s used in regression analysis...yep, that’s machine learning...and has cool mathematical applications for populations and samples (a part of a population). It helps economists, statisticians, and researchers estimate inferences based on their data. Basically, it helps them see if a relationship is likely there, or not. X and Y are either peas in a pod, or X friendzones Y...because it was a love triangle with the null hypothesis.

Related or Semi-related Video

Econ: What is a Production Possibilities...10 Views

00:00

And finance Allah Shmoop What is the production possibilities Curve

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Okay people Maybe Willy Wonka was onto something And with

00:11

all that pure imagination talk the people in charge of

00:14

making stuff have to survey their production like you know

00:18

your dog's surveys the yard every morning as if she's

00:21

never seen it before You're imagining all the possibility to

00:24

make more of this for more of that Yes well

00:27

but of course firms aren't imagining that can make unlimited

00:30

amounts of stuff They're imagining riel possibilities Things they could

00:34

do with the resources they have on hand Will this

00:37

imaginary world too constrained Fourth fun stuff like triple rainbows

00:41

unicorns and trees that grow video games is the stuff

00:44

of the production possibilities curve Will the production possibilities curve

00:48

also known as the production possibilities Frontier shows the different

00:52

combinations of two goods that can be made with a

00:54

given bucket of stuff we already have Like labor inputs

00:58

hardware all that stuff We'll call it the PPC for

01:01

short To save ourselves You know some precious breath Well

01:03

the PPC usually looks like this kind of bowing out

01:07

there Yeah on the X axis is one good and

01:10

the Y axis Another good So every point on this

01:13

graph not just the curve The whole box is a

01:15

different combination of two things The curve tells us what

01:19

our best options are Well in the nineteen nineties there

01:22

was a prankster company called Texcoco The name alone messed

01:25

with people which made fake mustache is and whoopee cushions

01:28

in its factory using things like rubber glue plastic labor

01:32

and capital Yeah all that factory equipment stuff Well Texaco

01:36

had some decisions to make It could make only fake

01:39

mustache is with resource is on hand which would result

01:41

in the production of one hundred mustache Is it Could

01:44

also on ly make whoopee cushions like Texaco could make

01:47

a thousand whoopee cushions if it only dealt in the

01:50

whoopee cushion underground Are you know market Or maybe it

01:53

could make mostly whoopee cushions like nine hundred of them

01:56

And some mustache is Well let's see if we can

01:59

make a nine hundred What big oceans that leaves enough

02:01

resource is for twenty five Fake mustache is Yeah And

02:05

all these production options are options on our PPC This

02:09

thing Well why do economists go with a fancy shmancy

02:11

curve over a boring table Well tables are hard to

02:14

look at All those numbers air dizzying you know and

02:17

economists are on the brink of a heart attack all

02:19

the time anyway thanks to those boom and bust cycles

02:21

But that's another story A curve is a nifty tool

02:24

because it shows us all of that info without all

02:27

the numbers It's also handy because unlike a table a

02:30

curve is continuous Justus There are an infinite number of

02:34

numbers between zero and one right It's continuous if we

02:37

missed an option in our table while we won't miss

02:40

it in the curve because while it will be part

02:42

of the curves it's all the little dots in here

02:43

We also like the curve because it tells us things

02:46

like a fortune teller you know but accurate For instance

02:49

all of our most efficient production possibilities are on the

02:52

curve Efficiency here means Bobby Joe and William Jr The

02:56

fifth are pumping out Moustache is and will be cushions

02:58

using their work time to be as productive as possible

03:01

Save the Hanji time for lovers Lane Yeah okay Well

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yeah they're not only being diligent workers on the clock

03:07

but are also using the rubber and glue and things

03:10

to the utmost capacity wasting as little as possible Yeah

03:13

it's a scarce world out there Well basically a firm

03:16

is getting the most bang and not the lover's lane

03:18

kind for its buck when production is efficient And that's

03:21

when we're walking the line of the PPC So what

03:24

if Bobby Joan William Jr The Fifth we're wasting time

03:27

making intense eye contact from across the factory floor Well

03:30

they're wasting time and letting glue fall to the floor

03:33

causing all kinds of waste and problems that will take

03:36

time to fix Yeah it's pretty bad Which would mean

03:38

Texaco is producing somewhere under the curve Not the best

03:42

use of our scarce resource is Well Texaco must do

03:45

its best to bring its pranks to the prankster of

03:47

the nineties Yeah What about this area over the curve

03:51

The land of unicorns and video game fruiting trees The

03:54

land of Well just not gonna happen Makes sense because

03:58

at the line we're already doing as much as we

04:01

simply can With the little we have we're at one

04:03

hundred percent We can't be doing one hundred eighteen percent

04:06

of our capacity right Well there's one case where we

04:08

could produce outside the curve If some of Bobby Joe

04:11

and William Juniors labor was replaced with robots that made

04:15

the stash is and cushions more efficiently while our curve

04:18

would shift outward It's just what technological innovation does It

04:22

helps us make things better than before Well the curve

04:24

also shows trade offs and opportunity costs You know the

04:27

reason we have to choose one option Things are limited

04:30

It shows that if we started making on ly whoopee

04:33

cushions while we can make a thousand if we put

04:35

all the resource is into just making those you know

04:37

remember we can trade off one hundred whoopee cushions to

04:40

make twenty five Moustache is it's kind of our equation

04:42

making nine hundred cushions and twenty five stashes instead of

04:46

a thousand and zero That's an opportunity cost of those

04:49

hundred whoopee cushions Twenty five Moustache will give a little

04:52

of one thing to get a little of another thing

04:54

The market you know where pranksters run rampant will help

04:56

companies like Texaco figure out which point on the PC

05:00

is their best bet Okay people to recap the production

05:03

possibilities Frontier shows us all the options for producing two

05:06

things as efficiently as possible With the scarce resource is

05:09

available It shows us things like our trade offs and

05:12

opportunity costs unfortunate things firms have to face in real

05:16

life because yeah there's scarcity People sees curve outward like

05:20

that because our trade offs aren't one toe one Our

05:23

opportunity cost increases We trade off one thing for another

05:26

moving along the curve Well the graph is better than

05:29

the table because we can literally see what the production

05:32

possibilities are how they're efficient and all that and which

05:35

ones are impossible Yeah And then of course the inefficient

05:38

ones that live down there Alright Yeah and we're looking

05:40

at you Bobby Joe Come on man Get your shoe

05:42

out of the glue before it hardens there When we

05:45

replacing you with a robot let's get back down Yeah

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