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
And finance Allah Shmoop What is the production possibilities Curve
Okay people Maybe Willy Wonka was onto something And with
all that pure imagination talk the people in charge of
making stuff have to survey their production like you know
your dog's surveys the yard every morning as if she's
never seen it before You're imagining all the possibility to
make more of this for more of that Yes well
but of course firms aren't imagining that can make unlimited
amounts of stuff They're imagining riel possibilities Things they could
do with the resources they have on hand Will this
imaginary world too constrained Fourth fun stuff like triple rainbows
unicorns and trees that grow video games is the stuff
of the production possibilities curve Will the production possibilities curve
also known as the production possibilities Frontier shows the different
combinations of two goods that can be made with a
given bucket of stuff we already have Like labor inputs
hardware all that stuff We'll call it the PPC for
short To save ourselves You know some precious breath Well
the PPC usually looks like this kind of bowing out
there Yeah on the X axis is one good and
the Y axis Another good So every point on this
graph not just the curve The whole box is a
different combination of two things The curve tells us what
our best options are Well in the nineteen nineties there
was a prankster company called Texcoco The name alone messed
with people which made fake mustache is and whoopee cushions
in its factory using things like rubber glue plastic labor
and capital Yeah all that factory equipment stuff Well Texaco
had some decisions to make It could make only fake
mustache is with resource is on hand which would result
in the production of one hundred mustache Is it Could
also on ly make whoopee cushions like Texaco could make
a thousand whoopee cushions if it only dealt in the
whoopee cushion underground Are you know market Or maybe it
could make mostly whoopee cushions like nine hundred of them
And some mustache is Well let's see if we can
make a nine hundred What big oceans that leaves enough
resource is for twenty five Fake mustache is Yeah And
all these production options are options on our PPC This
thing Well why do economists go with a fancy shmancy
curve over a boring table Well tables are hard to
look at All those numbers air dizzying you know and
economists are on the brink of a heart attack all
the time anyway thanks to those boom and bust cycles
But that's another story A curve is a nifty tool
because it shows us all of that info without all
the numbers It's also handy because unlike a table a
curve is continuous Justus There are an infinite number of
numbers between zero and one right It's continuous if we
missed an option in our table while we won't miss
it in the curve because while it will be part
of the curves it's all the little dots in here
We also like the curve because it tells us things
like a fortune teller you know but accurate For instance
all of our most efficient production possibilities are on the
curve Efficiency here means Bobby Joe and William Jr The
fifth are pumping out Moustache is and will be cushions
using their work time to be as productive as possible
Save the Hanji time for lovers Lane Yeah okay Well
yeah they're not only being diligent workers on the clock
but are also using the rubber and glue and things
to the utmost capacity wasting as little as possible Yeah
it's a scarce world out there Well basically a firm
is getting the most bang and not the lover's lane
kind for its buck when production is efficient And that's
when we're walking the line of the PPC So what
if Bobby Joan William Jr The Fifth we're wasting time
making intense eye contact from across the factory floor Well
they're wasting time and letting glue fall to the floor
causing all kinds of waste and problems that will take
time to fix Yeah it's pretty bad Which would mean
Texaco is producing somewhere under the curve Not the best
use of our scarce resource is Well Texaco must do
its best to bring its pranks to the prankster of
the nineties Yeah What about this area over the curve
The land of unicorns and video game fruiting trees The
land of Well just not gonna happen Makes sense because
at the line we're already doing as much as we
simply can With the little we have we're at one
hundred percent We can't be doing one hundred eighteen percent
of our capacity right Well there's one case where we
could produce outside the curve If some of Bobby Joe
and William Juniors labor was replaced with robots that made
the stash is and cushions more efficiently while our curve
would shift outward It's just what technological innovation does It
helps us make things better than before Well the curve
also shows trade offs and opportunity costs You know the
reason we have to choose one option Things are limited
It shows that if we started making on ly whoopee
cushions while we can make a thousand if we put
all the resource is into just making those you know
remember we can trade off one hundred whoopee cushions to
make twenty five Moustache is it's kind of our equation
making nine hundred cushions and twenty five stashes instead of
a thousand and zero That's an opportunity cost of those
hundred whoopee cushions Twenty five Moustache will give a little
of one thing to get a little of another thing
The market you know where pranksters run rampant will help
companies like Texaco figure out which point on the PC
is their best bet Okay people to recap the production
possibilities Frontier shows us all the options for producing two
things as efficiently as possible With the scarce resource is
available It shows us things like our trade offs and
opportunity costs unfortunate things firms have to face in real
life because yeah there's scarcity People sees curve outward like
that because our trade offs aren't one toe one Our
opportunity cost increases We trade off one thing for another
moving along the curve Well the graph is better than
the table because we can literally see what the production
possibilities are how they're efficient and all that and which
ones are impossible Yeah And then of course the inefficient
ones that live down there Alright Yeah and we're looking
at you Bobby Joe Come on man Get your shoe
out of the glue before it hardens there When we
replacing you with a robot let's get back down Yeah
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