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.

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Econ: What are Production Functions?2 Views

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And finance Allah Shmoop what Our production functions well Grandma's

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air The source of all A lot of useful wisdom

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good music since the the Elvis died Okay well maybe

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not Everything they say is golden But here's another good

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one You get out of something what you put into

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it Yeah well that one actually works for economics to

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it's the basic sentiment behind the production functions The production

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function is a process that economists used to show how

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much stuff you can make for every potential combination of

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input It's essentially a mathematical equation based on data gathered

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through the production process And it allows companies to graph

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what production would look like given different inputs You know

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they consider different questions Like what if we use more

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workers Or what if we bought Mohr equipment You know

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some big fancy factory with robots What if we replaced

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the dehydrated milk in our baby formula with pot ash

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All right well these are the kinds questions of production

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function answers and well then businesses can allocate their resource

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is in the most efficient way possible Well they find

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the point on the graph where they get the most

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out of what they're putting in and that's what they

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shoot for McDonald's is slowly replacing human workers with robots

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Well how do they know if it's a good investment

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Well they asked the production function or at least look

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at it a fry flipping robot Kaswell ten thousand dollars

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at volume It costs another two thousand dollars a year

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in maintenance and appreciation per year and that fry flipping

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baht can cover one friar And there are five fryers

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at the restaurant so it takes five bots to replace

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one worker or about fifty grand to replace that one

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worker Wealthy company does some trials and finds that a

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fry flipping robots can do the job two times faster

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than one person In actuality or reality that person cost

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twenty dollars an hour after salary of fifteen bucks and

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then taxes and all the everything's company has to pay

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pension health care all that stuff So over the course

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of a year a fulltime fried flipper cost McDonald's forty

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thousand dollars well to replace the employees the company needs

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five bots costing a total of fifty grand It'll cost

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another ten thousand dollars total in the maintenance and appreciation

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But the Frye body is twice as fast as the

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worker meaning McDonald's Khun turnover twice a cz many fries

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So you'd need to workers to match the output of

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the fry bots Well the bots cost say sixty thousand

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dollars in Year one And yes we're making up a

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lot of numbers The workers costal eighty thousand those two

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workers But the company is already in the black They've

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made twenty thousand dollars in savings by replacing those low

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skilled workers with robots Well the production function can have

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many variables in practice The production function depends on the

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product being produced Different products require different levels of inputs

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and the relationships between the inputs are different That cab

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all of relationships includes things like land and labor and

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capital in raw materials and time However many of these

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dropout is being irrelevant or they get combined and kind

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of fade away Key idea here is that the simple

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version of all of this has two variables to variable

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inputs There's labor that's usually represented by a big fancy

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capital L And then there's capital that's usually represented by

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you Hey there And this combo gives you the quantity

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of output like in the equation And this gets a

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queue right Belle Plus Que is cute that's in its

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simplest form and that's the production function And that's what

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it looks like The amount of labour and the amount

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of capital gives you the amount of output The production

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function can help measure the marginal productivity of one factor

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of production It can also help figure out the least

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expensive and most efficient way to make a product like

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to need to spend a little capital on ingredients and

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you know pie tins Well that's the capital That's the

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big K You've also got labor That's you And grandmama

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That's the big Al there for labor Enough for losers

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Sorry Grandma Alright now onto your production function right there

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ingredients will help you bake more pies Or if you

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call your cousins to help with the baking and Ad

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