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Finance allah shmoop what is r squared r squared It's

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a measure of the personage of change in one variable

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Do exclusively to changes in another variable Accidentally back into

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a car in the lot and need someone to blame

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it on late for work and need a scapegoat The

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boss will believe well r squared is here to find

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you up patsy To take the blame for well pretty

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much anything you can dream up well r squared won't

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take the fall for you It will find the fall

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guy best suited for that job So let's say we

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looked at a set of by various or to variable

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data that compares the top speed of remote control cars

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to the size of the tires on the car which

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end up having in our scored value of point seven

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nine That means seventy nine percent of the changes in

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the top speed of the car were due to changes

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in the size of the tires More simply the changes

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entire side are the primary cause then in changes in

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the top speed and you'd say in normal english the

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r squared between larger tires and faster speed was high

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like point eight Other factors affect top speed like wind

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resistance battery power and so on But change his entire

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speech of the primary cause for changes in top speed

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We need to be careful not to say that tire

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size is the primary cause of top speed See that

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was a little error there They just fill in You

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are square doesn't tell us that It just tells us

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that changes in the tire side are the primary cause

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for changes in the top speed meaning they're just related

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We don't know that one causes the other and the

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difference is subtle But while hugely important here So let's

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walk through how we might really work with r squared

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from beginning to end in a problem What We've got

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two variables like the daily price of a gallon gasoline

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and the average number of gallons purchased per customer on

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that same day It's not unreasonable to think that changes

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in the price of gas or a factor in how

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much gas people buy but how much of a factor

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like a gallon of gasoline costs You know eighteen dollars

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right there pete Fewer people buying instead of a god

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three bucks So r squared will tell us how much

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of the changes in how much people pump into their

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tank is due to changes in the price of gas

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And how much of those changes in the amount of

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gas purchased is due to other factors like time of

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season or the length of trip there taking or the

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amount of money they happen to have on hand or

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how loud the kids are screaming Are we there yet

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Are we there yet in the back seat Yeah okay

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well because we knew it would come in handy We

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collected data from our local gas and sip on seven

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different days Calculations like the coefficient of determination are squared

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and or the correlation coefficient are should only be attempted

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on data that has a linear ish shape It's always

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a good idea to whip up a scatter plot of

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the data just to make sure it's not obviously curved

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or has some other weird non linear pattern that we

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can't then generalize from Well the pattern here is linear

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enough and doesn't show an obvious curve or other pattern

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So we're good to go and we can calculate r

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squared by hand but almost nobody does Even for a

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very small data sets graphing calculator spreadsheets and web sites

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dedicated to finding our and only r and r squared

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Well all do a dandy job of getting us the

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values we want So let's do that well after popping

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this data into our jailbroken diamond plated solar powered voice

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activated t I eighty four plus i'd any um edition

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We get in our squared value of point one three

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five eight right there What does that mean for us

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And for our gas problem Well since r squared is

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the percentage of change in the uae variable that is

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do strictly to changes in the x variable It means

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that on ly thirteen point five eight percent of changes

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in the average amount of gas purchase are due to

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changes in the price of gas It also means that

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eighty six point four two percent of the changes in

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the amount of gas purchase are due to other factors

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like changes in how much money people have on hand

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It could also have to do with well changes in

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how far they're planning on driving That day could mean

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many other things but it doesn't For now we're just

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focused on the numbers And again we need to be

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very careful not to claim that r squared number tells

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us how much of a percentage cause one variable to

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do another thing that's a no no r squared is

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always an on ly the percentage of changes in one

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variable do ooh to changes in the other Also weaken

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Take r squared out back behind the wood shed and

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square roots The mess out of it to get the

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correlation coefficient are got it Okay Some important safety tips

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We should only find r squared for data that have

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a linear ish pattern We confined our squared by hand

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but that's a sign of insanity So used tech to

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do the grunt work for the actual calculations Well our

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scores the percentage of change in one variable that is

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do strictly to changes in another variable if we square

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root are squared while we get the correlation coefficient are

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positive number There never never ever suggest that ninety nine

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percent of the changes in a police person's weight is

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due to changes in doughnut consumption either just a extra 00:04:39.283 --> [endTime] free warning there from your friends at shmoop

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