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Finance: What is r-squared? 0 Views


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What is r-squared? R-squared in financial applications applies to the percentage of a security’s or fund’s price movements that can be attributed to sympathetic movements by an index or other trackable benchmark. An R-Squared under 70% would be too divergent to consider the security or fund in question to have a correlation with an index. An R-Squared of 85% would indicate a sympathetic relationship with an index.

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Transcript

00:00

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

00:09

a measure of the personage of change in one variable

00:12

Do exclusively to changes in another variable Accidentally back into

00:17

a car in the lot and need someone to blame

00:20

it on late for work and need a scapegoat The

00:22

boss will believe well r squared is here to find

00:25

you up patsy To take the blame for well pretty

00:28

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

00:30

take the fall for you It will find the fall

00:33

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

00:35

looked at a set of by various or to variable

00:38

data that compares the top speed of remote control cars

00:42

to the size of the tires on the car which

00:45

end up having in our scored value of point seven

00:47

nine That means seventy nine percent of the changes in

00:50

the top speed of the car were due to changes

00:52

in the size of the tires More simply the changes

00:56

entire side are the primary cause then in changes in

00:59

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

01:02

r squared between larger tires and faster speed was high

01:06

like point eight Other factors affect top speed like wind

01:09

resistance battery power and so on But change his entire

01:12

speech of the primary cause for changes in top speed

01:14

We need to be careful not to say that tire

01:16

size is the primary cause of top speed See that

01:19

was a little error there They just fill in You

01:21

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

01:24

that changes in the tire side are the primary cause

01:26

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

01:30

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

01:32

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

01:35

walk through how we might really work with r squared

01:38

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

01:40

two variables like the daily price of a gallon gasoline

01:43

and the average number of gallons purchased per customer on

01:46

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

01:49

in the price of gas or a factor in how

01:51

much gas people buy but how much of a factor

01:54

like a gallon of gasoline costs You know eighteen dollars

01:57

right there pete Fewer people buying instead of a god

01:59

three bucks So r squared will tell us how much

02:02

of the changes in how much people pump into their

02:04

tank is due to changes in the price of gas

02:07

And how much of those changes in the amount of

02:09

gas purchased is due to other factors like time of

02:12

season or the length of trip there taking or the

02:15

amount of money they happen to have on hand or

02:17

how loud the kids are screaming Are we there yet

02:20

Are we there yet in the back seat Yeah okay

02:22

well because we knew it would come in handy We

02:24

collected data from our local gas and sip on seven

02:27

different days Calculations like the coefficient of determination are squared

02:31

and or the correlation coefficient are should only be attempted

02:34

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

02:38

a good idea to whip up a scatter plot of

02:39

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

02:42

or has some other weird non linear pattern that we

02:44

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

02:47

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

02:50

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

02:52

squared by hand but almost nobody does Even for a

02:54

very small data sets graphing calculator spreadsheets and web sites

02:57

dedicated to finding our and only r and r squared

03:00

Well all do a dandy job of getting us the

03:02

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

03:05

this data into our jailbroken diamond plated solar powered voice

03:09

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

03:13

We get in our squared value of point one three

03:15

five eight right there What does that mean for us

03:17

And for our gas problem Well since r squared is

03:20

the percentage of change in the uae variable that is

03:22

do strictly to changes in the x variable It means

03:24

that on ly thirteen point five eight percent of changes

03:27

in the average amount of gas purchase are due to

03:29

changes in the price of gas It also means that

03:31

eighty six point four two percent of the changes in

03:33

the amount of gas purchase are due to other factors

03:36

like changes in how much money people have on hand

03:38

It could also have to do with well changes in

03:41

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

03:43

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

03:46

focused on the numbers And again we need to be

03:48

very careful not to claim that r squared number tells

03:51

us how much of a percentage cause one variable to

03:54

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

03:56

always an on ly the percentage of changes in one

04:00

variable do ooh to changes in the other Also weaken

04:02

Take r squared out back behind the wood shed and

04:05

square roots The mess out of it to get the

04:07

correlation coefficient are got it Okay Some important safety tips

04:11

We should only find r squared for data that have

04:13

a linear ish pattern We confined our squared by hand

04:17

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

04:19

do the grunt work for the actual calculations Well our

04:22

scores the percentage of change in one variable that is

04:24

do strictly to changes in another variable if we square

04:27

root are squared while we get the correlation coefficient are

04:30

positive number There never never ever suggest that ninety nine

04:33

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

04:35

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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