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Bivariate relationship linearity, strength and direction | AP Statistics | Khan Academy - YouTube
Channel: Khan Academy
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what we have here is six different
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scatter plots that show the relationship
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between different variables so for
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example in this one here in the
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horizontal axis we might have something
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like age and then here could be accident
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frequency
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accident frequency and i'm just making
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this up
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and i could just show these data points
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maybe for some kind of statistical
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survey that when the age is this
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whatever number this is maybe this is 20
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years old this is the accident frequency
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and it could be a number of accidents
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per hundred and that when the age is 21
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years old this is the frequency and so
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these data scientists or statisticians
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went and plotted all of these in this
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scatter plot this is often known as
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bivariate data which is a very fancy way
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of saying hey you're plotting things
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that take it two variables into
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consideration and you're trying to see
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whether there's a pattern with how they
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relate and what we're going to do in
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this video is think about well can we
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try to fit a line does it look like
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there's a linear or non-linear
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relationship between the variables on
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the different axes how strong is that
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variable is it a positive is it a
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negative relationship and then we'll
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think about this idea of outliers so
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let's just first think about whether
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there's a linear or non-linear
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relationship and i'll get my little
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ruler tool out here
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so this data right over here it looks
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like i could get a i could put a line
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through it that gets pretty close
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through the data you're not going to
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it's very unlikely you're going to be
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able to go through all of the data
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points but you can try to get a line and
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i'm just doing this there's more
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numerical more precise ways of doing
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this but i'm just eyeballing it right
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over here and it looks like i could plot
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a line that looks something like that
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that goes roughly through the data so
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this looks pretty linear so i would call
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this a linear
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relationship
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and since as we increase one variable it
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looks like the other variable decreases
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this is a downward sloping line i would
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say this is a negative
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this is a negative
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linear relationship but this one looks
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pretty strong so
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because the dots aren't that far from my
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line this one gets a little bit further
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but it's not you know there's not some
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dots way out there so most of them are
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pretty close to the line so i'll call
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this a negative reasonably strong linear
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relationship
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negative
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strong i'll call reasonably i'll just
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say strong but reasonably strong
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linear
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linear relationship between these two
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variables
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now let's look at this one and pause
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this video and think about what what
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this one would be for you
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well let's see i'll get my ruler tool
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out again
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it looks like i can try to put a line
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looks like generally speaking as one
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variable increases the other variable
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increases as well so something like this
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goes through the data and
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approximates the direction and this
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looks positive as one variable increases
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the other variable increases roughly so
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this is a positive relationship
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but this is weak a lot of the data is
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off well off of the line so positive
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weak
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but i'd say this is still linear it
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seems that as we increase one the other
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one increases at roughly the same rate
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although these data points are all over
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the place so i would still call this
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linear
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now there's also this notion of outliers
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if i said hey this line is trying to
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describe the data well we have some data
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that is
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fairly off the line so for example
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even though we're saying it's a positive
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weak linear relationship this one over
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here is reasonably high on the vertical
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variable but it's low on the horizontal
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variable and so this one right over here
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is an outlier it's quite far away from
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the line you could view that as an
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outlier and this is a little bit
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subjective outliers well what looks
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pretty far from the rest of the data
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this could also be an outlier let me
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label these
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out
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liar
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now pause the video and see if you can
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think about this one is this positive or
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negative is it linear non-linear is it
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strong or weak
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i'll get my ruler tool out here so this
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goes here
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it seems like i can fit a line pretty
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well to this
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so i could fit
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maybe i'll do the line in purple
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i could fit a line that looks like that
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and so this one looks like it's positive
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as one variable increases the other one
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does for these data points so it's a
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positive i'd say this is pretty strong
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the dots are pretty close to the line
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there it really does look like a little
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bit of a fat line if you just look at
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the dots so positive strong
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linear
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linear relationship
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and none of these data points are really
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strong outliers this one's a little bit
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further out but they're all pretty close
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to the line and seem to describe that
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trend roughly
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all right now let's look at this this
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data right over here
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so let me get my line tool out again
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so
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it looks like i can fit a line so it
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looks and it looks like it's a positive
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relationship the line would be upward
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sloping it would look something like
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this and once again i'm eyeballing it
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you can use computers and other methods
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to actually find a more precise line
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that minimizes the collective distance
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to all of the points
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but it looks like
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there is a
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positive
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but i would say this one is a weak
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linear relation because you have a lot
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of points that are far off the line so
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not so strong so i would call this a
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positive
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weak
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linear
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relationship and there's a lot of
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outliers here you know this one over
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here is pretty far
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pretty far out
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now let's look at this one
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pause this video and think about is
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positive negative is it strong or weak
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is this linear non-linear
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well the first thing we want to do is
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just think about linear non-linear i
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could try to put a line on it
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but if i try to put a line on it it's
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it's actually quite difficult if i try
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to align like this notice everything is
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kind of bending away from the line it
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looks like generally as one variable
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increases the other variable decreases
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but they're not doing it in a linear
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fashion
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it looks like there's some other type of
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curve at play
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so i could try to do a fancier curve
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that looks something like this and this
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seems to fit the data a lot better so
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this one i would describe as
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non-linear
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and it is a negative relationship as one
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variable increases the other variable
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decreases
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so this is a negative
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i would say reasonably strong non-linear
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relationship
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pretty strong
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pretty strong this is subjective
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so i'll say negative reasonably strong
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non-linear relationship
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and maybe you could call this one an
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outlier but it's not that far and i i
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might even be able to fit a curve that
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gets a little bit closer to that once
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again i'm eyeballing this now let's do
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this last one
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so this one
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looks like a negative linear
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relationship to me
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a fairly strong negative linear
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relationship although there's some
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outliers
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so
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let me draw this line
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so that seems to fit the data pretty
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good so this is a negative
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reasonably strong
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reasonably strong
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linear relationship
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but these are very clear outliers these
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are well away from the data or from the
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cluster of where most of the points are
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so with some significant with at least
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these two significant outliers here so
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hopefully this makes you a little bit
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familiar with some of this terminology
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and it's important to keep in mind this
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is a little bit subjective there'll be
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some cases that are more obvious than
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others so for and oftentimes you want to
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make a comparison that this is a
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stronger linear positive linear
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relationship than this one is right over
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here because you can see most of the
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data is closer to the line this one is
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for sure this is more non-linear than
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linear it depends how you want to
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describe
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oftentimes making a comparison or making
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a subjective call on how to describe the
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data
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