Descriptive Statistics

Categories: Metrics, Trading

Statistics that describe features of a data set.

Wait. You want more? Really? Okay, but that’s pretty much it.

Calculations like mean, median, mode, standard deviation, interquartile range, linear regressions, r-values, r-squared-values, etc. are all kinds of descriptive statistics. Anytime we crunch the numbers in a data set to try to describe the location of special features of the data set (like the middle) or the shape or how spread out it is, we’re calculating descriptive statistics.

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Finance: What are correlation coefficien...37 Views

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Finance allah shmoop what are correlation coefficients Kind of sounds

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like a new card game from the makers of cards

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against humanity or an exotic disease that spreads like wildfire

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on a cruise ship you know been there But a

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correlation coefficient is actually a measure of how strongly connected

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or correlated to different variables are It's also a measure

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of how close the points on a scatter plot are

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to the vest Fifth line this thing running through them

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A correlation coefficient is kind of like a ranch hand

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who's in charge of hurting data Okay so let's take

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a closer look at the data points in our corral

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taken from wild pizza restaurant Yeah they're a set of

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by vary it or to variable data In this case

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the data points on the x axis are the number

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of minutes a table has to wait for their food

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since ordering and the data points on the y axis

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are the percentage of the total bill left as a

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tip Interesting correlation here Pete the owner namesake of wild

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pete's pizza believes there's a relationship between how long a

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table waits for the food and how much they tip

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generally the first step in finding a correlation coefficient is

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to determine if the data points are in a roughly

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leaning your pattern So we need to whip up a

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quick scatter plot like this thing If the data points

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don't have an obvious linear pattern lily shouldn't even bother

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to calculate the correlation coefficient because it's not meaningful Once

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there appears to be a linear or roughly linear pattern

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to the data it's time to get calculate their partner

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okay The formula for the correlation coefficient which is denoted

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by the variable are here was a bit unwieldy and

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typically the correlation coefficient calculated using an actual calculator of

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some kind But still it's nice to know where these

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numbers come from so we'll do it by hand and

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double check our work So the process goes like this

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First we find the mean in standard deviation in the

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ecs data in the wide out of treating each set

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of data as its own list separate from each other

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We'll use a calculator just a shortcut this part of

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the process and now we need to take its data

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point in the x list Subtract the mean from it

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and divide that result by the standard deviation so twelve

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months fifteen point one six six seven which is negative

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Three point one six seven divided by five point six

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blah blah blah which is negative about a half then

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twenty minus fifteen point one six seven which is four

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point eight three three divided by five points You bubba

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blah blah blah which is point eight six and change

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and so on But we need the lather rinse Repeat

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that same process of subtracting the mean of the y

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data from each y value and then dividing the standard

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deviation in the y values Right Well that'll be sixteen

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months Fourteen which in california is too divided by three

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point two eight blah blah blah which is point six

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and change So we have thirteen months fourteen which is

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negative one divided by three point two eight six which

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is well negative point three ish So now we need

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to multiply each matched acts And why value from our

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previous calculations That'll be negative Point five six and change

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times a point six blah blah blah which is negative

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Point three four for one Then we have point eight

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six three times negative point three oh four which is

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a negative point two six two Then negative point seven

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four four times one point two one seven two which

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is Well what is that Negative point nine and so

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on Now he's some the values we just got which

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is all this stuff We adam all up and it

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comes out to negative Four point four five five four

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Okay one last step here Cowpokes We just need to

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divide one less than the number of data points We

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have six data points So we divide by negative Four

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point four five five four yeah by five Divide that

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And that means our correlation coefficient or our value is

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negative Point eight nine one one Interesting Excellent Well now

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we have a real correlation coefficient also What does it

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mean Well for starters we can interpret what it actually

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means here Say we did their correlation coefficient or our

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value is a measure of how strong your relationship is

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between the two variables Assuming that linear ish pattern exists

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It does not however mean that the one variable causes

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the other It just means there's some kind of relationship

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between them toe actually put a value on how strong

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the correlation is We need to examine the continuum of

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correlation Positive correlations represent situations where the scatter plot appears

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to climb from left to right Negative correlations represent situations

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where the scatter plot appears Toe fall from left to

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right like our tips versus time data Well strong correlations

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or values between point seven and one for positive correlations

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and between negative point seven and one four negative correlations

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That's just rough Numbers They're about point 7 And if

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it's a one to one relationship it means that if

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you let go of the apple it will fall every

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time we're assuming they're on earth Scatter plot points will

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be pretty darn close to the best fit line through

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the points there medium correlations are in the point for

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two point seven range and they got the negative ones

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And so on Scatter plot points will be a we

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distance from the best fit line Then it's not White

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is tightly packed around that line and then we correlations

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and just looks like a cloud It's like values from

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zero two point for and zero negative point for and

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they're just kind of like maybe there's a line through

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there but maybe not well in our case it's our

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our value is negative point eight nine one one While

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it's very very negatively correlated between the two time of

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ordering the food and when it shows up and the

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tip paid at least the tip percentage of the meal

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Which means that as it takes longer and longer for

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food to arrive after ordering in general the tip percentage

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goes down Also because this pattern is a strong correlation

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this pattern is likely to be predictable in terms of

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a certain weight time leading to a certain percentage A

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while back we mentioned that our values aren't often whipped

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up by hand Instead we use graphing calculator spreadsheets websites

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any of them you know to whip up a mess

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of our values in no time Pop the data into

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the list one into in a t i a graphing

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calculator Go to the count menu in the stat function

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and run a lynn rag Linear regression You know we

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see in our value of ours a negative point eight

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nine one which is very close to our by the

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hand value of point eight nine hundred eleven year negative

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and is on ly different dude around it So yeah

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when you need to rustle up in our value y'all

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should probably grab something Check unless you want to go

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through the headache of finding that our value by hand

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remember that the r value just suggests a relationship between

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the variables revenues saying one causes the other correlation does

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not equal causation Remember that tattoo that somewhere but not

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on your own body Also remember that the stronger correlations

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air closer to negative one in one and farther from

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zero in the middle And finally when they all go

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to a restaurant and takes a spell get your order

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Don't take it out on the server by stiffing them

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on the tip There's a strong positive correlation between stiffing

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service on tips and you know getting your food spat

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in next time And while just being a massive

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