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Statistics 101: Logistic Regression, An Introduction - YouTube
Channel: Brandon Foltz
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you
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hello and welcome Brandon here thanks
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for choosing my video if you liked the
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video please give it a thumbs up if you
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think someone you know can also benefit
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by watching please share and as always
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please subscribe I appreciate it very
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much
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so let's go ahead and get started so
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here we are in logistic regression a
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very useful if in my opinion
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underutilized statistical procedure that
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is not all that intuitive which is maybe
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why it's underutilized now as with many
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of my other videos we're going to start
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out with an actual problem now this
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problem is one that I made up so I made
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up the text and the data for it so just
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keep that in mind going forward however
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I do think it has the side benefit of
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being potentially useful in your
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everyday life so let's go ahead and take
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a look at it so we'll call it first time
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homebuyer so as a first time homebuyer
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you are busy organizing your financial
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records so you can apply for a home
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mortgage as part of this process you
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order a copy of your credit report to
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check for errors and gauge your credit
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score which can range at least here in
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the US from 300 to 850 now lenders will
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factor in your credit score when
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deciding to approve or not approve you
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for a mortgage they will factor in other
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things like your income how long you've
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been at your job and other things but
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your credit score is definitely an
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important part of their decision now it
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turns out your credit score is 720 on
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that scale of 300 to 850 now while doing
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your research which you are dutifully
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doing as a potential home buyer you find
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some raw data online so there's data
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floating around the web everywhere so
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you are lucky enough to come across this
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data set that has 1000 applicant credit
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scores and whether or not the
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application was approved so yes or no
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for the home mortgage now using the data
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you found you would like to do the
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following number one develop a model
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that will provide the probability and
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the odds of being approved for any given
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credit score and again we will do all of
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these as we progress throughout the
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video series
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number two discover approximately what
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credit score is associated with our
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probability of 50% so the odds are even
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for being approved so if I walk into the
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bank with a certain credit score it's
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basically like flipping a coin my
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probability is 50% of being approved
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which is the same way of saying the odds
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or even we want to know what credit
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score that is on our scale number three
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input your score of 720 into the model
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to determine the probability and the
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odds of you being approved for a
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mortgage which of course is very
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important to you and finally determine
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how improving your credit score from 720
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the 750 would affect your probability
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and odds for being approved for the
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mortgage so let's say your score is 720
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you find that out so you're going to
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wait a little bit and see if you can get
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your credit score a bit higher up to 750
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by paying down some debt maybe you know
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that you're going to get a promotion and
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a higher salary sometime soon or
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something like that and you think that
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your score may improve and you want to
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know how that improvement in your score
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would affect your probability and odds
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of being approved with the mortgage so
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here is just a little chunk of that
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1,000 observation data set so there are
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only 15 here but it's wanted you to see
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how it's organized so we have the credit
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score on the left and approved on the
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right so again the N is a thousand the
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credit score is the applicant's credit
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score from 300 all the way up to 850 now
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approved is coded as a 1/4 approved and
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0 4 not approved so it is binary
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it is a dichotomous variable and it is
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mutually exclusive so you're either
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approved or you're not approved there's
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no in-between now as a good analyst and
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a good stat student or whatever it is
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you might be you create a scatterplot of
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your 1,000 observations but it looks
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like this now what is this so if you
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look on the left hand side we have
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approve and we have 0 at the bottom
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so that means the application was not
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approved at the top we have a one so
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that means the application was approved
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but we have the data points in two lines
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to the credit score on the bottom so
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FICO score is just a certain type of
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credit score that's widely used so if
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the dot is on the bottom that means for
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whatever credit score that was the
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application was not approved if it's at
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the top it means it was approved now how
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can we put a best-fit regression line on
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a scatterplot that looks like this it
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doesn't make any sense to do it how we
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will usually do it in normal linear
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regression so obviously we're going to
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come up with some other technique and
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that's what logistic regression allows
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us to do now that we have set the stage
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with the problem we're going to look at
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what is logistic regression
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now logistic regression seeks to do the
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following among other things it seeks to
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model the probability of an event
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occurring depending on the values of the
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independent variables in this case
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credit score which can be categorical or
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numerical so model the probability of an
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event occurring depending on the other
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independent variables it seeks to
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estimate the probability that an event
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occurs for a randomly selected
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observation versus the probability that
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the event does not occur so for a random
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observation in the data or some other
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observation that we would want to
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predict we want to estimate the
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probability that the event occurs versus
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that it does not occur it seeks to
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predict the effect of a series of
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variables on a binary response variable
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so in this case we only have one
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independent variable credit score but we
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can have more so logistic regression can
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work a lot like multiple regression with
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several independent variables and the
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one dependent variable that is binary to
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0 or 1 you can also stick the classify
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observations by estimating the
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probability that an observation is in a
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particular category in this case the
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applicant is either in the approved
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category or they're in the not approved
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category so we can classify observations
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so model estimate predict and classify
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so let's try to understand and visualize
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the problem we're working with so in
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this case we have a bunch of credit
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scores so an applicant walks into the
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bank and they have some sort of credit
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score now the bank or other lending
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institution feeds that into their
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lending model the credit score goes into
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the model and then when it comes out
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it's either approved or it's not
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approved so this black box in the middle
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is what we're trying to understand so we
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could ask what is the probability that
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an application having a credit score of
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670 so it would end up in the approved
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category up here on the top so credit
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scores get put into some model a
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decision model by the bank or other
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lender and then the bank or the lender
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puts that application into the approved
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or not approved categories that's
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basically what we're trying to model in
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this logistic regression problem now I
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am kind of making the assumption that if
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you're studying logistic regression you
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have to some extent studied simple
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linear regression and multiple
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regression now if you studied those you
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might have a very good question
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why can I use one of those for this type
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of problem well here's why number one
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simple linear regression is one
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quantitative variable predicting another
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quantitative variable now in this case
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we have a dichotomous dependent variable
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so approve or not approve is 1 or 0 it's
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not a quantitative variable now multiple
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regression is just simple regression
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with more independent variables so those
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are basically the same type of problem
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now we have nonlinear regression that's
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still two quantitative variables but the
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data is curvilinear now if we ignored
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those morning's running a typical linear
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regression in the same way on this type
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of data
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has some major problems now binary data
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in this case approve are not approved
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does not have a normal distribution and
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you can see that by looking at the
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scatter plot which is a condition needed
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for most other types of regression the
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predicted values of the dependent
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variable can be beyond 0 & 1 in those
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other types of regression so remember in
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logistic regression we're dealing with
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probabilities and the rule of
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probability is that it has to be between
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0 & 1 if we use the other types of
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regression these values can be beyond 0
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& 1 which obviously is not going to work
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and probabilities are often not linear
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such as you shapes where the probability
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is very low or very high at the extremes
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of the X values so you can probably
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think of different examples so one
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example could be the probability of
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contracting the flu so the probability
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of getting the flu is higher if you're
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younger so a baby or an infant or
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toddler and if you're older so say in
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your 60s 70s and 80s so the probability
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is higher in the extremes than it is in
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the middle so probabilities often have
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different shapes in their distribution
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along the X variables so now that we
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have set the stage by introducing our
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problem and going over the basic
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conceptual foundation of what logistic
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regression is let's talk about where
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we're going in the next video so in the
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next video we will do the following we
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will review basic probability so we will
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go into much depth well let's go over
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the basics because I was the
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understanding probability is central to
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learning about logistic regression we
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will learn about what odds are and what
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the odds ratio is because again that's
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central to understanding logistic
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regression we will briefly discuss how
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to interpret the odds ratio in logistic
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regression context and finally we will
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note things we have to keep in mind when
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interpreting the odds ratio so the odds
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ratio is related to probability of
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course
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there are some dangers in how we
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interpret it and we'll definitely
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discuss that in the next video so let's
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go ahead and wrap up this video and I
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will see you in the next one
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you
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