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Correlations and Covariance in R with Example | R Tutorial 4.12 | MarinStatsLectures - YouTube
Channel: MarinStatsLectures-R Programming & Statistics
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hi I'm Mike Marin and in this video
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we'll talk about calculating correlation
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and covariance using our Pearson's
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correlation is a parametric measure of
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the linear association between two
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numeric variables Spearman's rank
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correlation is a nonparametric measure
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of the monotonic association between two
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numeric variables Kendall's rank
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correlation is another nonparametric
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measure of Association based on
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concordance or discordance of XY pairs
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we will be working with the lung
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capacity data that was introduced
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earlier in this series of videos I've
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already gone ahead and imported the data
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into R and attached it we will explore
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the relationship between age and lung
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capacity we will use the cor CoV and cor
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test commands to access the help menus
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in R you can type help and in brackets
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the name of the command you'd like help
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for or simply place a question mark in
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front of the command name the first
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thing that we'll want to do is produce a
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scatter plot of lung capacity verse age
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we can use the plot command and on the
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x-axis place age on the y-axis lung
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capacity we can add a title as well as
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rotate the values on the y-axis you can
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see my series two video on making
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scatter plots or modifying plots in R to
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learn more about how to change the look
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of this plot we can see there is a
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positive association between lung
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capacity and age we can calculate the
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correlation using the COR command here
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we'll calculate the correlation between
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age and lung capacity we can set the
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method argument equal to Pearson to have
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Pearson's correlation return you can
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also note that Pearson is the default so
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if you leave the method argument out of
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this command by default Pearson's
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correlation will be returned you can
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also note that the order that these
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variables are entered in does not make a
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difference the correlation between a
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lung capacity is the same as the
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correlation between lung capacity and
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age if you'd like to calculate
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Spearman's correlation we can set the
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method argument equal to Spearman and
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similarly if you'd like to calculate
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Kendall's rank correlation we can set
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the method argument equal to Kendall if
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we'd like we can have a confidence
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interval returned for the correlation as
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well as test the hypothesis that the
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correlation is equal to zero using the
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core test command here we'll do this for
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Pearson's correlation and we use the COR
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test command we can see we returned the
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estimate of the correlation we can also
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see a 95% confidence interval for the
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correlation as well as the test
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statistic and p-value for the test that
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the correlation equals zero again we can
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do the same for Spearman's correlation
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we can see that our returns a hypothesis
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test although it does not return any
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form of nonparametric confidence
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interval for the correlation we can also
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see we're given a warning message that
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our cannot compute an exact p-value when
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there are ties meaning we have a few
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people of the exact same age in this
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data set this isn't really a big deal
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but if we like we can use the exact
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argument and set this equal to false
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letting our know to only approximate a
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p-value for us now let's go back again
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to the Pearson's correlation test we did
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as we've seen with other tests in R we
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can use the alt argument to change the
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alternative hypothesis here we can set
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it to greater have an alternative
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hypothesis that the correlation is
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greater than zero by default the
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alternative will be a two-sided test we
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can also use the comfort level command
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to change the confidence level we're
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using for example we may want a 99%
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confidence interval returned while
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covariance is often of less interest in
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applied statistics we can calculate this
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using the CoV command here we like the
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covariance between age and lung capacity
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we can produce all possible pairwise
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plots using the Paris command here if we
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ask for Paris plot of the lungcapdata
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this will produce all possible pairwise
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plots you'll notice that a scatter plot
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is not really appropriate for
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categorical variables you can also
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notice that the first three variables in
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our data set are the numeric ones so
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let's produce a Paris plot only for
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those variables here we will produce a
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Paris plot for the length cap data
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subsetting taking only columns 1 2 3 to
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learn more about subsetting using square
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brackets in our check out my video and
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series one on subsetting using square
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brackets taking a look at the plots we
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can see this plot here is a scatter plot
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with lung capacity on the x-axis and age
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on the y-axis this plot here is a
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scatter plot with age on the x-axis and
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height on the y-axis the core command
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can also be used to produce a
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correlation matrix for all of the
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variables here we can try and calculate
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a correlation matrix for the lungcapdata
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if we enter this command you'll notice
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our returns an error this is because our
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will not calculate a correlation for
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categorical variables or factors like we
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just did with the pair's plot we can
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subset the data and make a correlation
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matrix for only variables in column 1 2
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3 or our numeric variables we can see
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Pearson's correlation between age and
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lung capacity here we can see Pearson's
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correlation between height and age as
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before we can also ask for Spearman's
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correlation using the method argument
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and setting this equal to Spearman
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if desired we can also go ahead and
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produce the covariance matrix using the
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CoV diamond in the next video in this
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series we'll talk about fitting a simple
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linear regression using our thanks for
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watching this video and make sure to
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check out my other instructional videos
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