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Hello and welcome to a module on Pearson correlations. First, let's load in our data and the packages we'll be using today.

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So we'll be importing Pandas as PD, Drive from Google.colab, numpy as np,

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mapplotlib.pyplot as PLT and we'll be importing pearsonr from scipy.stats.

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We'll be doing some scatter plots today, so that's why we've got matplotlib imported.

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So let's go ahead and create our variables for the class data set. This should look very familiar.

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Okay, and these are variables that we're used to seeing by now, and we know how these variables were created. So we're aware that

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there are relationships between IV1, IV2, DV, and the rest of these variables here. So let's

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investigate those relationships and see how closely related these variables actually are. Let's calculate

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the Pearson correlation between IV2 and RDV. In another video, we created a scatter plot between

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those two variables. Let's do that again and take a look. So we're going to create a scatter plot between

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IV2 and RDB, create our line of best fit, and then actually produce our

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scatter plot, label it, title it, and show it. If you need a review on how to do that,

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go visit the scatter plot video to see more. So looking at this

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scatter plot, we can see that our line is not completely flat, and it's not negative,

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so we have a positive correlation here, but it's maybe not a very strong positive correlation. We might

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guess that it's going to be moderate in size, which I already know what it's going to be, so

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my guess is a very good guess. But judging from our trend line, we might expect to see a moderate positive

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correlation between these two variables. Let's check with a Pearson calculation to see if that is the case.

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So here, we are giving Python two values to put our functions

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returns in because we know that we're going to get two returns

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from this function. We're going to give it two arguments, RIV-2 and RDV.

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It doesn't really matter what order you do them in, so long as they are both there.

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Next, we'll be calculating the T value using this correlation coefficient up here that we've already

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run. So N is equal to the length of DF. This is just returning how many data points are

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in our data frame. Len is short for length. Our T value is calculated

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using this formula, which uses the correlation coefficient, and next we're

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going to print the results. Okay,

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so we can see that we do have a moderate positive correlation between these two

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because we have a point .3246. So let's do this again for some of our other variables.

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What about the relationship between RIV1 and two IVs? Remember, two IVs was created

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by multiplying RIV1 and RIV2. So we should expect to see a pretty strong correlation

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here because the two are so highly related. Let's check out a visualization of this relationship by making a scatter

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plot first. So just as before, we'll make our scatter plot. I'll go ahead and run this. And

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yeah, we can see now our line looks very different. It's almost completely diagonal

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and our scatter - our points - are spread very closely around

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the line. So up here, we can see that things were spread out quite a bit more. Our line isn't

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quite as diagonal and here we have a very different looking graph.

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So it looks like a very strong correlation. Let's see if that's the case by running a Pearson correlation.

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So just as above, we did all the same things, we just used two different variables this time. And we have a Pearson correlation

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coefficient of 0.9303. That's pretty strong. And we should expect it again because

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those two variables are so highly related since one is a transformation of the other. All right.

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That's it for Pearson correlation coefficients. Happy coding!

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