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- [Instructor] The best way to understand part correlations
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is to compare them to partials,
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but also to realize that part correlations
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are very closely related to Delta R Squared, which is a
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stastic that we can request right in the Regression menus.
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Let's request it and take a look at the output, together.
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I'm going to go into Analyze, Regression, Linear,
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and Waste Tons is going to be my dependent
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and we're going to do something new now.
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We're going to go ahead and say that Retail Trade
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is our independent, then click on Next
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and then click on Restaurants.
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This is actually what you do when
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you're doing a hierarchical regression.
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And we have to do that to be able
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to request our Delta R Squared.
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So, we're going to go into Statistics
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and request Part and partial correlations,
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as well as R squared change, very
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frequently called Delta R Squared.
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We're going to click on Continue.
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We're going to click on OK.
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Let's scroll down and the first thing that we see
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is that the Zero order Correlation,
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let me put this is in its own window,
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the Zero order Correlation is the same as the numbers
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that we would get if we ran a Pearson Correlation.
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Just about point eight for both
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retail and restaurants and hotels.
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And then we notice, that the partial correlations
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are exactly what we would get by
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doing the partial correlation menu.
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One would be retail controlling for restaurants
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and the other is restaurants controlling for retail.
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So, what's the part correlation?
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Well, the part correlation is closely related to
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Delta R Squared and our Delta R Squared is
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further up in the output window.
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So, let's look at it first.
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What this is telling us is, is that our R Squared
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for the first variable, retail, is just under
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sixty percent of variance explained.
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Specifically, it's five point eight nine.
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Then, the R Square jumps up substantially
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when we add the second variable.
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That increase is called the
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R Squared change or the Delta R Squared.
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Here's where it gets a little tricky,
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we have to remember that R Squared
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is literally the correlation squared.
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So, since the part correlation is being
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reported as a correlation, but the Delta R Squared
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is being reported as an R Squared,
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we can't compare them directly
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without doing a tiny little bit of math.
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So, I'm going to bring out my calculator.
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And go down to the part correlation
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for restaurants and hotels, which is point two nine eight.
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Then square that and I get point oh eight eight.
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Which rounds up to point oh eight nine.
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What's the meaning of this though?
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Why would we want to know this?
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It's telling us how much the R Squared goes up
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when that variable is put in last.
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That's what the part correlation squared is telling us.
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The contribution of that variable
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having taken care of all the variance that's
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explained by all the previous independent variables.
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So, it's going to be a critical building block
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in understanding hierarchical regression.