Okay, so the denominator is these two numbers multiplied together? You get a pretty big number there, so it's I two times J. So that's the sum of Y squared minus the sum of why quantity squared? That's the B 18 right there. Is this a 18 over here? And I got that number and then I did the same thing for the female. 16 and then minus the summation of X quantity squared X quantity squared. So in is 10 and then the summation of X squared is D. And that's why I made, there's a small distinction there. So it's in times the sum of x squared minus the sum of x quantity squared. Okay, so then the denominator is a little trickier. So a 16 times The sum of why? So that's the B- 16. So what I did there was the sample size was 10, there are 10 states, I think. So the numerator remember was in times the sum summation of xy minus the sum of x times the sum of Y. Now you don't have to do it this way but I find that it leads to less mistakes or fewer mistakes if I kind of break it up in the numerator denominator. So that's uh most of the stuff in fact that's all the stuff that I need now I need to kind of piece it together using that formula and I kind of went in pieces. And then I added the ex wives together, so some of C. And then I squared that that's my summation of why quantity squared. And then I squared that so that's my some of X. So that's my formula equals some a 22811. So what I did was I just added A two all the way through 11. And I squared it and I did that 10 times. And I did a two and then raised to the second power. And then what's nice about excels you can do that as you can see a bunch of times there. So what I did here to look at that formula put equals a.
And then let's kind of look at what I did here. And then why is the female median salary? So I went ahead and enter those numbers in. So here I've kind of pre populated so X I think represents the male uh median salaries. So just keep those in mind whenever we look at this spreadsheet. Prime or Y hat squared divided by the sample size minus two. Is the square root of the summation of the actual minus that predicted. And then we do the standard area of the estimate. So that's how we find our and then we're gonna square that to find R squared. And then likewise, here we have the sample size times the summation of Y squared minus the summation of why quantity squared. So there's a subtle difference between those two. And this whole mess is the sample sized times the summation of X squared minus the summation of x quantity squared. But it's the sample size times the summation of the two variables multiplied minus the summation of your independent variable times the summation of your dependent variable divided by the square root of this whole mess. I very seldom do the formula here, but I'm gonna use Excel to use the formula. So what we're gonna do is we're gonna find our and then we're gonna square and that's our coefficient of determination. And we're asked to find the coefficient of determination which is actually R squared. So uh here's the are this stands for the court, the correlation coefficient.
The following is a solution to the correlation between male and female median salaries in different states.
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