00:01
All right, for this problem, we were given the following data, showing the midterm and final exam scores in an english writing class.
00:09
I have it here listed in column format, students 1 through 12, we have their midterm scores, and then we also have their final exam scores.
00:22
Now, what we're asked to do is we need to find the sample correlation coefficient of these scores.
00:30
So this sample correlation coefficient really it helps us to figure out if the two scores, two types of scores midterm and final exam, if there's any correlation between them.
00:44
If there's a strong one or a weak one.
00:47
So the formula to calculate this correlation coefficient, which is r, this is a formula right over here.
00:55
And as you can see, it's kind of, it's a lot involved.
00:58
There's a lot of adding involved, a lot of pieces.
01:04
So i'm going to actually show you how to do this using a spreadsheet because that will take away, you know, mimicking a bunch of mistakes.
01:12
But also just show you like the different pieces, what's really important with understanding this formula itself.
01:20
So let's get started here.
01:22
If you take a look at this formula, you'll notice that there's this one type of difference it keeps happening, subtraction.
01:30
We have xi minus x with the bar overhead.
01:34
We also have yi minus y with the bar overhead.
01:39
So what does that mean? it means that we are taking each x value.
01:44
We're going to call our bid terms scores the x.
01:49
So we're taking each of these x values and we're subtracting from these x values, the mean of the x values.
01:58
So that's something.
01:59
We have to find first.
02:01
And then very similarly with the ys, we'll let our final exam scores be the ys.
02:07
We're going to be taking each of these y values and subtracting the mean y value.
02:16
So let's find those means first.
02:21
Okay, so mean is pretty much what we think about the average.
02:26
We take all of the values and then we divide by how many values we have.
02:32
So if i need to stick that into my spreadsheet, i'll take all of these, add them together.
02:39
So sum them up.
02:41
And since there are 12 of them all together, divide by 12.
02:47
And i'll do the same thing with the ys.
02:52
So sum of all of them and then divide.
02:57
I need to write some here.
02:59
Some of these and then divide by 12.
03:05
Okay, great.
03:06
So these two numbers right here, this is going to be x with the bar overhead, and this is going to be y with the bar overhead.
03:15
Now, we need to figure out the values when we take each of these x values and subtract that number, and also when we take each of the y values and subtract this number.
03:26
So it's not going to be a single answer.
03:28
It's going to be a whole list of them.
03:30
So i am going to create another column.
03:32
I'll say xi minus x mean.
03:38
And that's going to be this part here inside the parentheses.
03:44
So what we can do is we'll take this x value, subtract off this mean right here.
03:51
I'm actually going to write that in.
03:56
90 .416.
03:57
I'm just going to put in a bunch of sixes.
04:02
And then so that's what we get for that first value.
04:05
Second one would be 95 minus is 90 .41666.
04:09
So already my spreadsheet is auto suggesting that it's going to do that for the whole column, which is great.
04:19
Okay, so that's going to be the x -is minus the x with the bar overhead.
04:24
That's all of these two.
04:26
And then we'll do the same thing with the ys.
04:29
Take each of the y values, yis, minus the one mean.
04:36
So take y value minus the mean, which in this case, the mean for the yis, was the 83 .333, et cetera.
04:49
And then we'll just have it auto fill.
04:50
So it does the same thing for the rest of them.
04:57
Awesome.
04:59
Now we have the pretty much what's on the inside.
05:04
We do need a couple of things.
05:06
We have a, well, we can either focus on the numerator first or we can focus on the denominator or a combination of two.
05:14
I'd like to do maybe one at a time...