00:02
Looking at some data on the amount of hours spent watching television and the iqs of those subjects.
00:10
And x is ours, y is iq.
00:13
And anytime we're doing something like this, i always like to look at the data.
00:16
What does the data look like? so here's the scatterplot.
00:20
And you can see there is a downward trend here.
00:23
So we're going to see how strong that is, how strong that the correlation is.
00:28
And we want to find the correlation coefficient.
00:30
And the formula i'm going to use is the following.
00:35
1 over n minus 1.
00:37
Applied by the sum of the x values, subtracting the mean minus the sample deviation of the x values times the y values minus the mean of the y's all over the standard deviation of the ys.
00:56
All right.
00:57
So let's go ahead and go through this.
00:59
And we're given the mean and standard deviation of the x's, so we just got to go ahead and do that for the y's.
01:04
And they're here.
01:05
The mean are pretty straightforward, but the standard deviation, we have to do a little work to get.
01:12
The sample standard deviation is equal to the square root of the y values minus the means.
01:28
There we go.
01:32
Divided by n minus 1.
01:37
And this is actually the sum of those values, square.
01:40
Of this sum like that there we go so that's what we have here so this is 154 minus 128 squared and you get that number 676 123 minus 128 squared it's 25 and you go down the line to do that and this number is the result of this you take a sum of all those divide that sum by seven because n is eight here so and minus one is seven and we have this.
02:17
That's our standardization.
02:18
And i went ahead and rounded it to two decimals for the next bit of our calculations.
02:24
So here what i did, the next piece is i did these calculations here.
02:29
And something to note, this is actually the z of the, you're like standardizing the x values.
02:37
And same thing with the y's.
02:38
That's what those are.
02:41
So i went ahead and went ahead and did that here.
02:46
And as you can see, i let my spread.
02:47
Sheet do the work for me, but this is the means of 58, the x value minus the mean, 13 .38, divided by 81 .48 and you get that negative value.
03:01
And you go on down the line.
03:03
Do that.
03:04
And then you do the same thing for the ys.
03:10
And you get all that...