00:01
All right, so we have a young person who is looking at the number of walks they shovel over the temperature in the day.
00:12
So when it was negative 10 degrees, they shoveled about 14.
00:15
When it was zero degrees, they shoveled 10 and 7.
00:19
So these are in different days and the temperature.
00:21
So you can see as the temperature increases, there's fewer walks.
00:25
And we see it's kind of linear.
00:26
And so the question is, is this a strong linear relationship? so we're going to test the null hypothesis that r is equal to zero.
00:33
The alternative that r is not equal to zero.
00:37
And we're going to do a t -test for this.
00:39
And this test statistic is found by doing t equal to r times the square root of n minus 2, where n is the number of samples.
00:47
So there's seven samples.
00:48
It's something to note.
00:49
N is seven.
00:55
And we, sorry, r times square root of n minus 2.
00:58
And then we divide that by 1 minus r squared, which is the same thing as r here, the correlation coefficient.
01:04
Okay, so let's go ahead and run through this.
01:06
Oh, before we go any further, let's say we're going to reject the null hypothesis at the alpha 0 .05 level of significance.
01:14
All right, so let's go ahead and do that.
01:18
So here's the correlation coefficient and the test statistic and the p -value along with the mean and standard deviation.
01:23
We'll talk more about that in a moment.
01:25
So we're just really looking right here.
01:29
Here's our r value.
01:30
And i get this by using our corel function, equals corel.
01:34
And what you do is you put in the references for your x data and the references for your y.
01:40
And that's how we get that.
01:41
And the test statistic, after we put negative 0 .914 into our t -statistic formula here, we get this, negative 5 .04.
01:49
Then to find the p -value, we do equals t -dist.
01:51
This is a spreadsheet formula where this is the absolute value of the test statistic.
01:56
This is the degrees of freedom at 5 .05 is.
01:58
And that's calculated with n minus 2.
02:00
N minus 2 degrees of freedom for a regression, a linear regression model with one variable.
02:06
And then 2, this thing, this 2, it refers to the number of tails.
02:11
And because we're looking not equal to 0, that means it's two tails.
02:15
If it was less than 0, it'd be one tail...