00:01
So in this question, we have that the correlation between these two variables is equals to 0 .9 to 4.
00:08
And we have here that we should consider a level significance is equals to 0 .05.
00:15
And in this question, first we need to say if we can do a regression analysis.
00:21
And yes, we can.
00:23
Because like we have a total number of like observations equals to 6.
00:30
So n is equal to 6.
00:32
And we need in the regression, which is given by y is equal to a intercept plus b times x.
00:41
So because we need to estimate these two values, oh, sorry, not this one, a and b.
00:47
So y and x are given.
00:49
In our case, this one here is for the women.
00:54
And this one here is men.
00:57
So basically, we have to estimate these two numbers, okay? so because we just need to estimate two, this sample size is enough to estimate these two numbers.
01:08
If the sample size was like equals to two, or like if you only have one observation, then we're going to say that it is not possible to estimate this regression.
01:20
But in our case, it's okay to estimate.
01:24
We are not going to get like good results.
01:26
It's better when we have a simple.
01:27
Size large, but it's possible to compute these numbers.
01:32
So the formula here for the b is given by the correlation coefficient times the standard deviation for the y, divided by the standard deviation for the x.
01:46
So first, we need to compute what is the x, y, which is the state of deviation.
01:52
So the standard deviation is given by the square root of the variance.
01:55
But the variance is basically the sum for all the values that we have here, in which we need to compute like the yi for each observation.
02:09
In this case, the y here is women.
02:13
So for each woman here, we should subtract the mean that we have.
02:19
Then for each difference, we should compute the square.
02:23
And then we're going to sum all these squares for all the observations that we have.
02:27
And divide this by n minus 1.
02:31
Basically, the thing here inside, as you can see, we need to know the sample mean, right? so first, let's complete the sample mean.
02:40
So the sample mean here is basically the sum of all the observations that we have divided by the total number of observations, which is six.
02:50
So for the woman, this is going to be like 47 .4 plus 72.
03:00
All the numbers that we have for the women in the last 158 .1 divided by 6 which is going to give us 348 .1 divided by 6 which is 58 .02.
03:17
Now we can also compute this for x which is this case man.
03:22
So basically he is just the sum of all the possible values that we have for the for the men here...