00:01
Ok, so we're told we've got 50 students in a class and we've got the regression equation for x on y.
00:09
Now, this is a bit annoying because usually you'd have y on x.
00:11
But here we've got an equation for x on y, which is x equals a y plus b.
00:18
And if we rearrange the equation, we can find that x is equal to three fifths of y plus 36.
00:30
So this is our regression equation.
00:32
Now we want to find the mean of the x's and the correlation coefficient, so those are what we're after.
00:47
The formula for those things is, well, x bar, we know that x bar minus a times y bar is equal to b, and we also know that the sum of each x value minus the mean of the x's times each y value minus the mean of the y's summed over all the pairs divided by the sum of squares of the x's is equal to now a is 3 fifths, b is 36 and y bar which is the mean of the accountancy scores we're told is 44.
01:46
So we can rearrange this quite easily to see that x bar is equal to 86 .4.
01:54
So that's x bar.
02:03
Now to find r, r is equal to the same numerator as a, as three fifths, but this time divided by the square root of the sum of squares of the x's times the sum of squares of the y's.
02:32
And we're not going to be able to figure out what this numerator is, except we can rearrange this equation up here to find it.
02:39
So we can see from this that the sum of the x minus the mean of the x's times the y minus the mean of the y's is given by 3 fifths of the sum of squares of the x's.
02:55
And if we sub that into here, we're going to get 3 fifths times the sum of squares of the x's divided by the square root of the sum of squares of the x's times the sum of squares of the y's.
03:09
So all we need now is just to sub in what we know about the sum of squares of the x's and y's.
03:15
And this comes from what we're told about the variance.
03:18
So remember the variance of marks in accountancy, which i'll call vy, dy is defined as the sum of squares of the y's divided by n minus 1, which here is 49...