00:01
Okay, so we've got a set of y and x values and we've got some questions about linear regression.
00:04
So we first want an estimate for sigma squared.
00:09
Now the sigma squared estimate is just given by the sum of squares of the errors divided by n minus 2.
00:16
N is the number of pairs of data that we have, which is 5.
00:19
We've got 5 x values and 5 y values.
00:22
And the sum of squares of the errors is given by each y value minus each predicted y value squared.
00:33
In order to do that we need to know what the predicted y values are and so we run our regression equation and we find that we get the regression equation minus 4016 plus 5374 x to the nearest integer on the coefficients.
00:47
And so we find that we get predicted y values of 8774, 16297, 15384, 18393 and 10332.
01:10
And if we do these minus the original y values and square them we can find the sum of squares of the errors.
01:17
And if we divide that by 3 we can find that our estimate for sigma squared is, pop it down here, so it's going to be 8774 minus 7440 squared plus and so on for all the others divided by 3...