00:01
So for this problem to begin, we have that our best point estimate for a given value of x is going to be y at the predicted value using a linear regression, which is equal to an intercept, b0, plus b1, a slope times the input x value, where the slope b1 is equal to the sum of...
00:32
So actually, i'll say it this way.
00:34
So the sum over all of the individual values, so the sum over i of xi minus x bar, so each individual x value minus the mean of the x values, times yi minus y bar, each individual y value minus the mean of the y values, divided by the sum over i of x i minus x bar squared.
01:02
So, and then we'll have that b0, the intercept, is equal to the mean value of y, y bar, minus the slope times the mean value of x.
01:14
So for calculating b1, i'm going to use excel as a fancy calculator, basically, just to make this a little bit faster.
01:21
So first thing that we'll do is find x bar and y bar.
01:26
X bar, we find by one way, the manual way, would be to add up all of the individual x, values, so we'd find the sum there is 20, then we divide by the number of x values, which gives us x bar is equal to 4.
01:40
Then for y bar, we would be able to do the same thing, or alternatively, i'm using the average command in xl.
01:47
We can see that the total for y is 15, 15 over 5 gives us that average of three.
01:52
Then i'll find x minus x bar times y minus y bar for each of these, as well as x minus x bar squared for each one of these.
02:01
So for the x minus x bar times y minus y bar, well that's one minus four times five, put that in brackets, times five minus three.
02:13
So we get the first term there would be negative six...