00:01
For this problem, to begin, i'll note that, basically, since the question here is focusing on doing the anova for a regression, i'm going to just go directly to assuming that we have the regression done, though i'll quickly note that when we're doing a linear regression, we have that our predicted value, y hat, is equal to beta 0 plus beta 1 times x, where we have that beta 0 is equal to the sum of xi minus x bar times yi minus y bar, divided by the sum of xi minus x bar squared, and beta 1 is equal to y bar minus beta 0, or pardon me, i have this mislabeled, pardon me, that should have been beta 1 and then this is beta 0, beta 0 is y bar minus beta 1 times x bar.
01:00
That being said, when we go through and do our regression analysis for this problem, we should get that our linear regression equation is going to be y hat is equal to, let's see here, 0 .687, roughly, plus 11 .87x.
01:21
Now what i'll do is quickly jump over into excel, because what we're going to need to do for actually doing our anova is first calculate our predicted value for each one of our x values.
01:36
So, using the values calculated, or using the regression calculated rather, 0 .687 plus 11 .87 times each x value, and i forgot to put in the equals sign first, let me fix that there, and then we calculate all of these out, so this, ok something's gone wrong here, pardon me.
01:57
Oh, the thing that went wrong here is that i got the values mixed around, pardon me, 0 .687x plus 11 .87, not, basically i got beta 0 and our predicted values, one thing that we're going to do is first calculate out y minus y hat for each one of these values, or actually, considering what we're going to need to do here, we'll do y minus y hat squared.
02:29
This is going to give us, when we take the sum, that's going to give us the sum of squared errors.
02:45
Let's see, so we have that our sum of squared errors, or our regression sum of squares, depending on our notation.
02:54
Yeah, this would be the ss for regression, so actually i'll label that ss reg for short, is roughly 45 .565, or pardon me, no, that is the residual, excuse me, so that's the residual sum of squares.
03:09
Then we need to get the regression sum of squares, which we'll find by taking the predicted value, y hat, minus the mean value, so i'll call it y hat minus y bar squared...