Resize a little bit, there you go.

Okay, and then I want to plot an ellipsoid of the fit,

and it turns out that the function, eclipse 3D can just take in

the fitted object by itself, and

it automatically just takes the first three coefficients, and

fits a simultaneous confidence ellipsoid for those three coefficients.

In this case, we only have three coefficients, so that's fine.

And I'm going to tell it I want color to be red.

The blending, this is not the type one error rate alpha,

this is the alpha blending for how transparent you want the object to be.

In this case I want it to be about 50% transparent.

I want aspect to equal true, that just means how it's going to

rescale the axis so I put it in and there it is, okay?

So this is now our confidence ellipsoid where displacement

is on one axis, the intercept is on the other axis and

the horsepower is on the third axis, okay?

So this is a three dimensional confidence ellipsoid for

those three coefficients simultaneously.

So the probability that the three dimensional point for beta one,

beta naught, beta one, and beta two lies in this confidence region is 95%,

under our assumptions, okay?

So now we can do this directly.

I think we should, given our discussion where we actually went through

the definition of an ellipse we should actually do it a little bit more directly.

So data is now just going to be coefficients from the fitted values.

Let me just show you what the data's are.

There's the betas.

30 for the intercept minus 0.03 for displacement, and

minus 0.24 for horsepower.

And then, my sigma is just going to be the variance,

covariance, of the fitted matrix.

So sigma is the variance covariance matrix of the beta matrix.

So there it is 1.77, you can see it.

Okay, and then N is the number of rows and

E is the number of columns of X.

So in this case it turns out that the specific way the ellipse 3D needs it,

is it needs the A matrix to be sigma times the relevant F quantile.

And then three here is from the three dimensions, it's from