If n = p + 1, and the x matrix is invertible, show that the hat matrix h is given by the (p + 1) ∗ (p + 1) identity matrix. in this case, what are hii and yˆi?

Step-by-step explanation:

Consider that we have a multiple linear model given by this:

And we assume that we have p independent variables and p+1 is the dimension with the vector including the intercept, so then n =p+1.

For this case we want to minimize the sum of error

And we have this:

And when we find the partial derivate respect to b we got:

We are assuming that the matrix X is invertible(non singular). And applying the inverse matrix X'X on both sides we got:

The estimator for [tex\beta[/tex] is given by:

And the predicted values can be written like this:

And we can see that and on this case if we find the dimensions for H, assuming that X is nxn. Then H is a matrix nxn since only depends of the matrix X.

On this case the elements represent the elements of the diagonal for the matrix H and are used in order to find the estimated values

the median here is 25. your lowest value is 14 and highest value is 48. to find the third quartile, find the medium number in between 25 and 48 which would be 42 i believe.

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1