Student council at school would like to hold an end of the school year event for the eighth grade students they would like to know what’s students enjoy doing but do not have time to poll everybody Provide a suggestion for them to implement that would be unbiased

you could have a pie the teacher event?

Step-by-step explanation:

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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