# Thread: Multiple regression and matracies?

1. ## Multiple regression and matracies?

So Iam supposed to have a test soon and I've never see people soving multiple regression using the matrix method. Since our class never uses the textbook, anyone have any links that show how to solve these kind of problems?

This is an exaple of the questions Iam getting

ImageShack

Soo yea any useful websites that explain how to solve them clearly? Cos Iam REALLY stumped

Thanks

2. YOU must solve these via matrices.
It's ridiculous to try to solve it via the normal equations.
My most recent class listened and did very well on the exam.

The model is $\displaystyle Y=X\beta +\epsilon$

Where $\displaystyle \epsilon$ is a column vector or your N(0,sigma^2) errors.
The Y is a column vector of your data.
$\displaystyle \beta$ is a column vector of your parameters.

The LSE of $\displaystyle \beta$ is $\displaystyle \hat\beta=(X^tX)^{-1}X^tY$.

X is the design matrix. The columns are the data via , x , x squared.... depending on the model.

SSE is $\displaystyle Y^tY-\hat\beta X^tY$

and MSE, your unbiased estimator of sigma^2 is SSE/(n-number of parameters in the beta vector).

page 8,9 of http://malroy.econ.ox.ac.uk/fisher/iss/isslecture1.pdf is decent

3. Thanks. Ill defenitly give this a read. I was searching Google all over for it.