Hat Matrix Is Identity

You rarely want to drop the intercept term but if you did you can do lm dist 0 speed cars or even lm dist speed - 1 cars.

Hat matrix is identity. The term unit matrix has also been widely used but the term identity matrix. The hat matrix H is defined in terms of the data matrix X. So you have actually fitted d i s t β 0 β 1 s p e e d ϵ.

John Fox in Encyclopedia of Social Measurement 2005. If any matrix is multiplied with the identity matrix the result will be given matrix. General an orthogonal matrix does not induce an orthogonal projection.

LaTeX symbols have either names denoted by backslash or special characters. In linear algebra an idempotent matrix is a matrix which when multiplied by itself yields itself. It describes the influence each response value has on each fitted value.

It is denoted by the notation I n or simply I. In statistics the projection matrix sometimes also called the influence matrix or hat matrix maps the vector of response values dependent variable values to the vector of fitted values or predicted values. These estimates are normal if Y is normal.

How can we prove that from first principles ie. That is the matrix is idempotent if and only if. I understand that the trace of the projection matrix also known as the hat matrix XInvXXX in linear regression is equal to the rank of X.

What is the rank of the Matrix. I prove these results. This is not a comprehensive list.