Linear Regression Formula Matrix. Y x b e. Fortunately a little application of linear algebra will let us abstract away from a lot of the book keeping details and make multiple linear regression hardly more complicated than the simple version1.
The input variable x and the output variable y. Frank wood fwood stat columbia edu linear regression models lecture 11 slide 20 hat matrix puts hat on y we can also directly express the fitted values in terms of only the x and y matrices and we can further define h the hat matrix the hat matrix plans an important role in diagnostics for regression analysis. Write h on board.
For simple linear regression meaning one predictor the model is yi β0 β1 xi εi for i 1 2 3 n this model includes the assumption that the εi s are a sample from a population with mean zero and standard deviation σ.
In matrix terms the same equation can be written. The model assumes that y is a linear function or a weighted sum of the input variable. A matrix formulation of the multiple regression model. Chapter 5 contains a lot of matrix theory.
