Statistics 350 Lecture 13

Today Last Day: Some Chapter 4 and start Chapter 5 Today: Some matrix results Mid-Term Friday…..Sections ; ; (READ)

Matrices Let A be a square matrix The inverse of A is:

Matrices If A contains any linear dependencies, then We will deal mainly with non-singular matrices

Matrices A special application is the model matrix for simple linear regression:

Matrices Other useful results:

Random Vectors A vector of random variables is called a random vector Expectation

Random Vectors If A is a vector of constants, the E(A)= If A is a matrix of constants and Y is a random vector, then E(AY )=

Random Vectors The variance-covariance matrix of Y is: If A is a vector of constants, its variance-covariance is

Random Vectors If A is a matrix of constants and Y is a random vector, then  2 (AY )=

Simple Linear Regression The model is: E(  )=  2 (  )=

Simple Linear Regression E(Y)  2 (Y)=

Simple Linear Regression Now, how do represent the least squares estimation in matrix notation?