1. Statistics 350 Lecture 13

2. Today Last Day: Some Chapter 4 and start Chapter 5 Today: Some matrix results Mid-Term Friday…..Sections 1.1-1.8; 2.1-2.7; 3.1-3.3 (READ)

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

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

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

6. Matrices Other useful results:

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

8. 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 )=

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

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

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

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

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