STAT 541: Introduction to Multiple Regression

# Statistics 541: Introduction to Multiple Regression

## Admistrivia

• return first homeworks
• collect 2nd homeworks
• read chapter 3 of Myers

## Introduction to Multiple Regression

Estimation in linear multiple regression (M:3.1, 3.2)
• What is a linear model?
• log, x2 are all linear???
• Cobb-Douglass is linear or not???
• General definition: "Mine is linear, yours is not"
• Matrix representation for multiple regression Y = X(beta) + epsilon
• Normal equations: X'X = X'Y
• Beta-hat = X'X-1X'Y
• estimating variance: MSE
Properties of least squares estimators (M:3.3)
• unbiased
• var(b) = sigma2(X'X)-1
• BLUE, UMVUE, MLE, generally the right stuff

## Hypothesis testing in multiple linear regression (M:3.4)

Sum of squares magic: SST = SSR + SSE (T=total, R=regression, E = error)
• Sequential SS: SSR = R(all betas) = R(some|rest) + R(rest)
• Testing: Is R(some|rest) significantlly bigger than zero?
• partical F test tests if R(some|rest) is significant
• if "some" is only one variable, then t-test tests significance

Last modified: Wed Feb 14 12:42:09 2001