STAT 541: Introduction to Multiple Regression
Statistics 541: Introduction to Multiple Regression
- 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)
Properties of least squares estimators (M:3.3)
- 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
- 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