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, x
2
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
-1
X'Y
estimating variance: MSE
Properties of least squares estimators (M:3.3)
unbiased
var(b) = sigma
2
(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