What Makes OLS Regression Linear

1
What Makes OLS Regression Linear?

• ESM 206
• Jan. 18, 2007

2
What makes it linear regression?

• Model is linear in parameters
• Parameters cant occur inside a nonlinear
  function
• Residuals are additive

• Nonlinearity in variables is OK

3
A fresh look at chlorophyll
4
Simple multiple regression
5
A subtler model

• Science tells us phosphorus is usually the
  limiting nutrient in lakes
• But what about when theres lots of phosphorus?
• Look at lakes with lots of phosphorus, and look
  for a relationship with nitrogen
• How to define lots of phosphorus?
• A better hypothesis Nitrogen becomes steadily
  more important as phosphorus levels go up
• Create an interaction variable NP
  NitrogenPhosphorus
• Eqn on board

6
(No Transcript)
7
Assumptions of OLS regression

• Model is linear in parameters
• The data are a random sample of the population
• The errors are statistically independent from one
  another
• The expected value of the errors is always zero
• The independent variables are not too strongly
  collinear
• The independent variables are measured precisely
• The residuals have constant variance
• The errors are normally distributed

• If assumptions 1-5 are satisfied, then OLS
  estimator is unbiased
• If assumption 6 is also satisfied, then
• OLS estimator has minimum variance of all
  unbiased estimators.
• If assumption 7 is also satisfied, then we can
  do hypothesis testing using t and F tests
• How can we test these assumptions?
• If assumptions are violated,
• what does this do to our conclusions?
• how do we fix the problem?

8
(No Transcript)