1. Objectives By the end of this lecture students will:
understand the simple linear regression model
understand the logic behind the method of ordinary least squares (OLS) estimation
CLRM topic is a review of the material covered in Quantitative Methods 2
References:
Gujarati., chapter 2
also pp

2. The Model True Model (Population Regression Function)
Yi is the ith observation of the dependent variable
Xi is the ith observation of the independent or explanatory variable
ui is the ith observation of the error or disturbance term
 and  are unknown parameters (coefficients)
i = 1,..., n observations

3. The Model Estimated model (Sample Regression Function) where
are the estimators of the coefficients (parameters)
are the i estimated residuals
Objective: estimate the PRF on basis of SRF

4. The Model In terms of the SRF the observed Yi can be written as
in terms of the PRF Yi can be written as
Given the SRF is an approximation to the PRF can we make this approximation as close as possible?

5. The Model Y Yi Yi ui
E(Y|Xi)
E(Y|Xi) X Xi

6. Ordinary Least Squares (OLS)
OLS obtains the estimators and minimising the sum of squared residuals (RSS) with respect to  and  :
Partially differentiate RSS w.r.t. the coefficients

7. Ordinary Least Squares (OLS)
The first order conditions are:
(1)
(2)

8. Ordinary Least Squares (OLS)
Solving (1) and (2) simultaneously gives
and
where and are the sample means

9. Ordinary Least Squares (OLS)
Example: Melbourne house prices
Y price of house in A$’000
X distance of house from GPO in kilometres
A=area of house in square metres
Interpret the results

12. Ordinary Least Squares (OLS)
What type of data is this?
Calculate the missing values of Y-hat and u-hat in the table

13. Ordinary Least Squares (OLS)
CHECK THE ANSWERS YOURSELVES!

14. Summary and conclusions
PRF vs SRF
OLS methodology
Next lecture
Gujarati p65 – 76 (Classical Assumptions)
Gujarati p107 – 112 (Normality Assumption)