1. CHAPTER 3: TWO VARIABLE REGRESSION MODEL: THE PROBLEM OF ESTIMATION
ECONOMETRICS I
CHAPTER 3: TWO VARIABLE REGRESSION MODEL: THE PROBLEM OF ESTIMATION
Textbook: Damodar N. Gujarati (2004) Basic Econometrics, 4th edition, The McGraw-Hill Companies

2. 3.1 THE METHOD OF ORDINARY LEAST SQUARES
PRF:
SRF:
How is SRF determined?
We do not minimize the sum of the residuals!
Why not?

3. Least squares criterion

4. 3.1 THE METHOD OF ORDINARY LEAST SQUARES
We adopt the least-squares criterion
We want to minimize the sum of the squared residuals.
This sum is a function of estimated parameters:
Normal equations:

5. 3.1 THE METHOD OF ORDINARY LEAST SQUARES
Solving the normal equations simultaneously, we obtain the following:
Beta2-hat can be alternatively expressed as the following:

6. Three Statistical Properties of OLS Estimators
I. The OLS estimators are expressed solely in terms of the observable quantities (i.e. X and Y). Therefore they can easily be computed.
II. They are point estimators (not interval estimators). Given the sample, each estimator provide only a single (point) value of the relevant population parameter.
III. Once the OLS estimates are obtained from the sample data, the sample regression line can be easily obtained.

7. The properties of the regression line
It passes through the sample means of Y and X.

8. The properties of the regression line2.

9. The properties of the regression line
3. The mean value of the residuals is zero.

10. The properties of the regression line4. 5.

11. 3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares

12. 3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares

13. 3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares

16. 3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares

18. 3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares

19. 3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares

21. Example of perfect multicollinearity: X1 = 2X2+X3
3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares
Example of perfect multicollinearity: X1 = 2X2+X3 Y X1 X2 X3 6 5 2 1 11 10 4 17 22 16 25 19 8 3 33 15

22. PRECISION OR STANDARD ERRORS OF LEAST SQUARES ESTIMATES
var: variance
se: standard error
: the constant homoscedastic variance of ui
: the standard error of the estimate
: OLS estimator of

23. Gauss – Markov Theorem
An estimator, say the OLS estimator , is said to be a best linear unbiased estimator (BLUE) of β2 if the following hold:

25. The coefficient of determination r2
TSS: total sum of squares
ESS: explained sum of squares
RSS: residual sum of squares

27. The coefficient of determination r2
The quantity r2 thus defined is known as the (sample) coefficient of determination and is the most commonly used measure of the goodness of fit of a regression line. Verbally, r2 measures the proportion or percentage of the total variation in Y explained by the regression model.

28. The coefficient of determination r2

29. The coefficient of determination r2

30. The coefficient of correlation r
r is the sample correlation coeffient

32. Some of the properties of r

33. Homework
Study the numerical example on pages There will be questions on the midterm exam similar to the ones in this example.
Data on page 88:

34. Homework

35. Homework