1. Econometrics Econometrics I Summer 2011/2012
Course Guarantor:  prof. Ing. Zlata Sojková, CSc., Lecturer: Ing. Martina Hanová, PhD.

2. Determining the Regression Coefficients Finding a Line of Best Fit
We can use the general equation for a straight line, to get the line that best “fits” the data.

3. Ordinary Least Squares (OLS)
The most common method used to fit a line to the data is known as OLS (ordinary least squares).
Actual and Fitted Value

4. The Theory of OLS min  ei2 = e12 + e22 + e32 +.........+ en2
E(YiXi) = o + 1Xi population regression line (PRF)
Ŷi= bo + b1Xi sample regression equation (SRF)
min  ei2 = e12 + e22 + e en2

5. How does OLS get estimates of the coefficients?
Excel Tools/data analysis/ regression
Matrix form
Formula – mathematical function

6. multiple regression model

7. multiple regression model
1) Calculation of predicted values of Y, residuals, sum of residuals, comparison of real (actual) and predicted values of Y.
Standardized Residual

8. multiple regression model
2) Calculation of residual variance, variances of parameters and their standard deviations.

9. 3) Calculation of correlation coefficient, coefficient of determination and corrected coefficient of determination.

10. 4) Calculation of confidence interval for estimated parameters

11. 5) test the statistical significance of the estimated regression parameters
Verification of the statistical significance of parameters by using T-test

12. 6) test the statistical significance of the model as a whole
Verification of the statistical significance of the model by using F-test

13. 7) Calculation of standardized coefficients or beta coefficients
βj adj. = βj * R2 *100 [%]