1. ECONOMETRICS
DR. DEEPTI

2. What is Regression
Study of relationship between the explained or dependent variable and one or more independent or explaining variables
Relationship does not imply causation
Is a conditional mean, i.e. if we are given the value of certain independent variables (Xi’s)
E(Y/Xi)
May be conducted for the following reasons :-
To find the conditional mean of Y, given X
To test the relationship between X and Y
To predict the value of Y for a given X

3. Population Regression Function (PRF)
Systematic
Determination
Component
Random
Component

4. What does error term represent
Sample Regression Function (SRF)
What does error term represent
Effect of variables not included in the model
Errors of measurment

5. What is Linear Regression
Why use a method
Since we would like to get the estimate of Y given the Xi
Plot a line that minimizes Ui’s
Since some Ui > 0 and some Ui <0
Several lines such that
Hence two options
- minimized
What is Linear Regression
Linear in variables
linear in parameter

6. The method of ordinary Least Squares
The two variable PRF :
We estimate from the SRF :

7. Least Square estimation method :-
When the actual values of X and Y are used
When the values are taken as the derivation from the actual mean
Squaring and summing on both sides we obtain
It has to be minimized
FOC

8. Matrix notation of Eq. (1) and Eq. (2)
By Cramer rule

9. And from Eq. (1)
SOC
Second order condition of minimization is that H>0, and second order partial differentiation must be positive.
(i)
(ii)

10. Assumptions of (Ui) Linear Regression Model
Ui is a random real variable and has normal distributions
The mean value of ui is zero
E(Ui)=0 {i=1,2,3,……….n}
The variance of ui is constant
E(Ui2)=2
This assumption is known as the assumption of Homoscedasticity
The disturbance terms of different observation (UiUj) are independent
E(UiUj)=0 (i≠j)
The assumption is known as the assumption of Non autocorrelation
The explanatory variables is non-stochastic variable and is measure without error, Ui is independent of the explanatory variables.
E(XiUj)= Xi E(Uj)=0
(for all j=1,2,3,………n)

11. Least Square estimation of
Standard error of estimate

12. Coefficient of determination r2
Is a measure of goodness of fitness
Measures what percentage of deviation of Y from its mean, is explained by the deviation of X from its mean

13. Coefficient of Correlation (R)
A measure of strength of linear relationship between two variables.
Is the square root of the coefficient of determination
R takes the same sign as the slope coefficient,

14. Functional forms of Regression Models
Semi log Model
How to measure the growth rate – The log – lin model
R= compound rate of growth of Y
This model is like any other linear regression model in that the parameters and are linear

15. THANK YOU