ECONOMETRICS DR. DEEPTI

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

Population Regression Function (PRF) Systematic Determination Component Random Component

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

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

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

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

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

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

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)

Least Square estimation of Standard error of estimate

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

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,

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

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