the study of the relationships between a dependent variable (Y) and one or more independent or explanatory variables (X1, X2,..).
Regression
Conditional Mean (or Expectation):
E(Y|X=Xi)
E(Y|X=Xi) = f(Xi) =
ß1 + ß2Xi
E(Y|X=Xi) = f(Xi) is
Population Regression Function (PRF) or Population Regression (PR).
E(Y|X=Xi) = f(Xi) = ß1 + ß2Xi
ß1 and ß2 are WHAT coefficients,
ß1 is WHAT and
ß2 is WHAT coefficient
ß1 and ß2 are regression coefficients,
ß1 is intercept and
ß2 is slope coefficient
- X appears with a power of 1 only (no X2 or √X)
- X is not multiplied or divided by another variable
Linearity in the variables
A function is linear in the parameter β1, if β2 appears with a power of 1 only.
Linearity in the Parameters
Stochastic Specification of prf
Ui =Y - E(Y|X=Xi)
or
Yi = E(Y|X=Xi) + Ui
WHAT IS Ui
Stochastic disturbance or stochastic error term. It is nonsystematic component.
Stochastic disturbance or stochastic error term.
Ui
It is nonsystematic component.
Ui
A component that is systematic or deterministic.
E(Y|X=Xi)
The assumption that the regression line passes through the conditional means of Y implies that E(Ui|Xi ) =
0
IT is a surrogate for all variables that are omitted from the model but they collectively affect
Ui = Stochastic Disturbance
7 reasons for using Ui
- Vagueness of theory
- Unavailability of Data
- Core Variables vs. Peripheral Variables
- Intrinsic randomness in human behavior
- Poor proxy variables
- Principle of parsimony
- Wrong functional form
A particular numerical value obtained by the estimator in an application.
Estimate
