文档介绍：Chapter 5: Basic Ideas of Linear Regression: the Two-Variable Model
The Population Regression
Function(PRF)
The Meaning of Regression
Analysis
Stochastic Specification of the
Population Regression Function(PRF)
The Nature of the Stochastic
Error Term
The Sample Regression
Function(SRF)
The Special Meaning
of the Term “Linear”
Regression
Two –Variable versus
Multiple Linear
Regression
Estimation of
Parameters
The Meaning of Regression Analysis
analysis——the study of the relationship between one variable Y (the explained,or dependent variable) and one or more other variables X/Xs (explanatory,or independent variables).
Y: the explained,or dependent variable
X/Xs: the explanatory,or independent variables
The Meaning of Regression Analysis
objective of regression analysis: (1)To estimate the mean,or average,value of the dependent variable,given the values of the independent variables. (2)To test hypotheses about the nature of the dependence-hypotheses suggested by the underlying economic theory. (3)To predict,or forecast,the mean value of the dependent variable,given the values of the independent variable(s).
The Meaning of Regression Analysis
3. Note:
(1) Regression does not necessarily imply must be justified,or inferred,from the theory that underlies the phenomenon that is tested empirically.
(2)
(3)
The Population Regression Function(PRF)
Regression Line (PRL)
PRL——a line that tells us how the average/mean value of Y (or any dependent variable) is related to each value of X(or any independent variable).
——a line that passes through the conditional means of Y.
E(Y|Xi) = B1+B2Xi ()
E(Y|Xi):the mean,or expected,value of Y corresponding to,or conditional upon,a given value of X.
~conditional expectation or conditional expected value of Y.
B1 and B2: the parameters, the regression coefficients.
B1: the intercept (coefficient)
B2: the slope (coefficient).—— The slope c