中国科学院数学与系统科学研究院 Academy of Mathematics and Systems Science Chinese Academy of Sciences General Regression Analysis Professor Yongmiao Hong March 23,2021
General Regression Analysis Professor Yongmiao Hong March 23, 2021
CONTENTS 2.1 Conditional Probability Distribution 2.2 Conditional Mean and Regression Analysis 2.3 Linear Regression Modelling 2.4 Correct Model Specification for Conditional Mean 2.5 Conclusion ADVANCED ECONOMETRICS General Regression Analysis May12,2021 2
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 2 2.1 Conditional Probability Distribution 2.2 Conditional Mean and Regression Analysis 2.3 Linear Regression Modelling 2.4 Correct Model Specification for Conditional Mean 2.5 Conclusion CONTENTS
Conditional Probability Distribution Some Notations: 。 Throughout this book,we use the following notational conventions:capital letters (e.g.,Y)denote random variables or random vectors,lower case letters (e.g.,y)denote realizations of random variables. We assume that 2=(Y,X')'is a random vector with E(Y2)<oo,where Y is a scalar,X is a (k+1)x 1 vector of variables with its first component being a constant,and X'denotes the transpose of X. ADVANCED ECONOMETRICS General Regression Analysis May12,2021 3
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 3 Some Notations: Conditional Probability Distribution
Conditional Probability Distribution .Statistically speaking,the relationship between two random variables or vectors X (e.g.,oil price change)and Y (e.g.,economic growth)can be characterized by their joint distribution function. 忆50 22 139 0.83 0.56 A2066 0.28 20.00 10 0.2 0.0 0.6 0204060.8 0.4Y 0.2 100.0 ADVANCED ECONOMETRICS General Regression Analysis May12,2021 4
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 4 Conditional Probability Distribution
Conditional Probability Distribution Suppose (X,Y)'are continuous random vectors,and the joint probability density function (pdf)of (X',Y)'is f(x,y).Then the marginal pdf of X is Jx(z)-f(z,u)dv, and the conditional pdf of Y given X =x is rx()= f(x,y) fx(x) provided fx()>0.The conditional pdf fyx(y)completely describes how Y depends on X.In other words,it characterizes a predictive rela- tionship of Y using X. ADVANCED ECONOMETRICS General Regression Analysis May12,2021
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 5 Conditional Probability Distribution