古典一元线性回归2011川大计量经济学.pptx
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1、第一篇第一篇古典线性回归模型古典线性回归模型 CHAPTER ONECLASSICAL TWO-VARIABLE LINEAR REGRESSION MODEL Two variable:one dependent variableTwo variable:one dependent variable only one explanatory varialbe only one explanatory varialbeLinear:Y is linear function of Linear:Y is linear function of parameters.parameters.IMPOR
2、TANT differentiation1、correlation:determinate stochastic(no-determinate)相关关系相关关系:确定性 非确定性非确定性2、Correlation and causality相关关系相关关系与因果关系3、Linearity:linearity in the variable linearity in the parameters 线性:变量线性 参数线性参数线性1.1 Two-variable linear regression modelPopulation:a set of all possible outcomes of
3、a random variableSubpopulation:1.1.1 population regression function and population regression linePRF:Y Yt t=0 0+1 1X Xt t+u+ut t stochastic E(E(Y Yt tX Xt t)=0 0+1 1X Xt determinatet determinate Y Yt t=E(E(Y Yt tX Xt t)+u+ut tSEE T.F 2.1SEE T.F 2.1X:explanatory ,independent variable,fixed-value var
4、iableY:dependent variable,random variable,:regression coefficientsU:disturbance or error term,is a random variableThe task of regression is to estimate the PDF,that is,to estimate the value of unknown,on the basis of observations on Y and X。error term u stands for the aggregate effect of all factors
5、 which are excluded from model but indeed affect Y:1、variables excluded from model with effect on Y vagueness of theory,negligible effect,noavailablity of data 2、intrinsic random of human beings behavoir 3、measurement error 4、error of model forms1.1.2 sample regression function and sample regression
6、 line(f 2.4,t 2.4,t2.5)SRF See f 2.5The task of regression is to estimate the PDF on the sample information of Y and XPrimary objective in regression analysis is to estimate the PRF on the basis of the SRF,or on the sample information of Y and Xon the sample information of Y and X,but the estimation
7、 of the PRF based on the SRF is at best an approximation。The next question is how the SRF should be constituted as close as possible to the PRF even though we never know what is the true PRF。Method of estimation:Ordinary least square:最小二乘法:最小二乘法Maximum likelyhood:最大似然法:最大似然法1.1.2 the meaning of the
8、term linearLinearity in variablesLinearity in parameters conditional means of Y is linear function of parameters.1.2 estimation methodordinary least square(OLS)Now,the and PRF is unknown,our task in regression analysis is to estimate the PRF on the basis of the SRF,or on the sample information of Y
9、and X,but the estimation of the PRF based on the SRF is at best an approximation。We assume that the closer the SRF is to a set of sample data on Y and X,the better the SRF fits the PRF.Scatter-graph Y 0 XPRF:E(PRF:E(Y Yi i)=0 0+1 1X Xi iEnlarged local areaactualestimateresidualfundamental thought of
10、 OLS:to make SRF as close as possible to PRF,the residual of every point should be as small as possibleHow to chose to make the sum of squared residuals as small as possible Criterion of minimizing the sum of squared residuals(The sum of squared residuals is a function of estimator of parameters.)1.
11、3 CLRMs AssumptionCLRM:classical linear regression model1、Model is linear in parameters,X is fixed-value2、Zero mean value of disturbance u ui iE E(u ui i|X|Xi i)=0=0It means that these factor excluded from the model dont systematically affect the mean value of Y.3 3、Homoscedasticity or equal varianc
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