Regression回归分析Regression回归分析.pdf

Regression Analysis (Spring, 2000) By Wonjae Purposes: a. Explaining the relationship between Y and X variables with a model (Explain a variable Y in terms of Xs) b. Estimating and testing the intensity of their relationship c. Given a fixed x value, we can predict y value . (How does a change of in X affect Y, ceteris paribus?) (By constructing SRF, we can estimate PRF.) OLS (ordinary least squares) method: A method to choose the SRF in such a way that the sum of the residuals is as small as possible. Cf. Think of ‘trigonometrical function’ and ‘the use of differentiation’ Steps of regression analysis: 1. Determine independent and dependent variables: Stare one dimension function model! 2. Look that the assumptions for dependent variables are satisfied: Residuals analysis! a. Linearity (assumption 1) b. Normality (assumption 3)— draw histogram for residuals (dependent variable) or normal P-P plot (Spssstatisticsregressionlinearplots ‘Histogram’, ‘Normal P-P plot of regression standardized’) c. Equal variance (homoscedasticity: assumption 4)—draw scatter plot for residuals (Spss statisticsregressionlinearplots: Y = *ZRESID, X =*ZPRED) Its form should be rectangular! If there were no symmetry form in the scatter plot, we should suspect the linearity. d. Independence (assumption 5,6: no autocorrelation between the disturbances, zero covariance between error term and X)—each individual should be independent 3. Look at the correlation between two variables by drawing scatter graph: (Spssgraphscattersimple) a. Is there any correlation? b. Is there a linear rel