北大暑期课程《回归分析》(linear regression analysis)讲义pku6.docVIP

Class 6: Auxiliary regression and partial regression plots. More independent variables? I. Consequences of Including Irrelevant Independent Variables What are the consequences of including irrelevant independent variables? In other words, should we always include as many independent variables as possible? The answer is no. You should always have good reasons for including your independent variables. Do not include irrelevant independent variables. There are four reasons: A. Missing Theoretically Interesting Findings B. Violating the Parsimony Rule Occoms Razor C. Wasting Degrees of Freedom D. Making Estimates Imprecise. e.g., through collinearity . Conclude: Inclusion of irrelevant variables reduces the precision of estimation. II. Consequences of Omitting Relevant Independent Variables Say the true model is the following: . But for some reason we only collect or consider data on y, x1 and x2. Therefore, we omit x3 in the regression. That is, we omit x3 in our model. The short story is that we are likely to have a bias due to the omission of a relevant variable in the model. This is so even though our primary interest is to estimate the effect of x1 or x2 on y. Give you an example. For a group of Chinese youths between ages 20-30: y earnings x1 education x2 party member status x3 age If we ignore age, the effects of education and party member status are likely to be biased 1 because party members are likely to be older than non-party members and old people earn more than the young. 2 because older people are likely to have more education in this age interval, and older people on average earn more than young people. But why? We will have a formal presentation of this problem. III: Empirical Example of Incremental R-Squares Xie and Wu’s 2008, China Quarterly study of earnings inequality in three Chinese cities: Shanghai, Wuhan, and Xi’an in 1999. See the following tables: Table 1: Percent Variance Explained in