By Jeffrey Wooldridge
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Extra info for Introductory Econometrics: A Modern Approach 2nd Edition by Jeffrey Wooldridge B01_0104
Example text
44 Part 1 Regression Analysis with Cross-Sectional Data In the social sciences, low R-squareds in regression equations are not uncommon, especially for cross-sectional analysis. We will discuss this issue more generally under multiple regression analysis, but it is worth emphasizing now that a seemingly low R-squared does not necessarily mean that an OLS regression equation is useless. 39) is a good estimate of the ceteris paribus relationship between salary and roe; whether or not this is true does not depend directly on the size of R-squared.
This case is appropriate for the vast majority of applications. 6. Unless explicitly stated otherwise, we always estimate an intercept along with a slope. 3 Properties of OLS on Any Sample of Data In the previous section, we went through the algebra of deriving the formulas for the OLS intercept and slope estimates. In this section, we cover some further algebraic properties of the fitted OLS regression line. The best way to think about these properties is to remember that they hold, by construction, for any sample of data.
Furthermore, because the ui are independent random variables across i (by random sampling), the variance of the sum is the sum of the variances. Using these facts, we have Θ ͚ d u Ι ϭ (1/SST ) Θ ͚ d Var(u ) Ι n Var( ˆ 1 ) ϭ (1/SST x ) 2 Var n iϭ1 Θ͚ d Ι i i x 2 i 2 iϭ1 i n ϭ (1/SSTx)2 2 2 i iϭ1 Θ͚ d n ϭ 2(1/SSTx)2 which is what we wanted to show.
Introductory Econometrics: A Modern Approach 2nd Edition by Jeffrey Wooldridge B01_0104 by Jeffrey Wooldridge
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