LinearRegression1

If one uses calculus to solve the minimization

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Unformatted text preview: nxy i =1 i =1 i =1 See Appendix 2 A of Wooldridge (2009). If one uses calculus to solve the minimization problem for the two parameters you obtain the following first order conditions, which are the same as we obtained before, multiplied by n n å (y i =1 n i ˆ ˆ - b0 - b1x i ) = 0 å x (y i =1 4 i i ˆ ˆ - b0 - b1x i ) = 0 Choosing a set of explanatory variables based on the size of the R-squared can lead to nonsensical models. We later see that R-squareds obtained from time series regressions can be artificially high and can result in misleading conclusions. Nothing about the classical linear model assumptions requires that R-squared be above any particular value; it is simply an estimate of how much variation in y is explained by x in the population. Regressions can have small R-squareds and still be useful. All this means isthat we have not accounted for several factors that affect y (explanatory variables, used in multivariate regression). Note that this does not mean that the u is correlated with x. The zero conditional mean VER. 9/25/2012. © P. KOLM 23 assumption is what determines whether we get unbiased estimators, and the size of the R-squared has no direct bearing on this. VER. 9/25/2012. © P. KOLM 24...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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