Assignment 5 - ECO 544 Assignment 5 1(1 Independent...

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ECO 544 Assignment 5 1. (1) Independent variable: dtmathssk ( x – axis ) Dependent variable: dtmathss1 ( y – axis ) (2) and are the coefficients in true regression line. True regression line is not directly observable, so that and do not appear in the graph. If we denote and as OLS estimates of and , is the intercept in the estimated regression line in the graph, and is the slope of the estimated regression line. and are unbiased estimators of and , respectively. This does not mean that or . The unbiased estimator means that the expected value of is equal to , which is , and the expected value of is equal to , . That is, we can estimate many s and ’s because of sampling fluctuations, and the means of ’s and ’s that we estimate are equal to and , respectively. Therefore, we cannot say that or . A method of point estimation with some stronger theoretical properties than the method of OLS is the method of maximum likelihood (ML). The ML and OLS estimators of the regression coefficients are identical. One of the difference between two methods is that ML estimator of
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