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Chapter 4.3 - C hapter-4.3 The regression R^2 is the...

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Chapter-4.3 The regression R^2 is the fraction of the sample variance of Yi, explained by ( or predicted by) Xi. Y(i) (dependent variable) = Y(hat)i + u (hat) i R^2= ratio of the sample variance of Y(hat)i / the sample variance of Y(i). R^2= ESS/TSS ( ESS) Explained Sum of Squares= Is the sum of squared deviations of the predicted values of Y i, Y (hat) I from their average. Total Sum of Squares: sum of squared deviations of Y I, from its average: R^2 can also be written as the fraction towards SSR- Sum of Squared residuals, the sum of the squared OLS residuals. R^2= 1- SSR/TSS SER== The standard error od the regression is an estimator i=of the standard deviation of the regression error. Ui The least squares assumption: Assumption 1- The conditional distribution of U(i) gives X(i) has a mean zero.
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The distribution of U(i), conditional on Xi= x, has a mean of zero, stated mathematically, E(Ui/Xi=x) = 0, in somewhat simpler notation Eu(i)/X(i)=0 is equivalent to assuming that the population regression line is the conditional mean of Yi given Xi.
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