Chapter4.3
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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 Spring '11
 sani
 Economics, Normal Distribution, Regression Analysis, Standard Deviation, Variance, Probability theory, Yi

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