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Unformatted text preview: i =1 ( yi − y )2 is the total sum of squares (SST) ( =total variation in yi , i.e., the 10 • ∑ n ˆ
u 2 is the residual sum of squares (SSR) ( =total variation in ui , i.e., the i =1 i object we minimize) Then SST=SSE+SSR. Rsquared of regression To measure the goodness of fit for a regression, we can compute the fraction of the total variation in Y (SST) that is explained by the model. It is called the Rsquared of regression SSE
SST Note that R 2 is a ratio, so it is scale free. It does not depend on the unit of measurement of Y and that of X. Interpretation: R 2 ⋅100% represents the percentage of variation in Y that can be explained by the model. A special Case: A model with only an intercept but no X, Y = α + u has R 2 = 0. Unbiasedness of OLS ˆˆ
Unbiasedness is about the mean/expected value of an estimator θ . θ is an unbiased ˆ
estimator of the parameter θ , if E (θ ) = θ . Unbiasedness refers to whether the distribution of the estimator is centered...
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