Question: (15 pts) Consider a simple linear regression model, Define the following, Sxx = (X-X), Yi Bot Y = o + 3X, tn Suv =

(15 pts) Consider a simple linear regression model, Define the following, Sxx

(15 pts) Consider a simple linear regression model, Define the following, Sxx = (X-X), Yi Bot Y = o + 3X, tn Suv = (Y-Y), x)3 = Say=(X-X)(Y-Y) Answer the following questions. (a) Express SSTO, SSR, SSE and R2 (coefficient of determination) in terms of Sr Say and Syy- (b) Suppose that for a certain data set, b0. What does this imply for R2? What does it tell us about the relationship between X and Y? (c) Suppose, that instead of estimating least-squares line using {(X,Y), we use the swapped pairs ((Y, X.)} (i.e. predictor and response variables are swapped). How are the least-squares estimates of the slopes in the two cases related? How does R change?

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