assign3 - PSTAT 120C Assignment 3(Revised These questions...

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PSTAT 120C: Assignment # 3 (Revised!) Due April 27, 2006 These questions are due at the beginning of lecture next Thursday. 1. For any one of the residuals e i = Y i - ˆ β 0 - ˆ β 1 x i , calculate the covariance of this with the estimate of β 0 Cov e i , ˆ β 0 . 2. These are four famous data sets produced by Frank Anscombe as a warning and an encour- agement to plot the data before fitting a line. x1 y1 x2 y2 x3 y3 x4 y4 10 21.26 10 22.4 10 20.7 8 21.2 8 20.57 8 21.84 8 20.43 8 18.74 13 20.15 13 21.35 13 25.31 8 21.98 9 22.28 9 22.15 9 20.56 8 19.7 11 21.36 11 22.27 11 20.8 8 22.66 14 22.3 14 20.43 14 21.19 8 19.32 6 21.35 6 20.25 6 20.21 8 21.62 4 18.81 4 17.66 4 19.9 8 20.91 12 23.63 12 21.9 12 20.95 8 20.13 7 18.73 7 21.15 7 20.31 8 20.44 5 20.01 5 19.05 5 20.09 19 23.75 mean 9 20.95 9 20.95 9 20.95 9 20.95 s 3.3167 1.496 3.3167 1.496 3.3167 1.496 3.3167 1.496 r 0.6208 0.6208 0.6208 0.6208 The mean and standard deviations of the x ’s and y ’s are the same in each data set as are the values of r . (a) Calculate ˆ β 0 , ˆ β 1 , s e for these data sets (we get the same estimates for each of the four sets of data.) (b) Test H 0 : β 1 = 0 versus H a : β 1 = 0. (c) Calculate the residuals for each of the data sets.
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