Ch._4_Exercise_Solutions

Ch._4_Exercise_Solutions - Sol - 1 Chapter 4 Solutions 1....

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Sol - 1 Chapter 4 Solutions 1. Consider the assessment data with simple model value age size residual =+ + + β 01 2 . Use the methods in this chapter to assess the fit of the model and to suggest remedies. Is the prediction of value for a building with size 13.9 and age 30 sensitive to any particular cases? We start by fitting the simple model and looking at various plots of the residuals and the qq plot of the standardized residuals to examine the fit. Note, for this fit, the 95% prediction interval for age=30, size=13.9 is -46.7 to 21.6, an interval so wide that it is useless. The one common feature of all of the plots is the two large residuals both of which correspond to a large fitted value and relatively small age and size. The qq plot of the standardized residuals is not linear but is highly distorted by the two large standardized residuals. If we delete these two points and repeat the fit we get the following plots. There is no evidence against the fit in any of these plots. With the two points deleted, the prediction interval is -17.0 to 25.6, much narrower but still not useful. The bottom line here is that it is not feasible to use these data to assess a building that is so much larger than any other in the sample. Adapted from Stat 371 course notes © R.J. MacKay, University of Waterloo
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Sol - 2 2. In an experimental Plan, there were three explanatory variates x x x 123 ,, t h a t e a c h were assigned two values, here coded as -1 and +1. There are 8 combinations. As well, the investigators looked at the response variate for the so-called center point x x x 00 === , , 0 . The data are shown below and can be found in the file c h5Exercise2.txt. x 1 x 2 x 3 y -1 -1 1 11.54 -1 1 -1 5.45 -1 1 1 7.34 1 -1 -1 17.21 1 -1 1 17.87 1 1 -1 9.40 1 1 1 11.30 0 0 0 11.57 0 0 0 11.97 0 0 0 11.89 0 0 0 12.15 Suppose we fit a model y x x x r =+ + + + β 01 12 23 3 . The summary output from R is Call: lm(formula = y ~ x1 + x2 + x3) Residuals: Min 1Q Median 3Q Max -1.2527 -0.1360 0.1465 0.4419 0.7615 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 11.6181 0.2372 48.985 3.87e-10 *** x1 2.4654 0.3000 8.218 7.68e-05 *** x2 -3.1071 0.3000 -10.357 1.70e-05 *** x3 0.5329 0.3000 1.776 0.119 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
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Ch._4_Exercise_Solutions - Sol - 1 Chapter 4 Solutions 1....

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