36 8 50 470 475 480 10 15 Fitted values Standardized residuals Scale

36 8 50 470 475 480 10 15 fitted values standardized

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36 8 50 47.0 47.5 48.0 48.5 0.0 0.5 1.0 1.5 Fitted values Standardized residuals ●● ●● Scale-Location 36 8 50 0.00 0.01 0.02 0.03 0.04 0.05 -3 -2 -1 0 1 2 3 Leverage Standardized residuals ●● ●● Cook's distance Residuals vs Leverage 8 113 1 Figure 5: Diagnostic plots (b) Then, using the same data set, fit a cubic-spline fit to the data (with temperature as the responsevariable and time as the explanatory variable), using the default amount of smoothing. Plotthe data with the cubic-spline fit superimposed and include your code in your answer. 7
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Homework 6 Solutions, W2018 PSTAT 127 Page 8 of 9 dev.off() detach(aatemp) ●● ●● 1850 1900 1950 2000 44 46 48 50 52 data(aatemp) and smoothing spline with default smoothing parameter choice year temp Figure 6: Cubic spline with default smoothing parameter choice Side-Note: these data were collected over time, so methods for dependent data may be more appro- priate than the methods used above; including a different method to choose the smoothing parameter if fitting a cubic-spline related model with autocorrelated errors. However, treat this simply as an illustrative example to explore the techniques we studied in class, realizing that you could extend these methods into the time series context by specifying dependence in the random errors (even though the latter extension is beyond the scope of PSTAT 127).
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