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Estimated Log Optical Depth Quantiles of Standard Normal

Figure 8.14: Left: Absolute studentized residuals plotted against ln „ for the ¬t of the model (8.32) to the

Landsat data described in [8.1.4].

Right: A probability plot of the ordinary residuals ln „ ’ ln „ .

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Figure 8.15: As Figure 8.14, except these diagrams illustrate the ¬t that is obtained when the large

outlier is removed.

Left: Absolute studentized residuals.

Right: Probability plot of ordinary residuals.

The sensitivity of the model is estimated from the

8.4.11 Multicolinearity. We have, by now,

condition number κ(X ) of the design matrix X ,

learned to think of the factors in a multiple

which is de¬ned as the ratio between the largest

regression as columns in the design matrix.

and smallest singular values of X (see Appendix

Two or more factors are multicolinear when

B). A good introduction to the use of κ(X ) for

the corresponding columns in the design matrix

point in similar directions in Rn , that is, when detecting multicolinearity and strategies for coping

they are strongly correlated. Therefore, one with estimator sensitivity are contained in [78,

way to look for multicolinearity is simply to pp. 138“144] (see also [104]). Some statistical

study the correlation matrix of the non-constant packages, such as SPlus [36], are able to produce

factors. Large correlations indicate potential sensitivity estimates.