By Alan Miller

Initially released in 1990, Subset choice in Regression crammed a spot within the literature. Its serious and renowned luck has persevered for greater than a decade, and the second one version offers to proceed that culture. the writer has completely up to date each one bankruptcy, additional fabric that displays advancements in thought and techniques, and incorporated extra examples and up to date references. His remedy now incorporates a new bankruptcy on Bayesian tools, better emphasis on least-squares projections, and extra fabric on cross-validation. The presentation is apparent, concise, and because the magazine of the ASA stated concerning the first version, is going "straight to the heart of a posh problem."

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**Example text**

X ¯i , y¯ denote the sample means of the appropriate variables. 14) with each quantity correctly rounded to t decimal digits. Now let us suppose that the ei ’s are of a smaller order of magnitude than the (yi − y¯)’s, which will be the case if the model ﬁts the data closely. The order © 2002 by Chapman & Hall/CRC GAUSS-JORDAN V. ORTHOGONAL REDUCTION METHODS 21 of magnitude could be deﬁned as the average absolute value of the quantities, or as their root-mean square, or as some such measure of their spread.

This seems to be particularly fast for producing the initial QRfactorization from the input ﬁle containing the X and Y data. 1 Objectives and limitations of this chapter In this chapter we look at the problem of ﬁnding one or more subsets of variables whose models ﬁt a set of data fairly well. Though we will only be looking at models that ﬁt well in the least-squares sense, similar ideas can be applied with other measures of goodness-of-ﬁt. g. Goodman (1971), Brown (1976), and Benedetti and Brown (1978), in which the measure of goodness-of-ﬁt is either a log-likelihood or a chi-squared quantity.

In the following comparisons, both the Hammarling and Gentleman algorithms have been used, the ﬁrst with the Hamiltonian cycle and the second with the binary sequence. For the comparisons of accuracy, ﬁve data sets were used. 2. The WAMPLER data set is an artiﬁcial set that was deliberately constructed to be very ill-conditioned; the other data sets are all real and were chosen to give a range of numbers of variables and to give a range of ill-conditioning such as is often experienced in real problems.