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Reducing the number of bits required for data representation is called compression, which actually consists of two phases: the encoding phase (compressing) and the decoding phase (uncompressing)

In real life, files can be quite large Many very large files are the output of some program, and there is usually a big disparity between the most frequently and least frequently used characters For instance, many large data files have an inordinately large number of digits, blanks, and newlines but few q's and x's In many situations reducing the size of a file is desirable For instance, disk space is precious on virtually every machine, so decreasing the amount of space required for files increases the effective capacity of the disk When data are being transmitted across phone lines by a modem, the effective rate of transmission is increased if the amount of data transmitted can be reduced Reducing the number of bits required for data representation is called compression, which actually consists of two phases: the encoding phase (compression) and the decoding phase (uncompression) A simple strategy discussed in this chapter achieves 25 percent savings on some large files and as much as 50 or 60 percent savings on some large data files Extensions provide somewhat better compression The general strategy is to allow the code length to vary from character to character and to ensure that frequently occurring characters have short codes If all characters occur with the same or very similar frequency, you cannot expect any savings

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In a binary trie, a left branch represents 0 and a right branch represents 1 The path to a node indicates its representation

standardized if the sum of the squares of its coefficients is equal to 1) Among all standardized linear combinations of the explanatory variables that are orthogonal to the first principal component, the second principal component is the one showing the most variability Continuing in this way, p principal components can be constructed Sometimes, by looking at the sizes and signs of the coefficients in the linear combination, a meaningful interpretation can be given to a principal component Explanatory variables that are collinear with one another will typically occur together with large coefficients in a single principal component In principal components regression, the first several principal components are taken as a new set of explanatory variables and least-squares estimates are calculated See Gunst and Mason (1980, Section 101) and Myers (1990, Section 84) Maximum Likelihood Estimation.

The binary code presented in Figure 131 can be represented by the binary tree shown in Figure 132 In this data structure, called a binary trie (pronounced "try"), characters are stored only in leaf nodes; the representation of each character is found by starting at the root and recording the path,

000 00 1 010 01 1 100 101 110

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If one is willing to assume that the error population has a particular kind of distribution, maximum likelihood (ML) estimation can be applied The error distribution is usually assumed to be continuous, which means that it can be described in terms of a probability density function (pdf) The exact error distribution is almost always unknown to us, but suppose we are willing to assume that the distribution is contained in a known family of distributions with pdJ's f(e; 0') indexed by the parameter 0' (More generally, the family could be indexed by a vector of parameters) Then the pdf of the sample of observed response variables is the product f( YI - f3' X I; 0') .. f( Y - f3' X n; 0') Regarded as a function of n f3 and 0', this is the likelihood function.

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Fig. 12.3 The 60Co experiment: the electron is emitted preferentially opposite the direction of the spin of the 60Co nucleus,

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