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17 shows that after omitting this fth outlier, we obtain a healthy plot of the standardized residuals versus tted values No clear patterns are evident in this plot, which would indicate violation of the regression assumptions of constant variance or independence Also, the normal probability plot in Figure 318 supports the normality assumption Therefore, apart from the multicollinearity, which we still need to address, we have reason to be quite happy with our model for estimating nutritional rating The regression results for this model are provided in Table 323 2 Some of these results, such as the reported value of 100% for R 2 and Radj , are quite extraordinary But a closer inspection of the results shows that these reportedly perfect 100% results are probably just due to rounding Note from Table 3.

Since pA + pB + pC + pD = 1, the product pD pA pB pC is maximized when the probabilities are equal (ie, the maximum value of the probability of a sequence of four distinct symbols is 1/256) On the other hand, if we consider a sequence A, B, A, B, the probability of this sequence is maximized if pA = pB = 1 , pC = pD = 0, and the maximum 2 1 probability for A, B, A, B is 16 A sequence of the form A, A, A, A could have a probability of 1 All these examples illustrate a basic point sequences with a large number of distinct symbols (or phrases) cannot have a large probability Ziv s inequality (Lemma 135.

5) is the extension of this idea to the Markov case, where the distinct symbols are the phrases of the distinct parsing of the source sequence Since the description length of a sequence after the parsing grows as c log c, the sequences that have very few distinct phrases can be compressed ef ciently and correspond to strings that could have a high probability On the other hand, strings that have a large number of distinct phrases do not compress as well; but the probability of these sequences could not be too large by Ziv s inequality Thus, Ziv s inequality enables us to connect the logarithm of the probability of the sequence with the number of phrases in its parsing, and this is nally used to show that the tree-structured Lempel Ziv algorithm is asymptotically optimal.

We rst prove a few lemmas that we need for the proof of the theorem The rst is a bound on the number of phrases possible in a distinct parsing of a binary sequence of length n..

Internally the SL has two hardware serial ports that are recognized by OpenWrt, but they operate at 3.3V, so you ll need a voltage converter if you plan on using them with Roomba or any other 5V-based system. The SL can be taken apart easily by removing the four rubber feet on the bottom of the unit to reveal four Phillips screws. Of course, like installing OpenWrt, opening the box voids the warranty.

estimates, the ratio of each parameter estimate to its standard error (a t statistic), and a p value based on the t statistic for testing the null hypothesis that the corresponding parameter is zero in the population (given that the other predictors are in the model) Some programs output a chi-square statistic in lieu of a t statistic; the accompanying p value assesses the improvement in t resulting from adding the predictor to a reduced model containing all the other predictors Researchers frequently provide tables of some, or all, of these summary statistics in the accounts of their analyses (see, eg, Ilardi, Craighead, & Evans, 1997, Tables 3 and 4) When you do so, however, do not ignore the sign and magnitude of the slope estimate by focusing on the associated p values.