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where the divisor n - 5 = 22 is used rather than n - 1 = 26. The subtraction of 5 from n corresponds to the fact that we must estimate five parameters {3o, {3" {32' {3~, and {34 in order to form the residuals e/. Note that Le i2 is the same as SSR full. Justification of Formula (3.10). The reduced model cannot possibly fit the data as well as the full model because it has fewer parameters and hence is less flexible. So it is always true that SSR reuuceu is larger than SSR full and the difference SSRreuuced - SSR full is positive. But when the reduced model is true, we expect this difference to be smaller than when the reduced model is false. It can be shown that when the reduced model is true, then the expected value of SSRreduced - SSR full is 4u 2 (The multiplier 4 in 4u 2 is the same as the number of parameters set equal to 0 in the hypothesis {3, = {32 = {33 = {34 = 0.) So when {3, = {32 = {33 = {34 = 0, we expect F to be close to 1. Having a preference for simpler models, we will decide {3, = {32 = {33 = {34 = 0 unless there is strong evidence against it as shown by a value of F that is much larger than I. The p-Value. The strength of the evidence against the null hypothesis {3, = {32 = {33 = {34 = 0 is measured by the largeness of F, which in turn is measured by the smallness of the p-value. The p-value of the test is the

Our main algorithmic idea is to use a map to store each identifier and the line numbers on which it occurs In the map, the identifier is the key, and the list of line numbers is the value After the source file has been read and the map built, we can iterate over the collection, outputting identifiers and their corresponding line numbers

We use a map to store identifiers and their line numbers We store the line numbers for each identifier in a list

+ cos 8)[ (2 '17d cos 8p; dPe )(4'17E}dEv )1S( Eo - Ee - Ev ),

1 2 3 4

/ / Xref class interface: generate cross-reference // ;/ CONSTRUCTION: with an open istream i/

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probability, assuming the null hypothesis, that the random variable F is as large or larger than the observed value of F. To interpret the meaning of the p-value, we should imagine repeating the turnip green experiment, that is, picking leaves from another random sample of 27 turnip plants and measuring the vitamin B2 concentration, sunlight, soil moisture, and air temperature for each plant. Imagine repeating this experiment an infinite number of times. For each experiment, calculate the value of the test statistic F. If the null hypothesis is true, then the p-value is the proportion of these values of F which would be as large or larger than the value of F in the original experiment. Suppose the p-value of a test is very small, say 0.01. This says that the observed value of F is so large that it would be very improbable if the null hypothesis were true. Rather than believe that such an unlikely event has occurred, it is more sensible to conclude that the null hypothesis is false. To calculate the p-value we need to know the distribution of the random variable F when the null hypothesis is true.

(12.22)

5 / / * * * * * * * * * * * * * * * * x X p u B L IOpERATIONS******X**************x* C 6 / / void generateCrossReference( ) - - > Name says it all

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

**********f*****x*ERRORS**********f*X**X**f*****X*******x*

where d 3Pe d 3pv has been replaced by the expression in the square brackets. Many experiments focus attention on the energy spectrum of the emitted positron. From (12.22), we obtain

#include <ctypeh> #include ifstream> #include <list> #include <string> #include <map> #include <functional> using namespace std; class Xref i public: Xref ( istream

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