Using R for Introductory Statistics : John Verzani

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Linear regression 297Let y t be the left-hand side. This may be written asbecause r can be interpreted as an unconstrained growth rate and K as a carrying capacity.Fit the model to the bay check (UsingR) data set and find values for r and K. To find y tyou can do the following:> attach(baycheck)> n = length(year)> yt = log(Nt[−1]/Nt[−n])> nt = Nt[−n]Recall that a negative index means all but that index.
Chapter 11Analysis of varianceAnalysis of variance, ANOVA, is a method of comparing means based on variationsfrom the mean. We begin by doing ANOVA the traditional way, but we will see that it isa special form of the linear model discussed in the previous chapter. As such, it can beapproached in a unified way, with much of the previous work being applicable.11.1 One-way ANOVAA one-way analysis of variance is a generalization of the t-test for two independentsamples, allowing us to compare means for several independent samples. Suppose wehave k populations of interest. From each we take a random sample. These samples areindependent if the knowledge of one sample does not effect the distribution of another.Notationally, for the ith sample, letdesignate the sample values.The one-way analysis of variance applies to normally distributed populations. Supposethe mean of the ith population is µ i and its standard deviation is σ i . We use a σ if these areall equivalent. A statistical model for the data with common standard deviation isX ij =µ i +ε ij ,where the error terms, ε ij , are independent with Normal(0, σ) distribution.■ Example 11.1: Number of calories consumed by month Consider 15 subjects splitat random into three groups. Each group is assigned a month. For each group we recordthe number of calories consumed on a randomly chosen day. Figure 11.1 shows the data.We assume that the amounts consumed are normally distributed with common variancebut perhaps different means. From the figure, we see that there appears to be moreclustering around the means for each month than around the grand mean or mean for allthe data. This would indicate that the means may be different. Perhaps more calories areconsumed in the winter?The goal of one-way analysis of variance is to decide whether the difference in thesample means is indicative of a difference in the population means of each sample or isattributable to sampling variation.
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Using R for Introductory Statistics
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This edition published in the Taylo
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PrefaceWhat is R?R is a computer la
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Web accompanimentsThe home page for
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Chapter 1Data1.1 What is data?When
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Data 3Journal of Economics that leg
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Data 5When R starts, it searches fo
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Data 71.2.3 AssignmentIt is often c
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Data 9Giving data vectors named ent
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Data 11> x = c(2,3,5,7,11)> xbar =
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Data 13Simple sequences A sequence
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Data 153. Find the differences of t
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Data 17> ebay[−1] # all but the f
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Data 19empty vector if i=0x[c (2, 3
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Data 21Many R functions have an arg
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Data 231.4 Reading in other sources
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Data 25A convenient method, which r
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Data 27Using source () to read in R
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Data 291.4.4 Problems1.20 The built
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Chapter 2Univariate dataIn statisti
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Univariate data 33The table() funct
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Univariate data 35There are names o
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Univariate data 37Why are pie chart
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Univariate data 392.5 Web developer
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Univariate data 4121:Read 20 items>
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Univariate data 43compare different
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Univariate data 45Figure 2.8 The me
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Univariate data 47numbers first and
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Univariate data 49> var(test.scores
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Univariate data 51As with the quant
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Univariate data 532.13 Can you copy
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Univariate data 55Comment on any pa
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Univariate data 57> hist(waiting) #
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Univariate data 59Figure 2.13 Frequ
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Univariate data 61Figure 2.15 Galax
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Univariate data 63Figure 2.17 Amoun
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Univariate data 652.3.4 Problems2.3
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Chapter 3Bivariate dataThis chapter
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Bivariate data 69> colnames(x) = c(
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Bivariate data 71unbuckled 56 8 64b
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Bivariate data 73Figure 3.1 Segment
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Bivariate data 75interested in comp
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Bivariate data 77> stripchart(list(
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Bivariate data 79Figure 3.5 Six qqn
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Bivariate data 81Figure 3.6 Assesse
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Bivariate data 83> plot(height, wei
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Bivariate data 85correlation only i
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Bivariate data 873.17 The data set
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Bivariate data 89Figure 3.10 Predic
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Bivariate data 91That is, the y-val
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Bivariate data 93■ Example 3.6: K
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Bivariate data 95[1] 13 50> florida
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Bivariate data 97Just like the mean
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Bivariate data 99Figure 3.16 Temper
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Bivariate data 101produce a scatter
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Multivariate data 10310 Y N Y N Nan
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Multivariate data 105Figure 4.1 Tax
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Multivariate data 107> plot(gestati
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Multivariate data 109Make the above
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Multivariate data 111One difference
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Multivariate data 113Accessing a da
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Multivariate data 115Figure 4.4 Sca
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Multivariate data 117To illustrate,
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Multivariate data 119mtcars[[’mpg
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Multivariate data 121We can apply f
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Multivariate data 123appropriate. T
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Multivariate data 125pickup 70 71 5
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Multivariate data 1272 42 stomach
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Multivariate data 129make several p
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Multivariate data 131+ subset=(wt !
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Multivariate data 133When a factor
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Multivariate data 135Coercion is th
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Multivariate data 137[1,] 1 3 5 7[2
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Describing populations 1395.1.1 Dis
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Describing populations 141This is a
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Describing populations 1435.1.3 Sam
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Describing populations 1455.7 Toss
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Describing populations 147In R the
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Describing populations 149variance
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Describing populations 151> res = r
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Describing populations 153> hist(re
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Describing populations 155more woul
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Describing populations 157Figure 5.
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Describing populations 159use the n
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Chapter 6SimulationOne informal des
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Simulation 163Figure 6.2 Quantile-n
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Simulation 1656.4 Defining a functi
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Simulation 1676.4.3 The function bo
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Simulation 169> summary(res.25)Min.
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Simulation 1716.5.2 The geometric d
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Simulation 173> xbarstar = c()> for
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Simulation 1756.3 For what value of
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Simulation 177This function will do
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Confidence intervals 179Figure 7.1
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Confidence intervals 181which, when
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Confidence intervals 183In R this b
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Confidence intervals 185alternative
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Confidence intervals 1877.3 Confide
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Confidence intervals 189> zstar = q
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Confidence intervals 191correlates
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Confidence intervals 193In general,
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Confidence intervals 195contains th
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Confidence intervals 197distributed
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Confidence intervals 199mean of x m
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Confidence intervals 201in Table 7.
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Confidence intervals 203data is mor
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Confidence intervals 205−18 282sa
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Chapter 8Significance testsFinding
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Significance tests 209against the a
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Significance tests 2111. Identify H
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Significance tests 213simple random
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Significance tests 2158.5 On a numb
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Significance tests 217> mpg =c(11.4
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Significance tests 2198.16 We can p
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Significance tests 221Sign test for
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Significance tests 223parameters. A
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Significance tests 225A natural tes
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Significance tests 227audience at t
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Significance tests 229If the two va
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Significance tests 231Figure 8.5 De
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Significance tests 233H 0 :µ x =µ
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Significance tests 235Figure 8.6 Tw
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Significance tests 237group n sechi
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Chapter 9Goodness of fitIn this cha
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Goodness of fit 241This gives the t
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Goodness of fit 243The function ret
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Goodness of fit 2459.3 A package of
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Page 262 and 263: Goodness of fit 251whether any diff
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Page 270 and 271: Goodness of fit 259A consequence is
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Page 274 and 275: Goodness of fit 2639.20 The rivers
Page 276 and 277: Linear regression 265response ~ pre
Page 278 and 279: Linear regression 26710.1.4 Using l
Page 280 and 281: Linear regression 269Extractor func
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Page 286 and 287: Linear regression 275Figure 10.5 Fo
Page 288 and 289: Linear regression 277the simulation
Page 290 and 291: Linear regression 279Confidence int
Page 292 and 293: Linear regression 281Signif. codes:
Page 294 and 295: Linear regression 283Figure 10.7 Re
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Page 298 and 299: Linear regression 287Let Y be a res
Page 300 and 301: Linear regression 289Coefficients:(
Page 302 and 303: Linear regression 291+ tot=a+ for(i
Page 304 and 305: Linear regression 293Y i =β 0 +β
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Page 310 and 311: Analysis of variance 299Figure 11.1
Page 312 and 313: Analysis of variance 301> SSE=(5-1)
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Page 318 and 319: Analysis of variance 307Repeat with
Page 320 and 321: Analysis of variance 309> dvalues i
Page 324 and 325: Analysis of variance 313> ewr.out=s
Page 326 and 327: Analysis of variance 31511.11 The T
Page 330 and 331: Analysis of variance 31911.24 The d
Page 332 and 333: Analysis of variance 321Signif. cod
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Page 338 and 339: Chapter 12Two extensions of the lin
Page 340 and 341: Two extensions of the linear model
Page 354 and 355: Appendix AGetting, installing, and
Page 356 and 357: Appendix A 345A.1.4 Installing from
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Appendix BGraphical user interfaces
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Appendix B 350Figure B.2 Multi-docu
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Appendix B 352If you forget to inst
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Appendix CTeaching with RUsing R in
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Appendix DMore on graphics with RTh
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Appendix D 358A device is set up wi
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Appendix D 360Adding a box around t
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Appendix D 362> x = seq(−2, 2, le
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Appendix D 364D.2 Creating new grap
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Appendix D 366Figure D.3 Per-capita
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Appendix EProgramming in ROne of R
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Appendix E 371arg1, arg2, arg3When
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Appendix E 373freedman-diaconis, sc
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Appendix E 375return(summary(x))sum
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Appendix E 377In this example varna
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Appendix E 379editor and ESS extend
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Appendix E 381[1] 26> size(data.fra
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Appendix E 383"[.String" = function
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Appendix E 385})We need to use the
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Appendix E 387For our String class
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Appendix E 389Now, instances of the
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Appendix E 391old.x=xx=x—(x^2—s
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Index 393heat.colors(), 378rainbow(
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Index 395pch=, 86, 378type=, 60, 86
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Index 397command line, 411>, 5confi
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Index 399extra sum of squares, 307f
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Index 401robust statistic, 193sampl
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Using R for Introductory Statistics : John Verzani

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