Using R for Introductory Statistics : John Verzani

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Analysis of variance 313> ewr.out=subset(ewr, subset=inorout=="out”,select=3:10)> out=stack(ewr.out)> names(out)=c("time","airline”)> levels(out$airline)[1] “AA" “CO" “DL" “HP" “NW" “TW" “UA" “US"In modeling, the reference level comes from the first level reported by the levels()function. This is AA, or American Airlines.Figure 11.5 Boxplots and plots ofconfidence intervals given by theTukey procedure for time it takes totakeoff at Newark Liberty airportby airlineNow plot (the boxplots in Figure 11.5) and fit the linear model as follows:> plot(time ~ airline, data=out)> res=lm(time ~ airline, data=out)> summary(res)Call:1m(formula=time ~ airline, data=out)…Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 27.0565 0.7204 37.56 < 2e−16 ***airlineCO 3.8348 1.0188 3.76 0.00023 ***airlineDL −2.0522 1.0188 −2.01 0.04550 *airlineHP 1.5261 1.0188 1.50 0.13595airlineNW −4.0609 1.0188 −3.99 9.8e−05 ***airlineTW −1.6522 1.0188 −1.62 0.10667airlineUA -0.0391 1.0188 -0 04 0.96941airlineUS -3.8304 1.0188 -3 76 0.00023 ***--
Using R for introductory statistics 314Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’ 1Residual standard error: 3.45 on 176 degrees of freedomMultiple R-Squared: 0.355, Adjusted R-squared: 0.329F-statistic: 13.8 on 7 and 176 DF, p-value: 3.27e-14The boxplots show many differences. Are they statistically significant? We assume fornow that the data is actually a collection of independent samples (rather than monthlyaverages of varying sizes) and proceed using the TukeyHSD() function.> TukeyHSD(res)Error in TukeyHSD(res) : no applicable method for“TukeyHSD"Oops, the TukeyHSD() function wants aov() to fit the linear model, notlm(). The commands are the same.> res.aov=aov(time ~ airline, data=out)> TukeyHSD(res.aov)Tukey multiple comparisons of means95% family-wise confidence levelFit: aov(formula=time ~ airline, data=out)$airlinediff lwr uprCO-AA 3.83478 0.7093 6.96025DL-AA −2.05217 −5.1776 1.07330…US-TW −2.17826 −5.3037 0.94721US-UA −3.79130 −6.9168 −0.66583> plot(TukeyHSD(res.aov), las=2)The output of TukeyHSD() is best viewed with the plot of the confidence intervals(Figure 11.5). This is created by calling plot() on the output. The argument las=2 turnsthe tick-mark labels perpendicular to the axes.Recall the duality between confidence intervals and tests of hypothesis discussed inChapter 8. For a given confidence level and sample, if the confidence interval excludes apopulation parameter, then the two-sided significance test of the same parameter will berejected. Applying this to the Newark airport example, we see several statisticallysignificant differences at the α=.05 level, the first few being CO-AA and NW-AA (justvisible on the graph shown).11.2.3 Problems11.10 The data set MLB At tend (UsingR) contains attendance data for major leaguebaseball between the years 1969 and 2000. Use 1m () to perform a t-test on attendancefor the two levels of league. Is the difference in mean attendance significant? Compareyour results to those provided by t. test ().
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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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Goodness of fit 247This is the squa
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Goodness of fit 249We now have all
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Goodness of fit 251whether any diff
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Goodness of fit 253Table 9.10 Accid
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Goodness of fit 255theoretical dens
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Goodness of fit 257D = 0.0745, p-va
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Goodness of fit 259A consequence is
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Goodness of fit 261( 78.69) ( 55.65
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Page 278 and 279: Linear regression 26710.1.4 Using l
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Page 288 and 289: Linear regression 277the simulation
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Page 298 and 299: Linear regression 287Let Y be a res
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Page 304 and 305: Linear regression 293Y i =β 0 +β
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Page 308 and 309: Linear regression 297Let y t be the
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 320 and 321: Analysis of variance 309> dvalues i
Page 326 and 327: Analysis of variance 31511.11 The T
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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
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Page 359 and 360: Appendix BGraphical user interfaces
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Page 365 and 366: Appendix CTeaching with RUsing R in
Page 367 and 368: Appendix DMore on graphics with RTh
Page 369 and 370: Appendix D 358A device is set up wi
Page 371 and 372: Appendix D 360Adding a box around t
Page 373 and 374: 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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