Using R for Introductory Statistics : John Verzani

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Simulation 177This function will do the simulation and make the plot:simpi n = 1000; x = runif(n,−1,1);y =runif(n,−1,1);sum(x~2+y^2
Chapter 7Confidence intervalsIn this chapter we use probability models to make statistical inferences about the parentdistribution of a sample. A motivating example is the way in which a public-opinion pollis used to make inferences about the unknown opinions of a population.7.1 Confidence interval ideas■ Example 7.1: How old is the universe? The age .universe (UsingR) data set containsestimates for the age of the universe, dating back to some early estimates based on theage of the earth. As of 2003, the best estimate for the age of the universe is 13.7 billionyears old, as computed by the Wilkinson microwave anisotropy probe(http://map.gsfc.nasa.gov/). This is reported to have a margin of error of 1% with 95%confidence. That is, the age is estimated to be in the interval (13.56, 13.84) with highprobability. Figure 7.1 shows other such intervals given by various people over time.Most, but not all, of the modern estimates contain the value of 13.7 billion years. Thisdoes not mean any of the estimates were calculated incorrectly. There is no guarantee,only a high probability, that a confidence interval will always contain the unknownparameter.7.1.1 Finding confidence intervals using simulationTo explore the main concepts of a confidence interval, let’s consider the example of asimple survey. We’ll assume the following scenario. A population exists of 10,000people; each has a strong opinion for or against some proposition. We
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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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Page 140 and 141: Multivariate data 129make several p
Page 142 and 143: Multivariate data 131+ subset=(wt !
Page 144 and 145: Multivariate data 133When a factor
Page 146 and 147: Multivariate data 135Coercion is th
Page 148 and 149: Multivariate data 137[1,] 1 3 5 7[2
Page 150 and 151: Describing populations 1395.1.1 Dis
Page 152 and 153: Describing populations 141This is a
Page 154 and 155: Describing populations 1435.1.3 Sam
Page 156 and 157: Describing populations 1455.7 Toss
Page 158 and 159: Describing populations 147In R the
Page 160 and 161: Describing populations 149variance
Page 162 and 163: Describing populations 151> res = r
Page 164 and 165: Describing populations 153> hist(re
Page 166 and 167: Describing populations 155more woul
Page 168 and 169: Describing populations 157Figure 5.
Page 170 and 171: Describing populations 159use the n
Page 172 and 173: Chapter 6SimulationOne informal des
Page 174 and 175: Simulation 163Figure 6.2 Quantile-n
Page 176 and 177: Simulation 1656.4 Defining a functi
Page 178 and 179: Simulation 1676.4.3 The function bo
Page 180 and 181: Simulation 169> summary(res.25)Min.
Page 182 and 183: Simulation 1716.5.2 The geometric d
Page 184 and 185: Simulation 173> xbarstar = c()> for
Page 186 and 187: Simulation 1756.3 For what value of
Page 190 and 191: Confidence intervals 179Figure 7.1
Page 192 and 193: Confidence intervals 181which, when
Page 194 and 195: Confidence intervals 183In R this b
Page 196 and 197: Confidence intervals 185alternative
Page 198 and 199: Confidence intervals 1877.3 Confide
Page 200 and 201: Confidence intervals 189> zstar = q
Page 202 and 203: Confidence intervals 191correlates
Page 204 and 205: Confidence intervals 193In general,
Page 206 and 207: Confidence intervals 195contains th
Page 208 and 209: Confidence intervals 197distributed
Page 210 and 211: Confidence intervals 199mean of x m
Page 212 and 213: Confidence intervals 201in Table 7.
Page 214 and 215: Confidence intervals 203data is mor
Page 216 and 217: Confidence intervals 205−18 282sa
Page 218 and 219: Chapter 8Significance testsFinding
Page 220 and 221: Significance tests 209against the a
Page 222 and 223: Significance tests 2111. Identify H
Page 224 and 225: Significance tests 213simple random
Page 226 and 227: Significance tests 2158.5 On a numb
Page 228 and 229: Significance tests 217> mpg =c(11.4
Page 230 and 231: Significance tests 2198.16 We can p
Page 232 and 233: Significance tests 221Sign test for
Page 234 and 235: Significance tests 223parameters. A
Page 236 and 237: 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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Goodness of fit 2639.20 The rivers
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Linear regression 265response ~ pre
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Linear regression 26710.1.4 Using l
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Linear regression 269Extractor func
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Linear regression 271should be appr
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Linear regression 273The scale-loca
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Linear regression 275Figure 10.5 Fo
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Linear regression 277the simulation
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Linear regression 279Confidence int
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Linear regression 281Signif. codes:
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Linear regression 283Figure 10.7 Re
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Linear regression 285home in 1970.
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Linear regression 287Let Y be a res
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Linear regression 289Coefficients:(
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Linear regression 291+ tot=a+ for(i
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Linear regression 293Y i =β 0 +β
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Linear regression 295Call:lm(formul
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Linear regression 297Let y t be the
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Analysis of variance 299Figure 11.1
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Analysis of variance 301> SSE=(5-1)
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Analysis of variance 303163.2 173.3
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Analysis of variance 305can be perf
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Analysis of variance 307Repeat with
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Analysis of variance 309> dvalues i
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Analysis of variance 313> ewr.out=s
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Analysis of variance 31511.11 The T
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Analysis of variance 31911.24 The d
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Analysis of variance 321Signif. cod
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Analysis of variance 323factors, al
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Analysis of variance 325(Intercept)
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Chapter 12Two extensions of the lin
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Two extensions of the linear model
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Appendix AGetting, installing, and
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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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