<\body> <\table-of-contents|toc> Lecture 1 > > > > > > > > > > > > > > > > > > > > > > Let us start R from the command line. First make a directory, and then run R inside it: or Then, in the shell do the following: <\output> Shell session inside TeXmacs <\input|shell] > cd class <\input|shell] > ls -la <\output> total 24 drwxr-sr-x \ \ \ 2 dirk \ \ \ \ dirk \ \ \ \ \ \ \ \ 4096 Jan 25 16:15 . drwxr-sr-x \ \ 79 dirk \ \ \ \ dirk \ \ \ \ \ \ \ 20480 Jan 25 16:15 .. \; <\input|shell] > R > Now we start R (here I am cheating, and starting R inside texmacs) <\output> library(TeXmacs,lib.loc="/usr/share/texmacs/TeXmacs/plugins/r/r/") \; \; R : Copyright 2003, The R Foundation for Statistical Computing Version 1.8.1 \ (2003-11-21), ISBN 3-900051-00-3 \; R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. \; R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R in publications. \; Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for a HTML browser interface to help. Type 'q()' to quit R. \; \; \; \\ <\input| >> a=5 <\input| >> q() <\input|>> y \; > To quit R use the function . After we quit, look at the directory again: <\input|shell] > ls -la <\output> total 32 drwxr-sr-x \ \ \ 2 dirk \ \ \ \ dirk \ \ \ \ \ \ \ \ 4096 Jan 25 16:17 . drwxr-sr-x \ \ 79 dirk \ \ \ \ dirk \ \ \ \ \ \ \ 20480 Jan 25 16:15 .. -rw-r--r-- \ \ \ 1 dirk \ \ \ \ dirk \ \ \ \ \ \ \ \ \ \ 56 Jan 25 16:17 .RData -rw------- \ \ \ 1 dirk \ \ \ \ dirk \ \ \ \ \ \ \ \ \ \ \ 8 Jan 25 16:17 .Rhistory \; <\input|shell] > \; > When you quit R asks whether to save everything. If you say yes, then all the data is saved, and loaded next time you start R from the same directory. The data is stored in the file .RData <\output> library(TeXmacs,lib.loc="/usr/share/texmacs/TeXmacs/plugins/r/r/") \; \; R : Copyright 2003, The R Foundation for Statistical Computing Version 1.8.1 \ (2003-11-21), ISBN 3-900051-00-3 \; R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. \; R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R in publications. \; Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for a HTML browser interface to help. Type 'q()' to quit R. \; \; \; \; \\ <\input| >> a <\output> [1] 5 <\input| >> \; > As you see, after restarting, R loaded the data, and thus the variable 'a' was restored. TeXmacs provides a nice interface for working with R. Do the same as before, but now start texmacs instead of R <\input|shell] > cd ~/class <\input|shell] > texmacs > TeXmacs is very similar to Emacs, so if you know Emacs keystrokes, they usually work in TeXmacs. \; To get help in TeXmacs, click on the Help menu :T\>\<^\\~\|dlTfT:\\44VTTJ\\D:L~tdlTV\|Įl\|^\\\|dfdDFt̜\<,L\|r\|lNL\\j\\\<2$Ҹ,~\|djLFD\<6\\\|jTT\>D\\JLdƤ\<2TDb\\ttfl,.,tv*$4.LT:\d\|ztLLt,PT424LF\\\|ܾDnl\|vl\\R\\\<2L\<:d,\0\0\0\0\0\0lHp*LpÆJHqŊ/jqǎ ? Irɒ(OLr˖0_ʌIs͚8osϞ@\n Jt7f$])ӧNBjժXju׮` Kvlq]-۷neKMٻfw߾\nLx)&^Xǃ#Cf˖3clόCq̹Ӧ 36!Λ \0dsϮu^#23ծ85yXkSFR7\|3÷ۭgiT2޻oiDVuٷXgѥ݀(B\0g)\|V\0p@I\t/@x\u@4fB(GH߼'KJ\n88čX0I}Qz@'đƌ\<$x'\0dah)@x53ei7\0:L,ML*%Hp= qYUFOK"AЕd\\RɨAzΉ_qS#G^lMO:qR,H~й(:!07`3',EsB"=&ReXxR\n&'vQfadFzo=}Mɖf\n \>ߧbUN('hitrV!ҲĴ\0\>(禔XV+ؐ;\>MT9ΥY[HH;jJze`GQ5syw2&IdӜ15%AWґu$5V":cl+Xi @'j]֑&9R64x2f[dQVNlp"YeSh)\\WX `'µWRV*=\0PqëbCS2\n\t \> ڡ4h%6I&G;RE\nn9 fc%!\'m-pA bǽwτ'WbSp7WrA\>\\:\|7_&w 3;K?5/[/_edH7Osw\t\08Xgr\nKJ1Rр (xH8 8N"ȁO1,X؂#!%82x\>؃1HAovHJL؄NPR8TXVhv?C\\^؅`8dXfxhjl؆npXIMtXvxxz\|؇~x(OXhvXK؈xR8Hh؉N8IPHHLG(艎xoƉV;8x'Șʘ̸،؈Xxؘڸ؍8(C蘎hH8Xˆ~8SY8 )aEY9\tN !YNXoVĠ 29\O4YJxbgyo\|c Jx4JYx fZ-,Y@ рD\t\0eg9z\07I~\0\n}\tr\tF{\trؕXRhk;=q~ɇn}i~ɘĖhIu7;k)똙gKCE4E!&Lꁇat1ҚYdn?I \0L%"ÓG%;M\0@\>a @P\0 \0!ꙓ~I%~\0 N Пɜ7\<비ҹ=iЉYj)\nY=DtȡM",@ҙE\t \|ТB}]e\ni*t 9A5iv21%Bx:rXr PTƙ!Uyؙuݠ ` @SuJzxqUʢ}閽3 d_*1*=]~ 嘠)\nf7&IG)#ts&Uj\0jp%jjz\\ M$MdzJ/\n#JPX7]bc򅨬H1y$Z؛Y+\0ɠJZ=ɜ&ńcJdڢJH m\0\nX Np ʠٞ۞ %*%ș:oi [\0Gٰb޺;zG٘મ]p?@#3;2+z"г,fP'z2@%F LL O8"3\>fKvHV4c (C3Q@\\R3a I dgJp.(Y\tr઩ߚIiFױ`::\t)D@PG`PPo\0q쩞\nQ*yH+뱵YE`E+$ۜ\>ٲ:$ҫa*;Kz15¡{jt\0,\>A+\\"G;IF?K2`)F-rBi23BY=rPhe; !#`jS#A5JHFnqk\\`(\nJzB)b% \0* 񉝘V\npp @ѐMȗĮhSJK0\tb\t j{ \0cL\tu*z"t)j۽j "P%*zV0ܸu52p&qE]J1@UI¡9rM#˕3 kK-~ թ- ;L\0\t*Qr8Kz JF &N`\tr Ew"j{ܒ"\<"~Pn\<`cB !t\\ϒ\tf@ ,W=۲s\\Wѻ;Р;\|\|}! Ȃ\\\0RҰ*p\|霰5*';v' \>5dbuVUB&dS,A\|y\0Qhuۜd,JϺ)`\\9D@\nE`P@9PYS0'\t[]̍ lml*e\\c"kIڣ}bz;7K]:Ȅ ,҈8\<3ۏlf;&q-L;t^d)5Ko;&gVR[NbbZh}\>K(ߒܻ Mfim)Ffa\0\0 \tK0 =0052wUo\| Miλۻ$^Mb 쪕q]m/u*J-sCх\\#-ʾ.ҾҺz'\|T h\> v_\>vIec!M\a--'y}:-ೝF t@1\0ߊO7i߂Z^Bٛ f -Mjڵk7ԡ:oIȄIiݸOj.f;CU'ν6~FnV.kvviJ\taY1LLөط(\|\>+G0NpP\t00&0 @w~VƒkZL򖭘\0ǾcLݦyp{!Q\t@ sPePK% +.-hz[L7Bt Gv -dJTkwv\|WQ\n? 3־;1?ןj*?70\tF\0[@ #Pp uU\<lj\n N z6.Ml`_MF:Xr64[$Rޟ'%_.fx0\0a+\t,P@\>QD^\<0#Æ\t1")5VDRJ-]li@\0l\t\0̂51Y!ϟ\0X\0\0\>SU,`I\01br82D+q`Z 7Kt&\0\0\?(2ڰa %Iwj0\0#9\>@+4`8\|#C\0b:FAtک'@YċT/'/Tʊ\0Z\n:ӆ$ϊ!Y)D\n"#ڀX7\|cai˼j\|ȁDS,&5-*͎@DsM9N;р*VO0j\n0B$EB7(-,O!B24\nR[=#zT\\{!Coly7x7*\tT$f6uvZmeBEl7\\q- VDW%,5]tw_( tTB(m\_F;k;͈~6ζ]xn~n%ޭ#!Fa%{S^\\|z':Y?c}߇?~秿~'9۝\0PxnG\tX@I -\tNx`'A \n5B\nzЅ3bPAt\n\> \nGYl(5щOb8E*B1_E.vы_c8F2ьg"F61\>Cc8G-B̂hG\<шJDҐucH񐋋V9IJ!$d&5&ѓe(E9JRҔ@;NJV!T+e9K)n{M%syK^җLbA:`Ӑ"1Ivzu#%49MjVӚXf'ʹETe˗ BIRN\|!fg\ِl&c92`vdh&2џC%J3iŢ]\0{F0rlz:Qz=#EI\t%ӥTv6\0:)NqA\0jP9TK$,\tA31=q\0\08\0lYH2\0IJEUQ(9{R+Ԯ(R"ȕ+0`=,Npa ,d։Vֲr\nЋ9)\00pār28Bڜ]vs;keͪ9\\ߠYWy6y^XjSЅ0Ac\<m_{3,vl\0&ͲpɦgQs1[Y,TodkLQY0R3tRIIJR )G\>ϴkl)#ȫJ1ln!9@\n\0.C)62pBx \n.VBd'69&dIꥤ0\n\0S\n  9G;sl [VP+P5\0AVUV+.y\\\t\<w9ρ/[9ENr7\\W{Jn\<'O켁Ws\08M!P\0uy T \0\\"\tI\02v`f[35Hܔnq3TUkZ\0 pU\0jO2`vlV\0wVZ ͗ڛ=T=\t,\0NJ3RzAiщֶ0\<O? Ulv6&bPWs)\0a6` HʣdS1m\n$ݡ W-uiSW~zB̍p/1NAdDo)\08X&n-;;-ww~@ {6IO\t\0fk~\\W{aj;N\05\0vw`?4.qK4^@+ \t7e5dj\t[s;VRl0•OUy8bU;lUD-ݵBU1\>"q'ɘs0m8ȦRS\n\0UP+2{0=[8rP\0GG=/',+"\>+ 74A7,(9nI :w %2XAA\|Bh?3 ӒT3Co*\C*\08,AP(wK( D4 0H4k63̂1Hd})l4ɞ\< 3\t{ـ*0I P+.!GR5k;DxM ;7+\0\0\\%h&X\tTƸ\<"D )á˙S B(m+CKTf %jILSZI_ڒ8 z808.q B̟dؼR#(U\0(ᬁ؁(ȃ@p\t:~\n\|s@ǟɤ9ƸMrS%ÛѸLlMkL yR.Ґ9.M\0P93+,(SMrwT\n!p8((Ht5촛82PPږ-z)ӑ4L\tДJ*`3D,=L 3 5NHD\ttY؁j\ҍk-[;C*;\X2;2\>w%K"7&Hy񵫃g@Upn`h+(7erH19Uhgpq 4q']9{:(z2#^H3(;'ij5#7C#flR~\0pq5H.`oUv`MѢoWR_q (DukQ\|{@pPHvp+\0kkFa'-Znr1NgrIeGwp#l 49SvSY_bu ,U,:I+02[7J7.{aN803\\rhv^vO_-WtSwSx 3t+ 2S8`d#W*\|Gc7ggoIxM'xc9f9f_o68xGE\0Hv74 2 `ٺaWw\t]t[9Htf*Lq&nY/l\>y6FOxdaSz"LWW\|gVjh@:,U1T\|#vx\|2w@owv?S+\vs\~=y\0_) :xZJ8!ZF2Ær!8%x"-"1(#)al#=Sm'7$EGH_K:$Qfd@)\0\\%ay&iQ{R&q6eR;3\0+NMp\nH z(dF\t(Bzi)^])wIzI*Xx4FH*+kQ\n+Hmz,WR\00qhV2\0\0z\0A;Vy奨\n.{:)uɑ)yۯ)V`A3lvӯJ\|({qU7rxFqh9F N)w)둼99 A7 832M;.odD;9-џ\\\nmr\0#5eVFo\<ۦX~JG}ftO7Ӕ'[a\<;x0HХ&m=S˺~9_}:ºGuXy*'S+\|zzZAJ0lL*7cǭk38VrN;()U*Y/Vǻ*^ m~r+f%zg\0]w\0¥}4\0SC\|D U:VXH:OG8p$[LbPx T5}VVxV5.xVP\nY\02p_ҒݮfFh1AR!L_fĽ[b̀)\0U੎I祀C{ę#2RFH\0BIֆd\|ȩpU!hGTNRHTE^&{%0u:PsxPlF\0jwHib\tG\nVhľ5ptm&u5\|g[:I(bf&3O4L#VEE ay"0CVBt*"l%y΍rT0ff$\|V ]ij*~$BxKJj닩µ 07Α@(T 'P\n)MHUq\nr\|q! UA\tȗR}+\\RչDkz2ɺ^t Ը\>+b\>&&XAq,a*Y6u/ +MW~TL$,fSUd/"ioؖЕ~%iliwU%lZ1\0b_i;'}˅RiDRʏf\n].\>+\tӭ.zȗ R8s/~AZ!Ҟ7%aZ;\nS@xzi֤SU`\\Am}n~)M,mcCbs\<T\|'$ Z 8m?cvz\o /N\<\0yf4W]+.Twr˘\>X4~HIJ$y 8\I܈"**"xȇ +".blȌT Ddʘ\\JTKfXF3(:6܁[#3~Lb]p9vs(:ƅ$ʝ6v#$8cl;;\<#}c:\>\>B"=ڣC`AN;&B^`\0@ndd.H\|H"IHIJ$/bKGC\>LއZa!2ʽN2FLqdg\t\tB$R!=Fh \\LV[%U@_ 8re}E^%Y.ZvqT\nߜB_\\\\W Gdy xMLq \\p\t6P\\ͥc-ݳ\|`حKLZl\0~cЏc&M"HpY1[nDLNbvIhA$j';!Z\nRMm!Y)و&~ $Aܚqvgzm%t&4 H4`AS@RoR_4Fvqz'~M@%$فօD,a ^urghb槄bI˳^\|\*\t'异)]Yv*·=Am_gxbUj{hc\|X&&+"a :TdNݑ^.MCW\|PȖ[JlZlhN YĪ8HXuJ0ݸ)I@ı\t&lM\>'Y(tvfQ.ՙ^Lbg7*,\n#"q_IQ*nxɧ@h},ªSqDB.XS2 ΁hb9"HVm82Ưy: N }?ΆZF G,h޴zafaɔKbsn\|܌a[x_b_bYS5bN])RD6=^&] 81eiUlЛ\tiʮ vc\0c)DdFE1i.iV#Bf`To(f£Up/mTTe/q\|ro2%RN22.&S*ڥNd{լ^*p\tDz\\zq1Q0phKQ\tfFčƱeM턚 u 8Վ_Z\t8TP^F]b0²0.1AQ$HPM \0_пx1˨f anoO0ɀQGřJ\0z6.3 mLaF")p!2g'gF2-ld#^I+ 0?"h!)d'}r*2"`F(:(ߢIR4\|Kh!`\n9gmn2/Cd 6蒱@O^2@Ts1clNExi%o\ `:::\<`zU꺯){Z;_nUzKҲkO;FR;KopԼ\>m?;do{\tz_^p+;[-{c;X\nf\|S,8ĕӂŁ5}s+(!ys1Ha^Yq\<ɚ͔ \>qΫc]]G皊Ԋ\<{\|[("m*^IQ\t8 q)f'z6Ϊwγk{3+d͔%G2-M zD_\n3\0\0ZLy8+εE24_lK-}ֻ++}HT?_ZKV8}~D@ a\>#3L4^aa~p{q!\>f=UEf\|Xa:skUm:{G?bek!\>{?;0ǿο+jV$@8%@ TXB !\>„1nrXGA9dI'QTeK/aƔ9fM7qԹgϕ}:T 3&UiSOF:jM+o4^fkW_2lYczYo•۵m]wxj_\R)qB/v\0\08 \0NJ s \0hg \ YKsz .G#cu1=:I.`Msf8[Ӕ1n`Z,\<ts&E-㳻s:ni); nRo}2dO\|$_QZ1D)oAV\\߾=qIosU9O]Ow2\>\\v[zquk?t{2_݃O\>ٗE@^z(W^^̧{w^hÿO_}opt9\|\\lXДotY  ܕbf]YD\tZ-вy\\$B17 Ĩ(Kl,uu.F)Dj[Xh,8obe/*f?@%80%04d\$CF\n}C\n362^fkrB#,Q\tE9N0RSDe.z!rX9QLwH)f@`HͶ(p;0ZNwXOT{S\<ȱT󣩕dPrLMH`,k^\tN\n LKEp4a*\>g-Qok1(NZ…n\tR~ձvRh&b㥱챝#kj~RN}rKTQ~^y;ٲKifoc[lg3"PrR韀Md䊯kRC8YvtDkt\|1qa#,&p'6TJ%( r(E˻mBNğ{Ekt'cէSz}k_7;}`\|ugw{y\<ֱ{Swɝߥ\>yI,"_ET'd\<1yOAzя7Qzկwa{Ϟq{\|7\|/w}Oշ}o~7џ~wϟ0\0p\0\t\0 \00p!0%p)-105p9=A0EpIMQ0UpY]a0epimq0upy}0pc- \0\0;>|gif>|*5/8|*5/8||||> The tutorials are very basic. Try opening one of them. To close the help that you open, click on File-\Close buffer, Or select another buffer from the 'Go' menu. \; To open a file, select 'File-\Load', or click on the file open icon. \<^\\Ġx\|~\|Tddd~lܜfTľtа,RFδTtd}x\\<:\44VT̮9:g~tdZ'hjdl\<6Lttn\|\|^\\dfd\|tDFtܺ\\R\\tfpLKnlNL\|Ҹ\<2$\|\\JLTvt,~\|LFD\\V\<2D\<6Y\|jTT\>DƤ\<2T,.,d^d\\R~lndLfdt$$,\0\0\0\0\0\0\0g8 5p†\n6Y‹6V1HT9C\n9f›8sɳϟ@\nMhH*%jԠjd@Mj*դQjʵ+"Ȅ v,bb3[v۷pʝ\\x~Z$_:X*o#^Ɛ'F2ʏ1Gy̚Seɟ9O^4љ;f1*s+ލ M\)e3N%m%`~)fM:8`pQ\0_liCpq'Kb8 y x&&89 'bkA90=3FVy搟Lj*'=bc\0\02\tٰyy@K^W-~V+alᬥ!'zd\0@jFݾ8ù\0b0ob}G'pΖ0#6\\bw[\0flWb 7Vjz%#a}XrB\<3z8\0pc33c3ʇ\n\0v@5:/7~idF5!2er]C6Ü;g\n\0cicGxvUl;pK7 ;vf_c-]J?ԃAi{G!:3Zk\0nt\\zɡ,ԓϚȽ' \00I*2ѦܯF3lpbWNi#Sa~/zNޞci,p[W4\0cYvAp*ǴciPPtݡ;t(?\t\|șRLXtcVv)aѶen9\0ظ,l!f;BQϡ:b\0 ]5nU0O7ܡLVٶs:Ɵű\n{bȄ1k5\tblˏST\06ǂFploPx4g0B( $U]\0:jN}.ܼQY;T bbK+d+6=fŬ10nLY8EΑnpg^19~[:۩;4d 'm\0=\}PyIjRi'f FTBUMesbssf_(h[*\|S5DЗc a\n%MofkY65nlR^&VfN[ 6\\^4vZ\t19$$XNuU$6b(6)\taؼq`F+n*,έ_g,:eX4FA){['^ܟbĜunj挟ў9̮t;Zj)s}5:tIR#ὂO0Սn3φwVQvjg4JQ'kGEՊٌiʍN,'W'tzt;R5vX\0j EFQ\0\0wӀGmƸF{Ҏ^rdTU}RU\01gҝsiU:eõu%1qOo iBuPц:Ɨd\ty6qEnro! "280C\<{q%q٩2$8˼BE9)lH\|KѴprWǛ\\On]cw{~ZcHH獷\>Wiw\Wl??\>sM\tcO}'~`^_}+W}܋o?o?'{ק~^q}7~ۇ\nȀ ؀w8Xx؁ "8$X&x(*".0284X6x8:\<؃\>@B8DXC8$HJL؄NPR8TXVxXZ\\؅^`QMQ 'ghj.XlpCrXvx9o@\\}lp} bH$d8]H(ee\0\n#vh~\\\0\n5(5xUP ؉w\0H2hoxtL(UePk\|؊ǨR7HK\0hRON\n n\05$h U8x\0Ʉ(HURȐS-98hx1bF\t\n\0P\0PI0(,&EQ8\\0\0P0\0 \0 \0GQH03'.9'ٌ1 8.H07XY9RL`\tZV/5鑚p7#&U b:\n:p\0p9Gk)\t"؍5Y Y؇U鍂Ӓ8h9(H\08y `Q \0T녛G5\0WI)FE W"oYM "a9$9iY\00yCA)Y :`)YXk1 \0ٟEiY؝ȒmI1ap9r\t  O gEyx_)zlp=e^)C9WҝEzu"`ir"),`ХA]Ao\0`jz\0)iFHop؀0k\|Z둝5Y ~\t\0ؙLj-92(FzA+ Ppڰh&.\nZHqE92IV*e0fڙ X)YúSS*aI8*a[ hy\0﹦loJUzYw)s8){hZk\0&F*j(\0@6X$0 ` \| ` W`NJ026ʖϚ:2cг^V;[\>O9ZD;es\0 SUT:@^˦\tR\\ cp˶kꗁVx9bĩEˉ z +^1KY @kP ,a \tʰ e`5+KZ(I6n\tHya@ Huj\0\n {$8˒yyXӛ-\n\\۵^ \0n\nKY7n۟k(2vK=3pZlS-I0SC39\t P\t 60 Y0& x\<1O5&yJ8[)\\\nZp6YOF \ni3Mɋ&iU:\0]b:[9b Y\0:ixڶd̾h9jEIոz{+ryzdžke\n,h;p0\n`!@zl%W'&ѫkʵ&y=SH*ikK+g̛E }xDW \0 EDc̟{ql뾌X Т$̶lEڿ[H˪15"\<̽l0 L`\0   C .:6:D']?D'= \n\+l_5swH ‘4"%4?^_Y Hos'њ?"72Oa1ͩωp$[q\\`?{?WS\>gNA}H'o}h\|\|8O \0{{\0{W~\0AF@ DP\>$D-^XM=~RȐ7DRJ-]F5męSN=}TP9ET7L2UԤRŚUV]~ZeFe͞EVZm*dL%ZW^}KW`… FVN ;W2dʕ-k1e2N/ZhxWu⎒UI2 4-[n޽\t?-dc@vK#  B0{UOݽÝy[G^=Ի4hO\0ṭ 1\0\0$8P\0 Kjl 50\0CH*\0dp7\0\\F*1wLl*=`񺪂ŎJR [\<P\t\0+Ļ˂@\A+_\0'w]ҕ]a1{tн2\0 ;`,ar1H\t%6h?pg+yBf-"U 2TPZӚEaYpӶ\\ X\0ţ\\a7/Jnj(kt +eWA)FP\t+\0ёpHn:p'A;e˱ʪ\0()g(\|k8Uiu\tr ױy姐cII**(FQ\<Ԡh:L- C3 ,m/i\n_3Ч%B\0@\\/?\0pDڈ*x]\0\t,!\\$I؄42a^\\B+JP3:0\0PǜI64\t`\nc$0RrUHl#.Q*0?CD(2A;fܥjPGQVgt&]"1!1g^B:uGb$HDq\thT.lM7HRp(;pLJ\0ݗpҡ20K=p:γ(ff#xjZ/l wbe43 &F\x-.sӝNO.aHӔ* 4j\\\\appЄسgBPniz5֭BpG@v}@\nSp"D%\0\|\09,la2[L5q] XIf]Ɂy_qG'.2ut[\0WB\0dHDA\0^ZlGST e0-x9`98`9oA,.{V`\n#0t0#\nX?\0WF`~WNmBꀗzwt=g("1Q' mHjJ6P aqaBG֛\\5n6It*glh#Ѭ\<\0ԅ=Pbϻ\0(@ғ \\\0h;D 6uK!GB_w8nF;/u^ #nW@Z_{C,1\t=CZi&Htiu\n4؛؃lG=F7bRZ/aR@}@J\<E b@u¶^doc{Op#\\״3%pn&`$ B@O2b?a.Ήd[6jb\>!Zٚe~W@=)pn a?,0\0Tá:\nDzS @x'[\0I XTW0pz\<(S =J9J?P#؀:={i*@+EĢd\0C%2?",,TBO$!sSPЁD؇#(+X30P8\|,lCB,BDDDYQ\> tPC,D4J \>+64;(̝;߳DF R\<\>yDTŀK\>7H!ĥXERES  6^EcDFTEdcF+d\>Z,GjF pp(r Gq4Dr1ȁn\n8.0DZ#GqǀǂH8G2HHrLȅȆHȇHDd,4t4ȂǒdDɔTɕdI\n"1 KDlBjDN*r 9`!`ʦtʧʨʩ\nC1\0X*8%\tQ썠,28P;{@\00oǩ˻7\t(VE"2!K*\<("A$(踐eLt L1!)Ь000ID;yj͒)4\\M@\>B!{I\t%( KiƯj\tK)\n)Aˍ(AyN"P!,?BШR8I!!\<; !PJqbwƺN.!BOQQ!D $\n d}Mᝯ 7U:{ؤq)ZR,#5'L + 1J\0 -)U5e6uӨLl*X2")A}'@8TxO\0a׈7IJmS \n -% u&d)N)1iO*"-Ҩ*[\|-ͳ0*XTKUeefHא0)Qy ۪AJ.ɱм$-뒑ynzWC7f\t%:ItփE؄=d\t!Nk.E[CZ $=Ҷ`@S\0ťTؑ%ْQhmXưDvrXT͟뙙0ٜٛ-\n\tYG]E%\>PEڤUZ@ٞ%ڧFj%]ګڒڝZơZ;ڬ%۲Mئ\t j%U8Z۹eӸ5[c @ۿ[ŗ0\\eƕJʼn[͊Bu\\ܜύEX*5ӽ̵`,BR/XM $]Eڭ@EҽLFlx\<^݀+֊М0QK,H^P]TD\|ϫ%jd/Q\0K0-[ᵉ9M,LމQe'T,^Hѝ0qv\\ӹ01N\|L4MlȒS\ts.1]Fa0{\|a^0SQzADV\tߚ_$}z!6_Oi`2f$-ޔ@ic,OT*jUOR3bϙ7FF,τ)fd`8 \oKm\0\0`%_JTv\|n* 6}b~fZpF)7Eۊo pf\nWR̓ \t Ȕ$NJLIlɎtLt\<qdPDGȊlqHt f!$7%Zt(V&* ,\trf\tr 7i3'5./Ts6F\<\>w@ \>w2uX8JG= sCwoI ^y\nNw^ÈKsDJrδ,OV'iX':tx F,󄑨NE^ \n5%.uÈJuVud\0yvP%患`m_׬$\tWP6\\~v_LљO\|7!̩A: wzPZ} yhG,TIQ-mUa%u0SOxWxzRPS+uUbWc"̞Z^y%x"}f"78UYwۇz'7ڬ; \0\<;_'J:M2_ԪW{zٮOkv]_Amo⺶p\fm=mf#8?swl\nQ_w \tgJ;XeoaFU`0!t}m%"Wz\n"sx5'Їsܨa7ޓ273PO=}#i=H~@=CS4] 6 beyfK TqoS\|cƛ3 t#s\\\|bdg\0P \0d(8w&j(s@o\0 @o1gTt~ 0A6YŲX*l&Fᴉ~HNXж_b1lx?H)O,ڛ[&ȭΊ\0Z~\n+&J~o /j+Flsݓ1{/%EIv3zXyܴBt!g&@=9TyOW O{Qg2]/62I9qvd~Kvל)=CZdaybi\n\\5yU@o C\|TWQ#k k^{K(tAUYl"oOT{iֹC(NU"Ns?;ip\>=P+\>vKO=p\>\>&[?Ra]пȗ{u@P\0\| Y-0D :#a— pS \\SIX`\tcD6\\a\nA8P\>\\\tq( # A7\t\>"[["3Ĝt,MQ'CLcG%1&)0--ʏYk`ȻP'e\|d\\DO9a#!!rTAHG8nB\ti]:RƆ#Dd:Ar$![c4'RBvlhHΔ*\tNrXq\0TO"o7I\nC͟SmjQZ5s2ʍ}Z%*թ\0e%TW~\>3,Xu UZ1¨FE6&J#oX+`.5eFIZI[ʥ9뱚VA`=eJ%-[B}ijJIS4UcU3+a?H\0ҧ\0FJ:*׺D!T6)WuK3hYa2b7:TWzR\\t$GySaI*ZӉҒ=\|{}*wI$#ÒG0rS\0vKmkY;*GsgbL-vAR-T Am":Q~wu\nefJȆxjI0=0b%620ݐ}'`mx&¡/v~ޯlha;5'`!ƕ6FI]c6Q b dE~o\\%S9$2̺^u#5沌P\>dӱ\0ɲZ/+\nFULBXeO%d(H`2zV M4m8qn8A݄BSLZ \\\0 LιasC:\|Er0IpMm0[QfV鴱\\hy=cp2$ GkΔ\|dHW6&(`FڎS馀Tv7g֧?U'd֨y?m\>c (oZ\|H?\|4L:pjXصaEkUyQ0&Qme%g2lG}17pU\\k ْ,_A@M~wCjqؤ$7͗\>\tEu)*~a\>a L a,ӝtguk{a&7xęOEj.Iw.63glVVJlPH;{.؁6ի N FL D^q{NIk@\|[Y]Rk.g@J%;j/U{AF=_\Y̠͠鄚 \>\n :NuvŦ zM\t]AD9&2=JqЪQvzPN*Ȏh@4W܌l[ʹeķHU!!?TrlSXH6}S!8L\f`&aaNef&fbZ`2ffb6fh&h&g&jj&kk&lll&l&an"og Lq"r"!\0(@'uJgV@"@BV\0uj'@u.\\\0;>|gif>|*5/8|*5/8||||> Notice that some entries list their keyboard equivalents. At the bottom of the TeXmacs window is the status line. Sometimes, TeXmacs will ask you a question there - remember to look! +6W(VkfvH覫%k '\0\0$:\0\0Dw\0/p%@\0$ p\|(@@tCpr\0 4@‰2 :LżȬ@%\0\0s)l X͊&3# 2bw5QO@Q\\X7~Fd8;wvk\|zt3ߘgnڈ \0=@\0 /墓ͣSl:E8OL \0ZQ2/N1E{1 ױ7O6cG{[C6\03@\|gif>|*6/8|*6/8||||> To start R, you need to click on the little monitor icon ]T*"rrrr}ҦiYB\n\nʮβJ^ZkS\>:.zJKv&&nzff~f~XTxFKr¶FDlʮbbbjji0.VgMC&22ҲƤ*vzHA7xaܾ.RD;6NnnnvZήçZL?8:hҸ6.NWRBSplvv82AYXRVZ^Zc^^CA^-*/tfffjj^^Z\|ZTjr3.Jv^~zbʮβ\>2&:\>:\|~ŚҾ~96a˾ʪRRrή+&0::bzzwKMJ̺RBFJJnzbb@:UrZޚ&"1*~~:ffnZVL^vfp\\jdB\>T3*DƲ[Wk*.*Ά\>~hZr2.D72QV::nn^^^hdzg22.SNrtvp^N...N6\>Fb^z::ZNJf?kk~~~΢FFFuvu^\\ZZZ&""~rtZNz,\0\0\0\0"V\0\0eEஃ\\h0Ç7HȰŋ3:۸G.!q’2Dɒʗ'np(S.8 )r+@ڴC=/t‹EHUfeµ׮ZV K֯hӪebvZa[O`x{߿LTÇ+ދ~{.jˍ8⬩y",ÂFyjɫGy%I'W3]4M{dV\\I7ûRr.hUwiQNh/]z[PDҾG\0~́& *_ρG~\ng_N~\tvX!G߁ާ2hƋf8hc wc ~:+"vC2y_MY8"K8ߊ vqU Q\>T"$U=\\4!=ɠj衊`袋裐\>ȤF*)DZʦv=i)کj飛:駠zJ뭀~뮷*(R\n" ;jVjiV+("h:i:K-bƼlhFo$+Ϳ+\0;G(hդҊ`t!-\t3\> /&滯 \tG0,*;pʌ@IA 0 @C\\40Rp't)g}BqWS/DG-J(u$=S#6= :(XkʡN.6lGr,,~w]m^\>yۭŅTJ*0"l9S.))B"kk4;pЋs3S9c0)\tc.3\|\|=\|~^͂[~+o/\|&-xqr\\5.s! [*T,GuQ ĠNu)c[pe\n֡r:W첁s `\n:(xG=R\<#0&\0&`XLRpMT3e.t-~d\\ծ5t/Ý1rO2n_T緁%M{H} hR /qo`p pMn/ܖɗ,f~dZvrl\03)\t/nW$&&02h8Z!fs9P\0fb=pf g 6&%LF5fJmS6J~-o֬\\!Iҩoa4CVz\a]\0\0Tܶ%ȑ7N!UA񊗋\njU@fTQ9PZؔ2gkΗiO}^WT?zZ jmAR5Ey/.\>0' \0j\\EXBLC(kr_~% ?0~]=(1W:6vכ@O&b7Bwc.ޢ,2Z"[^D}[Bxu4QDo7C\>\tm/J\n0-&'O10yPՃYZϕ{"t8(%A:O0=P(wKH90[ѣGCC\\ Bh\0\t}p p spr3eWuM$oPJD5`CHsVjbwMSt'w~{cqw/\t7mvu'"8 3:U\KaM\|›{Tk/+8ǭʪf۩‘빳ʰ{aF,Ί\t\\,¦uY\*n\n A-`V\<ڮ~Lͱ-ķkNMyn\\~\\ }\03;^hJ2*{@\|ݎ\n.m!\0\>[ ŭ"N\\U+][pOߑ{ԁ\0ߡMņ.wձ}@\0 \0\<\0 \0\t: p\0Np7\tͤ)0ޓ\0\0`\0p[z=\nP`q\0\te q}+/D?jԡ\t\|Fm\0\0q -CyY~\0d}pq@K\\+/@\t0]d 0\t8\tH~*IFO D\|t]#t}\tI ݗ~WqV u*+-ޛ \0 Q\0tC޺zb7g#:s0n:p \\A' R/ `1#z}¥bM\0q*v;L Ď5(GLꉁ$]g^ˈә=\0ҳƼθ =\0&a6\\J\\R9BrcdžZg/ĈIҬBY8\0z sq^Hjy\<.ԣD ⌉Y׻WivQ"-9͠89Ϟi?\ts& #kN+*\n#H₮h B*u08z/9kۜ B0\tFB\n%b"C.7*\t1Ɔk""%z\<8*jĊzC0Piq̋tn\|O\>ݐ.$.nЙO\0Ğ .2"T&ҹz NzRDd?ĈUl"z%\0uR3qKﳕ\0m(ZɨT]KS 8¤(e{\\NZd !\t&!ݬ09\>(Lk=.ף B]2\nSrĆX炙Ą*~[4+!ͧwQʹ\<_xs~#'OZW;S\n\t\\q`}fb \n쩉 f,x'SxM\n#(}/`X/\\a.& l2?l/\>0\n!qı!i19q\n?1CSLmT3sQoaG!5ԝ:\n.7w.8GxӴF؜uI A2$o#t}C7!DQ 7ҡ0d HAԋwȆ![iD$'$\tnVv*"#,M=\0X;W:$=Q}xzItHK?{ܳʦ@Yj\|BnuKL'X.9\0l߹H0 e \tB*zkfDJ0} cV L`YXWĆ.@Kǰ;Bz@![\tɔ.#+CAL7Pi \tAŎ\>"̌$l\t\>jCɆ/3*!tF\>JmIDČr7?1`֜A4uĸ\>p5 $YK;.RqAs!/a2c:b\;h{U%4y;ˏ0\thx.\\ ǣAE^8ǟ6)#'j^i"E)2vf#&[Wmz\\HvaW1d9t.PU](kGb SlN\|nd12drq9^J:lPx].sYM?2 Gnj3"]hs02r9؂B9q YfZѓ.\Yʅ X✓ݬxQ{iKs*_2k҂a5A׼}Z2(Vr0iMس䢕{AqxDKuIl EpB=1v.-7%iC05:!NmSW6yezW^LZY\>nV8v~uE\.\wyF{ۻA#m l}90u?Jq\|J%\>z1was\>Uuz\>/7#236Y\<=k'\\I;ϡ:߸s+7\\3Ê!3 447\>k8Ly\<*1.;-.s#:x87 {kW Dg;ٿS;cҷhz/AScS\<\\\<#A:'ثJ-.Ubg{=26\0KkC9@Ѓ{\>,҃~yI02\$T I;.aŽآ۴[8s7 ˬ[1s@\\9#J ` F`Fa$ \ bDFcEf4cl_aTfLbFiFgkoFpeFo4gdLGrFp ldGg\!u,MNt94.˄R9\tLL4ϨϩKD:ElPDP Ll&$$KλsB;SFmT\tH}KrPKP OE3P!dMPOSÈ555bSˣT\0!^S=\0T%U*Ό*X\0pxrPKke\tAכU.^HDjeA+֗$W\\tpJM]&-%\nS1].:MW_-9XX\0\teIHXm)0My8\0T`$ hhh .dۓE@[ @=ŅUP5?"VP2VU4wE׮V5V=.mv D\0`U`+5ȅ\\@LP_`?x'd\0}UPhK-VbZb=Y;5L\0\\e4˕Dh()DM$\ޘYR-$`/ˇZU\nq`bO^hߎe"`c`^%1eRfY}@-HwP@4WxSO\\-]fB_]ޣ5V= \>!5ڮy\0Pꁦ9ގ_fZ\n9E$8=umh\08_kr\>_n 5ERuG^55r\t=#VZdxd2dd\n8RZKk8f`vP 00PQe˚W^bӎU]!f+d\\``ɭljI7DY`8l&VF\0M)-_HEۊ\tr1\tn95빦k\0%}j߁gik@TNh6l(Jɹ%~`US3ɖRYHq5a; mӽo(%}H+@m4`4mNl\0FAM0^LhjIfn/j.KtfΆ1hf)k\LCD6RmG6CɖuXWn;Q'\\_fk)kx\\؄WHk+h_Vus@VҘi_P\o) ^&QPgkhh\|_S\|tg8mlFX(ŖV?\t"3)^lUݒԏC ;SVS0Kxf8v8 e&4^ួeD]jjdhwOVj]r+l--\>\0{-}s4KVsL-Aikĉj_C?\>xuLEUM=Rut=l0!EpedMvťU/\0xڕw ?Ѕ.i ؀9_?%v _MvUSnezllk]z9nWt\>OFoBx/g8`k/[=ksqgg~΂OzH BtC\t'R5*ĘPbł#f33@*W0eaz(Ѭi\0\0F:P@Π\0Ř􌘱\trBuK) :$9)ۘ&\0\08O=R'OBRe_(116\|8[i)0rܣZPq,s2d^ MqIIwݸ-Ж3\ yǗPD$T4S0Bx!\\fHd]Br-r#A\0h@]P\\rM}vWeHVR"tJQx}V\|(j^6$b\>Bgc9@~SNEUF]x\|A=\t8tu%i]=(`;qTa@Bbzt]yY#jla(AR0:cbiTIdԜm$M?n\t@i) ި\|𝶧.O!e}d1LЃ"*d D^AL@h@9\0  WeymWыWeR{G φt5\>/gm Z*E^\n)'t\0q\nlGQRQ^K_!fĊ@aS*\04#9 *LRGؙ/^gL%7K-Oq5zN.~^^1=7C'&ݻ?]~^!?q}6G?^~+?YQG8\tj \\A9Gz6@i7=}iNXB"B5UG36*wVJSz c2TE6zI`}DAp~`86Ne~?1W@4*Nt9tĹ9*{lw$o}R]%-\>LA\F:OxWLeeiaԣ n ]cϗcEA 3&x`7i7*o$ٖI'h~LLL懕ԴG/\\H שv̠^'5'.Qd*u'L~1E:=\>xNmӛԦAOӡF=*RӤT@]*QT\>Uբ⴫OݩWSG*ZjԞ^gM[ZUBU:*S׵εhkVՠ5{%,[:XJuiW"5xf3r,hC+ђ=-jSղ}-l5*)u)n;?tq\nd$9uwo)H=nnz&LFb.dKBS.ՈeINu8NV\|o{gq\|TȷvP *G8Wfkn*w`y??uO(mGR.ĺ$%m[EE7\\Cm9Fq\<5y[PUApg{k\> mw=\>8_)kbgX+ F"X9WjS\tDYAv{7 6S\<[\>5AD#o̰)+2G͎bNLh0YqՖCa+uHD\t\D؁\<I7&~v&ij7fOzǧiA{܈L\n\\3^t!vD rgBz_h'F\|wC=&\0\0 P \@;,Cİ\t\0"H"8\0HO\0\<\0`\\\0tC0,"Gp,\>0"4B-4 \04M$85Sf\0\tl\0 QR- xmRLYQZ㜀D2L!pEtC4#B,hB4P7$@8c \n$Qc\n\nU{L;H\0A?jߜ9\0X8@!,D,8\\4v\0\0-\|E,\0@*AI7,ZdHO7\0G#(1\nY:+n -R@\|SІeZ;nZ˝^D PlŅ$aЮD%4Q6Y% ^#34rA5~8e\0a!oZ"B$Ml QJ\0x\0bz\0仰CܱB\A=t=i2"\\q\0&LLA@Ap@4d$-Hq\0\t \<\0BhJy}un40qYYԴۢ%V^]\|75c9n7g{BEibe9:4ΚP&qnaQ)%I]t\\3A=@۱]-\\H\<e\>!fڃ0q$A\,D\|$\0r)!4A @dA$C QQܠ\t.e\nϵ Tsɠxc9mct8\nj[SP%%͡exn%ĐY\\HhvhˈP`\>=Nޣ0\n@7ă8\\e?B9g"d=\0)4,3@v\~Gm-ǯKL Ž]gFk(uxCأ`3dlCVe6, El:CE\>\01-tkN,Ԍ14p.a-\>(^ $\0\0C\>Jk `iS^\\)x6̉T!ҜEǤDj}e6.l~~R.`!蘁]H:{c棆n / ?eake3Dh&$Z"@-&\0AfpLkTJ^(F(،6p*p9\0\>\0vi2/HB\<\0ikMRnY.gxrzB\>u#5,4MjP6J9[Glª#ԙZNa&lA\0ςA;0AcD0 7\n\<-3,\0[0Eh-&cpTIv-$ $X):\n\0\0! @ԁ ;NZ\tj*SҩS` rxaނIbnY\0߸}ALnGnP^\>}ĄenLL@b"1 \0@(Ď`\0 D6$ C4DA\\‹:#q,E3"*8"ί\<`\0p$ub$b$,"ȳx\0\0DtDg\0 \0!,0\t`_wv% +,L-`lθtB,wt%zڄvTa0R 쁮R\tb\0Vcu9q CE\|70+B3ă5Ȃ,@83"-4!Cҕԃlf(Pp,"%0$6b\<3\0\<@HD\0@?pGi!\0ar`r\>%nM/\0tkBVan\0(=aM'@.Չ\tgʛ\tJ]ąؑ\t'ѧ0/ l7hD:A346\>Mo6\|&ALR$[0\0܃`td\>\>dNHYRE(b,l\0r!m@D@ +@H;AkYH'EpơtdK5 M,,?j\\O2#8#9Hc`qݣbFJ^^rK.{(ΠW$7;)Ck\0띞u6âLʤ\tb" 6 }y*06\>CG܌, *i$ 0@Gk[*l3yz2A X\t'#.~nW\n@並D#P{ OV4m8T.\tK, slaNY¦R (37;t\nsNFP%b6eO!Vplz:5\n\0 (BEK\<(@\t!,SJB/Jw[ӆvt\nϯq$HcX]3?\\ Kɹ\^I 4n`\\Qѳʿ&o\<6Vl=ŤHcԔe:Ǡ ;yC9 {@8@gLP…F'z.:0"FݺQ6dI$#RǥC1\n!ƗXT"K t3'́-YrٲJ\\ȅIU&T7Z s%͂_z +P :$vBJ\m5J~+==~\| O羦:vS\+迦,-^k+.f:- Kr,@t ˭(K+ -\ \0{g&C񐩦k͚ͥρ6(} F.f I]o՝\tf\0׉ſ nlg@O١o^a$q\0\n}ۃ_ܙ=!oIaU-o8fƐq=쁻\| \\GLbm^s 0X*eԂ{L\0؛mnV\>\|@:O7p(MAG~;"\|&0F l[Db;Văm?H6E1J6: md:1\tH =9qG\0?:cpч=d#U!{Lv8hO0Gj ze@ra$)A$)N~"̱$3"J9Rt,%A0kfPI;)͑l5ԉpr#e"Rs\0b(&(O3yФ.tk~':sp-L9 KF+Xrxg\C*o{amJ6_;́m=qoȰؒ+}m\|5\t]7CFycӡf\0_Xa 8_r̂}#\\H=ř\\\0G\>AlfۮJz{X@HFq}lj"8:@;U=̌-ZgtYY%3 T\06\0 BȗBۅp\|~f Ɛ(_19O\nsO֑p $?9vZ\> Q5bxFwzh h;xg$\<5(mUG=ȴD')nFjwwn}oIga.3h*\nYL2eGnŃ8g njWɬph[$5u\|E#ag /}suqkBo,Yn ȐIkӊ$_ꖀϥa\eh\|5d9z$vc5]'ҍ@B\<\t=g%NM՝Va'úc#2Xr{4;ѫ(x\t~UM,zH&!k E5\0lS\>rztyLI8-iJ\|T^Y蔃샺[]cqتqM{#+ &ӻ^!dSsUǎ^&pG\| p !{hrl6F \0r.OT@:pV$\>gHwu!Ɇy"Űu F,2-"-U-tq,2vd('\0@"x{dlq A T&A 08\>p e9jv"8&f̽Gp"a7pץ\0H0\<4\0(+xa]('\|\\Gy AqZ- #RJ wzg.rء0X\0g\|qac}#1TJC14!2N\t+'g\|Tqhr\0%a2xHfMqTCBM\|l%\<"h\n2.@\>1q#;#j):h,D՘0:\\n7q$1"C,BS\|nCg4E&/&))7V##B":b"&!,"'2%v-$E:\>#+ #%Q'K0-7M\<LX+C@\t"w)yc\>p#IТH0`xD.",윣/*\nJJ+R'R\n\\D\0$$/=\0 $3Vj4D .&n )/o2_e"l\nB?'rK"3.2\0\>NZ~Е@@34Gq4IsyGa%1ڑK1jE(R23`da#;/cJvBc9`lglR'!aܫrtj)#p))rbp1\\0odoXq r¬qMAyrN$BvH n)9u2"47j"cGm2N3@7Xc*ۢ2+K&QT4zDd\nb808TKT;UTF?i4/6^ܴZJ`3WG0S{+]'o6*]*"USR$/ک6'lH_ߓ_#U.a'Tc`au9!D*Fl23-3@\>[fq]Ig=7+ɵ[ӆM]eG1fTbbdR $nmJ{g1d@t9JN\0"6ui$f#CB:72 E[6TJk n\6rA*4 t?\tP hz1wZ̊Rp7ipECbFN+QX"\0lpY78%u BfDk7l lx÷" 'O K1p`gtS0,ZgLUM)U*3M)IksB1{WL\|e-N'ico-?+uJg\>hZpO /NS0r&l6(%Z=/,;yDga%sXpCc\tRrG8b&̯2EXq.F6I.#^zBIRn-e]5ADg_7[.d\>ѓvϱߔW2gW%6W`T0/74KAl#cDD\|'Ȋro7n.XfW*&"t늢cDJ:RNMT٘ۊXb.2Q2!۰ٗJ.Cn$y}%,G9cmImoBiRW.T١\tGW wVR-٣k,'4s!r'u9tƦgs=zg+\\ w?4wKѾfx\|z14ӾgGz" pTm5paM."t% T4MW@\0NǬwXMsMMݶaUi#)F:pBPAT'!\0ǚv'uS,l@pa\\Spbt(BaڡBc#dZuZ 8@mC2"zB0qڣcgGR6kW.q#2,r9By&bQzQy\<[.dֵYz6bv1-)Ҍ{Ab3{1¹"4k\n)x,I:6/;c[+'#nQkϑś$A\n0Î5eo\n(`m;'Bª;%a\0h\\_;~\nÓc;{ؾ:I-[(\\uR\>cۺW'lͫ7,\n.y8":\\\<S˕s\nLS ~m0܋J ݼF x7O!ߜ\>\<;9,߶Ɖ\5aR+OaѼ!\>cdr@&7?#\\anWK񧿘#c7.ƩslXos1n0{z:wЙ„.1ĉ+Z1ƍ;z2ȑ$K\<2ʕ,=R\n2̙4kڼAqȳaD;y.\<4ҥL\|\n5ԩ-)ᡊ5֭\\[:L8†G~-1Z]ۺ}%ܹt%9hJl\n8w \>UČ;pW)]93ǜ;S5ӳў:[% ;Jne۾vegY3{\0}[\03 }"AS=\0"xvc\<\>\tg6O& \|ADqD`=-xXh \> ~\tDA_ Ust^{AH"\\u5\0ā733\>q\>?1\tBbY9hdu\0\<A8zUz\0z#*\t&N'IfcU=Ah\<=ߠ3 YzƄ~u^ba=-x[\\q$ BIcfV酏 A揶8OUz'u\nG}J+T$tb7UQPYJ\>Ki鸎 j$\0=\0@$\<Iނ:*n+ݧנ\\ڦOBXeɋ~\>\tEzÕ{«q(O\0oO\0(i/KH@6 %n#o\|r;\|VˀdTYA?g\|uC-Go}2۝\\Q,K=5$c:@~9[B`N@\\<Q}톧{r Eo݀E{7lexH{SzţJIu_O6b_SJ5\|joOYt\|#8\<;W\|kaEap{\\ , i Y!x 4x*hp4bw\n5,ϱ"2"F d9"ʶ߬Fw#,;rtE1AbAeU!N\0UYZȋc)1W\\{&0礧!8=*\t$ 990УI&)DUJY$%K\>۽i jQ=`KAa=_U~NIBM\nQXJJ \\%)iSbBCB(4]B3K urNw')f]i,\>JGϘ'uzqZ3g\\H\MX%nkӆG/p\t7 [[@O(qLS`uIeMnr\tw.-sBwt.uGawCn ^-՟wˋ^7\> _đ6E{_7} xC.pkj\nnp,a28M@\0\0;>|gif>|*5/8|*5/8||||> Which should give you the following: <\output> library(TeXmacs,lib.loc="/usr/share/texmacs/TeXmacs/plugins/r/r/") \; \; R : Copyright 2003, The R Foundation for Statistical Computing Version 1.8.1 \ (2003-11-21), ISBN 3-900051-00-3 \; R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. \; R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R in publications. \; Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for a HTML browser interface to help. Type 'q()' to quit R. \; [Previously saved workspace restored] \; \; \; \\ <\input| >> \; > There are two important icons: the 'STOP' and the 'scissors': hiAmnG`^HLHI_ZJ?1JE8O)OPCPPCPmjProQnkTroTUtqVI6VtqWI6WVGX\\XYYZk\\Z[[[_`N8`abdaOe[6ghhghhhhlhiiijlmlnnmoZ@o\\EooooxdtbJwk@x\|xxx{\|\|}hP~xajLkLlNx\\ĿſƗ^f8Su`md`⮪ϲj\|ָnvszžtíjŦhIǩ~ɬ̮̱ЬӰӰӸԹԺָ׷ٽܹݾŦġǥ˫̬ѷҶӹ}~ր\0\0tt\0\0\0\0 \0N\0\0X\|(=@\0PP\0tt\0\0\0(\|\0=D\0\0@@\0PPtt(N\|GD@@Pt\0\0\0 Pt-@XL{\|`D!@@`P t\|\0@\0\0\0\0\0\0-\0\0@\0Tt0\0X\0\0\0\0\0\0\0P\0qt\0!\0@ (=@`\|D`\0\0\0\0\0\0Pzt \0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0,\0\0\0\0\0\0\0`H*\\ȰÇ#JHŋ3jȱǏ Dɓ(S\\ɲ˗0cʜI͛8sɳϟ@$"ѣH*]ʴӧPSJ$LU]ʵׯ`N tkUdӪ]˶ʱ;ȝ \\twK&/\t\#Y%U_]J p=C"EAG` 8`I,ȭN̓\>a^g%R~2b54~a1G$qB Bp5\0pW\|tqUB{I /D'KD$E4t v5`  cbi ʪ\0x=$a;a\nPTd$j^ˤ3LfJٶcřʌ&2)jZ?&6nH8IrL:v\~6JHJЂMBІ: }D'JъZͨF \0;>|gif>|*5/8|*5/8||||> You see them only when you are inside the R session. The hiAmnG`^HLHI_ZJ?1JE8O)OPCPPCPmjProQnkTroTUtqVI6VtqWI6WVGX\\XYYZk\\Z[[[_`N8`abdaOe[6ghhghhhhlhiiijlmlnnmoZ@o\\EooooxdtbJwk@x\|xxx{\|\|}hP~xajLkLlNx\\ĿſƗ^f8Su`md`⮪ϲj\|ָnvszžtíjŦhIǩ~ɬ̮̱ЬӰӰӸԹԺָ׷ٽܹݾŦġǥ˫̬ѷҶӹ}~ր\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0,\0\0\0\0\0\0\0\0\tH*TpC/I8`C3J4xQƏ;fDdFG,yR`ʉ+cRQ"8srD\0$\nK71\tUQPس&ҥ9^\tb̕3vQdYkcQmAû˷/\0;>|gif>|*5/8|*5/8||||> will stop the current R session, maybe in a long calculation. The hiAmnG`^HLHI_ZJ?1JE8O)OPCPPCPmjProQnkTroTUtqVI6VtqWI6WVGX\\XYYZk\\Z[[[_`N8`abdaOe[6ghhghhhhlhiiijlmlnnmoZ@o\\EooooxdtbJwk@x\|xxx{\|\|}hP~xajLkLlNx\\ĿſƗ^f8Su`md`⮪ϲj\|ָnvszžtíjŦhIǩ~ɬ̮̱ЬӰӰӸԹԺָ׷ٽܹݾŦġǥ˫̬ѷҶӹ}~ր\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0,\0\0\0\0\0\0\0n\0\tH*\\Ȱ!K&p xqaF\0h"kFZǍ0ntē#C1J&\teBSv4jpFzǝ\|gif>|*5/8|*5/8||||> will exit the current R session, and a new one will be started when another R command is entered. If, for some reason the output from the R session becomes uncoordinated with your input, just enter @@@ on \ an empty input line: <\input| >> @@@ <\input| >> a=6 <\input| >> \; > \ (You might then need to hit the hiAmnG`^HLHI_ZJ?1JE8O)OPCPPCPmjProQnkTroTUtqVI6VtqWI6WVGX\\XYYZk\\Z[[[_`N8`abdaOe[6ghhghhhhlhiiijlmlnnmoZ@o\\EooooxdtbJwk@x\|xxx{\|\|}hP~xajLkLlNx\\ĿſƗ^f8Su`md`⮪ϲj\|ָnvszžtíjŦhIǩ~ɬ̮̱ЬӰӰӸԹԺָ׷ٽܹݾŦġǥ˫̬ѷҶӹ}~ր\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0,\0\0\0\0\0\0\0\0\tH*TpC/I8`C3J4xQƏ;fDdFG,yR`ʉ+cRQ"8srD\0$\nK71\tUQPس&ҥ9^\tb̕3vQdYkcQmAû˷/\0;>|gif>|*5/8|*5/8||||> to regain the input) To enter text (i.e. non-R input), just click beyond the blue lines that deliniate the R session. To continue with the R session, just select R from the menu on the monitor icon. <\input| >> a <\output> [1] 6 <\input| >> \; > When you enter an exression without parentheses at the end, R prints the expression <\input| >> a <\output> [1] 6 <\input| >> q <\output> function (save = "default", status = 0, runLast = TRUE)\ .Internal(quit(save, status, runLast)) \environment: namespace:base\ <\input| >> \; > as you see, when we entered '', and not '', R printed the function . To actually call that function, we have to call it with ''. h - brings up a help system: <\input| >> help.start() <\output> Making links in per-session dir ... \; If netscape is already running, it is *not* restarted, and you must \ \ \ \ switch to its window. Otherwise, be patient ... \; <\input| >> \; > lists all objects in memory: <\input| >> ls() <\output> [1] "a" <\input| >> b=5 <\input| >> ls() <\output> [1] "a" "b" <\input| >> \; > removes an object: <\input| >> rm(b) <\input| >> ls() <\output> [1] "a" <\input| >> \; \; > Data in R is in general stored as vectors, or lists. First we'll learn about vectors. When we printed the value of > before, we also saw '': <\input| >> a <\output> [1] 5 <\input| >> \; > That is because a is actually a vector that contains one element, 5. There are many methods to create longer vectors: <\input| >> 3:9 <\output> [1] 3 4 5 6 7 8 9 <\input| >> \; > the collon creates a vector in ascending order. The '[1]' in front of the first element tells us that 3 is element number 1. This is usefull for longer vectors: <\input| >> -50:50 <\output> \ \ [1] -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 \ [19] -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 \ [37] -14 -13 -12 -11 -10 \ -9 \ -8 \ -7 \ -6 \ -5 \ -4 \ -3 \ -2 \ -1 \ \ 0 \ \ 1 \ \ 2 \ \ 3 \ [55] \ \ 4 \ \ 5 \ \ 6 \ \ 7 \ \ 8 \ \ 9 \ 10 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16 \ 17 \ 18 \ 19 \ 20 \ 21 \ [73] \ 22 \ 23 \ 24 \ 25 \ 26 \ 27 \ 28 \ 29 \ 30 \ 31 \ 32 \ 33 \ 34 \ 35 \ 36 \ 37 \ 38 \ 39 \ [91] \ 40 \ 41 \ 42 \ 43 \ 44 \ 45 \ 46 \ 47 \ 48 \ 49 \ 50 <\input| >> \; > Here we see that -32 is the 19th element of the vector. We can store a vector in a variable: <\input| >> b = 5:100 <\input| >> b <\output> \ [1] \ \ 5 \ \ 6 \ \ 7 \ \ 8 \ \ 9 \ 10 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16 \ 17 \ 18 \ 19 \ 20 \ 21 \ 22 \ 23 [20] \ 24 \ 25 \ 26 \ 27 \ 28 \ 29 \ 30 \ 31 \ 32 \ 33 \ 34 \ 35 \ 36 \ 37 \ 38 \ 39 \ 40 \ 41 \ 42 [39] \ 43 \ 44 \ 45 \ 46 \ 47 \ 48 \ 49 \ 50 \ 51 \ 52 \ 53 \ 54 \ 55 \ 56 \ 57 \ 58 \ 59 \ 60 \ 61 [58] \ 62 \ 63 \ 64 \ 65 \ 66 \ 67 \ 68 \ 69 \ 70 \ 71 \ 72 \ 73 \ 74 \ 75 \ 76 \ 77 \ 78 \ 79 \ 80 [77] \ 81 \ 82 \ 83 \ 84 \ 85 \ 86 \ 87 \ 88 \ 89 \ 90 \ 91 \ 92 \ 93 \ 94 \ 95 \ 96 \ 97 \ 98 \ 99 [96] 100 <\input| >> length(b) <\output> [1] 96 <\input| >> ls() <\output> [1] "a" "b" <\input| >> \; > length() tells us home many elements are in a vector. We can also see that the result of ls() is also a vector, a vector of strings. The function c() allows us to list elements in the vector one after the other: <\input| >> c(1,4,10,2) <\output> [1] \ 1 \ 4 10 \ 2 <\input| >> \; > With c() you can also join several vectors to one longer one <\input| >> c(1,4:9,2) <\output> [1] 1 4 5 6 7 8 9 2 <\input| >> c(1:3,1:3,1:3) <\output> [1] 1 2 3 1 2 3 1 2 3 <\input| >> a=1:4 <\input| >> c(a,a,a) <\output> \ [1] 1 2 3 4 1 2 3 4 1 2 3 4 <\input| >> c(a,ls()) <\output> [1] "1" "2" "3" "4" "a" "b" <\input| >> \; > In the last example you see that when you put a vector of numbers together with a vector of strings, the result is a vector of strings. With rep() you can repeat something several times, to create a long vector: <\input| >> rep(3,4) <\output> [1] 3 3 3 3 <\input| >> rep("R",5) <\output> [1] "R" "R" "R" "R" "R" <\input| >> rep(1:4,10) <\output> \ [1] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 [39] 3 4 <\input| >> \; > It is easy to get elements of a vector: <\input| >> b <\output> \ [1] \ \ 5 \ \ 6 \ \ 7 \ \ 8 \ \ 9 \ 10 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16 \ 17 \ 18 \ 19 \ 20 \ 21 \ 22 \ 23 [20] \ 24 \ 25 \ 26 \ 27 \ 28 \ 29 \ 30 \ 31 \ 32 \ 33 \ 34 \ 35 \ 36 \ 37 \ 38 \ 39 \ 40 \ 41 \ 42 [39] \ 43 \ 44 \ 45 \ 46 \ 47 \ 48 \ 49 \ 50 \ 51 \ 52 \ 53 \ 54 \ 55 \ 56 \ 57 \ 58 \ 59 \ 60 \ 61 [58] \ 62 \ 63 \ 64 \ 65 \ 66 \ 67 \ 68 \ 69 \ 70 \ 71 \ 72 \ 73 \ 74 \ 75 \ 76 \ 77 \ 78 \ 79 \ 80 [77] \ 81 \ 82 \ 83 \ 84 \ 85 \ 86 \ 87 \ 88 \ 89 \ 90 \ 91 \ 92 \ 93 \ 94 \ 95 \ 96 \ 97 \ 98 \ 99 [96] 100 <\input| >> b[2] <\output> [1] 6 <\input| >> b[2]=13 <\input| >> b[2] <\output> [1] 13 <\input| >> b <\output> \ [1] \ \ 5 \ \ \ 7 \ \ 8 \ \ 9 \ 10 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16 \ 17 \ 18 \ 19 \ 20 \ 21 \ 22 \ 23 [20] \ 24 \ 25 \ 26 \ 27 \ 28 \ 29 \ 30 \ 31 \ 32 \ 33 \ 34 \ 35 \ 36 \ 37 \ 38 \ 39 \ 40 \ 41 \ 42 [39] \ 43 \ 44 \ 45 \ 46 \ 47 \ 48 \ 49 \ 50 \ 51 \ 52 \ 53 \ 54 \ 55 \ 56 \ 57 \ 58 \ 59 \ 60 \ 61 [58] \ 62 \ 63 \ 64 \ 65 \ 66 \ 67 \ 68 \ 69 \ 70 \ 71 \ 72 \ 73 \ 74 \ 75 \ 76 \ 77 \ 78 \ 79 \ 80 [77] \ 81 \ 82 \ 83 \ 84 \ 85 \ 86 \ 87 \ 88 \ 89 \ 90 \ 91 \ 92 \ 93 \ 94 \ 95 \ 96 \ 97 \ 98 \ 99 [96] 100 <\input| >> \; > But it is also easy to address subvectors of vectors: <\input| >> b[1:4] <\output> [1] \ 5 13 \ 7 \ 8 <\input| >> b[3:7] <\output> [1] \ 7 \ 8 \ 9 10 11 <\input| >> b[c(1,3,5)] <\output> [1] 5 7 9 <\input| >> \; > You just list inside the square brackets the vector of the elements you are addressing. You can also set them: <\input| >> b[2:6] <\output> [1] 13 \ 7 \ 8 \ 9 10 <\input| >> b[2:6]=rep(1,5) <\input| >> b[2:6] <\output> [1] 1 1 1 1 1 <\input| >> b <\output> \ [1] \ \ 5 \ \ 1 \ \ 1 \ \ 1 \ \ 1 \ \ 1 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16 \ 17 \ 18 \ 19 \ 20 \ 21 \ 22 \ 23 [20] \ 24 \ 25 \ 26 \ 27 \ 28 \ 29 \ 30 \ 31 \ 32 \ 33 \ 34 \ 35 \ 36 \ 37 \ 38 \ 39 \ 40 \ 41 \ 42 [39] \ 43 \ 44 \ 45 \ 46 \ 47 \ 48 \ 49 \ 50 \ 51 \ 52 \ 53 \ 54 \ 55 \ 56 \ 57 \ 58 \ 59 \ 60 \ 61 [58] \ 62 \ 63 \ 64 \ 65 \ 66 \ 67 \ 68 \ 69 \ 70 \ 71 \ 72 \ 73 \ 74 \ 75 \ 76 \ 77 \ 78 \ 79 \ 80 [77] \ 81 \ 82 \ 83 \ 84 \ 85 \ 86 \ 87 \ 88 \ 89 \ 90 \ 91 \ 92 \ 93 \ 94 \ 95 \ 96 \ 97 \ 98 \ 99 [96] 100 <\input| >> \; \; > Mathematical operations will usually work on a whole vector: <\input| >> a=1:4; print(a) <\output> [1] 1 2 3 4 <\input| >> a+2 <\output> [1] 3 4 5 6 <\input| >> a * 3 <\output> [1] \ 3 \ 6 \ 9 12 <\input| >> a ^ 7 <\output> [1] \ \ \ \ 1 \ \ 128 \ 2187 16384 <\input| >> sin(a) <\output> [1] \ 0.8414710 \ 0.9092974 \ 0.1411200 -0.7568025 <\input| >> \; > Other than strings and numbers, there are also vectors of boolean values (i.e. TRUE and FALSE) <\input| >> a = 1:4 ; print(a) <\output> [1] 1 2 3 4 <\input| >> a\2 <\output> [1] \ TRUE FALSE FALSE FALSE <\input| >> a\2 <\output> [1] FALSE FALSE \ TRUE \ TRUE <\input| >> a==2 <\output> [1] FALSE \ TRUE FALSE FALSE <\input| >> c(T,T,F) <\output> [1] \ TRUE \ TRUE FALSE <\input| >> \; > You see that one can use T and F as an abbreviation for TRUE and FALSE. Also notice that to test for equality, we used two equal signs: '=='. Boolean vectors give an alternative way to get at elements of a vector: instead of listing the elements that we want to address, we can give a boolean vector saying if we want or don't want certain elements: <\input| >> a <\output> [1] 1 2 3 4 <\input| >> a[c(F,T,T,F)] <\output> [1] 2 3 <\input| >> \; > This gives us very convenient access to elements: <\input| >> b <\output> \ [1] \ \ 5 \ \ 1 \ \ 1 \ \ 1 \ \ 1 \ \ 1 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16 \ 17 \ 18 \ 19 \ 20 \ 21 \ 22 \ 23 [20] \ 24 \ 25 \ 26 \ 27 \ 28 \ 29 \ 30 \ 31 \ 32 \ 33 \ 34 \ 35 \ 36 \ 37 \ 38 \ 39 \ 40 \ 41 \ 42 [39] \ 43 \ 44 \ 45 \ 46 \ 47 \ 48 \ 49 \ 50 \ 51 \ 52 \ 53 \ 54 \ 55 \ 56 \ 57 \ 58 \ 59 \ 60 \ 61 [58] \ 62 \ 63 \ 64 \ 65 \ 66 \ 67 \ 68 \ 69 \ 70 \ 71 \ 72 \ 73 \ 74 \ 75 \ 76 \ 77 \ 78 \ 79 \ 80 [77] \ 81 \ 82 \ 83 \ 84 \ 85 \ 86 \ 87 \ 88 \ 89 \ 90 \ 91 \ 92 \ 93 \ 94 \ 95 \ 96 \ 97 \ 98 \ 99 [96] 100 <\input| >> b[b\12] <\output> [1] \ 5 \ 1 \ 1 \ 1 \ 1 \ 1 11 <\input| >> b[b\90] = b[b\90] + 4 <\input| >> b <\output> \ [1] \ \ 5 \ \ 1 \ \ 1 \ \ 1 \ \ 1 \ \ 1 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16 \ 17 \ 18 \ 19 \ 20 \ 21 \ 22 \ 23 [20] \ 24 \ 25 \ 26 \ 27 \ 28 \ 29 \ 30 \ 31 \ 32 \ 33 \ 34 \ 35 \ 36 \ 37 \ 38 \ 39 \ 40 \ 41 \ 42 [39] \ 43 \ 44 \ 45 \ 46 \ 47 \ 48 \ 49 \ 50 \ 51 \ 52 \ 53 \ 54 \ 55 \ 56 \ 57 \ 58 \ 59 \ 60 \ 61 [58] \ 62 \ 63 \ 64 \ 65 \ 66 \ 67 \ 68 \ 69 \ 70 \ 71 \ 72 \ 73 \ 74 \ 75 \ 76 \ 77 \ 78 \ 79 \ 80 [77] \ 81 \ 82 \ 83 \ 84 \ 85 \ 86 \ 87 \ 88 \ 89 \ \ 95 \ 96 \ 97 \ 98 \ 99 100 101 102 103> [96] \; > When you join a boolean vector to a numeric vector, TRUE becomes 1, and FALSE becomes 0: <\input| >> c(T,F,3) <\output> [1] 1 0 3 <\input| >> a\10 <\output> \ [1] \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE FALSE FALSE FALSE [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE [25] FALSE FALSE FALSE FALSE FALSE FALSE <\input| >> (a\10)+2 <\output> \ [1] 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 <\input| >> \; > The paratheses above are necessary, and one often needs them in R. Compare: <\input| >> a\10 <\output> \ [1] \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE FALSE FALSE FALSE [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE [25] FALSE FALSE FALSE FALSE FALSE FALSE <\input| >> a\10+2 <\output> \ [1] \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE \ TRUE FALSE [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE [25] FALSE FALSE FALSE FALSE FALSE FALSE <\input| >> 1:10 <\output> \ [1] \ 1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 10 <\input| >> 1:10+2 <\output> \ [1] \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 10 11 12 <\input| >> 1:(10+2) <\output> \ [1] \ 1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 10 11 12 <\input| >> length(a) <\output> [1] 30 <\input| >> 1:length(a)-1 <\output> \ [1] \ 0 \ 1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 [26] 25 26 27 28 29 <\input| >> 1:(length(a)-1) <\output> \ [1] \ 1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 [26] 26 27 28 29 \; > I often make the above mistake. If you want to address all elements but some, you use negative indexes: <\input| >> a <\output> \ [1] \ 1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 [26] 26 27 28 29 30 <\input| >> a[-1] <\output> \ [1] \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 [26] 27 28 29 30 <\input| >> a[-(1:10)] <\output> \ [1] 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 <\input| >> \; > ``Statistics is the science of learning from experience'' (Brad Efron) Statistics can do various things, here we will deal with the following: <\itemize-minus> Given an experiment we would like to estimate a parameter (in the world). Given an experiment, we would like to test whether a certain hypothesis is can be said to be unlikely. These are essencially the same thing. If we knew the world exactly, we would be able to say for sure if a hypothesis is true or false, and we would know the parameter exactly. Two factors prevent us from gaining certainty: <\enumerate-numeric> Sampling Measurement error Let us look at an example: Let us say that in a school there are 3000 students, and that we wish to know the average height. First, let us chose the heights: <\input| >> heights=rnorm(3000,mean=170,sd=10) <\input| >> hist(heights);v() <\output> |ps>||||||> <\input| >> \; > These are the heights of all the students in school. We can easily calculate their mean: <\input| >> mean(heights) <\output> [1] 170.2498 <\input| >> \; > Now let us assume that we want to estimate the mean height. we take 10 students, measure their height with an error of around 1cm, and then round to the nearest cm: <\input| >> measured.heights=sample(heights,10)+rnorm(10,mean=0,sd=1) <\input| >> measured.heights=round(measured.heights) <\input| >> measured.heights <\output> \ [1] 176 172 149 186 179 168 146 187 166 160 <\input| >> \; > Now we can calculate the mean height in the sample <\input| >> mean(measured.heights) <\output> [1] 168.9 <\input| >> \; > So, we know that this is the mean of the sample. But what does it say about the real mean? What are the ranges that we believe now the real mean to be? If we knew the sampling process, and all the various errors involved in measuring (and in this case we do know it), then we could estimate how far we are from the real mean.\ But how would we know all those parameters? We would have to estimate them, too! Bootstraping (boot-straping) allows us some magic without all the estimation. It says that a good estimate for distribution that we measured are our measurements. so instead of trying to estimate heights and their error and sampling, we just sample from the measurements we have: <\input| >> b=sample(measured.heights,10,replace=T) <\input| >> mean(b) <\output> [1] 170.7 <\input| >> b=sample(measured.heights,10,replace=T) <\input| >> mean(b) <\output> [1] 172.2 <\input| >> b=sample(measured.heights,10,replace=T) <\input| >> mean(b) <\output> [1] 169.3 <\input| >> \; > \ Now we have some idea in what range the real mean could be. This was done to show two things: <\enumerate-numeric> R is really conventient for addressing such matters. We can easily simulate situations and then assess our statistical methods. Bootstraping is useful, simple, and (as we'll see later), convenient to do with R. \; We saw the following 2 ways of generating random data in R: > Sample randomly: Roll a die <\input| >> sample(1:6,1) <\output> [1] 3 <\input| >> \; > Roll 50 die: <\input| >> sample(1:6,50,replace=T) <\output> \ [1] 3 5 6 1 6 5 1 3 2 2 6 5 5 4 1 1 4 6 6 3 4 2 5 5 4 3 3 2 5 5 5 2 2 2 6 5 2 4 [39] 5 1 6 5 6 1 6 3 5 6 4 3 <\input| >> \; > or <\input| >> sample(6,50,replace=T) <\output> \ [1] 3 1 3 5 3 2 4 4 3 4 1 1 3 3 5 5 4 5 2 5 1 4 3 1 4 2 2 2 1 1 3 6 5 6 6 1 4 5 [39] 2 6 1 5 2 1 3 1 2 2 4 1 <\input| >> \; > > Sample from a normal distibution <\input| >> rnorm(10) <\output> \ [1] -1.9329962 \ 1.0924528 \ 0.5751292 -0.3561676 \ 0.2812530 -1.3551893 \ [7] -1.4555352 \ 1.7605307 -0.6611010 \ 0.6395928 <\input| >> rnorm(10,mean=3,sd=0.1) <\output> \ [1] 3.032633 3.123962 2.989857 3.142417 2.874144 2.855629 3.048683 2.898982 \ [9] 2.923673 2.987789 <\input| >> hist(rnorm(1000));v() <\output> |ps>||||||> <\input| >> \; > \; <\initial> <\collection> <\references> <\collection> > |6>> > |6>> > |7>> > |7>> > |7>> |9>> |12>> > > > |2>> |2>> |4>> |4>> |4>> |4>> |4>> |5>> |5>> <\auxiliary> <\collection> <\associate|toc> Lecture 1 |Using R> |TeXmacs> |> |The TeXmacs interface> |font-size||Help in TeXmacs> |font-size||Opening files> |font-size||The status line> |font-size||Starting R inside TeXmacs> |font-size||Important hints for the R interface in TeXmacs> |font-size||Managing R input and Text> |The basics of R> |font-size||More usefull functions in R> |font-size||Vectors> |font-size||Subsetting vectors, and operation on vectors> |What is statistics?> |font-size||So?> |Some simple random functions in R> |> |> |font-size||> |font-size|||language||sample>> |font-size|||language||rnorm>>