R for beginners. 2 The few things to know before st. 8 Index 31

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1 ; & & & 8 * ( 0 " & 9 1 R f Eu l 1 W R? 3 T fw kw f T <- 5. L l j 5.3 T -l l 6 D w R T j 8 3. R f f # S & ' G R l ) q R ) q M l j * A f j A l fu ( M, x 16 G. / w R M l ' G fu ( L -l " & ' G 1 5 S l 4 5 l 4 w R 3 6 T / lu 7 R 6 : L l x 6 6. W u w fu ( 7 Hw < f.. w R? 30 8 Ix 31

2 @ T l 4 f < /. 5 u 7 > 5? v. 5 / 5 < f. / / 5 wl R. I / lf 6 u 7 I u 7 l x / l k l ll, wl v? fu 7 l l, w l. C, u 7 x / l w Cu A f. I k B J l Clu 7, C / Dlq, F L M u 7 R f u 7 l? v f u 7. I l fu 7 l ll f R Dv? l / C T f l ff v? l / R u 7 l -l /. Tk l R w qu 7 l / w R f. 000, C E > > 5 l 4 D. (0. 000)

3 R / X??. 4 J * " # U S 3 8 ^ W W S [ S + ` 1 Z [ # T S T Q q E W F G H R? 3 R l l 6 6 R Ik & R G l (1996, I J. C K u. G L K M. N S L., 5: ). R lu 7 f w; k l f : 5 f < < f? v 5 l < f, u 7 f < /.. < f. l 4 u , >., 5. > / x /. 5, l,, ll f l f l l 6, u 7 u 7 / l fl w / u 7 ll 6 flx l, / l ff v? / lu 7 w lu 7 6 fl. R 5 u 7 5. l 4 f < 5 u 7 S. A T&T Bl L... S v? f < w. S- D R LUS > >. l 4 z M Sf < ( :/ U U / www. /. > f <. > / < f. >. 5 < f. > 5 ). T.. > /. 5 < f < f. 5 / f R S, 6 f : w w kw / / / G l & Ik (1996) R-FAQ ( / :/ U U /.- / j V./ U / U FAQ/ U R-FAQ. l), / f w l w f w. R < f. l > f < GNU D R L 5 f < X F. Sf < w. Fu (f <. >. 5 < f. > 5 : / :/ U U / www. 5.. / U ); v? l 4 / > v? l kw R Dv? l / C T. A k 6 -l v? l / C / v? R Av? N wk (CRAN W ). R v? l l v? l f: u 7 w C ( u 7 F 77) 6 / l, ll 6 f Ux Lu 7 x, 6 f (f <.? v. 6 5 l 4 5 ). 5 < fl 4 w 5. A Y Z [ Y Z \ u [ ] _ Z ( ) Il W0w 9 5 f / 9 8 f / N T & 4.0 f / 000 L, x ( D.j, + M k k 9 7.1, j R l H 6.x, j # S # S 5.3 f / 6.4/ f ) C Al # S S MS Lu ( xc 5.0 D l Ux 4.0 Lu ( x ( R H 6.x) Lu ( x ( R H 6.x) T < f 5 l / :/ U U / /. j V.. / U 5 U / (x / < f. M 5 v 1 ) w u 7 f ll u 7 f / 6 wll. R lu 7 w 6 fu 7 f l l 6 / ; l vu 7 lz l 6 w ww v?? vu 7 f (f x > /, V j /, / 5, > /, /,. w > < f 5. W 5 w, /, > /, / x 5. U 5 x ). T u 7 < f. > l 4 5 l 4 5 / , > 5. >. u 7 ( -v? l 4,.. 5 f < < f 5 ) 5 w. 5 5 < f. 5 u 7 qu l 4. T R l 5 u 7 l 4 w., < f. 5 5, /.. > / f < > > 5 u 7? vl 4 5 l 4 1 T + M f R j f # S f I < k k. > j, CRAN.

4 < <. < < v? l. I l / l l / ff l fu 5 /. < f. > >. > / x 5 l 4. T R. > 6 5 f < f <. 5 >. f u 7 5 w. 5 < f. S 5 v? (f <. x > / : / :/ U U /. >.u 7 U / S/ U ), > f. u w R. A f, R u 7 > > / x < f / l 4 (f <. 5 5, l 4 ). T >. l I 5 < f, /. > 5 5 < f. f < R < f x. W. l 4 l f < w. (SAS, S D SS, S,...) / 6 (l 4 > ) l 4. u 7 f < 5 5 l 4, R. u 7 l j u, l 6 w u 7 l / l 6. T 6 u 7 / u 7, u 7 f? v 6 fu 7 l. I, x l / f u 7 l w f. F x / l, f u 7 f 0 5 w 5 > /. < f < f f < < f 5, R 5 / 6 5 > f < < f 5 :. u 7 w k v 0 5, w. l 4 l 4 f < w. u 7 wl 4 / 0. u 7 w 5 w. 5 u 7 > 5. x > /. 5 u 7 /.. f < 6 > u 7 R > /. l 4 l 4 f < w. I /.. w 5? v 5 f < f <.. 5 u 7 > 5. 4

5 S < 4 4 <. ˆ ˆ S 5 T w f w w x kw f w H G F G 5 5 R 5 l 4 5 u 7. > /., f < w. u / 5 5 x u 7 (RGu 7.x u 7 R. >.x 5. W 5 w, R 5. U 5 x ). T /. > / > 5 R w f u 7. U Ww, l 6 ( -l l /, / fl,...) 5 x u 7? v / -w 5 > 5, > f < > > v? / v k 6.. W l 4 5 < f. /. / f < R:. 5 5 > < f 5 l 4 > 5, l 5 5 l 4 5 V j 5 > >., l 4 5 l 4 /.. z 1 T { } ~ <- R j u - lu 7 :? v l,,, fu 7, u 7 l,. v? 6 f / f f V j w v? : V j / 5 > f < V j / X F. x > /, < f 5 V j f.? vl 4 10 : > [1] 10 T 1 w k / l 6 f l f ( 3.4.1). T 6 l L ƒ v?? vlu 7 V j. T 6 l w w k v (<. >). w 5 > 5 6 > k v > l 4.. w w 5. < f. > f <.,.. v?. : > <- 15 > [1] 15 > 5 -> > [1] 5 T? vl 4 w? v 5 5. u 7 f < 5. > x /. 5 : > <- 10+ > [1] 1 W N u 7 5 > / / 5 x /. 5 w u 7 5 5? vl 4 5 V j,. u 7 u 7 / l 6 6 : > (10+)*5 [1] 60. z L ~ } l ~ Š ~ { Œ j ~ Š Ž T fu 7 l() l / l 6 V j 6 : l 6 f V j / l 6. > <- "Lu A "; 1 <- 10; <- 100; <- 0.5 > l() [1] " " " 1" " " " " W N f -l ";" / l. If

6 5 <. < ž Q 6 4 l f V j 6, 6 fu 7 l l w v? > : 5 5 w / 5 (w 5. v? w ) : > l( "") [1] " " " " If w w l f V j w w : > l( "^ ") [1] "" T / 6 5 V j 5 > >., w 5 < f 5 5 l. (): > l. () : u 0.5 1: u 10 : u 100 : " " T / 5 5 l 4. v?. A 5. f < / 5 f < l. () x.lv l w / < f v? l 4 f < / 6 < f. > / V j. B f < u 7, l. () / 6 f < l 4 V j 5 > >., 5 l 4 5 l 4 > 5 f < f >, >. 5, w 5. u 7 5? v. 5 / v? / 6 l l w / x.lvl-1: > š M <-.f ( 1,, ) > l. ( "M") M:.f : 1. f 3 v l: $ 1: A u 10 $ : u A 100 $ : A u 0.5 > l. ( "M", x.lvl-1) M:.f : 1. f 3 v l: T l V j 6, w fu 7 (): (x) l V j x, (x, œ ) V j x, (l l()) l V j 6 ; / f. < f 5 5 l() 5 5 l 4 l 4? vl 4 > V j : (l l( " ")). z. 3 Ÿ T { -l Š { l T 5 -l 4 5 l 4 / f < R? v >? v. f < 5 < f. > 5 5 w < f 5 5. T l 4 / 5 > < f. > l 4 / 5 : > l. () A. w v k 6 -w. / w > l 4 /. A. f < < f w ("w ") w l fu 7 w "w " : > ("v") [1] " v " " v.l " " v.l. A ull" " v.l l " [5] "v.l" "v.l.u A ll" "v.l" "vl.l" [9] ". v " ". v.l " ". v.l " ". v " T l / v? l l x f f v? fu 7, f : 6

7 >?l 9 7 / l 6 l / fl f fu 7 l(). T fu 7 l (l) l ("l") ff. T l fu 7 u 7 l / w -v? l.. : >?* E: œ x > l ("*") A k: R Du A A...

8 ž ž 5 5 > ˆ œ ˆ ˆ } ~ Š œ ^ ¹ ª [ Š ˆ «[ [ [ _ ª «Z [ ^ ± ª [ œ. 3 D F w R 3z. 1 T { Ž Œ j ~ 8 R w. v k w V j w l 4 v? w : 5 l. T > v k 5 f < l 4 > 5 f < 5 V j ;.. < fu 7. > : A u,, lx, 5 ll. T.. > 5.. z, < f. 5 5 : fu A, x,. f A ul. T l l 4 5 >. f < l 4 > 5 f < V j. T fllw l u 7 z ff V j / l R. j l v f x.f l u ( j,, j l x, j l l u ( j, u ( j,, j l x, j l l u ( j,, j l x, j l l u ( j,, j l x, j l l u ( j,, j l x, j l l j, j,, xj, j, fu ( j,, x j, f u ( l vl l [ _ [ j [ Y Z? N N N N Y Y ² Y A? v.? v. 5 > > 5 > > 5 5. A < f.. l 4? v.. A w ³ k > 5 5, >. x 5 /. u 7. f < w ³ k. N l f f x ll f. A.f l / w v? l? v ll f l / l 6 f ff. A - u 7 / / l 6 u 7 fqu 7 6. A f < 5 V j, 5 v k / 5 > 5 : w / f u 7 l v? V j. F x / l, x w l lu 7 f / f? vlu 7 [,], l 4. I f < v k 5 w R. > 5, < f. 5 > f < V j, / /. -.. < f. > w. - 5 (.., - 5? v), x 5 X 5 > 5 V j (v? 5 5. W 5 w): > x <- 1; X <- 10 > l() [1] "X" "x" > X [1] 10 > x [1] 1 3z. µ L Š Ž é à u f { R I) < f ;. < f :. l() (w w? v. 5 :.v () 5.v ()), () 5.fw º f(). X F x > /, < f w v? < f., 5 5 V j / : > œ <-. l(". ")

9 7 $ " " $ " " f f 0 Å Å " k " 5 < wll.f,? v l wll, fu 7 l,» V1,» 4 V,... 5? v u 7 l 4 œ $V ¼ 1, œ $V ¼,...,. œ ["V ¼ ¼ 1"], "],...,., 5. l 4 5, œ [,1], œ [,],. T.. v? l l f fu 7. l() w? vlu 7 fu 7 l (.. 6 R f ) l v? fllw l: œ 5 u 7 l œ ["V v? l / u >. l(fl, F ½ ¾ ALSE, "", qu A "\" ", ".", w º., l.,.f ½ ¾ ALSE,. "N À ¾ A", k 0, k. TR Á  U E,.w FALSE) j j j j j j j j j j j j fl f fl ( w ""), l w ( l \ llw u l /, v u Ww) ll ( FALSE RUE) f fl f vl f l fl u fl, f "\" f ul qu u vl f u f l w. v w f l w v f, u ( ) f vl f fl ( ful: 1,, 3,...) l. v w f vl ( ful: V1, V, V3,...). l v f vl f ( f FALSE) k ( TRUE). vlu v ( v NA) k u f l k f k. f TRUE, k vl vl f R.w ( l ) f TRUE, l x f f vl Tw? v f. l() fu 7 l u 7 6 v? ff fu 7 l / :.v (fl, TR Á  U E, ",", qu A "\"", ".",...).v (fl, TR Á  U E, ";", qu A "\"", ",",...) T < f 5 5 () >. < f x 5. l() 5 >. / 5. T > < f < f. 5 / / < f > f <? v., < f. x > / : > œ <- (". ", w l ("",0,0)). 5 < f..? v., < f. f < > x w. f u 7. T / fllw. > (fl"", w u A l(0), x-1, -1, "", qu A f ( "\") " " \"", ".", k 0, l 0,. "N À ¾ A", flu A F ½ ¾ ALSE,.w FALSE, qu A FALSE) 9 fl w f fl ( "") j, l ( l à \ ll u ( l / j, 8 W ); f fl"", j k k ( w lk l) f ( ) f Nvlj, ff : $V1 [,1] ["V1"].f.

10 ž Ç ž ¼ S " " 0 $ " } ( 5 < j j j j j j j j j j x u f,, f w l, u f l ( ful, u f fl) u f ( ful, l) fl u fl qu u vl f u f l k u f l k f l u f l. vlu v ( v NA) flu ll, f TRUE, x l u f lu ( llw u fl).w ( l ) f TRUE, l x f f vl qu ll, f FALSE, l l w w fl v T < f 5 5.fw º f() 5. 5 < f > 5 < f x w < f. > : >.fwf(fl, w, "\ ",.FALSE, k 0, w., l. ) T / f. l() x / w w / f w f fl. F x / l, f fl. x fllw : ¾ A A B B C C > w : > œ <-.fw º f(". x ", º w (1,4,3)) > œ V1 ¼ V ¼ V3 1 A ¾ A Ç B B C C z. 3 È S } É v Š } ~ T < f 5 5 º w (x, fl". x ") w. 5 V j x (? v., >. x,... 6 ) 5 < f. x. T.. w / 5 : (. l) w f < 5 5 >. f lu 7 fl ( fu 7 l 1 f x f, 5 f ), ( ll) w u 7 / l 6 l 6 / fl (T RU C E),.. 5 (F X A R LSE C, f < u 7? vl 4 ). T < f 5 5 º w. l() w. 5 < f.f. T / 5. : > w. l(x, fl, FALSE, qu A TRU  E, " ", l"\", "N À ¾ A", ".", w º. TR Á  U E, l. TR Á  U E) 10

11 ž > Í Ë ` \ ª _ [ Ò \ [ Y [ } j. 11 l. w. qu l f l fl ll f lu ( fl. f f ; f T R U Å Ej, f ) q ""; f j, f ) q "". I, f f ) q "" f. f f f ("\" - ) T... u 7 / f < V j 5 5. < f. >, w 5 < f 5 5 v (x, œ, z, fl"m œ A uff.rd "). T f f w ff, / TRU  E. T (w w ll ) l l >. w l("m š œ A uff.r Á Ê D "). T < f 5 5 v. (). -u 7 < f v (l l(lltr Á  U E), fl".r Á Ê D "). 3z. 4 Ì G } ~ } ~ 3Î. Ï 4Î. Ð 1 Ñ R [ ul qu A u 7 l qu 7 f, f x / l f 1 30, w : > x <- 1:30 T u 7 l? v x 30 élé. T / : / / w x / : > 1:10-1 [1] > 1:(10-1) [1] T < f 5 5 q() 5 5. qu 7 5. l 4 5 >. < fl 4 w: > q(1, 5, 0.5) [1] w. < f. 5 >. 5. f < qu 7 5, 5 5 5, 5 qu 7. l: > q(l 9, f1, 5) [1] I l / l / l 6? vlu 7 fu 7 () : > (1, 1.5,,.5, 3, 3.5, 4, 4.5, 5) [1] w? v x >. u 7,? v u 7 l W l 4 fu 7 () fu 7 l. T fu 7 ()? v w l ll l: > (1, 30) [1]

12 5 7 > > /.. < T < f 5 5 qu A ().. f < qu 7 5 f < u.? v 5. u 7 > 5 : > qu A (4:5) [1] > qu A ((10,5)) [1] T fu 7 l()? v 6 fu 7 l u 7 u 7 l f f? v l. T u f f l(k, ) w k u 7 f lv? l ( l), u. f <. / 5 5 v? l 4. Tw / 5 > 6 : l / < f 5 > f < /. u 7, 5 l l / < f 5 > f < < f.. C E x > / : > l(3,5) [1] Lv l: 1 3 > l(3,5,30) [1] Lvl: 1 3 > l(,8, l l("c l","t ")) [1] C l C l C l C l C l C l C l C l T [10] T T T T T T T Lv l: C l T > l(, 1, 0) [1] Lvl: 1 > l(,, 0) [1] Lvl: 1 Fll 6, x.().f w ll f? v f v? u 7 : > x.(q(60,80,10), º wq(100,300,100), x ("M š l","f ½ l")) w x š Ml š Ml Ml š Ml Ml š Ml š Ml Ml š Ml Fl ½ F l Fl ½ F l Fl Fl ½ F l Fl ½ F l 3Î. Í 3Î. R _ [ Ò q \ u [ Y [ I l 4 l < f 5 > fu(, [1], [],...) >, 5 R 5 < f.. 5 >. f 5. T < f < fl 4 w 5 < f. > : 1

13 4 / W? ž Í? 5 Ö } ~ Š ` _ ' ( ^ 8 ª Ä Ô " " _ Ž Œ Z Y ««_ [ < 4 4 w fu lw f / l, u 7 f....? vl 4 < f. /. >. f < w. T < fl 4 w 5? v lw, 5 / f < u 7? vl 4 ( < f 5 5 f < u 7? vl 4 5, > u 7 / f )., l Gu ( l) (, 0, 1) x l x(, 1) 8 W ( ( (,, l1) (, l) Wul wull(,, l1) Cu u(, l0, l1) S # ( Ó ) F ( F) Õ ( χ ) l (, 1, ) (, f) f(, f1, f) q(, f) (, z, ) (, ) (,,, k) l l l v $ l ( uf l x l(, l0, l1) l(, l0, l1) (, z, ) uf(, 0, x1) wlx(,, ), j k(, ) 13 4 [1], [], l < f. 5 N l 4 < f / 5. w,. q,. /? vl 4, /. 5 (fu(x )), u 7 >? v /. 5 ( fu(x )), 5 vl 4 f < qu 7 5 (qfu( ), w 0 < < 1). 3z. 4 M } Š ul j ~ 3Î. 4. Î 1 A Y Y [ Z Y \ ul _ v _ lu \ [ f _ j [ Y T, < f. x > /,.? vl 4 u.f,? vl 4 f < 5 vlu 7 f lu 7, w / : > x[,3] < f <? v. x, w V j / I < f x >. x. 5 V j l 4 > 5 w x[,j]. T 5 l T 5 x 5 6 > 5. l 4.. 6, w > >. f f 6 (f x / l, l 6 : x[,j,k], x[,,3],...). I ufu 7 l k / x w k [], w /. < f.. u 7 > 5 f < < f 5 5 : > x(1) E: u A l f fu A "x" Ix 5 5 u 7 / /. 5. v?. l 4 5. l 4 > 5. X F. x > /, x[-1,] w l u 7 / /. < f. 5,. x[-(1,15),] w > < f

14 » C W Í œ œ œ ^ S C œ W X F.? v., > , /? vl 4 f < 5 l 4 > 5 w > /. 5 x /. 5 5 x : > x <- 1:10 > x[x > 5] <- 0 > x [1] > x[x 1] <- 5 > x [1] T x / / R : < (l ), > ( ), < (l qu 7 l ), > ( qu 7 l ), (qu 7 l ), (ff f). N /.... 5? v. f < > l 4 (T RUE. X FA R LSE C ). 3Î. 4. Î A Z [ Z Y _ l [ fu \ Y Z T u 7 u 7 fu 7 R / l. W v? l 6 / l, () w 5 5 V j 5 /. 5. X F. x > / : > (1:5, q(10, 11, 0.)) [1] » V. 5 > 5 / w l 4 l 4. > x /. 5 : > x <- (1,,3,4) > œ <- (1,1,1,1) > z <- x + > z [1] V. f < < f < f ; 5,.? v.. 6 l 4. Ex > / : > x <- (1,,3,4) > œ <- (1,) > z <- x+ > z [1] > x <- (1,,3) > œ <- (1,) > z <- x+ W : l j l A ul l f j l : x + > z [1] 4 4 N R v? w, u 7 /. If w w 7 l / l 6 )? vlu 7 ll l f? v : > x <- (1,,3,4) > <- 10 > z <- *x > z [1] T. > /... +, -, *, /, 5 ^ < f. / w.. 14

15 5. < ( $ $ 0,, œ,,, j 4 15 Tw. f < /... x < f. x > u 7, 5 x ( /. f <? v 5 f < x ). / œ < f. 5.? v 5 T fu 7 v? l l R 6 l. f ll l fu 7 (l, x, l10, l,,,,,,,, q,...), / l 4 < f 5 5 (,,, li,...), wl 4? v. < f 5 5 f < l. S > f < < f < fl 4 w 5. $ j j u(x) u f l f x (x) u f l f x x(x) xu f l f x (x) u f l f x w.x(x) u x f l f x w.(x) u x f ll l f x (x) ul ((x),x(x)) l(x) u f l x (x) f l f x (x) f l f x v(x) u v(x) v f l f x ( lul 1) ; f x x.f, v -v x lul (x) l x f x f x.f ( 1 f x v) v(x,) u v w x, w lu f x lu f f v(x,).f (x,) l l w x, l x f.f T fu 7 l? vlu 7 ( u 7? v f l ), x / () w. 5? v. f < 5 w, 5 v(), v () 5 () w > >. x. T fl 4 w 5 < f >. > / x. u 7. u(x,) v(x) (x) k(x) l(x,) (x,,...) x(x,,...) uu(x) u(x) u(x) ux(x) (x,) w(x) w(x)... f, x f x l f x ; : v((x)) k f l f x l f x l u ( f x[], j [], j.... f, x f x[1] x[]. f. f u (. f xu ( f l x l f x ( l NA) f f x f u ( ( TRU E) j,.. vlu ( f f x[] ( x; f fu ( u ( l f ll)

16 Í < 7 5 > ^ \ Z _ Z Ù (,k).(x).fl(x) l(x) u(x,...) f Ø k / f [( Ø k )k Ø ] v $ ( NA) ( l f x x.f) ( u f, x N * A ( ) ( u f ff f, x ( f f ) ( u f x (...) f x ( : x$v1 < 10) ; f x.f, j l f l k ( u ( -) 16 3Î. 4. Î Í 3 M _ Z x Y u R < f < f. >. fu 5 x (): > / 5 5 > 5 / 5. A >. x 5. w > x(5,, ) [,1] [,] [1,] 5 5 [,] 5 5 > x(1:6,, 3) [,1] [,] [,3] [1,] [,] 4 6 T < f 5 5 () 5 / v? l 6 : () > 1 <- x(1,, ) > <- x(,, ) > (1,) [,1] [,] [1,] 1 1 [,] 1 1 [3,] [4,] > (1,) [,1] [,] [,3] [,4] [1,] 1 1 [,] >. w. / 5. l 4 > 5, T /.. < f. /. u 7 f < w >. *. X F. x > /, 5. 5 w. > 1 5 > v? : > (1,) * (1,) [,1] [,] [,3] [,4] [1,] 4 4 [,] 4 4 [3,] [4,] > (1,) * (1,) [,1] [,] [1,] [,] T. 5 / 5 f < >. x.f. 5 w < f 5 5 (); < f 5 5 l 4 w T fu 7 () x f 6 l f x, l l x.

17 17 9 > ( 1) [1] 1 1 > ( ( 1, ) * ( 1, )) [1] 8 8 > (1) <- 10 > 1 [,1] [,] [1,] 10 1 [,] 1 10 > (3) [,1] [,] [,3] [1,] [,] [3,] > v <- (10,0,30) > (v) [,1] [,] [,3] [1,] [,] [3,] > (.1, 3, 5) [,1] [,] [,3] [,4] [,5] [1,] [,] [3,]

18 <. Ë Ï / Ð Ö ^ [ ` [ [ _ ª ` _ ^ Ü Y ` _ ` ^ Ý Ý Ý 6 4 Ú G Û w G R 18 R ff k l? v f /. T, / ( ). I / l l / l f R f /, / u 7 ll 6 / fu 7 l u 7 f / k / u 7 f /? v 6 flx l. I wll f? v < fw 5 w > 5. / w 5 w. 4z. 1 M } } } { Š w Š w 4Î. Ð 1Î. 1 ] vl ww W / fu 7 l / ww > x11() /, / ww / w / qu 7. I / : T ww / v? ww, u 7 qu 7 / wll / l 6 5. T v k 5 w. / w 5 w w. u / 5 : > v.l () ww ww 3 T fu 7 / l 6 ww u 7 f ww w v? ww: > v. () ww 4. Î 1. Î _ Z Z _ Y Ý w w T < f 5 5 l. () l. ((1,))? v /. 5? v. / w 5 w. X F. 5 5, w 5 w 5 w /. w 5 l 4 w (1) ();.() l w /. T fu 7 l œ u A () llw / lx / : / v? / w 5 w 5 v?. l 4 /. w.. / w / 6 u 7? vl 4. X F. x > /,? v w 5 w 5 < fu 7. qu 7 l 4 /. : > l œ u A ( x((1,,3,4),, )) w.? v.? v 5 >. f < u 7 -w 5 w, 5 w < f u 7. 5 ww wll v? w w w lu 7. T : > l œ u A ( x((1,,3,4,5,6), 3, )) w. x -w 5 w,. 5. w, 5 w 5 l 4 > 5, w. : u 7 > l œ u A ( x((1,,3,4,5,6),, 3)) w l 4. x u 7 -w 5 w, w 5. w, 5. 5 l 4 > 5. T u 7 -w 5 w > f ff z: > l œ u A ( x((1,,3,3),, ))

19 Ë? " " ( " ( $ ä, 0 wll / w u 7 -ww w lf lf f ww, u 7 -ww. l 4 < f. X F 5 l 4, / : > l œ u A ( x((1,1,,1),, ), (3,1), (1,3))? v. (3,1) 5 (1,3)? v 5. l 4? v > 5 5 f < u 7 -w 5 w. T? v u 7 l 4 z /. 5. l œ u A () f <.. w 5. /, w 5 fu 7 l œ u A.w(), f, f x / l, w u 7 -ww v? f. 4z. G } { Š ¹ fu ~ Ž H f v? v? w f / fu 7 R. ( j ã j ã j j j j j j l(x) l f vlu f x ( -x) x-x l(x,) v l f x ( x-x) ( -x) uflwl(x,) l() u w l w flw w l u u f (x) ul - xl(x) x--wk l l(x) l vlu f x l ( lv xl()f ll l z) l(x~ z) v l f x f vlu f z ( f z f).l f f1 f f, l f ( -x) w vlu (f1,f,x) f f1 ( x-x) f f ( ff uv) ; fu llw u f ( ful fu) l(x,) v l f f lu f x v. f f, f x v. f,. l(x) f x.f, l Clvl l ( k l l--l lu--lu) (x) f x x.f, w ll l v l w lu f x l.(x) f x j f l, l f x w, x ulv u u v fqu.l(x). u f x ulv v ff u v fqu (x) f fqu f x l(x) f vlu f x qq(x) qul f x w vlu x u l lw qql(x,) qul f w qul f x u(x,,z) u l ( l w uv), x u v z u x (z)(l(x),l()) (x,,z). u w lu l l) (x,,z). u 3-D l l) X F. < f 5 5, / 5 > 6 < fu 7 5 w 5 -l 4 5 l 4 / 5 R. S > f < / 5. 5 l 4 < f. v?. l 4. / < f 5 5 ;.. > 5 5 (w. / f < u 7 vl 4 ): 3 T fu (.l() k k f fu ( l ( 5 f k k R ). 19

20 4 > ˆ É? S C C $ " " j ç 6 j. F ½ ¾ ALSE < f TRUE u 7 /. / / 5 /. v? u 7 5 ( < f x ) x TR Á  U E < f X FA R LSE 5. w x œ " " / f / f / l, " ": /, "l": l, " ": / l, "":. l v? /, "":? v l l, "": /,.. /. 5 / f <? v. l 4 5, "S":... /. 5 > f <? v. l 4 5. xl, œ l 5 5 x, >? v. f < > (.. v l, w "") l, u 7? v l f u A u 7 - (w. 5 5 > l 4. < f 5 ) 4. z ž 3 Lw-lvl l ~ ~ Š } R f <. / < f 5 5 w f < < f 5 l 4. 6 x 5. / : 6. l 4 w- lv? l 4 / 5 > > 5. ; H.. > 5 5 : (x,) l(x,) x(x,,ll,...) (x0,0,x1,1) w(x0,0,x1,1, l30, ) l(,) l() l(vx) l(l æ.j) (x1,1,x,) l(x,) l(x,,l) l() x(,v) u(x) l(, "",...) ( )., x ll (, x, ); : l(x,,""); x(x,,) l f ( ß x å 0j, Þ å 0) ( ß x1, j Þ 1). ( ß x å 0j, Þ å 0) f, j ( ß x1, j Þ 1) f 1, j f 3; l l l f f f f l f l 0 w à z x l v $ l.j ( 5) l l f j, j,, j l x1, j x, j 1, j, vl k k, x l ( x, j ) l v $ l l ll - l x ( 1) j, l f ( ) j, ( 3) j, ( 4) ; v ( l) v $ ( ) k- k 0 w x ß x- x ll l l ( ß xj, Þ ) f k k ; ( "") ( "l") l (...) ; f ( "") W N / l l x / / l w x (x, œ, x (...)), w. < f 5 5 x (). 5 f <. >. u 7 > 5 5 > l 4 qu / - 5 TX. X F. x > /, x (x, œ, x (U  k[37]v (1, 1+^{- l *(T- )}))) w / 6, 5 /, < fl 4 w 5 qu 7 5 / 5 f <. 5 (x è, é ): 0 S Uk 37 ê ë 1ì 1 ð ñ ò ó T í î ï

21 4 X 5 " ˆ, " k " k $ " " T 5 l x /. 5? v. w 5 < f 5 5 u A A u (). w < f 5 5.x (); < f. x > / 5 l 4? vl 4 f < ô R ( /. v? u 7 l 4 > / V j Rqu A ): > x (x, œ,.x (u A A u (R Á ^, l (R Á qu A )))) w / 6 5 / / 5 f <. 5 (x, 6 ): R õ T / 6 5. > l 4, w 5 > < f < fl 4 w: > x (x, œ,.x (u A A u (R^, l (u A (Rqu A,3))))) w w. u 7 5 : R õ Fl 4, w. R 5 l 4 (. > > l 4 5? v 5 5 ): > x (x, œ,.x (u A A u ( l(r Á )^, l (u A (Rqu A,3))))) 4. z 4 G } { } } ~ ô R I lw-lv? l / l, / f / / v? w / /. T 6 / f / fu 7 ( wk f ll), w fu 7 () / l 6 / /,.. u 7 qu 7 5 / w. / /. >. / < f.. X F. 5 5, l 5. 5 u 7? v 5 : > ( " œ llw") w. w l 4 u 7 qu 7 5 / w l 4 w k v. u 7 5. T / /. >., > f < > v?? v. l 4 < f 5 5. T x u 7? v f <. / /. >. 5. w? I w > < fl 4 w 5 > u 7 l 4 5. j x l f l x j f ( 0 l f -j f j, 0.5 j, 1 -j f ) f f k k (..: "", j "lu", j... f l l()) f, x j, : "", j "l", j "7", j "", j "u" "]" ( x lk lk ) ; f "", x lu ( l z f x l f l ; f ll v l f, x j, x.x, j, x j, x.l, j lj, x.l, j - j, x.u l l f l ; f x : l.x, j l.l, j l.l, j l.u l l f x ( 0: l, j 1: l j, : l j, 3: l l ); f x : f.x, j f.l, j f.l, j f.u 1

22 0 " " l l lw fl fw k l xx x l f x ( 0: ll l x j, 1: z l, j : l x j, 3: l) l f l j, ( 1: l j, : j, 3: j, 4:, j 5: l, j 6: w) j, f ( "0" "9") f lj,, x j, f k k j, f, x l"44" ff l u ( l f l f 4 u ( lu ( l x f f f f (, lf,, ), j f l lu ( (5.1, 4.1, 4.1,.1) f f (,) x f l lu ( j, l lu ( ( f. 4.1.). l ( f. 4.1.) l f l, j 1 5 j, l "" à z f, x f f j, "": ) q j, "":, x l f f k k- k k, x f f f f ; f k1 lu ( f l f k- k x f f f l f x ( f l-0.5) f xx"" ß x- x ( fu ( l j x(1,...)) f x"" Þ - x ( fu ( l j x(,...))

23 / / / G 6 ö 5 S H G F l F l ø H w w R 3 Ev? f /, / l l f / l f < < f. R w. / l 4 5 l 4. A w. 5 f < < f 5 5 v? 5 / k v w. Sv?. l 4 5. / k v 5. / 5 l 4 f < R. T 6.. /. l 4 5 > 5 > >. R. A 5 x u 7? v f < 5. k, w /, fllw S URL: / :/ U U /.j V./ U / U U / ACKAGES. l. A k l, : A u l v l u A vvl5 l qu 7 > ;? v. 5 l 4, 5 l 4.. / l 4 ( 5. v w. w ) ; l l l w x-ff ; u 7 v? v? l l 6 ; lf ; > -. 5 l 4 ( >. > 5 w. w ). B J K. L 6 ( / :/ U U / l /.lu 7.. / U ~j V l 6 U /. l) v? l / k: > 5 / 5 f < > l 4 u 7. qu 7 5 ( 5 l 4 /. f < Cl 4 l 4 W 5 f < < f / 5 ) l 4 z > l 4 / ; l fu 7 lz f l ; l f l / u 7 ; l f -l / u 7 ; l / u 7 f l / (,,...) l 4 < f / > u 7.. l l w v A u l A I u 7 R ( / / 51-63) v? xll u 7 l l w R. l 6 / v? w k f /. T fv? l fu 7 / k: l l v v ll l X F. x > /, < f w v? w? v. x f l f x: > x <- 1:5 > œ <- (5) > l( œ ~x) Cll: l (f A ul œ ~ x) Cff : 5. > l 4 ; 5. l 4 5. > l 4 ; l 6 f? v / f l; l-l l; l f fu 7. 5 w < f? v.? v 5, 5 w w

24 7 / Á ½ (I) x A < f. 5 < f R,. u 7 f < l ( œ ~x ) 5 / 5 5 V j : 4 > œ l <- l ( œ ~x ) f w / œ l, / l 6 wll / v? u 7 l 6. Sv? l fu 7 llw u. / 6. l 4? v l 4 > l 4, > 5 f < 5 u A œ () / 6 5. u 7 f < > l 4 < f 5 /. u 7. ( l 4,...), u A l() / l 6 u 7 l, () / l 6? vlu 7 / l, f() / l 6? v w /. > u A œ ( œ l) Cll: l(fu A l œ ~ x) Á Ru A l: Cff : E S. E vlu A ù (> ) (I ) x Ru A l : f f Mu A l l R-Squ A : , Aju A R-qu A : F- : f f, -v lu A : > ul(l) > (l) > f( œ l) (I ) x I 6 fu 7 l? vlu 7 u 7 qu 7 /, f, /? vlu 7 w l f w : > <- f( œ l)[1] > <- f( œ l)[] > w º <- (11, 13, 18) > + *w [1] T l l u 7 l f l 6, w fu 7 (); f, fu 7 6 w 6 V j R. > ( œ l) [1] "ff " "u A l" "ff " " k" [5] "f.vlu A " "" "q" "f.u A l" [9] "x lv l" "ll" " " " l"

25 5 û ü ý þ ü ÿ é œ é é œ 6. > (u A œ ( œ l)) [1] "ll" " " "u A l" [5] " " "f" ".qu A " [9] "f " "v.u A l" T l 4 > 5 > 6 x. 5 < fl 4 w 5 w 6 : > u A œ ( œ l)[".qu A "] $.qu A [1] "ff " "j..qu A " 5 Fu 7 l k 6 - l l 6 w R: ll 6 f (l ) ll fu 7. A fu 7 l / ll 6 f f ~ l w l 6 / l f f w /. T. >. /. w. > 6 > l 4 6 v?. /. u 7. > 5 5. v? ff f f + : v? ff w * l + +: l œ (, ) / l 4 5 > l 4 f < /. ^ 5 l 4 l / + ++: +:+ : T ff f -. > v? f < < f f <, < f + ++:+ :, œ ~x -1 < f. 0+ œ ~x ) v? l 4,.. (+ +)^ 5 l 4 ( l +:. ) x > / : (+ +)^ -: 5 l u 7. 5 (. < f. œ ~x +0, W / f R v? fu 7 l ff v? ll x /. F x / l, fu 7 l œ ~x1+x f l β è 1 x1 + βú è x + α, (f / + wu 7 l v? u 7 l ) β(x è 1 + è x) + α. T l 4. > /. 5 5 < f. >, w 5 < f 5 5 I(): < f. > œ ~I(x 1+x ) f < 5 > l 4 β(x è 1 + x õ ) + α. T fllw l l / k w w. è k lq v l l fu D ý l l ( F, j S #, j 8 Wl x, j, j B l j, K l -S # j,...) Ex l l Tu ( k é f : l l u ( l v $ l fu ( - A / k u 7 l 6 : > l œ ()

26 ?? > 6 / ˆ W < < 6 T x F l F u w R 6 6. z 1 L } ~ } l xu ~ Ž A v? f R / f w w / ll-w u 7 / l / / l 6 f l 6 w wll xu 7 u 7 v? l 6. L fw x / l. Su 7 / / w v?? v. x, 5 < f. l 4 > 5 f < x w? vl 4, w w 5? v vl ? v., l 4 1. W < f..? v. f < > 5 5 x: > œ <- u A (l (x)) > f ( 1:l (x )) f (x [] ) œ [] <- 0 l œ [] <- 1 Sv? l u 7 xu 7 f 6 / l w : > f ( 1:l (x )) > { > œ [] < > } > f (x[] ) > { > œ [] < > } A / l xu 7 u 7 l u 7 : > º wl ( œ fu A > A u ) > {... > } Tl 4, 5 R /.. > w. 5 5 < f v? 5 I < f. > 5 5 > w x 5 I 5 < fl 4 w 5 x > /, w w 5 > / < f.. < f < f. 5 /, < f, < f 5 > 5 / 5 >. v l. T f / / ww w. l œ u A ( x((1,,3), 3, 1,)) # ww f( 1:3) { f (1) { fl <- "Swl. "; <- "wllw" } f () { fl <- "W. "; <- "w" } f (3) { fl <- "Du A. "; <- "u A k" } <-. l(fl) # l ( $V ¼ 1, $V ¼, œ "l") l( ) # l } T # /, R x l. N.. 5. k v "". u 7 5 fl 5 < f 5 5. l() 5? v. f. T > > 5 l 5 / l 4. 6 / 6. A? v. 5 f /.. >? v 5 :

27 / / 5 7 > 7 < 7 5 ~ W l œ u A ( x((1,,3), 3, 1,)) # ww <- ("w º llw º ", "w º ", "u A k") fl <- ("Sw º l. ", "W. ", "D Ê A u. ") f( 1:3) { <-. l(fl[]) # l ( $V1, $V, œ "l") l( []) # l } T / wll wk l 6 f fl *. l wk f R; f 6, u 7 wk 6, / f 6 / / (f x / l: fl <- "C:/ /Swl. "). If / w fl M 6.R, wll ll / : > u A ("C:/ /M š œ.r Á "). l 4 5 w / /. /. / -w 5 > 5 5. W 5 w. N u 7 u 6 l l (/ U ) kl (\ ), v? Ww. 6. z W Š ~ Š u w ¹ fu Ž W v? f wk f R w fu 7 w u 7 v? w. T ll 6 w / U w fu 7, 6 wll v? / 6 fu 7 R. W u 7 w fu 7 llw u 7 ff, flx l, l f R. L k v? x / l f fl, / l. If w w l l 6 w 6 /, 6 < f 5 5 V j : œ fu A <- fu A (S, ½ F) { <-. l(f) l ( $V ¼ 1, $V ¼ ) l(s) } T, w, w l, / l, f x / l œ fu A ("wllw", "Swl. "). T w / v? u 7 /, w / : > l œ u A ( x ((1,,3), 3, 1,)) > œ fu A ("wllw", "Swl. ") > œ fu A ("w º ", "W. ") > œ fu A ("u A k", "D Ê A u. ") A 5 x > /,. < f 5 5. / > / w / u >. - > / 5 f <? v. x. T 5 qu 7. l 4. 5 > 5.? v 5 w / u 7 - u 7 f lw ; / / 6 u 7 f v?. T f / x / l z f x w fu 7 l ; x /? v l ( / u 7 l wll v? (,...) x). A u. 5 < f. >. w w 5 5. u x 5.? vl 4 u 5 < f 5 5 l () w? v. 5 f < u A () (?u A < f. >. 5? v ) : u 7 l w l 6 w 1. T /? vlu 7 f x x l w fll 6 fu 5 A u ().

28 @ < < 7 5 / À 5 <- fu A (x) { <- l (x ) l <- x f ( 1:) { A u <- l (u A f(1, 0, )) l[] <- x[u A ] } A u ( l) } 8 Tu 7,, w fw, l v? l 6 / l l f, / f / w R. T < f l 4 5 < f 5 5 > / f < > /. >., < f. 5 5 > 5 : <- fu A (x, 500) { M <- u A ( ) f ( 1: ) M[] <- ( (x)) (v (M š )) } W N? vlu 7 fu 7 l f u 7, f w f w 500 é / l. T w fllw wll u 7 v? ff : > (x ) > (x, 500) If w w >. f <. / 5, w 5, < f. x > / : > (x, 5000) T f < f < u 7? vl 4 5 f < 5 5 f < < f 5 5, f < u 7.,? v. f < 5 < f x f < 6 >. T l x / l f fu 7 / l 6 l, llu 7 wll flx l f R. C w w 6 v? u 7 f l l: Rk l f : N 1 N x / 1 N K T > l 4 w l 4 5 / / >, /. u 7. f < < f. W w 5, 5 fu 5, > > l 4 w. /. w. 5 5 l 4 5 >. 5 / l N 0 ( 6 / K f k qu 7 l 1? vlu 7 wll k fu 7 l ); u 7 l wll / l 6 / l f u 7 w /. W wll / llw / l 6 l 6 u 7 l / ( fu 7 l ll u 7 l wll / l ). T fu 7 lw u 7 l l 6 f Rk l. k <- fu A (z,, K1, 100, f0, ) { N <- A u ( +1) N[1] <- z f ( 1: ) À N[+1] <- À N[]*x (*(1 - À N[]/K )) T <- 0: l (T, À N, œ "l", xl (f, )) }

29 T 6 u 7 lf w : 9 > l œ u A ( x (1:3, 3, 1)) > k(0.1, 1); l(" 1") > k(0.1, ); l(" ") > k(0.1, 3); l(" 3")

30 / J / / / S U 4 S 4 W S S U 7 H w G x f w R? 30 T f R ll v? u 7 v? l / ( R Dv? l / C T ): R Dv? l 4 / > 5 C. T > A I 5. u 7 5 R. :/ U U / /. j V.. / U / U > 5 l 4 / U R- 5.. / f <. If u 7 ll l? v f R (1.1.1), u 7 wll f 6 RHME/ U / U u 7 l/ (RHME / w R ll), fl DF f, lu 7 A I u 7 R, f u 7 l T R Rf Ix (f. / f) l ll fu 7 f R. T R-F X AQ? v? v. 5. l 4 5. u 7 5 R: :/ U U / /. j V.. / U / U X F AQ/ U R-F X AQ. > l F 6 v? l / f R: Ik R R: Fu 7 H 6. / :/ U U /.- / j V./ U / U l/ U f98- / / / U / /. l. T... u R; u 7. : :/ U U / /. j V.. / U / U > U / >. > l Sv? l v? w u 7 R, f x / l: Al.M.E I u 7 lz l ll R. Uv? f C, S l L 6. / :/ U U / www. l...u 7 k/ U ~ /. Ml B J.H D Al 6 G / U R A I u 7. S l Cu 7 l U f Gu 7 Sl, Au 7 l N l Uv?. :/ U U /. >. 5.u 7.u 7 U / ~j V 5 > / Fll 6, f u 7 R / l, l l: Ik R. & G l R R: lu 7 f l 6 /. I Ju L l f C K u L L l L G L K M L l N S L 5:

31 9 & & 9 & 8 I w x T 5 x 5 < f /.. 5. u 7 5 u 7 > 5. # 6 15 * 16 / 15 5 * 15 j, j, 5-15 j, 5 / : 11, j 5 ; 6 < 14 < 14 < > 14 > 14? 7 [] 13 ^ 15 j, 5 {} 6 ~ 5 l 0 15 v 3 v w x 0 l li 15 xl f 4 lx 8 u 19 l v 15 ux 16 u 16 u 16 uu 16.f 8 v.l 18 v l 19 l x 15 x. 1 x 0 f 6 fu 7 15 l 1 l 3 l 7 l I 5 f 6 19 j lu 18 lu.w 18 l 0 l 8, 15 l 5 l 0 l 8 l 3 l 11 l 0 l 15 l10 15 l 15 ll 8 ll 3 l 5 l. 6 j 16 x 8, 16 l 19 x fl l 3 u l 19 l. 19 x l 5 l qq 19 qql k u 13 q 13.v 9.v 9.fwf 10.l ul 4 v 15 x 13 f l 13 l u k u 0 uf 13 wull 13 wlx 13 v 11 v q 11 qu u 7 l. 18 q 15 l 19 u 16 uu 1 u 15 u 4 uflwl l x 0 l 0 8.l 19 v 15 w 16 w.x 15 w. 15 wl 6 w 10 w.l 10 x

Emigration The movement of individuals out of an area The population decreases

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