DAA04

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2 # plot(x,y, ) plot(dat$shoesize, dat$h, main="relationship b/w shoesize and height, xlab = 'shoesize, ylab='height, pch=19, col='red ) Relationship b/w shoesize and height height shoesize

3 txt = paste("r =", round(cor(dat$shoesize,dat$h), 4)) text(22, 175, txt, cex = 1.5) Relationship b/w shoesize and height height r = shoesize

4 abline: abline(h = mean(dat$h), col='blue'); abline(v = mean(dat$shoesize), col='green'); H V height r = mean height Relationship b/w shoesize and height mean shoesize shoesize

5 abline(lm(dat$h~dat$shoesize), lty=2, lwd=2) Relationship b/w shoesize and height height r = shoesize

6 plot(dat[dat$gender=='f',]$shoesize, dat[dat$gender=='f',]$h, main="relationship b/w shoesize and height", xlab='shoesize', ylab='height', cex.lab=1.5, pch=19, col='blue', xlim=c(20,29), ylim=c(140,190)) Relationship b/w shoesize and height height Female Male shoesize

7 plot(dat[dat$gender=='m',]$shoesize, dat[dat$gender=='m',]$h, main="relationship b/w shoesize and height", xlab='shoesize', ylab='height', cex.lab=1.5, pch=15, col='green', xlim=c(20,29), ylim=c(140,190)) Relationship b/w shoesize and height height Female Male shoesize

8 Relationship b/w shoesize and height height Female Male shoesize

9 plot(dat[dat$gender=='f',]$shoesize, dat[dat$gender=='f',]$h, main="relationship b/w shoesize and height", xlab='shoesize', ylab='height', cex.lab=1.5, pch=19, col='blue', xlim=c(20,29), ylim=c(140,190)) points(dat[dat$gender=='m',]$shoesize,dat[dat$gender=='m',]$h, pch = 15, col = 'green') legend("topleft", c('female','male'), pch =c(19,15), col = c('blue','green'), cex = 1.5) points: lines height Female Male Relationship b/w shoesize and height shoesize

10 dat<-read.csv(" plot(dat, pch=20, col='blue') material price design sales

11 plot(dat.pca, pch = rownames(dat.pca), cex = 1.7, col = 'blue ) > dat.pca writing thesis interview a b c d e f g h i d d writing c b g h i e b c g h i e a a f f e d d e i i a h g b thesis b g ha c c f f e d e d i i a h a h interview c g b g b f f c

15 ( "% " = $ %&' )

16 ! = # $ = $ % & % + $ ( & ( + + $ * & * = + $, &, *,-%! = # $ = $ % & % + $ ( & ( + + $ * & * =. 0 /0 $1 $ 2$

18 ! " # = %&' ( = ) ( + # = ) ( ) ( # %&' ( = (, + # -, + ( # + # - # + + ( 0 + # - 0 = 1 = 1 2 = 1 2 ( 2 # 2( # - 2 = 1 2 ( 2 # = ) ( # # 5 1 = ) ( # ) ( # 2 ( # , ( 2 # - 2 2( # - 2 ( 2 + # - 2

20 ! " = $%&&'( = ()*

21 ! $ "# = &'( ), + =, ), ), +, + =, )+, ) +, + ) +, ), + =, )+, ), +, ), + +, ), + =, )+, ), +! $ "" = &'( ), ) =, )), ), ) =, ) $, ) $ =! $ " = (/0 )

22 : cov(x,y) = cov(y,x) cov(x,x) = var(x) cov(ax, by) = ab*cov(x,y) cov(a+x, b+y) = cov(x,y) cov(x, Y+Z) = cov(x,y)+cov(x,z) cov(σx, ΣY)=ΣΣcov(X,Y)

23 " #$ = &'(( ), + = &',(), +),/( ),/((+) = &',(), +) 0 # 1 0 $ 1 = &',(), +) 0 # 0 $

25 ( "% " = $ %&' ( * +, = $ %&' ) ( /01 = $ %&' " % ", ) 1 /01(", 2) 4 = * + * 8 " % " 2 % 32 ) 1 9 = : " ; +, = : " 9, = : " : ", ; +8 = : " : " : 2 : 2 /01(", 2) < = ;, + ;, 8 )

26 ! " # = % ) *&,- # &'(. 1 ). 1! " # = % &'( ) = % &'( ) = % &'( ) = % &'( ) * &,- # = % &'( ) * & 1 # + % &'( ) * & + 1 1,- # = % &'( ),- 1 # 2,- 1 % &'( * & 1 # +.,- 1 # 2,- 1.,- 1 * & 1 #.,- 1 # ). 1 3! # " = % 3 * & 1 #.3,- 1 # 3! " # = 4 " # &'( # =.4 # ".45, =.4 # ". 4 " #. # =. 1 4 " * & + 1,- 1 # * & 1

29 ( ) = E ( X 1 ) + E ( X 2 ) +!+ E ( X n ) = µ + µ +!+ µ = nµ ( ) = var( X 1 ) + var( X 2 ) +!+ var( X n ) = σ 2 +σ 2 +!+σ 2 = nσ 2 E X 1 + X 2 +!+ X n var X 1 + X 2 +!+ X n ( ) = E X 1 + X 2 +!+ X # n E X var X! " ( ) = var! # " n X 1 + X 2 +!+ X n n $! & = E X $! 1 # &+!+ E X $ n # & = nµ % " n % " n % n = µ $ & = 1 % n var X 2 1 ( ) +!+ 1 n var ( X 2 n) = nσ 2 = σ 2 n 2 n

30 dat<-read.table(" > head(dat) shoesize h gender affil club M psy tetsudo M cs tennis M psy karate M psy tennis F cs tetsudo F psy tennis > summary(dat) shoesize h gender affil club Min. :21.00 Min. :145.0 F:36 cs :35 karate :24 1st Qu.: st Qu.:157.2 M:34 psy:35 tennis :23 Median :24.50 Median :164.0 tetsudo:23 Mean :24.82 Mean : rd Qu.: rd Qu.:170.9 Max. :28.00 Max. :182.3

31 > mean(dat$shoesize) [1] > mean(dat$h) [1] > var(dat$shoesize) [1] > var(dat$h) [1] > cov(dat[,1:2]) shoesize h shoesize h > cor(dat[,1:2]) shoesize h shoesize h

32 )! "# = % &'( ) "* & + & = "* ( + ( + "* "* ) + ) = " % * & + & = "! "# &'( > dat.meter = dat[,1:2]*0.01 > mean(dat.meter$h) [1] > mean(dat$h)*0.01 [1] > mean(dat$h) [1]

33 *! " + $ = & '() * + ', ' + $ &, ' = & + ', ' + $ - 1 =! " + $ '() * '() > dat.h.ext5 = dat$h+5 [1] > mean(dat.h.ext5) [1] > mean(dat$h) [1] > mean(dat$h)+5 [1]

34 *! " + $ = & + ', " = + ' + & - ', $ = - ' =! " +! $ '() * '() > handshoe = dat$h+dat$shoesize > mean(handshoe) [1] > mean(dat$h)+mean(dat$shoesize) [1]

35 ! "# + % =! "# +! % = "! # + % > dat.h.meter.ext5 = dat$h* > mean(dat.h.meter.ext5) [1] > 0.01*mean(dat$h)+0.05 [1]

36 !"# $% = ' $% ' $% ) > var(dat.meter$h) [1] = ' $% $* ) = ' $ ) % * ) = $ ) ' % * ) = $ )!"# % > var(dat$h)*(0.01^2) [1]

37 !"# $ + & = ( $ + & ( $ + & = ( $ + & + + & * = ( $ + * =!"# $ * > var(dat.h.ext5) [1] > var(dat$h) [1]

38 !"# $% + ' = ) $% + ' ) $% + ' + > var(dat.h.meter.ext5) [1] > var(dat$h)*(0.01^2) [1] = ) $% + ' $, + ' + = ) $ % +, + = $ + ) %, + = $ +!"# %

39 !"# $ + & = ( $ + & * + + *, - > var(handshoe) [1] = ( $ + & - 2 $ + & * + + *, + * + + *, - = ( $ - + 2$& + & - + 2$* + 2$*, 2&* + 2&*, + * * + *, + *, - = ( $ - 2$* + + * & - 2&*, + *, - + 2$& 2$*, 2&* + + 2* + *, = ( $ * ( & *, - + 2/01 $, & > var(dat$h)+var(dat$shoesize)+2*cov(dat$h,dat$shoesize) [1]

40 !"# $, $ = ' $$ ' $ ' $ = ' $ ) ' $ ) = *+, $ > cov(dat$h,dat$h) [1] > var(dat$h) [1]

41 !"# $%, '( = * $% * $% '( * '( = * $'%( * $% '( * '( $% + * $% * '( = $'* %( $'* % * ( $'* % * ( + $'* % * ( = $' * %( * % * ( = $' -!"# %, ( > cov(dat.meter$h,dat.meter$shoesize) [1] > (0.01*0.01)*cov(dat$h,dat$shoesize) [1]

42 !"# $ + &, ( + ) = + $ + & + $ + & ( + ) + ( + ) = + $ + & ( + ) + $ + & ( + ) + ( + ) $ + & + + $ + & + ( + ). = + $ + & ( + ) + $ + & + ( + ) + $ + & + ( + ) + + $ + & + ( + ) = + $( + (& + $) + &) $ + + & ( + + ) = $( + (+ & + $+ ) + + &) $( (+ & $+ ) + & + ) = + &) + & + ) =!"# &, ) > cov(dat.h.ext5,dat.ss.ext1) [1] > cov(dat$h,dat$shoesize) [1]

43 !"# $, & + ( = * $ * $ & + ( * & + ( = * $ & + ( * $ & + ( * & + ( $ + * $ * & + (. = * $ & + ( * $ * & + ( * $ * & + ( + * $ * & + ( = * $ & + ( * $ * & + ( = * $& + $( * $ * & + * $ * ( = * $& * $ * & + * $( * $ * ( =!"# $, & +!"# $, ( > cov(dat$h,handshoe) [1] > cov(dat$h,dat$shoesize)+cov(dat$h,dat$h) [1]

44 !"# $1 + $2, )1 + )2 = + $1 + $2 + $1 + $2 )1 + )2 + )1 + )2 = + $1 + $2 )1 + )2 + $1 + $2 + )1 + )2 = + $1)2 + $1)2 + $2)1 + $2)2 + $1 + )1 + + $1 + )2 + + $ $2 + )2 = + $1)1 + $1 + )1 + + $1)2 + $1 + )2 + + $2)1 + $2 + )1 + + $2)2 + $2 + )2 =!"# $1, )1 +!"# $1, )2 +!"# $2, )1 +!"# $2, )2 =..!"# $ / + ) 0 / $ / =..!"# $ / + ) 0 =. 123 $ / +..!"# $ / + $ 0 / / 0 / / 04/ =. 123 $ / +..!"# $ / + $ 0 / / 05/

DAA03

DAA03 par(mfrow=c(1,2)) # figure Dist. of Height for Female Participants Dist. of Height for Male Participants Density 0.00 0.02 0.04 0.06 0.08 Density 0.00 0.02 0.04 0.06 0.08 140 150 160 170 180 190 Height