Plot

•Generic function for plotting of Robjects.

•General Form plot(x, y, …)

•Possible type to be drawn

1.“p”for points

2.“l”for lines

3.“b”for both

4.“c”for the lines part alone of “b”

5.“o”for overplotted

6.“h”for histogram like

7.“s”for stair steps

8.“S”for other steps

9.“n”for no plotting

Pilihan Warna Grafik

•Numeric 1-8 (recycle)

•Character “colorname”(colors())

•Fungsirainbow(…), rgb(…)

•Package “colorspace”, “colourpicker”, "RColorBrewer“

•dll

Ilustrasi

#dasarplot
x <-1:40
y <-rnorm(40,5,1)
plot(x,y,type="p")

plot(x,y,type="o")

plot(x,y,type="n")

plot(x,y,type="p",xlab="Sumbu x",ylab="Sumbu y",
main="Bilangan Acak Normal",col=2,pch=16)

plot(x,y,type="p",xlab="Sumbu x",ylab="Sumbu y",
main="Bilangan Acak Normal",col=rainbow(40),
pch=16,cex=2,xlim=c(0,50),ylim=c(2.5,7.5))
#menambahkanamatan
x1 <-41:50
y1 <-rnorm(10,5,1)
points(x1,y1,cex=2)

#menambahkan garis
x2 <-rep(40.5,20)
y2 <-seq(min(c(y,y1)),max(c(y,y1)),length=20)
lines(x2,y2,col=4,lwd=2,lty=2)
abline(h=mean(y),col="red",lwd=2.5)
abline(a=2,b=1/10,col="maroon3",lwd=2,lty=2)
#menambahkan tanda panah
arrows(x0=30,y0=3.5,x1=40,y1=mean(y)-.1,lwd=2)
#menambahkan tulisan
text(x=29,y=3.3,labels="Titik potong",cex=0.7)
text(x=3,y=7.3,labels="Data awal",cex=0.7)
text(x=46,y=7.3,labels="Data baru",cex=0.7)

Latihan 1

Could you explain what are these programs do for ?

•plot(sin,-pi, 2*pi)

Jawaban: Syntax ini akan menampilkan tabel sin dari nilai -pi sampai 2 kali pi

•plot(table(rpois(100,5)),type=“h”,col=“red”,lwd=1,main=“rpois(100,lambda=5)”)

Jawaban: Syntax ini akan menghasilkan histogram dari tabel rpois

Berikut hasil tabel jika dimasukan dalam R:

plot(sin,-pi, 2*pi)

plot(table(rpois(100,5)),type="h",col="red",lwd=1,main="rpois(100,lambda=5)")

Latihan 2

Create some programs to make the graph below

a1 <- 1:25
a2 <- rnorm(25,4,2)
plot(a1,a2,pch="w",main="W")

Latihan 3

plot(a1,a2,type="n",main="W")
text(a1,a2,labels=paste("w",1:25,sep=""),col=rainbow(25),cex=0.8)

Latihan 4

Create some programs to make the graph below, using 100 observation of 𝑋~𝜒2 (4)

x <- rchisq(100,df=4)
hist(x,freq=FALSE,ylim=c(0,0.2))
curve(dchisq(x,df=4),col=2,lty=2,lwd=2,add=TRUE)

Latihan 5

Create 4 graph in one window from 100 random numbers which follow N(5,1)

windows()
yb<-rnorm(100,5,1)
split.screen(c(2,2))

## [1] 1 2 3 4

screen(3)
boxplot(yb)
title("BoxplotBilangan Acak Normal",cex.main=0.7)
screen(4)
xb<-1:100
plot(xb,yb,type="l",lwd=2,col="blue")
title("LinePlot Bilangan Acak Normal",cex.main=0.7)
screen(2)
hist(yb,freq=FALSE,main=NULL,ylim=c(0,0.5))
x <-yb
curve(dnorm(x,5,1),col="red",lty=2,lwd=2,add=TRUE)
title("Histogram Bilangan Acak Normal",cex.main=0.7)
screen(1)
plot(xb,yb,pch=16,col=rainbow(100))
title("ScatterPlot Bilangan Acak Normal",cex.main=0.7)

Inverse Transform Method

Ide dasar

•0≤𝐹𝑥≤1 sehingga𝑈=𝐹𝑥~𝑈𝑛𝑖𝑓𝑜𝑟𝑚(0,1)

•Jika𝑋=𝐹−1(𝑢)maka𝑋~𝑓(𝑥)

Algoritme

•Tentukanfsk 𝐹𝑥darisebaranyang diinginkan

•Tentukan𝐹−1(𝑥)

•Bangkitkan𝑈~𝑈𝑛𝑖𝑓𝑜𝑟𝑚(0,1)

•Transformasi𝑋=𝐹−1(𝑢)

Keunggulan: bisa digunakan untuk berbagai sebaran(termasuksebarandiskret)

Kesulitan utama: memperolehkebalikandarifungsisebarankumulatif

Latihan 1

•Membangkitkan bilangan acak Eksponensial(lamda)

•X ~ Eksponensial(lamda)

•Algoritma:

•Bangkitkan U, bilangan acak Seragam (0, 1)

•Hitung X = –ln(1 –U) / lamda

•Ulangi berkali-kali sesuai dengan banyaknya bilangan yang diinginkan

#Eksponensial(lambda=3)
set.seed(10)
eks <-function(n,lambda){
U <-runif(n)
X <--log(1-U)/lambda
return(X)
}
yy1 <-eks(1000,3) #inverse transform method
yy2 <-rexp(1000,rate=3) #fungsi bawaan R
par(mfrow=c(1,2))
hist(yy1,main="Exp dari Inverse Transform")
hist(yy2,main="Exp dari fungsi rexp")

Acceptance-Rejection Method

## Latihan 2

Bangkitkan bilangan acak yang memiliki fkp𝑓(y)=3y^2; 0<𝑦<1 menggunakan acceptance-rejection method!

ar <-function(n,x0,x1,f) {
xx <-seq(x0,x1,length=10000)
c<-max(f(xx))
terima <-0;iterasi <-0
hasil <-numeric(n)
while(terima<n) {
x <-runif(1,x0,x1)
y1<-runif(1,0,c)
y2<-f(x)
if(y1<=y2) {
terima <-terima+1
hasil[terima]<-x}
iterasi <-iterasi+1}
list(hasil=hasil,iterasi=iterasi)
}
set.seed(10)
f <-function(x) {3*x^2}
yyy <-ar(100,0,1,f)
yyy

## $hasil
##   [1] 0.8647212 0.7751099 0.8382877 0.7707715 0.5355970 0.8613824 0.2036477
##   [8] 0.7979930 0.7438394 0.3443435 0.9837322 0.6935082 0.6331153 0.8880315
##  [15] 0.7690405 0.6483695 0.8795432 0.9360689 0.7233519 0.7620444 0.9868082
##  [22] 0.8760261 0.7240640 0.8140516 0.5588949 0.8900940 0.7456896 0.8480646
##  [29] 0.8703302 0.8223331 0.8508123 0.7709219 0.8953595 0.5803863 0.5982260
##  [36] 0.9235285 0.7367755 0.6898170 0.8301572 0.9293209 0.9095163 0.5347576
##  [43] 0.3478601 0.8759762 0.7286815 0.8749293 0.6988356 0.8312562 0.5572238
##  [50] 0.6647687 0.7400502 0.9806898 0.3800746 0.7553169 0.5184889 0.8879149
##  [57] 0.9177773 0.8084086 0.8537441 0.4232184 0.7604306 0.3405763 0.3886568
##  [64] 0.4774175 0.5387605 0.9485434 0.7124685 0.9081691 0.9457656 0.7716899
##  [71] 0.6946655 0.5368832 0.8481593 0.8242752 0.5123742 0.3152032 0.9924487
##  [78] 0.9327120 0.9892809 0.6283590 0.5254605 0.8810815 0.5291748 0.5765517
##  [85] 0.7231807 0.8761180 0.3995670 0.8986123 0.9335217 0.7859216 0.7784128
##  [92] 0.6955333 0.9060413 0.9916424 0.4729846 0.9770567 0.9386110 0.9959093
##  [99] 0.8543663 0.8309547
## 
## $iterasi
## [1] 322

#Diagram
par(mfrow=c(1,1))
hist(yyy$hasil, main="f(x)=3*x^2",prob=T)
x <-seq(0, 1, 0.01)
lines(x, f(x), lwd=2, col=4)

Direct Tansformation

Memanfaatkan beberapa fungsi transformasi dari berbagai sebaran yang ada

•Contoh: •Jika X~𝑈0,1menggunakan 𝑌=𝑏−𝑎𝑋+𝑎maka 𝑌~𝑈(𝑎,𝑏) Membangkitkanbilanganacak𝑌~𝑈(3,5)𝑌=2𝑋+3 x <-runif(1000) y <-2*x+3

x <-runif(1000)
y <-2*x+3
y

##    [1] 4.595651 4.168212 3.865580 3.368448 3.685894 3.168929 4.232466 3.471525
##    [9] 3.816635 4.432023 3.654097 3.025882 4.017800 3.645034 4.035468 4.220792
##   [17] 4.369285 4.777494 4.474976 4.379829 3.045420 3.458973 3.489782 4.082726
##   [25] 3.896056 4.563540 3.730657 3.726081 3.958200 3.236057 4.076578 3.582958
##   [33] 4.210074 3.726026 4.420964 3.973593 4.783335 3.698059 4.224458 3.630964
##   [41] 3.646383 3.750261 4.467030 3.371470 3.469069 4.693028 4.894643 4.280374
##   [49] 3.537450 4.790113 4.299423 4.519895 4.965529 3.051509 3.303683 3.906797
##   [57] 3.375193 4.141702 4.796323 3.377092 3.108475 3.419335 4.738254 4.080452
##   [65] 4.969106 4.856840 4.331528 3.915997 4.770318 3.073207 4.697783 4.413223
##   [73] 4.486807 4.246549 4.955789 4.387593 4.726321 3.386577 4.532412 4.993235
##   [81] 3.161616 3.375557 3.197817 4.397423 3.332837 3.218048 3.082443 4.578633
##   [89] 4.594420 4.758882 3.447881 4.580076 4.968844 3.084786 3.672106 3.884082
##   [97] 3.995492 3.071297 4.311110 3.813428 3.714606 3.236832 3.667819 3.942326
##  [105] 4.193309 4.102471 4.973566 4.951496 4.246684 3.942961 3.572900 4.492391
##  [113] 3.137360 3.982451 4.322077 3.751640 3.597455 4.001769 3.725986 4.395659
##  [121] 4.534990 4.707527 3.577784 4.937220 3.147125 3.566941 3.292801 3.264311
##  [129] 3.494709 3.345439 3.539915 3.026146 4.941346 4.853478 3.884387 3.050453
##  [137] 3.522547 3.310321 3.680943 4.031377 4.268245 4.580220 3.257111 3.599641
##  [145] 4.052678 4.027126 4.030312 4.403521 4.642983 4.886053 4.967236 3.922478
##  [153] 3.548622 3.377231 4.786665 4.642731 3.936669 4.018760 4.762696 3.363010
##  [161] 4.971195 4.327953 4.315386 3.614140 3.460296 3.062097 3.050408 3.744086
##  [169] 3.051171 4.354773 3.346706 3.725468 4.769000 4.526478 3.532470 3.834602
##  [177] 3.894296 4.798221 3.986260 3.234679 3.645782 3.086577 4.859232 3.050443
##  [185] 4.969942 3.187620 3.002687 4.369433 3.076397 4.112787 3.715231 3.806230
##  [193] 4.291993 3.315377 3.217174 4.120446 4.365137 3.564720 4.782446 3.341252
##  [201] 3.553095 4.455447 4.548107 3.554820 4.459492 4.290764 3.819135 3.092542
##  [209] 3.480910 3.737291 4.781122 3.456868 4.871115 4.384660 4.821405 3.713408
##  [217] 3.901560 3.308500 4.649646 4.521387 4.015555 4.857621 4.593943 4.782217
##  [225] 3.760751 3.087453 3.952728 4.439325 4.686256 4.284194 3.168267 4.869526
##  [233] 3.315281 4.150718 3.981427 4.437502 4.878076 4.042365 3.447635 4.644413
##  [241] 4.685966 4.115470 4.216081 3.375351 3.935933 4.295949 3.366233 3.346195
##  [249] 4.363890 3.628338 4.835012 3.815494 4.027718 4.390839 3.196155 4.508844
##  [257] 4.755563 3.952660 3.127663 3.486304 3.011791 4.950004 3.479238 4.126829
##  [265] 3.773781 3.515035 3.663339 3.868293 3.731539 4.564783 3.968643 4.505326
##  [273] 4.624903 3.351114 3.718886 3.149059 3.466030 3.876820 4.920182 3.604485
##  [281] 3.931436 3.851931 4.731431 4.749438 3.984699 3.443737 3.135317 4.509235
##  [289] 4.993079 3.632973 3.457061 4.919519 4.713212 4.893936 3.974407 3.498106
##  [297] 3.589225 3.288184 3.054149 4.625688 4.686465 3.231876 3.780065 4.845464
##  [305] 3.211458 3.840869 4.788149 4.815876 3.847575 4.974608 4.638219 4.271901
##  [313] 3.030907 4.954875 4.802814 3.227271 3.668571 3.904605 3.798721 4.781529
##  [321] 4.815544 3.656805 4.598357 4.052858 3.142921 3.067473 3.537728 4.267681
##  [329] 4.084502 4.700150 3.065181 4.197046 3.106003 4.154466 4.180102 4.051311
##  [337] 4.643063 3.554346 3.740491 4.782274 4.801987 4.384187 4.045663 3.493019
##  [345] 3.027529 3.214891 3.601037 3.660628 4.720207 4.644854 3.807896 4.375866
##  [353] 3.363114 3.900362 3.385230 4.943052 4.615413 4.420358 3.496498 4.019566
##  [361] 4.137517 3.663136 3.873324 3.399394 4.572513 4.569445 4.909801 4.239187
##  [369] 4.785013 3.465037 4.023484 4.060217 4.902524 4.148773 4.742039 4.878590
##  [377] 3.160793 4.536739 4.124574 3.323276 4.614337 3.178618 3.973487 4.737529
##  [385] 4.659949 4.963217 4.741565 3.446988 4.306195 3.833228 4.293684 3.338345
##  [393] 3.801240 3.163310 4.385805 4.209765 3.183583 4.442544 3.905830 4.058087
##  [401] 3.526571 3.962961 4.502033 3.884139 3.765793 4.085434 4.469945 3.784377
##  [409] 4.906737 3.246651 3.016395 3.021085 3.177066 4.960241 4.770640 3.963674
##  [417] 4.804280 4.375579 3.952479 4.962703 3.493305 4.968655 3.146102 3.376815
##  [425] 4.804378 3.767460 4.760473 3.138694 4.612437 4.526004 3.021634 3.744841
##  [433] 3.163980 3.631048 3.165785 3.683686 3.283250 3.737113 3.346487 4.695052
##  [441] 3.557584 3.530328 4.699201 4.113038 4.353739 4.803387 3.232695 4.243600
##  [449] 4.571575 4.263495 3.076344 3.388704 3.556719 3.713973 3.199713 3.681986
##  [457] 3.754938 3.085458 3.484692 4.643762 3.008197 4.676406 4.590641 3.282191
##  [465] 4.241101 3.690541 3.953717 4.524971 4.645850 3.423704 3.826890 4.164745
##  [473] 4.679355 4.809141 3.054438 3.643403 3.292472 3.574535 4.626748 3.457478
##  [481] 4.999602 4.428614 4.541616 4.046089 3.835642 4.207878 4.142799 3.668253
##  [489] 4.846237 3.173952 3.657645 3.948126 4.286523 3.747317 4.513459 4.484815
##  [497] 4.649410 4.672014 4.864272 4.989662 4.753757 3.485692 4.179418 4.599828
##  [505] 3.195160 4.490126 3.949943 4.482142 4.679428 3.352180 3.314449 3.395827
##  [513] 3.452662 3.902255 4.918844 3.761364 3.234991 3.361696 3.676700 3.658317
##  [521] 3.116457 3.073477 3.779114 4.891029 3.558328 3.567479 4.490951 3.030119
##  [529] 3.523791 4.140343 3.589872 4.926635 4.658660 4.447436 3.915916 3.447092
##  [537] 3.708353 3.577917 3.860111 3.520046 4.217823 3.469950 4.186825 4.009659
##  [545] 4.960761 4.663596 3.197030 3.339365 4.432129 4.634356 4.925802 4.272933
##  [553] 4.168626 4.954075 4.623677 4.177371 3.367073 3.954232 3.956338 4.033501
##  [561] 3.174859 4.450297 4.248931 3.222602 4.837201 4.414659 3.225810 3.461793
##  [569] 3.838243 3.014711 3.120554 3.293754 4.395576 4.572241 3.675333 3.467193
##  [577] 3.087367 3.367471 4.986978 4.200105 4.381540 3.404015 3.500395 3.453344
##  [585] 3.375089 3.230314 3.083384 4.929557 4.454521 3.762533 3.383604 4.935798
##  [593] 4.531758 3.546295 3.975483 3.449228 3.906684 3.617831 4.078245 3.133104
##  [601] 3.498497 3.095699 3.960723 3.293161 3.574989 3.776852 4.983567 4.034965
##  [609] 3.928389 3.297234 3.411277 4.795526 3.774142 3.597192 4.104445 3.426783
##  [617] 3.288198 4.798747 4.536796 4.074385 4.253072 3.400720 3.727104 4.490435
##  [625] 4.800692 3.538431 3.310350 3.387320 3.610006 4.521122 3.867236 4.123544
##  [633] 3.762143 3.619385 4.957283 4.589340 4.632362 3.734138 4.107727 3.190931
##  [641] 3.840473 3.063554 3.419761 4.101204 4.480505 3.335551 3.736374 4.556347
##  [649] 3.083326 4.414239 4.206617 3.770268 3.359301 3.676023 3.569652 3.155290
##  [657] 3.386589 3.570812 4.590909 4.524650 3.423634 3.188275 4.670851 4.008845
##  [665] 4.993068 3.570497 3.892304 4.282780 3.915558 3.453340 3.178928 3.771504
##  [673] 4.342322 3.476966 4.663507 3.074694 3.809217 3.975703 4.066113 4.942717
##  [681] 3.717558 4.438593 4.261515 4.868353 4.209460 4.378453 4.997412 4.186681
##  [689] 3.730297 3.844101 4.712017 4.604720 3.465583 4.094532 4.045095 4.956168
##  [697] 4.360094 3.730014 3.709412 3.571868 4.166459 3.285475 4.802813 3.410562
##  [705] 3.103771 4.930671 3.433312 3.629858 4.390588 3.646413 4.776634 3.443542
##  [713] 4.239717 3.058778 4.166561 4.556808 4.360835 3.151751 3.056866 4.371048
##  [721] 4.784433 4.894728 4.304202 4.876747 3.975111 3.056864 3.105490 4.607493
##  [729] 4.348202 3.825592 3.489664 4.047145 4.840111 4.381992 3.088879 4.344586
##  [737] 4.152450 4.382661 3.482083 3.152124 3.418771 3.672935 3.523344 4.098084
##  [745] 4.917674 3.125032 3.023792 3.352062 3.106859 4.448480 4.486721 4.953225
##  [753] 4.633411 3.515097 4.549516 3.502145 3.820571 3.471089 3.486448 4.379599
##  [761] 4.387598 3.217931 4.462260 3.665351 3.095538 3.702529 3.736679 4.759911
##  [769] 4.387971 3.180551 3.089623 4.191134 3.836067 3.263177 3.690190 3.049972
##  [777] 3.234589 4.124177 4.349138 4.343698 4.164451 4.373908 3.226232 3.741214
##  [785] 4.557165 4.857548 3.549154 3.417801 3.118530 3.808807 3.319413 4.696115
##  [793] 4.725716 4.473617 4.640932 4.620981 3.439493 4.008431 3.634191 3.146057
##  [801] 3.258180 3.486712 3.668043 3.569197 3.401142 3.357883 3.547849 4.657281
##  [809] 3.438995 3.970205 3.372129 4.077384 3.971496 4.567775 3.760992 4.005694
##  [817] 3.002594 3.857844 3.044588 3.937043 3.963014 4.170063 3.719193 3.152707
##  [825] 3.845376 3.627579 3.129907 3.438821 3.372375 4.916585 3.388299 4.098514
##  [833] 4.419020 4.473513 3.850693 3.426815 3.745070 3.338124 3.591310 3.336311
##  [841] 3.710282 4.104672 4.530202 4.209216 4.772064 4.567791 4.763648 3.686085
##  [849] 4.497901 4.330342 4.760206 3.460885 4.149536 3.826504 4.382265 4.910413
##  [857] 3.051461 4.665443 4.326053 3.222537 4.759395 3.248831 3.148112 4.744803
##  [865] 3.713805 3.605298 3.543323 3.536265 4.250934 4.321638 4.728602 3.304895
##  [873] 3.684716 4.978813 4.984080 4.507777 4.753503 4.254134 4.264930 3.120719
##  [881] 4.351738 3.016930 3.753487 3.608348 4.839784 3.526077 3.681608 3.255639
##  [889] 3.929795 3.787575 4.254725 3.102797 4.764022 3.313598 3.798330 3.102817
##  [897] 4.623546 4.145303 3.625152 4.554414 3.466996 4.238963 3.234733 3.263493
##  [905] 3.590617 4.564968 4.095003 3.331838 4.812556 4.309262 4.851002 3.554039
##  [913] 4.196659 3.473372 4.585330 4.985140 3.462578 4.505041 4.203711 4.297979
##  [921] 3.393737 4.094990 4.170738 4.369566 3.478194 4.223525 4.522832 3.555257
##  [929] 3.654607 4.375362 3.735138 3.017994 4.395007 3.065458 4.078626 3.762759
##  [937] 4.542933 3.843434 3.780590 4.038624 4.410163 3.913584 3.929607 4.931056
##  [945] 3.455814 4.747601 3.118741 4.301843 4.721172 3.875542 3.019229 3.604486
##  [953] 4.163448 3.752417 4.555575 3.242685 3.033581 3.864228 4.397758 3.879327
##  [961] 3.962973 3.970135 3.250362 3.526578 4.470872 3.082856 3.467550 3.220450
##  [969] 3.699188 3.228758 3.501766 3.592546 4.632085 4.836780 4.624836 4.725689
##  [977] 4.303669 4.760358 3.353661 4.767130 4.544235 4.009297 4.379276 4.318141
##  [985] 3.982503 3.481575 4.443483 4.440020 4.550645 3.715663 3.621288 4.462299
##  [993] 3.463366 3.380312 3.999186 4.768694 4.579657 4.360228 4.732703 3.965204

Pembangkitan Bilangan Acak untuk Model Regresi

set.seed(123)
X1 <-runif(25,10,25)
X2 <-runif(25,90,200)
Y <-10 + 2.3*X1 + 0.7*X2 + rnorm(25,0,9)
model1 <-lm(Y~X1)
summary(model1)

## 
## Call:
## lm(formula = Y ~ X1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.991 -17.738  -2.632  17.896  33.171 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  131.846     19.741   6.679 8.18e-07 ***
## X1             1.049      1.015   1.033    0.312    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.42 on 23 degrees of freedom
## Multiple R-squared:  0.04433,    Adjusted R-squared:  0.002775 
## F-statistic: 1.067 on 1 and 23 DF,  p-value: 0.3124

model2 <-lm(Y~X2)
summary(model2)

## 
## Call:
## lm(formula = Y ~ X2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -31.804  -4.850  -1.606  10.011  20.569 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 70.83913   13.86879   5.108 3.57e-05 ***
## X2           0.58213    0.09767   5.960 4.46e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.38 on 23 degrees of freedom
## Multiple R-squared:  0.607,  Adjusted R-squared:  0.5899 
## F-statistic: 35.52 on 1 and 23 DF,  p-value: 4.464e-06

model3 <-lm(Y~X1+X2)
summary(model3)

## 
## Call:
## lm(formula = Y ~ X1 + X2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.8291  -4.5994  -0.4576   5.0602  20.5307 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.62881   13.40229  -0.047    0.963    
## X1           2.72951    0.40701   6.706 9.67e-07 ***
## X2           0.72459    0.06105  11.869 4.91e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.427 on 22 degrees of freedom
## Multiple R-squared:  0.8709, Adjusted R-squared:  0.8592 
## F-statistic: 74.21 on 2 and 22 DF,  p-value: 1.66e-10

model4 <-lm(Y~X1:X2)
summary(model4)

## 
## Call:
## lm(formula = Y ~ X1:X2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -20.929  -7.009  -1.430   2.856  37.374 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 80.645221  10.481428   7.694 8.32e-08 ***
## X1:X2        0.027491   0.003929   6.997 3.94e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.97 on 23 degrees of freedom
## Multiple R-squared:  0.6804, Adjusted R-squared:  0.6665 
## F-statistic: 48.96 on 1 and 23 DF,  p-value: 3.942e-07

model5 <-lm(Y~X1*X2)
summary(model5)

## 
## Call:
## lm(formula = Y ~ X1 * X2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.4425  -4.5808  -0.6702   4.6431  20.2409 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 11.625896  37.941991   0.306   0.7623  
## X1           2.063573   1.967526   1.049   0.3062  
## X2           0.635870   0.263687   2.411   0.0251 *
## X1:X2        0.004905   0.014165   0.346   0.7326  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.6 on 21 degrees of freedom
## Multiple R-squared:  0.8716, Adjusted R-squared:  0.8533 
## F-statistic: 47.53 on 3 and 21 DF,  p-value: 1.548e-09

R2 <-matrix(c(summary(model1)$r.squared,summary(model1)$adj.r.squared,summary(model2)$r.squared,summary(model2)$adj.r.squared,summary(model3)$r.squared,summary(model3)$adj.r.squared,summary(model4)$r.squared,summary(model4)$adj.r.squared,summary(model5)$r.squared,summary(model5)$adj.r.squared),5,byrow=T)
colnames(R2)<-c("R2","R2.adj"); R2*100

##             R2     R2.adj
## [1,]  4.432592  0.2774876
## [2,] 60.699195 58.9904640
## [3,] 87.090357 85.9167529
## [4,] 68.036265 66.6465370
## [5,] 87.163648 85.3298839

coef(model3)

## (Intercept)          X1          X2 
##  -0.6288095   2.7295126   0.7245911

confint(model3)

##                   2.5 %     97.5 %
## (Intercept) -28.4234482 27.1658292
## X1            1.8854322  3.5735929
## X2            0.5979779  0.8512044

cbind(coef(model3),confint(model3))

##                              2.5 %     97.5 %
## (Intercept) -0.6288095 -28.4234482 27.1658292
## X1           2.7295126   1.8854322  3.5735929
## X2           0.7245911   0.5979779  0.8512044

anova(model3)

## Analysis of Variance Table
## 
## Response: Y
##           Df  Sum Sq Mean Sq  F value    Pr(>F)    
## X1         1   536.4   536.4   7.5538   0.01173 *  
## X2         1 10002.4 10002.4 140.8614 4.911e-11 ***
## Residuals 22  1562.2    71.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

par(mfrow=c(2,2)); plot(model3)

Demikian, Terima Kasih