ashish mahabal aybi199, caltech 7 may 2009george/aybi199/old... · 2009. 5. 8. · ashish mahabal...
TRANSCRIPT
![Page 1: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/1.jpg)
R2
AshishMahabalAyBi199,Caltech
7May2009
![Page 2: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/2.jpg)
Quickrecap
• ?Togethelp• #forcomments• ‐>or<‐(or=)forassignments• ==forcomparison
• Concatenatewithc #x=c(a,b)• seqtocreatesequence #z=seq(‐30,30)• is.na(x)tolookfornotavailableness
![Page 3: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/3.jpg)
• summary(x)• data(x)• read.table(file)• save(file)• source(file) #input
• sink(file) #output
![Page 4: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/4.jpg)
CommonrouSnes
• length(a) #lengthofvector• max(a) #similarlymin,mean
• sort(a),orsort(a,decreasing=T)• unique(a)• duplicated(a) #returnsalogicalarray!
![Page 5: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/5.jpg)
TomShort’sRrefcardhWp://www.rpad.org/Rpad/R‐refcard.pdf
![Page 6: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/6.jpg)
Example
• a=rnorm(100,mean=5,sd=1)• b=rnorm(200,mean=5,sd=1)
• c=c(100*a,100*b)• length(c)• c
![Page 7: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/7.jpg)
![Page 8: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/8.jpg)
• d=as.integer(c)• d• mean(d);max(d);min(d);sd(d)
![Page 9: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/9.jpg)
• unique(d)• duplicated(d)• plot(duplicated(d)) #coercion
![Page 10: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/10.jpg)
• duplicated(unique(d))• five(d) #whatsthefive‐of‐d• ?five #nothing?Doyouknowfive?• ??five #atleastsomethingthathasfive?• fivenum(d) #ah,soitsfivenum.I’lltakethat• ?fivenum #whatisitBTW?…minimum,lower‐hinge,median,upper‐hinge,maximum…
![Page 11: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/11.jpg)
• fivenum(x,na.rm=TRUE) #opSons!• g=d• g[duplicated(d)]<‐NA• fivenum(d)– [1]264.0425.5483.5561.5742.0
• fivenum(g,na.rm=TRUE)– [1]264.0419.5492.0571.5742.0
![Page 12: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/12.jpg)
• boxplot.stats(x,coef=1.5,do.conf=TRUE,do.out=TRUE)
• quanSle,range,bxp
![Page 13: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/13.jpg)
• whichselectsindices:• a=which(d<500) #returnsindices• a=d[which(d<500)] #returnstheelements
• which.max(d) #indexofmaxelement
![Page 14: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/14.jpg)
• match(x,y) #elementsofxiny,elseNA• merge(a,b) #usingcommoncolumns/rows
![Page 15: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/15.jpg)
choose(n,k) #combinaSonsofkfromnchoose(5,3)returns10
sample(x,size) #resamplessizeelementsfromx(withtheopSonofreplacement)
![Page 16: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/16.jpg)
• >sample(cards,5)[1]"S9""H4""D5""C3""C9"
• >sample(cards,2)
[1]"H10""D10"
![Page 17: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/17.jpg)
• Conj(4+3i)• fft(x)• solve(a) #matrixinverseofa
• solve(a,b) #solvesa%*%x=bforx
![Page 18: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/18.jpg)
![Page 19: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/19.jpg)
![Page 20: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/20.jpg)
![Page 21: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/21.jpg)
Stringsanddate/Sme
• paste(…) #concatenaSngvectors• substr(x,start,stop) #canalsoassign• grep(paWern,x)• as.Date(s)
![Page 22: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/22.jpg)
Graphicsdevices
• x11(),windows()• postscript(file)• png,pdf,jpeg,…
![Page 23: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/23.jpg)
NextfewslidesfromhWp://scc.stat.ucla.edu/mini‐courses
![Page 24: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/24.jpg)
![Page 25: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/25.jpg)
![Page 26: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/26.jpg)
![Page 27: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/27.jpg)
![Page 28: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/28.jpg)
Replacerbyd,p,qtogetprobdensity,cumulaSveprobdensityandthevalueofthequanSle
![Page 29: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/29.jpg)
• pnorm(4,5,1) – #howmanybelow4formean5andsd1(asafracSon)
– [1]0.1586553• pnorm(6,5,1)–pnorm(4,5,1)– #between4and6– [1]0.6826895
• qnorm(0.9,5,1)– #90thpercenSle?– [1]6.281552
![Page 30: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/30.jpg)
GeometricdistribuSon
• dgeom(4,0.35)– Probabilityoffirstsuccessonthe5thtrialgiventhattheprobabilityofsuccessonagiventryis0.35
– [1]0.06247719
Forafaircoinits0.5,0.25,0.125etc.pgeom(n,p)givestheprobabilityofsuccessunSlthatpoint.Soitwillbe0.5,0.75,0.875,…
![Page 31: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/31.jpg)
BinomialdistribuSon
• dbinom(m,n,p)givesprobabilityofsuccessinmoutofnaWemptsgiventhatthesuccessatanygivenaWemptisp– dbinom(3,5,0.35) #successin3of5
• [1]0.1811469– sum(dbinom(3:5,5,0.35))#in3or4or5of5
• [1]0.2351694
![Page 32: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/32.jpg)
![Page 33: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/33.jpg)
StaSsScaltests
• shapiro.test Shapiro‐Wilk’sWtest(u)• ks.testKolmogorov‐Smirnov2‐sampletest(b)
• kruskal.test Kruskal‐Wallisk‐sampletest(b)
• wilcox.test Wilcoxonrank‐sumtest(b)
• cor.test BivariatecorrelaSoncoefficient(b)
• cov Covarience(b)
• rcorr CorrelaSonMatrix(m)
• prcomp PrincipleComponentAnalysis(m)
![Page 34: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/34.jpg)
Linearregressionhelp(parSalsnapshot)
![Page 35: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/35.jpg)
• library(Hmisc)• table<‐read.table(fname,header=F)• tposed=t(table)• rcorr(tposed,type="pearson”)• rcorr(tposed,type="spearman”)
![Page 36: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/36.jpg)
![Page 37: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/37.jpg)
CorrelaSonwithopSonSpearman
![Page 38: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/38.jpg)
CorrelaSonwithopSonPearson
![Page 39: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/39.jpg)
![Page 40: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/40.jpg)
• library()• RCMDINSTALL‐llibpath~/Hmisc_3.6‐0.tar.gz
• Includethisinyour.Rprofilefile
![Page 41: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/41.jpg)
![Page 42: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/42.jpg)
PrincipalComponentAnalysis
• library(mva)• table<‐read.table(”fname",header=T)
• prcomp(table)
• summary(prcomp(table))
![Page 43: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/43.jpg)
![Page 44: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/44.jpg)
![Page 45: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/45.jpg)
![Page 46: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/46.jpg)
![Page 47: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/47.jpg)
RediscoveringHRdiagram
• Hyadesstars(Hipparcusmaincatalog)• Mean/median/boxplot
• DensityesSmaSon(Histogram)
• Kernelsmoothing
• CorrelaSonmatrix
• X‐Yplot• MulSvariateclustering
![Page 48: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/48.jpg)
HydStat(30Dec2004)AshishMahabal
• X‐YplotbetweenVmagandB‐Vrevealsthefamousstructureinthedataset:thecolor‐magnitudeofbrightstarsshowingthemainsequence,giantbranch(withredclumpstars),andafewHyadeswhitedwarfs.
![Page 49: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/49.jpg)
FPofGlobularclusters
• MatrixofpairwisecorrelaSoncoefficients• Pairwiseplots• PrincipalComponentAnalysis
![Page 50: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/50.jpg)
HydStat(30Dec2004)AshishMahabal
• Coreparametersasagrouptendtobehighlycorrelated,unlikethehalf‐lightparameters.ThisisindicaSveofthedynamicalevoluSondrivenbythecorecollapse.
![Page 51: Ashish Mahabal AyBi199, Caltech 7 May 2009george/aybi199/Old... · 2009. 5. 8. · Ashish Mahabal • X‐Y plot between Vmag and B‐V reveals the famous structure in the dataset:](https://reader035.vdocument.in/reader035/viewer/2022071014/5fcd18270606426d5a2690d0/html5/thumbnails/51.jpg)
• RGUI(RcommanderhWp://socserv.mcmaster.ca/jfox/Misc/Rcmdr/)
• hWp://vostat.org• hWp://scc.stat.ucla.edu/mini‐courses
• hWp://cran.r‐project.org• hWp://www.r‐project.org• hWp://en.wikipedia.org/wiki/R_(programming_language)