R

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R is a statistical computing language. It has lots of libraries for uploading and cleaning data sets, running statistical procedures, and making graphs. You can also run R commands within a LaTeX document.

1# Comments start with hash signs, also known as number symbols (#). 2 3# You can't make multi-line comments, 4# but you can stack multiple comments like so. 5 6# in Windows you can use CTRL-ENTER to execute a line. 7# on Mac it is COMMAND-ENTER 8 9 10 11############################################################################# 12# Stuff you can do without understanding anything about programming 13############################################################################# 14 15# In this section, we show off some of the cool stuff you can do in 16# R without understanding anything about programming. Do not worry 17# about understanding everything the code does. Just enjoy! 18 19data() # browse pre-loaded data sets 20data(rivers) # get this one: "Lengths of Major North American Rivers" 21ls() # notice that "rivers" now appears in the workspace 22head(rivers) # peek at the data set 23# 735 320 325 392 524 450 24 25length(rivers) # how many rivers were measured? 26# 141 27summary(rivers) # what are some summary statistics? 28# Min. 1st Qu. Median Mean 3rd Qu. Max. 29# 135.0 310.0 425.0 591.2 680.0 3710.0 30 31# make a stem-and-leaf plot (a histogram-like data visualization) 32stem(rivers) 33 34# The decimal point is 2 digit(s) to the right of the | 35# 36# 0 | 4 37# 2 | 011223334555566667778888899900001111223333344455555666688888999 38# 4 | 111222333445566779001233344567 39# 6 | 000112233578012234468 40# 8 | 045790018 41# 10 | 04507 42# 12 | 1471 43# 14 | 56 44# 16 | 7 45# 18 | 9 46# 20 | 47# 22 | 25 48# 24 | 3 49# 26 | 50# 28 | 51# 30 | 52# 32 | 53# 34 | 54# 36 | 1 55 56stem(log(rivers)) # Notice that the data are neither normal nor log-normal! 57# Take that, Bell curve fundamentalists. 58 59# The decimal point is 1 digit(s) to the left of the | 60# 61# 48 | 1 62# 50 | 63# 52 | 15578 64# 54 | 44571222466689 65# 56 | 023334677000124455789 66# 58 | 00122366666999933445777 67# 60 | 122445567800133459 68# 62 | 112666799035 69# 64 | 00011334581257889 70# 66 | 003683579 71# 68 | 0019156 72# 70 | 079357 73# 72 | 89 74# 74 | 84 75# 76 | 56 76# 78 | 4 77# 80 | 78# 82 | 2 79 80# make a histogram: 81hist(rivers, col = "#333333", border = "white", breaks = 25) 82hist(log(rivers), col = "#333333", border = "white", breaks = 25) 83# play around with these parameters, you'll do more plotting later 84 85# Here's another neat data set that comes pre-loaded. R has tons of these. 86data(discoveries) 87plot(discoveries, col = "#333333", lwd = 3, xlab = "Year", 88 main="Number of important discoveries per year") 89plot(discoveries, col = "#333333", lwd = 3, type = "h", xlab = "Year", 90 main="Number of important discoveries per year") 91 92# Rather than leaving the default ordering (by year), 93# we could also sort to see what's typical: 94sort(discoveries) 95# [1] 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 96# [26] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 97# [51] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 98# [76] 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 8 9 10 12 99 100stem(discoveries, scale = 2) 101# 102# The decimal point is at the | 103# 104# 0 | 000000000 105# 1 | 000000000000 106# 2 | 00000000000000000000000000 107# 3 | 00000000000000000000 108# 4 | 000000000000 109# 5 | 0000000 110# 6 | 000000 111# 7 | 0000 112# 8 | 0 113# 9 | 0 114# 10 | 0 115# 11 | 116# 12 | 0 117 118max(discoveries) 119# 12 120summary(discoveries) 121# Min. 1st Qu. Median Mean 3rd Qu. Max. 122# 0.0 2.0 3.0 3.1 4.0 12.0 123 124# Roll a die a few times 125round(runif(7, min = .5, max = 6.5)) 126# 1 4 6 1 4 6 4 127# Your numbers will differ from mine unless we set the same random.seed(31337) 128 129# Draw from a standard Gaussian 9 times 130rnorm(9) 131# [1] 0.07528471 1.03499859 1.34809556 -0.82356087 0.61638975 -1.88757271 132# [7] -0.59975593 0.57629164 1.08455362 133 134 135 136################################################## 137# Data types and basic arithmetic 138################################################## 139 140# Now for the programming-oriented part of the tutorial. 141# In this section you will meet the important data types of R: 142# integers, numerics, characters, logicals, and factors. 143# There are others, but these are the bare minimum you need to 144# get started. 145 146# INTEGERS 147# Long-storage integers are written with L 1485L # 5 149class(5L) # "integer" 150# (Try ?class for more information on the class() function.) 151# In R, every single value, like 5L, is considered a vector of length 1 152length(5L) # 1 153# You can have an integer vector with length > 1 too: 154c(4L, 5L, 8L, 3L) # 4 5 8 3 155length(c(4L, 5L, 8L, 3L)) # 4 156class(c(4L, 5L, 8L, 3L)) # "integer" 157 158# NUMERICS 159# A "numeric" is a double-precision floating-point number 1605 # 5 161class(5) # "numeric" 162# Again, everything in R is a vector; 163# you can make a numeric vector with more than one element 164c(3, 3, 3, 2, 2, 1) # 3 3 3 2 2 1 165# You can use scientific notation too 1665e4 # 50000 1676.02e23 # Avogadro's number 1681.6e-35 # Planck length 169# You can also have infinitely large or small numbers 170class(Inf) # "numeric" 171class(-Inf) # "numeric" 172# You might use "Inf", for example, in integrate(dnorm, 3, Inf); 173# this obviates Z-score tables. 174 175# BASIC ARITHMETIC 176# You can do arithmetic with numbers 177# Doing arithmetic on a mix of integers and numerics gives you another numeric 17810L + 66L # 76 # integer plus integer gives integer 17953.2 - 4 # 49.2 # numeric minus numeric gives numeric 1802.0 * 2L # 4 # numeric times integer gives numeric 1813L / 4 # 0.75 # integer over numeric gives numeric 1823 %% 2 # 1 # the remainder of two numerics is another numeric 183# Illegal arithmetic yields you a "not-a-number": 1840 / 0 # NaN 185class(NaN) # "numeric" 186# You can do arithmetic on two vectors with length greater than 1, 187# so long as the larger vector's length is an integer multiple of the smaller 188c(1, 2, 3) + c(1, 2, 3) # 2 4 6 189# Since a single number is a vector of length one, scalars are applied 190# elementwise to vectors 191(4 * c(1, 2, 3) - 2) / 2 # 1 3 5 192# Except for scalars, use caution when performing arithmetic on vectors with 193# different lengths. Although it can be done, 194c(1, 2, 3, 1, 2, 3) * c(1, 2) # 1 4 3 2 2 6 195# Matching lengths is better practice and easier to read most times 196c(1, 2, 3, 1, 2, 3) * c(1, 2, 1, 2, 1, 2) # 1 4 3 2 2 6 197 198# CHARACTERS 199# There's no difference between strings and characters in R 200"Horatio" # "Horatio" 201class("Horatio") # "character" 202class("H") # "character" 203# Those were both character vectors of length 1 204# Here is a longer one: 205c("alef", "bet", "gimmel", "dalet", "he") 206# => "alef" "bet" "gimmel" "dalet" "he" 207length(c("Call","me","Ishmael")) # 3 208# You can do regex operations on character vectors: 209substr("Fortuna multis dat nimis, nulli satis.", 9, 15) # "multis " 210gsub('u', 'ø', "Fortuna multis dat nimis, nulli satis.") # "Fortøna møltis dat nimis, nølli satis." 211# R has several built-in character vectors: 212letters 213# => 214# [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" 215# [20] "t" "u" "v" "w" "x" "y" "z" 216month.abb # "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov" "Dec" 217 218# LOGICALS 219# In R, a "logical" is a boolean 220 221class(TRUE) # "logical" 222class(FALSE) # "logical" 223# Their behavior is normal 224TRUE == TRUE # TRUE 225TRUE == FALSE # FALSE 226FALSE != FALSE # FALSE 227FALSE != TRUE # TRUE 228# Missing data (NA) is logical, too 229class(NA) # "logical" 230# Use | and & for logic operations. 231# OR 232TRUE | FALSE # TRUE 233# AND 234TRUE & FALSE # FALSE 235# Applying | and & to vectors returns elementwise logic operations 236c(TRUE, FALSE, FALSE) | c(FALSE, TRUE, FALSE) # TRUE TRUE FALSE 237c(TRUE, FALSE, TRUE) & c(FALSE, TRUE, TRUE) # FALSE FALSE TRUE 238# You can test if x is TRUE 239isTRUE(TRUE) # TRUE 240# Here we get a logical vector with many elements: 241c("Z", "o", "r", "r", "o") == "Zorro" # FALSE FALSE FALSE FALSE FALSE 242c("Z", "o", "r", "r", "o") == "Z" # TRUE FALSE FALSE FALSE FALSE 243 244# FACTORS 245# The factor class is for categorical data 246# Factors can be ordered (like grade levels) or unordered (like colors) 247factor(c("blue", "blue", "green", NA, "blue")) 248# blue blue green <NA> blue 249# Levels: blue green 250# The "levels" are the values the categorical data can take 251# Note that missing data does not enter the levels 252levels(factor(c("green", "green", "blue", NA, "blue"))) # "blue" "green" 253# If a factor vector has length 1, its levels will have length 1, too 254length(factor("green")) # 1 255length(levels(factor("green"))) # 1 256# Factors are commonly seen in data frames, a data structure we will cover later 257data(infert) # "Infertility after Spontaneous and Induced Abortion" 258levels(infert$education) # "0-5yrs" "6-11yrs" "12+ yrs" 259 260# NULL 261# "NULL" is a weird one; use it to "blank out" a vector 262class(NULL) # NULL 263parakeet = c("beak", "feathers", "wings", "eyes") 264parakeet # "beak" "feathers" "wings" "eyes" 265parakeet <- NULL 266parakeet # NULL 267 268# TYPE COERCION 269# Type-coercion is when you force a value to take on a different type 270as.character(c(6, 8)) # "6" "8" 271as.logical(c(1,0,1,1)) # TRUE FALSE TRUE TRUE 272# If you put elements of different types into a vector, weird coercions happen: 273c(TRUE, 4) # 1 4 274c("dog", TRUE, 4) # "dog" "TRUE" "4" 275as.numeric("Bilbo") 276# => 277# [1] NA 278# Warning message: 279# NAs introduced by coercion 280 281# Also note: those were just the basic data types 282# There are many more data types, such as for dates, time series, etc. 283 284 285 286################################################## 287# Variables, loops, if/else 288################################################## 289 290# A variable is like a box you store a value in for later use. 291# We call this "assigning" the value to the variable. 292# Having variables lets us write loops, functions, and if/else statements 293 294# VARIABLES 295# Lots of way to assign stuff: 296x = 5 # this is possible 297y <- "1" # this is preferred traditionally 298TRUE -> z # this works but is weird 299# Refer to the Internet for the behaviors and preferences about them. 300 301# LOOPS 302# We've got for loops 303for (i in 1:4) { 304 print(i) 305} 306# We've got while loops 307a <- 10 308while (a > 4) { 309 cat(a, "...", sep = "") 310 a <- a - 1 311} 312# Keep in mind that for and while loops run slowly in R 313# Operations on entire vectors (i.e. a whole row, a whole column) 314# or apply()-type functions (we'll discuss later) are preferred 315 316# IF/ELSE 317# Again, pretty standard 318if (4 > 3) { 319 print("4 is greater than 3") 320} else { 321 print("4 is not greater than 3") 322} 323# => 324# [1] "4 is greater than 3" 325 326# FUNCTIONS 327# Defined like so: 328jiggle <- function(x) { 329 x = x + rnorm(1, sd=.1) # add in a bit of (controlled) noise 330 return(x) 331} 332# Called like any other R function: 333jiggle(5) # 5±ε. After set.seed(2716057), jiggle(5)==5.005043 334 335 336 337########################################################################### 338# Data structures: Vectors, matrices, data frames, and arrays 339########################################################################### 340 341# ONE-DIMENSIONAL 342 343# Let's start from the very beginning, and with something you already know: vectors. 344vec <- c(8, 9, 10, 11) 345vec # 8 9 10 11 346# We ask for specific elements by subsetting with square brackets 347# (Note that R starts counting from 1) 348vec[1] # 8 349letters[18] # "r" 350LETTERS[13] # "M" 351month.name[9] # "September" 352c(6, 8, 7, 5, 3, 0, 9)[3] # 7 353# We can also search for the indices of specific components, 354which(vec %% 2 == 0) # 1 3 355# grab just the first or last few entries in the vector, 356head(vec, 1) # 8 357tail(vec, 2) # 10 11 358# or figure out if a certain value is in the vector 359any(vec == 10) # TRUE 360# If an index "goes over" you'll get NA: 361vec[6] # NA 362# You can find the length of your vector with length() 363length(vec) # 4 364# You can perform operations on entire vectors or subsets of vectors 365vec * 4 # 32 36 40 44 366vec[2:3] * 5 # 45 50 367any(vec[2:3] == 8) # FALSE 368# and R has many built-in functions to summarize vectors 369mean(vec) # 9.5 370var(vec) # 1.666667 371sd(vec) # 1.290994 372max(vec) # 11 373min(vec) # 8 374sum(vec) # 38 375# Some more nice built-ins: 3765:15 # 5 6 7 8 9 10 11 12 13 14 15 377seq(from = 0, to = 31337, by = 1337) 378# => 379# [1] 0 1337 2674 4011 5348 6685 8022 9359 10696 12033 13370 14707 380# [13] 16044 17381 18718 20055 21392 22729 24066 25403 26740 28077 29414 30751 381 382# TWO-DIMENSIONAL (ALL ONE CLASS) 383 384# You can make a matrix out of entries all of the same type like so: 385mat <- matrix(nrow = 3, ncol = 2, c(1, 2, 3, 4, 5, 6)) 386mat 387# => 388# [,1] [,2] 389# [1,] 1 4 390# [2,] 2 5 391# [3,] 3 6 392# Unlike a vector, the class of a matrix is "matrix", no matter what's in it 393class(mat) # "matrix" "array" 394# Ask for the first row 395mat[1, ] # 1 4 396# Perform operation on the first column 3973 * mat[, 1] # 3 6 9 398# Ask for a specific cell 399mat[3, 2] # 6 400 401# Transpose the whole matrix 402t(mat) 403# => 404# [,1] [,2] [,3] 405# [1,] 1 2 3 406# [2,] 4 5 6 407 408# Matrix multiplication 409mat %*% t(mat) 410# => 411# [,1] [,2] [,3] 412# [1,] 17 22 27 413# [2,] 22 29 36 414# [3,] 27 36 45 415 416# cbind() sticks vectors together column-wise to make a matrix 417mat2 <- cbind(1:4, c("dog", "cat", "bird", "dog")) 418mat2 419# => 420# [,1] [,2] 421# [1,] "1" "dog" 422# [2,] "2" "cat" 423# [3,] "3" "bird" 424# [4,] "4" "dog" 425class(mat2) # matrix 426# Again, note what happened! 427# Because matrices must contain entries all of the same class, 428# everything got converted to the character class 429c(class(mat2[, 1]), class(mat2[, 2])) 430 431# rbind() sticks vectors together row-wise to make a matrix 432mat3 <- rbind(c(1, 2, 4, 5), c(6, 7, 0, 4)) 433mat3 434# => 435# [,1] [,2] [,3] [,4] 436# [1,] 1 2 4 5 437# [2,] 6 7 0 4 438# Ah, everything of the same class. No coercions. Much better. 439 440# TWO-DIMENSIONAL (DIFFERENT CLASSES) 441 442# For columns of different types, use a data frame 443# This data structure is so useful for statistical programming, 444# a version of it was added to Python in the package "pandas". 445 446students <- data.frame(c("Cedric", "Fred", "George", "Cho", "Draco", "Ginny"), 447 c( 3, 2, 2, 1, 0, -1), 448 c( "H", "G", "G", "R", "S", "G")) 449names(students) <- c("name", "year", "house") # name the columns 450class(students) # "data.frame" 451students 452# => 453# name year house 454# 1 Cedric 3 H 455# 2 Fred 2 G 456# 3 George 2 G 457# 4 Cho 1 R 458# 5 Draco 0 S 459# 6 Ginny -1 G 460class(students$year) # "numeric" 461class(students[,3]) # "factor" 462# find the dimensions 463nrow(students) # 6 464ncol(students) # 3 465dim(students) # 6 3 466# The data.frame() function used to convert character vectors to factor 467# vectors by default; This has changed in R 4.0.0. If your R version is 468# older, turn this off by setting stringsAsFactors = FALSE when you 469# create the data.frame 470?data.frame 471 472# There are many twisty ways to subset data frames, all subtly unalike 473students$year # 3 2 2 1 0 -1 474students[, 2] # 3 2 2 1 0 -1 475students[, "year"] # 3 2 2 1 0 -1 476 477# An augmented version of the data.frame structure is the data.table 478# If you're working with huge or panel data, or need to merge a few data 479# sets, data.table can be a good choice. Here's a whirlwind tour: 480install.packages("data.table") # download the package from CRAN 481require(data.table) # load it 482students <- as.data.table(students) 483students # note the slightly different print-out 484# => 485# name year house 486# 1: Cedric 3 H 487# 2: Fred 2 G 488# 3: George 2 G 489# 4: Cho 1 R 490# 5: Draco 0 S 491# 6: Ginny -1 G 492students[name == "Ginny"] # get rows with name == "Ginny" 493# => 494# name year house 495# 1: Ginny -1 G 496students[year == 2] # get rows with year == 2 497# => 498# name year house 499# 1: Fred 2 G 500# 2: George 2 G 501# data.table makes merging two data sets easy 502# let's make another data.table to merge with students 503founders <- data.table(house = c("G" , "H" , "R" , "S"), 504 founder = c("Godric", "Helga", "Rowena", "Salazar")) 505founders 506# => 507# house founder 508# 1: G Godric 509# 2: H Helga 510# 3: R Rowena 511# 4: S Salazar 512setkey(students, house) 513setkey(founders, house) 514students <- founders[students] # merge the two data sets by matching "house" 515setnames(students, c("house", "houseFounderName", "studentName", "year")) 516students[, order(c("name", "year", "house", "houseFounderName")), with = F] 517# => 518# studentName year house houseFounderName 519# 1: Fred 2 G Godric 520# 2: George 2 G Godric 521# 3: Ginny -1 G Godric 522# 4: Cedric 3 H Helga 523# 5: Cho 1 R Rowena 524# 6: Draco 0 S Salazar 525 526# data.table makes summary tables easy 527students[, sum(year), by = house] 528# => 529# house V1 530# 1: G 3 531# 2: H 3 532# 3: R 1 533# 4: S 0 534 535# To drop a column from a data.frame or data.table, 536# assign it the NULL value 537students$houseFounderName <- NULL 538students 539# => 540# studentName year house 541# 1: Fred 2 G 542# 2: George 2 G 543# 3: Ginny -1 G 544# 4: Cedric 3 H 545# 5: Cho 1 R 546# 6: Draco 0 S 547 548# Drop a row by subsetting 549# Using data.table: 550students[studentName != "Draco"] 551# => 552# house studentName year 553# 1: G Fred 2 554# 2: G George 2 555# 3: G Ginny -1 556# 4: H Cedric 3 557# 5: R Cho 1 558# Using data.frame: 559students <- as.data.frame(students) 560students[students$house != "G", ] 561# => 562# house houseFounderName studentName year 563# 4 H Helga Cedric 3 564# 5 R Rowena Cho 1 565# 6 S Salazar Draco 0 566 567# MULTI-DIMENSIONAL (ALL ELEMENTS OF ONE TYPE) 568 569# Arrays creates n-dimensional tables 570# All elements must be of the same type 571# You can make a two-dimensional table (sort of like a matrix) 572array(c(c(1, 2, 4, 5), c(8, 9, 3, 6)), dim = c(2, 4)) 573# => 574# [,1] [,2] [,3] [,4] 575# [1,] 1 4 8 3 576# [2,] 2 5 9 6 577# You can use array to make three-dimensional matrices too 578array(c(c(c(2, 300, 4), c(8, 9, 0)), c(c(5, 60, 0), c(66, 7, 847))), dim = c(3, 2, 2)) 579# => 580# , , 1 581# 582# [,1] [,2] 583# [1,] 2 8 584# [2,] 300 9 585# [3,] 4 0 586# 587# , , 2 588# 589# [,1] [,2] 590# [1,] 5 66 591# [2,] 60 7 592# [3,] 0 847 593 594# LISTS (MULTI-DIMENSIONAL, POSSIBLY RAGGED, OF DIFFERENT TYPES) 595 596# Finally, R has lists (of vectors) 597list1 <- list(time = 1:40) 598list1$price = c(rnorm(40, .5*list1$time, 4)) # random 599list1 600# You can get items in the list like so 601list1$time # one way 602list1[["time"]] # another way 603list1[[1]] # yet another way 604# => 605# [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 27 28 29 30 31 32 33 606# [34] 34 35 36 37 38 39 40 607# You can subset list items like any other vector 608list1$price[4] 609 610# Lists are not the most efficient data structure to work with in R; 611# unless you have a very good reason, you should stick to data.frames 612# Lists are often returned by functions that perform linear regressions 613 614################################################## 615# The apply() family of functions 616################################################## 617 618# Remember mat? 619mat 620# => 621# [,1] [,2] 622# [1,] 1 4 623# [2,] 2 5 624# [3,] 3 6 625# Use apply(X, MARGIN, FUN) to apply function FUN to a matrix X 626# over rows (MAR = 1) or columns (MAR = 2) 627# That is, R does FUN to each row (or column) of X, much faster than a 628# for or while loop would do 629apply(mat, MAR = 2, jiggle) 630# => 631# [,1] [,2] 632# [1,] 3 15 633# [2,] 7 19 634# [3,] 11 23 635# Other functions: ?lapply, ?sapply 636 637# Don't feel too intimidated; everyone agrees they are rather confusing 638 639# The plyr package aims to replace (and improve upon!) the *apply() family. 640install.packages("plyr") 641require(plyr) 642?plyr 643 644 645 646######################### 647# Loading data 648######################### 649 650# "pets.csv" is a file on the internet 651# (but it could just as easily be a file on your own computer) 652require(RCurl) 653pets <- read.csv(textConnection(getURL("https://learnxinyminutes.com/pets.csv"))) 654pets 655head(pets, 2) # first two rows 656tail(pets, 1) # last row 657 658# To save a data frame or matrix as a .csv file 659write.csv(pets, "pets2.csv") # to make a new .csv file 660# set working directory with setwd(), look it up with getwd() 661 662# Try ?read.csv and ?write.csv for more information 663 664 665 666######################### 667# Statistical Analysis 668######################### 669 670# Linear regression! 671linearModel <- lm(price ~ time, data = list1) 672linearModel # outputs result of regression 673# => 674# Call: 675# lm(formula = price ~ time, data = list1) 676# 677# Coefficients: 678# (Intercept) time 679# 0.1453 0.4943 680summary(linearModel) # more verbose output from the regression 681# => 682# Call: 683# lm(formula = price ~ time, data = list1) 684# 685# Residuals: 686# Min 1Q Median 3Q Max 687# -8.3134 -3.0131 -0.3606 2.8016 10.3992 688# 689# Coefficients: 690# Estimate Std. Error t value Pr(>|t|) 691# (Intercept) 0.14527 1.50084 0.097 0.923 692# time 0.49435 0.06379 7.749 2.44e-09 *** 693# --- 694# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 695# 696# Residual standard error: 4.657 on 38 degrees of freedom 697# Multiple R-squared: 0.6124, Adjusted R-squared: 0.6022 698# F-statistic: 60.05 on 1 and 38 DF, p-value: 2.44e-09 699coef(linearModel) # extract estimated parameters 700# => 701# (Intercept) time 702# 0.1452662 0.4943490 703summary(linearModel)$coefficients # another way to extract results 704# => 705# Estimate Std. Error t value Pr(>|t|) 706# (Intercept) 0.1452662 1.50084246 0.09678975 9.234021e-01 707# time 0.4943490 0.06379348 7.74920901 2.440008e-09 708summary(linearModel)$coefficients[, 4] # the p-values 709# => 710# (Intercept) time 711# 9.234021e-01 2.440008e-09 712 713# GENERAL LINEAR MODELS 714# Logistic regression 715set.seed(1) 716list1$success = rbinom(length(list1$time), 1, .5) # random binary 717glModel <- glm(success ~ time, data = list1, family=binomial(link="logit")) 718glModel # outputs result of logistic regression 719# => 720# Call: glm(formula = success ~ time, 721# family = binomial(link = "logit"), data = list1) 722# 723# Coefficients: 724# (Intercept) time 725# 0.17018 -0.01321 726# 727# Degrees of Freedom: 39 Total (i.e. Null); 38 Residual 728# Null Deviance: 55.35 729# Residual Deviance: 55.12 AIC: 59.12 730summary(glModel) # more verbose output from the regression 731# => 732# Call: 733# glm( 734# formula = success ~ time, 735# family = binomial(link = "logit"), 736# data = list1) 737 738# Deviance Residuals: 739# Min 1Q Median 3Q Max 740# -1.245 -1.118 -1.035 1.202 1.327 741# 742# Coefficients: 743# Estimate Std. Error z value Pr(>|z|) 744# (Intercept) 0.17018 0.64621 0.263 0.792 745# time -0.01321 0.02757 -0.479 0.632 746# 747# (Dispersion parameter for binomial family taken to be 1) 748# 749# Null deviance: 55.352 on 39 degrees of freedom 750# Residual deviance: 55.121 on 38 degrees of freedom 751# AIC: 59.121 752# 753# Number of Fisher Scoring iterations: 3 754 755 756######################### 757# Plots 758######################### 759 760# BUILT-IN PLOTTING FUNCTIONS 761# Scatterplots! 762plot(list1$time, list1$price, main = "fake data") 763# Plot regression line on existing plot 764abline(linearModel, col = "red") 765# Get a variety of nice diagnostics 766plot(linearModel) 767# Histograms! 768hist(rpois(n = 10000, lambda = 5), col = "thistle") 769# Barplots! 770barplot(c(1, 4, 5, 1, 2), names.arg = c("red", "blue", "purple", "green", "yellow")) 771 772# GGPLOT2 773# But these are not even the prettiest of R's plots 774# Try the ggplot2 package for more and better graphics 775install.packages("ggplot2") 776require(ggplot2) 777?ggplot2 778pp <- ggplot(students, aes(x = house)) 779pp + geom_bar() 780ll <- as.data.table(list1) 781pp <- ggplot(ll, aes(x = time, price)) 782pp + geom_point() 783# ggplot2 has excellent documentation (available http://docs.ggplot2.org/current/)

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