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----
-language: R
-contributors:
-    - ["e99n09", "http://github.com/e99n09"]
-<<<<<<< HEAD
-=======
-    - ["isomorphismes", "http://twitter.com/isomorphisms"]
-    - ["kalinn", "http://github.com/kalinn"]
->>>>>>> 6e38442b857a9d8178b6ce6713b96c52bf4426eb
-filename: learnr.r
----
-
-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.
-
-```r
-
-# Comments start with number symbols.
-
-# You can't make multi-line comments,
-# but you can stack multiple comments like so.
-
-# in Windows you can use CTRL-ENTER to execute a line.
-# on Mac it is COMMAND-ENTER
-
-
-
-#############################################################################
-# Stuff you can do without understanding anything about programming
-#############################################################################
-
-# In this section, we show off some of the cool stuff you can do in
-# R without understanding anything about programming. Do not worry
-# about understanding everything the code does. Just enjoy!
-
-data()	        # browse pre-loaded data sets
-data(rivers)	# get this one: "Lengths of Major North American Rivers"
-ls()	        # notice that "rivers" now appears in the workspace
-head(rivers)	# peek at the data set
-# 735 320 325 392 524 450
-
-length(rivers)	# how many rivers were measured?
-# 141
-summary(rivers) # what are some summary statistics?
-#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-#  135.0   310.0   425.0   591.2   680.0  3710.0
-
-# make a stem-and-leaf plot (a histogram-like data visualization)
-stem(rivers)
-
-#  The decimal point is 2 digit(s) to the right of the |
-#
-#   0 | 4
-#   2 | 011223334555566667778888899900001111223333344455555666688888999
-#   4 | 111222333445566779001233344567
-#   6 | 000112233578012234468
-#   8 | 045790018
-#  10 | 04507
-#  12 | 1471
-#  14 | 56
-#  16 | 7
-#  18 | 9
-#  20 |
-#  22 | 25
-#  24 | 3
-#  26 |
-#  28 |
-#  30 |
-#  32 |
-#  34 |
-#  36 | 1
-
-stem(log(rivers)) # Notice that the data are neither normal nor log-normal!
-# Take that, Bell curve fundamentalists.
-
-#  The decimal point is 1 digit(s) to the left of the |
-#
-#  48 | 1
-#  50 |
-#  52 | 15578
-#  54 | 44571222466689
-#  56 | 023334677000124455789
-#  58 | 00122366666999933445777
-#  60 | 122445567800133459
-#  62 | 112666799035
-#  64 | 00011334581257889
-#  66 | 003683579
-#  68 | 0019156
-#  70 | 079357
-#  72 | 89
-#  74 | 84
-#  76 | 56
-#  78 | 4
-#  80 |
-#  82 | 2
-
-# make a histogram:
-hist(rivers, col="#333333", border="white", breaks=25) # play around with these parameters
-hist(log(rivers), col="#333333", border="white", breaks=25) # you'll do more plotting later
-
-# Here's another neat data set that comes pre-loaded. R has tons of these.
-data(discoveries)
-plot(discoveries, col="#333333", lwd=3, xlab="Year",
-     main="Number of important discoveries per year")
-plot(discoveries, col="#333333", lwd=3, type = "h", xlab="Year",
-     main="Number of important discoveries per year")
-
-# Rather than leaving the default ordering (by year),
-# we could also sort to see what's typical:
-sort(discoveries)
-#  [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
-# [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
-# [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
-# [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
-
-stem(discoveries, scale=2)
-#
-#  The decimal point is at the |
-#
-#   0 | 000000000
-#   1 | 000000000000
-#   2 | 00000000000000000000000000
-#   3 | 00000000000000000000
-#   4 | 000000000000
-#   5 | 0000000
-#   6 | 000000
-#   7 | 0000
-#   8 | 0
-#   9 | 0
-#  10 | 0
-#  11 |
-#  12 | 0
-
-max(discoveries)
-# 12
-summary(discoveries)
-#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-#    0.0     2.0     3.0     3.1     4.0    12.0
-
-# Roll a die a few times
-round(runif(7, min=.5, max=6.5))
-# 1 4 6 1 4 6 4
-# Your numbers will differ from mine unless we set the same random.seed(31337)
-
-# Draw from a standard Gaussian 9 times
-rnorm(9)
-# [1]  0.07528471  1.03499859  1.34809556 -0.82356087  0.61638975 -1.88757271
-# [7] -0.59975593  0.57629164  1.08455362
-
-
-
-##################################################
-# Data types and basic arithmetic
-##################################################
-
-# Now for the programming-oriented part of the tutorial.
-# In this section you will meet the important data types of R:
-# integers, numerics, characters, logicals, and factors.
-# There are others, but these are the bare minimum you need to
-# get started.
-
-# INTEGERS
-# Long-storage integers are written with L
-5L # 5
-class(5L) # "integer"
-# (Try ?class for more information on the class() function.)
-# In R, every single value, like 5L, is considered a vector of length 1
-length(5L) # 1
-# You can have an integer vector with length > 1 too:
-c(4L, 5L, 8L, 3L) # 4 5 8 3
-length(c(4L, 5L, 8L, 3L)) # 4
-class(c(4L, 5L, 8L, 3L)) # "integer"
-
-# NUMERICS
-# A "numeric" is a double-precision floating-point number
-5 # 5
-class(5) # "numeric"
-# Again, everything in R is a vector;
-# you can make a numeric vector with more than one element
-c(3,3,3,2,2,1) # 3 3 3 2 2 1
-# You can use scientific notation too
-5e4 # 50000
-6.02e23 # Avogadro's number
-1.6e-35 # Planck length
-# You can also have infinitely large or small numbers
-class(Inf)	# "numeric"
-class(-Inf)	# "numeric"
-# You might use "Inf", for example, in integrate(dnorm, 3, Inf);
-# this obviates Z-score tables.
-
-# BASIC ARITHMETIC
-# You can do arithmetic with numbers
-# Doing arithmetic on a mix of integers and numerics gives you another numeric
-10L + 66L # 76      # integer plus integer gives integer
-53.2 - 4  # 49.2    # numeric minus numeric gives numeric
-2.0 * 2L  # 4       # numeric times integer gives numeric
-3L / 4    # 0.75    # integer over numeric gives numeric
-3 %% 2	  # 1       # the remainder of two numerics is another numeric
-# Illegal arithmetic yeilds you a "not-a-number":
-0 / 0 # NaN
-class(NaN) # "numeric"
-# You can do arithmetic on two vectors with length greater than 1,
-# so long as the larger vector's length is an integer multiple of the smaller
-c(1,2,3) + c(1,2,3) # 2 4 6
-# Since a single number is a vector of length one, scalars are applied 
-# elementwise to vectors
-(4 * c(1,2,3) - 2) / 2 # 1 3 5
-# Except for scalars, use caution when performing arithmetic on vectors with 
-# different lengths. Although it can be done, 
-c(1,2,3,1,2,3) * c(1,2) # 1 4 3 2 2 6
-# Matching lengths is better practice and easier to read
-c(1,2,3,1,2,3) * c(1,2,1,2,1,2) 
-
-# CHARACTERS
-# There's no difference between strings and characters in R
-"Horatio" # "Horatio"
-class("Horatio") # "character"
-class('H') # "character"
-# Those were both character vectors of length 1
-# Here is a longer one:
-c('alef', 'bet', 'gimmel', 'dalet', 'he')
-# =>
-# "alef"   "bet"    "gimmel" "dalet"  "he"
-length(c("Call","me","Ishmael")) # 3
-# You can do regex operations on character vectors:
-substr("Fortuna multis dat nimis, nulli satis.", 9, 15) # "multis "
-gsub('u', 'ø', "Fortuna multis dat nimis, nulli satis.") # "Fortøna møltis dat nimis, nølli satis."
-# R has several built-in character vectors:
-letters
-# =>
-#  [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s"
-# [20] "t" "u" "v" "w" "x" "y" "z"
-month.abb # "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov" "Dec"
-
-# LOGICALS
-# In R, a "logical" is a boolean
-class(TRUE)	# "logical"
-class(FALSE)	# "logical"
-# Their behavior is normal
-TRUE == TRUE	# TRUE
-TRUE == FALSE	# FALSE
-FALSE != FALSE	# FALSE
-FALSE != TRUE	# TRUE
-# Missing data (NA) is logical, too
-class(NA)	# "logical"
-# Use | and & for logic operations.
-# OR
-TRUE | FALSE	# TRUE
-# AND
-TRUE & FALSE	# FALSE
-# Applying | and & to vectors returns elementwise logic operations
-c(TRUE,FALSE,FALSE) | c(FALSE,TRUE,FALSE) # TRUE TRUE FALSE
-c(TRUE,FALSE,TRUE) & c(FALSE,TRUE,TRUE) # FALSE FALSE TRUE
-# You can test if x is TRUE
-isTRUE(TRUE)	# TRUE
-# Here we get a logical vector with many elements:
-c('Z', 'o', 'r', 'r', 'o') == "Zorro" # FALSE FALSE FALSE FALSE FALSE
-c('Z', 'o', 'r', 'r', 'o') == "Z" # TRUE FALSE FALSE FALSE FALSE
-
-# FACTORS
-# The factor class is for categorical data
-# Factors can be ordered (like childrens' grade levels) or unordered (like gender)
-factor(c("female", "female", "male", NA, "female"))
-#  female female male   <NA>   female
-# Levels: female male
-# The "levels" are the values the categorical data can take
-# Note that missing data does not enter the levels
-levels(factor(c("male", "male", "female", NA, "female"))) # "female" "male"
-# If a factor vector has length 1, its levels will have length 1, too
-length(factor("male")) # 1
-length(levels(factor("male"))) # 1
-# Factors are commonly seen in data frames, a data structure we will cover later
-data(infert) # "Infertility after Spontaneous and Induced Abortion"
-levels(infert$education) # "0-5yrs"  "6-11yrs" "12+ yrs"
-
-# NULL
-# "NULL" is a weird one; use it to "blank out" a vector
-class(NULL)	# NULL
-parakeet = c("beak", "feathers", "wings", "eyes")
-parakeet
-# =>
-# [1] "beak"     "feathers" "wings"    "eyes"
-parakeet <- NULL
-parakeet
-# =>
-# NULL
-
-# TYPE COERCION
-# Type-coercion is when you force a value to take on a different type
-as.character(c(6, 8)) # "6" "8"
-as.logical(c(1,0,1,1)) # TRUE FALSE  TRUE  TRUE
-# If you put elements of different types into a vector, weird coercions happen:
-c(TRUE, 4) # 1 4
-c("dog", TRUE, 4) # "dog"  "TRUE" "4"
-as.numeric("Bilbo")
-# =>
-# [1] NA
-# Warning message:
-# NAs introduced by coercion
-
-# Also note: those were just the basic data types
-# There are many more data types, such as for dates, time series, etc.
-
-
-
-##################################################
-# Variables, loops, if/else
-##################################################
-
-# A variable is like a box you store a value in for later use.
-# We call this "assigning" the value to the variable.
-# Having variables lets us write loops, functions, and if/else statements
-
-# VARIABLES
-# Lots of way to assign stuff:
-x = 5 # this is possible
-y <- "1" # this is preferred
-TRUE -> z # this works but is weird
-
-# LOOPS
-# We've got for loops
-for (i in 1:4) {
-  print(i)
-}
-# We've got while loops
-a <- 10
-while (a > 4) {
-	cat(a, "...", sep = "")
-	a <- a - 1
-}
-# Keep in mind that for and while loops run slowly in R
-# Operations on entire vectors (i.e. a whole row, a whole column)
-# or apply()-type functions (we'll discuss later) are preferred
-
-# IF/ELSE
-# Again, pretty standard
-if (4 > 3) {
-	print("4 is greater than 3")
-} else {
-	print("4 is not greater than 3")
-}
-# =>
-# [1] "4 is greater than 3"
-
-# FUNCTIONS
-# Defined like so:
-jiggle <- function(x) {
-	x = x + rnorm(1, sd=.1)	#add in a bit of (controlled) noise
-	return(x)
-}
-# Called like any other R function:
-jiggle(5)	# 5±ε. After set.seed(2716057), jiggle(5)==5.005043
-
-
-
-###########################################################################
-# Data structures: Vectors, matrices, data frames, and arrays
-###########################################################################
-
-# ONE-DIMENSIONAL
-
-# Let's start from the very beginning, and with something you already know: vectors.
-vec <- c(8, 9, 10, 11)
-vec	#  8  9 10 11
-# We ask for specific elements by subsetting with square brackets
-# (Note that R starts counting from 1)
-vec[1]		# 8
-letters[18]	# "r"
-LETTERS[13]	# "M"
-month.name[9]	# "September"
-c(6, 8, 7, 5, 3, 0, 9)[3]	# 7
-# We can also search for the indices of specific components,
-which(vec %% 2 == 0)	# 1 3
-# grab just the first or last few entries in the vector,
-head(vec, 1)	# 8
-tail(vec, 2)	# 10 11
-# or figure out if a certain value is in the vector
-any(vec == 10) # TRUE
-# If an index "goes over" you'll get NA:
-vec[6]	# NA
-# You can find the length of your vector with length()
-length(vec)	# 4
-# You can perform operations on entire vectors or subsets of vectors
-vec * 4	# 16 20 24 28
-vec[2:3] * 5	# 25 30
-any(vec[2:3] == 8) # FALSE
-# and R has many built-in functions to summarize vectors
-mean(vec)	# 9.5
-var(vec)	# 1.666667
-sd(vec)		# 1.290994
-max(vec)	# 11
-min(vec)	# 8
-sum(vec)	# 38
-# Some more nice built-ins:
-5:15	# 5  6  7  8  9 10 11 12 13 14 15
-seq(from=0, to=31337, by=1337)
-# =>
-#  [1]     0  1337  2674  4011  5348  6685  8022  9359 10696 12033 13370 14707
-# [13] 16044 17381 18718 20055 21392 22729 24066 25403 26740 28077 29414 30751
-
-# TWO-DIMENSIONAL (ALL ONE CLASS)
-
-# You can make a matrix out of entries all of the same type like so:
-mat <- matrix(nrow = 3, ncol = 2, c(1,2,3,4,5,6))
-mat
-# =>
-#      [,1] [,2]
-# [1,]    1    4
-# [2,]    2    5
-# [3,]    3    6
-# Unlike a vector, the class of a matrix is "matrix", no matter what's in it
-class(mat) # => "matrix"
-# Ask for the first row
-mat[1,]	# 1 4
-# Perform operation on the first column
-3 * mat[,1]	# 3 6 9
-# Ask for a specific cell
-mat[3,2]	# 6
-
-# Transpose the whole matrix
-t(mat)
-# =>
-#      [,1] [,2] [,3]
-# [1,]    1    2    3
-# [2,]    4    5    6
-
-# Matrix multiplication
-mat %*% t(mat)
-# =>
-#      [,1] [,2] [,3]
-# [1,]   17   22   27
-# [2,]   22   29   36
-# [3,]   27   36   45
-
-# cbind() sticks vectors together column-wise to make a matrix
-mat2 <- cbind(1:4, c("dog", "cat", "bird", "dog"))
-mat2
-# =>
-#      [,1] [,2]
-# [1,] "1"  "dog"
-# [2,] "2"  "cat"
-# [3,] "3"  "bird"
-# [4,] "4"  "dog"
-class(mat2)	# matrix
-# Again, note what happened!
-# Because matrices must contain entries all of the same class,
-# everything got converted to the character class
-c(class(mat2[,1]), class(mat2[,2]))
-
-# rbind() sticks vectors together row-wise to make a matrix
-mat3 <- rbind(c(1,2,4,5), c(6,7,0,4))
-mat3
-# =>
-#      [,1] [,2] [,3] [,4]
-# [1,]    1    2    4    5
-# [2,]    6    7    0    4
-# Ah, everything of the same class. No coercions. Much better.
-
-# TWO-DIMENSIONAL (DIFFERENT CLASSES)
-
-# For columns of different types, use a data frame
-# This data structure is so useful for statistical programming,
-# a version of it was added to Python in the package "pandas".
-
-students <- data.frame(c("Cedric","Fred","George","Cho","Draco","Ginny"),
-                       c(3,2,2,1,0,-1),
-                       c("H", "G", "G", "R", "S", "G"))
-names(students) <- c("name", "year", "house") # name the columns
-class(students)	# "data.frame"
-students
-# =>
-#     name year house
-# 1 Cedric    3     H
-# 2   Fred    2     G
-# 3 George    2     G
-# 4    Cho    1     R
-# 5  Draco    0     S
-# 6  Ginny   -1     G
-class(students$year)	# "numeric"
-class(students[,3])	# "factor"
-# find the dimensions
-nrow(students)	# 6
-ncol(students)	# 3
-dim(students)	# 6 3
-# The data.frame() function converts character vectors to factor vectors
-# by default; turn this off by setting stringsAsFactors = FALSE when
-# you create the data.frame
-?data.frame
-
-# There are many twisty ways to subset data frames, all subtly unalike
-students$year	# 3  2  2  1  0 -1
-students[,2]	# 3  2  2  1  0 -1
-students[,"year"]	# 3  2  2  1  0 -1
-
-# An augmented version of the data.frame structure is the data.table
-# If you're working with huge or panel data, or need to merge a few data
-# sets, data.table can be a good choice. Here's a whirlwind tour:
-install.packages("data.table") # download the package from CRAN
-require(data.table) # load it
-students <- as.data.table(students)
-students # note the slightly different print-out
-# =>
-#      name year house
-# 1: Cedric    3     H
-# 2:   Fred    2     G
-# 3: George    2     G
-# 4:    Cho    1     R
-# 5:  Draco    0     S
-# 6:  Ginny   -1     G
-students[name=="Ginny"] # get rows with name == "Ginny"
-# =>
-#     name year house
-# 1: Ginny   -1     G
-students[year==2] # get rows with year == 2
-# =>
-#      name year house
-# 1:   Fred    2     G
-# 2: George    2     G
-# data.table makes merging two data sets easy
-# let's make another data.table to merge with students
-founders <- data.table(house=c("G","H","R","S"),
-                       founder=c("Godric","Helga","Rowena","Salazar"))
-founders
-# =>
-#    house founder
-# 1:     G  Godric
-# 2:     H   Helga
-# 3:     R  Rowena
-# 4:     S Salazar
-setkey(students, house)
-setkey(founders, house)
-students <- founders[students] # merge the two data sets by matching "house"
-setnames(students, c("house","houseFounderName","studentName","year"))
-students[,order(c("name","year","house","houseFounderName")), with=F]
-# =>
-#    studentName year house houseFounderName
-# 1:        Fred    2     G           Godric
-# 2:      George    2     G           Godric
-# 3:       Ginny   -1     G           Godric
-# 4:      Cedric    3     H            Helga
-# 5:         Cho    1     R           Rowena
-# 6:       Draco    0     S          Salazar
-
-# data.table makes summary tables easy
-students[,sum(year),by=house]
-# =>
-#    house V1
-# 1:     G  3
-# 2:     H  3
-# 3:     R  1
-# 4:     S  0
-
-# To drop a column from a data.frame or data.table,
-# assign it the NULL value
-students$houseFounderName <- NULL
-students
-# =>
-#    studentName year house
-# 1:        Fred    2     G
-# 2:      George    2     G
-# 3:       Ginny   -1     G
-# 4:      Cedric    3     H
-# 5:         Cho    1     R
-# 6:       Draco    0     S
-
-# Drop a row by subsetting
-# Using data.table:
-students[studentName != "Draco"]
-# =>
-#    house studentName year
-# 1:     G        Fred    2
-# 2:     G      George    2
-# 3:     G       Ginny   -1
-# 4:     H      Cedric    3
-# 5:     R         Cho    1
-# Using data.frame:
-students <- as.data.frame(students)
-students[students$house != "G",]
-# =>
-#   house houseFounderName studentName year
-# 4     H            Helga      Cedric    3
-# 5     R           Rowena         Cho    1
-# 6     S          Salazar       Draco    0
-
-# MULTI-DIMENSIONAL (ALL ELEMENTS OF ONE TYPE)
-
-# Arrays creates n-dimensional tables
-# All elements must be of the same type
-# You can make a two-dimensional table (sort of like a matrix)
-array(c(c(1,2,4,5),c(8,9,3,6)), dim=c(2,4))
-# =>
-#      [,1] [,2] [,3] [,4]
-# [1,]    1    4    8    3
-# [2,]    2    5    9    6
-# You can use array to make three-dimensional matrices too
-array(c(c(c(2,300,4),c(8,9,0)),c(c(5,60,0),c(66,7,847))), dim=c(3,2,2))
-# =>
-# , , 1
-#
-#      [,1] [,2]
-# [1,]    2    8
-# [2,]  300    9
-# [3,]    4    0
-#
-# , , 2
-#
-#      [,1] [,2]
-# [1,]    5   66
-# [2,]   60    7
-# [3,]    0  847
-
-# LISTS (MULTI-DIMENSIONAL, POSSIBLY RAGGED, OF DIFFERENT TYPES)
-
-# Finally, R has lists (of vectors)
-list1 <- list(time = 1:40)
-list1$price = c(rnorm(40,.5*list1$time,4)) # random
-list1
-# You can get items in the list like so
-list1$time # one way
-list1[["time"]] # another way
-list1[[1]] # yet another way
-# =>
-#  [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
-# [34] 34 35 36 37 38 39 40
-# You can subset list items like any other vector
-list1$price[4]
-
-# Lists are not the most efficient data structure to work with in R;
-# unless you have a very good reason, you should stick to data.frames
-# Lists are often returned by functions that perform linear regressions
-
-##################################################
-# The apply() family of functions
-##################################################
-
-# Remember mat?
-mat
-# =>
-#      [,1] [,2]
-# [1,]    1    4
-# [2,]    2    5
-# [3,]    3    6
-# Use apply(X, MARGIN, FUN) to apply function FUN to a matrix X
-# over rows (MAR = 1) or columns (MAR = 2)
-# That is, R does FUN to each row (or column) of X, much faster than a
-# for or while loop would do
-apply(mat, MAR = 2, jiggle)
-# =>
-#      [,1] [,2]
-# [1,]    3   15
-# [2,]    7   19
-# [3,]   11   23
-# Other functions: ?lapply, ?sapply
-
-# Don't feel too intimidated; everyone agrees they are rather confusing
-
-# The plyr package aims to replace (and improve upon!) the *apply() family.
-install.packages("plyr")
-require(plyr)
-?plyr
-
-
-
-#########################
-# Loading data
-#########################
-
-# "pets.csv" is a file on the internet
-# (but it could just as easily be be a file on your own computer)
-pets <- read.csv("http://learnxinyminutes.com/docs/pets.csv")
-pets
-head(pets, 2) # first two rows
-tail(pets, 1) # last row
-
-# To save a data frame or matrix as a .csv file
-write.csv(pets, "pets2.csv") # to make a new .csv file
-# set working directory with setwd(), look it up with getwd()
-
-# Try ?read.csv and ?write.csv for more information
-
-
-
-#########################
-# Statistical Analysis
-#########################
-
-# Linear regression!
-linearModel <- lm(price  ~ time, data = list1)
-linearModel # outputs result of regression
-# =>
-# Call:
-# lm(formula = price ~ time, data = list1)
-# 
-# Coefficients:
-# (Intercept)         time  
-#      0.1453       0.4943  
-summary(linearModel) # more verbose output from the regression
-# =>
-# Call:
-# lm(formula = price ~ time, data = list1)
-#
-# Residuals:
-#     Min      1Q  Median      3Q     Max 
-# -8.3134 -3.0131 -0.3606  2.8016 10.3992 
-#
-# Coefficients:
-#             Estimate Std. Error t value Pr(>|t|)    
-# (Intercept)  0.14527    1.50084   0.097    0.923    
-# time         0.49435    0.06379   7.749 2.44e-09 ***
-# ---
-# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-#
-# Residual standard error: 4.657 on 38 degrees of freedom
-# Multiple R-squared:  0.6124,	Adjusted R-squared:  0.6022 
-# F-statistic: 60.05 on 1 and 38 DF,  p-value: 2.44e-09
-coef(linearModel) # extract estimated parameters
-# =>
-# (Intercept)        time 
-#   0.1452662   0.4943490 
-summary(linearModel)$coefficients # another way to extract results
-# =>
-#              Estimate Std. Error    t value     Pr(>|t|)
-# (Intercept) 0.1452662 1.50084246 0.09678975 9.234021e-01
-# time        0.4943490 0.06379348 7.74920901 2.440008e-09
-summary(linearModel)$coefficients[,4] # the p-values 
-# =>
-#  (Intercept)         time 
-# 9.234021e-01 2.440008e-09 
-
-# GENERAL LINEAR MODELS
-# Logistic regression
-set.seed(1)
-list1$success = rbinom(length(list1$time), 1, .5) # random binary
-glModel <- glm(success  ~ time, data = list1, 
-	family=binomial(link="logit"))
-glModel # outputs result of logistic regression
-# =>
-# Call:  glm(formula = success ~ time, 
-#	family = binomial(link = "logit"), data = list1)
-#
-# Coefficients:
-# (Intercept)         time  
-#     0.17018     -0.01321  
-# 
-# Degrees of Freedom: 39 Total (i.e. Null);  38 Residual
-# Null Deviance:	    55.35 
-# Residual Deviance: 55.12 	 AIC: 59.12
-summary(glModel) # more verbose output from the regression
-# =>
-# Call:
-# glm(formula = success ~ time, 
-#	family = binomial(link = "logit"), data = list1)
-
-# Deviance Residuals: 
-#    Min      1Q  Median      3Q     Max  
-# -1.245  -1.118  -1.035   1.202   1.327  
-# 
-# Coefficients:
-#             Estimate Std. Error z value Pr(>|z|)
-# (Intercept)  0.17018    0.64621   0.263    0.792
-# time        -0.01321    0.02757  -0.479    0.632
-# 
-# (Dispersion parameter for binomial family taken to be 1)
-#
-#     Null deviance: 55.352  on 39  degrees of freedom
-# Residual deviance: 55.121  on 38  degrees of freedom
-# AIC: 59.121
-# 
-# Number of Fisher Scoring iterations: 3
-
-
-#########################
-# Plots
-#########################
-
-# BUILT-IN PLOTTING FUNCTIONS
-# Scatterplots!
-plot(list1$time, list1$price, main = "fake data")
-# Plot regression line on existing plot
-abline(linearModel, col = "red")
-# Get a variety of nice diagnostics
-plot(linearModel)
-# Histograms!
-hist(rpois(n = 10000, lambda = 5), col = "thistle")
-# Barplots!
-barplot(c(1,4,5,1,2), names.arg = c("red","blue","purple","green","yellow"))
-
-# GGPLOT2
-# But these are not even the prettiest of R's plots
-# Try the ggplot2 package for more and better graphics
-install.packages("ggplot2")
-require(ggplot2)
-?ggplot2
-pp <- ggplot(students, aes(x=house))
-pp + geom_histogram()
-ll <- as.data.table(list1)
-pp <- ggplot(ll, aes(x=time,price))
-pp + geom_point()
-# ggplot2 has excellent documentation (available http://docs.ggplot2.org/current/)
-
-
-
-```
-
-## How do I get R?
-
-* Get R and the R GUI from [http://www.r-project.org/](http://www.r-project.org/)
-* [RStudio](http://www.rstudio.com/ide/) is another GUI