Quick R Tutorial for Beginners

Transcription

1 Quick R Tutorial for Beginners Version Rintaro Saito, University of California San Diego Haruo Suzuki, Keio University

2 0. Introduction R is one of the best languages to perform statistical analyses; it can analyze huge amount of data through scientific calculations, find tendencies among the data and visualize them. In this tutorial, you will learn fundamentals of R language. 1. Starting and ending R How to start R depends on the system you are using. In the UNIX system with R installed, you may be able to start R by just typing R. In Windows or Macintosh, double-click R icon to start. To end R, just type q() 2. Simple value assignments to variables Variables temporarily keep values. For example, if we want to have variable x to keep the value 123, type x <- 123 After that, you can just type x, then you will see value assigned to x. x <- 123 x [1] 123 Actually, R is capable of handling not only single value, but also vector 1. For example, if you want to assign vector (1, 3, 5) to variable y, you can do so with "c" before vector. y <- c(1, 3, 5) You can make vectors having numbers from 2 to 5 by y <- c(2,3,4,5). Alternatively you can simply type 1 Single value (scalar) can be deemed as one-dimensional vector. 2

3 y <- 2:5 as vectors are composed of consecutive numbers from 2 to 5. Exercise 2-1: Assign (10, 11, 12) to variable z, and display information of variable z. 3. Simple Arithmetic R can perform various arithmetic including addition, subtraction, multiplication and division. For example, if you input 1+2, you will get an answer of 3 as follows: [1] 3 In R, like most of other programming languages, +, -, * and / denotes to addition, subtraction, multiplication and division respectively. R can also manipulate vectors. For example, c(1, 2, 3) + c(4, 5, 6) will give (5, 7, 9), and c(1, 2, 3) * 2 will give (2, 4, 6). Arithmetic calculations with variables can also be performed. If (1, 2, 3) and (4, 5, 6) is assigned to x and y respectively, x + y will give a vector (5, 7, 9). A value of variables can be changed based on result of calculation. For example, after doing x <- c(1, 2, 3), x <- x * 2 will multiply x by 2, and the result will be overwritten to x itself. Exercise 3-1: Assign vector (1, 2, 3) to variable x and assign 2 to variable y. Then calculate x * y. What answer do you get? Exercise 3-2: Assign (1, 2, 3) to vector x, and multiply it by three. Put the result into x itself. 4. Simple vector arithmetic As already explained, list of numbers in bracket immediately after c represents vector. Dimension of vector, i.e. number of numbers in the given vector x can be obtained by length(x) 3

4 One can extract desired number from the vector. For example, after inputting x <- c(2,4,6,8,10), x[3] will give you 6 which is the third number of the vector. x[c(2,4)] will give you second and fourth numbers of the vector, and x[2:4] will give you numbers from second to fourth elements of the vector. You can also perform vector comparison. For example, x 5 will give you vectors containing TRUE and/or FALSE (abbreviated as T and F, respectively), where each element denotes whether corresponding number in x is greater than x or not. x <- c(2,4,6,8,10) x [1] x 5 [1] FALSE FALSE TRUE TRUE TRUE R function which will returns where the T s are in the given vector as index numbers. Using the vector c(f, F, T, T, T) returned by x 5, which(c(f, F, T, T, T)) will give you vector (3,4,5). More easily, which(x 5) will give you exactly the same answer. x <- c(2,4,6,8,10) which(x 5) [1] Using this vector which is composed of T and F, we can extract elements which correspond to T. x[ c(f, F, T, T, T)] By putting above together, it is sufficient to just type x[ x 5 ] to extract elements whose values are above 5. 4

5 Actually, we can also deal with set of strings as vector. For example, after typing x <- c("sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday") x[2] will give you second string Monday. Various manipulations are available for a vector containing strings. grep("es", x) will give you indices of strings in vector x where string contain substring es. Thus the below inputs will return strings containing es. x <- c("sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday") x[ grep("es", x) ] [1] "Tuesday" "Wednesday" You can assign name for each element in a vector using function name. For example, x <- c(2, 4, 6) names(x) <- c("first", "Second", "Third") will assign ( First, Second, Third ) to name attribute of variable x. x[[ "Second" ]] will give you second element. Various statistical functions are defined for vectors containing only numerical values. For example, sum(x) will give you sum of numerical elements in vector x, and mean(x) will give you average of numerical elements in x. The function sum will count number of T s in vector x containing only T and/or F. Thus x <- c(2,4,6,8,10) sum(x 5) will count number of numerical elements greater than 5 (i.e. 3 will be returned). Exercise 4-1: Create vector containing numerical values larger than 5 in vector (3, 1, 4, 1, 5, 9, 2, 6, 5). 5

6 Exercise 4-2: Assign names ( Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec ) for respective element of vector (1,2,3,4,5,6,7,8,9,10,11,12). Then extract third element from the vector using the string Mar. The extracted element should be Simple matrix construction and arithmetic By gathering vectors, it is possible to create a matrix using the function rbind. For example, if you want to create a matrix x = æ ç è ö where the first and second rows are (1,2,3) ø and (4,5,6), respectively, type x <- rbind(c(1,2,3), c(4,5,6)) Then just type x to display the matrix you have created. x <- rbind(c(1,2,3), c(4,5,6)) x [,1] [,2] [,3] [1,] [2,] Alternatively, x <- matrix(c(1, 4, 2, 5, 3, 6), nrow=2, ncol=3) or x <- matrix(c(1, 2, 3, 4, 5, 6), nrow=2, ncol=3, byrow=t) should return the identical matrix. The latter one means that matrix of size 2 3 will be created (nrow=2, ncol=3), and numbers are filled in each row first (byrow=t). Various functions are available for a matrix. nrow(x) and ncol(x) will return number of rows and columns of the matrix x respectively. x+1 will add 1 to all the elements in x and x * 2 will multiply all the elements in x by 2. Various kinds of arithmetic between matrices are also available. For example, after typing y <- rbind(c(2, 4, 6), c(8, 10, 12)), x + y will give you matrix where each element correspond to sum of corresponding element of x and y. x * y will give you matrix where each element correspond to product of corresponding element of 6

7 x and y 2. Any specific row or column can be extracted from a given matrix. For example, if you want to extract second row, you type: x[2,] [1] If you want to extract second column, you type: x[,2] [1] 2 5 t(x) will transpose the matrix x. t(x) [,1] [,2] [1,] 1 4 [2,] 2 5 [3,] 3 6 Average of each row of matrix x can be calculated as below 3. apply(x, 1, mean) [1] 2 5 Average of each column of matrix x can be calculated as below. apply(x, 2, mean) [1] Actually, matrix can be deemed as set of numbers in two dimensional array. R can also deal with array having n dimensions using array(vector, numbers of elements in each 2 Product of the matrices based on canonical mathematical definition can be calculated by the operator %*%. 3 Second parameter of 1 in apply function denotes that we will calculate average for each position of the first dimension (in this case, the first dimension is row number). Similarly, second parameter of 2 denotes that we will calculate average for each position of the second dimension (in this case, the second dimension is column number). 7

8 dimension). For example, x <- array(1:24, c(3,4,2)) will create three dimensional array with size of 3 4 2, and fills numbers in the given vector from the first dimension to the third dimension. x <- array(1:24, c(3,4,2)) x,, 1 # The first 3 4 array of the third dimension [,1] [,2] [,3] [,4] [1,] [2,] [3,] ,, 2 # The second 3 4 array of the third dimension [,1] [,2] [,3] [,4] [1,] [2,] [3,] Exercise 5-1: Calculate æ ç è ö æ + ç ø è ö. ø Exercise 5-2: For the matrix obtained in the above calculation, calculate row average and column average. 6. Simple list creation A list in R can gather various kinds of data into a single object to manage them. x <- list("ichiro", Seattle, "Right fielder") will create a list containing "Ichiro", Seattle, "Right fielder". Although a vector cannot 8

9 contain another vector, a list can contain a vector as shown in the example below. x <- list("ichiro", "Seattle", "Right fielder", c(184, 214, 225)) To extract the second element, you can type: x[[2]] You can assign names to each element as below: x <- list(player = "Ichiro", team = "Seattle", position = "Right fielder", hits = c(184, 214, 225)) Type x to confirm that names are given to each element: x $player [1] "Ichiro" $team [1] "Seattle" $position [1] "Right fielder" $hits [1] You can use assigned name to extract corresponding element. For example, x[["team"]] or x$team will extract Seattle. Exercise 6-2: Create a list containing San Diego, vector (32, 117), and California. Give names city, coordinates, area, and state to respective element. 9

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11 7. Simple data frame creation Data frame is one of data class in R. It is one type of list and has two dimensional structure just like a matrix. Each row can be deemed as a sample, and each column can be deemed as attribute of the sample. Using this idea, data frame can represent a table. Following table gives data of five retired major league baseball players. Team at.bats hits home.runs Rose Reds Aaron Brewers Yastrzemski Red Sox Ripken Orioles Cobb Athletics The above table can be represented by data frame as follows: x <- data.frame( row.names = c("rose", "Aaron", "Yastrzemski", "Ripken", "Cobb"), team = c("reds", "Brewers", "Red Sox", "Orioles", "Athletics"), at.bats = c(14053, 12364, 11988, 11551, 11434), hits = c(4256, 3771, 3419, 3184, 4191), home.runs = c(160, 755, 452, 431, 117)) The function data.frame can generate a data frame and can be used in the format of data.frame(row.names = vector for column labels, column name 1 = vector 1, column name 2 = vector 2, ). You can check the content of x by typing x: x team at.bats hits home.runs Rose Reds Aaron Brewers Yastrzemski Red Sox Ripken Orioles Cobb Athletics Like a regular list, column name can be used to extract corresponding vector. x$hits [1]

12 Any part of data frame can be extracted as another data frame. For example, x[ c(1,5), c(2,3,4) ] will extract row 1, 5 and column 2, 3, 4 as a new data frame. You can also use row names and column names to do the same thing: x[ c("rose", "Cobb"), c("at.bats", "hits", "home.runs")] Various functions are defined for data frame. Let us get attributes associated with the data frame x. attributes(x) $names [1] "team" "at.bats" "hits" "home.runs" $row.names [1] "Rose" "Aaron" "Yastrzemski" "Ripken" "Cobb" $class [1] "data.frame" We got names, row.names and class. Type names(x), row.names(x) and class(x). You can obtain row names, column names and class of x respectively. Exercise 7-1: The below table shows characteristic values of each planet in solar system. Masses are represented in kg and diameters are represented in km. Make a data frame representing the table 4. Mass Diameter Satellites Mercury ,879 0 Venus ,690 0 Earth , As all the elements are numeric in this case, this data frame can be dealt as a matrix. as.matrix(x) will return x as a matrix. 12

13 Mars ,794 2 Jupiter , Saturn , Uranus , Neptune , Exercise 7-2: Using the created data frame in the previous exercise, calculate averages of mass, diameter and number of satellites. 8. Data reading from file So far, we have been inputting data directly. However in most of cases, numerical data may be prepared by files. So we will learn how to import data into a variable in R. First, prepare a text file with the following values. Let us name the file testdata.txt. We assume that the file is placed under the directory /Users/smith/TMP/ Using setwd, we change the working directory to /Users/smith/TMP. setwd("/users/smith/tmp") Then using scan function, read the data to a variable x. x <- scan("testdata.txt") Read 5 items x [1] You notice that the values are stored in x as a vector. R has a function, read.table, to read a table where each line is separated by TABs like the following example (file name is batters.txt ). Team At_Bat Hits Home_Runs 13

14 Bonds Giants Aaron Braves Ruth Yankees Rodriguez Yankees Mays Giants read.table can read this as data frame. x <- read.table("batters.txt", header = T, sep = "\t", row.names = 1) x Team At_Bat Hits Home_Runs Bonds Giants Aaron Braves Ruth Yankees Rodriguez Yankees Mays Giants The first parameter of the function read.table states that the name of the file to read is batters.txt. Subsequently, header = T states that there is a header for the table. sep = \t indicates that each line is separated by TAB. Finally, we can specify that there is one column for row names by row.names = 1. Since x will be a data frame, we can get number of hits by $Hits. Exercise 8: Save table in exercise 7-1 as tab-delimited file, and read it as data frame. 9. Writing data to file There are many cases where we want to have statistical results written in file rather than temporary seeing the results on screen. In this way, we can open the results by spreadsheet software or process the results using other programming language afterwards. Using "write function" is one of the simplest ways to output the results to files. This function enables us to output numerical values assigned to variable to file. For example, after assigning the vector to x as shown below, x <- c(10, 12, 15, 19, 21, 34) 14

15 the following line write(x, "outfile1.txt", ncolumns = 1) will write content of x to the file outfile1.txt. ncolumns = 1 states that the vector will be written to the file by one column. Content of outfile1.txt: write function also enable us to write matrix data to file as shown below: x <- matrix(c(1,2,3,4,5,6), nrow=2, ncol=3, byrow=t) x [,1] [,2] [,3] [1,] [2,] write(t(x), "outfile2.txt", ncolumns=ncol(x), sep="\t") t(x) transposes matrix x. If we do not do it, the matrix written in the file will look transposed. ncolumns=ncol(x) will tell R that the number of columns to output should be identical to that of matrix x. sep = \t indicates that the columns in the output file will be separated by tabs. Content of outfile2.txt: For writing data frame to a file, write.table function is provided. x <- data.frame( row.names = c("bonds", "Aaron", "Ruth", "Rodriguez", "Mays"), Team = c("giants", "Braves", "Yankees", "Yankees", "Giants"), 15

16 At_Bat = c(9847, 12364, 8398, 10341, 10881), Hits = c(2935, 3771, 2873, 3070, 3283), Home_Runs = c(762, 755, 714, 687, 660)) x[,c("hits", "Home_Runs")] Hits Home_Runs Bonds Aaron Ruth Rodriguez Mays write.table(x[,c("hits", "Home_Runs")], "outfile3.txt", sep="\t", row.names=t, col.names=na) With row.names=t and col.names=na, row names and column names will be added respectively (blank on the top-left). Content of outfile3: "" "Hits" "Home_Runs" "Bonds" "Aaron" "Ruth" "Rodriguez" "Mays" By giving quote=f, output will be without double quotations. Excercise 9: Using the data frame in the above example, calculate ratio of hits and at bat, and write the result to outfile4.txt. 10. Writing a program in a file So far, we have done our works interactively without saving what R codes we have written. However, when we repeat the same works with R, it is laborious to interactively write the same codes again and again. To solve this issue, we can write the set of codes in a file, and R can read the file to execute the codes written in the file. For example, we can prepare a text file with the following code. Let us name the 16

17 file "vecsumtest.r". x <- c(1,2,3,4,5) y <- c(2,4,6,8,10) z <- x + y Then giving source( "vecsumtest.r") will let R execute the set of codes in the file vecsumtest.r. You can check that based on the codes in vecsumtest.r, vectors are assigned to each of x, y and z. source( "vecsumtest.r") x [1] y [1] z [1] Exercise 10: Write the procedure in exercise 8 to a file dframetest.r and execute the procedure using source. 11. Defining functions In mathematics, function outputs the value which is determined by the input value. In programming, it often represents a defined set of procedures 5. For example, let us consider a function f which divides the sum of two given input values. In mathematics, it can be written as f(x, y) = (x + y) / 2. In R, it is written as follows by introducing the keyword function : f <- function(x, y){ return ((x + y) / 2) } In this way, a function with two parameters (x and y) is defined. And the returned value (output) will be (x + y) / 2. After defining f, 5 Probably subroutine may be the better terminology. 17

18 f(10, 20) will assign 10 and 20 to parameters x and y respectively and 15 will be returned as (x +y) / 2 = ( ) / 2 = 15. Here, return statement will return the value given just after it. You can also explicitly give the parameter names, x and y, as follows: f(x = 10, y = 20) The general way to define a function is name_of_function <- function(parameter 1, parameter 2,, ){ } # various procedures possibly using the given parameters 6 # return(return_value) Exercise 11: Implement a mathematical function f(x, a, b, c) = ax 2 + bx + c in R. Then calculate f(4, 3, 2, 1). 12. Making graphs R is equipped with functions capable of making graphs easily. plot function may be one of the simplest ones. It creates a plot in the two-dimensional space. For example, assigning the following vectors to x and y will create a plot with points on the locations (1,2), (3,4), (5,9), (7,7) and (9,8). x <- c(1,3,5,7,9) y <- c(2,4,9,7,8) plot(x, y, xlab="x Value", ylab="y Value") Labels on the x and y axes can be given to the parameters xlab and ylab respectively. 6 Optional parameters can be access with list( ) as a list. 18

19 X Value A plot created by plot function A bar graph can be created using barplot function. In the following example, a bar graph is created by giving the heights of each bar by vector x. The labels of each bar are given by the element names of the vector x, i.e. names(x). x <- c(1,2,3,2,10,1) names(x) <- c("a", "B", "C", "D", "E", "F") barplot(x) Y Value A B C D E F A bar graph created by barplot function hist function generates a histogram for a set of numbers given by a vector. 19

20 x <- c(3.2, 1.2, 4.2, 2.3, 3.4, 5.9, 5.2, 5.3, 4.1, 5.2, 3.2, 1.4) hist(x, xlab = "Test Value", main = "Test Histogram") The parameter main is used to state the title of the histogram. Test Histogram Frequency Test Value A generated histogram using hist function boxplot function creates a boxplot for the numbers given by the vectors. x1 <- c(11,12,11,10,11,11,12,13,15,12,11,10,12,13) x2 <- c(20,21,27,9,12,23,23,12,11,9,21,15,7,12,12,9,23,15) boxplot(x1, x2, names=c("data 1", "Data 2")) 20

21 Median Outlier The top 25% excluding outliers 50% of the data are within this range The bottom 25% excluding outliers Data 1 Data 2 Example of a box plot Exercise 12: Using the table (data frame) given in exercise 7-1, make a plot which describes relationship between masses of the planets and number of satellites. 13. Basic program structure R is equipped with programming grammars which are important and common in other programming languages. Here, some of the most important ones will be described briefly if-statement if statement gives you a way to execute a specific procedure only if a specified condition 7 is satisfied. For example, if you want to assign 1 to y when x 0, and otherwise assign 0 to y, you can write as follows: if (x 0){ y <- 1 7 When specifying a condition, logical operators such as & (logical AND) and (logical OR) can be used. 21

22 } else { y <- 0 } Investigate the value of y after doing x <- -5. Then after doing x <- 3, investigate the value of y again to make sure that the value has changed. The general form of if-statement is as follows: if (condition 1){ Set of procedures to execute when the condition 1 is satisfied } else if (condition 2){ Set of procedures to execute when the condition the condition 2 is satisfied (but the condition 1 is NOT met) } else if(condition 3){ Se of procedures to execute when condition 3 is satisfied (but condition 1 to 2 are NOT met) } else if : } else { Set of procedures to execute when NONE of the above conditions are satisfied } Exercise 13-1: Define a function which returns 1 when the input parameter is 0, and otherwise returns while-statement while-statement iterates a set of given procedures as long as the given condition is satisfied. The general form of while-statement is as follows 8 : while(condition){ 8 next-statement in the while-statement forces program to start the next iteration immediately. break-statement in while-statement forces the program to immediately stop the iteration and get out of the while-loop. 22

23 } A set of procedures to execute when the condition is satisfied For example, executing while(x <= 3){ print(x); x <- x + 1 } after doing x <- 1 will generate the output of 1 to 3. x <- 1 while (x <= 3){ print(x); x <- x + 1 } [1] 1 [1] 2 [1] 3 If you are to write this procedure as a program in a file, you may want to write each step line by line as follows so that the program will be easy to read. x <- 1 while (x <= 3){ print(x) x <- x + 1 } Initially, the value of x is 1, and the condition of the while-block i.e. x 3 is met. Thus, R goes into the while-block. The first procedure, print(x), which displays the value of x, is executed and 1 will be displayed. In the next procedure in the while-block (x <- x + 1), the value of x is increased by 1. Thus at the end of the first loop of while-block, x is 2. R interpreter then comes back to the condition check at the beginning of the while-block (x <= 3). The variable x is 2 at this point and still x 3 holds, so the procedures in the while-block will be executed again, i.e. displaying the value of x, 2, by print(x), and increasing the value of x by 1 by x <- x + 1. At the end of the while-block, x is 3. 23

24 R interpreter will then come back again to the condition check at the beginning of the while-block (x <= 3). The variable x is 3 at this point and still x 3 holds, so the procedures in the while-block will be executed again, i.e. displaying the value of x, which is 3, by print(x), and increasing the value of x by 1 by x <- x + 1. At the end of the while-block, x is 4. R interpreter will then come back again to the condition check at the beginning of the while-block (x <= 3). The variable x is 4 at this point and x 3 is NOT satisfied any more. Thus, R interpreter steps out of the while-loop. Final value of x is 4. Exercise 13-2: Using while-statement, display 1,3,5,7,9 and 11 respectively in each line for-statement for-statement also does iteration like while-statement. The for-statement assigns each of given elements to the given variable, starting from the first element to the last element in the given elements. After each assignment, the procedures in the for-block are executed. The general form of for-statement is: for(variables in elements){ } procedures For example, for (i in c(1,3,5)){ print(i) } will assign each of 1, 3, 5 into the variable i, and after each assignment, the procedures in the file-block are executed. Thus in this case, number 1 is displayed in the first iteration after the assignment, 3 is displayed in the second iteration after the assignment, and finally 5 is displayed in the third iteration after the assignment. The following example makes a vector of set of squared values of 1 to 5 9. x <- NULL for (i in 1:5){ x <- append(x, i**2) } 9 Actually using for-statement is unnecessary here. Just do x <- (1:5)**2. 24

25 x <- NULL assigns an empty vector to x. NULL represents an empty vector. In the for-statement, each value of 1 to 5 is assigned to i and after the assignment, the procedure in the for-block is executed. In the procedure in the for-block, the squared value of i (represented as i**2) is concatenated to the vector x. The function append(x, i) concatenates i to vector x 10 Exercise 13-3: Rewrite procedure in 12-2 using for-statement. 14. Other useful functions Here, some of the frequently used R functions are introduced briefly How to use help(function_name) will display how to use function_name variables and attributes ls() or objects() will display currently defined variables. class(variable_name) or mode(variable_name) will give you the type of the variable (object. For example, whether it is numerical variable, character, list or matrix) attributes(variable_name) will return attributes defined for the given variable variabl_name Family of "apply" functions sapply function will return a vector containing a set of output values from a given function after using each value in the given vector as a single input to that given function, each by each. func1_sub <- function(elm){ # a function expecting a single number as a parameter if(-1 <= elm & elm <= 1){ return (1) } else { return (0) } 10 The same procedure can be done with x <- c(x, i**2). c can be used to concatenate given vectors. 25

26 } func1 <- function(x){ # a function with a vector parameter x return(sapply(x, func1_sub)) } 14.4 Making figures curve function generates a graph for a given function. See help for details. Example: curve(dnorm, -7, +7) # Draws normal (Gaussian) distribution curve(cos(x)+cos(2*x), -2*pi, 2*pi, 1000) # 1000 is number of points curve(func1, -3, 3) # The function defined in 14.3 Family of "apply" functions. 26

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