Getting Started with R

1+1

[1] 2

7-8

[1] -1

#Complex Numbers
(2+5i) + (3-1i)

[1] 5+4i

#addition
2-3

[1] -1

#Division
2/3

[1] 0.6666667

#Exponentiation
2^3

[1] 8

#Square Root
sqrt(2)

[1] 1.414214

#Logarithms
log(2)

[1] 0.6931472

#Question _1: Compute the log base 5 of 10 and the log of 10
log10(10) #log of 10, base 10

[1] 1

log(10,5)#log of 10, base 5

[1] 1.430677

log(100,10) #log of 100, base 10

[1] 2

log(10,2) #log of 10, base 2

[1] 3.321928

Computing some offensive metrics in Baseball

#Battling Average=(No of Hits)/(No. of Bats)
#What is the battling average of a player that bats 29 hits in 112 at bats?
BA=(29)/(112)
BA

[1] 0.2589286

Battling_Average=round(BA,digits = 3)
Battling_Average

[1] 0.259

#Question_2:What is the battling average of a player that bats 42 hits in 212 at bats?
#On Base Percentage
#OBP=(H+BB+HBP)/(At Bats+BB+HBP+SF)
#Let us compute the OBP for a player with the following general stats
#AB=515,H=172,BB=84,HBP=5,SF=6
OBP=(172+84+5)/(515+84+5+6)
OBP

[1] 0.4278689

On_Base_Percentage=round(OBP,digits = 3)
On_Base_Percentage

[1] 0.428

#Question_3:Compute the OBP for a player with the following general stats:
#AB=565,H=156,BB=65HBP=3,SF=7
OBP=(156+65+3)/(565+65+3+7)
OBP

[1] 0.35

Often you will want to test whether something is less than, greater than or equal to something

3 == 8 #Does 3 equal 8

[1] FALSE

3 != 8 # Is 3 different from 8?

[1] TRUE

3 <= 8 #Is less than or equal to 8?

[1] TRUE

3>4 #Is 3 greater than 4

[1] FALSE

#The logical operators are & for logical AND, | for logical OR, and ! for NOT. These are some examples:
#Logical Disjunction (or)
FALSE|FALSE #False OR False

[1] FALSE

#Logical Conjunction (and)
TRUE&FALSE #True AND False

[1] FALSE

#Negation
!FALSE #NOT False

[1] TRUE

#Combination of statements
2<3|1==5 #2<3 is True, 1==5 is False, True or False is True

[1] TRUE

Assigning Values to Variables

# In R, you create a variable and assign it a value using <- as follows
Total_Bases<-6+5
Total_Bases*3

[1] 33

#To see the variables that are currently defined, use ls (as in "list")
ls()

[1] "BA"                 "Battling_Average"   "OBP"                "On_Base_Percentage"
[5] "pitches_by_innings" "player_positions"   "strikes_by_innings" "Total_Bases"       

# to delete the variables that are currently defined, use rm (as in "remove")
rm(Total_Bases)
ls()

[1] "BA"                 "Battling_Average"   "OBP"                "On_Base_Percentage"
[5] "pitches_by_innings" "player_positions"   "strikes_by_innings"

Either <- or = can be used to assign a value to a variable,but I prefer <- because is less likely to be confused with the logical operator ==

Vectors

#The basic type of object in R is a vector, which is an ordered list of values of the same type. You can create a vector using the c() function (as in "concatenate")
pitches_by_innings <- c(12, 15, 10, 20, 10)
pitches_by_innings

[1] 12 15 10 20 10

strikes_by_innings <- c(9, 12, 6, 14, 9)

strikes_by_innings

#Question_4:Define two vectors, runs_per_9inings and hits_per_9innings, each with five elements

runs_per_9inings <-c(67,87,76,45,67)
runs_per_9inings

[1] 67 87 76 45 67

hits_per_9inings <-c(30,27,26,23,15)
hits_per_9inings

[1] 30 27 26 23 15

#There are also some functions that will create vectors with regular patterns, like repeated elements.

#replicate function

rep(2,5)

[1] 2 2 2 2 2

rep(1,4)

[1] 1 1 1 1

rep(3,3)

[1] 3 3 3

#consecutive numbers
1:5

[1] 1 2 3 4 5

2:10

#sequence from 1 to 10 with a step of 2
seq(1,10, by=2)

[1] 1 3 5 7 9

seq(2, 13, by=3)

[1]  2  5  8 11

seq(5, 25,by=5)

[1]  5 10 15 20 25

#Many functions and operators like + or - will work on all elements of the vector.
#add vectors
pitches_by_innings+strikes_by_innings

[1] 21 27 16 34 19

#compare vectors
pitches_by_innings

[1] 12 15 10 20 10

strikes_by_innings

[1]  9 12  6 14  9

pitches_by_innings == strikes_by_innings

[1] FALSE FALSE FALSE FALSE FALSE

#find length of vector
length(pitches_by_innings)

[1] 5

#find minimum value in vector
min(pitches_by_innings)

[1] 10

#find average value in vector
mean(pitches_by_innings)

[1] 13.4

#You can access parts of a vector by using. Recall what the value is of the vector pitches_by_innings
pitches_by_innings

[1] 12 15 10 20 10

#If you want to get the first element
pitches_by_innings[1]

[1] 12

#Question_5:Get the first element of hits_per_9innings

hits_per_9inings[1]

[1] 30

hits_per_9inings

[1] 30 27 26 23 15

hits_per_9inings[c(2,3,4)]

[1] 27 26 23

hits_per_9inings[c(2:4)]

[1] 27 26 23

#If you want to get the last element of pitches_by_innings without explicitly typing the number of elements of pitches_by_innings, make use of the length function, which calculates the length of a vector
pitches_by_innings[length(pitches_by_innings)]

[1] 10

#Question_6:Get the last element of hits_per_9innings.
hits_per_9inings[5]

[1] 15

#You can also extract multiple values from a vector. For instance to get the 2nd through 4th values use:
pitches_by_innings

[1] 12 15 10 20 10

pitches_by_innings[c(2,3,4)]

[1] 15 10 20

pitches_by_innings[c(2:4)]

[1] 15 10 20

#Vectors can also be strings or logical values
player_positions <-c("catcher","pitcher","infielders","outfielders")
player_positions

[1] "catcher"     "pitcher"     "infielders"  "outfielders"

Data Frames

#In statistical applications, data is often stored as a data frame, which is like a spreadsheet, with rows as observations and columns as variables
#To manually create a data frame, use the data.frame() function
data.frame(bonus = c(2,3,1),#in millions
           active_roster = c("yes","no","yes"),
           salary = c(1.5,2.5,1))#in millions

Most often you will be using data frames loaded from a file. For example, load the results of a fan’s survey. The function load or read.table can be used for this.

How to Make a Random Sample

#To randomly select  a sample use the function sample(). The following code selects 5 numbers beweeen 1 and 10 at random (without duplication)
sample(1:10, size=5)

[1]  9  5  7 10  4

The first argument gives the vector of data to select elements form The second argument (size=) gives the size of the sample to select.

Taking a simple random sample from a data frame is only slightly more complicated, having two steps: 1. Use sample() to select a sample of size n from a vector of the row numbers of the data frame. 2. Use the index operator [ to select those rows from the data frame.

#Consider the following example with fake data. First, make up a data frame with two columns. (LETTERS is a character vector of length 26 with capital letters a to z and A to Z. LETTERS is automatically defined and pre-loaded in R)
bar<- data.frame(var1 = LETTERS[1:10], var2 =1:10)
#Check data frame
bar

Suppose you want to select a random sample of size 5. First, define a variable n with the size of the sample, i.e.5

n<-5
n

[1] 5

Now, select a sample of size 5 from the vector with 1 to 10 (the number of rows in bar). Use the function nrow() to find the number of rows in bar instead of manually entering that number.

#Use:to create a vector with all the integers between 1 and the number of rows in bar.

samplerows <- sample(1:nrow(bar),size=n)
samplerows

[1] 10  2  3  9  1

The variable samplerows contains the rows of bar which make a random sample from all the rows in bar. Extract those rows from bar with

#extract rows
barsample <- bar[samplerows, ]
print(barsample)

The code above creates a new data frame called barsample with a random sample of rows from bar. In a single line of code.

bar[sample(1:nrow(bar),n),]

Using Tables

The table()command allows us to look at tables. Its simplest usage looks like table(x) where x is a categorical variable.

For example, a survey asks people if they support the home team or not. The data is Yes, No, No, Yes, Yes

#We can enter this into R with the c() command, and summarize with the table() command as follows
x<-c("Yes","No","No","Yes","Yes")
table(x)

x
 No Yes 
  2   3 

Numerical measures of center and spread Suppose MLB Teams’ CEOs yearly compensations are sampled and the following are found (in millions) 12 .4 5 2 50 8 3 1 4 0.25

sals<-c(12,.4,5,2,50,8,3, 1, 4, 0.25)
# the average
mean(sals)
# the variance
var(sals)
#the standard deviation
sd(sals)
#the median
median(sals)

Tukey’s five number summary, useful for boxplots five numbers:min,lower hinge, median, upper hinge,max

fivenum(sals)
#summary statistics
summary(sals)

How about the mode?

In R we can write our own functions, and a first example of a function is shown below in order to compute the mode of a vector of observations x

#Function to find the mode, i.e. most frequent value
getMode <-function(x){
  ux<-unique(x)
  ux[which.max(tabulate(match(x, ux)))]
}

As an example, we can use the function defined above to find the most frequent value of the number of pitches_by_inings

#Most frequent value in pitches _by_inings
getMode(pitches_by_innings)

#Question_7:Find the most frequent value of hits_per_9inings
hits_per_9inings

[1] 30 27 26 23 15

getMode(hits_per_9inings)

[1] 30

runs_per_9inings

[1] 67 87 76 45 67

getMode(runs_per_9inings)

[1] 67

Question_8:Summarize the following survey with ‘table’ command:

#What is your favorite day of the week to watch baseball? A total of 10 fans submitted this survey.
#Saturday, Saturday, Sunday, Monday, Saturday, Tuesday, Sunday, Friday, Friday, Monday
game_day<-c("Saturday", "Saturday", "Sunday", "Monday", "Saturday", "Tuesday", "Sunday", "Friday", "Friday", "Monday")
game_day

Question_9:What is the most frequent answer recorded in the survey? Use the getMode function to compute results

getMode(game_day)

[1] "Saturday"