Manuel Madalena

You can use R for basic computations you would perform in a calculator

Addition

2+3
## [1] 5

Subtraction

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.

# Compute log base 5 of 10
log_5_10 <- log(10, base = 5)
log_5_10
## [1] 1.430677
# Compute log base 10 of 10 (common log)
log_10_10 <- log(10)
log_10_10
## [1] 2.302585

Computing some offensive metrics in Baseball

Batting Average=(No. of Hits)/(No. of At Bats) What is the batting average of a player that bats 29 hits in 112 at bats?

BA=(29)/(112)
BA
## [1] 0.2589286
Batting_Average=round(BA,digits = 3)
Batting_Average
## [1] 0.259

Question_2:What is the batting average of a player that bats 42 hits in 212 at bats?

BA2=(42)/(212)
BA2
## [1] 0.1981132

On Base Percentage

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=65,HBP=3,SF=7

OBP2=(156+65+3)/(565+65+3+7)
OBP2
## [1] 0.35

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

3 == 8  # Does 3 equals 8?
## [1] FALSE
3 != 8# Is 3 different from 8?
## [1] TRUE
3 <= 8# Is 3 less than or equal to 8?
## [1] TRUE
3>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"                 "BA2"                "Batting_Average"   
## [4] "log_10_10"          "log_5_10"           "OBP"               
## [7] "OBP2"               "On_Base_Percentage" "Total_Bases"

To delete a variable, use rm (as in “remove”)

rm(Total_Bases)
ls() # to verify Total_Bases was removed
## [1] "BA"                 "BA2"                "Batting_Average"   
## [4] "log_10_10"          "log_5_10"           "OBP"               
## [7] "OBP2"               "On_Base_Percentage"

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
## [1]  9 12  6 14  9

Question_4: Define two vectors,runs_per_9innings and hits_per_9innings, each with five elements.

runs_per_9innings <- c(8, 6, 10, 7, 3)
runs_per_9innings
## [1]  8  6 10  7  3
hits_per_9innings <- c(5, 4, 8, 11, 2)
hits_per_9innings
## [1]  5  4  8 11  2

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

consecutive numbers

1:5
## [1] 1 2 3 4 5
2:10
## [1]  2  3  4  5  6  7  8  9 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

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 == 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_9innings
## [1]  5  4  8 11  2
hits_per_9innings[1]
## [1] 5

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.

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

pitches_by_innings[c(2, 3, 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 
##   bonus active_roster salary
## 1     2           yes    1.5
## 2     3            no    2.5
## 3     1           yes    1.0

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 between 1 and 10 at random (without duplication)

sample(1:10, size=5)
## [1]  3 10  8  9  4

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”; LETTERS is automatically defined and pre-loaded in R)
bar <- data.frame(var1 = LETTERS[1:10], var2 = 1:10)
bar
##    var1 var2
## 1     A    1
## 2     B    2
## 3     C    3
## 4     D    4
## 5     E    5
## 6     F    6
## 7     G    7
## 8     H    8
## 9     I    9
## 10    J   10

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

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] 6 9 2 1 7

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, ]
barsample
##   var1 var2
## 6    F    6
## 9    I    9
## 2    B    2
## 1    A    1
## 7    G    7

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), ]
##    var1 var2
## 10    J   10
## 5     E    5
## 6     F    6
## 8     H    8
## 1     A    1

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

Support_HomeTeam <- c("Yes","No","No","Yes","Yes") 
table(Support_HomeTeam)
## Support_HomeTeam
##  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)
sals
##  [1] 12.00  0.40  5.00  2.00 50.00  8.00  3.00  1.00  4.00  0.25

the average

mean(sals) 
## [1] 8.565

the variance

var(sals)
## [1] 225.5145

the standard deviation

sd(sals)
## [1] 15.01714

the median

median(sals)
## [1] 3.5

Tukey’s five number summary, usefull for boxplots

five numbers: min, lower hinge, median, upper hinge, max

fivenum(sals)
## [1]  0.25  1.00  3.50  8.00 50.00

summary statistics

summary(sals)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.250   1.250   3.500   8.565   7.250  50.000

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_innings

Most frequent value in pitches_by_innings

getMode(pitches_by_innings)
## [1] 10

Question_7: Find the most frequent value of hits_per_9innings.

getMode(hits_per_9innings)
## [1] 5

Question_8: Summarize the following survey with the 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
##  [1] "Saturday" "Saturday" "Sunday"   "Monday"   "Saturday" "Tuesday" 
##  [7] "Sunday"   "Friday"   "Friday"   "Monday"

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

getMode(game_day)
## [1] "Saturday"