Activity 4: First Steps with R

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.

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

[1] 1.430677

# natural log of 10
log(10)

[1] 2.302585

Computing some offensive metrics in Baseball

Batting Average

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?

BA_2 <- 42 / 212
BA_2

[1] 0.1981132

Batting_Average_2 <- round(BA_2, digits = 3)
Batting_Average_2

[1] 0.198

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 = 65, HBP = 3, SF = 7

OBP_2 <- (156 + 65 + 3) / (565 + 65 + 3 + 7)
OBP_2

[1] 0.35

On_Base_Percentage_2 <- round(OBP_2, digits = 3)
On_Base_Percentage_2

[1] 0.35

Logical comparisons

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 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 # 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"                   "BA_2"                 "bar"                  "barsample"           
 [5] "Batting_Average"      "Batting_Average_2"    "course"               "hits_per_9innings"   
 [9] "n"                    "name"                 "OBP"                  "OBP_2"               
[13] "On_Base_Percentage"   "On_Base_Percentage_2" "pitches_by_innings"   "runs_per_9innings"   
[17] "samplerows"           "scores"               "strikes_by_innings"   "students"            
[21] "teams"                "Total_Bases"          "x"                    "y"                   

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

rm(Total_Bases)

Either <- or = can be used to assign a value to a variable, but I prefer <- because it 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(4, 3, 5, 2, 6)
hits_per_9innings <- c(8, 7, 10, 6, 9)

runs_per_9innings

[1] 4 3 5 2 6

hits_per_9innings

[1]  8  7 10  6  9

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]

[1] 8

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_9innings[length(hits_per_9innings)]

[1] 9

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
)

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] 4 6 8 2 5

The first argument gives the vector of data to select elements from. 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”; 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

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)

# print sample rows
samplerows

[1]  3  6  8  1 10

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 sample
print(barsample)

   var1 var2
3     C    3
6     F    6
8     H    8
1     A    1
10    J   10

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, 0.4, 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)

[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, useful 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] 8

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"
)

table(game_day)

game_day
  Friday   Monday Saturday   Sunday  Tuesday 
       2        2        3        2        1 

Question 9

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

getMode(game_day)

[1] "Saturday"