You can use R for basic computations you would perform in a calculator.
# Addition (Try changing the numbers below to perform other additions/subtractions)
63-23## [1] 40# Division (Try changing these numbers to divide different values)
5/8## [1] 0.625# Exponentiation (e.g. 2 raised to the power of 3)
42^-3 ## [1] 1.349746e-05# Square root
sqrt(4)## [1] 2# Logarithms (natural log by default)
log(32)## [1] 3.465736#Question_1: Compute the log base 5 of 10 and the log of 10.
# Write your code here (uncomment the lines below to test):
log(10, base = 5)## [1] 1.430677log(10)## [1] 2.302585Computing 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?
# (You can change 29 or 112 to calculate other batting averages)
BA = (30) / (107)
BA## [1] 0.2803738Batting_Average = round(BA, digits = 3)
Batting_Average## [1] 0.28#Question_2: What is the batting average of a player that bats 42 hits in 212 at bats?
# Write your code here (uncomment below to test):
BA_q2 = 42 / 212
round(BA_q2, digits = 3)## [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
# (Feel free to edit these stats to calculate OBP for different players)
OBP = (172 + 84 + 5) / (515 + 84 + 5 + 6)
OBP## [1] 0.4278689On_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
# Write your code here:
OBP_q3 <- (156 + 65 + 3) / (565 + 65 + 3 + 7)
round(OBP_q3, digits = 3)## [1] 0.35Often you will want to test whether something is less than, greater than or equal to something.
3 == 8 # Does 3 equals 8?## [1] FALSE3 != 8 # Is 3 different from 8?## [1] TRUE3 <= 8 # Is 3 less than or equal to 8?## [1] TRUE3 > 4## [1] FALSEThe 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] TRUEIn R, you create a variable and assign it a value using
<- as follows.
Total_Bases <- 6 + 5
Total_Bases * 3## [1] 33To see the variables that are currently defined, use ls
(as in “list”).
ls()## [1] "AB" "BA" "BA_q2"
## [4] "Batting_Average" "BB" "H"
## [7] "HBP" "OBP" "OBP_q3"
## [10] "On_Base_Percentage" "SF" "Total_Bases"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 <- is preferred because it is
less likely to be confused with the logical comparison operator
==.
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”).
# (Change the numbers in c() to define different pitches per inning)
pitches_by_innings <- c(15, 11, 11, 19, 10)
pitches_by_innings## [1] 15 11 11 19 10# (Change the numbers in c() to define different strikes per inning)
strikes_by_innings <- c(10, 15, 7, 12, 8)
strikes_by_innings## [1] 10 15 7 12 8#Question_4: Define two vectors, runs_per_9innings and hits_per_9innings, each with five elements.
# Write your code here (e.g. uncomment and edit):
runs_per_9innings <- c(3, 5, 2, 4, 1)
hits_per_9innings <- c(8, 10, 6, 9, 5)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 2rep(1, 4)## [1] 1 1 1 1# consecutive numbers
1:5## [1] 1 2 3 4 52:10## [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 9seq(2, 13, by = 3)## [1] 2 5 8 11Many functions and operators like + or -
will work on all elements of the vector.
# add vectors element-wise
pitches_by_innings + strikes_by_innings## [1] 25 26 18 31 18# compare vectors element-wise
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] 13.2You can access parts of a vector by using [. Recall the
value of the vector pitches_by_innings:
pitches_by_innings## [1] 15 11 11 19 10# If you want to get the first element:
pitches_by_innings[1]## [1] 15#Question_5: Get the first element of hits_per_9innings.
# Write your code here:
hits_per_9innings[1]## [1] 8If 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:
pitches_by_innings[length(pitches_by_innings)]## [1] 10#Question_6: Get the last element of hits_per_9innings.
# Write your code here:You can also extract multiple values from a vector. For instance, to get the 2nd through 4th values:
pitches_by_innings[c(2, 3, 4)]## [1] 11 11 19Vectors can also contain strings or logical values.
player_positions <- c("catcher", "pitcher", "infielders", "outfielders")
player_positions## [1] "catcher" "pitcher" "infielders" "outfielders"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.
# (You can change values or add more columns here)
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.
To randomly select a sample, use the function sample().
The following code selects 5 numbers between 1 and 10 at random (without
duplication).
# (Change the size or range to sample differently)
sample(1:10, size = 5)## [1] 7 2 6 10 1size =) 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:
sample() to select a sample of size n
from a vector of the row numbers of the data frame.[ 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”; it is automatically
pre-defined in R).
bar <- data.frame(var1 = LETTERS[1:10], var2 = 1:10)
# Check data frame
barSuppose 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 <- 5Now, 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] 4 1 8 3 7The variable samplerows contains the row indexes of
bar which make a random sample. Extract those rows from
bar with:
# extract rows
barsample <- bar[samplerows, ]
# print sample
print(barsample)## var1 var2
## 4 D 4
## 1 A 1
## 8 H 8
## 3 C 3
## 7 G 7The 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), ]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 3Suppose, 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
# (You can change these compensation numbers to calculate metrics for a different sample)
sals <- c(11, .6, 5, 16, 2, 8, 3, 10, 5, 0.25)# the average
mean(sals) ## [1] 6.085# the variance
var(sals)## [1] 26.01669# the standard deviation
sd(sals)## [1] 5.100656# the median
median(sals)## [1] 5# Tukey's five number summary, useful for boxplots
# five numbers: min, lower hinge, median, upper hinge, max
fivenum(sals)## [1] 0.25 2.00 5.00 10.00 16.00# summary statistics
summary(sals)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.250 2.250 5.000 6.085 9.500 16.000In 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] 11#Question_7: Find the most frequent value of hits_per_9innings.
# Write your code here:
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")
# Write your table code here:table(game_day)
#Question_9: What is the most frequent answer recorded in the survey? Use the getMode function to compute results.
# Write your code here (uncomment below to test):
getMode(game_day)## [1] "Saturday"