#First Steps with R activity #Basic calculations
#Additon
2+3## [1] 5#Division
2/3## [1] 0.6666667# Exponentiation
2^3## [1] 8#square root
sqrt(100)## [1] 10#Logarithms
log(2)## [1] 0.6931472#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?
bats= 29
total_bats= 112
ans= (bats)/(total_bats)
ans## [1] 0.2589286#round the batting average to 3 decimal places
Batting_average=round(ans, 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?
bats2= 42
totalbats2= 212
ans2= (bats2)/(totalbats2)
ans2## [1] 0.1981132#On Base Percentage
#OBP=(H+BB+HBP)/(At Bats+H+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= (H+BB+HBP)/(AB+H+BB+HBP+SF)
OBP## [1] 0.3337596#round the OBP 3 decimal places
round(OBP, digits = 3)## [1] 0.334#Question_3:Compute the OBP for a player with the following general stats:
AB=565
H=156
BB=65
HBP=3
SF=7
OBP2= (H+BB+HBP)/(AB+H+BB+HBP+SF)
OBP2## [1] 0.281407#Often you will want to test whether something is less than, greater than or equal to something.
3 == 8 # Does 3 equals 8? == (refers to being equivalen terms or numbers)## [1] FALSE3 != 8# Is 3 different from 8? (!= is not equal)## [1] TRUE#Less than or equal
# Is 2 less than or equal to 0?
2<=0## [1] FALSE#greater than
3>4## [1] FALSE#The logical operators are & for logical AND, | for logical OR, and ! for NOT. These are some examples:
#use & first
3&3## [1] TRUE#now use OR
FALSE | FALSE## [1] FALSE# Not true is the same as false
!TRUE## [1] FALSE#True and false will always equal false
TRUE & FALSE## [1] FALSE#negation is the same as saying not
!TRUE## [1] FALSE# Combination of statements
2 < 3 | 1==5 #the first statement 2<3 is TRUE, the second is 1=5 which is false, so we say: TRUE or FALSE = TRUE## [1] TRUE#Assigning Values to Variables
Total_Bases <- 6+5
Total_Bases*3## [1] 33#To see the variables that are currently defined, use ls (as in “list”)
ls()## [1] "AB" "ans" "ans2" "bats"
## [5] "bats2" "Batting_average" "BB" "H"
## [9] "HBP" "OBP" "OBP2" "SF"
## [13] "Total_Bases" "total_bats" "totalbats2"#remove values from the list
rm(Total_Bases)#see the change
ls()## [1] "AB" "ans" "ans2" "bats"
## [5] "bats2" "Batting_average" "BB" "H"
## [9] "HBP" "OBP" "OBP2" "SF"
## [13] "total_bats" "totalbats2"#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”).
#create a vector called "pitches_by_innings" and assign 5 random values
pitches_by_innings <- c(12,15,10,20,10)
pitches_by_innings## [1] 12 15 10 20 10#create a vector called "strikes_by_innings" and assign 5 random values
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(10,5,4,18,22)
hits_per_9innings <- c(9,13,1,7,20)#show the first new vector
runs_per_9innings## [1] 10 5 4 18 22#show the second new vector
hits_per_9innings## [1] 9 13 1 7 20#There are also some functions that will create vectors with regular patterns, like repeated elements.
#replicate function
rep(2,10) #creates a sequence of 10 2's## [1] 2 2 2 2 2 2 2 2 2 2# replicate the number 1, 4 times
rep(1,4)## [1] 1 1 1 1#create a list of consecutive numbers from 1-5
1:5## [1] 1 2 3 4 5#create a sequence of consecutive numbers from 2-10
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# sequence from 2 to 13 with a step of 3
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
#this compares the numbers inside of the vectors one-by-one and in order
pitches_by_innings == strikes_by_innings## [1] FALSE FALSE FALSE FALSE FALSE#if i create 2 more vectors with the same numbers, it should show TRUE for all values
X <- c(10,12)
Z <- c(10,12)
X == Z ## [1] TRUE TRUE#Find the length of vectors
length(pitches_by_innings) #this refers to the number of elements in the variable## [1] 5# find minimum value in vector
min(pitches_by_innings)## [1] 10#find the average value in the 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#get the first element
pitches_by_innings[1]## [1] 12#Question_5: Get the first element of hits_per_9innings.
hits_per_9innings[5]## [1] 20#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)] #this will print the last value in the vector## [1] 10#Question_6: Get the last element of hits_per_9innings.
hits_per_9innings[length(hits_per_9innings)]## [1] 20#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")#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.
#the data is in millions
data.frame(bonus = c(2,3,1),
active_roster = c("yes", "no", "yes"),
salary = c(1.5, 2.5, 1))###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] 2 4 8 9 10#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:
#Use sample() to select a sample of size n from a vector of the row numbers of the data frame.
#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 âAâ to âZâ; 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] 1 3 6 7 4#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
## 1 A 1
## 3 C 3
## 6 F 6
## 7 G 7
## 4 D 4#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
#create a variable with the salaries in millions
sals <- c(12, .4, 5, 2, 50, 8, 3, 1, 4, 0.25)
# the average
mean(sals) ## [1] 8.565#get the variance of the salaries
var(sals)## [1] 225.5145#calculate 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#get the summary of the statistics of the data
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 in x
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
#use the formula to get the mode
getMode(pitches_by_innings)## [1] 10#Question_7: Find the most frequent value of hits_per_9innings.
getMode(hits_per_9innings)## [1] 9#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"