Activity 4

#Addition
2+3

[1] 5

#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)

[1] 1

log10(100)

[1] 2

log(10,base=5)

[1] 1.430677

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

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?

#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=(H+BB+HBP)/(AB+BB+HBP+SF)
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 equals 8? FALSE

[1] FALSE

3 != 8# Is 3 different from 8? TRUE

[1] TRUE

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

[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

ls()

 [1] "AB"                 "BA"                 "bar"                "barsample"         
 [5] "Batting_Average"    "BB"                 "game_day"           "getMode"           
 [9] "H"                  "HBP"                "hits_per_9innings"  "n"                 
[13] "OBP"                "On_Base_Percentage" "pitches_by_innings" "player_positions"  
[17] "runs_per_9innings"  "sals"               "samplerows"         "SF"                
[21] "strikes_by_innings" "Total_Bases"        "x"                 

rm(Total_Bases)

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(1, 2, 3, 4, 5)

hits_per_9innings <- c(1, 2, 3, 4, 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 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] 1

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] 5

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.

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]  2 10  8  7  4

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 “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] 10  2  3  8  1

The variable sample rows 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
10    J   10
2     B    2
3     C    3
8     H    8
1     A    1

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) 

[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

# 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] 1

#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"