This is our first in-class activity for **module 2* shift+ctrl+enter will run the cell chunk ctrl + alt+ i to insert a new cell chunk

# 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(10, base = 5)
## [1] 1.430677
log(10, base = 10)
## [1] 1

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

26% is considered to be a good percentage for batting average

#Rounding results of Batting Average to only three decimal places
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?

FRom 212 times at bats the player batted 42 times.

BA = (42)/(212)
BA
## [1] 0.1981132
#round the BA results to three decimals places.
Batting_Average2 = round(BA, digits = 3)
Batting_Average2
## [1] 0.198
#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=(172+84+5)/(515+172+84+5+6)
OBP
## [1] 0.3337596
#Rounding results of OBP to only three decimal places
On_Base_Percentage=round(OBP,digits = 3)
On_Base_Percentage
## [1] 0.334

A successful baseball player succeeds roughly 30% of the time at the plate – the best OBP is right around the .300/.320 mark. Therefore the results above are really good.

#Question_3:Compute the OBP for a player with the following general stats: #AB=565,H=156,BB=65,HBP=3,SF=7

OBP = (156 +65+3)/(565+156+65+3+7)
OBP = round(OBP, digits = 3)
OBP
## [1] 0.281

The threshold we are going to use for OBP is in .300. Therefore 0.281 is not good result in this case.

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

# Does 3 equals 8?

3 == 8
## [1] FALSE
# Is 3 different from 8?

3 != 8
## [1] TRUE
# Is 3 less than or equal to 8?

3 <= 8
## [1] TRUE

The logical operators are & for logical AND, | for logical OR, and ! for NOT. These are some examples:

# Logical Disjunction (or)
# False OR False
FALSE | FALSE 
## [1] FALSE
# Logical Conjunction (and)
#True AND False

TRUE & FALSE 
## [1] FALSE
# Negation
# Not False

! FALSE 
## [1] TRUE
# Combination of statements
# 2<3 is True, 1==5 is False, True OR False is True

2 < 3 | 1 == 5 
## [1] TRUE

##Assigning Values to Variables

In R, you create a variable and assign it a value using <- as follows

Total_Bases <- 6 + 5  #11
Total_Bases*3         # 3 times 11
## [1] 33

To see the variables that are currently defined, use ls (as in “list”)

ls()
## [1] "BA"                 "Batting_Average"    "Batting_Average2"  
## [4] "OBP"                "On_Base_Percentage" "Total_Bases"

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

# I will delete here "bar"
rm(bar)
## Warning in rm(bar): object 'bar' not found

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”).

#creating a vector with the numbers of pitching by inning
pitches_by_innings <- c(12, 15, 10, 20, 10) 
pitches_by_innings
## [1] 12 15 10 20 10
#creating a vector with the numbers of strickes a pitcher throw by innings.
strickes_by_innings <- c(9,12,6,14,9)
strickes_by_innings
## [1]  9 12  6 14  9

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

#creating two vectors using random numbers
runs_per_9innings <- c(5,10,13,3,6)
runs_per_9innings
## [1]  5 10 13  3  6
hits_per_9innings <- c(10,5,3,11,4)
hits_per_9innings
## [1] 10  5  3 11  4

There are also some functions that will create vectors with regular patterns, like repeated elements.

# replicate function
#This will repeat the number in the first argument 5 times (number in the second argument)

rep(2, 5)
## [1] 2 2 2 2 2
# consecutive numbers
#this will display numbers from 1 to 5 in order.

1:5
## [1] 1 2 3 4 5
# sequence of numbers from 1 to 10 in steps of 2

seq(1, 10, by=2)
## [1] 1 3 5 7 9

Many functions and operators like + or - will work on all elements of the vector.

# add vectors
pitches_by_innings+strickes_by_innings
## [1] 21 27 16 34 19
# compare vectors
pitches_by_innings == strickes_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] 10

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.

#getting the last element
hits_per_9innings[length(hits_per_9innings)]
## [1] 4

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]  1  5 10  2  3

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]  9  7 10  4  2

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
## 9     I    9
## 7     G    7
## 10    J   10
## 4     D    4
## 2     B    2

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(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 inning.

getMode(pitches_by_innings)
## [1] 10

#Question_7: Find the most frequent value of hits_per_9innings.

getMode(hits_per_9innings)
## [1] 10

#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"
table(game_day)
## game_day
##   Friday   Monday Saturday   Sunday  Tuesday 
##        2        2        3        2        1

Saturday is the day of the week that the survey participants prefer to watch Baseball.

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

#using the getMode function we created as part of the activity.
getMode(game_day)
## [1] "Saturday"

We are confirming that the people favorite day to watch Baseball is on Saturday as per the Survey.