Activity#4

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

#log 
log (10)

[1] 2.302585

log(2.72, base =2.72)

[1] 1

##Question_1: Compute the log base 5 of 10 and the log of 10.

log(10)

[1] 2.302585

log(100)

[1] 4.60517

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

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=(42)/(212)
BA

[1] 0.1981132

Batting_Average=round(BA,digits = 3)
Batting_Average

[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=(156+65+3)/(565+65+3+7)
OBP

[1] 0.35

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

[1] TRUE

3>5

[1] FALSE

3==5

[1] FALSE

!FALSE #no false  is true 

[1] TRUE

!TRUE # no true is false 

[1] FALSE

2<3| 1==5 # 2<3 is true , 1==5 is false , true or false is true 

[1] TRUE

2>3 | 2==3

[1] FALSE

2>1 & 3>=3

[1] TRUE

2>1 & 3<=3

[1] TRUE

#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

#Assigning Values to Variables

Total_Bases <- 6 + 5
Total_Bases*3

[1] 33

ls()

[1] "BA"                 "Batting_Average"    "OBP"               
[4] "OBS"                "On_Base_Percentage" "Total_Bases"       

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

rm(Total_Bases)

#Vectors

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

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

runs_per_9innings<-c(2,5,7,11,13)
hits_per_9innings<-c(11,13,16,18,19)
runs_per_9innings

[1]  2  5  7 11 13

hits_per_9innings

[1] 11 13 16 18 19

2:4

[1] 2 3 4

#sequence 
seq(1,20, by=3)

[1]  1  4  7 10 13 16 19

# 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

#First

# If you want to get the first element:
pitches_by_innings[1]

#Last 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)]

#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)]

#Vectors can also be strings or logical values

player_positions <- c("catcher", "pitcher", "infielders", "outfielders")

Data Frames 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 

#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] 5 6 4 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)

x <- c("Yes","No","No","Yes","Yes") 
table(x)

x
 No Yes 
  2   3 

sals <- c(12, .4, 5, 2, 50, 8, 3, 1, 4, 0.25)
# the average
mean(sals) 

[1] 8.565

var(sals)

[1] 225.5145

sd(sals)

[1] 15.01714

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 

# Function to find the mode, i.e. most frequent value
getMode <- function(x) {
     ux <- unique(x)
     ux[which.max(tabulate(match(x, ux)))]
 }

# 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(pitches_by_innings)

[1] 10

getMode(hits_per_9innings)

[1] 11

#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<-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"