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plot(cars)

mean(cars$speed)
## [1] 15.4
mean(cars$dist)
## [1] 42.98
max(cars$dist)
## [1] 120
max(cars$speed)
## [1] 25
4+1
## [1] 5
5-2
## [1] 3
2^2
## [1] 4
sqrt(25)
## [1] 5
2^5
## [1] 32
# Natural log of 2
log(2.72)
## [1] 1.000632
log10(5)
## [1] 0.69897
log10(10)
## [1] 1
log10(100)
## [1] 2
# Computing log base 10
log(10, base=5)
## [1] 1.430677
log(10, base=2)
## [1] 3.321928
log(1000, base=10)
## [1] 3

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

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
Batting_Average=round(BA,digits=3)
Batting_Average
## [1] 0.198

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

#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=565,H=156,BB=156,HBP=3,SF=7
OBP=(156+65+3)/(565+156+65+3+7)
OBP
## [1] 0.281407

Test whether something is less than, greater than or equal to something

3 == 8# Does 3 equals 8?
## [1] FALSE
3 != 8# Is 3 different from 8?
## [1] TRUE
3 <= 8# Is 3 less than or equal to 8?
## [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, create a variable and assign it a value using <- as follows

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

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

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

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

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
testing_vector <- c(54, 27, 17, 9, 7)
testing_vector
## [1] 54 27 17  9  7
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(15, 13, 10, 9, 18)
hits_per_9innings <- c(12, 10, 15, 9, 13)
runs_per_9innings
## [1] 15 13 10  9 18
hits_per_9innings
## [1] 12 10 15  9 13

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
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] 12

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] 13

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

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] 9 8 1 3 5

Create a dataframe with first 10 letters and number them

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  6  3  7  8

The variable samplerows contains the rows of bar which make a random sample from all the rows in bar. 

# extract rows
barsample <- bar[samplerows, ]
# print sample
print(barsample)
##    var1 var2
## 10    J   10
## 6     F    6
## 3     C    3
## 7     G    7
## 8     H    8
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.

x <- c("Yes","No","No","Yes","Yes") 
table(x)
## x
##  No Yes 
##   2   3

Numerical measures of center and spread

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

Mode function 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
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(hits_per_9innings)
## [1] 12

#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"