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# 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.
log10(10)## [1] 1log10(100)## [1] 2log(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] 0.2589286Batting_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#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] 0.4278689On_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)/(At Bats+BB+HBP+SF)
OBP=(156+65+3)/(565+65+3+7)
On_Base_Percentage=round(OBP,digits = 3)
On_Base_Percentage## [1] 0.35#Often you will want to test whether something is less than, greater than or equal to something.
3 <= 8# Is 3 less than or equal to 8?## [1] TRUE3 == 8# Does 3 equals 8?## [1] FALSE3 != 8# Is 3 different from 8?## [1] TRUE3 <= 8# Is 3 less than or equal to 8?## [1] TRUE3>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] TRUE2>3|2==5## [1] FALSE2>1 & 3>=3## [1] TRUE2>1 & 3>=5## [1] FALSE#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] 33ls()## [1] "BA" "Batting_Average" "OBP"
## [4] "On_Base_Percentage" "Total_Bases"rm(Total_Bases)ls()## [1] "BA" "Batting_Average" "OBP"
## [4] "On_Base_Percentage"#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”).
pitches_by_innings <- c(12, 15, 10, 20, 10)
pitches_by_innings## [1] 12 15 10 20 10strikes_by_innings <- c(9, 12, 6, 14, 9)
strikes_by_innings## [1] 9 12 6 14 9
``` r
#Question_4: Define two vectors,runs_per_9innings and hits_per_9innings, each with five elements.
#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 2rep(1,4)## [1] 1 1 1 1# consecutive numbers
1:5## [1] 1 2 3 4 52:10## [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 9seq(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.
#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.
#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] 3 8 10 7 1The 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
barSuppose 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 <- 5Now, 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] 2 10 4 5 6The 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
## 2 B 2
## 10 J 10
## 4 D 4
## 5 E 5
## 6 F 6The 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 3Numerical 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 50.000How 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 (most frequent value)
#Question_7: Find the most frequent value of hits_per_9innings.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] 10runs_per_9_innings<-c(2,5,7,11,13)
hits_per_9_innings<-c(11,13,16,18,19)
runs_per_9_innings## [1] 2 5 7 11 13hits_per_9_innings## [1] 11 13 16 18 19getMode(strikes_by_innings)## [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")#Question_9: What is the most frequent answer recorded in the survey? Use the getMode function to compute results.
getMode(game_day)## [1] "Saturday"player_positions <- c("catcher", "pitcher", "infielders", "outfielders")
player_positions## [1] "catcher" "pitcher" "infielders" "outfielders"data.frame(bonus = c(2, 3, 1),#in millions
active_roster = c("yes", "no", "yes"),
salary = c(1.5, 2.5, 1))#in millions When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the Preview button or press Ctrl+Shift+K to preview the HTML file).
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