# Jet win total for the past 20 years
vector_num1 = c(2,7,4,5,5,10,4,8,6,8,11,9,9,4,10,4,10,6,9,10)
length(vector_num1) # 20## [1] 20vector_char1 <- as.character(vector_num1)
class(vector_char1) # character## [1] "character"
3. Use R to convert the vector from question 1 into a vector of factors
vector_factor1<-factor(vector_char1)
class(vector_factor1) # factor## [1] "factor"
4. Use R to show how many levels the vector in the previous question has.
# note: R puts 10 and 11 before 2 since we created it from characters
nlevels(vector_factor1) # 9## [1] 9levels(vector_factor1) # "10" "11" "2" "4" "5" "6" "7" "8" "9"## [1] "10" "11" "2" "4" "5" "6" "7" "8" "9"
5. Use R to create a vector that takes the vector from question 1 and performs on it the formula 3^2−4X+1.
(3*vector_num1^2) - (4*vector_num1) + 1## [1] 5 120 33 56 56 261 33 161 85 161 320 208 208 33 261 33 261 85 208
## [20] 261
6. Create a named list.
jets_defense = list(dline=c("Williams","Fatukasi","Anderson"), linebackers =c("Hewitt","Jenkins","Langi","Williamson"), secondary= c("Poole","Austin","Maye","Desir") )
names(jets_defense)## [1] "dline" "linebackers" "secondary"jets_defense["dline"]## $dline
## [1] "Williams" "Fatukasi" "Anderson"
7. Create a data frame with four columns – one each character, factor (with three levels), numeric, and date.
player = c("Norm Van Brocklin", "Matt Schaub", "Warren Moon", "Boomer Esiason")
era = c("Fifties","Current","Nineties","Nineties")
yards = c(554,527,527,522)
date = c(as.Date("1951-09-28"),as.Date("2012-11-18"), as.Date("1990-12-16"), as.Date("1996-11-10"))
# note: my data frames converted to character by default so here i have to explicitly call factor()
qb_best_games <- data.frame(player,era = factor(era), yards, date)
8. Illustrate how to add a row with a value for the factor column that isn’t already in the list of levels.
# this requires to replace the era column with itself, but specify the levels with the new level added
lvls <- levels(qb_best_games$era)
lvls[length(lvls) + 1] <- 'Eighties'
qb_best_games$era <- factor(qb_best_games$era, levels = lvls)
qb_best_games<-rbind(qb_best_games,data.frame(player= "Phil Sims", era= factor("Eighties"), yards = 513, date= as.Date('1085-10-13')))
9. Show the code that would read in a CSV file called temperatures.csv
qb_games <- read.csv("C:\\Users\\arono\\Documents\\R\\SportsStats\\qb_best_games.csv")
head(qb_games,10)## Rank Player Yds Tm Date Decade
## 1 1 Norm Van Brocklin 554 RAM 1951-09-28 50s
## 2 2 Matt Schaub 527 HOU 2012-11-18 10s
## 3 3 Warren Moon 527 HOU 1990-12-16 90s
## 4 4 Boomer Esiason 522 ARI 1986-11-10 80s
## 5 5 Ben Roethlisberger 522 PIT 2014-10-26 10s
## 6 6 Dan Marino 521 MIA 1988-10-23 80s
## 7 7 Matthew Stafford 520 DET 2012-01-01 10s
## 8 8 Tom Brady 517 NWE 2011-09-12 10s
## 9 9 Jared Goff 517 LAR 2019-09-29 10s
## 10 10 Phil Simms 513 NYG 1985-10-13 80s
10. Use a loop to calculate the final balance, rounded to the nearest cent, in an account that earns 3.24% interest compounded monthly after six years if the original balance is $1,500.
principal <- 1500
rate <- .0324
freq <- 12
years <- 6
for (rolls in 1:(freq*years))
{
principal=principal*(1+(rate/freq))
}
sprintf("%.2f",principal)## [1] "1821.40" # format method perhaps not as functional as sprintf
format(principal, digits=6, nsmall=2)## [1] "1821.40"
11. Create a numeric vector of length 20 and then write code to calculate the sum of every third element of the vector you have created.
# Jet win total for the past 20 years
vector_num1 = c(2,7,4,5,5,10,4,8,6,8,11,9,9,4,10,4,10,6,9,10)
vector_num1%%3 # all the values of vector_num1 mod 3## [1] 2 1 1 2 2 1 1 2 0 2 2 0 0 1 1 1 1 0 0 1vector_num1[1:20%%3==0] # the values of every 3rd number, i.e. 4 10 6 9 10 6## [1] 4 10 6 9 10 6sum(vector_num1[1:20%%3==0]) # 45 = 4+10+6+9+10+6## [1] 45x=2
sumx=0
for (i in 1:10)
{
sumx=sumx+x^i # series is {2,4,8,16...1024}
}
sumx # 2046## [1] 2046
13. Use a while loop to accomplish the same task as in the previous exercise
x=2
sumx=0
i=1
while (i <= 10)
{
sumx=sumx+x^i # series is {2,4,8,16...1024}
i=i+1
}
print(sumx) # 2046## [1] 2046
14. Solve the problem from the previous two exercises without using a loop.
sumx<-sum(2^(1:10))
sumx## [1] 2046See here for more info
Inline mathematical material is set off by the use of single dollar-sign characters. This is better to integrate text and equations.
This ($_{i=1}^n X_i$) is inline: \(\sum_{i=1}^n X_i\)
Display form uses 2 dollar signs. ( use backslash if you every want to display a dollar sign )
\[\sum_{i=1}^n X_i\]
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$$_{i=1}^{10} 2^i$$ \[\sum_{i=1}^{10} 2^i\]
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\[\alpha, \beta, \gamma, \Gamma\]
\(x \ge 15\) \(x \le 15\)
n choose k \[n \choose k\]
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