Q1a (8 points)

Create and print a vector x with all integers from 1 to 80 and a vector y containing multiples of 3 in the same range. Hint: use seq()function. Calculate the difference in lengths of the vectors x and y. Hint: use length()

#INSERT YOUR ANSWER HERE
x<-c(1:80)
x

##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
## [51] 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
## [76] 76 77 78 79 80

y<-seq(3,80,3)
y

##  [1]  3  6  9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75
## [26] 78

length(x)-length(y)

## [1] 54

Q1b (8 points)

Create a new vector, x_square, with the square of elements at indices 1, 3, 5, 7, 9, 15, 20, 23, 24, and 29 from the variable x. Hint: Use indexing rather than a for loop. Calculate the mean and median of the FIRST five values from x_square.

#INSERT YOUR ANSWER HERE
x<-c(1,3,5,7,9,15,20,23,24,29)
x_square<-x^2
mean(x_square[1:5])

## [1] 33

median(x_square[1:5])

## [1] 25

Q1c (8 points)

To convert factor to number, would it be correct to use the following commands? Explain your answer.

factorVar <- factor(c(1, 6, 5.4, 3.2)) as.numeric(factorVar)

#INSERT YOUR ANSWER HERE
#The following command is incomplete, although it prints the factorVar variable 
#as numeric in the console, the variable itself is still classified as 
#a factor (class(factorVar) = "factor"). The correct method of completing the 
#command would be to reassign/assign and apply the "as.numeric" function 
#under a new variable. After that, the class would come up as numeric 
#(class(factorVar) = "numeric") as shown below.

factorVar <- factor(c(1, 6, 5.4, 3.2))
factorVar<-as.numeric(factorVar)

## To check if the factor converted to a number
class(factorVar)

## [1] "numeric"

Q1d (8 points)

A comma-separated values file dataset.csv consists of missing values represented by Not A Number (NaN) and question mark (?). How can you read this type of files in R? NOTE: Please make sure you have saved the dataset.csv file at your current working directory.

#INSERT YOUR ANSWER HERE
getwd()

## [1] "C:/Users/ryant/OneDrive/Desktop"

dataset <- read.csv(file = 'C:/Users/ryant/OneDrive/Desktop/dataset.csv' , header=FALSE, stringsAsFactors = FALSE, na.strings=c("?","NaN"))
na.omit(dataset)

##     V1  V2  V3  V4  V5  V6  V7  V8  V9 V10
## 1    1   2   3   4   5   6   7   8   9  10
## 2   11  12  13  14  15  16  17  18  19  20
## 3   21  22  23  24  25  26  27  28  29  30
## 4   31  32  33  34  35  36  37  38  39  40
## 7   61  62  63  64  65  66  67  68  69  70
## 10  91  92  93  94  95  96  97  98  99 100
## 12 111 112 113 114 115 116 117 118 119 120
## 13 121 122 123 124 125 126 127 128 129 130
## 15 141 142 143 144 145 146 147 148 149 150
## 16 151 152 153 154 155 156 157 158 159 160

Q2a (8 points)

Compute:

$$\sum_{n=1}^{50}\frac{3^{n}}{n!}$$ Hint: Use factorial(n) to compute $n!$.

#INSERT YOUR ANSWER HERE
n<-1:50
sum(3^n/(factorial(n)))

## [1] 19.08554

Q2b (8 points)

Compute:

$$\prod_{n=2}^{22} \left( 3n + \frac{3}{\sqrt[3]{n}} \right)$$ NOTE: The symbol $\Pi$ represents multiplication.

#INSERT YOUR ANSWER HERE
n<-2:22
pie<-prod((3*n)+(3/n^(1/3)))

Q2c (8 points)

Describe what the following R command does: c(0:5)[NA]

#INSERT YOUR ANSWER HERE
#The following command creates a character vector from 0 to 5 and indexes for [NA], the command prints "NA"
#5 times as there are no null values within the vector and the command is 
#"recycled" by the length of the vector

Q2d (8 points)

What is the difference between is.vector() and is.numeric() functions?

#INSERT YOUR ANSWER HERE
#the is.vector() command checks whether an object is a vector or not. The 
#is.numeric() function checks whether a vector consists of numeric data 
#(integer,double, etc.). Both functions return TRUE or FALSE

install.packages("datasets")

## Warning: package 'datasets' is in use and will not be installed

library(datasets)

Q3a (4 points)

Display the first 6 rows of the airquality data set.

#INSERT YOUR ANSWER HERE
head(airquality)

##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 5    NA      NA 14.3   56     5   5
## 6    28      NA 14.9   66     5   6

Q3b (8 points)

Compute the average of the first four variables (Ozone, Solar.R, Wind and Temp) using the sapply() function. Hint: You might need to consider removing the NA values; otherwise, the average will not be computed.

#INSERT YOUR ANSWER HERE
airquality<-na.omit(airquality)

sapply(airquality[1:4],mean)

##     Ozone   Solar.R      Wind      Temp 
##  42.09910 184.80180   9.93964  77.79279

Q3c (8 points)

Construct a boxplot for the Ozone and Solar.R variables, then display the values of all the outliers which lie beyond the whiskers.

#INSERT YOUR ANSWER HERE
#airquality<-na.omit(airquality)
par(mfcol=c(1,2))

ozone<-boxplot(airquality$Ozone, main="Ozone")
ozone$out

## [1] 135 168

solar<-boxplot(airquality$Solar.R, main="Solar")

solar$out

## numeric(0)

Q3d (8 points)

Compute the upper quartile of the Ozone variable with two different methods. HINT: Only show the upper quartile using indexing. For the type of quartile, please see https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/quantile.

#INSERT YOUR ANSWER HERE
#airquality<-na.omit(airquality)
quartile <- quantile(airquality$Ozone, na.rm = TRUE)
quartile[4]

## 75% 
##  62

quartile2 <- quantile(airquality$Ozone, probs = seq(0, 1, 1/4), na.rm = TRUE) 
quartile2[4]

## 75% 
##  62

Q3e (8 points)

Construct a pie chart to describe the number of entries by Month. HINT: use the table() function to count and tabulate the number of entries within a Month.

#INSERT YOUR ANSWER HERE
rm(airquality)
month_names<-c("May (5)","June (6)","July (7)","August (8)","September (9)")
months<-table(airquality$Month)
rownames(months)<-month_names

pie(months,main="Entries by Month (Null values included)")

END of Assignment #1.