Question 1
# Assign to the variable n_dims a single random integer between 3 and 10.
n_dims <- sample(3:10,1)
print(n_dims)## [1] 9# Create a vector of consecutive integers from 1 to n_dims^2.
my_vec <- 1:n_dims^2
# Use the sample function to randomly reshuffle these values.
my_vec <- sample(my_vec)
print(my_vec)## [1] 35 4 44 16 56 10 79 81 57 19 32 23 74 12 69 31 78 37 18 73 3 22 75 80 59
## [26] 58 17 2 64 24 28 51 49 25 61 34 76 55 60 48 63 46 53 27 77 52 11 62 36 29
## [51] 45 66 72 68 67 47 21 13 39 20 26 54 41 14 6 65 50 42 33 30 70 38 8 71 9
## [76] 15 43 5 1 40 7# Create a square matrix with these elements
my_square <- matrix(data=(my_vec^2),nrow= n_dims, ncol=n_dims)
# and print matrix
print(my_square)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 1225 361 324 4 5776 2704 4489 196 64
## [2,] 16 1024 5329 4096 3025 121 2209 36 5041
## [3,] 1936 529 9 576 3600 3844 441 4225 81
## [4,] 256 5476 484 784 2304 1296 169 2500 225
## [5,] 3136 144 5625 2601 3969 841 1521 1764 1849
## [6,] 100 4761 6400 2401 2116 2025 400 1089 25
## [7,] 6241 961 3481 625 2809 4356 676 900 1
## [8,] 6561 6084 3364 3721 729 5184 2916 4900 1600
## [9,] 3249 1369 289 1156 5929 4624 1681 1444 49# Find a function in R to transpose the matrix
my_matrix <- t(my_square)
# print it out again and not how it has changed
print(my_matrix)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 1225 16 1936 256 3136 100 6241 6561 3249
## [2,] 361 1024 529 5476 144 4761 961 6084 1369
## [3,] 324 5329 9 484 5625 6400 3481 3364 289
## [4,] 4 4096 576 784 2601 2401 625 3721 1156
## [5,] 5776 3025 3600 2304 3969 2116 2809 729 5929
## [6,] 2704 121 3844 1296 841 2025 4356 5184 4624
## [7,] 4489 2209 441 169 1521 400 676 2916 1681
## [8,] 196 36 4225 2500 1764 1089 900 4900 1444
## [9,] 64 5041 81 225 1849 25 1 1600 49# It work, it transposed the matrix!
# Calculate the sum and the means of the elements in the first row and then the last row
my_sum_f <- sum(my_matrix[1,])
print(my_sum_f)## [1] 22720my_mean_f <- mean(my_matrix[1,])
print(my_mean_f)## [1] 2524.444my_sum_l <- sum(my_matrix[length(n_dims),])
print(my_sum_l)## [1] 22720my_mean_l <- mean(my_matrix[length(n_dims),])
print(my_mean_l)## [1] 2524.444# Read about the eigen() function and use it on your matrix
eigen_matrix <- eigen(my_matrix)
print(eigen_matrix)## eigen() decomposition
## $values
## [1] 19844.455+ 0.000i -5963.134+ 0.000i 1284.944+3735.881i
## [4] 1284.944-3735.881i -2984.477+2033.212i -2984.477-2033.212i
## [7] 3196.602+1276.192i 3196.602-1276.192i -2214.458+ 0.000i
##
## $vectors
## [,1] [,2] [,3]
## [1,] -0.3374539+0i 0.23339550+0i -0.18866408-0.10605857i
## [2,] -0.3085932+0i 0.13986584+0i -0.33633414+0.22516307i
## [3,] -0.4415847+0i 0.72039933+0i 0.27736248+0.07344453i
## [4,] -0.2646210+0i 0.25299946+0i -0.00593569+0.07282964i
## [5,] -0.4803840+0i -0.44764157+0i 0.60078402+0.00000000i
## [6,] -0.3697507+0i -0.27310919+0i -0.04143706+0.09986092i
## [7,] -0.2299261+0i -0.04744670+0i -0.22875024+0.18323319i
## [8,] -0.2865558+0i -0.24783623+0i -0.11830932-0.41984158i
## [9,] -0.1530006+0i 0.06583754+0i 0.05502700+0.22327380i
## [,4] [,5] [,6]
## [1,] -0.18866408+0.10605857i -0.19728299+0.178485653i -0.19728299-0.178485653i
## [2,] -0.33633414-0.22516307i 0.31852146+0.201274684i 0.31852146-0.201274684i
## [3,] 0.27736248-0.07344453i 0.52982304+0.000000000i 0.52982304+0.000000000i
## [4,] -0.00593569-0.07282964i 0.18536061-0.007757309i 0.18536061+0.007757309i
## [5,] 0.60078402+0.00000000i -0.27005483-0.070715102i -0.27005483+0.070715102i
## [6,] -0.04143706-0.09986092i -0.32382136+0.060922033i -0.32382136-0.060922033i
## [7,] -0.22875024-0.18323319i 0.33925681+0.022427321i 0.33925681-0.022427321i
## [8,] -0.11830932+0.41984158i -0.26406280-0.008536903i -0.26406280+0.008536903i
## [9,] 0.05502700-0.22327380i -0.03577675-0.314549688i -0.03577675+0.314549688i
## [,7] [,8] [,9]
## [1,] -0.38521839-0.14868749i -0.38521839+0.14868749i 0.1122273+0i
## [2,] 0.32812995+0.22629281i 0.32812995-0.22629281i -0.2955412+0i
## [3,] -0.22957920+0.06566572i -0.22957920-0.06566572i -0.4723249+0i
## [4,] 0.33645480+0.03824555i 0.33645480-0.03824555i -0.3421512+0i
## [5,] -0.01051847-0.33247301i -0.01051847+0.33247301i 0.2893754+0i
## [6,] -0.26772060+0.08888306i -0.26772060-0.08888306i 0.2785243+0i
## [7,] -0.22439590-0.05056777i -0.22439590+0.05056777i -0.4948972+0i
## [8,] -0.05724408+0.06462965i -0.05724408-0.06462965i 0.2949452+0i
## [9,] 0.49834728+0.00000000i 0.49834728+0.00000000i 0.2582099+0i# Look carefully at the elements of $values and $vectors in the output. What kind of numbers are these?
typeof(eigen_matrix)## [1] "list"# They are decimal(imaginary) numbers. It's a list!
# If the code is set up properly, you should be able to re-run it and create a matrix of different sizes because n_dims will change. Question 2
# Create a list with the following named elements:
# my_matrix, which is a 4 x 4 matrix filled with random uniform values
my_matrix <- matrix(data=runif(4),nrow=4, ncol=4)
print(my_matrix)## [,1] [,2] [,3] [,4]
## [1,] 0.68338604 0.68338604 0.68338604 0.68338604
## [2,] 0.17099994 0.17099994 0.17099994 0.17099994
## [3,] 0.06096987 0.06096987 0.06096987 0.06096987
## [4,] 0.86764981 0.86764981 0.86764981 0.86764981# my_logical which is a 100-element vector of TRUE or FALSE values. Do this efficiently by setting up a vector of random values and then applying an inequality to it.
my_logical <- runif(100) < 0.5
print(my_logical)## [1] FALSE TRUE FALSE TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## [37] TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE TRUE FALSE TRUE TRUE
## [49] FALSE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE TRUE TRUE
## [61] FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [73] TRUE FALSE FALSE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE TRUE
## [85] TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE
## [97] FALSE FALSE FALSE TRUE# my_letters, which is a 26-element vector of all the lower-case letters in random order.
my_letters <- sample(letters, 26)
print(my_letters)## [1] "o" "v" "t" "n" "x" "u" "f" "h" "z" "c" "m" "j" "s" "g" "p" "l" "d" "i" "r"
## [20] "q" "y" "w" "e" "k" "b" "a"# Then, complete the following steps
# Create a new list, which has the element [2,2] from the matrix, the second element of the logical vector, and the second element of the letters vector
group_list <- list(my_matrix[2,2], my_logical[2],my_letters[2])
print(group_list)## [[1]]
## [1] 0.1709999
##
## [[2]]
## [1] TRUE
##
## [[3]]
## [1] "v"# use the typeof() function to confirm the underlying data types of each component in this list.
typeof(my_matrix)## [1] "double"typeof(my_logical)## [1] "logical"typeof(my_letters)## [1] "character"# combine the underlying elements from the new list into a single atomic with the c() function
group_con <- c(my_matrix[2,2], my_logical[2],my_letters[2])
print(group_con)## [1] "0.170999940251932" "TRUE" "v"# What is the data type of this vector?
typeof(group_con)## [1] "character"# It's character!Question 3
# Create a data frame with the two variables (=columns) and 26 cases (=rows) below:
my_unis_10<- sample(0:10)
my_unis_20<- sample(0:10)
my_unis_26<- sample(0:10, 4)
my_unis <- c(my_unis_10,my_unis_20,my_unis_26)
print(my_unis)## [1] 7 9 1 4 2 3 10 5 6 0 8 1 8 9 5 2 4 7 6 10 3 0 5 0 10
## [26] 3# Call the second variable my_letters and fill it with capital letters in random order.
my_letters <- sample(LETTERS, 26)
print(my_letters)## [1] "X" "U" "Q" "P" "K" "A" "G" "J" "W" "M" "E" "Z" "N" "L" "Y" "I" "H" "D" "R"
## [20] "F" "V" "O" "S" "C" "B" "T"df <- data.frame(my_unis,my_letters)
print(df)## my_unis my_letters
## 1 7 X
## 2 9 U
## 3 1 Q
## 4 4 P
## 5 2 K
## 6 3 A
## 7 10 G
## 8 5 J
## 9 6 W
## 10 0 M
## 11 8 E
## 12 1 Z
## 13 8 N
## 14 9 L
## 15 5 Y
## 16 2 I
## 17 4 H
## 18 7 D
## 19 6 R
## 20 10 F
## 21 3 V
## 22 0 O
## 23 5 S
## 24 0 C
## 25 10 B
## 26 3 T# For the first variable, use a single line of code to select 4 random rows and replace the numerical values in those rows with NA
df$my_unis[sample(0:nrow(df), 4)] <- NA
print(df)## my_unis my_letters
## 1 7 X
## 2 9 U
## 3 1 Q
## 4 4 P
## 5 2 K
## 6 3 A
## 7 10 G
## 8 NA J
## 9 6 W
## 10 0 M
## 11 8 E
## 12 1 Z
## 13 8 N
## 14 9 L
## 15 5 Y
## 16 NA I
## 17 4 H
## 18 7 D
## 19 6 R
## 20 10 F
## 21 3 V
## 22 0 O
## 23 5 S
## 24 0 C
## 25 NA B
## 26 NA T# For the first variable, write a single line to identify which rows have the missing values.
which(!complete.cases(df$my_unis))## [1] 8 16 25 26# re-order the entire data frame to arrange the second variable in alphabetical order
df_letters <- df[order(df$my_letters),]
print(df_letters)## my_unis my_letters
## 6 3 A
## 25 NA B
## 24 0 C
## 18 7 D
## 11 8 E
## 20 10 F
## 7 10 G
## 17 4 H
## 16 NA I
## 8 NA J
## 5 2 K
## 14 9 L
## 10 0 M
## 13 8 N
## 22 0 O
## 4 4 P
## 3 1 Q
## 19 6 R
## 23 5 S
## 26 NA T
## 2 9 U
## 21 3 V
## 9 6 W
## 1 7 X
## 15 5 Y
## 12 1 Z# calculate the column mean for the first variable
unis_means <- mean(df$my_unis, na.rm = TRUE)
print(unis_means)## [1] 4.909091