Chapter2 Statistical Learning

Vector and Matrix in R

Creating vector in R

x = c(2,7,5)
x

[1] 2 7 5

y = seq(from = 4, length = 3, by = 3)
y

[1]  4  7 10

Vector Operation

x + y

[1]  6 14 15

x^y

[1]      16  823543 9765625

x[2]

[1] 7

x[2:3]

[1] 7 5

x[-2] ## remove the 2nd elements

[1] 2 5

Create matrix in R

z = matrix(seq(1,12),4,3)
z

     [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
[4,]    4    8   12

z[3:4,2:3]

     [,1] [,2]
[1,]    7   11
[2,]    8   12

z[,2:3]

     [,1] [,2]
[1,]    5    9
[2,]    6   10
[3,]    7   11
[4,]    8   12

z[,1] ## will return as vector type 

[1] 1 2 3 4

z[,1,drop = FALSE] ## Remain Matrix

     [,1]
[1,]    1
[2,]    2
[3,]    3
[4,]    4

dim(z) ## Check dimension

[1] 4 3

Other Useful function

ls() ## list all variables within the env

[1] "x" "y" "z"

rm(y) ## Remove a typical variable
ls()

[1] "x" "z"

Data Simulating

Generate Random data, graphics

set.seed(11)
x = runif(50)  ## 50 random variable follows uniform distribution
y = rnorm(50)  ## 50 random variable follows standard normal distribution

plot(x,y, xlab = "Random Uniform", ylab = "Random Noraml", pch = "*", col = "blue")

Make parallel plot

par(mfrow = c(2,1))  ## 2 rows, 1 cols

plot(x,y, xlab = "Random Uniform", ylab = "Random Noraml", pch = "*", col = "blue")
hist(y)

par(mfrow = c(1,1))  ## Restore the setting

Example

auto = read.csv("./Data/Auto.csv") ### Read data
names(auto)  ## check all variables

[1] "mpg"          "cylinders"    "displacement" "horsepower"   "weight"       "acceleration" "year"        
[8] "origin"       "name"        

summary(auto)

      mpg          cylinders      displacement    horsepower            weight      acceleration        year      
 Min.   : 9.00   Min.   :3.000   Min.   : 68.0   Length:397         Min.   :1613   Min.   : 8.00   Min.   :70.00  
 1st Qu.:17.50   1st Qu.:4.000   1st Qu.:104.0   Class :character   1st Qu.:2223   1st Qu.:13.80   1st Qu.:73.00  
 Median :23.00   Median :4.000   Median :146.0   Mode  :character   Median :2800   Median :15.50   Median :76.00  
 Mean   :23.52   Mean   :5.458   Mean   :193.5                      Mean   :2970   Mean   :15.56   Mean   :75.99  
 3rd Qu.:29.00   3rd Qu.:8.000   3rd Qu.:262.0                      3rd Qu.:3609   3rd Qu.:17.10   3rd Qu.:79.00  
 Max.   :46.60   Max.   :8.000   Max.   :455.0                      Max.   :5140   Max.   :24.80   Max.   :82.00  
     origin          name          
 Min.   :1.000   Length:397        
 1st Qu.:1.000   Class :character  
 Median :1.000   Mode  :character  
 Mean   :1.574                     
 3rd Qu.:2.000                     
 Max.   :3.000                     

table(auto$horsepower)

  ? 100 102 103 105 107 108 110 112 113 115 116 120 122 125 129 130 132 133 135 137 138 139 140 142 145 148 149 
  5  17   1   1  12   1   1  18   3   1   5   1   4   1   3   2   5   1   1   1   1   1   2   7   1   7   1   1 
150 152 153 155 158 160 165 167 170 175 180 190 193 198 200 208 210 215 220 225 230  46  48  49  52  53  54  58 
 22   1   2   2   1   2   4   1   5   5   5   3   1   2   1   1   1   3   1   3   1   2   3   1   4   2   1   2 
 60  61  62  63  64  65  66  67  68  69  70  71  72  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88 
  5   1   2   3   1  10   1  12   6   3  12   5   6   3  14   4   1   6   2   7   2   1   4   6   9   5   2  19 
 89  90  91  92  93  94  95  96  97  98 
  1  20   1   6   1   1  14   3   9   2 

dim(auto)

[1] 397   9

class(auto)

[1] "data.frame"

plot(auto$cylinders, auto$mpg)
lowess_model <- lowess(auto$cylinders, auto$mpg) 
lines(lowess_model, col="red") ### add the lowess soomth line

attach(auto) ## make a columns as an variable and store into the env

search()

 [1] ".GlobalEnv"        "auto"              "tools:rstudio"     "package:stats"     "package:graphics" 
 [6] "package:grDevices" "package:utils"     "package:datasets"  "package:methods"   "Autoloads"        
[11] "package:base"     

## boxplot
plot(as.factor(cylinders),mpg)