Basic Calculation with Vectors

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Intro to R Webpage

1. R is case sensitive

X = 3   # This assigns 3 to object X. But you can't see it.
X       # now you see what's inside X

## [1] 3

x       # "x" is not same as "X". 

2. Vectors

R uses vectors.

X = c(1, 4, 6)      # create vector 
X

## [1] 1 4 6

X = 1:10            # 1 through 10
X

##  [1]  1  2  3  4  5  6  7  8  9 10

X = seq(1,30, 4)    # 1 to 30 in step of 2
X

## [1]  1  5  9 13 17 21 25 29

X = rep(0, 10)
X

##  [1] 0 0 0 0 0 0 0 0 0 0

Apply funciton to vector

When you apply a function to a vector, it usually work on EACH element in the vector.

X = rnorm(10)  # draw random sample of size 10 from Standard Normal 
X

##  [1]  0.3715996 -1.1136593  2.0159279 -1.1937884 -0.5616618  2.7588894  0.9342664
##  [8] -0.8875176  1.0410657 -0.1927468

Y = X ^ 2      # square each number 
Y

##  [1] 0.13808623 1.24023700 4.06396550 1.42513072 0.31546397 7.61147093 0.87285367
##  [8] 0.78768748 1.08381780 0.03715132

Y = X * 2      # multiple 2 to each number 
Y 

##  [1]  0.7431991 -2.2273186  4.0318559 -2.3875768 -1.1233236  5.5177789  1.8685328
##  [8] -1.7750352  2.0821314 -0.3854935

Y = exp(X)     # take exponential power of each number
Y

##  [1]  1.4500522  0.3283552  7.5076909  0.3030709  0.5702606 15.7823060  2.5453455
##  [8]  0.4116764  2.8322337  0.8246908

3. Descriptive statistics

X = rnorm(10)  # draw random sample of n=10 from Standard Normal 
X

##  [1] -0.09462892  0.85454775 -1.27328384 -0.05242463 -1.97524773  0.23774602
##  [7] -1.43303988  1.41962163 -0.10879648  0.55092360

length(X)      # get length of X

## [1] 10

mean(X)        # sample mean 

## [1] -0.1874582

var(X)         # variance 

## [1] 1.150468

sd(X)          # Standard Deviation

## [1] 1.072599

summary(X)     # 5-number summary

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -1.97525 -0.98216 -0.07353 -0.18746  0.47263  1.41962

Correlation

X = rnorm(10)  # draw random sample of n=10 from Standard Normal 
Y = runif(10)  # draw random sample of n=10 from Unif(0,1)
cor(X,Y)       # correlation between vector X and vector Y

## [1] 0.1434796