ANLY 505 - Data Simulation in R
Week 1
Raavi, Anvesh
2020-01-20
Directions
The objective of this assignment is to introduce you to R and R markdown and to complete some basic data simulation exercises.
Please include all code needed to perform the tasks. This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.
To submit this homework you will create the document in Rstudio, using the knitr package (button included in Rstudio) and then submit the document to your Rpubs account. Once uploaded you will submit the link to that document on Canvas. Please make sure that this link is hyperlinked and that I can see the visualization and the code required to create it.
Questions
- Simulate data for 30 draws from a normal distribution where the means and standard deviations vary among three distributions.
set.seed(42)
rnorm(30, mean = c(50,40,30), sd=c(10,20,30))## [1] 63.70958 28.70604 40.89385 56.32863 48.08537 26.81626 65.11522
## [8] 38.10682 90.55271 49.37286 66.09739 98.59936 36.11139 34.42422
## [15] 26.00036 56.35950 34.31494 -49.69366 25.59533 66.40227 20.80084
## [22] 32.18692 36.56165 66.44024 68.95193 31.39062 22.28192 32.36837
## [29] 49.20195 10.80015- Simulate 2 continuous variables (normal distribution) (n=20) and plot the relationship between them
x = rnorm(20,0,1)
y = rnorm(20)
plot(y~x)
- Simulate 3 variables (x1, x2 and y). x1 and x2 should be drawn from a uniform distribution and y should be drawn from a normal distribution. Fit a multiple linear regression.
x1 = runif(100, min = 0, max = 1)
x2 = runif(100, min = 10, max = 20)
y = rnorm(100)
model = lm(y~x1+x2)
plot(model)
- Simulate 3 letters repeating each letter twice, 2 times.
rep(letters[1:3], each = 2, times = 2)## [1] "a" "a" "b" "b" "c" "c" "a" "a" "b" "b" "c" "c"- Create a dataframe (n = 27) with 3 groups, 2 factors and two quantitative response variables. Use the replicate function.
frame = replicate(n = 27, expr = data.frame(group = rep(letters[1:3], each = 2),factor = rep(LETTERS[3:4],each=3), response = rep(1:2,2,each =3)),simplify = FALSE)
str(frame)## List of 27
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...
## $ :'data.frame': 12 obs. of 3 variables:
## ..$ group : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## ..$ factor : Factor w/ 2 levels "C","D": 1 1 1 2 2 2 1 1 1 2 ...
## ..$ response: int [1:12] 1 1 1 2 2 2 1 1 1 2 ...