ANLY 505 - Data Simulation in R
Week 1
Hua Qiu
2019-11-02
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(10)
rnorm(30,mean=c(0,5,10),sd=c(1,5,20))## [1] 0.01874617 4.07873729 -17.42661100 -0.59916772 6.47272563
## [6] 17.79588601 -1.20807618 3.18161991 -22.53345363 -0.25647839
## [11] 10.50889752 25.11563016 -0.23823356 9.93722352 24.82780257
## [16] 0.08934727 0.22528072 6.09699231 0.92552126 7.41489262
## [21] -1.92621273 -2.18528684 1.62567031 -32.38122384 -1.26519802
## [26] 3.13169222 -3.75110861 -0.87215883 4.49119497 4.92438940- Simulate 2 continuous variables (normal distribution) (n=20) and plot the relationship between them
set.seed(10)
x=rnorm(20,0,1)
y=rnorm(20,0,1)
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.
set.seed(10)
x1=runif(100,1,2)
x2=runif(100,1,2)
y=rnorm(100,0,1)
Model <-lm(y~x1+x2)
plot(Model,which=c(1,1))
Model##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Coefficients:
## (Intercept) x1 x2
## -0.4639 0.1364 0.1144- Simulate 3 letters repeating each letter twice, 2 times.
rep(letters[4:6],each=2,times=2)## [1] "d" "d" "e" "e" "f" "f" "d" "d" "e" "e" "f" "f"- Create a list of 6 datasets (n = 30) each with 3 groups, 2 factors and two quantitative response variables. Use the replicate function.
set.seed(10)
simlist=replicate(5,
expr = data.frame(group=rep(letters[1:3]),
factor=rep(letters[4:5]),
x=runif(30,10,15),
y=runif(30,100,150)) ,
simplify = FALSE)
simlist## [[1]]
## group factor x y
## 1 a d 12.53739 126.7799
## 2 b e 11.53384 104.6544
## 3 c d 12.13454 108.4902
## 4 a e 13.46551 144.9916
## 5 b d 10.42568 121.1319
## 6 c e 11.12718 137.3873
## 7 a d 11.37265 141.1326
## 8 b e 11.36153 147.7327
## 9 c d 13.07915 134.2722
## 10 a e 12.14836 125.0252
## 11 b d 13.25828 113.7742
## 12 c e 12.83869 111.4452
## 13 a d 10.56754 100.7217
## 14 b e 12.97963 136.4482
## 15 c d 11.79025 112.4940
## 16 a e 12.14405 108.0592
## 17 b d 10.25952 100.8521
## 18 c e 11.32089 124.3050
## 19 a d 11.99395 105.1450
## 20 b e 14.18067 140.0774
## 21 c d 14.32361 117.7164
## 22 a e 13.07676 146.8216
## 23 b d 13.87555 112.2933
## 24 c e 11.77784 123.6571
## 25 a d 12.02925 109.5780
## 26 b e 13.53323 129.1611
## 27 c d 14.19144 122.9737
## 28 a e 11.19795 123.3717
## 29 b d 13.85386 119.9916
## 30 c e 11.77949 125.2643
##
## [[2]]
## group factor x y
## 1 a d 10.15944 124.4253
## 2 b e 10.57234 135.5705
## 3 c d 12.34468 129.5967
## 4 a e 11.98493 125.8578
## 5 b d 14.16810 119.0814
## 6 c e 13.80561 141.7389
## 7 a d 12.86678 112.4504
## 8 b e 12.23754 127.0301
## 9 c d 10.41901 137.1920
## 10 a e 11.09569 101.5006
## 11 b d 10.37785 117.2172
## 12 c e 12.67213 103.0661
## 13 a d 13.20678 118.4490
## 14 b e 12.62870 120.3797
## 15 c d 10.19641 145.7168
## 16 a e 12.72930 144.4353
## 17 b d 11.86382 149.1866
## 18 c e 14.80651 123.8598
## 19 a d 11.28671 134.6754
## 20 b e 11.03976 121.2873
## 21 c d 14.30691 139.2083
## 22 a e 12.32196 142.1348
## 23 b d 11.11434 109.1736
## 24 c e 13.11775 126.4270
## 25 a d 11.01824 135.1474
## 26 b e 10.09837 145.6636
## 27 c d 13.98997 112.9587
## 28 a e 11.37159 139.6312
## 29 b d 10.83305 130.7235
## 30 c e 10.85076 135.0310
##
## [[3]]
## group factor x y
## 1 a d 10.53967 143.9772
## 2 b e 11.66933 109.8558
## 3 c d 11.62066 103.4730
## 4 a e 12.82713 107.8670
## 5 b d 11.01589 116.6728
## 6 c e 11.09852 109.0031
## 7 a d 13.16558 107.3241
## 8 b e 11.76260 114.5288
## 9 c d 14.28437 146.8034
## 10 a e 14.75361 105.1230
## 11 b d 14.44016 136.1676
## 12 c e 10.23429 125.8201
## 13 a d 13.84520 120.5950
## 14 b e 11.15113 120.6633
## 15 c d 11.57592 138.1022
## 16 a e 11.41335 112.9588
## 17 b d 13.56598 138.1595
## 18 c e 14.31069 149.1202
## 19 a d 10.53162 133.5060
## 20 b e 12.75164 129.4964
## 21 c d 13.24185 128.1549
## 22 a e 11.17393 138.0898
## 23 b d 10.38149 137.2649
## 24 c e 14.61548 135.3914
## 25 a d 10.73608 149.3404
## 26 b e 14.11195 122.5815
## 27 c d 12.06759 105.9109
## 28 a e 13.06260 111.9318
## 29 b d 10.34060 123.5261
## 30 c e 14.52066 117.6162
##
## [[4]]
## group factor x y
## 1 a d 11.69288 135.6671
## 2 b e 10.63651 133.5311
## 3 c d 12.12037 137.2845
## 4 a e 12.36655 120.6741
## 5 b d 12.63861 102.4327
## 6 c e 13.13477 138.2342
## 7 a d 14.38013 142.4032
## 8 b e 13.39579 126.6081
## 9 c d 13.62032 143.5165
## 10 a e 10.90924 106.1853
## 11 b d 10.38928 105.0123
## 12 c e 10.36099 134.3489
## 13 a d 10.27031 143.5262
## 14 b e 12.58637 138.5326
## 15 c d 14.07026 116.0638
## 16 a e 12.24524 111.4702
## 17 b d 12.79447 118.8046
## 18 c e 11.39940 140.1897
## 19 a d 14.45047 141.1167
## 20 b e 13.57925 119.4155
## 21 c d 11.11544 126.5373
## 22 a e 12.67947 122.7920
## 23 b d 13.31265 142.5406
## 24 c e 14.24035 110.8760
## 25 a d 10.74592 138.5461
## 26 b e 13.35050 113.7820
## 27 c d 13.80818 144.7680
## 28 a e 14.99317 126.1820
## 29 b d 11.31649 141.4589
## 30 c e 14.42593 136.7720
##
## [[5]]
## group factor x y
## 1 a d 11.57564 108.1393
## 2 b e 12.74158 149.7687
## 3 c d 12.90193 134.4909
## 4 a e 10.27021 111.3823
## 5 b d 12.43670 138.3012
## 6 c e 13.54700 149.5468
## 7 a d 10.57965 137.3855
## 8 b e 14.47896 136.4732
## 9 c d 13.66791 141.5079
## 10 a e 13.67001 101.2990
## 11 b d 10.90074 102.3467
## 12 c e 14.37556 149.7808
## 13 a d 12.99113 105.7033
## 14 b e 11.08856 146.4452
## 15 c d 10.71988 101.2404
## 16 a e 14.08430 148.5755
## 17 b d 11.78968 146.4660
## 18 c e 12.20368 127.7742
## 19 a d 10.56859 132.2615
## 20 b e 14.15836 143.8228
## 21 c d 14.61764 142.8380
## 22 a e 11.48598 148.4090
## 23 b d 13.68388 135.1085
## 24 c e 12.07001 149.6896
## 25 a d 10.11461 127.0308
## 26 b e 11.95207 122.4353
## 27 c d 11.23836 145.4758
## 28 a e 12.33425 104.7115
## 29 b d 11.61369 126.7379
## 30 c e 14.39089 108.0919