ANLY 505 - Data Simulation in R
Week 1
Sanath Ama
2020-01-23
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.
# place the code to simulate the data here
random = rnorm(30, mean = c(0,10,15), sd= c(1,10,15))
random## [1] 0.04234419 19.42119050 -3.95479323 0.09587249 -11.55391971
## [6] 1.25486930 0.42952044 -4.08173062 28.34804285 0.76950597
## [11] 5.69970601 5.66903042 -0.11247435 -3.32118975 21.76707827
## [16] -2.17521579 21.22360083 25.01348132 -0.70347591 3.20077530
## [21] 3.77232841 -0.81555328 3.86329722 7.22337982 0.58427312
## [26] 10.31222783 12.86797706 1.45203162 7.82917491 1.67358472- Simulate 2 continuous variables (normal distribution) (n=20) and plot the relationship between them
# place the code to simulate the data here
set.seed(9)
x=rnorm(20, mean = 1, sd=2.5)
set.seed(9)
y=rnorm(20, mean = 2.5, sd=4)
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.
# place the code to simulate the data here
set.seed(10)
y=rnorm(40, mean= 0, sd=1)
x1 =runif(40, min = 10, max = 50 )
x2= runif(40, min= 200, max= 500)
model =lm(y~x1+x2)
plot(model)
- Simulate 3 letters repeating each letter twice, 2 times.
# place the code to simulate the data here
rep(letters[1:3], each=2, times =2)## [1] "a" "a" "b" "b" "c" "c" "a" "a" "b" "b" "c" "c"- Create a list of 6 datasets (n = 30) each with 3 groups, 2 factors and two quantitative response variables. Use the replicate function.
# place the code to simulate the data here
set.seed(16)
DataFrame1 = data.frame(group=rep(LETTERS[1:3], length.out=30),factor= rep(letters[7:8],length.out=30),
response1 = rnorm(30, mean= 10, sd= 20), response2 = rnorm(30, mean= 100, sd= 150))
set.seed(16)
DataFrame2 = data.frame(group=rep(LETTERS[2:4], length.out=30),factor= rep(letters[8:9],length.out=30),
response1 = rnorm(30, mean= 10, sd= 20), response2 = rnorm(30, mean= 10, sd= 15))
set.seed(16)
DataFrame3 = data.frame(group=rep(LETTERS[3:5], length.out=30),factor= rep(letters[8:9],length.out=30),
response1 = rnorm(30, mean= 0, sd= 1), response2 = rnorm(30, mean= 1, sd= 15))
set.seed(16)
DataFrame4 = data.frame(group=rep(LETTERS[1:3], length.out=30),factor= rep(letters[9:10],length.out=30),
response1 = rnorm(30, mean= 10, sd= 100), response2 = rnorm(30, mean= 1, sd= 2))
set.seed(16)
DataFrame5 = data.frame(group=rep(LETTERS[2:4], length.out=30),factor= rep(letters[10:11],length.out=30),
response1 = rnorm(30, mean= 100, sd= 250), response2 = rnorm(30, mean= 1, sd= 20))
set.seed(16)
DataFrame6 = data.frame(group=rep(LETTERS[2:4], length.out=30),factor= rep(letters[5:6],length.out=30),
response1 = rnorm(30, mean= 100, sd= 250), response2 = rnorm(30, mean= 150, sd= 200))
DataFrame6## group factor response1 response2
## 1 B e 219.10335 15.49488
## 2 C f 68.65500 176.51971
## 3 D e 374.05405 135.81453
## 4 B f -261.05726 -38.53909
## 5 C e 386.95732 -54.40620
## 6 D f -17.10301 206.11102
## 7 B e -151.48765 258.95667
## 8 C f 115.89067 176.17395
## 9 D e 356.24315 206.36888
## 10 B f 243.28550 91.45385
## 11 C e 561.79553 -115.07062
## 12 D f 127.98334 563.02713
## 13 B e -86.50933 198.43461
## 14 C f 514.55342 80.18055
## 15 D e 280.43014 23.83753
## 16 B f -315.77012 206.78134
## 17 C e 243.97738 174.31540
## 18 D f 218.19003 263.26882
## 19 B e -35.68291 263.80658
## 20 C f 381.92177 131.88265
## 21 D e -311.94940 196.09930
## 22 B f 21.45651 300.57076
## 23 C e 54.32961 322.67708
## 24 D f 467.61962 317.63973
## 25 B e -116.47470 -203.17042
## 26 C f 481.86675 286.69890
## 27 D e 363.54451 382.60226
## 28 B f 357.51775 -90.12037
## 29 C e 310.04021 799.90602
## 30 D f 154.24118 14.85285DataFrame5## group factor response1 response2
## 1 B j 219.10335 -12.4505115
## 2 C k 68.65500 3.6519705
## 3 D j 374.05405 -0.4185469
## 4 B k -261.05726 -17.8539094
## 5 C j 386.95732 -19.4406200
## 6 D k -17.10301 6.6111025
## 7 B j -151.48765 11.8956673
## 8 C k 115.89067 3.6173950
## 9 D j 356.24315 6.6368878
## 10 B k 243.28550 -4.8546150
## 11 C j 561.79553 -25.5070624
## 12 D k 127.98334 42.3027130
## 13 B j -86.50933 5.8434608
## 14 C k 514.55342 -5.9819446
## 15 D j 280.43014 -11.6162475
## 16 B k -315.77012 6.6781343
## 17 C j 243.97738 3.4315397
## 18 D k 218.19003 12.3268822
## 19 B j -35.68291 12.3806579
## 20 C k 381.92177 -0.8117353
## 21 D j -311.94940 5.6099299
## 22 B k 21.45651 16.0570757
## 23 C j 54.32961 18.2677082
## 24 D k 467.61962 17.7639728
## 25 B j -116.47470 -34.3170423
## 26 C k 481.86675 14.6698900
## 27 D j 363.54451 24.2602256
## 28 B k 357.51775 -23.0120370
## 29 C j 310.04021 65.9906021
## 30 D k 154.24118 -12.5147146DataFrame4## group factor response1 response2
## 1 A i 57.641339 -0.3450512
## 2 B j -2.538000 1.2651971
## 3 C i 119.621620 0.8581453
## 4 A j -134.422904 -0.8853909
## 5 B i 124.782930 -1.0440620
## 6 C j -36.841204 1.5611102
## 7 A i -90.595059 2.0895667
## 8 B j 16.356268 1.2617395
## 9 C i 112.497260 1.5636888
## 10 A j 67.314202 0.4145385
## 11 B i 194.718210 -1.6507062
## 12 C j 21.193337 5.1302713
## 13 A i -64.603732 1.4843461
## 14 B j 175.821366 0.3018055
## 15 C i 82.172057 -0.2616247
## 16 A j -156.308050 1.5678134
## 17 B i 67.590953 1.2431540
## 18 C j 57.276012 2.1326882
## 19 A i -44.273166 2.1380658
## 20 B j 122.768707 0.8188265
## 21 C i -154.779762 1.4609930
## 22 A j -21.417395 2.5057076
## 23 B i -8.268157 2.7267708
## 24 C j 157.047849 2.6763973
## 25 A i -76.589878 -2.5317042
## 26 B j 162.746698 2.3669890
## 27 C i 115.417806 3.3260226
## 28 A j 113.007101 -1.4012037
## 29 B i 94.016086 7.4990602
## 30 C j 31.696470 -0.3514715DataFrame3## group factor response1 response2
## 1 C h 0.47641339 -9.0878836
## 2 D i -0.12538000 2.9889779
## 3 E h 1.09621620 -0.0639102
## 4 C i -1.44422904 -13.1404321
## 5 D h 1.14782930 -14.3304650
## 6 E i -0.46841204 5.2083269
## 7 C h -1.00595059 9.1717505
## 8 D i 0.06356268 2.9630463
## 9 E h 1.02497260 5.2276659
## 10 C i 0.57314202 -3.3909613
## 11 D h 1.84718210 -18.8802968
## 12 E i 0.11193337 31.9770348
## 13 C h -0.74603732 4.6325956
## 14 D i 1.65821366 -4.2364584
## 15 E h 0.72172057 -8.4621856
## 16 C i -1.66308050 5.2586007
## 17 D h 0.57590953 2.8236548
## 18 E i 0.47276012 9.4951616
## 19 C h -0.54273166 9.5354935
## 20 D i 1.12768707 -0.3588014
## 21 E h -1.64779762 4.4574474
## 22 C i -0.31417395 12.2928068
## 23 D h -0.18268157 13.9507812
## 24 E i 1.47047849 13.5729796
## 25 C h -0.86589878 -25.4877818
## 26 D i 1.52746698 11.2524175
## 27 E h 1.05417806 18.4451692
## 28 C i 1.03007101 -17.0090277
## 29 D h 0.84016086 49.7429516
## 30 E i 0.21696470 -9.1360360DataFrame2## group factor response1 response2
## 1 B h 19.5282679 -0.08788364
## 2 C i 7.4924000 11.98897791
## 3 D h 31.9243240 8.93608980
## 4 B i -18.8845807 -4.14043206
## 5 C h 32.9565859 -5.33046500
## 6 D i 0.6317591 14.20832686
## 7 B h -10.1190119 18.17175050
## 8 C i 11.2712536 11.96304628
## 9 D h 30.4994520 14.22766589
## 10 B i 21.4628403 5.60903873
## 11 C h 46.9436420 -9.88029682
## 12 D i 12.2386674 40.97703478
## 13 B h -4.9207464 13.63259561
## 14 C i 43.1642732 4.76354156
## 15 D h 24.4344114 0.53781440
## 16 B i -23.2616099 14.25860074
## 17 C h 21.5181907 11.82365480
## 18 D i 19.4552023 18.49516164
## 19 B h -0.8546331 18.53549346
## 20 C i 32.5537414 8.64119856
## 21 D h -22.9559523 13.45744741
## 22 B i 3.7165210 21.29280677
## 23 C h 6.3463686 22.95078117
## 24 D i 39.4095699 22.57297957
## 25 B h -7.3179757 -16.48778176
## 26 C i 40.5493397 20.25241750
## 27 D h 31.0835612 27.44516919
## 28 B i 30.6014202 -8.00902772
## 29 C h 26.8032171 58.74295156
## 30 D i 14.3392941 -0.13603598DataFrame1## group factor response1 response2
## 1 A g 19.5282679 -0.8788364
## 2 B h 7.4924000 119.8897791
## 3 C g 31.9243240 89.3608980
## 4 A h -18.8845807 -41.4043206
## 5 B g 32.9565859 -53.3046500
## 6 C h 0.6317591 142.0832686
## 7 A g -10.1190119 181.7175050
## 8 B h 11.2712536 119.6304628
## 9 C g 30.4994520 142.2766589
## 10 A h 21.4628403 56.0903873
## 11 B g 46.9436420 -98.8029682
## 12 C h 12.2386674 409.7703478
## 13 A g -4.9207464 136.3259561
## 14 B h 43.1642732 47.6354156
## 15 C g 24.4344114 5.3781440
## 16 A h -23.2616099 142.5860074
## 17 B g 21.5181907 118.2365480
## 18 C h 19.4552023 184.9516164
## 19 A g -0.8546331 185.3549346
## 20 B h 32.5537414 86.4119856
## 21 C g -22.9559523 134.5744741
## 22 A h 3.7165210 212.9280677
## 23 B g 6.3463686 229.5078117
## 24 C h 39.4095699 225.7297957
## 25 A g -7.3179757 -164.8778176
## 26 B h 40.5493397 202.5241750
## 27 C g 31.0835612 274.4516919
## 28 A h 30.6014202 -80.0902772
## 29 B g 26.8032171 587.4295156
## 30 C h 14.3392941 -1.3603598