ANLY 505 - Data Simulation in R
Week 1
Neha Katti
2019-10-29
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
set.seed(92)
rnorm(30, mean = c(8,15,60), sd = c(2,9,6))## [1] 5.0424332 10.5224962 65.5819882 5.6235491 -0.7077369 54.1105535
## [7] 10.8366850 14.1792491 53.5173676 7.4725326 10.2650370 58.7785346
## [13] 12.8531737 7.0825120 65.9754692 5.7505306 15.8708250 50.5377752
## [19] 8.8181637 9.9592328 66.2472177 8.3775257 10.2181805 68.2474596
## [25] 10.1261494 15.7742990 59.4581200 10.9135541 -1.0471757 52.8438867- Simulate 2 continuous variables (normal distribution) (n=20) and plot the relationship between them
# place the code to simulate the data here
x = rnorm(30, mean=1, sd=2)
y = rnorm(30, mean=2, sd=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.
# place the code to simulate the data here
set.seed(48)
y = rnorm(20, mean = 0, sd = 1)
x1 = runif(20, min = 3, max = 5)
x2 = runif(20, min = 4, max = 7)
lm(y ~ x1 + x2)##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Coefficients:
## (Intercept) x1 x2
## -0.69050 0.09120 0.08408- Simulate 3 letters repeating each letter twice, 2 times.
# place the code to simulate the data here
rep(letters[6:9], each = 2, times =2)## [1] "f" "f" "g" "g" "h" "h" "i" "i" "f" "f" "g" "g" "h" "h" "i" "i"- 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
replicate(5, expr = data.frame(group = rep(LETTERS[6:8]),factor = rep(LETTERS[2:3]),x = rnorm(30, mean =1, sd=2),y = rnorm(30, mean = 3, sd =4)),simplify = FALSE)## [[1]]
## group factor x y
## 1 F B 1.97376510 0.46505832
## 2 G C 0.39153907 2.71232244
## 3 H B -1.28701807 0.18055729
## 4 F C 1.25479636 10.30501411
## 5 G B 0.78046164 -2.59402589
## 6 H C -1.42898531 -1.65035629
## 7 F B 1.53109030 -0.33408259
## 8 G C 3.05061136 3.59509189
## 9 H B 2.39992045 8.02454259
## 10 F C -2.81022659 -0.67894539
## 11 G B 0.39321423 0.77065940
## 12 H C -0.01240637 6.88614312
## 13 F B -0.25412878 6.73654704
## 14 G C 3.32111915 4.19602861
## 15 H B -0.10295588 0.01469073
## 16 F C 1.00077731 1.53474223
## 17 G B -0.81681299 2.71811533
## 18 H C 2.45949260 -2.06674553
## 19 F B 3.74399357 6.54127771
## 20 G C 0.58094257 3.49730648
## 21 H B 1.09748741 5.42331012
## 22 F C 0.12246283 9.22966180
## 23 G B 0.67134538 4.69273457
## 24 H C 4.96528864 -0.50623249
## 25 F B -1.16010519 7.29838916
## 26 G C 1.63311298 3.29642124
## 27 H B -1.17045116 6.60704274
## 28 F C -0.79367186 1.69403438
## 29 G B 0.17147625 4.66541474
## 30 H C 0.29500416 3.07927600
##
## [[2]]
## group factor x y
## 1 F B -0.3103297 0.21848379
## 2 G C 2.2292985 -1.09972180
## 3 H B 2.8229980 11.24321651
## 4 F C 0.2109362 2.17593882
## 5 G B 0.5432433 3.41172420
## 6 H C -0.3719472 4.79237525
## 7 F B 5.6743811 7.32202874
## 8 G C 1.8632791 7.03985153
## 9 H B 2.1620664 6.57986192
## 10 F C 4.7733692 -5.31717670
## 11 G B -0.4052713 7.11748373
## 12 H C 5.2601108 -4.15305367
## 13 F B 0.6295660 4.59818645
## 14 G C 3.6144746 -1.36527886
## 15 H B 0.7903762 -2.61546448
## 16 F C -1.2502382 -5.58465040
## 17 G B 2.8193494 0.07671808
## 18 H C 6.3403219 3.31618960
## 19 F B 1.4976667 3.56147142
## 20 G C -2.8820563 1.13667982
## 21 H B -0.9659221 -3.14068443
## 22 F C -1.1269738 0.40679440
## 23 G B 2.7559404 11.12012049
## 24 H C 0.4571783 4.26433345
## 25 F B 1.9506409 3.41116965
## 26 G C 2.7339131 9.07459885
## 27 H B 0.8729705 2.87138364
## 28 F C -1.5917197 8.06246019
## 29 G B -0.1288361 3.86789275
## 30 H C 0.8179231 7.38636348
##
## [[3]]
## group factor x y
## 1 F B -0.6097633 -8.41749217
## 2 G C 3.8787568 6.71342797
## 3 H B -0.7846704 3.64241778
## 4 F C -1.1745095 6.26614224
## 5 G B 0.9568513 2.66137028
## 6 H C 0.1119448 -3.24184229
## 7 F B 1.0877539 0.04645112
## 8 G C 0.1244332 6.35227613
## 9 H B 2.2260535 0.93363815
## 10 F C 1.4058465 7.45174031
## 11 G B 1.6415034 -0.38675955
## 12 H C 0.3592179 4.72827234
## 13 F B 0.4070662 9.26721630
## 14 G C 0.9595911 3.27270260
## 15 H B -0.2861462 5.40501001
## 16 F C 3.4014000 -0.82489610
## 17 G B 1.6041430 5.13398978
## 18 H C 2.3354933 6.19125808
## 19 F B -1.3263465 4.26967882
## 20 G C 3.3442391 4.97492186
## 21 H B 2.6668971 7.85683892
## 22 F C 3.1113048 0.98012696
## 23 G B -0.5362307 1.61730983
## 24 H C 0.6261865 0.42466179
## 25 F B 2.5091145 1.42325737
## 26 G C 0.5145827 2.22288702
## 27 H B 2.6364976 1.41331587
## 28 F C -0.1805537 0.86290148
## 29 G B 0.8229117 9.99654976
## 30 H C 0.8520883 2.22000551
##
## [[4]]
## group factor x y
## 1 F B 1.79497682 7.78727088
## 2 G C -2.63139971 10.05108244
## 3 H B 0.69615198 4.44480066
## 4 F C 0.51011728 7.78867541
## 5 G B 4.45841105 2.43361312
## 6 H C -1.68776988 1.33483265
## 7 F B -0.09053330 2.16480149
## 8 G C -0.77462298 5.30829376
## 9 H B -1.39971307 5.04605774
## 10 F C 4.78499835 1.34703895
## 11 G B -0.71089850 1.36744332
## 12 H C -0.46393622 0.06418924
## 13 F B -1.76322419 7.30763863
## 14 G C -1.00956277 -1.47469542
## 15 H B 2.18837086 -3.19920622
## 16 F C -0.24287802 7.90828423
## 17 G B 0.01944427 2.51189444
## 18 H C 2.55523483 -0.80472699
## 19 F B 1.76715831 8.54445944
## 20 G C 1.97649970 -2.32772020
## 21 H B -2.46852373 4.69073695
## 22 F C 2.21936687 -2.02160441
## 23 G B 3.20001019 1.84413142
## 24 H C 6.14428214 -0.74609686
## 25 F B -0.12607852 -1.90740729
## 26 G C -1.06438226 -3.13071305
## 27 H B 2.49836490 2.78117976
## 28 F C -1.03269857 3.31379898
## 29 G B 1.36994903 4.32754210
## 30 H C 2.35446716 3.25517805
##
## [[5]]
## group factor x y
## 1 F B -0.085248957 -2.13391511
## 2 G C -0.153107687 6.30156186
## 3 H B 1.263101685 6.35944304
## 4 F C -2.013602958 -0.01299013
## 5 G B 1.289198834 4.55968583
## 6 H C 5.068129976 7.29426214
## 7 F B -2.100516815 -0.38606957
## 8 G C 1.957194620 6.74588317
## 9 H B 3.013215330 2.15875430
## 10 F C 3.607741088 7.08365411
## 11 G B 0.006982119 8.07876353
## 12 H C 4.148918747 6.87221445
## 13 F B -0.665046564 10.27761883
## 14 G C -0.227039202 -3.21996504
## 15 H B -1.332532504 2.45749924
## 16 F C 4.288040560 4.99913722
## 17 G B 2.652260755 -0.32317090
## 18 H C 4.091488606 3.46816064
## 19 F B 2.742519155 2.96378347
## 20 G C 1.629553926 -0.18909875
## 21 H B 1.337931322 5.60894586
## 22 F C 2.787898063 3.98076319
## 23 G B 1.959865884 2.68107182
## 24 H C 0.671924465 1.70897892
## 25 F B 0.566112079 -0.98534150
## 26 G C -1.393650825 -0.16271735
## 27 H B 0.051909195 -0.24395411
## 28 F C 3.065151904 -3.46838118
## 29 G B 2.110012178 -0.11077817
## 30 H C -0.623636412 3.33303095