ANLY 505 - Problem Set #1
Kaiyan Wei
April 22, 2019
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 Moodle. 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(300)
rnorm(30, mean = c(0,5,10), sd = c(4,10,18))## [1] 5.495164 13.621069 18.522804 2.805051 4.149447 38.236638
## [7] 3.269568 8.947686 31.828574 1.420323 27.162742 8.370273
## [13] -5.266112 5.665348 19.219107 0.200119 19.673972 -13.211369
## [19] -1.030766 7.930513 3.926435 2.533032 1.868214 12.428076
## [25] -4.579020 1.886018 14.228351 5.354695 4.006378 28.664188- Simulate 2 continuous variables (normal distribution) (n=20) and plot the relationship between them
X1=rnorm(20,mean=0,sd=1)
X2=rnorm(20,mean=0,sd=1)
plot(X1~X2)
- 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(300)
x1 = runif(100, min = 0, max = 1)
x2 = runif(100, min = 50, max = 100)
y = rnorm(100, mean = 100, sd = 200)
lm(y ~ x1 + x2)##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Coefficients:
## (Intercept) x1 x2
## 131.2672 39.0462 -0.3189- Simulate 3 letters repeating each letter twice, 2 times.
rep(letters[2:4], each = 2, times =2)## [1] "b" "b" "c" "c" "d" "d" "b" "b" "c" "c" "d" "d"- Create a dataframe with 3 groups, 2 factors and two quantitative response variables. Use the replicate function (n = 25).
data.frame(group = rep(letters[2:4]),
factor = rep(LETTERS[1:2]),x = rnorm(60, mean =5, sd=3), y = rnorm(60, mean = 15, sd =10))## group factor x y
## 1 b A 8.1330283 16.053435
## 2 c B -2.1242363 24.264978
## 3 d A 4.4814803 17.117219
## 4 b B 10.4463761 3.399281
## 5 c A 3.8505541 23.237738
## 6 d B 2.6065334 29.283453
## 7 b A 2.0211903 11.030972
## 8 c B -0.3665134 -2.947162
## 9 d A 8.5149705 7.375006
## 10 b B 2.5759629 13.114750
## 11 c A 2.9281414 2.599585
## 12 d B 2.0639907 1.341067
## 13 b A 6.8130158 24.279705
## 14 c B 7.0416926 39.035403
## 15 d A 2.2437711 12.395507
## 16 b B 6.0499605 4.954977
## 17 c A 8.9685162 6.270899
## 18 d B 7.9743273 5.529763
## 19 b A 5.9085361 21.767418
## 20 c B 2.5380284 -16.425972
## 21 d A 5.8029407 16.413481
## 22 b B 3.1457546 16.717194
## 23 c A -0.9226167 26.004767
## 24 d B 3.7078095 27.750845
## 25 b A 3.2365745 3.421114
## 26 c B 3.3289279 24.404386
## 27 d A -0.2439076 -5.849829
## 28 b B 4.0327120 10.401353
## 29 c A 0.4234821 5.340665
## 30 d B 1.7611799 10.687284
## 31 b A 3.3964023 21.947766
## 32 c B 1.1126575 13.666098
## 33 d A 15.5124226 5.055455
## 34 b B 9.6071274 1.130144
## 35 c A 1.7184013 5.782464
## 36 d B 5.4539961 4.093898
## 37 b A -0.3536090 11.825729
## 38 c B 3.5654138 22.041320
## 39 d A 2.4960854 16.521464
## 40 b B 2.9770579 -1.718889
## 41 c A 8.9683358 39.976913
## 42 d B 6.6418132 22.888032
## 43 b A -1.3817656 1.466668
## 44 c B 3.1770986 12.977920
## 45 d A 7.2190703 5.210985
## 46 b B 9.7395380 4.085985
## 47 c A 2.6238806 7.048133
## 48 d B 4.7362789 16.896287
## 49 b A 7.0797103 11.693749
## 50 c B 8.4456995 3.495470
## 51 d A 7.3501475 20.981640
## 52 b B 9.8068564 38.295432
## 53 c A 5.4906941 5.737993
## 54 d B 4.9671220 22.582676
## 55 b A 7.3276913 19.800254
## 56 c B 9.3259904 35.261985
## 57 d A 3.4333643 7.669852
## 58 b B 8.8644089 18.258907
## 59 c A 10.0820753 2.529527
## 60 d B 5.6744274 10.588737simulate <- replicate(3, expr = data.frame(group = rep(letters[2:4]),factor = rep(LETTERS[1:2]),x = rnorm(60, mean =5, sd=3),y = rnorm(60, mean = 15, sd =10)),simplify = FALSE)
simulate## [[1]]
## group factor x y
## 1 b A 3.9650584 -1.7231944
## 2 c B 5.9596677 19.7679055
## 3 d A 0.5625022 11.9689096
## 4 b B 4.8588309 23.3471366
## 5 c A 4.4905708 22.9712584
## 6 d B 6.2718199 9.8891125
## 7 b A 9.4197248 20.0836720
## 8 c B 6.9006073 9.7128128
## 9 d A 7.7516581 23.5367446
## 10 b B 2.5318829 0.5959490
## 11 c A 6.3176834 17.3151701
## 12 d B 0.6352415 17.5895195
## 13 b A 3.1212168 14.9061675
## 14 c B -2.4645661 14.1571420
## 15 d A 5.5828525 13.5955684
## 16 b B 6.6669902 12.2695439
## 17 c A 6.7116115 20.3994319
## 18 d B 6.2382541 13.3469971
## 19 b A 2.6638289 39.7068458
## 20 c B 5.9246907 6.9432870
## 21 d A 7.3385355 22.1765517
## 22 b B 11.6588626 18.8882149
## 23 c A 8.5964587 24.2417995
## 24 d B 7.3752961 2.1877804
## 25 b A 3.5630013 21.2474493
## 26 c B 8.9621337 22.7703323
## 27 d A 8.1427950 12.6549833
## 28 b B 2.8547352 23.2791801
## 29 c A 5.3014752 13.5679940
## 30 d B 7.0293797 19.9097990
## 31 b A 1.9506471 20.4338341
## 32 c B 8.1447864 22.3154312
## 33 d A 3.3173572 27.5758051
## 34 b B 1.3125283 4.6220470
## 35 c A 2.9546562 17.8583800
## 36 d B 7.0813334 27.0170885
## 37 b A 1.2100130 26.5330411
## 38 c B 13.9701880 20.3627588
## 39 d A 3.5803915 16.6624219
## 40 b B 4.3734138 11.8515775
## 41 c A 4.0304108 24.1464450
## 42 d B 4.5927390 22.8631058
## 43 b A 4.8342233 25.0191862
## 44 c B 4.3033598 21.6197502
## 45 d A 8.4365494 18.8581002
## 46 b B 4.0502607 23.9296663
## 47 c A 1.4159048 7.0012554
## 48 d B 5.5789724 18.9615987
## 49 b A 7.5205957 22.6097213
## 50 c B 6.7758249 8.2236018
## 51 d A 3.2413183 21.2040359
## 52 b B 4.0898702 7.6270620
## 53 c A 5.8770459 -0.2131952
## 54 d B 4.4282912 39.6282907
## 55 b A 9.2777093 27.0364059
## 56 c B 6.2297653 15.3825674
## 57 d A 4.9061190 26.4235400
## 58 b B 3.2738048 13.6293519
## 59 c A 2.8826320 17.2965472
## 60 d B 2.0224662 3.5319231
##
## [[2]]
## group factor x y
## 1 b A 1.67981226 8.9627119
## 2 c B 6.90304769 16.7495000
## 3 d A 7.76321299 20.7901921
## 4 b B 3.42806026 12.6495698
## 5 c A 7.16114622 17.3151515
## 6 d B 3.38173617 43.9874077
## 7 b A 1.85065206 8.1303615
## 8 c B 4.87119878 -4.9692778
## 9 d A 5.96844765 9.7480063
## 10 b B 4.51023060 11.5991956
## 11 c A 8.20212378 16.8691973
## 12 d B 5.90927821 7.4314160
## 13 b A 6.38474095 28.6457749
## 14 c B 3.86629839 32.2778395
## 15 d A 0.06048081 18.8664119
## 16 b B -1.59743290 6.8972228
## 17 c A 7.36937742 16.5681191
## 18 d B 11.89006552 2.4630421
## 19 b A 4.87425361 6.8283850
## 20 c B 5.55059398 19.1460700
## 21 d A 1.09223712 31.4858791
## 22 b B 4.26782510 12.4117014
## 23 c A 2.15469809 11.2287902
## 24 d B 5.76164899 13.5379357
## 25 b A 3.10597497 13.2646526
## 26 c B 4.29081414 -0.2523517
## 27 d A 12.22349396 24.3874151
## 28 b B 7.78682865 14.0118979
## 29 c A 9.72422481 13.9900617
## 30 d B 6.62256789 -2.6074715
## 31 b A 4.70265052 22.2798879
## 32 c B 8.34249032 21.1457019
## 33 d A 4.30023430 3.0629273
## 34 b B 4.29663248 10.4837950
## 35 c A 3.18274792 22.9802117
## 36 d B 5.38181216 33.3491399
## 37 b A 8.46135834 13.0117147
## 38 c B 3.31009276 31.4902287
## 39 d A 0.74325106 10.9501040
## 40 b B 5.70509576 30.9259154
## 41 c A 5.08435163 22.8741196
## 42 d B -0.83782790 12.2563852
## 43 b A 5.14909918 26.3047843
## 44 c B 7.68746973 9.6525500
## 45 d A 10.35659711 16.8448366
## 46 b B 5.97600724 11.2669802
## 47 c A 2.06801366 19.2508503
## 48 d B 4.90865529 4.1067644
## 49 b A 5.28184481 11.0405287
## 50 c B 6.30721598 10.8214511
## 51 d A -0.65047030 11.0063514
## 52 b B 2.95915970 17.1431218
## 53 c A 1.75492160 6.7521368
## 54 d B -0.32769146 25.0368761
## 55 b A 1.20849588 -1.0383898
## 56 c B 6.96241196 15.5427622
## 57 d A 9.37165241 13.4100376
## 58 b B 3.69714978 9.9238619
## 59 c A -0.77797183 12.3513264
## 60 d B 4.18237868 21.4362984
##
## [[3]]
## group factor x y
## 1 b A 4.74898491 17.10959101
## 2 c B 8.01414362 3.78983056
## 3 d A 4.60283807 1.64607711
## 4 b B 5.76452997 19.94876965
## 5 c A 2.76397381 12.71522569
## 6 d B 2.13232047 17.27455517
## 7 b A 8.53026400 -6.59710770
## 8 c B 1.92651297 -0.81156900
## 9 d A 2.81779706 15.68617095
## 10 b B 6.92695569 19.13785290
## 11 c A 5.74029789 19.00575550
## 12 d B 7.62368574 22.46138162
## 13 b A 4.72218824 21.47971413
## 14 c B 4.48977717 -1.30168692
## 15 d A 1.53333894 14.73683744
## 16 b B 5.50545826 20.25498694
## 17 c A 3.34522987 0.22863356
## 18 d B 7.25990147 28.91852708
## 19 b A 0.58075831 5.71538457
## 20 c B 7.55119150 2.09091305
## 21 d A 5.35150890 14.56184274
## 22 b B 2.64432413 -8.30717847
## 23 c A 0.07939278 11.27929066
## 24 d B 0.70454907 23.56536519
## 25 b A 3.86214353 18.35102012
## 26 c B 7.08529008 26.83200244
## 27 d A 9.97456742 36.22473096
## 28 b B 8.02922724 16.81278826
## 29 c A 6.23177734 35.09793170
## 30 d B 0.90038994 2.50705783
## 31 b A 2.91277797 30.85823324
## 32 c B 4.20409741 21.24158801
## 33 d A 7.06308337 25.65892137
## 34 b B 5.53757283 13.59403225
## 35 c A 14.02529382 -1.41988304
## 36 d B 9.24343415 11.70454400
## 37 b A 6.35934858 27.94162008
## 38 c B 1.46613330 22.69541719
## 39 d A 7.58555815 24.70914173
## 40 b B 1.19511979 12.45012679
## 41 c A 6.29269268 14.96277947
## 42 d B 5.09574698 -0.94324583
## 43 b A 3.15561090 -0.05677246
## 44 c B 7.71493702 -7.47979370
## 45 d A 4.99259532 23.85912301
## 46 b B 3.61116224 31.32828212
## 47 c A 3.58297133 -0.30505688
## 48 d B 5.61340297 25.08757738
## 49 b A 7.32914169 9.32525245
## 50 c B 6.71018971 20.84830693
## 51 d A 6.30694340 31.61123728
## 52 b B 5.84238196 15.75536161
## 53 c A 5.21903120 26.12427992
## 54 d B 3.48577109 -16.72029706
## 55 b A 7.32354879 32.31637717
## 56 c B 6.18029139 14.94686506
## 57 d A 3.34368637 2.83360973
## 58 b B 3.37276077 0.54719610
## 59 c A 1.89098721 3.19330862
## 60 d B 0.55532572 1.19541712simulate <- replicate(3, expr = data.frame(group = rep(letters[2:4]),factor = rep(LETTERS[1:2]),x = rnorm(60, mean =5, sd=3),y = rnorm(60, mean = 15, sd =10)),simplify = FALSE)
simulate## [[1]]
## group factor x y
## 1 b A 5.815165 -1.61708441
## 2 c B 3.275532 25.08822628
## 3 d A 2.586307 3.10415376
## 4 b B 5.617827 -8.51830284
## 5 c A 7.284343 3.47338574
## 6 d B 5.380332 -0.89948476
## 7 b A 4.303481 7.15079497
## 8 c B 2.572327 22.93969156
## 9 d A 1.345583 27.88910445
## 10 b B 3.839355 19.04541359
## 11 c A 7.925749 27.59553832
## 12 d B 4.901023 28.77246329
## 13 b A 7.842530 23.97441511
## 14 c B 5.339202 31.75331678
## 15 d A 7.326968 20.66070099
## 16 b B 7.403216 -2.88267416
## 17 c A 12.214611 8.30782169
## 18 d B 3.075111 12.30644802
## 19 b A 10.374530 -0.08911894
## 20 c B 5.932746 33.73910844
## 21 d A 1.013353 32.84100616
## 22 b B 7.849398 39.01810886
## 23 c A 6.667709 28.55309407
## 24 d B 8.702884 21.64732556
## 25 b A 6.464381 23.71738677
## 26 c B 3.722307 7.81705331
## 27 d A 2.851478 10.50507413
## 28 b B 4.116453 0.76860723
## 29 c A 8.313267 13.62326583
## 30 d B 3.710091 29.90166190
## 31 b A 4.632794 10.78122828
## 32 c B 4.301034 16.01242467
## 33 d A 4.958963 24.53095298
## 34 b B 4.673809 8.18155892
## 35 c A 5.515694 29.77286987
## 36 d B 2.010016 27.02332101
## 37 b A 5.284673 23.88369085
## 38 c B 3.757055 9.26943013
## 39 d A 7.999686 28.84159866
## 40 b B 3.338982 21.91036025
## 41 c A 5.865286 14.52013145
## 42 d B 5.103818 10.45017916
## 43 b A 1.311780 -2.17701127
## 44 c B 9.778198 9.53048068
## 45 d A 1.067100 36.48291662
## 46 b B 4.347159 8.54210400
## 47 c A 4.541457 5.89755801
## 48 d B 6.281625 23.15323869
## 49 b A 7.427289 4.85759089
## 50 c B 6.155896 8.80895114
## 51 d A 2.412833 20.94874301
## 52 b B 1.710740 21.71241019
## 53 c A 5.328405 26.32494011
## 54 d B 7.013583 15.18361430
## 55 b A 1.940115 29.36650177
## 56 c B 8.140917 22.91764547
## 57 d A 3.573834 25.76248602
## 58 b B 1.897875 16.28004710
## 59 c A -1.172073 4.64020358
## 60 d B 4.379428 33.49104171
##
## [[2]]
## group factor x y
## 1 b A 6.6073886 14.873919
## 2 c B 10.4826600 7.031971
## 3 d A 5.3749472 15.430715
## 4 b B 4.2390393 20.575914
## 5 c A 3.9086876 19.229255
## 6 d B 9.3002081 19.902845
## 7 b A 5.8688948 1.660762
## 8 c B 6.0248779 29.503029
## 9 d A 2.7566973 -4.731682
## 10 b B 6.1158761 6.728312
## 11 c A 3.6931420 12.893551
## 12 d B 6.2540259 -4.375077
## 13 b A 3.0756134 15.229020
## 14 c B 8.3494436 11.571990
## 15 d A -0.4364417 8.401219
## 16 b B 4.1004596 15.909592
## 17 c A -1.5874469 17.104413
## 18 d B 6.3062963 10.046832
## 19 b A -2.5457833 31.399828
## 20 c B 6.0198118 15.187497
## 21 d A 8.8348900 11.329076
## 22 b B 5.8201163 1.535103
## 23 c A -1.8320123 26.039093
## 24 d B 1.6074172 12.783545
## 25 b A 3.8247513 16.503807
## 26 c B 3.0202080 12.861533
## 27 d A 4.9270145 26.767054
## 28 b B 8.2420378 13.002316
## 29 c A 10.3161438 19.050893
## 30 d B 5.9506308 14.171664
## 31 b A 5.3427701 18.029402
## 32 c B 2.5743825 8.715358
## 33 d A 5.2133312 13.393968
## 34 b B 9.7900999 16.405056
## 35 c A 0.5145843 5.771104
## 36 d B 1.0948092 23.694824
## 37 b A 5.1685294 6.675079
## 38 c B 7.0021387 18.654123
## 39 d A 10.7615837 20.072118
## 40 b B 5.5851361 17.552401
## 41 c A 1.8187687 6.273395
## 42 d B -0.8212130 28.488112
## 43 b A 3.9786634 12.502276
## 44 c B 3.6823425 20.546942
## 45 d A 3.7784604 -2.951947
## 46 b B 5.8936576 13.158968
## 47 c A 1.8892254 22.449477
## 48 d B 1.0593072 32.001467
## 49 b A 9.4360571 14.542597
## 50 c B 1.3700556 9.508814
## 51 d A 6.5166031 9.967639
## 52 b B 4.4870378 23.270462
## 53 c A 3.4930146 32.478850
## 54 d B 4.0554166 -1.209938
## 55 b A 2.2087883 -1.941274
## 56 c B 6.1313107 18.547291
## 57 d A 3.9248131 25.237982
## 58 b B -3.6453649 22.013555
## 59 c A -2.9285918 9.943649
## 60 d B 1.6543954 23.346315
##
## [[3]]
## group factor x y
## 1 b A 3.6224690 0.1999734
## 2 c B 8.6725414 14.0039876
## 3 d A 0.6233899 -4.0007000
## 4 b B 5.3964575 30.4787792
## 5 c A 7.3803853 20.5966568
## 6 d B 8.6354800 13.9039546
## 7 b A 6.9064448 6.3721051
## 8 c B 6.4542617 44.8058615
## 9 d A 9.8190330 13.7985569
## 10 b B 7.3160904 35.0899257
## 11 c A 8.4474446 9.1554031
## 12 d B 6.4671776 33.7018737
## 13 b A 7.1846029 18.9013656
## 14 c B -1.4967970 6.5520777
## 15 d A 9.3016010 2.1452659
## 16 b B 1.8736478 19.6981730
## 17 c A 3.5835723 32.4892496
## 18 d B 3.2863897 13.2807678
## 19 b A 3.3258108 -12.2819871
## 20 c B 3.1954961 17.4660971
## 21 d A 8.9514680 21.3970782
## 22 b B 3.2081189 6.1209054
## 23 c A 5.1078833 32.9491940
## 24 d B 6.8576457 10.1336617
## 25 b A 2.9576674 4.6198500
## 26 c B 4.7741927 19.5242437
## 27 d A 4.5672009 14.2586270
## 28 b B 4.7681854 14.1850044
## 29 c A 6.4740795 22.7880469
## 30 d B 8.0916542 12.5344250
## 31 b A 6.8048466 23.4515411
## 32 c B 3.4714061 19.5977766
## 33 d A 6.5316774 17.2670567
## 34 b B 7.4439028 25.4194762
## 35 c A 4.8850984 1.7203817
## 36 d B 11.9665922 24.2307739
## 37 b A -2.1587497 12.0740496
## 38 c B 7.7813033 27.7808589
## 39 d A 6.0175376 10.6278733
## 40 b B -0.3633616 -14.4920023
## 41 c A 4.0500952 28.2819778
## 42 d B 5.2010839 4.2856227
## 43 b A 3.7029928 22.8275874
## 44 c B 2.1599655 16.4762960
## 45 d A 3.3626318 23.3328532
## 46 b B 5.7139194 18.8781788
## 47 c A 7.8323719 4.1434827
## 48 d B 8.1716108 6.6685523
## 49 b A 10.2326297 2.1742216
## 50 c B 2.9605151 34.7017368
## 51 d A 5.6985781 13.3289435
## 52 b B 2.6646266 11.0424101
## 53 c A 9.9155198 24.1446218
## 54 d B 9.8994927 5.2205480
## 55 b A 4.6704713 12.5488689
## 56 c B 2.2013094 35.6569671
## 57 d A 2.9769509 12.5088877
## 58 b B 10.3317791 6.1373590
## 59 c A 2.0776865 23.8047144
## 60 d B 7.1019413 15.1139607