ANLY 505 - Problem Set #1
Alan Hitch
April 4, 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(16)
rnorm(30, mean = c(25,40,55), sd = c(4,10,18))## [1] 26.90565 38.74620 74.73189 19.22308 51.47829 46.56858 20.97620
## [8] 40.63563 73.44951 27.29257 58.47182 57.01480 22.01585 56.58214
## [15] 67.99097 18.34768 45.75910 63.50968 22.82907 51.27687 25.33964
## [22] 23.74330 38.17318 81.46861 21.53640 55.27467 73.97521 29.12028
## [29] 48.40161 58.90536- 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(16)
x1 = runif(20, min = 1, max = 2)
x2 = runif(20, min = 50, max = 100)
y = rnorm(20, mean = 0, sd = 1)
lm(y ~ x1 + x2)##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Coefficients:
## (Intercept) x1 x2
## 0.342626 -0.552292 0.006669- 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 dataframe with 3 groups, 2 factors and two quantitative response variables. Use the replicate function (n = 25).
df = data.frame(group = rep(letters[1:3]),factor = rep(LETTERS[1:2]),x = rnorm(150, mean =5, sd=3), y = rnorm(150, mean = 15, sd =10))
df## group factor x y
## 1 a A 1.0239406 10.9952005
## 2 b B 11.1954070 22.0911285
## 3 c A 5.7265191 10.5966665
## 4 a B 3.9527083 15.3608768
## 5 b A 3.1075629 12.1275677
## 6 c B 5.8517201 22.3063755
## 7 a A 5.3647310 14.1526489
## 8 b B 6.6990323 22.6660870
## 9 c A 6.7070987 9.3755017
## 10 a B 4.7282397 18.2525481
## 11 b A 5.6914895 11.3545163
## 12 c B 7.2585614 26.6665340
## 13 a A 7.5901562 9.8065966
## 14 b B 7.5145959 21.4115316
## 15 c A -0.2975564 -0.3287460
## 16 a B 7.0504835 17.2882883
## 17 b A 8.4890338 -0.9020580
## 18 c B 1.3981945 1.6223912
## 19 a A 14.7485903 20.6833931
## 20 b B 2.9727928 19.9839404
## 21 c A 1.3612183 21.9611896
## 22 a B 3.7488488 7.5783445
## 23 b A 3.3033410 10.2063116
## 24 c B 0.5308093 13.1294895
## 25 a A 1.4495130 27.2612754
## 26 b B 2.8186636 19.1769676
## 27 c A 2.9469703 7.2034309
## 28 a B 2.8789451 25.2685401
## 29 b A 7.6392760 23.2247709
## 30 c B 3.4703941 17.7603988
## 31 a A 1.1176129 22.4612072
## 32 b B 4.6606244 10.7266248
## 33 c A 7.6591278 37.1418772
## 34 a B 5.0511384 26.3322048
## 35 b A 7.3281244 32.0768855
## 36 c B 5.2188658 19.5893206
## 37 a A -1.0465174 12.1091112
## 38 b B 1.9768952 11.1910430
## 39 c A 4.5335399 18.4324084
## 40 a B 7.8156261 11.3012664
## 41 b A 9.6945956 20.0290970
## 42 c B 8.2572070 -1.5731096
## 43 a A 8.6598647 7.6757366
## 44 b B 3.7600846 11.4065156
## 45 c A 4.6086629 24.5253893
## 46 a B 4.5510205 23.5208116
## 47 b A 7.4776597 20.4973318
## 48 c B 4.6297463 3.5895755
## 49 a A 8.7754045 30.3631409
## 50 b B -1.9553718 26.2942402
## 51 c A 3.0904775 -7.4570952
## 52 a B 5.9299273 21.3953158
## 53 b A -1.3677213 0.9315630
## 54 c B 6.6894012 2.4181390
## 55 a A 6.8089831 17.8874534
## 56 b B 1.6791081 19.5080005
## 57 c A 6.9483290 18.0640984
## 58 a B 6.9335288 14.4998730
## 59 b A 2.8788236 7.4314537
## 60 c B 9.3880912 11.3518307
## 61 a A 10.1507844 11.2471714
## 62 b B 6.6673108 13.5174594
## 63 c A 12.8881177 12.7615293
## 64 a B 6.5034663 9.9267031
## 65 b A 5.2398110 25.1032275
## 66 c B 2.7149194 31.0451923
## 67 a A 3.6512162 9.3514891
## 68 b B 3.6820937 31.5663710
## 69 c A 12.0157548 17.2074453
## 70 a B 8.5304094 -0.3258645
## 71 b A 6.6262151 16.0283708
## 72 c B 4.7620521 18.5038167
## 73 a A 3.2489053 13.9597418
## 74 b B 2.7686663 1.1426243
## 75 c A 3.3507858 23.8437675
## 76 a B 3.9267859 24.9438112
## 77 b A -1.7164901 9.4394264
## 78 c B 2.4913546 1.2781179
## 79 a A 8.4633063 25.2066296
## 80 b B 9.4643342 7.8564983
## 81 c A 4.2549215 23.0089280
## 82 a B 4.4724864 11.2033509
## 83 b A -0.6583091 25.4305499
## 84 c B 8.1372869 5.6788877
## 85 a A 1.1096363 3.1788157
## 86 b B 5.7611927 4.1293748
## 87 c A 4.2293593 9.8754133
## 88 a B 5.9313408 13.6074613
## 89 b A 9.6495064 4.9444075
## 90 c B 4.3752707 21.3100485
## 91 a A 6.0677645 12.2217792
## 92 b B 4.3034944 25.5238448
## 93 c A 5.8721187 16.1540804
## 94 a B 4.8198985 15.9416023
## 95 b A 4.3488957 9.8501847
## 96 c B 1.1201843 22.5090405
## 97 a A 3.3082246 11.8286579
## 98 b B 3.1288244 23.6991372
## 99 c A 4.3014945 18.3878460
## 100 a B -1.8085423 31.4970676
## 101 b A 1.7495648 20.3009005
## 102 c B -0.1283186 12.7875971
## 103 a A 5.0107322 10.6500987
## 104 b B 6.8468007 12.6038943
## 105 c A 5.9236748 4.4984877
## 106 a B 1.8789233 14.8736913
## 107 b A 6.2382967 23.0340316
## 108 c B 4.9066041 10.5646128
## 109 a A 6.9816560 24.9557374
## 110 b B 6.6459255 31.7154670
## 111 c A 2.4817380 -4.3066788
## 112 a B 1.0865714 5.9776947
## 113 b A 6.1711111 5.5741985
## 114 c B 3.6524464 10.3606637
## 115 a A 3.2597804 17.7136055
## 116 b B 3.5978335 11.1367644
## 117 c A 4.6827720 -12.5366038
## 118 a B 4.0282285 7.5099286
## 119 b A 8.7119852 19.3378604
## 120 c B 3.3495924 25.1488071
## 121 a A 8.3122329 21.0982141
## 122 b B 3.7723611 26.8476693
## 123 c A 1.9317054 4.6862742
## 124 a B 8.6513422 11.5182570
## 125 b A 6.2770263 2.4909336
## 126 c B 10.1860091 11.9939178
## 127 a A 0.4763433 -1.0475353
## 128 b B 7.2782789 5.8765127
## 129 c A 5.9232234 9.6058865
## 130 a B 5.9033193 5.8104205
## 131 b A 7.1045651 23.1643058
## 132 c B 10.1186563 2.2663775
## 133 a A 6.1632133 -1.7903794
## 134 b B 3.8910458 16.2053499
## 135 c A 5.7092682 20.2200827
## 136 a B 3.7920758 10.1225964
## 137 b A 8.6777690 24.5222236
## 138 c B 12.7539493 12.1601419
## 139 a A -0.6469606 19.9315866
## 140 b B -1.2889880 46.2723929
## 141 c A 2.1364272 20.9946816
## 142 a B 7.3848095 26.2858023
## 143 b A 3.1581790 25.2281367
## 144 c B 2.0271287 25.0013313
## 145 a A 5.4249442 6.0917808
## 146 b B 7.8927735 16.6322239
## 147 c A 9.4469343 6.8622221
## 148 a B 8.7849803 13.3600821
## 149 b A 4.3607620 34.5741410
## 150 c B 2.3519202 9.7718158simulate <- replicate(3, expr = df,simplify = FALSE)
simulate## [[1]]
## group factor x y
## 1 a A 1.0239406 10.9952005
## 2 b B 11.1954070 22.0911285
## 3 c A 5.7265191 10.5966665
## 4 a B 3.9527083 15.3608768
## 5 b A 3.1075629 12.1275677
## 6 c B 5.8517201 22.3063755
## 7 a A 5.3647310 14.1526489
## 8 b B 6.6990323 22.6660870
## 9 c A 6.7070987 9.3755017
## 10 a B 4.7282397 18.2525481
## 11 b A 5.6914895 11.3545163
## 12 c B 7.2585614 26.6665340
## 13 a A 7.5901562 9.8065966
## 14 b B 7.5145959 21.4115316
## 15 c A -0.2975564 -0.3287460
## 16 a B 7.0504835 17.2882883
## 17 b A 8.4890338 -0.9020580
## 18 c B 1.3981945 1.6223912
## 19 a A 14.7485903 20.6833931
## 20 b B 2.9727928 19.9839404
## 21 c A 1.3612183 21.9611896
## 22 a B 3.7488488 7.5783445
## 23 b A 3.3033410 10.2063116
## 24 c B 0.5308093 13.1294895
## 25 a A 1.4495130 27.2612754
## 26 b B 2.8186636 19.1769676
## 27 c A 2.9469703 7.2034309
## 28 a B 2.8789451 25.2685401
## 29 b A 7.6392760 23.2247709
## 30 c B 3.4703941 17.7603988
## 31 a A 1.1176129 22.4612072
## 32 b B 4.6606244 10.7266248
## 33 c A 7.6591278 37.1418772
## 34 a B 5.0511384 26.3322048
## 35 b A 7.3281244 32.0768855
## 36 c B 5.2188658 19.5893206
## 37 a A -1.0465174 12.1091112
## 38 b B 1.9768952 11.1910430
## 39 c A 4.5335399 18.4324084
## 40 a B 7.8156261 11.3012664
## 41 b A 9.6945956 20.0290970
## 42 c B 8.2572070 -1.5731096
## 43 a A 8.6598647 7.6757366
## 44 b B 3.7600846 11.4065156
## 45 c A 4.6086629 24.5253893
## 46 a B 4.5510205 23.5208116
## 47 b A 7.4776597 20.4973318
## 48 c B 4.6297463 3.5895755
## 49 a A 8.7754045 30.3631409
## 50 b B -1.9553718 26.2942402
## 51 c A 3.0904775 -7.4570952
## 52 a B 5.9299273 21.3953158
## 53 b A -1.3677213 0.9315630
## 54 c B 6.6894012 2.4181390
## 55 a A 6.8089831 17.8874534
## 56 b B 1.6791081 19.5080005
## 57 c A 6.9483290 18.0640984
## 58 a B 6.9335288 14.4998730
## 59 b A 2.8788236 7.4314537
## 60 c B 9.3880912 11.3518307
## 61 a A 10.1507844 11.2471714
## 62 b B 6.6673108 13.5174594
## 63 c A 12.8881177 12.7615293
## 64 a B 6.5034663 9.9267031
## 65 b A 5.2398110 25.1032275
## 66 c B 2.7149194 31.0451923
## 67 a A 3.6512162 9.3514891
## 68 b B 3.6820937 31.5663710
## 69 c A 12.0157548 17.2074453
## 70 a B 8.5304094 -0.3258645
## 71 b A 6.6262151 16.0283708
## 72 c B 4.7620521 18.5038167
## 73 a A 3.2489053 13.9597418
## 74 b B 2.7686663 1.1426243
## 75 c A 3.3507858 23.8437675
## 76 a B 3.9267859 24.9438112
## 77 b A -1.7164901 9.4394264
## 78 c B 2.4913546 1.2781179
## 79 a A 8.4633063 25.2066296
## 80 b B 9.4643342 7.8564983
## 81 c A 4.2549215 23.0089280
## 82 a B 4.4724864 11.2033509
## 83 b A -0.6583091 25.4305499
## 84 c B 8.1372869 5.6788877
## 85 a A 1.1096363 3.1788157
## 86 b B 5.7611927 4.1293748
## 87 c A 4.2293593 9.8754133
## 88 a B 5.9313408 13.6074613
## 89 b A 9.6495064 4.9444075
## 90 c B 4.3752707 21.3100485
## 91 a A 6.0677645 12.2217792
## 92 b B 4.3034944 25.5238448
## 93 c A 5.8721187 16.1540804
## 94 a B 4.8198985 15.9416023
## 95 b A 4.3488957 9.8501847
## 96 c B 1.1201843 22.5090405
## 97 a A 3.3082246 11.8286579
## 98 b B 3.1288244 23.6991372
## 99 c A 4.3014945 18.3878460
## 100 a B -1.8085423 31.4970676
## 101 b A 1.7495648 20.3009005
## 102 c B -0.1283186 12.7875971
## 103 a A 5.0107322 10.6500987
## 104 b B 6.8468007 12.6038943
## 105 c A 5.9236748 4.4984877
## 106 a B 1.8789233 14.8736913
## 107 b A 6.2382967 23.0340316
## 108 c B 4.9066041 10.5646128
## 109 a A 6.9816560 24.9557374
## 110 b B 6.6459255 31.7154670
## 111 c A 2.4817380 -4.3066788
## 112 a B 1.0865714 5.9776947
## 113 b A 6.1711111 5.5741985
## 114 c B 3.6524464 10.3606637
## 115 a A 3.2597804 17.7136055
## 116 b B 3.5978335 11.1367644
## 117 c A 4.6827720 -12.5366038
## 118 a B 4.0282285 7.5099286
## 119 b A 8.7119852 19.3378604
## 120 c B 3.3495924 25.1488071
## 121 a A 8.3122329 21.0982141
## 122 b B 3.7723611 26.8476693
## 123 c A 1.9317054 4.6862742
## 124 a B 8.6513422 11.5182570
## 125 b A 6.2770263 2.4909336
## 126 c B 10.1860091 11.9939178
## 127 a A 0.4763433 -1.0475353
## 128 b B 7.2782789 5.8765127
## 129 c A 5.9232234 9.6058865
## 130 a B 5.9033193 5.8104205
## 131 b A 7.1045651 23.1643058
## 132 c B 10.1186563 2.2663775
## 133 a A 6.1632133 -1.7903794
## 134 b B 3.8910458 16.2053499
## 135 c A 5.7092682 20.2200827
## 136 a B 3.7920758 10.1225964
## 137 b A 8.6777690 24.5222236
## 138 c B 12.7539493 12.1601419
## 139 a A -0.6469606 19.9315866
## 140 b B -1.2889880 46.2723929
## 141 c A 2.1364272 20.9946816
## 142 a B 7.3848095 26.2858023
## 143 b A 3.1581790 25.2281367
## 144 c B 2.0271287 25.0013313
## 145 a A 5.4249442 6.0917808
## 146 b B 7.8927735 16.6322239
## 147 c A 9.4469343 6.8622221
## 148 a B 8.7849803 13.3600821
## 149 b A 4.3607620 34.5741410
## 150 c B 2.3519202 9.7718158
##
## [[2]]
## group factor x y
## 1 a A 1.0239406 10.9952005
## 2 b B 11.1954070 22.0911285
## 3 c A 5.7265191 10.5966665
## 4 a B 3.9527083 15.3608768
## 5 b A 3.1075629 12.1275677
## 6 c B 5.8517201 22.3063755
## 7 a A 5.3647310 14.1526489
## 8 b B 6.6990323 22.6660870
## 9 c A 6.7070987 9.3755017
## 10 a B 4.7282397 18.2525481
## 11 b A 5.6914895 11.3545163
## 12 c B 7.2585614 26.6665340
## 13 a A 7.5901562 9.8065966
## 14 b B 7.5145959 21.4115316
## 15 c A -0.2975564 -0.3287460
## 16 a B 7.0504835 17.2882883
## 17 b A 8.4890338 -0.9020580
## 18 c B 1.3981945 1.6223912
## 19 a A 14.7485903 20.6833931
## 20 b B 2.9727928 19.9839404
## 21 c A 1.3612183 21.9611896
## 22 a B 3.7488488 7.5783445
## 23 b A 3.3033410 10.2063116
## 24 c B 0.5308093 13.1294895
## 25 a A 1.4495130 27.2612754
## 26 b B 2.8186636 19.1769676
## 27 c A 2.9469703 7.2034309
## 28 a B 2.8789451 25.2685401
## 29 b A 7.6392760 23.2247709
## 30 c B 3.4703941 17.7603988
## 31 a A 1.1176129 22.4612072
## 32 b B 4.6606244 10.7266248
## 33 c A 7.6591278 37.1418772
## 34 a B 5.0511384 26.3322048
## 35 b A 7.3281244 32.0768855
## 36 c B 5.2188658 19.5893206
## 37 a A -1.0465174 12.1091112
## 38 b B 1.9768952 11.1910430
## 39 c A 4.5335399 18.4324084
## 40 a B 7.8156261 11.3012664
## 41 b A 9.6945956 20.0290970
## 42 c B 8.2572070 -1.5731096
## 43 a A 8.6598647 7.6757366
## 44 b B 3.7600846 11.4065156
## 45 c A 4.6086629 24.5253893
## 46 a B 4.5510205 23.5208116
## 47 b A 7.4776597 20.4973318
## 48 c B 4.6297463 3.5895755
## 49 a A 8.7754045 30.3631409
## 50 b B -1.9553718 26.2942402
## 51 c A 3.0904775 -7.4570952
## 52 a B 5.9299273 21.3953158
## 53 b A -1.3677213 0.9315630
## 54 c B 6.6894012 2.4181390
## 55 a A 6.8089831 17.8874534
## 56 b B 1.6791081 19.5080005
## 57 c A 6.9483290 18.0640984
## 58 a B 6.9335288 14.4998730
## 59 b A 2.8788236 7.4314537
## 60 c B 9.3880912 11.3518307
## 61 a A 10.1507844 11.2471714
## 62 b B 6.6673108 13.5174594
## 63 c A 12.8881177 12.7615293
## 64 a B 6.5034663 9.9267031
## 65 b A 5.2398110 25.1032275
## 66 c B 2.7149194 31.0451923
## 67 a A 3.6512162 9.3514891
## 68 b B 3.6820937 31.5663710
## 69 c A 12.0157548 17.2074453
## 70 a B 8.5304094 -0.3258645
## 71 b A 6.6262151 16.0283708
## 72 c B 4.7620521 18.5038167
## 73 a A 3.2489053 13.9597418
## 74 b B 2.7686663 1.1426243
## 75 c A 3.3507858 23.8437675
## 76 a B 3.9267859 24.9438112
## 77 b A -1.7164901 9.4394264
## 78 c B 2.4913546 1.2781179
## 79 a A 8.4633063 25.2066296
## 80 b B 9.4643342 7.8564983
## 81 c A 4.2549215 23.0089280
## 82 a B 4.4724864 11.2033509
## 83 b A -0.6583091 25.4305499
## 84 c B 8.1372869 5.6788877
## 85 a A 1.1096363 3.1788157
## 86 b B 5.7611927 4.1293748
## 87 c A 4.2293593 9.8754133
## 88 a B 5.9313408 13.6074613
## 89 b A 9.6495064 4.9444075
## 90 c B 4.3752707 21.3100485
## 91 a A 6.0677645 12.2217792
## 92 b B 4.3034944 25.5238448
## 93 c A 5.8721187 16.1540804
## 94 a B 4.8198985 15.9416023
## 95 b A 4.3488957 9.8501847
## 96 c B 1.1201843 22.5090405
## 97 a A 3.3082246 11.8286579
## 98 b B 3.1288244 23.6991372
## 99 c A 4.3014945 18.3878460
## 100 a B -1.8085423 31.4970676
## 101 b A 1.7495648 20.3009005
## 102 c B -0.1283186 12.7875971
## 103 a A 5.0107322 10.6500987
## 104 b B 6.8468007 12.6038943
## 105 c A 5.9236748 4.4984877
## 106 a B 1.8789233 14.8736913
## 107 b A 6.2382967 23.0340316
## 108 c B 4.9066041 10.5646128
## 109 a A 6.9816560 24.9557374
## 110 b B 6.6459255 31.7154670
## 111 c A 2.4817380 -4.3066788
## 112 a B 1.0865714 5.9776947
## 113 b A 6.1711111 5.5741985
## 114 c B 3.6524464 10.3606637
## 115 a A 3.2597804 17.7136055
## 116 b B 3.5978335 11.1367644
## 117 c A 4.6827720 -12.5366038
## 118 a B 4.0282285 7.5099286
## 119 b A 8.7119852 19.3378604
## 120 c B 3.3495924 25.1488071
## 121 a A 8.3122329 21.0982141
## 122 b B 3.7723611 26.8476693
## 123 c A 1.9317054 4.6862742
## 124 a B 8.6513422 11.5182570
## 125 b A 6.2770263 2.4909336
## 126 c B 10.1860091 11.9939178
## 127 a A 0.4763433 -1.0475353
## 128 b B 7.2782789 5.8765127
## 129 c A 5.9232234 9.6058865
## 130 a B 5.9033193 5.8104205
## 131 b A 7.1045651 23.1643058
## 132 c B 10.1186563 2.2663775
## 133 a A 6.1632133 -1.7903794
## 134 b B 3.8910458 16.2053499
## 135 c A 5.7092682 20.2200827
## 136 a B 3.7920758 10.1225964
## 137 b A 8.6777690 24.5222236
## 138 c B 12.7539493 12.1601419
## 139 a A -0.6469606 19.9315866
## 140 b B -1.2889880 46.2723929
## 141 c A 2.1364272 20.9946816
## 142 a B 7.3848095 26.2858023
## 143 b A 3.1581790 25.2281367
## 144 c B 2.0271287 25.0013313
## 145 a A 5.4249442 6.0917808
## 146 b B 7.8927735 16.6322239
## 147 c A 9.4469343 6.8622221
## 148 a B 8.7849803 13.3600821
## 149 b A 4.3607620 34.5741410
## 150 c B 2.3519202 9.7718158
##
## [[3]]
## group factor x y
## 1 a A 1.0239406 10.9952005
## 2 b B 11.1954070 22.0911285
## 3 c A 5.7265191 10.5966665
## 4 a B 3.9527083 15.3608768
## 5 b A 3.1075629 12.1275677
## 6 c B 5.8517201 22.3063755
## 7 a A 5.3647310 14.1526489
## 8 b B 6.6990323 22.6660870
## 9 c A 6.7070987 9.3755017
## 10 a B 4.7282397 18.2525481
## 11 b A 5.6914895 11.3545163
## 12 c B 7.2585614 26.6665340
## 13 a A 7.5901562 9.8065966
## 14 b B 7.5145959 21.4115316
## 15 c A -0.2975564 -0.3287460
## 16 a B 7.0504835 17.2882883
## 17 b A 8.4890338 -0.9020580
## 18 c B 1.3981945 1.6223912
## 19 a A 14.7485903 20.6833931
## 20 b B 2.9727928 19.9839404
## 21 c A 1.3612183 21.9611896
## 22 a B 3.7488488 7.5783445
## 23 b A 3.3033410 10.2063116
## 24 c B 0.5308093 13.1294895
## 25 a A 1.4495130 27.2612754
## 26 b B 2.8186636 19.1769676
## 27 c A 2.9469703 7.2034309
## 28 a B 2.8789451 25.2685401
## 29 b A 7.6392760 23.2247709
## 30 c B 3.4703941 17.7603988
## 31 a A 1.1176129 22.4612072
## 32 b B 4.6606244 10.7266248
## 33 c A 7.6591278 37.1418772
## 34 a B 5.0511384 26.3322048
## 35 b A 7.3281244 32.0768855
## 36 c B 5.2188658 19.5893206
## 37 a A -1.0465174 12.1091112
## 38 b B 1.9768952 11.1910430
## 39 c A 4.5335399 18.4324084
## 40 a B 7.8156261 11.3012664
## 41 b A 9.6945956 20.0290970
## 42 c B 8.2572070 -1.5731096
## 43 a A 8.6598647 7.6757366
## 44 b B 3.7600846 11.4065156
## 45 c A 4.6086629 24.5253893
## 46 a B 4.5510205 23.5208116
## 47 b A 7.4776597 20.4973318
## 48 c B 4.6297463 3.5895755
## 49 a A 8.7754045 30.3631409
## 50 b B -1.9553718 26.2942402
## 51 c A 3.0904775 -7.4570952
## 52 a B 5.9299273 21.3953158
## 53 b A -1.3677213 0.9315630
## 54 c B 6.6894012 2.4181390
## 55 a A 6.8089831 17.8874534
## 56 b B 1.6791081 19.5080005
## 57 c A 6.9483290 18.0640984
## 58 a B 6.9335288 14.4998730
## 59 b A 2.8788236 7.4314537
## 60 c B 9.3880912 11.3518307
## 61 a A 10.1507844 11.2471714
## 62 b B 6.6673108 13.5174594
## 63 c A 12.8881177 12.7615293
## 64 a B 6.5034663 9.9267031
## 65 b A 5.2398110 25.1032275
## 66 c B 2.7149194 31.0451923
## 67 a A 3.6512162 9.3514891
## 68 b B 3.6820937 31.5663710
## 69 c A 12.0157548 17.2074453
## 70 a B 8.5304094 -0.3258645
## 71 b A 6.6262151 16.0283708
## 72 c B 4.7620521 18.5038167
## 73 a A 3.2489053 13.9597418
## 74 b B 2.7686663 1.1426243
## 75 c A 3.3507858 23.8437675
## 76 a B 3.9267859 24.9438112
## 77 b A -1.7164901 9.4394264
## 78 c B 2.4913546 1.2781179
## 79 a A 8.4633063 25.2066296
## 80 b B 9.4643342 7.8564983
## 81 c A 4.2549215 23.0089280
## 82 a B 4.4724864 11.2033509
## 83 b A -0.6583091 25.4305499
## 84 c B 8.1372869 5.6788877
## 85 a A 1.1096363 3.1788157
## 86 b B 5.7611927 4.1293748
## 87 c A 4.2293593 9.8754133
## 88 a B 5.9313408 13.6074613
## 89 b A 9.6495064 4.9444075
## 90 c B 4.3752707 21.3100485
## 91 a A 6.0677645 12.2217792
## 92 b B 4.3034944 25.5238448
## 93 c A 5.8721187 16.1540804
## 94 a B 4.8198985 15.9416023
## 95 b A 4.3488957 9.8501847
## 96 c B 1.1201843 22.5090405
## 97 a A 3.3082246 11.8286579
## 98 b B 3.1288244 23.6991372
## 99 c A 4.3014945 18.3878460
## 100 a B -1.8085423 31.4970676
## 101 b A 1.7495648 20.3009005
## 102 c B -0.1283186 12.7875971
## 103 a A 5.0107322 10.6500987
## 104 b B 6.8468007 12.6038943
## 105 c A 5.9236748 4.4984877
## 106 a B 1.8789233 14.8736913
## 107 b A 6.2382967 23.0340316
## 108 c B 4.9066041 10.5646128
## 109 a A 6.9816560 24.9557374
## 110 b B 6.6459255 31.7154670
## 111 c A 2.4817380 -4.3066788
## 112 a B 1.0865714 5.9776947
## 113 b A 6.1711111 5.5741985
## 114 c B 3.6524464 10.3606637
## 115 a A 3.2597804 17.7136055
## 116 b B 3.5978335 11.1367644
## 117 c A 4.6827720 -12.5366038
## 118 a B 4.0282285 7.5099286
## 119 b A 8.7119852 19.3378604
## 120 c B 3.3495924 25.1488071
## 121 a A 8.3122329 21.0982141
## 122 b B 3.7723611 26.8476693
## 123 c A 1.9317054 4.6862742
## 124 a B 8.6513422 11.5182570
## 125 b A 6.2770263 2.4909336
## 126 c B 10.1860091 11.9939178
## 127 a A 0.4763433 -1.0475353
## 128 b B 7.2782789 5.8765127
## 129 c A 5.9232234 9.6058865
## 130 a B 5.9033193 5.8104205
## 131 b A 7.1045651 23.1643058
## 132 c B 10.1186563 2.2663775
## 133 a A 6.1632133 -1.7903794
## 134 b B 3.8910458 16.2053499
## 135 c A 5.7092682 20.2200827
## 136 a B 3.7920758 10.1225964
## 137 b A 8.6777690 24.5222236
## 138 c B 12.7539493 12.1601419
## 139 a A -0.6469606 19.9315866
## 140 b B -1.2889880 46.2723929
## 141 c A 2.1364272 20.9946816
## 142 a B 7.3848095 26.2858023
## 143 b A 3.1581790 25.2281367
## 144 c B 2.0271287 25.0013313
## 145 a A 5.4249442 6.0917808
## 146 b B 7.8927735 16.6322239
## 147 c A 9.4469343 6.8622221
## 148 a B 8.7849803 13.3600821
## 149 b A 4.3607620 34.5741410
## 150 c B 2.3519202 9.7718158