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1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
1.4.2.3. Random Walk

1.4.2.3.1.

Background and Data

Generation A random walk can be generated from a set of uniform random numbers by the formula:
    \( R_{i} = \sum_{j=1}^{i}(U_{j} - 0.5) \)
where U is a set of uniform random numbers.

The motivation for studying a set of random walk data is to illustrate the effects of a known underlying autocorrelation structure (i.e., non-randomness) in the data.

Software The analyses used in this case study can be generated using both Dataplot code and R code.
Data The following is the set of random walk numbers used for this case study.

  -0.399027
  -0.645651
  -0.625516
  -0.262049
  -0.407173
  -0.097583
   0.314156
   0.106905
  -0.017675
  -0.037111
   0.357631
   0.820111
   0.844148
   0.550509
   0.090709
   0.413625
  -0.002149
   0.393170
   0.538263
   0.070583
   0.473143
   0.132676
   0.109111
  -0.310553
   0.179637
  -0.067454
  -0.190747
  -0.536916
  -0.905751
  -0.518984
  -0.579280
  -0.643004
  -1.014925
  -0.517845
  -0.860484
  -0.884081
  -1.147428
  -0.657917
  -0.470205
  -0.798437
  -0.637780
  -0.666046
  -1.093278
  -1.089609
  -0.853439
  -0.695306
  -0.206795
  -0.507504
  -0.696903
  -1.116358
  -1.044534
  -1.481004
  -1.638390
  -1.270400
  -1.026477
  -1.123380
  -0.770683
  -0.510481
  -0.958825
  -0.531959
  -0.457141
  -0.226603
  -0.201885
  -0.078000
   0.057733
  -0.228762
  -0.403292
  -0.414237
  -0.556689
  -0.772007
  -0.401024
  -0.409768
  -0.171804
  -0.096501
  -0.066854
   0.216726
   0.551008
   0.660360
   0.194795
  -0.031321
   0.453880
   0.730594
   1.136280
   0.708490
   1.149048
   1.258757
   1.102107
   1.102846
   0.720896
   0.764035
   1.072312
   0.897384
   0.965632
   0.759684
   0.679836
   0.955514
   1.290043
   1.753449
   1.542429
   1.873803
   2.043881
   1.728635
   1.289703
   1.501481
   1.888335
   1.408421
   1.416005
   0.929681
   1.097632
   1.501279
   1.650608
   1.759718
   2.255664
   2.490551
   2.508200
   2.707382
   2.816310
   3.254166
   2.890989
   2.869330
   3.024141
   3.291558
   3.260067
   3.265871
   3.542845
   3.773240
   3.991880
   3.710045
   4.011288
   4.074805
   4.301885
   3.956416
   4.278790
   3.989947
   4.315261
   4.200798
   4.444307
   4.926084
   4.828856
   4.473179
   4.573389
   4.528605
   4.452401
   4.238427
   4.437589
   4.617955
   4.370246
   4.353939
   4.541142
   4.807353
   4.706447
   4.607011
   4.205943
   3.756457
   3.482142
   3.126784
   3.383572
   3.846550
   4.228803
   4.110948
   4.525939
   4.478307
   4.457582
   4.822199
   4.605752
   5.053262
   5.545598
   5.134798
   5.438168
   5.397993
   5.838361
   5.925389
   6.159525
   6.190928
   6.024970
   5.575793
   5.516840
   5.211826
   4.869306
   4.912601
   5.339177
   5.415182
   5.003303
   4.725367
   4.350873
   4.225085
   3.825104
   3.726391
   3.301088
   3.767535
   4.211463
   4.418722
   4.554786
   4.987701
   4.993045
   5.337067
   5.789629
   5.726147
   5.934353
   5.641670
   5.753639
   5.298265
   5.255743
   5.500935
   5.434664
   5.588610
   6.047952
   6.130557
   5.785299
   5.811995
   5.582793
   5.618730
   5.902576
   6.226537
   5.738371
   5.449965
   5.895537
   6.252904
   6.650447
   7.025909
   6.770340
   7.182244
   6.941536
   7.368996
   7.293807
   7.415205
   7.259291
   6.970976
   7.319743
   6.850454
   6.556378
   6.757845
   6.493083
   6.824855
   6.533753
   6.410646
   6.502063
   6.264585
   6.730889
   6.753715
   6.298649
   6.048126
   5.794463
   5.539049
   5.290072
   5.409699
   5.843266
   5.680389
   5.185889
   5.451353
   5.003233
   5.102844
   5.566741
   5.613668
   5.352791
   5.140087
   4.999718
   5.030444
   5.428537
   5.471872
   5.107334
   5.387078
   4.889569
   4.492962
   4.591042
   4.930187
   4.857455
   4.785815
   5.235515
   4.865727
   4.855005
   4.920206
   4.880794
   4.904395
   4.795317
   5.163044
   4.807122
   5.246230
   5.111000
   5.228429
   5.050220
   4.610006
   4.489258
   4.399814
   4.606821
   4.974252
   5.190037
   5.084155
   5.276501
   4.917121
   4.534573
   4.076168
   4.236168
   3.923607
   3.666004
   3.284967
   2.980621
   2.623622
   2.882375
   3.176416
   3.598001
   3.764744
   3.945428
   4.408280
   4.359831
   4.353650
   4.329722
   4.294088
   4.588631
   4.679111
   4.182430
   4.509125
   4.957768
   4.657204
   4.325313
   4.338800
   4.720353
   4.235756
   4.281361
   3.795872
   4.276734
   4.259379
   3.999663
   3.544163
   3.953058
   3.844006
   3.684740
   3.626058
   3.457909
   3.581150
   4.022659
   4.021602
   4.070183
   4.457137
   4.156574
   4.205304
   4.514814
   4.055510
   3.938217
   4.180232
   3.803619
   3.553781
   3.583675
   3.708286
   4.005810
   4.419880
   4.881163
   5.348149
   4.950740
   5.199262
   4.753162
   4.640757
   4.327090
   4.080888
   3.725953
   3.939054
   3.463728
   3.018284
   2.661061
   3.099980
   3.340274
   3.230551
   3.287873
   3.497652
   3.014771
   3.040046
   3.342226
   3.656743
   3.698527
   3.759707
   4.253078
   4.183611
   4.196580
   4.257851
   4.683387
   4.224290
   3.840934
   4.329286
   3.909134
   3.685072
   3.356611
   2.956344
   2.800432
   2.761665
   2.744913
   3.037743
   2.787390
   2.387619
   2.424489
   2.247564
   2.502179
   2.022278
   2.213027
   2.126914
   2.264833
   2.528391
   2.432792
   2.037974
   1.699475
   2.048244
   1.640126
   1.149858
   1.475253
   1.245675
   0.831979
   1.165877
   1.403341
   1.181921
   1.582379
   1.632130
   2.113636
   2.163129
   2.545126
   2.963833
   3.078901
   3.055547
   3.287442
   2.808189
   2.985451
   3.181679
   2.746144
   2.517390
   2.719231
   2.581058
   2.838745
   2.987765
   3.459642
   3.458684
   3.870956
   4.324706
   4.411899
   4.735330
   4.775494
   4.681160
   4.462470
   3.992538
   3.719936
   3.427081
   3.256588
   3.462766
   3.046353
   3.537430
   3.579857
   3.931223
   3.590096
   3.136285
   3.391616
   3.114700
   2.897760
   2.724241
   2.557346
   2.971397
   2.479290
   2.305336
   1.852930
   1.471948
   1.510356
   1.633737
   1.727873
   1.512994
   1.603284
   1.387950
   1.767527
   2.029734
   2.447309
   2.321470
   2.435092
   2.630118
   2.520330
   2.578147
   2.729630
   2.713100
   3.107260
   2.876659
   2.774242
   3.185503
   3.403148
   3.392646
   3.123339
   3.164713
   3.439843
   3.321929
   3.686229
   3.203069
   3.185843
   3.204924
   3.102996
   3.496552
   3.191575
   3.409044
   3.888246
   4.273767
   3.803540
   4.046417
   4.071581
   3.916256
   3.634441
   4.065834
   3.844651
   3.915219

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