Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationMon, 11 Dec 2017 14:23:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/11/t1512998727tmck5wkcl6e58dc.htm/, Retrieved Wed, 15 May 2024 04:31:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308972, Retrieved Wed, 15 May 2024 04:31:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Normality Plot] [Test] [2017-12-11 13:23:14] [453a4fcb74c301cf89bf197d0ef2c60e] [Current]
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Dataseries X:
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308972&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308972&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308972&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center







Box-Cox Normality Plot
# observations x144
maximum correlation0.988903262851653
optimal lambda0.22
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 144 \tabularnewline
maximum correlation & 0.988903262851653 \tabularnewline
optimal lambda & 0.22 \tabularnewline
transformation formula & for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308972&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]144[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.988903262851653[/C][/ROW]
[ROW][C]optimal lambda[/C][C]0.22[/C][/ROW]
[ROW][C]transformation formula[/C][C]for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308972&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308972&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Box-Cox Normality Plot
# observations x144
maximum correlation0.988903262851653
optimal lambda0.22
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda







Obs.OriginalTransformed
11128.28982359190115
21188.43803285374662
31328.76226329390214
41298.69512685001578
51218.50994299200564
61358.82821993874988
71489.10147333855519
81489.10147333855519
91368.84995138940858
101198.46215975106548
111048.08225703110083
121188.43803285374662
131158.364682249774
141268.62676131437388
151418.95677615024752
161358.82821993874988
171258.60369068252195
181499.12170606945975
191709.52396181005032
201709.52396181005032
211589.29919217996436
221338.78437758621956
231148.33990040474863
241408.93565032223542
251459.04012844130026
261509.14183315970288
271789.66702064831661
281639.39441123355153
291729.56021084645933
301789.66702064831661
3119910.0200319869468
3219910.0200319869468
331849.77105806814484
341629.37555150982637
351469.06068583493981
361669.45045408283629
371719.54212766513112
381809.70199967880636
391939.92225986047658
401819.71937562848881
411839.75390409947135
4221810.3151934709793
4323010.4914153858504
4424210.6606054511229
4520910.1779926162008
461919.88914234381911
471729.56021084645933
481949.93871833255018
491969.97143775595241
501969.97143775595241
5123610.576849297885
5223510.5627288802444
5322910.4770078410432
5424310.6744069186442
5526410.9544913812896
5627211.0566246512594
5723710.5909231231932
5821110.2088743179716
591809.70199967880636
6020110.0521115992846
6120410.0997673425599
621889.83895521340684
6323510.5627288802444
6422710.4480448941308
6523410.5485615167706
6626410.9544913812896
6730211.4199102635215
6829311.3139981418416
6925910.889425806741
7022910.4770078410432
7120310.0839431935411
7222910.4770078410432
7324210.6606054511229
7423310.5343468497563
7526710.9930706625766
7626911.0186027460442
7727011.0313133007946
7831511.5686301147655
7936412.0894235876376
8034711.9153024503844
8131211.5347411525047
8227411.0817912473729
8323710.5909231231932
8427811.1316976406289
8528411.2055172556443
8627711.1192738193284
8731711.5910831510213
8831311.5460656056794
8931811.6022682579461
9037412.1889040711468
9141312.5580981702438
9240512.4846543228915
9335511.9980515902361
9430611.4661934174461
9527111.0439871890362
9630611.4661934174461
9731511.5686301147655
9830111.4082648163515
9935612.0082926595805
10034811.9257269557472
10135511.9980515902361
10242212.6394078275788
10346513.0101976742097
10446713.0267816801034
10540412.4753944781858
10634711.9153024503844
10730511.4546670749057
10833611.7990575250942
10934011.8416672258106
11031811.6022682579461
11136212.0692722634059
11234811.9257269557472
11336312.0793587506282
11443512.7544997474099
11549113.2215923006927
11650513.3318246353522
11740412.4753944781858
11835912.0388818306271
11931011.5120070438533
12033711.8097468891496
12136012.049033911214
12234211.8628256073501
12340612.4938963509593
12439612.4006647773351
12542012.6214567498302
12647213.0680006456641
12754813.6561234934495
12855913.7358808700789
12946312.9935579379813
13040712.5031206404268
13136212.0692722634059
13240512.4846543228915
13341712.5944047058291
13439112.3533586750856
13541912.6124561964916
13646112.9768620421832
13747213.0680006456641
13853513.5602384136753
13962214.1704664737241
14060614.0634709238992
14150813.3551350589366
14246112.9768620421832
14339012.343840893049
14443212.7281806519939

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 112 & 8.28982359190115 \tabularnewline
2 & 118 & 8.43803285374662 \tabularnewline
3 & 132 & 8.76226329390214 \tabularnewline
4 & 129 & 8.69512685001578 \tabularnewline
5 & 121 & 8.50994299200564 \tabularnewline
6 & 135 & 8.82821993874988 \tabularnewline
7 & 148 & 9.10147333855519 \tabularnewline
8 & 148 & 9.10147333855519 \tabularnewline
9 & 136 & 8.84995138940858 \tabularnewline
10 & 119 & 8.46215975106548 \tabularnewline
11 & 104 & 8.08225703110083 \tabularnewline
12 & 118 & 8.43803285374662 \tabularnewline
13 & 115 & 8.364682249774 \tabularnewline
14 & 126 & 8.62676131437388 \tabularnewline
15 & 141 & 8.95677615024752 \tabularnewline
16 & 135 & 8.82821993874988 \tabularnewline
17 & 125 & 8.60369068252195 \tabularnewline
18 & 149 & 9.12170606945975 \tabularnewline
19 & 170 & 9.52396181005032 \tabularnewline
20 & 170 & 9.52396181005032 \tabularnewline
21 & 158 & 9.29919217996436 \tabularnewline
22 & 133 & 8.78437758621956 \tabularnewline
23 & 114 & 8.33990040474863 \tabularnewline
24 & 140 & 8.93565032223542 \tabularnewline
25 & 145 & 9.04012844130026 \tabularnewline
26 & 150 & 9.14183315970288 \tabularnewline
27 & 178 & 9.66702064831661 \tabularnewline
28 & 163 & 9.39441123355153 \tabularnewline
29 & 172 & 9.56021084645933 \tabularnewline
30 & 178 & 9.66702064831661 \tabularnewline
31 & 199 & 10.0200319869468 \tabularnewline
32 & 199 & 10.0200319869468 \tabularnewline
33 & 184 & 9.77105806814484 \tabularnewline
34 & 162 & 9.37555150982637 \tabularnewline
35 & 146 & 9.06068583493981 \tabularnewline
36 & 166 & 9.45045408283629 \tabularnewline
37 & 171 & 9.54212766513112 \tabularnewline
38 & 180 & 9.70199967880636 \tabularnewline
39 & 193 & 9.92225986047658 \tabularnewline
40 & 181 & 9.71937562848881 \tabularnewline
41 & 183 & 9.75390409947135 \tabularnewline
42 & 218 & 10.3151934709793 \tabularnewline
43 & 230 & 10.4914153858504 \tabularnewline
44 & 242 & 10.6606054511229 \tabularnewline
45 & 209 & 10.1779926162008 \tabularnewline
46 & 191 & 9.88914234381911 \tabularnewline
47 & 172 & 9.56021084645933 \tabularnewline
48 & 194 & 9.93871833255018 \tabularnewline
49 & 196 & 9.97143775595241 \tabularnewline
50 & 196 & 9.97143775595241 \tabularnewline
51 & 236 & 10.576849297885 \tabularnewline
52 & 235 & 10.5627288802444 \tabularnewline
53 & 229 & 10.4770078410432 \tabularnewline
54 & 243 & 10.6744069186442 \tabularnewline
55 & 264 & 10.9544913812896 \tabularnewline
56 & 272 & 11.0566246512594 \tabularnewline
57 & 237 & 10.5909231231932 \tabularnewline
58 & 211 & 10.2088743179716 \tabularnewline
59 & 180 & 9.70199967880636 \tabularnewline
60 & 201 & 10.0521115992846 \tabularnewline
61 & 204 & 10.0997673425599 \tabularnewline
62 & 188 & 9.83895521340684 \tabularnewline
63 & 235 & 10.5627288802444 \tabularnewline
64 & 227 & 10.4480448941308 \tabularnewline
65 & 234 & 10.5485615167706 \tabularnewline
66 & 264 & 10.9544913812896 \tabularnewline
67 & 302 & 11.4199102635215 \tabularnewline
68 & 293 & 11.3139981418416 \tabularnewline
69 & 259 & 10.889425806741 \tabularnewline
70 & 229 & 10.4770078410432 \tabularnewline
71 & 203 & 10.0839431935411 \tabularnewline
72 & 229 & 10.4770078410432 \tabularnewline
73 & 242 & 10.6606054511229 \tabularnewline
74 & 233 & 10.5343468497563 \tabularnewline
75 & 267 & 10.9930706625766 \tabularnewline
76 & 269 & 11.0186027460442 \tabularnewline
77 & 270 & 11.0313133007946 \tabularnewline
78 & 315 & 11.5686301147655 \tabularnewline
79 & 364 & 12.0894235876376 \tabularnewline
80 & 347 & 11.9153024503844 \tabularnewline
81 & 312 & 11.5347411525047 \tabularnewline
82 & 274 & 11.0817912473729 \tabularnewline
83 & 237 & 10.5909231231932 \tabularnewline
84 & 278 & 11.1316976406289 \tabularnewline
85 & 284 & 11.2055172556443 \tabularnewline
86 & 277 & 11.1192738193284 \tabularnewline
87 & 317 & 11.5910831510213 \tabularnewline
88 & 313 & 11.5460656056794 \tabularnewline
89 & 318 & 11.6022682579461 \tabularnewline
90 & 374 & 12.1889040711468 \tabularnewline
91 & 413 & 12.5580981702438 \tabularnewline
92 & 405 & 12.4846543228915 \tabularnewline
93 & 355 & 11.9980515902361 \tabularnewline
94 & 306 & 11.4661934174461 \tabularnewline
95 & 271 & 11.0439871890362 \tabularnewline
96 & 306 & 11.4661934174461 \tabularnewline
97 & 315 & 11.5686301147655 \tabularnewline
98 & 301 & 11.4082648163515 \tabularnewline
99 & 356 & 12.0082926595805 \tabularnewline
100 & 348 & 11.9257269557472 \tabularnewline
101 & 355 & 11.9980515902361 \tabularnewline
102 & 422 & 12.6394078275788 \tabularnewline
103 & 465 & 13.0101976742097 \tabularnewline
104 & 467 & 13.0267816801034 \tabularnewline
105 & 404 & 12.4753944781858 \tabularnewline
106 & 347 & 11.9153024503844 \tabularnewline
107 & 305 & 11.4546670749057 \tabularnewline
108 & 336 & 11.7990575250942 \tabularnewline
109 & 340 & 11.8416672258106 \tabularnewline
110 & 318 & 11.6022682579461 \tabularnewline
111 & 362 & 12.0692722634059 \tabularnewline
112 & 348 & 11.9257269557472 \tabularnewline
113 & 363 & 12.0793587506282 \tabularnewline
114 & 435 & 12.7544997474099 \tabularnewline
115 & 491 & 13.2215923006927 \tabularnewline
116 & 505 & 13.3318246353522 \tabularnewline
117 & 404 & 12.4753944781858 \tabularnewline
118 & 359 & 12.0388818306271 \tabularnewline
119 & 310 & 11.5120070438533 \tabularnewline
120 & 337 & 11.8097468891496 \tabularnewline
121 & 360 & 12.049033911214 \tabularnewline
122 & 342 & 11.8628256073501 \tabularnewline
123 & 406 & 12.4938963509593 \tabularnewline
124 & 396 & 12.4006647773351 \tabularnewline
125 & 420 & 12.6214567498302 \tabularnewline
126 & 472 & 13.0680006456641 \tabularnewline
127 & 548 & 13.6561234934495 \tabularnewline
128 & 559 & 13.7358808700789 \tabularnewline
129 & 463 & 12.9935579379813 \tabularnewline
130 & 407 & 12.5031206404268 \tabularnewline
131 & 362 & 12.0692722634059 \tabularnewline
132 & 405 & 12.4846543228915 \tabularnewline
133 & 417 & 12.5944047058291 \tabularnewline
134 & 391 & 12.3533586750856 \tabularnewline
135 & 419 & 12.6124561964916 \tabularnewline
136 & 461 & 12.9768620421832 \tabularnewline
137 & 472 & 13.0680006456641 \tabularnewline
138 & 535 & 13.5602384136753 \tabularnewline
139 & 622 & 14.1704664737241 \tabularnewline
140 & 606 & 14.0634709238992 \tabularnewline
141 & 508 & 13.3551350589366 \tabularnewline
142 & 461 & 12.9768620421832 \tabularnewline
143 & 390 & 12.343840893049 \tabularnewline
144 & 432 & 12.7281806519939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308972&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]112[/C][C]8.28982359190115[/C][/ROW]
[ROW][C]2[/C][C]118[/C][C]8.43803285374662[/C][/ROW]
[ROW][C]3[/C][C]132[/C][C]8.76226329390214[/C][/ROW]
[ROW][C]4[/C][C]129[/C][C]8.69512685001578[/C][/ROW]
[ROW][C]5[/C][C]121[/C][C]8.50994299200564[/C][/ROW]
[ROW][C]6[/C][C]135[/C][C]8.82821993874988[/C][/ROW]
[ROW][C]7[/C][C]148[/C][C]9.10147333855519[/C][/ROW]
[ROW][C]8[/C][C]148[/C][C]9.10147333855519[/C][/ROW]
[ROW][C]9[/C][C]136[/C][C]8.84995138940858[/C][/ROW]
[ROW][C]10[/C][C]119[/C][C]8.46215975106548[/C][/ROW]
[ROW][C]11[/C][C]104[/C][C]8.08225703110083[/C][/ROW]
[ROW][C]12[/C][C]118[/C][C]8.43803285374662[/C][/ROW]
[ROW][C]13[/C][C]115[/C][C]8.364682249774[/C][/ROW]
[ROW][C]14[/C][C]126[/C][C]8.62676131437388[/C][/ROW]
[ROW][C]15[/C][C]141[/C][C]8.95677615024752[/C][/ROW]
[ROW][C]16[/C][C]135[/C][C]8.82821993874988[/C][/ROW]
[ROW][C]17[/C][C]125[/C][C]8.60369068252195[/C][/ROW]
[ROW][C]18[/C][C]149[/C][C]9.12170606945975[/C][/ROW]
[ROW][C]19[/C][C]170[/C][C]9.52396181005032[/C][/ROW]
[ROW][C]20[/C][C]170[/C][C]9.52396181005032[/C][/ROW]
[ROW][C]21[/C][C]158[/C][C]9.29919217996436[/C][/ROW]
[ROW][C]22[/C][C]133[/C][C]8.78437758621956[/C][/ROW]
[ROW][C]23[/C][C]114[/C][C]8.33990040474863[/C][/ROW]
[ROW][C]24[/C][C]140[/C][C]8.93565032223542[/C][/ROW]
[ROW][C]25[/C][C]145[/C][C]9.04012844130026[/C][/ROW]
[ROW][C]26[/C][C]150[/C][C]9.14183315970288[/C][/ROW]
[ROW][C]27[/C][C]178[/C][C]9.66702064831661[/C][/ROW]
[ROW][C]28[/C][C]163[/C][C]9.39441123355153[/C][/ROW]
[ROW][C]29[/C][C]172[/C][C]9.56021084645933[/C][/ROW]
[ROW][C]30[/C][C]178[/C][C]9.66702064831661[/C][/ROW]
[ROW][C]31[/C][C]199[/C][C]10.0200319869468[/C][/ROW]
[ROW][C]32[/C][C]199[/C][C]10.0200319869468[/C][/ROW]
[ROW][C]33[/C][C]184[/C][C]9.77105806814484[/C][/ROW]
[ROW][C]34[/C][C]162[/C][C]9.37555150982637[/C][/ROW]
[ROW][C]35[/C][C]146[/C][C]9.06068583493981[/C][/ROW]
[ROW][C]36[/C][C]166[/C][C]9.45045408283629[/C][/ROW]
[ROW][C]37[/C][C]171[/C][C]9.54212766513112[/C][/ROW]
[ROW][C]38[/C][C]180[/C][C]9.70199967880636[/C][/ROW]
[ROW][C]39[/C][C]193[/C][C]9.92225986047658[/C][/ROW]
[ROW][C]40[/C][C]181[/C][C]9.71937562848881[/C][/ROW]
[ROW][C]41[/C][C]183[/C][C]9.75390409947135[/C][/ROW]
[ROW][C]42[/C][C]218[/C][C]10.3151934709793[/C][/ROW]
[ROW][C]43[/C][C]230[/C][C]10.4914153858504[/C][/ROW]
[ROW][C]44[/C][C]242[/C][C]10.6606054511229[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]10.1779926162008[/C][/ROW]
[ROW][C]46[/C][C]191[/C][C]9.88914234381911[/C][/ROW]
[ROW][C]47[/C][C]172[/C][C]9.56021084645933[/C][/ROW]
[ROW][C]48[/C][C]194[/C][C]9.93871833255018[/C][/ROW]
[ROW][C]49[/C][C]196[/C][C]9.97143775595241[/C][/ROW]
[ROW][C]50[/C][C]196[/C][C]9.97143775595241[/C][/ROW]
[ROW][C]51[/C][C]236[/C][C]10.576849297885[/C][/ROW]
[ROW][C]52[/C][C]235[/C][C]10.5627288802444[/C][/ROW]
[ROW][C]53[/C][C]229[/C][C]10.4770078410432[/C][/ROW]
[ROW][C]54[/C][C]243[/C][C]10.6744069186442[/C][/ROW]
[ROW][C]55[/C][C]264[/C][C]10.9544913812896[/C][/ROW]
[ROW][C]56[/C][C]272[/C][C]11.0566246512594[/C][/ROW]
[ROW][C]57[/C][C]237[/C][C]10.5909231231932[/C][/ROW]
[ROW][C]58[/C][C]211[/C][C]10.2088743179716[/C][/ROW]
[ROW][C]59[/C][C]180[/C][C]9.70199967880636[/C][/ROW]
[ROW][C]60[/C][C]201[/C][C]10.0521115992846[/C][/ROW]
[ROW][C]61[/C][C]204[/C][C]10.0997673425599[/C][/ROW]
[ROW][C]62[/C][C]188[/C][C]9.83895521340684[/C][/ROW]
[ROW][C]63[/C][C]235[/C][C]10.5627288802444[/C][/ROW]
[ROW][C]64[/C][C]227[/C][C]10.4480448941308[/C][/ROW]
[ROW][C]65[/C][C]234[/C][C]10.5485615167706[/C][/ROW]
[ROW][C]66[/C][C]264[/C][C]10.9544913812896[/C][/ROW]
[ROW][C]67[/C][C]302[/C][C]11.4199102635215[/C][/ROW]
[ROW][C]68[/C][C]293[/C][C]11.3139981418416[/C][/ROW]
[ROW][C]69[/C][C]259[/C][C]10.889425806741[/C][/ROW]
[ROW][C]70[/C][C]229[/C][C]10.4770078410432[/C][/ROW]
[ROW][C]71[/C][C]203[/C][C]10.0839431935411[/C][/ROW]
[ROW][C]72[/C][C]229[/C][C]10.4770078410432[/C][/ROW]
[ROW][C]73[/C][C]242[/C][C]10.6606054511229[/C][/ROW]
[ROW][C]74[/C][C]233[/C][C]10.5343468497563[/C][/ROW]
[ROW][C]75[/C][C]267[/C][C]10.9930706625766[/C][/ROW]
[ROW][C]76[/C][C]269[/C][C]11.0186027460442[/C][/ROW]
[ROW][C]77[/C][C]270[/C][C]11.0313133007946[/C][/ROW]
[ROW][C]78[/C][C]315[/C][C]11.5686301147655[/C][/ROW]
[ROW][C]79[/C][C]364[/C][C]12.0894235876376[/C][/ROW]
[ROW][C]80[/C][C]347[/C][C]11.9153024503844[/C][/ROW]
[ROW][C]81[/C][C]312[/C][C]11.5347411525047[/C][/ROW]
[ROW][C]82[/C][C]274[/C][C]11.0817912473729[/C][/ROW]
[ROW][C]83[/C][C]237[/C][C]10.5909231231932[/C][/ROW]
[ROW][C]84[/C][C]278[/C][C]11.1316976406289[/C][/ROW]
[ROW][C]85[/C][C]284[/C][C]11.2055172556443[/C][/ROW]
[ROW][C]86[/C][C]277[/C][C]11.1192738193284[/C][/ROW]
[ROW][C]87[/C][C]317[/C][C]11.5910831510213[/C][/ROW]
[ROW][C]88[/C][C]313[/C][C]11.5460656056794[/C][/ROW]
[ROW][C]89[/C][C]318[/C][C]11.6022682579461[/C][/ROW]
[ROW][C]90[/C][C]374[/C][C]12.1889040711468[/C][/ROW]
[ROW][C]91[/C][C]413[/C][C]12.5580981702438[/C][/ROW]
[ROW][C]92[/C][C]405[/C][C]12.4846543228915[/C][/ROW]
[ROW][C]93[/C][C]355[/C][C]11.9980515902361[/C][/ROW]
[ROW][C]94[/C][C]306[/C][C]11.4661934174461[/C][/ROW]
[ROW][C]95[/C][C]271[/C][C]11.0439871890362[/C][/ROW]
[ROW][C]96[/C][C]306[/C][C]11.4661934174461[/C][/ROW]
[ROW][C]97[/C][C]315[/C][C]11.5686301147655[/C][/ROW]
[ROW][C]98[/C][C]301[/C][C]11.4082648163515[/C][/ROW]
[ROW][C]99[/C][C]356[/C][C]12.0082926595805[/C][/ROW]
[ROW][C]100[/C][C]348[/C][C]11.9257269557472[/C][/ROW]
[ROW][C]101[/C][C]355[/C][C]11.9980515902361[/C][/ROW]
[ROW][C]102[/C][C]422[/C][C]12.6394078275788[/C][/ROW]
[ROW][C]103[/C][C]465[/C][C]13.0101976742097[/C][/ROW]
[ROW][C]104[/C][C]467[/C][C]13.0267816801034[/C][/ROW]
[ROW][C]105[/C][C]404[/C][C]12.4753944781858[/C][/ROW]
[ROW][C]106[/C][C]347[/C][C]11.9153024503844[/C][/ROW]
[ROW][C]107[/C][C]305[/C][C]11.4546670749057[/C][/ROW]
[ROW][C]108[/C][C]336[/C][C]11.7990575250942[/C][/ROW]
[ROW][C]109[/C][C]340[/C][C]11.8416672258106[/C][/ROW]
[ROW][C]110[/C][C]318[/C][C]11.6022682579461[/C][/ROW]
[ROW][C]111[/C][C]362[/C][C]12.0692722634059[/C][/ROW]
[ROW][C]112[/C][C]348[/C][C]11.9257269557472[/C][/ROW]
[ROW][C]113[/C][C]363[/C][C]12.0793587506282[/C][/ROW]
[ROW][C]114[/C][C]435[/C][C]12.7544997474099[/C][/ROW]
[ROW][C]115[/C][C]491[/C][C]13.2215923006927[/C][/ROW]
[ROW][C]116[/C][C]505[/C][C]13.3318246353522[/C][/ROW]
[ROW][C]117[/C][C]404[/C][C]12.4753944781858[/C][/ROW]
[ROW][C]118[/C][C]359[/C][C]12.0388818306271[/C][/ROW]
[ROW][C]119[/C][C]310[/C][C]11.5120070438533[/C][/ROW]
[ROW][C]120[/C][C]337[/C][C]11.8097468891496[/C][/ROW]
[ROW][C]121[/C][C]360[/C][C]12.049033911214[/C][/ROW]
[ROW][C]122[/C][C]342[/C][C]11.8628256073501[/C][/ROW]
[ROW][C]123[/C][C]406[/C][C]12.4938963509593[/C][/ROW]
[ROW][C]124[/C][C]396[/C][C]12.4006647773351[/C][/ROW]
[ROW][C]125[/C][C]420[/C][C]12.6214567498302[/C][/ROW]
[ROW][C]126[/C][C]472[/C][C]13.0680006456641[/C][/ROW]
[ROW][C]127[/C][C]548[/C][C]13.6561234934495[/C][/ROW]
[ROW][C]128[/C][C]559[/C][C]13.7358808700789[/C][/ROW]
[ROW][C]129[/C][C]463[/C][C]12.9935579379813[/C][/ROW]
[ROW][C]130[/C][C]407[/C][C]12.5031206404268[/C][/ROW]
[ROW][C]131[/C][C]362[/C][C]12.0692722634059[/C][/ROW]
[ROW][C]132[/C][C]405[/C][C]12.4846543228915[/C][/ROW]
[ROW][C]133[/C][C]417[/C][C]12.5944047058291[/C][/ROW]
[ROW][C]134[/C][C]391[/C][C]12.3533586750856[/C][/ROW]
[ROW][C]135[/C][C]419[/C][C]12.6124561964916[/C][/ROW]
[ROW][C]136[/C][C]461[/C][C]12.9768620421832[/C][/ROW]
[ROW][C]137[/C][C]472[/C][C]13.0680006456641[/C][/ROW]
[ROW][C]138[/C][C]535[/C][C]13.5602384136753[/C][/ROW]
[ROW][C]139[/C][C]622[/C][C]14.1704664737241[/C][/ROW]
[ROW][C]140[/C][C]606[/C][C]14.0634709238992[/C][/ROW]
[ROW][C]141[/C][C]508[/C][C]13.3551350589366[/C][/ROW]
[ROW][C]142[/C][C]461[/C][C]12.9768620421832[/C][/ROW]
[ROW][C]143[/C][C]390[/C][C]12.343840893049[/C][/ROW]
[ROW][C]144[/C][C]432[/C][C]12.7281806519939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308972&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308972&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Obs.OriginalTransformed
11128.28982359190115
21188.43803285374662
31328.76226329390214
41298.69512685001578
51218.50994299200564
61358.82821993874988
71489.10147333855519
81489.10147333855519
91368.84995138940858
101198.46215975106548
111048.08225703110083
121188.43803285374662
131158.364682249774
141268.62676131437388
151418.95677615024752
161358.82821993874988
171258.60369068252195
181499.12170606945975
191709.52396181005032
201709.52396181005032
211589.29919217996436
221338.78437758621956
231148.33990040474863
241408.93565032223542
251459.04012844130026
261509.14183315970288
271789.66702064831661
281639.39441123355153
291729.56021084645933
301789.66702064831661
3119910.0200319869468
3219910.0200319869468
331849.77105806814484
341629.37555150982637
351469.06068583493981
361669.45045408283629
371719.54212766513112
381809.70199967880636
391939.92225986047658
401819.71937562848881
411839.75390409947135
4221810.3151934709793
4323010.4914153858504
4424210.6606054511229
4520910.1779926162008
461919.88914234381911
471729.56021084645933
481949.93871833255018
491969.97143775595241
501969.97143775595241
5123610.576849297885
5223510.5627288802444
5322910.4770078410432
5424310.6744069186442
5526410.9544913812896
5627211.0566246512594
5723710.5909231231932
5821110.2088743179716
591809.70199967880636
6020110.0521115992846
6120410.0997673425599
621889.83895521340684
6323510.5627288802444
6422710.4480448941308
6523410.5485615167706
6626410.9544913812896
6730211.4199102635215
6829311.3139981418416
6925910.889425806741
7022910.4770078410432
7120310.0839431935411
7222910.4770078410432
7324210.6606054511229
7423310.5343468497563
7526710.9930706625766
7626911.0186027460442
7727011.0313133007946
7831511.5686301147655
7936412.0894235876376
8034711.9153024503844
8131211.5347411525047
8227411.0817912473729
8323710.5909231231932
8427811.1316976406289
8528411.2055172556443
8627711.1192738193284
8731711.5910831510213
8831311.5460656056794
8931811.6022682579461
9037412.1889040711468
9141312.5580981702438
9240512.4846543228915
9335511.9980515902361
9430611.4661934174461
9527111.0439871890362
9630611.4661934174461
9731511.5686301147655
9830111.4082648163515
9935612.0082926595805
10034811.9257269557472
10135511.9980515902361
10242212.6394078275788
10346513.0101976742097
10446713.0267816801034
10540412.4753944781858
10634711.9153024503844
10730511.4546670749057
10833611.7990575250942
10934011.8416672258106
11031811.6022682579461
11136212.0692722634059
11234811.9257269557472
11336312.0793587506282
11443512.7544997474099
11549113.2215923006927
11650513.3318246353522
11740412.4753944781858
11835912.0388818306271
11931011.5120070438533
12033711.8097468891496
12136012.049033911214
12234211.8628256073501
12340612.4938963509593
12439612.4006647773351
12542012.6214567498302
12647213.0680006456641
12754813.6561234934495
12855913.7358808700789
12946312.9935579379813
13040712.5031206404268
13136212.0692722634059
13240512.4846543228915
13341712.5944047058291
13439112.3533586750856
13541912.6124561964916
13646112.9768620421832
13747213.0680006456641
13853513.5602384136753
13962214.1704664737241
14060614.0634709238992
14150813.3551350589366
14246112.9768620421832
14339012.343840893049
14443212.7281806519939







Maximum Likelihood Estimation of Lambda
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x     0.148           0      -0.2374       0.5335
Likelihood ratio tests about transformation parameters
                             LRT df         pval
LR test, lambda = (0)  0.5662479  1 4.517538e-01
LR test, lambda = (1) 18.6270205  1 1.589516e-05

\begin{tabular}{lllllllll}
\hline
Maximum Likelihood Estimation of Lambda \tabularnewline
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x     0.148           0      -0.2374       0.5335
Likelihood ratio tests about transformation parameters
                             LRT df         pval
LR test, lambda = (0)  0.5662479  1 4.517538e-01
LR test, lambda = (1) 18.6270205  1 1.589516e-05
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=308972&T=3

[TABLE]
[ROW][C]Maximum Likelihood Estimation of Lambda[/C][/ROW]
[ROW][C]
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x     0.148           0      -0.2374       0.5335
Likelihood ratio tests about transformation parameters
                             LRT df         pval
LR test, lambda = (0)  0.5662479  1 4.517538e-01
LR test, lambda = (1) 18.6270205  1 1.589516e-05
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308972&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308972&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Maximum Likelihood Estimation of Lambda
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x     0.148           0      -0.2374       0.5335
Likelihood ratio tests about transformation parameters
                             LRT df         pval
LR test, lambda = (0)  0.5662479  1 4.517538e-01
LR test, lambda = (1) 18.6270205  1 1.589516e-05



Parameters (Session):
par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; par4 = 0 ; par5 = Yes ;
Parameters (R input):
par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; par4 = 0 ; par5 = Yes ;
R code (references can be found in the software module):
par5 <- 'No'
par4 <- '0'
par3 <- '2'
par2 <- '-2'
par1 <- 'Full Box-Cox transform'
library(car)
par2 <- abs(as.numeric(par2)*100)
par3 <- as.numeric(par3)*100
if(par4=='') par4 <- 0
par4 <- as.numeric(par4)
numlam <- par2 + par3 + 1
x <- x + par4
n <- length(x)
c <- array(NA,dim=c(numlam))
l <- array(NA,dim=c(numlam))
mx <- -1
mxli <- -999
for (i in 1:numlam)
{
l[i] <- (i-par2-1)/100
if (l[i] != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^l[i] - 1) / l[i]
if (par1 == 'Simple Box-Cox transform') x1 <- x^l[i]
} else {
x1 <- log(x)
}
c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),sort(x1))
if (mx < c[i])
{
mx <- c[i]
mxli <- l[i]
x1.best <- x1
}
}
print(c)
print(mx)
print(mxli)
print(x1.best)
if (mxli != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxli
if (par1 == 'Simple Box-Cox transform') x1 <- x^mxli
} else {
x1 <- log(x)
}
mypT <- powerTransform(x)
summary(mypT)
bitmap(file='test1.png')
plot(l,c,main='Box-Cox Normality Plot', xlab='Lambda',ylab='correlation')
mtext(paste('Optimal Lambda =',mxli))
grid()
dev.off()
bitmap(file='test2.png')
hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test3.png')
hist(x1,main='Histogram of Transformed Data', xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test4.png')
qqPlot(x)
grid()
mtext('Original Data')
dev.off()
bitmap(file='test5.png')
qqPlot(x1)
grid()
mtext('Transformed Data')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Box-Cox Normality Plot',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'# observations x',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'maximum correlation',header=TRUE)
a<-table.element(a,mx)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'optimal lambda',header=TRUE)
a<-table.element(a,mxli)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'transformation formula',header=TRUE)
if (par1 == 'Full Box-Cox transform') {
a<-table.element(a,'for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda')
} else {
a<-table.element(a,'for all lambda <> 0 : T(Y) = Y^lambda')
}
a<-table.row.end(a)
if(mx<0) {
a<-table.row.start(a)
a<-table.element(a,'Warning: maximum correlation is negative! The Box-Cox transformation must not be used.',2)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
if(par5=='Yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Obs.',header=T)
a<-table.element(a,'Original',header=T)
a<-table.element(a,'Transformed',header=T)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i)
a<-table.element(a,x[i])
a<-table.element(a,x1.best[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Maximum Likelihood Estimation of Lambda',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('summary(mypT)'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')