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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationSun, 19 Nov 2017 22:32:40 +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/Nov/19/t1511127640oe8mkl3he99dkgl.htm/, Retrieved Sat, 18 May 2024 16:22:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308131, Retrieved Sat, 18 May 2024 16:22:21 +0000
QR Codes:

Original text written by user:v
IsPrivate?No (this computation is public)
User-defined keywordsv
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Normality Plot] [v] [2017-11-19 21:32:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,8
30,2
17
12,5
512,5
655
342,5
1020
82,5
19
9,3
27,5
270
282,5
172,5
172,5
45,8
77,5
195,8
33
20
337,5
70
83,8
40
287,5
67,5
7,5
35
17,5
10
1950
670
262,5
1050
145
22
5,8
22,5
237,5
710
237,5
155
52,5
62,5
262,5
22,5
15
117,5
147,5
62,5
40
450
77,5
12,5
22,5
12,5
7,5
2070
450
410
970
162,5
17,5
5
15
337,5
650
210
257,5
62,5
70
252,5
15
17,5
105
60
132,5
22,5
482,5
45
41,5
45
20
12,5
3030
1700
322,5
1230
145
25
12,5
20
717,5
547,5
190
435
57,5
113,8
276,3
27,5
17,5
177,5
147,5
105
60
495
107,5

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308131&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]6 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308131&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308131&T=0

As an alternative you can also use a QR Code:  
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 time6 seconds
R ServerBig Analytics Cloud Computing Center






Box-Cox Normality Plot
# observations x108
maximum correlation0.989870067647921
optimal lambda-0.04
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 108 \tabularnewline
maximum correlation & 0.989870067647921 \tabularnewline
optimal lambda & -0.04 \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=308131&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]108[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.989870067647921[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-0.04[/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=308131&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308131&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Box-Cox Normality Plot
# observations x108
maximum correlation0.989870067647921
optimal lambda-0.04
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda






Obs.OriginalTransformed
19.82.18129648130533
230.23.18577788029186
3172.67856804587576
412.52.40233281391458
5512.55.52164602525772
66555.71185968770074
7342.55.20508753325656
810206.05057650540088
982.54.04528054874271
10192.77765607767285
119.32.13344760239788
1227.53.10390337398858
132705.01586024890048
14282.55.05200408613065
15172.54.65449637453813
16172.54.65449637453813
1745.83.54614260323089
1877.53.99281110630145
19195.84.75734370530897
20333.26300772274578
21202.82320362517108
22337.55.19343983172405
23703.90711003554305
2483.84.05838129373404
25403.42962928826781
26287.55.0659981279294
2767.53.87640375798799
287.51.93584446253867
29353.31410818340682
3017.52.70443477999291
31102.19972901610226
3219506.53545440880093
336705.72932102988913
34262.54.99332872694141
3510506.0725356565976
361454.51267350582476
37222.90758964402857
385.81.69748002478712
3922.52.92743990298591
40237.54.91307471794092
417105.77396738454062
42237.54.91307471794092
431554.56725379131969
4452.53.66298627685757
4562.53.81127580474696
46262.54.99332872694141
4722.52.92743990298591
48152.56653500860178
49117.54.33961101330133
50147.54.52667748697527
5162.53.81127580474696
52403.42962928826781
534505.42005317029378
5477.53.99281110630145
5512.52.40233281391458
5622.52.92743990298591
5712.52.40233281391458
587.51.93584446253867
5920706.57950931062437
604505.42005317029378
614105.34700903915123
629706.01244087119218
63162.54.60583756409259
6417.52.70443477999291
6551.55872614994961
66152.56653500860178
67337.55.19343983172405
686505.70594667894589
692104.81395500893213
70257.54.97793258447589
7162.53.81127580474696
72703.90711003554305
73252.54.96222233876108
74152.56653500860178
7517.52.70443477999291
761054.24644803918169
77603.77664890233676
78132.54.43866194323748
7922.52.92743990298591
80482.55.47459207336082
81453.53101521958425
8241.53.46136955473109
83453.53101521958425
84202.82320362517108
8512.52.40233281391458
8630306.85811943319484
8717006.43384158142596
88322.55.15738893256782
8912306.1919485469635
901454.51267350582476
91253.02026721147776
9212.52.40233281391458
93202.82320362517108
94717.55.78204675526593
95547.55.57304904643154
961904.73298146694272
974355.3934835361587
9857.53.74048782546458
99113.84.31315224873446
100276.35.03428933166276
10127.53.10390337398858
10217.52.70443477999291
103177.54.67773667703794
104147.54.52667748697527
1051054.24644803918169
106603.77664890233676
1074955.49455778919697
108107.54.26597250535894

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 9.8 & 2.18129648130533 \tabularnewline
2 & 30.2 & 3.18577788029186 \tabularnewline
3 & 17 & 2.67856804587576 \tabularnewline
4 & 12.5 & 2.40233281391458 \tabularnewline
5 & 512.5 & 5.52164602525772 \tabularnewline
6 & 655 & 5.71185968770074 \tabularnewline
7 & 342.5 & 5.20508753325656 \tabularnewline
8 & 1020 & 6.05057650540088 \tabularnewline
9 & 82.5 & 4.04528054874271 \tabularnewline
10 & 19 & 2.77765607767285 \tabularnewline
11 & 9.3 & 2.13344760239788 \tabularnewline
12 & 27.5 & 3.10390337398858 \tabularnewline
13 & 270 & 5.01586024890048 \tabularnewline
14 & 282.5 & 5.05200408613065 \tabularnewline
15 & 172.5 & 4.65449637453813 \tabularnewline
16 & 172.5 & 4.65449637453813 \tabularnewline
17 & 45.8 & 3.54614260323089 \tabularnewline
18 & 77.5 & 3.99281110630145 \tabularnewline
19 & 195.8 & 4.75734370530897 \tabularnewline
20 & 33 & 3.26300772274578 \tabularnewline
21 & 20 & 2.82320362517108 \tabularnewline
22 & 337.5 & 5.19343983172405 \tabularnewline
23 & 70 & 3.90711003554305 \tabularnewline
24 & 83.8 & 4.05838129373404 \tabularnewline
25 & 40 & 3.42962928826781 \tabularnewline
26 & 287.5 & 5.0659981279294 \tabularnewline
27 & 67.5 & 3.87640375798799 \tabularnewline
28 & 7.5 & 1.93584446253867 \tabularnewline
29 & 35 & 3.31410818340682 \tabularnewline
30 & 17.5 & 2.70443477999291 \tabularnewline
31 & 10 & 2.19972901610226 \tabularnewline
32 & 1950 & 6.53545440880093 \tabularnewline
33 & 670 & 5.72932102988913 \tabularnewline
34 & 262.5 & 4.99332872694141 \tabularnewline
35 & 1050 & 6.0725356565976 \tabularnewline
36 & 145 & 4.51267350582476 \tabularnewline
37 & 22 & 2.90758964402857 \tabularnewline
38 & 5.8 & 1.69748002478712 \tabularnewline
39 & 22.5 & 2.92743990298591 \tabularnewline
40 & 237.5 & 4.91307471794092 \tabularnewline
41 & 710 & 5.77396738454062 \tabularnewline
42 & 237.5 & 4.91307471794092 \tabularnewline
43 & 155 & 4.56725379131969 \tabularnewline
44 & 52.5 & 3.66298627685757 \tabularnewline
45 & 62.5 & 3.81127580474696 \tabularnewline
46 & 262.5 & 4.99332872694141 \tabularnewline
47 & 22.5 & 2.92743990298591 \tabularnewline
48 & 15 & 2.56653500860178 \tabularnewline
49 & 117.5 & 4.33961101330133 \tabularnewline
50 & 147.5 & 4.52667748697527 \tabularnewline
51 & 62.5 & 3.81127580474696 \tabularnewline
52 & 40 & 3.42962928826781 \tabularnewline
53 & 450 & 5.42005317029378 \tabularnewline
54 & 77.5 & 3.99281110630145 \tabularnewline
55 & 12.5 & 2.40233281391458 \tabularnewline
56 & 22.5 & 2.92743990298591 \tabularnewline
57 & 12.5 & 2.40233281391458 \tabularnewline
58 & 7.5 & 1.93584446253867 \tabularnewline
59 & 2070 & 6.57950931062437 \tabularnewline
60 & 450 & 5.42005317029378 \tabularnewline
61 & 410 & 5.34700903915123 \tabularnewline
62 & 970 & 6.01244087119218 \tabularnewline
63 & 162.5 & 4.60583756409259 \tabularnewline
64 & 17.5 & 2.70443477999291 \tabularnewline
65 & 5 & 1.55872614994961 \tabularnewline
66 & 15 & 2.56653500860178 \tabularnewline
67 & 337.5 & 5.19343983172405 \tabularnewline
68 & 650 & 5.70594667894589 \tabularnewline
69 & 210 & 4.81395500893213 \tabularnewline
70 & 257.5 & 4.97793258447589 \tabularnewline
71 & 62.5 & 3.81127580474696 \tabularnewline
72 & 70 & 3.90711003554305 \tabularnewline
73 & 252.5 & 4.96222233876108 \tabularnewline
74 & 15 & 2.56653500860178 \tabularnewline
75 & 17.5 & 2.70443477999291 \tabularnewline
76 & 105 & 4.24644803918169 \tabularnewline
77 & 60 & 3.77664890233676 \tabularnewline
78 & 132.5 & 4.43866194323748 \tabularnewline
79 & 22.5 & 2.92743990298591 \tabularnewline
80 & 482.5 & 5.47459207336082 \tabularnewline
81 & 45 & 3.53101521958425 \tabularnewline
82 & 41.5 & 3.46136955473109 \tabularnewline
83 & 45 & 3.53101521958425 \tabularnewline
84 & 20 & 2.82320362517108 \tabularnewline
85 & 12.5 & 2.40233281391458 \tabularnewline
86 & 3030 & 6.85811943319484 \tabularnewline
87 & 1700 & 6.43384158142596 \tabularnewline
88 & 322.5 & 5.15738893256782 \tabularnewline
89 & 1230 & 6.1919485469635 \tabularnewline
90 & 145 & 4.51267350582476 \tabularnewline
91 & 25 & 3.02026721147776 \tabularnewline
92 & 12.5 & 2.40233281391458 \tabularnewline
93 & 20 & 2.82320362517108 \tabularnewline
94 & 717.5 & 5.78204675526593 \tabularnewline
95 & 547.5 & 5.57304904643154 \tabularnewline
96 & 190 & 4.73298146694272 \tabularnewline
97 & 435 & 5.3934835361587 \tabularnewline
98 & 57.5 & 3.74048782546458 \tabularnewline
99 & 113.8 & 4.31315224873446 \tabularnewline
100 & 276.3 & 5.03428933166276 \tabularnewline
101 & 27.5 & 3.10390337398858 \tabularnewline
102 & 17.5 & 2.70443477999291 \tabularnewline
103 & 177.5 & 4.67773667703794 \tabularnewline
104 & 147.5 & 4.52667748697527 \tabularnewline
105 & 105 & 4.24644803918169 \tabularnewline
106 & 60 & 3.77664890233676 \tabularnewline
107 & 495 & 5.49455778919697 \tabularnewline
108 & 107.5 & 4.26597250535894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308131&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]9.8[/C][C]2.18129648130533[/C][/ROW]
[ROW][C]2[/C][C]30.2[/C][C]3.18577788029186[/C][/ROW]
[ROW][C]3[/C][C]17[/C][C]2.67856804587576[/C][/ROW]
[ROW][C]4[/C][C]12.5[/C][C]2.40233281391458[/C][/ROW]
[ROW][C]5[/C][C]512.5[/C][C]5.52164602525772[/C][/ROW]
[ROW][C]6[/C][C]655[/C][C]5.71185968770074[/C][/ROW]
[ROW][C]7[/C][C]342.5[/C][C]5.20508753325656[/C][/ROW]
[ROW][C]8[/C][C]1020[/C][C]6.05057650540088[/C][/ROW]
[ROW][C]9[/C][C]82.5[/C][C]4.04528054874271[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]2.77765607767285[/C][/ROW]
[ROW][C]11[/C][C]9.3[/C][C]2.13344760239788[/C][/ROW]
[ROW][C]12[/C][C]27.5[/C][C]3.10390337398858[/C][/ROW]
[ROW][C]13[/C][C]270[/C][C]5.01586024890048[/C][/ROW]
[ROW][C]14[/C][C]282.5[/C][C]5.05200408613065[/C][/ROW]
[ROW][C]15[/C][C]172.5[/C][C]4.65449637453813[/C][/ROW]
[ROW][C]16[/C][C]172.5[/C][C]4.65449637453813[/C][/ROW]
[ROW][C]17[/C][C]45.8[/C][C]3.54614260323089[/C][/ROW]
[ROW][C]18[/C][C]77.5[/C][C]3.99281110630145[/C][/ROW]
[ROW][C]19[/C][C]195.8[/C][C]4.75734370530897[/C][/ROW]
[ROW][C]20[/C][C]33[/C][C]3.26300772274578[/C][/ROW]
[ROW][C]21[/C][C]20[/C][C]2.82320362517108[/C][/ROW]
[ROW][C]22[/C][C]337.5[/C][C]5.19343983172405[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]3.90711003554305[/C][/ROW]
[ROW][C]24[/C][C]83.8[/C][C]4.05838129373404[/C][/ROW]
[ROW][C]25[/C][C]40[/C][C]3.42962928826781[/C][/ROW]
[ROW][C]26[/C][C]287.5[/C][C]5.0659981279294[/C][/ROW]
[ROW][C]27[/C][C]67.5[/C][C]3.87640375798799[/C][/ROW]
[ROW][C]28[/C][C]7.5[/C][C]1.93584446253867[/C][/ROW]
[ROW][C]29[/C][C]35[/C][C]3.31410818340682[/C][/ROW]
[ROW][C]30[/C][C]17.5[/C][C]2.70443477999291[/C][/ROW]
[ROW][C]31[/C][C]10[/C][C]2.19972901610226[/C][/ROW]
[ROW][C]32[/C][C]1950[/C][C]6.53545440880093[/C][/ROW]
[ROW][C]33[/C][C]670[/C][C]5.72932102988913[/C][/ROW]
[ROW][C]34[/C][C]262.5[/C][C]4.99332872694141[/C][/ROW]
[ROW][C]35[/C][C]1050[/C][C]6.0725356565976[/C][/ROW]
[ROW][C]36[/C][C]145[/C][C]4.51267350582476[/C][/ROW]
[ROW][C]37[/C][C]22[/C][C]2.90758964402857[/C][/ROW]
[ROW][C]38[/C][C]5.8[/C][C]1.69748002478712[/C][/ROW]
[ROW][C]39[/C][C]22.5[/C][C]2.92743990298591[/C][/ROW]
[ROW][C]40[/C][C]237.5[/C][C]4.91307471794092[/C][/ROW]
[ROW][C]41[/C][C]710[/C][C]5.77396738454062[/C][/ROW]
[ROW][C]42[/C][C]237.5[/C][C]4.91307471794092[/C][/ROW]
[ROW][C]43[/C][C]155[/C][C]4.56725379131969[/C][/ROW]
[ROW][C]44[/C][C]52.5[/C][C]3.66298627685757[/C][/ROW]
[ROW][C]45[/C][C]62.5[/C][C]3.81127580474696[/C][/ROW]
[ROW][C]46[/C][C]262.5[/C][C]4.99332872694141[/C][/ROW]
[ROW][C]47[/C][C]22.5[/C][C]2.92743990298591[/C][/ROW]
[ROW][C]48[/C][C]15[/C][C]2.56653500860178[/C][/ROW]
[ROW][C]49[/C][C]117.5[/C][C]4.33961101330133[/C][/ROW]
[ROW][C]50[/C][C]147.5[/C][C]4.52667748697527[/C][/ROW]
[ROW][C]51[/C][C]62.5[/C][C]3.81127580474696[/C][/ROW]
[ROW][C]52[/C][C]40[/C][C]3.42962928826781[/C][/ROW]
[ROW][C]53[/C][C]450[/C][C]5.42005317029378[/C][/ROW]
[ROW][C]54[/C][C]77.5[/C][C]3.99281110630145[/C][/ROW]
[ROW][C]55[/C][C]12.5[/C][C]2.40233281391458[/C][/ROW]
[ROW][C]56[/C][C]22.5[/C][C]2.92743990298591[/C][/ROW]
[ROW][C]57[/C][C]12.5[/C][C]2.40233281391458[/C][/ROW]
[ROW][C]58[/C][C]7.5[/C][C]1.93584446253867[/C][/ROW]
[ROW][C]59[/C][C]2070[/C][C]6.57950931062437[/C][/ROW]
[ROW][C]60[/C][C]450[/C][C]5.42005317029378[/C][/ROW]
[ROW][C]61[/C][C]410[/C][C]5.34700903915123[/C][/ROW]
[ROW][C]62[/C][C]970[/C][C]6.01244087119218[/C][/ROW]
[ROW][C]63[/C][C]162.5[/C][C]4.60583756409259[/C][/ROW]
[ROW][C]64[/C][C]17.5[/C][C]2.70443477999291[/C][/ROW]
[ROW][C]65[/C][C]5[/C][C]1.55872614994961[/C][/ROW]
[ROW][C]66[/C][C]15[/C][C]2.56653500860178[/C][/ROW]
[ROW][C]67[/C][C]337.5[/C][C]5.19343983172405[/C][/ROW]
[ROW][C]68[/C][C]650[/C][C]5.70594667894589[/C][/ROW]
[ROW][C]69[/C][C]210[/C][C]4.81395500893213[/C][/ROW]
[ROW][C]70[/C][C]257.5[/C][C]4.97793258447589[/C][/ROW]
[ROW][C]71[/C][C]62.5[/C][C]3.81127580474696[/C][/ROW]
[ROW][C]72[/C][C]70[/C][C]3.90711003554305[/C][/ROW]
[ROW][C]73[/C][C]252.5[/C][C]4.96222233876108[/C][/ROW]
[ROW][C]74[/C][C]15[/C][C]2.56653500860178[/C][/ROW]
[ROW][C]75[/C][C]17.5[/C][C]2.70443477999291[/C][/ROW]
[ROW][C]76[/C][C]105[/C][C]4.24644803918169[/C][/ROW]
[ROW][C]77[/C][C]60[/C][C]3.77664890233676[/C][/ROW]
[ROW][C]78[/C][C]132.5[/C][C]4.43866194323748[/C][/ROW]
[ROW][C]79[/C][C]22.5[/C][C]2.92743990298591[/C][/ROW]
[ROW][C]80[/C][C]482.5[/C][C]5.47459207336082[/C][/ROW]
[ROW][C]81[/C][C]45[/C][C]3.53101521958425[/C][/ROW]
[ROW][C]82[/C][C]41.5[/C][C]3.46136955473109[/C][/ROW]
[ROW][C]83[/C][C]45[/C][C]3.53101521958425[/C][/ROW]
[ROW][C]84[/C][C]20[/C][C]2.82320362517108[/C][/ROW]
[ROW][C]85[/C][C]12.5[/C][C]2.40233281391458[/C][/ROW]
[ROW][C]86[/C][C]3030[/C][C]6.85811943319484[/C][/ROW]
[ROW][C]87[/C][C]1700[/C][C]6.43384158142596[/C][/ROW]
[ROW][C]88[/C][C]322.5[/C][C]5.15738893256782[/C][/ROW]
[ROW][C]89[/C][C]1230[/C][C]6.1919485469635[/C][/ROW]
[ROW][C]90[/C][C]145[/C][C]4.51267350582476[/C][/ROW]
[ROW][C]91[/C][C]25[/C][C]3.02026721147776[/C][/ROW]
[ROW][C]92[/C][C]12.5[/C][C]2.40233281391458[/C][/ROW]
[ROW][C]93[/C][C]20[/C][C]2.82320362517108[/C][/ROW]
[ROW][C]94[/C][C]717.5[/C][C]5.78204675526593[/C][/ROW]
[ROW][C]95[/C][C]547.5[/C][C]5.57304904643154[/C][/ROW]
[ROW][C]96[/C][C]190[/C][C]4.73298146694272[/C][/ROW]
[ROW][C]97[/C][C]435[/C][C]5.3934835361587[/C][/ROW]
[ROW][C]98[/C][C]57.5[/C][C]3.74048782546458[/C][/ROW]
[ROW][C]99[/C][C]113.8[/C][C]4.31315224873446[/C][/ROW]
[ROW][C]100[/C][C]276.3[/C][C]5.03428933166276[/C][/ROW]
[ROW][C]101[/C][C]27.5[/C][C]3.10390337398858[/C][/ROW]
[ROW][C]102[/C][C]17.5[/C][C]2.70443477999291[/C][/ROW]
[ROW][C]103[/C][C]177.5[/C][C]4.67773667703794[/C][/ROW]
[ROW][C]104[/C][C]147.5[/C][C]4.52667748697527[/C][/ROW]
[ROW][C]105[/C][C]105[/C][C]4.24644803918169[/C][/ROW]
[ROW][C]106[/C][C]60[/C][C]3.77664890233676[/C][/ROW]
[ROW][C]107[/C][C]495[/C][C]5.49455778919697[/C][/ROW]
[ROW][C]108[/C][C]107.5[/C][C]4.26597250535894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308131&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308131&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Obs.OriginalTransformed
19.82.18129648130533
230.23.18577788029186
3172.67856804587576
412.52.40233281391458
5512.55.52164602525772
66555.71185968770074
7342.55.20508753325656
810206.05057650540088
982.54.04528054874271
10192.77765607767285
119.32.13344760239788
1227.53.10390337398858
132705.01586024890048
14282.55.05200408613065
15172.54.65449637453813
16172.54.65449637453813
1745.83.54614260323089
1877.53.99281110630145
19195.84.75734370530897
20333.26300772274578
21202.82320362517108
22337.55.19343983172405
23703.90711003554305
2483.84.05838129373404
25403.42962928826781
26287.55.0659981279294
2767.53.87640375798799
287.51.93584446253867
29353.31410818340682
3017.52.70443477999291
31102.19972901610226
3219506.53545440880093
336705.72932102988913
34262.54.99332872694141
3510506.0725356565976
361454.51267350582476
37222.90758964402857
385.81.69748002478712
3922.52.92743990298591
40237.54.91307471794092
417105.77396738454062
42237.54.91307471794092
431554.56725379131969
4452.53.66298627685757
4562.53.81127580474696
46262.54.99332872694141
4722.52.92743990298591
48152.56653500860178
49117.54.33961101330133
50147.54.52667748697527
5162.53.81127580474696
52403.42962928826781
534505.42005317029378
5477.53.99281110630145
5512.52.40233281391458
5622.52.92743990298591
5712.52.40233281391458
587.51.93584446253867
5920706.57950931062437
604505.42005317029378
614105.34700903915123
629706.01244087119218
63162.54.60583756409259
6417.52.70443477999291
6551.55872614994961
66152.56653500860178
67337.55.19343983172405
686505.70594667894589
692104.81395500893213
70257.54.97793258447589
7162.53.81127580474696
72703.90711003554305
73252.54.96222233876108
74152.56653500860178
7517.52.70443477999291
761054.24644803918169
77603.77664890233676
78132.54.43866194323748
7922.52.92743990298591
80482.55.47459207336082
81453.53101521958425
8241.53.46136955473109
83453.53101521958425
84202.82320362517108
8512.52.40233281391458
8630306.85811943319484
8717006.43384158142596
88322.55.15738893256782
8912306.1919485469635
901454.51267350582476
91253.02026721147776
9212.52.40233281391458
93202.82320362517108
94717.55.78204675526593
95547.55.57304904643154
961904.73298146694272
974355.3934835361587
9857.53.74048782546458
99113.84.31315224873446
100276.35.03428933166276
10127.53.10390337398858
10217.52.70443477999291
103177.54.67773667703794
104147.54.52667748697527
1051054.24644803918169
106603.77664890233676
1074955.49455778919697
108107.54.26597250535894






Maximum Likelihood Estimation of Lambda
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x   -0.0505           0      -0.1779        0.077
Likelihood ratio tests about transformation parameters
                              LRT df      pval
LR test, lambda = (0)   0.6071002  1 0.4358817
LR test, lambda = (1) 260.4754492  1 0.0000000


\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   -0.0505           0      -0.1779        0.077
Likelihood ratio tests about transformation parameters
                              LRT df      pval
LR test, lambda = (0)   0.6071002  1 0.4358817
LR test, lambda = (1) 260.4754492  1 0.0000000

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308131&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   -0.0505           0      -0.1779        0.077
Likelihood ratio tests about transformation parameters
                              LRT df      pval
LR test, lambda = (0)   0.6071002  1 0.4358817
LR test, lambda = (1) 260.4754492  1 0.0000000

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308131&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308131&T=3

As an alternative you can also use a QR Code:  
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   -0.0505           0      -0.1779        0.077
Likelihood ratio tests about transformation parameters
                              LRT df      pval
LR test, lambda = (0)   0.6071002  1 0.4358817
LR test, lambda = (1) 260.4754492  1 0.0000000


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Full Box-Cox transform ; par2 = -8 ; par3 = 8 ; par4 = 0 ; par5 = Yes ;
Parameters (R input):
par1 = Full Box-Cox transform ; par2 = -8 ; par3 = 8 ; par4 = 0 ; par5 = Yes ;
R code (references can be found in the software module):
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')