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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 30 Jul 2011 10:03:13 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jul/30/t1312034998ypbx1ltqo5ilgjx.htm/, Retrieved Thu, 16 May 2024 23:53:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123200, Retrieved Thu, 16 May 2024 23:53:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsvicky koopmans
Estimated Impact242
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks1-stap32] [2011-07-30 14:03:13] [30681199eb2b91d06bf445c1ee7d20a2] [Current]
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Dataseries X:
5115
5105
5094
5074
5280
5270
5115
5012
5022
5022
5032
5053
5053
4960
4919
4960
5105
5084
4888
4722
4691
4629
4671
4722
4702
4660
4578
4660
4733
4712
4474
4371
4268
4185
4175
4237
4154
4123
4092
4268
4288
4185
3906
3782
3586
3503
3544
3606
3606
3555
3544
3710
3844
3782
3575
3472
3255
3121
3224
3327
3327
3193
3183
3358
3472
3431
3224
3090
2800
2687
2728
2904
2914
2656
2749
2976
3079
3017
2738
2542
2315
2139
2211
2366
2325
2098
2170
2397
2521
2449
2170
2046
1860
1664
1695
1850
1870
1684
1715
1974
2036
1932
1550
1354
1095
837
920
1033
1013
816
930
1209
1333
1271
1023
827
620
382
424
496




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123200&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123200&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.400887078073623
beta0.0368953016619442
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.400887078073623 \tabularnewline
beta & 0.0368953016619442 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123200&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.400887078073623[/C][/ROW]
[ROW][C]beta[/C][C]0.0368953016619442[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123200&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.400887078073623
beta0.0368953016619442
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1350535134.57425213675-81.5742521367501
1449605009.76703465207-49.7670346520663
1549194953.30815625135-34.3081562513453
1649604988.83076232781-28.8307623278142
1751055131.37275337806-26.3727533780566
1850845105.92671968991-21.9267196899054
1948884888.98039530782-0.980395307815343
2047224771.16668082402-49.1666808240243
2146914751.01682348452-60.0168234845205
2246294714.3379176762-85.3379176761955
2346714676.24589209157-5.24589209157057
2447224684.1841334192137.8158665807878
2547024642.2390842708259.7609157291799
2646604589.2370733654170.7629266345866
2745784588.23110241152-10.2311024115234
2846604634.915975450525.0840245495037
2947334799.57028803105-66.5702880310464
3047124759.1046579016-47.1046579015983
3144744542.6730334804-68.6730334804006
3243714365.910953562925.08904643707592
3342684358.87130863013-90.8713086301314
3441854292.05693275599-107.056932755989
3541754290.32484851842-115.324848518417
3642374275.387199781-38.3871997810038
3741544210.36826550895-56.3682655089533
3841234110.0127410688612.9872589311381
3940924029.0758585994962.9241414005146
4042684119.08267718653148.917322813468
4142884273.1376802674814.8623197325232
4241854272.852702737-87.8527027370046
4339064022.43438483321-116.43438483321
4437823865.28134424841-83.2813442484139
4535863758.58112242211-172.581122422107
4635033641.36182344073-138.361823440733
4735443613.71207390119-69.7120739011866
4836063655.41446436159-49.4144643615937
4936063567.2991784897738.7008215102346
5035553540.1105911387814.8894088612196
5135443483.3853996585560.6146003414465
5237103617.4831312796792.5168687203322
5338443661.27677790313182.723222096872
5437823661.89291656113120.107083438871
5535753475.9409833106299.0590166893758
5634723426.4478570210245.5521429789792
5732553321.20920036054-66.2092003605367
5831213272.02212165388-151.022121653883
5932243285.12658467591-61.1265846759079
6033273347.25894414923-20.2589441492282
6133273328.88156805102-1.88156805101562
6231933275.81688417757-82.8168841775741
6331833210.5304804094-27.5304804094048
6433583330.3147337114927.6852662885094
6534723403.1127904562168.8872095437878
6634313319.84644336075111.153556639248
6732243116.82959636256107.17040363744
6830903037.786143359652.2138566404033
6928002867.6135315883-67.6135315883002
7026872766.38330122489-79.3833012248947
7127282862.45636217538-134.456362175383
7229042918.98342592645-14.9834259264471
7329142913.116422789560.883577210443491
7426562812.09711742084-156.09711742084
7527492748.898798289340.101201710661826
7629762911.5917836136864.4082163863191
7730793023.0904571430555.9095428569531
7830172959.0461391686457.9538608313551
7927382730.631287718467.36871228153541
8025422575.49272160444-33.4927216044393
8123152294.7429130789420.2570869210617
8221392218.55873790893-79.5587379089329
8322112278.43517200471-67.4351720047125
8423662431.267931039-65.267931039004
8523252411.86488188994-86.8648818899396
8620982177.43755193563-79.4375519356254
8721702235.50371493741-65.5037149374111
8823972406.40556946653-9.40556946652987
8925212478.111685406842.8883145931973
9024492404.7696080396244.2303919603823
9121702135.0415027776434.9584972223602
9220461961.3853119240884.6146880759175
9318601756.8349515857103.165048414302
9416641651.9623445577312.0376554422669
9516951755.05255080266-60.0525508026626
9618501911.48310125054-61.4831012505415
9718701880.05408187972-10.0540818797222
9816841681.400868205982.5991317940211
9917151782.44766144669-67.4476614466944
10019741987.89582617294-13.895826172941
10120362090.78187257378-54.7818725737779
10219321979.29458476832-47.2945847683218
10315501666.17210451106-116.172104511055
10413541458.29564134765-104.295641347648
10510951182.94955476129-87.949554761293
106837937.861449998685-100.861449998685
107920941.827291723873-21.8272917238733
10810331102.61577947788-69.6157794778799
10910131088.50896148573-75.5089614857266
110816859.998999835046-43.9989998350461
111930888.5126029512241.4873970487804
11212091159.4396012356849.5603987643224
11313331253.9322207489579.0677792510492
11412711193.2321609557177.7678390442907
1151023883.472859076899139.527140923101
116827783.49295175869443.5070482413058
117620577.65302252308442.3469774769164
118382379.4514442843762.54855571562405
119424476.140942104756-52.140942104756
120496599.615549517899-103.615549517899

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5053 & 5134.57425213675 & -81.5742521367501 \tabularnewline
14 & 4960 & 5009.76703465207 & -49.7670346520663 \tabularnewline
15 & 4919 & 4953.30815625135 & -34.3081562513453 \tabularnewline
16 & 4960 & 4988.83076232781 & -28.8307623278142 \tabularnewline
17 & 5105 & 5131.37275337806 & -26.3727533780566 \tabularnewline
18 & 5084 & 5105.92671968991 & -21.9267196899054 \tabularnewline
19 & 4888 & 4888.98039530782 & -0.980395307815343 \tabularnewline
20 & 4722 & 4771.16668082402 & -49.1666808240243 \tabularnewline
21 & 4691 & 4751.01682348452 & -60.0168234845205 \tabularnewline
22 & 4629 & 4714.3379176762 & -85.3379176761955 \tabularnewline
23 & 4671 & 4676.24589209157 & -5.24589209157057 \tabularnewline
24 & 4722 & 4684.18413341921 & 37.8158665807878 \tabularnewline
25 & 4702 & 4642.23908427082 & 59.7609157291799 \tabularnewline
26 & 4660 & 4589.23707336541 & 70.7629266345866 \tabularnewline
27 & 4578 & 4588.23110241152 & -10.2311024115234 \tabularnewline
28 & 4660 & 4634.9159754505 & 25.0840245495037 \tabularnewline
29 & 4733 & 4799.57028803105 & -66.5702880310464 \tabularnewline
30 & 4712 & 4759.1046579016 & -47.1046579015983 \tabularnewline
31 & 4474 & 4542.6730334804 & -68.6730334804006 \tabularnewline
32 & 4371 & 4365.91095356292 & 5.08904643707592 \tabularnewline
33 & 4268 & 4358.87130863013 & -90.8713086301314 \tabularnewline
34 & 4185 & 4292.05693275599 & -107.056932755989 \tabularnewline
35 & 4175 & 4290.32484851842 & -115.324848518417 \tabularnewline
36 & 4237 & 4275.387199781 & -38.3871997810038 \tabularnewline
37 & 4154 & 4210.36826550895 & -56.3682655089533 \tabularnewline
38 & 4123 & 4110.01274106886 & 12.9872589311381 \tabularnewline
39 & 4092 & 4029.07585859949 & 62.9241414005146 \tabularnewline
40 & 4268 & 4119.08267718653 & 148.917322813468 \tabularnewline
41 & 4288 & 4273.13768026748 & 14.8623197325232 \tabularnewline
42 & 4185 & 4272.852702737 & -87.8527027370046 \tabularnewline
43 & 3906 & 4022.43438483321 & -116.43438483321 \tabularnewline
44 & 3782 & 3865.28134424841 & -83.2813442484139 \tabularnewline
45 & 3586 & 3758.58112242211 & -172.581122422107 \tabularnewline
46 & 3503 & 3641.36182344073 & -138.361823440733 \tabularnewline
47 & 3544 & 3613.71207390119 & -69.7120739011866 \tabularnewline
48 & 3606 & 3655.41446436159 & -49.4144643615937 \tabularnewline
49 & 3606 & 3567.29917848977 & 38.7008215102346 \tabularnewline
50 & 3555 & 3540.11059113878 & 14.8894088612196 \tabularnewline
51 & 3544 & 3483.38539965855 & 60.6146003414465 \tabularnewline
52 & 3710 & 3617.48313127967 & 92.5168687203322 \tabularnewline
53 & 3844 & 3661.27677790313 & 182.723222096872 \tabularnewline
54 & 3782 & 3661.89291656113 & 120.107083438871 \tabularnewline
55 & 3575 & 3475.94098331062 & 99.0590166893758 \tabularnewline
56 & 3472 & 3426.44785702102 & 45.5521429789792 \tabularnewline
57 & 3255 & 3321.20920036054 & -66.2092003605367 \tabularnewline
58 & 3121 & 3272.02212165388 & -151.022121653883 \tabularnewline
59 & 3224 & 3285.12658467591 & -61.1265846759079 \tabularnewline
60 & 3327 & 3347.25894414923 & -20.2589441492282 \tabularnewline
61 & 3327 & 3328.88156805102 & -1.88156805101562 \tabularnewline
62 & 3193 & 3275.81688417757 & -82.8168841775741 \tabularnewline
63 & 3183 & 3210.5304804094 & -27.5304804094048 \tabularnewline
64 & 3358 & 3330.31473371149 & 27.6852662885094 \tabularnewline
65 & 3472 & 3403.11279045621 & 68.8872095437878 \tabularnewline
66 & 3431 & 3319.84644336075 & 111.153556639248 \tabularnewline
67 & 3224 & 3116.82959636256 & 107.17040363744 \tabularnewline
68 & 3090 & 3037.7861433596 & 52.2138566404033 \tabularnewline
69 & 2800 & 2867.6135315883 & -67.6135315883002 \tabularnewline
70 & 2687 & 2766.38330122489 & -79.3833012248947 \tabularnewline
71 & 2728 & 2862.45636217538 & -134.456362175383 \tabularnewline
72 & 2904 & 2918.98342592645 & -14.9834259264471 \tabularnewline
73 & 2914 & 2913.11642278956 & 0.883577210443491 \tabularnewline
74 & 2656 & 2812.09711742084 & -156.09711742084 \tabularnewline
75 & 2749 & 2748.89879828934 & 0.101201710661826 \tabularnewline
76 & 2976 & 2911.59178361368 & 64.4082163863191 \tabularnewline
77 & 3079 & 3023.09045714305 & 55.9095428569531 \tabularnewline
78 & 3017 & 2959.04613916864 & 57.9538608313551 \tabularnewline
79 & 2738 & 2730.63128771846 & 7.36871228153541 \tabularnewline
80 & 2542 & 2575.49272160444 & -33.4927216044393 \tabularnewline
81 & 2315 & 2294.74291307894 & 20.2570869210617 \tabularnewline
82 & 2139 & 2218.55873790893 & -79.5587379089329 \tabularnewline
83 & 2211 & 2278.43517200471 & -67.4351720047125 \tabularnewline
84 & 2366 & 2431.267931039 & -65.267931039004 \tabularnewline
85 & 2325 & 2411.86488188994 & -86.8648818899396 \tabularnewline
86 & 2098 & 2177.43755193563 & -79.4375519356254 \tabularnewline
87 & 2170 & 2235.50371493741 & -65.5037149374111 \tabularnewline
88 & 2397 & 2406.40556946653 & -9.40556946652987 \tabularnewline
89 & 2521 & 2478.1116854068 & 42.8883145931973 \tabularnewline
90 & 2449 & 2404.76960803962 & 44.2303919603823 \tabularnewline
91 & 2170 & 2135.04150277764 & 34.9584972223602 \tabularnewline
92 & 2046 & 1961.38531192408 & 84.6146880759175 \tabularnewline
93 & 1860 & 1756.8349515857 & 103.165048414302 \tabularnewline
94 & 1664 & 1651.96234455773 & 12.0376554422669 \tabularnewline
95 & 1695 & 1755.05255080266 & -60.0525508026626 \tabularnewline
96 & 1850 & 1911.48310125054 & -61.4831012505415 \tabularnewline
97 & 1870 & 1880.05408187972 & -10.0540818797222 \tabularnewline
98 & 1684 & 1681.40086820598 & 2.5991317940211 \tabularnewline
99 & 1715 & 1782.44766144669 & -67.4476614466944 \tabularnewline
100 & 1974 & 1987.89582617294 & -13.895826172941 \tabularnewline
101 & 2036 & 2090.78187257378 & -54.7818725737779 \tabularnewline
102 & 1932 & 1979.29458476832 & -47.2945847683218 \tabularnewline
103 & 1550 & 1666.17210451106 & -116.172104511055 \tabularnewline
104 & 1354 & 1458.29564134765 & -104.295641347648 \tabularnewline
105 & 1095 & 1182.94955476129 & -87.949554761293 \tabularnewline
106 & 837 & 937.861449998685 & -100.861449998685 \tabularnewline
107 & 920 & 941.827291723873 & -21.8272917238733 \tabularnewline
108 & 1033 & 1102.61577947788 & -69.6157794778799 \tabularnewline
109 & 1013 & 1088.50896148573 & -75.5089614857266 \tabularnewline
110 & 816 & 859.998999835046 & -43.9989998350461 \tabularnewline
111 & 930 & 888.51260295122 & 41.4873970487804 \tabularnewline
112 & 1209 & 1159.43960123568 & 49.5603987643224 \tabularnewline
113 & 1333 & 1253.93222074895 & 79.0677792510492 \tabularnewline
114 & 1271 & 1193.23216095571 & 77.7678390442907 \tabularnewline
115 & 1023 & 883.472859076899 & 139.527140923101 \tabularnewline
116 & 827 & 783.492951758694 & 43.5070482413058 \tabularnewline
117 & 620 & 577.653022523084 & 42.3469774769164 \tabularnewline
118 & 382 & 379.451444284376 & 2.54855571562405 \tabularnewline
119 & 424 & 476.140942104756 & -52.140942104756 \tabularnewline
120 & 496 & 599.615549517899 & -103.615549517899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123200&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]5053[/C][C]5134.57425213675[/C][C]-81.5742521367501[/C][/ROW]
[ROW][C]14[/C][C]4960[/C][C]5009.76703465207[/C][C]-49.7670346520663[/C][/ROW]
[ROW][C]15[/C][C]4919[/C][C]4953.30815625135[/C][C]-34.3081562513453[/C][/ROW]
[ROW][C]16[/C][C]4960[/C][C]4988.83076232781[/C][C]-28.8307623278142[/C][/ROW]
[ROW][C]17[/C][C]5105[/C][C]5131.37275337806[/C][C]-26.3727533780566[/C][/ROW]
[ROW][C]18[/C][C]5084[/C][C]5105.92671968991[/C][C]-21.9267196899054[/C][/ROW]
[ROW][C]19[/C][C]4888[/C][C]4888.98039530782[/C][C]-0.980395307815343[/C][/ROW]
[ROW][C]20[/C][C]4722[/C][C]4771.16668082402[/C][C]-49.1666808240243[/C][/ROW]
[ROW][C]21[/C][C]4691[/C][C]4751.01682348452[/C][C]-60.0168234845205[/C][/ROW]
[ROW][C]22[/C][C]4629[/C][C]4714.3379176762[/C][C]-85.3379176761955[/C][/ROW]
[ROW][C]23[/C][C]4671[/C][C]4676.24589209157[/C][C]-5.24589209157057[/C][/ROW]
[ROW][C]24[/C][C]4722[/C][C]4684.18413341921[/C][C]37.8158665807878[/C][/ROW]
[ROW][C]25[/C][C]4702[/C][C]4642.23908427082[/C][C]59.7609157291799[/C][/ROW]
[ROW][C]26[/C][C]4660[/C][C]4589.23707336541[/C][C]70.7629266345866[/C][/ROW]
[ROW][C]27[/C][C]4578[/C][C]4588.23110241152[/C][C]-10.2311024115234[/C][/ROW]
[ROW][C]28[/C][C]4660[/C][C]4634.9159754505[/C][C]25.0840245495037[/C][/ROW]
[ROW][C]29[/C][C]4733[/C][C]4799.57028803105[/C][C]-66.5702880310464[/C][/ROW]
[ROW][C]30[/C][C]4712[/C][C]4759.1046579016[/C][C]-47.1046579015983[/C][/ROW]
[ROW][C]31[/C][C]4474[/C][C]4542.6730334804[/C][C]-68.6730334804006[/C][/ROW]
[ROW][C]32[/C][C]4371[/C][C]4365.91095356292[/C][C]5.08904643707592[/C][/ROW]
[ROW][C]33[/C][C]4268[/C][C]4358.87130863013[/C][C]-90.8713086301314[/C][/ROW]
[ROW][C]34[/C][C]4185[/C][C]4292.05693275599[/C][C]-107.056932755989[/C][/ROW]
[ROW][C]35[/C][C]4175[/C][C]4290.32484851842[/C][C]-115.324848518417[/C][/ROW]
[ROW][C]36[/C][C]4237[/C][C]4275.387199781[/C][C]-38.3871997810038[/C][/ROW]
[ROW][C]37[/C][C]4154[/C][C]4210.36826550895[/C][C]-56.3682655089533[/C][/ROW]
[ROW][C]38[/C][C]4123[/C][C]4110.01274106886[/C][C]12.9872589311381[/C][/ROW]
[ROW][C]39[/C][C]4092[/C][C]4029.07585859949[/C][C]62.9241414005146[/C][/ROW]
[ROW][C]40[/C][C]4268[/C][C]4119.08267718653[/C][C]148.917322813468[/C][/ROW]
[ROW][C]41[/C][C]4288[/C][C]4273.13768026748[/C][C]14.8623197325232[/C][/ROW]
[ROW][C]42[/C][C]4185[/C][C]4272.852702737[/C][C]-87.8527027370046[/C][/ROW]
[ROW][C]43[/C][C]3906[/C][C]4022.43438483321[/C][C]-116.43438483321[/C][/ROW]
[ROW][C]44[/C][C]3782[/C][C]3865.28134424841[/C][C]-83.2813442484139[/C][/ROW]
[ROW][C]45[/C][C]3586[/C][C]3758.58112242211[/C][C]-172.581122422107[/C][/ROW]
[ROW][C]46[/C][C]3503[/C][C]3641.36182344073[/C][C]-138.361823440733[/C][/ROW]
[ROW][C]47[/C][C]3544[/C][C]3613.71207390119[/C][C]-69.7120739011866[/C][/ROW]
[ROW][C]48[/C][C]3606[/C][C]3655.41446436159[/C][C]-49.4144643615937[/C][/ROW]
[ROW][C]49[/C][C]3606[/C][C]3567.29917848977[/C][C]38.7008215102346[/C][/ROW]
[ROW][C]50[/C][C]3555[/C][C]3540.11059113878[/C][C]14.8894088612196[/C][/ROW]
[ROW][C]51[/C][C]3544[/C][C]3483.38539965855[/C][C]60.6146003414465[/C][/ROW]
[ROW][C]52[/C][C]3710[/C][C]3617.48313127967[/C][C]92.5168687203322[/C][/ROW]
[ROW][C]53[/C][C]3844[/C][C]3661.27677790313[/C][C]182.723222096872[/C][/ROW]
[ROW][C]54[/C][C]3782[/C][C]3661.89291656113[/C][C]120.107083438871[/C][/ROW]
[ROW][C]55[/C][C]3575[/C][C]3475.94098331062[/C][C]99.0590166893758[/C][/ROW]
[ROW][C]56[/C][C]3472[/C][C]3426.44785702102[/C][C]45.5521429789792[/C][/ROW]
[ROW][C]57[/C][C]3255[/C][C]3321.20920036054[/C][C]-66.2092003605367[/C][/ROW]
[ROW][C]58[/C][C]3121[/C][C]3272.02212165388[/C][C]-151.022121653883[/C][/ROW]
[ROW][C]59[/C][C]3224[/C][C]3285.12658467591[/C][C]-61.1265846759079[/C][/ROW]
[ROW][C]60[/C][C]3327[/C][C]3347.25894414923[/C][C]-20.2589441492282[/C][/ROW]
[ROW][C]61[/C][C]3327[/C][C]3328.88156805102[/C][C]-1.88156805101562[/C][/ROW]
[ROW][C]62[/C][C]3193[/C][C]3275.81688417757[/C][C]-82.8168841775741[/C][/ROW]
[ROW][C]63[/C][C]3183[/C][C]3210.5304804094[/C][C]-27.5304804094048[/C][/ROW]
[ROW][C]64[/C][C]3358[/C][C]3330.31473371149[/C][C]27.6852662885094[/C][/ROW]
[ROW][C]65[/C][C]3472[/C][C]3403.11279045621[/C][C]68.8872095437878[/C][/ROW]
[ROW][C]66[/C][C]3431[/C][C]3319.84644336075[/C][C]111.153556639248[/C][/ROW]
[ROW][C]67[/C][C]3224[/C][C]3116.82959636256[/C][C]107.17040363744[/C][/ROW]
[ROW][C]68[/C][C]3090[/C][C]3037.7861433596[/C][C]52.2138566404033[/C][/ROW]
[ROW][C]69[/C][C]2800[/C][C]2867.6135315883[/C][C]-67.6135315883002[/C][/ROW]
[ROW][C]70[/C][C]2687[/C][C]2766.38330122489[/C][C]-79.3833012248947[/C][/ROW]
[ROW][C]71[/C][C]2728[/C][C]2862.45636217538[/C][C]-134.456362175383[/C][/ROW]
[ROW][C]72[/C][C]2904[/C][C]2918.98342592645[/C][C]-14.9834259264471[/C][/ROW]
[ROW][C]73[/C][C]2914[/C][C]2913.11642278956[/C][C]0.883577210443491[/C][/ROW]
[ROW][C]74[/C][C]2656[/C][C]2812.09711742084[/C][C]-156.09711742084[/C][/ROW]
[ROW][C]75[/C][C]2749[/C][C]2748.89879828934[/C][C]0.101201710661826[/C][/ROW]
[ROW][C]76[/C][C]2976[/C][C]2911.59178361368[/C][C]64.4082163863191[/C][/ROW]
[ROW][C]77[/C][C]3079[/C][C]3023.09045714305[/C][C]55.9095428569531[/C][/ROW]
[ROW][C]78[/C][C]3017[/C][C]2959.04613916864[/C][C]57.9538608313551[/C][/ROW]
[ROW][C]79[/C][C]2738[/C][C]2730.63128771846[/C][C]7.36871228153541[/C][/ROW]
[ROW][C]80[/C][C]2542[/C][C]2575.49272160444[/C][C]-33.4927216044393[/C][/ROW]
[ROW][C]81[/C][C]2315[/C][C]2294.74291307894[/C][C]20.2570869210617[/C][/ROW]
[ROW][C]82[/C][C]2139[/C][C]2218.55873790893[/C][C]-79.5587379089329[/C][/ROW]
[ROW][C]83[/C][C]2211[/C][C]2278.43517200471[/C][C]-67.4351720047125[/C][/ROW]
[ROW][C]84[/C][C]2366[/C][C]2431.267931039[/C][C]-65.267931039004[/C][/ROW]
[ROW][C]85[/C][C]2325[/C][C]2411.86488188994[/C][C]-86.8648818899396[/C][/ROW]
[ROW][C]86[/C][C]2098[/C][C]2177.43755193563[/C][C]-79.4375519356254[/C][/ROW]
[ROW][C]87[/C][C]2170[/C][C]2235.50371493741[/C][C]-65.5037149374111[/C][/ROW]
[ROW][C]88[/C][C]2397[/C][C]2406.40556946653[/C][C]-9.40556946652987[/C][/ROW]
[ROW][C]89[/C][C]2521[/C][C]2478.1116854068[/C][C]42.8883145931973[/C][/ROW]
[ROW][C]90[/C][C]2449[/C][C]2404.76960803962[/C][C]44.2303919603823[/C][/ROW]
[ROW][C]91[/C][C]2170[/C][C]2135.04150277764[/C][C]34.9584972223602[/C][/ROW]
[ROW][C]92[/C][C]2046[/C][C]1961.38531192408[/C][C]84.6146880759175[/C][/ROW]
[ROW][C]93[/C][C]1860[/C][C]1756.8349515857[/C][C]103.165048414302[/C][/ROW]
[ROW][C]94[/C][C]1664[/C][C]1651.96234455773[/C][C]12.0376554422669[/C][/ROW]
[ROW][C]95[/C][C]1695[/C][C]1755.05255080266[/C][C]-60.0525508026626[/C][/ROW]
[ROW][C]96[/C][C]1850[/C][C]1911.48310125054[/C][C]-61.4831012505415[/C][/ROW]
[ROW][C]97[/C][C]1870[/C][C]1880.05408187972[/C][C]-10.0540818797222[/C][/ROW]
[ROW][C]98[/C][C]1684[/C][C]1681.40086820598[/C][C]2.5991317940211[/C][/ROW]
[ROW][C]99[/C][C]1715[/C][C]1782.44766144669[/C][C]-67.4476614466944[/C][/ROW]
[ROW][C]100[/C][C]1974[/C][C]1987.89582617294[/C][C]-13.895826172941[/C][/ROW]
[ROW][C]101[/C][C]2036[/C][C]2090.78187257378[/C][C]-54.7818725737779[/C][/ROW]
[ROW][C]102[/C][C]1932[/C][C]1979.29458476832[/C][C]-47.2945847683218[/C][/ROW]
[ROW][C]103[/C][C]1550[/C][C]1666.17210451106[/C][C]-116.172104511055[/C][/ROW]
[ROW][C]104[/C][C]1354[/C][C]1458.29564134765[/C][C]-104.295641347648[/C][/ROW]
[ROW][C]105[/C][C]1095[/C][C]1182.94955476129[/C][C]-87.949554761293[/C][/ROW]
[ROW][C]106[/C][C]837[/C][C]937.861449998685[/C][C]-100.861449998685[/C][/ROW]
[ROW][C]107[/C][C]920[/C][C]941.827291723873[/C][C]-21.8272917238733[/C][/ROW]
[ROW][C]108[/C][C]1033[/C][C]1102.61577947788[/C][C]-69.6157794778799[/C][/ROW]
[ROW][C]109[/C][C]1013[/C][C]1088.50896148573[/C][C]-75.5089614857266[/C][/ROW]
[ROW][C]110[/C][C]816[/C][C]859.998999835046[/C][C]-43.9989998350461[/C][/ROW]
[ROW][C]111[/C][C]930[/C][C]888.51260295122[/C][C]41.4873970487804[/C][/ROW]
[ROW][C]112[/C][C]1209[/C][C]1159.43960123568[/C][C]49.5603987643224[/C][/ROW]
[ROW][C]113[/C][C]1333[/C][C]1253.93222074895[/C][C]79.0677792510492[/C][/ROW]
[ROW][C]114[/C][C]1271[/C][C]1193.23216095571[/C][C]77.7678390442907[/C][/ROW]
[ROW][C]115[/C][C]1023[/C][C]883.472859076899[/C][C]139.527140923101[/C][/ROW]
[ROW][C]116[/C][C]827[/C][C]783.492951758694[/C][C]43.5070482413058[/C][/ROW]
[ROW][C]117[/C][C]620[/C][C]577.653022523084[/C][C]42.3469774769164[/C][/ROW]
[ROW][C]118[/C][C]382[/C][C]379.451444284376[/C][C]2.54855571562405[/C][/ROW]
[ROW][C]119[/C][C]424[/C][C]476.140942104756[/C][C]-52.140942104756[/C][/ROW]
[ROW][C]120[/C][C]496[/C][C]599.615549517899[/C][C]-103.615549517899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123200&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1350535134.57425213675-81.5742521367501
1449605009.76703465207-49.7670346520663
1549194953.30815625135-34.3081562513453
1649604988.83076232781-28.8307623278142
1751055131.37275337806-26.3727533780566
1850845105.92671968991-21.9267196899054
1948884888.98039530782-0.980395307815343
2047224771.16668082402-49.1666808240243
2146914751.01682348452-60.0168234845205
2246294714.3379176762-85.3379176761955
2346714676.24589209157-5.24589209157057
2447224684.1841334192137.8158665807878
2547024642.2390842708259.7609157291799
2646604589.2370733654170.7629266345866
2745784588.23110241152-10.2311024115234
2846604634.915975450525.0840245495037
2947334799.57028803105-66.5702880310464
3047124759.1046579016-47.1046579015983
3144744542.6730334804-68.6730334804006
3243714365.910953562925.08904643707592
3342684358.87130863013-90.8713086301314
3441854292.05693275599-107.056932755989
3541754290.32484851842-115.324848518417
3642374275.387199781-38.3871997810038
3741544210.36826550895-56.3682655089533
3841234110.0127410688612.9872589311381
3940924029.0758585994962.9241414005146
4042684119.08267718653148.917322813468
4142884273.1376802674814.8623197325232
4241854272.852702737-87.8527027370046
4339064022.43438483321-116.43438483321
4437823865.28134424841-83.2813442484139
4535863758.58112242211-172.581122422107
4635033641.36182344073-138.361823440733
4735443613.71207390119-69.7120739011866
4836063655.41446436159-49.4144643615937
4936063567.2991784897738.7008215102346
5035553540.1105911387814.8894088612196
5135443483.3853996585560.6146003414465
5237103617.4831312796792.5168687203322
5338443661.27677790313182.723222096872
5437823661.89291656113120.107083438871
5535753475.9409833106299.0590166893758
5634723426.4478570210245.5521429789792
5732553321.20920036054-66.2092003605367
5831213272.02212165388-151.022121653883
5932243285.12658467591-61.1265846759079
6033273347.25894414923-20.2589441492282
6133273328.88156805102-1.88156805101562
6231933275.81688417757-82.8168841775741
6331833210.5304804094-27.5304804094048
6433583330.3147337114927.6852662885094
6534723403.1127904562168.8872095437878
6634313319.84644336075111.153556639248
6732243116.82959636256107.17040363744
6830903037.786143359652.2138566404033
6928002867.6135315883-67.6135315883002
7026872766.38330122489-79.3833012248947
7127282862.45636217538-134.456362175383
7229042918.98342592645-14.9834259264471
7329142913.116422789560.883577210443491
7426562812.09711742084-156.09711742084
7527492748.898798289340.101201710661826
7629762911.5917836136864.4082163863191
7730793023.0904571430555.9095428569531
7830172959.0461391686457.9538608313551
7927382730.631287718467.36871228153541
8025422575.49272160444-33.4927216044393
8123152294.7429130789420.2570869210617
8221392218.55873790893-79.5587379089329
8322112278.43517200471-67.4351720047125
8423662431.267931039-65.267931039004
8523252411.86488188994-86.8648818899396
8620982177.43755193563-79.4375519356254
8721702235.50371493741-65.5037149374111
8823972406.40556946653-9.40556946652987
8925212478.111685406842.8883145931973
9024492404.7696080396244.2303919603823
9121702135.0415027776434.9584972223602
9220461961.3853119240884.6146880759175
9318601756.8349515857103.165048414302
9416641651.9623445577312.0376554422669
9516951755.05255080266-60.0525508026626
9618501911.48310125054-61.4831012505415
9718701880.05408187972-10.0540818797222
9816841681.400868205982.5991317940211
9917151782.44766144669-67.4476614466944
10019741987.89582617294-13.895826172941
10120362090.78187257378-54.7818725737779
10219321979.29458476832-47.2945847683218
10315501666.17210451106-116.172104511055
10413541458.29564134765-104.295641347648
10510951182.94955476129-87.949554761293
106837937.861449998685-100.861449998685
107920941.827291723873-21.8272917238733
10810331102.61577947788-69.6157794778799
10910131088.50896148573-75.5089614857266
110816859.998999835046-43.9989998350461
111930888.5126029512241.4873970487804
11212091159.4396012356849.5603987643224
11313331253.9322207489579.0677792510492
11412711193.2321609557177.7678390442907
1151023883.472859076899139.527140923101
116827783.49295175869443.5070482413058
117620577.65302252308442.3469774769164
118382379.4514442843762.54855571562405
119424476.140942104756-52.140942104756
120496599.615549517899-103.615549517899







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121571.314266998137429.383753816474713.244780179799
122396.036024609914242.331888009282549.740161210546
123498.138172952431332.736350719653663.539995185209
124761.390325372645584.326811246678938.453839498611
125857.080309839828668.3610707263311045.79954895332
126766.121943900901565.729912567221966.513975234581
127463.254819470832251.154968081648675.354670860016
128248.81718446494524.9602942053511472.67407472454
12923.2011006276869-212.473380781475258.875582036849
130-218.08665797592-465.6484128270129.4750968751702
131-157.487798901486-417.013915202737102.038317399764
132-45.4822260294756-317.055830809372226.091378750421

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 571.314266998137 & 429.383753816474 & 713.244780179799 \tabularnewline
122 & 396.036024609914 & 242.331888009282 & 549.740161210546 \tabularnewline
123 & 498.138172952431 & 332.736350719653 & 663.539995185209 \tabularnewline
124 & 761.390325372645 & 584.326811246678 & 938.453839498611 \tabularnewline
125 & 857.080309839828 & 668.361070726331 & 1045.79954895332 \tabularnewline
126 & 766.121943900901 & 565.729912567221 & 966.513975234581 \tabularnewline
127 & 463.254819470832 & 251.154968081648 & 675.354670860016 \tabularnewline
128 & 248.817184464945 & 24.9602942053511 & 472.67407472454 \tabularnewline
129 & 23.2011006276869 & -212.473380781475 & 258.875582036849 \tabularnewline
130 & -218.08665797592 & -465.64841282701 & 29.4750968751702 \tabularnewline
131 & -157.487798901486 & -417.013915202737 & 102.038317399764 \tabularnewline
132 & -45.4822260294756 & -317.055830809372 & 226.091378750421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123200&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]571.314266998137[/C][C]429.383753816474[/C][C]713.244780179799[/C][/ROW]
[ROW][C]122[/C][C]396.036024609914[/C][C]242.331888009282[/C][C]549.740161210546[/C][/ROW]
[ROW][C]123[/C][C]498.138172952431[/C][C]332.736350719653[/C][C]663.539995185209[/C][/ROW]
[ROW][C]124[/C][C]761.390325372645[/C][C]584.326811246678[/C][C]938.453839498611[/C][/ROW]
[ROW][C]125[/C][C]857.080309839828[/C][C]668.361070726331[/C][C]1045.79954895332[/C][/ROW]
[ROW][C]126[/C][C]766.121943900901[/C][C]565.729912567221[/C][C]966.513975234581[/C][/ROW]
[ROW][C]127[/C][C]463.254819470832[/C][C]251.154968081648[/C][C]675.354670860016[/C][/ROW]
[ROW][C]128[/C][C]248.817184464945[/C][C]24.9602942053511[/C][C]472.67407472454[/C][/ROW]
[ROW][C]129[/C][C]23.2011006276869[/C][C]-212.473380781475[/C][C]258.875582036849[/C][/ROW]
[ROW][C]130[/C][C]-218.08665797592[/C][C]-465.64841282701[/C][C]29.4750968751702[/C][/ROW]
[ROW][C]131[/C][C]-157.487798901486[/C][C]-417.013915202737[/C][C]102.038317399764[/C][/ROW]
[ROW][C]132[/C][C]-45.4822260294756[/C][C]-317.055830809372[/C][C]226.091378750421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123200&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121571.314266998137429.383753816474713.244780179799
122396.036024609914242.331888009282549.740161210546
123498.138172952431332.736350719653663.539995185209
124761.390325372645584.326811246678938.453839498611
125857.080309839828668.3610707263311045.79954895332
126766.121943900901565.729912567221966.513975234581
127463.254819470832251.154968081648675.354670860016
128248.81718446494524.9602942053511472.67407472454
12923.2011006276869-212.473380781475258.875582036849
130-218.08665797592-465.6484128270129.4750968751702
131-157.487798901486-417.013915202737102.038317399764
132-45.4822260294756-317.055830809372226.091378750421



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[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,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')