Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 15:00:14 +0200
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/Aug/16/t1502888492gonyc171j5dljo3.htm/, Retrieved Sat, 11 May 2024 06:37:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307384, Retrieved Sat, 11 May 2024 06:37:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2017-08-16 13:00:14] [41db9c2917eeaa94887144dd7479aea5] [Current]
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Dataseries X:
4213144
4197453
4181541
4148612
4474366
4457128
4213144
4050930
4066621
4066621
4084080
4115462
4164303
4164303
4132921
4050930
4474366
4538898
4441437
4213144
4310826
4164303
4230382
4261985
4294914
4213144
4230382
4115462
4474366
4587739
4490278
4310826
4505969
4294914
4490278
4474366
4523207
4343755
4538898
4523207
4816032
4749953
4490278
4359446
4538898
4294914
4474366
4505969
4572048
4425746
4505969
4554810
4734262
4587739
4392596
4181541
4376905
3839875
4099771
4246073
4392596
4181541
4181541
4181541
4294914
4132921
3920319
3742414
3871478
3367598
3676335
3855787
3888716
3709264
3724955
3676335
3839875
3724955
3498430
3334669
3611582
3010241
3400748
3578653
3578653
3367598
3172455
3156764
3334669
3172455
2863939
2651337
2879630
2342821
2830789
3090464
3172455
2993003
2766257
2928471
2993003
2944162
2455973
2229448
2391441
1903473
2407353
2586805
2733107
2489123
2260830
2391441
2455973
2326909
1838941
1626339
1821482
1284673
1870323
2229448




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307384&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307384&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238474
beta0.0645195510983794
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238474 \tabularnewline
beta & 0.0645195510983794 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307384&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]0.405343002238474[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983794[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307384&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
alpha0.405343002238474
beta0.0645195510983794
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1341643034164121.90277778181.09722221829
1441643034154982.503756769320.49624323845
1541329214117746.4509040415174.5490959566
1640509304035359.9838751315570.0161248716
1744743664463047.3039082211318.6960917776
1845388984528368.3521979710529.6478020297
1944414374284714.56741035156722.432589653
2042131444202219.4042739110924.5957260877
2143108264238807.6059100672018.3940899437
2241643034289041.04907408-124738.049074083
2342303824271691.59363905-41309.5936390506
2442619854293524.76098247-31539.7609824734
2542949144326547.69889322-31633.6988932155
2642131444311839.5414026-98695.5414026044
2742303824233368.54130681-2986.54130680673
2841154624142448.2560599-26986.2560599009
2944743664547837.14223358-73471.1422335813
3045877394573582.0699266314156.9300733656
3144902784413690.0639132376587.9360867739
3243108264205274.44091427105551.559085731
3345059694312284.81242341193684.187576588
3442949144293749.846112541164.15388746187
3544902784379255.75423182111022.24576818
3644743664474839.60365893-473.603658929467
3745232074527405.92700441-4198.92700440809
3843437554491663.75438277-147908.754382772
3945388984456595.7844988182302.2155011883
4045232074394642.85507952128564.144920479
4148160324848176.23775362-32144.2377536222
4247499534956597.98007608-206644.980076085
4344902784752372.5635284-262094.563528397
4443594464423082.43393655-63636.4339365484
4545388984508682.2769836430215.7230163561
4642949144299887.96658815-4973.96658815164
4744743664438558.0254836935807.9745163079
4845059694425709.7762873380259.2237126734
4945720484499253.9328296772794.0671703322
5044257464401744.4763054824001.5236945227
5145059694570233.78993381-64264.7899338063
5245548104469525.9209145785284.0790854301
5347342624801962.77374018-67700.7737401752
5445877394783287.04777678-195548.047776777
5543925964541959.63761747-149363.637617471
5641815414370700.3418738-189159.3418738
5743769054452269.07688145-75364.0768814525
5838398754168030.63983153-328155.639831527
5940997714179778.21287202-80007.2128720209
6042460734123215.14918407122857.850815926
6143925964187498.03108903205097.968910968
6241815414095973.1696394285567.8303605784
6341815414219910.85135828-38369.8513582833
6441815414202287.89216729-20746.8921672935
6542949144381657.63558146-86743.6355814552
6641329214259625.03939941-126704.039399413
6739203194055854.6919637-135535.691963695
6837424143849085.04222229-106671.042222292
6938714784016465.64117416-144987.641174164
7033675983536567.33229299-168969.332292995
7136763353747452.11198609-71117.1119860904
7238557873802409.1692645153377.830735493
7338887163872897.8444180215818.1555819754
7437092643614084.5237929895179.4762070216
7537249553648983.400164775971.5998353022
7636763353671943.475427564391.52457244368
7738398753806670.8198605133204.1801394913
7837249553697045.7837312527909.2162687513
7934984303542288.85028962-43858.8502896186
8033346693383835.73255199-49166.7325519877
8136115823547235.3513875464346.6486124648
8230102413138898.26079122-128657.260791224
8334007483426335.93676547-25587.9367654696
8435786533576994.592097921658.40790208476
8535786533606046.31935138-27393.3193513756
8633675983377642.48610003-10044.4861000297
8731724553356447.78449689-183992.784496894
8831567643222649.10881351-65885.108813507
8933346693335367.6316028-698.631602795329
9031724553197308.66839222-24853.6683922214
9128639392965564.42971138-101625.429711375
9226513372766106.06446942-114769.064469421
9328796302954266.49596872-74636.4959687199
9423428212355038.40391745-12217.4039174509
9528307892734226.2238054596562.7761945478
9630904642937055.76578705153408.234212948
9731724553000766.77542992171688.224570083
9829930032859006.71283148133996.287168523
9927662572792156.24598837-25899.2459883699
10029284712796205.67278256132265.327217443
10129930033036721.25904739-43718.2590473858
10229441622874450.132347269711.8676528027
10324559732645447.13974032-189474.139740324
10422294482410329.125478-180881.125477997
10523914412601592.77472647-210151.774726468
10619034731987044.55905569-83571.5590556916
10724073532402622.37023214730.62976789987
10825868052600256.30244625-13451.3024462503
10927331072601062.84736524132044.152634756
11024891232413643.3264095475479.6735904631
11122608302219283.9665749941546.0334250089
11223914412337782.806151953658.1938481019
11324559732432787.1635281323185.8364718733
11423269092357838.36858519-30929.3685851926
11518389411924033.56351624-85092.5635162373
11616263391729184.81244317-102845.81244317
11718214821929563.38130681-108081.381306808
11812846731429219.74524379-144546.745243791
11918703231868555.798246011767.20175398653
12022294482050063.60358886179384.396411138

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4164303 & 4164121.90277778 & 181.09722221829 \tabularnewline
14 & 4164303 & 4154982.50375676 & 9320.49624323845 \tabularnewline
15 & 4132921 & 4117746.45090404 & 15174.5490959566 \tabularnewline
16 & 4050930 & 4035359.98387513 & 15570.0161248716 \tabularnewline
17 & 4474366 & 4463047.30390822 & 11318.6960917776 \tabularnewline
18 & 4538898 & 4528368.35219797 & 10529.6478020297 \tabularnewline
19 & 4441437 & 4284714.56741035 & 156722.432589653 \tabularnewline
20 & 4213144 & 4202219.40427391 & 10924.5957260877 \tabularnewline
21 & 4310826 & 4238807.60591006 & 72018.3940899437 \tabularnewline
22 & 4164303 & 4289041.04907408 & -124738.049074083 \tabularnewline
23 & 4230382 & 4271691.59363905 & -41309.5936390506 \tabularnewline
24 & 4261985 & 4293524.76098247 & -31539.7609824734 \tabularnewline
25 & 4294914 & 4326547.69889322 & -31633.6988932155 \tabularnewline
26 & 4213144 & 4311839.5414026 & -98695.5414026044 \tabularnewline
27 & 4230382 & 4233368.54130681 & -2986.54130680673 \tabularnewline
28 & 4115462 & 4142448.2560599 & -26986.2560599009 \tabularnewline
29 & 4474366 & 4547837.14223358 & -73471.1422335813 \tabularnewline
30 & 4587739 & 4573582.06992663 & 14156.9300733656 \tabularnewline
31 & 4490278 & 4413690.06391323 & 76587.9360867739 \tabularnewline
32 & 4310826 & 4205274.44091427 & 105551.559085731 \tabularnewline
33 & 4505969 & 4312284.81242341 & 193684.187576588 \tabularnewline
34 & 4294914 & 4293749.84611254 & 1164.15388746187 \tabularnewline
35 & 4490278 & 4379255.75423182 & 111022.24576818 \tabularnewline
36 & 4474366 & 4474839.60365893 & -473.603658929467 \tabularnewline
37 & 4523207 & 4527405.92700441 & -4198.92700440809 \tabularnewline
38 & 4343755 & 4491663.75438277 & -147908.754382772 \tabularnewline
39 & 4538898 & 4456595.78449881 & 82302.2155011883 \tabularnewline
40 & 4523207 & 4394642.85507952 & 128564.144920479 \tabularnewline
41 & 4816032 & 4848176.23775362 & -32144.2377536222 \tabularnewline
42 & 4749953 & 4956597.98007608 & -206644.980076085 \tabularnewline
43 & 4490278 & 4752372.5635284 & -262094.563528397 \tabularnewline
44 & 4359446 & 4423082.43393655 & -63636.4339365484 \tabularnewline
45 & 4538898 & 4508682.27698364 & 30215.7230163561 \tabularnewline
46 & 4294914 & 4299887.96658815 & -4973.96658815164 \tabularnewline
47 & 4474366 & 4438558.02548369 & 35807.9745163079 \tabularnewline
48 & 4505969 & 4425709.77628733 & 80259.2237126734 \tabularnewline
49 & 4572048 & 4499253.93282967 & 72794.0671703322 \tabularnewline
50 & 4425746 & 4401744.47630548 & 24001.5236945227 \tabularnewline
51 & 4505969 & 4570233.78993381 & -64264.7899338063 \tabularnewline
52 & 4554810 & 4469525.92091457 & 85284.0790854301 \tabularnewline
53 & 4734262 & 4801962.77374018 & -67700.7737401752 \tabularnewline
54 & 4587739 & 4783287.04777678 & -195548.047776777 \tabularnewline
55 & 4392596 & 4541959.63761747 & -149363.637617471 \tabularnewline
56 & 4181541 & 4370700.3418738 & -189159.3418738 \tabularnewline
57 & 4376905 & 4452269.07688145 & -75364.0768814525 \tabularnewline
58 & 3839875 & 4168030.63983153 & -328155.639831527 \tabularnewline
59 & 4099771 & 4179778.21287202 & -80007.2128720209 \tabularnewline
60 & 4246073 & 4123215.14918407 & 122857.850815926 \tabularnewline
61 & 4392596 & 4187498.03108903 & 205097.968910968 \tabularnewline
62 & 4181541 & 4095973.16963942 & 85567.8303605784 \tabularnewline
63 & 4181541 & 4219910.85135828 & -38369.8513582833 \tabularnewline
64 & 4181541 & 4202287.89216729 & -20746.8921672935 \tabularnewline
65 & 4294914 & 4381657.63558146 & -86743.6355814552 \tabularnewline
66 & 4132921 & 4259625.03939941 & -126704.039399413 \tabularnewline
67 & 3920319 & 4055854.6919637 & -135535.691963695 \tabularnewline
68 & 3742414 & 3849085.04222229 & -106671.042222292 \tabularnewline
69 & 3871478 & 4016465.64117416 & -144987.641174164 \tabularnewline
70 & 3367598 & 3536567.33229299 & -168969.332292995 \tabularnewline
71 & 3676335 & 3747452.11198609 & -71117.1119860904 \tabularnewline
72 & 3855787 & 3802409.16926451 & 53377.830735493 \tabularnewline
73 & 3888716 & 3872897.84441802 & 15818.1555819754 \tabularnewline
74 & 3709264 & 3614084.52379298 & 95179.4762070216 \tabularnewline
75 & 3724955 & 3648983.4001647 & 75971.5998353022 \tabularnewline
76 & 3676335 & 3671943.47542756 & 4391.52457244368 \tabularnewline
77 & 3839875 & 3806670.81986051 & 33204.1801394913 \tabularnewline
78 & 3724955 & 3697045.78373125 & 27909.2162687513 \tabularnewline
79 & 3498430 & 3542288.85028962 & -43858.8502896186 \tabularnewline
80 & 3334669 & 3383835.73255199 & -49166.7325519877 \tabularnewline
81 & 3611582 & 3547235.35138754 & 64346.6486124648 \tabularnewline
82 & 3010241 & 3138898.26079122 & -128657.260791224 \tabularnewline
83 & 3400748 & 3426335.93676547 & -25587.9367654696 \tabularnewline
84 & 3578653 & 3576994.59209792 & 1658.40790208476 \tabularnewline
85 & 3578653 & 3606046.31935138 & -27393.3193513756 \tabularnewline
86 & 3367598 & 3377642.48610003 & -10044.4861000297 \tabularnewline
87 & 3172455 & 3356447.78449689 & -183992.784496894 \tabularnewline
88 & 3156764 & 3222649.10881351 & -65885.108813507 \tabularnewline
89 & 3334669 & 3335367.6316028 & -698.631602795329 \tabularnewline
90 & 3172455 & 3197308.66839222 & -24853.6683922214 \tabularnewline
91 & 2863939 & 2965564.42971138 & -101625.429711375 \tabularnewline
92 & 2651337 & 2766106.06446942 & -114769.064469421 \tabularnewline
93 & 2879630 & 2954266.49596872 & -74636.4959687199 \tabularnewline
94 & 2342821 & 2355038.40391745 & -12217.4039174509 \tabularnewline
95 & 2830789 & 2734226.22380545 & 96562.7761945478 \tabularnewline
96 & 3090464 & 2937055.76578705 & 153408.234212948 \tabularnewline
97 & 3172455 & 3000766.77542992 & 171688.224570083 \tabularnewline
98 & 2993003 & 2859006.71283148 & 133996.287168523 \tabularnewline
99 & 2766257 & 2792156.24598837 & -25899.2459883699 \tabularnewline
100 & 2928471 & 2796205.67278256 & 132265.327217443 \tabularnewline
101 & 2993003 & 3036721.25904739 & -43718.2590473858 \tabularnewline
102 & 2944162 & 2874450.1323472 & 69711.8676528027 \tabularnewline
103 & 2455973 & 2645447.13974032 & -189474.139740324 \tabularnewline
104 & 2229448 & 2410329.125478 & -180881.125477997 \tabularnewline
105 & 2391441 & 2601592.77472647 & -210151.774726468 \tabularnewline
106 & 1903473 & 1987044.55905569 & -83571.5590556916 \tabularnewline
107 & 2407353 & 2402622.3702321 & 4730.62976789987 \tabularnewline
108 & 2586805 & 2600256.30244625 & -13451.3024462503 \tabularnewline
109 & 2733107 & 2601062.84736524 & 132044.152634756 \tabularnewline
110 & 2489123 & 2413643.32640954 & 75479.6735904631 \tabularnewline
111 & 2260830 & 2219283.96657499 & 41546.0334250089 \tabularnewline
112 & 2391441 & 2337782.8061519 & 53658.1938481019 \tabularnewline
113 & 2455973 & 2432787.16352813 & 23185.8364718733 \tabularnewline
114 & 2326909 & 2357838.36858519 & -30929.3685851926 \tabularnewline
115 & 1838941 & 1924033.56351624 & -85092.5635162373 \tabularnewline
116 & 1626339 & 1729184.81244317 & -102845.81244317 \tabularnewline
117 & 1821482 & 1929563.38130681 & -108081.381306808 \tabularnewline
118 & 1284673 & 1429219.74524379 & -144546.745243791 \tabularnewline
119 & 1870323 & 1868555.79824601 & 1767.20175398653 \tabularnewline
120 & 2229448 & 2050063.60358886 & 179384.396411138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307384&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]4164303[/C][C]4164121.90277778[/C][C]181.09722221829[/C][/ROW]
[ROW][C]14[/C][C]4164303[/C][C]4154982.50375676[/C][C]9320.49624323845[/C][/ROW]
[ROW][C]15[/C][C]4132921[/C][C]4117746.45090404[/C][C]15174.5490959566[/C][/ROW]
[ROW][C]16[/C][C]4050930[/C][C]4035359.98387513[/C][C]15570.0161248716[/C][/ROW]
[ROW][C]17[/C][C]4474366[/C][C]4463047.30390822[/C][C]11318.6960917776[/C][/ROW]
[ROW][C]18[/C][C]4538898[/C][C]4528368.35219797[/C][C]10529.6478020297[/C][/ROW]
[ROW][C]19[/C][C]4441437[/C][C]4284714.56741035[/C][C]156722.432589653[/C][/ROW]
[ROW][C]20[/C][C]4213144[/C][C]4202219.40427391[/C][C]10924.5957260877[/C][/ROW]
[ROW][C]21[/C][C]4310826[/C][C]4238807.60591006[/C][C]72018.3940899437[/C][/ROW]
[ROW][C]22[/C][C]4164303[/C][C]4289041.04907408[/C][C]-124738.049074083[/C][/ROW]
[ROW][C]23[/C][C]4230382[/C][C]4271691.59363905[/C][C]-41309.5936390506[/C][/ROW]
[ROW][C]24[/C][C]4261985[/C][C]4293524.76098247[/C][C]-31539.7609824734[/C][/ROW]
[ROW][C]25[/C][C]4294914[/C][C]4326547.69889322[/C][C]-31633.6988932155[/C][/ROW]
[ROW][C]26[/C][C]4213144[/C][C]4311839.5414026[/C][C]-98695.5414026044[/C][/ROW]
[ROW][C]27[/C][C]4230382[/C][C]4233368.54130681[/C][C]-2986.54130680673[/C][/ROW]
[ROW][C]28[/C][C]4115462[/C][C]4142448.2560599[/C][C]-26986.2560599009[/C][/ROW]
[ROW][C]29[/C][C]4474366[/C][C]4547837.14223358[/C][C]-73471.1422335813[/C][/ROW]
[ROW][C]30[/C][C]4587739[/C][C]4573582.06992663[/C][C]14156.9300733656[/C][/ROW]
[ROW][C]31[/C][C]4490278[/C][C]4413690.06391323[/C][C]76587.9360867739[/C][/ROW]
[ROW][C]32[/C][C]4310826[/C][C]4205274.44091427[/C][C]105551.559085731[/C][/ROW]
[ROW][C]33[/C][C]4505969[/C][C]4312284.81242341[/C][C]193684.187576588[/C][/ROW]
[ROW][C]34[/C][C]4294914[/C][C]4293749.84611254[/C][C]1164.15388746187[/C][/ROW]
[ROW][C]35[/C][C]4490278[/C][C]4379255.75423182[/C][C]111022.24576818[/C][/ROW]
[ROW][C]36[/C][C]4474366[/C][C]4474839.60365893[/C][C]-473.603658929467[/C][/ROW]
[ROW][C]37[/C][C]4523207[/C][C]4527405.92700441[/C][C]-4198.92700440809[/C][/ROW]
[ROW][C]38[/C][C]4343755[/C][C]4491663.75438277[/C][C]-147908.754382772[/C][/ROW]
[ROW][C]39[/C][C]4538898[/C][C]4456595.78449881[/C][C]82302.2155011883[/C][/ROW]
[ROW][C]40[/C][C]4523207[/C][C]4394642.85507952[/C][C]128564.144920479[/C][/ROW]
[ROW][C]41[/C][C]4816032[/C][C]4848176.23775362[/C][C]-32144.2377536222[/C][/ROW]
[ROW][C]42[/C][C]4749953[/C][C]4956597.98007608[/C][C]-206644.980076085[/C][/ROW]
[ROW][C]43[/C][C]4490278[/C][C]4752372.5635284[/C][C]-262094.563528397[/C][/ROW]
[ROW][C]44[/C][C]4359446[/C][C]4423082.43393655[/C][C]-63636.4339365484[/C][/ROW]
[ROW][C]45[/C][C]4538898[/C][C]4508682.27698364[/C][C]30215.7230163561[/C][/ROW]
[ROW][C]46[/C][C]4294914[/C][C]4299887.96658815[/C][C]-4973.96658815164[/C][/ROW]
[ROW][C]47[/C][C]4474366[/C][C]4438558.02548369[/C][C]35807.9745163079[/C][/ROW]
[ROW][C]48[/C][C]4505969[/C][C]4425709.77628733[/C][C]80259.2237126734[/C][/ROW]
[ROW][C]49[/C][C]4572048[/C][C]4499253.93282967[/C][C]72794.0671703322[/C][/ROW]
[ROW][C]50[/C][C]4425746[/C][C]4401744.47630548[/C][C]24001.5236945227[/C][/ROW]
[ROW][C]51[/C][C]4505969[/C][C]4570233.78993381[/C][C]-64264.7899338063[/C][/ROW]
[ROW][C]52[/C][C]4554810[/C][C]4469525.92091457[/C][C]85284.0790854301[/C][/ROW]
[ROW][C]53[/C][C]4734262[/C][C]4801962.77374018[/C][C]-67700.7737401752[/C][/ROW]
[ROW][C]54[/C][C]4587739[/C][C]4783287.04777678[/C][C]-195548.047776777[/C][/ROW]
[ROW][C]55[/C][C]4392596[/C][C]4541959.63761747[/C][C]-149363.637617471[/C][/ROW]
[ROW][C]56[/C][C]4181541[/C][C]4370700.3418738[/C][C]-189159.3418738[/C][/ROW]
[ROW][C]57[/C][C]4376905[/C][C]4452269.07688145[/C][C]-75364.0768814525[/C][/ROW]
[ROW][C]58[/C][C]3839875[/C][C]4168030.63983153[/C][C]-328155.639831527[/C][/ROW]
[ROW][C]59[/C][C]4099771[/C][C]4179778.21287202[/C][C]-80007.2128720209[/C][/ROW]
[ROW][C]60[/C][C]4246073[/C][C]4123215.14918407[/C][C]122857.850815926[/C][/ROW]
[ROW][C]61[/C][C]4392596[/C][C]4187498.03108903[/C][C]205097.968910968[/C][/ROW]
[ROW][C]62[/C][C]4181541[/C][C]4095973.16963942[/C][C]85567.8303605784[/C][/ROW]
[ROW][C]63[/C][C]4181541[/C][C]4219910.85135828[/C][C]-38369.8513582833[/C][/ROW]
[ROW][C]64[/C][C]4181541[/C][C]4202287.89216729[/C][C]-20746.8921672935[/C][/ROW]
[ROW][C]65[/C][C]4294914[/C][C]4381657.63558146[/C][C]-86743.6355814552[/C][/ROW]
[ROW][C]66[/C][C]4132921[/C][C]4259625.03939941[/C][C]-126704.039399413[/C][/ROW]
[ROW][C]67[/C][C]3920319[/C][C]4055854.6919637[/C][C]-135535.691963695[/C][/ROW]
[ROW][C]68[/C][C]3742414[/C][C]3849085.04222229[/C][C]-106671.042222292[/C][/ROW]
[ROW][C]69[/C][C]3871478[/C][C]4016465.64117416[/C][C]-144987.641174164[/C][/ROW]
[ROW][C]70[/C][C]3367598[/C][C]3536567.33229299[/C][C]-168969.332292995[/C][/ROW]
[ROW][C]71[/C][C]3676335[/C][C]3747452.11198609[/C][C]-71117.1119860904[/C][/ROW]
[ROW][C]72[/C][C]3855787[/C][C]3802409.16926451[/C][C]53377.830735493[/C][/ROW]
[ROW][C]73[/C][C]3888716[/C][C]3872897.84441802[/C][C]15818.1555819754[/C][/ROW]
[ROW][C]74[/C][C]3709264[/C][C]3614084.52379298[/C][C]95179.4762070216[/C][/ROW]
[ROW][C]75[/C][C]3724955[/C][C]3648983.4001647[/C][C]75971.5998353022[/C][/ROW]
[ROW][C]76[/C][C]3676335[/C][C]3671943.47542756[/C][C]4391.52457244368[/C][/ROW]
[ROW][C]77[/C][C]3839875[/C][C]3806670.81986051[/C][C]33204.1801394913[/C][/ROW]
[ROW][C]78[/C][C]3724955[/C][C]3697045.78373125[/C][C]27909.2162687513[/C][/ROW]
[ROW][C]79[/C][C]3498430[/C][C]3542288.85028962[/C][C]-43858.8502896186[/C][/ROW]
[ROW][C]80[/C][C]3334669[/C][C]3383835.73255199[/C][C]-49166.7325519877[/C][/ROW]
[ROW][C]81[/C][C]3611582[/C][C]3547235.35138754[/C][C]64346.6486124648[/C][/ROW]
[ROW][C]82[/C][C]3010241[/C][C]3138898.26079122[/C][C]-128657.260791224[/C][/ROW]
[ROW][C]83[/C][C]3400748[/C][C]3426335.93676547[/C][C]-25587.9367654696[/C][/ROW]
[ROW][C]84[/C][C]3578653[/C][C]3576994.59209792[/C][C]1658.40790208476[/C][/ROW]
[ROW][C]85[/C][C]3578653[/C][C]3606046.31935138[/C][C]-27393.3193513756[/C][/ROW]
[ROW][C]86[/C][C]3367598[/C][C]3377642.48610003[/C][C]-10044.4861000297[/C][/ROW]
[ROW][C]87[/C][C]3172455[/C][C]3356447.78449689[/C][C]-183992.784496894[/C][/ROW]
[ROW][C]88[/C][C]3156764[/C][C]3222649.10881351[/C][C]-65885.108813507[/C][/ROW]
[ROW][C]89[/C][C]3334669[/C][C]3335367.6316028[/C][C]-698.631602795329[/C][/ROW]
[ROW][C]90[/C][C]3172455[/C][C]3197308.66839222[/C][C]-24853.6683922214[/C][/ROW]
[ROW][C]91[/C][C]2863939[/C][C]2965564.42971138[/C][C]-101625.429711375[/C][/ROW]
[ROW][C]92[/C][C]2651337[/C][C]2766106.06446942[/C][C]-114769.064469421[/C][/ROW]
[ROW][C]93[/C][C]2879630[/C][C]2954266.49596872[/C][C]-74636.4959687199[/C][/ROW]
[ROW][C]94[/C][C]2342821[/C][C]2355038.40391745[/C][C]-12217.4039174509[/C][/ROW]
[ROW][C]95[/C][C]2830789[/C][C]2734226.22380545[/C][C]96562.7761945478[/C][/ROW]
[ROW][C]96[/C][C]3090464[/C][C]2937055.76578705[/C][C]153408.234212948[/C][/ROW]
[ROW][C]97[/C][C]3172455[/C][C]3000766.77542992[/C][C]171688.224570083[/C][/ROW]
[ROW][C]98[/C][C]2993003[/C][C]2859006.71283148[/C][C]133996.287168523[/C][/ROW]
[ROW][C]99[/C][C]2766257[/C][C]2792156.24598837[/C][C]-25899.2459883699[/C][/ROW]
[ROW][C]100[/C][C]2928471[/C][C]2796205.67278256[/C][C]132265.327217443[/C][/ROW]
[ROW][C]101[/C][C]2993003[/C][C]3036721.25904739[/C][C]-43718.2590473858[/C][/ROW]
[ROW][C]102[/C][C]2944162[/C][C]2874450.1323472[/C][C]69711.8676528027[/C][/ROW]
[ROW][C]103[/C][C]2455973[/C][C]2645447.13974032[/C][C]-189474.139740324[/C][/ROW]
[ROW][C]104[/C][C]2229448[/C][C]2410329.125478[/C][C]-180881.125477997[/C][/ROW]
[ROW][C]105[/C][C]2391441[/C][C]2601592.77472647[/C][C]-210151.774726468[/C][/ROW]
[ROW][C]106[/C][C]1903473[/C][C]1987044.55905569[/C][C]-83571.5590556916[/C][/ROW]
[ROW][C]107[/C][C]2407353[/C][C]2402622.3702321[/C][C]4730.62976789987[/C][/ROW]
[ROW][C]108[/C][C]2586805[/C][C]2600256.30244625[/C][C]-13451.3024462503[/C][/ROW]
[ROW][C]109[/C][C]2733107[/C][C]2601062.84736524[/C][C]132044.152634756[/C][/ROW]
[ROW][C]110[/C][C]2489123[/C][C]2413643.32640954[/C][C]75479.6735904631[/C][/ROW]
[ROW][C]111[/C][C]2260830[/C][C]2219283.96657499[/C][C]41546.0334250089[/C][/ROW]
[ROW][C]112[/C][C]2391441[/C][C]2337782.8061519[/C][C]53658.1938481019[/C][/ROW]
[ROW][C]113[/C][C]2455973[/C][C]2432787.16352813[/C][C]23185.8364718733[/C][/ROW]
[ROW][C]114[/C][C]2326909[/C][C]2357838.36858519[/C][C]-30929.3685851926[/C][/ROW]
[ROW][C]115[/C][C]1838941[/C][C]1924033.56351624[/C][C]-85092.5635162373[/C][/ROW]
[ROW][C]116[/C][C]1626339[/C][C]1729184.81244317[/C][C]-102845.81244317[/C][/ROW]
[ROW][C]117[/C][C]1821482[/C][C]1929563.38130681[/C][C]-108081.381306808[/C][/ROW]
[ROW][C]118[/C][C]1284673[/C][C]1429219.74524379[/C][C]-144546.745243791[/C][/ROW]
[ROW][C]119[/C][C]1870323[/C][C]1868555.79824601[/C][C]1767.20175398653[/C][/ROW]
[ROW][C]120[/C][C]2229448[/C][C]2050063.60358886[/C][C]179384.396411138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307384&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307384&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
1341643034164121.90277778181.09722221829
1441643034154982.503756769320.49624323845
1541329214117746.4509040415174.5490959566
1640509304035359.9838751315570.0161248716
1744743664463047.3039082211318.6960917776
1845388984528368.3521979710529.6478020297
1944414374284714.56741035156722.432589653
2042131444202219.4042739110924.5957260877
2143108264238807.6059100672018.3940899437
2241643034289041.04907408-124738.049074083
2342303824271691.59363905-41309.5936390506
2442619854293524.76098247-31539.7609824734
2542949144326547.69889322-31633.6988932155
2642131444311839.5414026-98695.5414026044
2742303824233368.54130681-2986.54130680673
2841154624142448.2560599-26986.2560599009
2944743664547837.14223358-73471.1422335813
3045877394573582.0699266314156.9300733656
3144902784413690.0639132376587.9360867739
3243108264205274.44091427105551.559085731
3345059694312284.81242341193684.187576588
3442949144293749.846112541164.15388746187
3544902784379255.75423182111022.24576818
3644743664474839.60365893-473.603658929467
3745232074527405.92700441-4198.92700440809
3843437554491663.75438277-147908.754382772
3945388984456595.7844988182302.2155011883
4045232074394642.85507952128564.144920479
4148160324848176.23775362-32144.2377536222
4247499534956597.98007608-206644.980076085
4344902784752372.5635284-262094.563528397
4443594464423082.43393655-63636.4339365484
4545388984508682.2769836430215.7230163561
4642949144299887.96658815-4973.96658815164
4744743664438558.0254836935807.9745163079
4845059694425709.7762873380259.2237126734
4945720484499253.9328296772794.0671703322
5044257464401744.4763054824001.5236945227
5145059694570233.78993381-64264.7899338063
5245548104469525.9209145785284.0790854301
5347342624801962.77374018-67700.7737401752
5445877394783287.04777678-195548.047776777
5543925964541959.63761747-149363.637617471
5641815414370700.3418738-189159.3418738
5743769054452269.07688145-75364.0768814525
5838398754168030.63983153-328155.639831527
5940997714179778.21287202-80007.2128720209
6042460734123215.14918407122857.850815926
6143925964187498.03108903205097.968910968
6241815414095973.1696394285567.8303605784
6341815414219910.85135828-38369.8513582833
6441815414202287.89216729-20746.8921672935
6542949144381657.63558146-86743.6355814552
6641329214259625.03939941-126704.039399413
6739203194055854.6919637-135535.691963695
6837424143849085.04222229-106671.042222292
6938714784016465.64117416-144987.641174164
7033675983536567.33229299-168969.332292995
7136763353747452.11198609-71117.1119860904
7238557873802409.1692645153377.830735493
7338887163872897.8444180215818.1555819754
7437092643614084.5237929895179.4762070216
7537249553648983.400164775971.5998353022
7636763353671943.475427564391.52457244368
7738398753806670.8198605133204.1801394913
7837249553697045.7837312527909.2162687513
7934984303542288.85028962-43858.8502896186
8033346693383835.73255199-49166.7325519877
8136115823547235.3513875464346.6486124648
8230102413138898.26079122-128657.260791224
8334007483426335.93676547-25587.9367654696
8435786533576994.592097921658.40790208476
8535786533606046.31935138-27393.3193513756
8633675983377642.48610003-10044.4861000297
8731724553356447.78449689-183992.784496894
8831567643222649.10881351-65885.108813507
8933346693335367.6316028-698.631602795329
9031724553197308.66839222-24853.6683922214
9128639392965564.42971138-101625.429711375
9226513372766106.06446942-114769.064469421
9328796302954266.49596872-74636.4959687199
9423428212355038.40391745-12217.4039174509
9528307892734226.2238054596562.7761945478
9630904642937055.76578705153408.234212948
9731724553000766.77542992171688.224570083
9829930032859006.71283148133996.287168523
9927662572792156.24598837-25899.2459883699
10029284712796205.67278256132265.327217443
10129930033036721.25904739-43718.2590473858
10229441622874450.132347269711.8676528027
10324559732645447.13974032-189474.139740324
10422294482410329.125478-180881.125477997
10523914412601592.77472647-210151.774726468
10619034731987044.55905569-83571.5590556916
10724073532402622.37023214730.62976789987
10825868052600256.30244625-13451.3024462503
10927331072601062.84736524132044.152634756
11024891232413643.3264095475479.6735904631
11122608302219283.9665749941546.0334250089
11223914412337782.806151953658.1938481019
11324559732432787.1635281323185.8364718733
11423269092357838.36858519-30929.3685851926
11518389411924033.56351624-85092.5635162373
11616263391729184.81244317-102845.81244317
11718214821929563.38130681-108081.381306808
11812846731429219.74524379-144546.745243791
11918703231868555.798246011767.20175398653
12022294482050063.60358886179384.396411138







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212216484.876264262014718.177803012418251.57472552
1221939382.66378761719633.958060672159131.36951453
1231689752.229064731451391.521551471928112.93657798
1241793029.680216351535455.443017172050603.91741553
1251841176.589672671563811.913795712118541.26554963
1261717056.350099681419345.85051812014766.84968126
1271256795.66438427938202.962824431575388.36594411
1281081322.52128659741328.1763178971421316.86625528
1291318406.25949312956506.0462578921680306.47272835
130841145.581367057456849.0473176951225442.11541642
1311430816.834467611023646.075145741837987.59378948
1321721920.983806991291409.595756682152432.3718573

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2216484.87626426 & 2014718.17780301 & 2418251.57472552 \tabularnewline
122 & 1939382.6637876 & 1719633.95806067 & 2159131.36951453 \tabularnewline
123 & 1689752.22906473 & 1451391.52155147 & 1928112.93657798 \tabularnewline
124 & 1793029.68021635 & 1535455.44301717 & 2050603.91741553 \tabularnewline
125 & 1841176.58967267 & 1563811.91379571 & 2118541.26554963 \tabularnewline
126 & 1717056.35009968 & 1419345.8505181 & 2014766.84968126 \tabularnewline
127 & 1256795.66438427 & 938202.96282443 & 1575388.36594411 \tabularnewline
128 & 1081322.52128659 & 741328.176317897 & 1421316.86625528 \tabularnewline
129 & 1318406.25949312 & 956506.046257892 & 1680306.47272835 \tabularnewline
130 & 841145.581367057 & 456849.047317695 & 1225442.11541642 \tabularnewline
131 & 1430816.83446761 & 1023646.07514574 & 1837987.59378948 \tabularnewline
132 & 1721920.98380699 & 1291409.59575668 & 2152432.3718573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307384&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]2216484.87626426[/C][C]2014718.17780301[/C][C]2418251.57472552[/C][/ROW]
[ROW][C]122[/C][C]1939382.6637876[/C][C]1719633.95806067[/C][C]2159131.36951453[/C][/ROW]
[ROW][C]123[/C][C]1689752.22906473[/C][C]1451391.52155147[/C][C]1928112.93657798[/C][/ROW]
[ROW][C]124[/C][C]1793029.68021635[/C][C]1535455.44301717[/C][C]2050603.91741553[/C][/ROW]
[ROW][C]125[/C][C]1841176.58967267[/C][C]1563811.91379571[/C][C]2118541.26554963[/C][/ROW]
[ROW][C]126[/C][C]1717056.35009968[/C][C]1419345.8505181[/C][C]2014766.84968126[/C][/ROW]
[ROW][C]127[/C][C]1256795.66438427[/C][C]938202.96282443[/C][C]1575388.36594411[/C][/ROW]
[ROW][C]128[/C][C]1081322.52128659[/C][C]741328.176317897[/C][C]1421316.86625528[/C][/ROW]
[ROW][C]129[/C][C]1318406.25949312[/C][C]956506.046257892[/C][C]1680306.47272835[/C][/ROW]
[ROW][C]130[/C][C]841145.581367057[/C][C]456849.047317695[/C][C]1225442.11541642[/C][/ROW]
[ROW][C]131[/C][C]1430816.83446761[/C][C]1023646.07514574[/C][C]1837987.59378948[/C][/ROW]
[ROW][C]132[/C][C]1721920.98380699[/C][C]1291409.59575668[/C][C]2152432.3718573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307384&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307384&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
1212216484.876264262014718.177803012418251.57472552
1221939382.66378761719633.958060672159131.36951453
1231689752.229064731451391.521551471928112.93657798
1241793029.680216351535455.443017172050603.91741553
1251841176.589672671563811.913795712118541.26554963
1261717056.350099681419345.85051812014766.84968126
1271256795.66438427938202.962824431575388.36594411
1281081322.52128659741328.1763178971421316.86625528
1291318406.25949312956506.0462578921680306.47272835
130841145.581367057456849.0473176951225442.11541642
1311430816.834467611023646.075145741837987.59378948
1321721920.983806991291409.595756682152432.3718573



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')