Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 07 Aug 2017 17:19:53 +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/07/t1502119430oy2rcno3sd0c9js.htm/, Retrieved Sat, 11 May 2024 21:40:13 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 11 May 2024 21:40:13 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
3221816
3209817
3197649
3172468
3421574
3408392
3221816
3097770
3109769
3109769
3123120
3147118
3184467
3184467
3160469
3097770
3421574
3470922
3396393
3221816
3296514
3184467
3234998
3259165
3284346
3221816
3234998
3147118
3421574
3508271
3433742
3296514
3445741
3284346
3433742
3421574
3458923
3321695
3470922
3458923
3682848
3632317
3433742
3333694
3470922
3284346
3421574
3445741
3496272
3384394
3445741
3483090
3620318
3508271
3359044
3197649
3347045
2936375
3135119
3246997
3359044
3197649
3197649
3197649
3284346
3160469
2997891
2861846
2960542
2575222
2811315
2948543
2973724
2836496
2848495
2811315
2936375
2848495
2675270
2550041
2761798
2301949
2600572
2736617
2736617
2575222
2425995
2413996
2550041
2425995
2190071
2027493
2202070
1791569
2164721
2363296
2425995
2288767
2115373
2239419
2288767
2251418
1878097
1704872
1828749
1455597
1840917
1978145
2090023
1903447
1728870
1828749
1878097
1779401
1406249
1243671
1392898
982397
1430247
1704872




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.405343002238568
beta0.0645195510985084
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238568 \tabularnewline
beta & 0.0645195510985084 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.405343002238568[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510985084[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.405343002238568
beta0.0645195510985084
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1331844673184328.51388889138.486111110076
1431844673177339.561696357127.43830365408
1531604693148864.9330442711604.0669557308
1630977703085863.5170809811906.4829190169
1734215743412918.526518068655.47348194243
1834709223462869.916386698052.08361331141
1933963933276546.43390204119846.566097964
2032218163213461.897385968354.10261404235
2132965143241441.1104018355072.889598167
2231844673279854.91988021-95387.9198802128
2332349983266587.68925341-31589.6892534066
2432591653283283.64075131-24118.6407513134
2532843463308536.47562423-24190.4756242288
2632218163297289.06107258-75473.0610725791
2732349983237281.82570519-2283.82570519252
2831471183167754.54875168-20636.5487516765
2934215743477757.81464919-56183.814649194
3035082713497445.1122968210825.8877031845
3134337423375174.7547571458567.2452428569
3232965143215798.101875680715.8981243973
3334457413297629.56244143148111.43755857
3432843463283455.76467433890.235325671732
3534337423348842.6355890784899.3644109275
3634215743421936.16750393-362.167503932491
3734589233462133.94417989-3210.94417988556
3833216953434801.69452805-113106.694528047
3934709223407985.0116755862936.9883244191
4034589233360609.2421196698313.7578803403
4136828483707428.88769399-24580.8876939882
4236323173790339.63182292-158022.631822919
4334337423634167.25446288-200425.254462885
4433336943382357.1553632-48663.1553631974
4534709223447815.8588697823106.1411302174
4632843463288149.62150854-3803.62150854478
4734215743394191.431252227382.5687478036
4834457413384366.2995138261374.7004861846
4934962723440605.9486344555666.0513655534
5033843943366039.8936453818354.1063546152
5134457413494884.66289057-49143.6628905716
5234830903417872.7630523165217.2369476859
5336203183672089.17991897-51771.1799189686
5435082713657807.74241755-149536.742417552
5533590443473263.25229572-114219.252295715
5631976493342300.26143288-144651.261432878
5733470453404676.35290928-57631.3529092767
5829363753187317.54810638-250942.548106382
5931351193196300.98631378-61181.9863137794
6032469973153046.878787793950.1212123027
6133590443202204.37671504156839.623284957
6231976493132214.7767830365434.2232169709
6331976493226990.65103865-29341.6510386541
6431976493213514.27048083-15865.2704808293
6532843463350679.36838579-66333.3683857857
6631604693257360.32424659-96891.32424659
6729978913101535.94091339-103644.940913393
6828618462943417.97346407-81571.9734640745
6929605423071414.90207431-110872.902074305
7025752222704433.84234164-129211.84234164
7128113152865698.67387162-54383.6738716206
7229485432907724.658849240818.341150796
7329737242961627.7633783612096.2366216434
7428364962763711.694665172784.3053349028
7528484952790399.0707140958095.9292859086
7628113152807956.775326893358.22467311425
7729363752910983.5681285725391.4318714272
7828484952827152.658147421342.3418526007
7926752702708809.1208097-33539.120809705
8025500412587639.08959858-37598.0895985807
8127617982712591.7392963549206.2607036503
8223019492400333.96413448-98384.9641344789
8326005722620139.24576182-19567.2457618159
8427366172735348.805721891268.19427810749
8527366172757564.83244511-20947.8324451065
8625752222582903.07760582-7681.07760582259
8724259952566695.36461519-140700.364615188
8824139962464378.73026906-50382.7302690567
8925500412550575.24769616-534.24769616453
9024259952445000.74641751-19005.7464175075
9121900712267784.56389688-77713.5638968819
9220274932115257.57871187-87764.5787118673
9322020702259144.96750544-57074.9675054424
9417915691800911.72064272-9342.72064272175
9521647212090878.8770276673842.1229723357
9623632962245983.82089595117312.179104053
9724259952294704.0047405131290.995259505
9822887672186299.25098875102467.749011251
9921153732135178.3057558-19805.305755802
10022394192138274.92624546101144.073754536
10122887672322198.60985975-33431.6098597543
10222514182198108.9247360853309.0752639216
10318780972022988.9892132-144891.989213199
10417048721843192.86065965-138320.860659648
10518287491989453.29832023-160704.298320231
10614555971519504.66280727-63907.6628072688
10718409171837299.459589223617.54041078244
10819781451988431.29010591-10286.2901059131
10920900231989048.05974984100974.940250163
11019034471845727.2496072457719.7503927571
11117288701697099.5038514331770.4961485709
11218287491787716.2635278841032.7364721179
11318780971860366.6544626617730.3455373435
11417794011803052.87009453-23651.8700945294
11514062491471319.78386535-65070.783865348
11612436711322317.79775066-78646.7977506588
11713928981475548.46805815-82650.4680581517
1189823971092932.7463629-110535.746362895
11914302471428895.61042341351.38957660343
12017048721567695.69686204137176.303137959

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3184467 & 3184328.51388889 & 138.486111110076 \tabularnewline
14 & 3184467 & 3177339.56169635 & 7127.43830365408 \tabularnewline
15 & 3160469 & 3148864.93304427 & 11604.0669557308 \tabularnewline
16 & 3097770 & 3085863.51708098 & 11906.4829190169 \tabularnewline
17 & 3421574 & 3412918.52651806 & 8655.47348194243 \tabularnewline
18 & 3470922 & 3462869.91638669 & 8052.08361331141 \tabularnewline
19 & 3396393 & 3276546.43390204 & 119846.566097964 \tabularnewline
20 & 3221816 & 3213461.89738596 & 8354.10261404235 \tabularnewline
21 & 3296514 & 3241441.11040183 & 55072.889598167 \tabularnewline
22 & 3184467 & 3279854.91988021 & -95387.9198802128 \tabularnewline
23 & 3234998 & 3266587.68925341 & -31589.6892534066 \tabularnewline
24 & 3259165 & 3283283.64075131 & -24118.6407513134 \tabularnewline
25 & 3284346 & 3308536.47562423 & -24190.4756242288 \tabularnewline
26 & 3221816 & 3297289.06107258 & -75473.0610725791 \tabularnewline
27 & 3234998 & 3237281.82570519 & -2283.82570519252 \tabularnewline
28 & 3147118 & 3167754.54875168 & -20636.5487516765 \tabularnewline
29 & 3421574 & 3477757.81464919 & -56183.814649194 \tabularnewline
30 & 3508271 & 3497445.11229682 & 10825.8877031845 \tabularnewline
31 & 3433742 & 3375174.75475714 & 58567.2452428569 \tabularnewline
32 & 3296514 & 3215798.1018756 & 80715.8981243973 \tabularnewline
33 & 3445741 & 3297629.56244143 & 148111.43755857 \tabularnewline
34 & 3284346 & 3283455.76467433 & 890.235325671732 \tabularnewline
35 & 3433742 & 3348842.63558907 & 84899.3644109275 \tabularnewline
36 & 3421574 & 3421936.16750393 & -362.167503932491 \tabularnewline
37 & 3458923 & 3462133.94417989 & -3210.94417988556 \tabularnewline
38 & 3321695 & 3434801.69452805 & -113106.694528047 \tabularnewline
39 & 3470922 & 3407985.01167558 & 62936.9883244191 \tabularnewline
40 & 3458923 & 3360609.24211966 & 98313.7578803403 \tabularnewline
41 & 3682848 & 3707428.88769399 & -24580.8876939882 \tabularnewline
42 & 3632317 & 3790339.63182292 & -158022.631822919 \tabularnewline
43 & 3433742 & 3634167.25446288 & -200425.254462885 \tabularnewline
44 & 3333694 & 3382357.1553632 & -48663.1553631974 \tabularnewline
45 & 3470922 & 3447815.85886978 & 23106.1411302174 \tabularnewline
46 & 3284346 & 3288149.62150854 & -3803.62150854478 \tabularnewline
47 & 3421574 & 3394191.4312522 & 27382.5687478036 \tabularnewline
48 & 3445741 & 3384366.29951382 & 61374.7004861846 \tabularnewline
49 & 3496272 & 3440605.94863445 & 55666.0513655534 \tabularnewline
50 & 3384394 & 3366039.89364538 & 18354.1063546152 \tabularnewline
51 & 3445741 & 3494884.66289057 & -49143.6628905716 \tabularnewline
52 & 3483090 & 3417872.76305231 & 65217.2369476859 \tabularnewline
53 & 3620318 & 3672089.17991897 & -51771.1799189686 \tabularnewline
54 & 3508271 & 3657807.74241755 & -149536.742417552 \tabularnewline
55 & 3359044 & 3473263.25229572 & -114219.252295715 \tabularnewline
56 & 3197649 & 3342300.26143288 & -144651.261432878 \tabularnewline
57 & 3347045 & 3404676.35290928 & -57631.3529092767 \tabularnewline
58 & 2936375 & 3187317.54810638 & -250942.548106382 \tabularnewline
59 & 3135119 & 3196300.98631378 & -61181.9863137794 \tabularnewline
60 & 3246997 & 3153046.8787877 & 93950.1212123027 \tabularnewline
61 & 3359044 & 3202204.37671504 & 156839.623284957 \tabularnewline
62 & 3197649 & 3132214.77678303 & 65434.2232169709 \tabularnewline
63 & 3197649 & 3226990.65103865 & -29341.6510386541 \tabularnewline
64 & 3197649 & 3213514.27048083 & -15865.2704808293 \tabularnewline
65 & 3284346 & 3350679.36838579 & -66333.3683857857 \tabularnewline
66 & 3160469 & 3257360.32424659 & -96891.32424659 \tabularnewline
67 & 2997891 & 3101535.94091339 & -103644.940913393 \tabularnewline
68 & 2861846 & 2943417.97346407 & -81571.9734640745 \tabularnewline
69 & 2960542 & 3071414.90207431 & -110872.902074305 \tabularnewline
70 & 2575222 & 2704433.84234164 & -129211.84234164 \tabularnewline
71 & 2811315 & 2865698.67387162 & -54383.6738716206 \tabularnewline
72 & 2948543 & 2907724.6588492 & 40818.341150796 \tabularnewline
73 & 2973724 & 2961627.76337836 & 12096.2366216434 \tabularnewline
74 & 2836496 & 2763711.6946651 & 72784.3053349028 \tabularnewline
75 & 2848495 & 2790399.07071409 & 58095.9292859086 \tabularnewline
76 & 2811315 & 2807956.77532689 & 3358.22467311425 \tabularnewline
77 & 2936375 & 2910983.56812857 & 25391.4318714272 \tabularnewline
78 & 2848495 & 2827152.6581474 & 21342.3418526007 \tabularnewline
79 & 2675270 & 2708809.1208097 & -33539.120809705 \tabularnewline
80 & 2550041 & 2587639.08959858 & -37598.0895985807 \tabularnewline
81 & 2761798 & 2712591.73929635 & 49206.2607036503 \tabularnewline
82 & 2301949 & 2400333.96413448 & -98384.9641344789 \tabularnewline
83 & 2600572 & 2620139.24576182 & -19567.2457618159 \tabularnewline
84 & 2736617 & 2735348.80572189 & 1268.19427810749 \tabularnewline
85 & 2736617 & 2757564.83244511 & -20947.8324451065 \tabularnewline
86 & 2575222 & 2582903.07760582 & -7681.07760582259 \tabularnewline
87 & 2425995 & 2566695.36461519 & -140700.364615188 \tabularnewline
88 & 2413996 & 2464378.73026906 & -50382.7302690567 \tabularnewline
89 & 2550041 & 2550575.24769616 & -534.24769616453 \tabularnewline
90 & 2425995 & 2445000.74641751 & -19005.7464175075 \tabularnewline
91 & 2190071 & 2267784.56389688 & -77713.5638968819 \tabularnewline
92 & 2027493 & 2115257.57871187 & -87764.5787118673 \tabularnewline
93 & 2202070 & 2259144.96750544 & -57074.9675054424 \tabularnewline
94 & 1791569 & 1800911.72064272 & -9342.72064272175 \tabularnewline
95 & 2164721 & 2090878.87702766 & 73842.1229723357 \tabularnewline
96 & 2363296 & 2245983.82089595 & 117312.179104053 \tabularnewline
97 & 2425995 & 2294704.0047405 & 131290.995259505 \tabularnewline
98 & 2288767 & 2186299.25098875 & 102467.749011251 \tabularnewline
99 & 2115373 & 2135178.3057558 & -19805.305755802 \tabularnewline
100 & 2239419 & 2138274.92624546 & 101144.073754536 \tabularnewline
101 & 2288767 & 2322198.60985975 & -33431.6098597543 \tabularnewline
102 & 2251418 & 2198108.92473608 & 53309.0752639216 \tabularnewline
103 & 1878097 & 2022988.9892132 & -144891.989213199 \tabularnewline
104 & 1704872 & 1843192.86065965 & -138320.860659648 \tabularnewline
105 & 1828749 & 1989453.29832023 & -160704.298320231 \tabularnewline
106 & 1455597 & 1519504.66280727 & -63907.6628072688 \tabularnewline
107 & 1840917 & 1837299.45958922 & 3617.54041078244 \tabularnewline
108 & 1978145 & 1988431.29010591 & -10286.2901059131 \tabularnewline
109 & 2090023 & 1989048.05974984 & 100974.940250163 \tabularnewline
110 & 1903447 & 1845727.24960724 & 57719.7503927571 \tabularnewline
111 & 1728870 & 1697099.50385143 & 31770.4961485709 \tabularnewline
112 & 1828749 & 1787716.26352788 & 41032.7364721179 \tabularnewline
113 & 1878097 & 1860366.65446266 & 17730.3455373435 \tabularnewline
114 & 1779401 & 1803052.87009453 & -23651.8700945294 \tabularnewline
115 & 1406249 & 1471319.78386535 & -65070.783865348 \tabularnewline
116 & 1243671 & 1322317.79775066 & -78646.7977506588 \tabularnewline
117 & 1392898 & 1475548.46805815 & -82650.4680581517 \tabularnewline
118 & 982397 & 1092932.7463629 & -110535.746362895 \tabularnewline
119 & 1430247 & 1428895.6104234 & 1351.38957660343 \tabularnewline
120 & 1704872 & 1567695.69686204 & 137176.303137959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]3184467[/C][C]3184328.51388889[/C][C]138.486111110076[/C][/ROW]
[ROW][C]14[/C][C]3184467[/C][C]3177339.56169635[/C][C]7127.43830365408[/C][/ROW]
[ROW][C]15[/C][C]3160469[/C][C]3148864.93304427[/C][C]11604.0669557308[/C][/ROW]
[ROW][C]16[/C][C]3097770[/C][C]3085863.51708098[/C][C]11906.4829190169[/C][/ROW]
[ROW][C]17[/C][C]3421574[/C][C]3412918.52651806[/C][C]8655.47348194243[/C][/ROW]
[ROW][C]18[/C][C]3470922[/C][C]3462869.91638669[/C][C]8052.08361331141[/C][/ROW]
[ROW][C]19[/C][C]3396393[/C][C]3276546.43390204[/C][C]119846.566097964[/C][/ROW]
[ROW][C]20[/C][C]3221816[/C][C]3213461.89738596[/C][C]8354.10261404235[/C][/ROW]
[ROW][C]21[/C][C]3296514[/C][C]3241441.11040183[/C][C]55072.889598167[/C][/ROW]
[ROW][C]22[/C][C]3184467[/C][C]3279854.91988021[/C][C]-95387.9198802128[/C][/ROW]
[ROW][C]23[/C][C]3234998[/C][C]3266587.68925341[/C][C]-31589.6892534066[/C][/ROW]
[ROW][C]24[/C][C]3259165[/C][C]3283283.64075131[/C][C]-24118.6407513134[/C][/ROW]
[ROW][C]25[/C][C]3284346[/C][C]3308536.47562423[/C][C]-24190.4756242288[/C][/ROW]
[ROW][C]26[/C][C]3221816[/C][C]3297289.06107258[/C][C]-75473.0610725791[/C][/ROW]
[ROW][C]27[/C][C]3234998[/C][C]3237281.82570519[/C][C]-2283.82570519252[/C][/ROW]
[ROW][C]28[/C][C]3147118[/C][C]3167754.54875168[/C][C]-20636.5487516765[/C][/ROW]
[ROW][C]29[/C][C]3421574[/C][C]3477757.81464919[/C][C]-56183.814649194[/C][/ROW]
[ROW][C]30[/C][C]3508271[/C][C]3497445.11229682[/C][C]10825.8877031845[/C][/ROW]
[ROW][C]31[/C][C]3433742[/C][C]3375174.75475714[/C][C]58567.2452428569[/C][/ROW]
[ROW][C]32[/C][C]3296514[/C][C]3215798.1018756[/C][C]80715.8981243973[/C][/ROW]
[ROW][C]33[/C][C]3445741[/C][C]3297629.56244143[/C][C]148111.43755857[/C][/ROW]
[ROW][C]34[/C][C]3284346[/C][C]3283455.76467433[/C][C]890.235325671732[/C][/ROW]
[ROW][C]35[/C][C]3433742[/C][C]3348842.63558907[/C][C]84899.3644109275[/C][/ROW]
[ROW][C]36[/C][C]3421574[/C][C]3421936.16750393[/C][C]-362.167503932491[/C][/ROW]
[ROW][C]37[/C][C]3458923[/C][C]3462133.94417989[/C][C]-3210.94417988556[/C][/ROW]
[ROW][C]38[/C][C]3321695[/C][C]3434801.69452805[/C][C]-113106.694528047[/C][/ROW]
[ROW][C]39[/C][C]3470922[/C][C]3407985.01167558[/C][C]62936.9883244191[/C][/ROW]
[ROW][C]40[/C][C]3458923[/C][C]3360609.24211966[/C][C]98313.7578803403[/C][/ROW]
[ROW][C]41[/C][C]3682848[/C][C]3707428.88769399[/C][C]-24580.8876939882[/C][/ROW]
[ROW][C]42[/C][C]3632317[/C][C]3790339.63182292[/C][C]-158022.631822919[/C][/ROW]
[ROW][C]43[/C][C]3433742[/C][C]3634167.25446288[/C][C]-200425.254462885[/C][/ROW]
[ROW][C]44[/C][C]3333694[/C][C]3382357.1553632[/C][C]-48663.1553631974[/C][/ROW]
[ROW][C]45[/C][C]3470922[/C][C]3447815.85886978[/C][C]23106.1411302174[/C][/ROW]
[ROW][C]46[/C][C]3284346[/C][C]3288149.62150854[/C][C]-3803.62150854478[/C][/ROW]
[ROW][C]47[/C][C]3421574[/C][C]3394191.4312522[/C][C]27382.5687478036[/C][/ROW]
[ROW][C]48[/C][C]3445741[/C][C]3384366.29951382[/C][C]61374.7004861846[/C][/ROW]
[ROW][C]49[/C][C]3496272[/C][C]3440605.94863445[/C][C]55666.0513655534[/C][/ROW]
[ROW][C]50[/C][C]3384394[/C][C]3366039.89364538[/C][C]18354.1063546152[/C][/ROW]
[ROW][C]51[/C][C]3445741[/C][C]3494884.66289057[/C][C]-49143.6628905716[/C][/ROW]
[ROW][C]52[/C][C]3483090[/C][C]3417872.76305231[/C][C]65217.2369476859[/C][/ROW]
[ROW][C]53[/C][C]3620318[/C][C]3672089.17991897[/C][C]-51771.1799189686[/C][/ROW]
[ROW][C]54[/C][C]3508271[/C][C]3657807.74241755[/C][C]-149536.742417552[/C][/ROW]
[ROW][C]55[/C][C]3359044[/C][C]3473263.25229572[/C][C]-114219.252295715[/C][/ROW]
[ROW][C]56[/C][C]3197649[/C][C]3342300.26143288[/C][C]-144651.261432878[/C][/ROW]
[ROW][C]57[/C][C]3347045[/C][C]3404676.35290928[/C][C]-57631.3529092767[/C][/ROW]
[ROW][C]58[/C][C]2936375[/C][C]3187317.54810638[/C][C]-250942.548106382[/C][/ROW]
[ROW][C]59[/C][C]3135119[/C][C]3196300.98631378[/C][C]-61181.9863137794[/C][/ROW]
[ROW][C]60[/C][C]3246997[/C][C]3153046.8787877[/C][C]93950.1212123027[/C][/ROW]
[ROW][C]61[/C][C]3359044[/C][C]3202204.37671504[/C][C]156839.623284957[/C][/ROW]
[ROW][C]62[/C][C]3197649[/C][C]3132214.77678303[/C][C]65434.2232169709[/C][/ROW]
[ROW][C]63[/C][C]3197649[/C][C]3226990.65103865[/C][C]-29341.6510386541[/C][/ROW]
[ROW][C]64[/C][C]3197649[/C][C]3213514.27048083[/C][C]-15865.2704808293[/C][/ROW]
[ROW][C]65[/C][C]3284346[/C][C]3350679.36838579[/C][C]-66333.3683857857[/C][/ROW]
[ROW][C]66[/C][C]3160469[/C][C]3257360.32424659[/C][C]-96891.32424659[/C][/ROW]
[ROW][C]67[/C][C]2997891[/C][C]3101535.94091339[/C][C]-103644.940913393[/C][/ROW]
[ROW][C]68[/C][C]2861846[/C][C]2943417.97346407[/C][C]-81571.9734640745[/C][/ROW]
[ROW][C]69[/C][C]2960542[/C][C]3071414.90207431[/C][C]-110872.902074305[/C][/ROW]
[ROW][C]70[/C][C]2575222[/C][C]2704433.84234164[/C][C]-129211.84234164[/C][/ROW]
[ROW][C]71[/C][C]2811315[/C][C]2865698.67387162[/C][C]-54383.6738716206[/C][/ROW]
[ROW][C]72[/C][C]2948543[/C][C]2907724.6588492[/C][C]40818.341150796[/C][/ROW]
[ROW][C]73[/C][C]2973724[/C][C]2961627.76337836[/C][C]12096.2366216434[/C][/ROW]
[ROW][C]74[/C][C]2836496[/C][C]2763711.6946651[/C][C]72784.3053349028[/C][/ROW]
[ROW][C]75[/C][C]2848495[/C][C]2790399.07071409[/C][C]58095.9292859086[/C][/ROW]
[ROW][C]76[/C][C]2811315[/C][C]2807956.77532689[/C][C]3358.22467311425[/C][/ROW]
[ROW][C]77[/C][C]2936375[/C][C]2910983.56812857[/C][C]25391.4318714272[/C][/ROW]
[ROW][C]78[/C][C]2848495[/C][C]2827152.6581474[/C][C]21342.3418526007[/C][/ROW]
[ROW][C]79[/C][C]2675270[/C][C]2708809.1208097[/C][C]-33539.120809705[/C][/ROW]
[ROW][C]80[/C][C]2550041[/C][C]2587639.08959858[/C][C]-37598.0895985807[/C][/ROW]
[ROW][C]81[/C][C]2761798[/C][C]2712591.73929635[/C][C]49206.2607036503[/C][/ROW]
[ROW][C]82[/C][C]2301949[/C][C]2400333.96413448[/C][C]-98384.9641344789[/C][/ROW]
[ROW][C]83[/C][C]2600572[/C][C]2620139.24576182[/C][C]-19567.2457618159[/C][/ROW]
[ROW][C]84[/C][C]2736617[/C][C]2735348.80572189[/C][C]1268.19427810749[/C][/ROW]
[ROW][C]85[/C][C]2736617[/C][C]2757564.83244511[/C][C]-20947.8324451065[/C][/ROW]
[ROW][C]86[/C][C]2575222[/C][C]2582903.07760582[/C][C]-7681.07760582259[/C][/ROW]
[ROW][C]87[/C][C]2425995[/C][C]2566695.36461519[/C][C]-140700.364615188[/C][/ROW]
[ROW][C]88[/C][C]2413996[/C][C]2464378.73026906[/C][C]-50382.7302690567[/C][/ROW]
[ROW][C]89[/C][C]2550041[/C][C]2550575.24769616[/C][C]-534.24769616453[/C][/ROW]
[ROW][C]90[/C][C]2425995[/C][C]2445000.74641751[/C][C]-19005.7464175075[/C][/ROW]
[ROW][C]91[/C][C]2190071[/C][C]2267784.56389688[/C][C]-77713.5638968819[/C][/ROW]
[ROW][C]92[/C][C]2027493[/C][C]2115257.57871187[/C][C]-87764.5787118673[/C][/ROW]
[ROW][C]93[/C][C]2202070[/C][C]2259144.96750544[/C][C]-57074.9675054424[/C][/ROW]
[ROW][C]94[/C][C]1791569[/C][C]1800911.72064272[/C][C]-9342.72064272175[/C][/ROW]
[ROW][C]95[/C][C]2164721[/C][C]2090878.87702766[/C][C]73842.1229723357[/C][/ROW]
[ROW][C]96[/C][C]2363296[/C][C]2245983.82089595[/C][C]117312.179104053[/C][/ROW]
[ROW][C]97[/C][C]2425995[/C][C]2294704.0047405[/C][C]131290.995259505[/C][/ROW]
[ROW][C]98[/C][C]2288767[/C][C]2186299.25098875[/C][C]102467.749011251[/C][/ROW]
[ROW][C]99[/C][C]2115373[/C][C]2135178.3057558[/C][C]-19805.305755802[/C][/ROW]
[ROW][C]100[/C][C]2239419[/C][C]2138274.92624546[/C][C]101144.073754536[/C][/ROW]
[ROW][C]101[/C][C]2288767[/C][C]2322198.60985975[/C][C]-33431.6098597543[/C][/ROW]
[ROW][C]102[/C][C]2251418[/C][C]2198108.92473608[/C][C]53309.0752639216[/C][/ROW]
[ROW][C]103[/C][C]1878097[/C][C]2022988.9892132[/C][C]-144891.989213199[/C][/ROW]
[ROW][C]104[/C][C]1704872[/C][C]1843192.86065965[/C][C]-138320.860659648[/C][/ROW]
[ROW][C]105[/C][C]1828749[/C][C]1989453.29832023[/C][C]-160704.298320231[/C][/ROW]
[ROW][C]106[/C][C]1455597[/C][C]1519504.66280727[/C][C]-63907.6628072688[/C][/ROW]
[ROW][C]107[/C][C]1840917[/C][C]1837299.45958922[/C][C]3617.54041078244[/C][/ROW]
[ROW][C]108[/C][C]1978145[/C][C]1988431.29010591[/C][C]-10286.2901059131[/C][/ROW]
[ROW][C]109[/C][C]2090023[/C][C]1989048.05974984[/C][C]100974.940250163[/C][/ROW]
[ROW][C]110[/C][C]1903447[/C][C]1845727.24960724[/C][C]57719.7503927571[/C][/ROW]
[ROW][C]111[/C][C]1728870[/C][C]1697099.50385143[/C][C]31770.4961485709[/C][/ROW]
[ROW][C]112[/C][C]1828749[/C][C]1787716.26352788[/C][C]41032.7364721179[/C][/ROW]
[ROW][C]113[/C][C]1878097[/C][C]1860366.65446266[/C][C]17730.3455373435[/C][/ROW]
[ROW][C]114[/C][C]1779401[/C][C]1803052.87009453[/C][C]-23651.8700945294[/C][/ROW]
[ROW][C]115[/C][C]1406249[/C][C]1471319.78386535[/C][C]-65070.783865348[/C][/ROW]
[ROW][C]116[/C][C]1243671[/C][C]1322317.79775066[/C][C]-78646.7977506588[/C][/ROW]
[ROW][C]117[/C][C]1392898[/C][C]1475548.46805815[/C][C]-82650.4680581517[/C][/ROW]
[ROW][C]118[/C][C]982397[/C][C]1092932.7463629[/C][C]-110535.746362895[/C][/ROW]
[ROW][C]119[/C][C]1430247[/C][C]1428895.6104234[/C][C]1351.38957660343[/C][/ROW]
[ROW][C]120[/C][C]1704872[/C][C]1567695.69686204[/C][C]137176.303137959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1331844673184328.51388889138.486111110076
1431844673177339.561696357127.43830365408
1531604693148864.9330442711604.0669557308
1630977703085863.5170809811906.4829190169
1734215743412918.526518068655.47348194243
1834709223462869.916386698052.08361331141
1933963933276546.43390204119846.566097964
2032218163213461.897385968354.10261404235
2132965143241441.1104018355072.889598167
2231844673279854.91988021-95387.9198802128
2332349983266587.68925341-31589.6892534066
2432591653283283.64075131-24118.6407513134
2532843463308536.47562423-24190.4756242288
2632218163297289.06107258-75473.0610725791
2732349983237281.82570519-2283.82570519252
2831471183167754.54875168-20636.5487516765
2934215743477757.81464919-56183.814649194
3035082713497445.1122968210825.8877031845
3134337423375174.7547571458567.2452428569
3232965143215798.101875680715.8981243973
3334457413297629.56244143148111.43755857
3432843463283455.76467433890.235325671732
3534337423348842.6355890784899.3644109275
3634215743421936.16750393-362.167503932491
3734589233462133.94417989-3210.94417988556
3833216953434801.69452805-113106.694528047
3934709223407985.0116755862936.9883244191
4034589233360609.2421196698313.7578803403
4136828483707428.88769399-24580.8876939882
4236323173790339.63182292-158022.631822919
4334337423634167.25446288-200425.254462885
4433336943382357.1553632-48663.1553631974
4534709223447815.8588697823106.1411302174
4632843463288149.62150854-3803.62150854478
4734215743394191.431252227382.5687478036
4834457413384366.2995138261374.7004861846
4934962723440605.9486344555666.0513655534
5033843943366039.8936453818354.1063546152
5134457413494884.66289057-49143.6628905716
5234830903417872.7630523165217.2369476859
5336203183672089.17991897-51771.1799189686
5435082713657807.74241755-149536.742417552
5533590443473263.25229572-114219.252295715
5631976493342300.26143288-144651.261432878
5733470453404676.35290928-57631.3529092767
5829363753187317.54810638-250942.548106382
5931351193196300.98631378-61181.9863137794
6032469973153046.878787793950.1212123027
6133590443202204.37671504156839.623284957
6231976493132214.7767830365434.2232169709
6331976493226990.65103865-29341.6510386541
6431976493213514.27048083-15865.2704808293
6532843463350679.36838579-66333.3683857857
6631604693257360.32424659-96891.32424659
6729978913101535.94091339-103644.940913393
6828618462943417.97346407-81571.9734640745
6929605423071414.90207431-110872.902074305
7025752222704433.84234164-129211.84234164
7128113152865698.67387162-54383.6738716206
7229485432907724.658849240818.341150796
7329737242961627.7633783612096.2366216434
7428364962763711.694665172784.3053349028
7528484952790399.0707140958095.9292859086
7628113152807956.775326893358.22467311425
7729363752910983.5681285725391.4318714272
7828484952827152.658147421342.3418526007
7926752702708809.1208097-33539.120809705
8025500412587639.08959858-37598.0895985807
8127617982712591.7392963549206.2607036503
8223019492400333.96413448-98384.9641344789
8326005722620139.24576182-19567.2457618159
8427366172735348.805721891268.19427810749
8527366172757564.83244511-20947.8324451065
8625752222582903.07760582-7681.07760582259
8724259952566695.36461519-140700.364615188
8824139962464378.73026906-50382.7302690567
8925500412550575.24769616-534.24769616453
9024259952445000.74641751-19005.7464175075
9121900712267784.56389688-77713.5638968819
9220274932115257.57871187-87764.5787118673
9322020702259144.96750544-57074.9675054424
9417915691800911.72064272-9342.72064272175
9521647212090878.8770276673842.1229723357
9623632962245983.82089595117312.179104053
9724259952294704.0047405131290.995259505
9822887672186299.25098875102467.749011251
9921153732135178.3057558-19805.305755802
10022394192138274.92624546101144.073754536
10122887672322198.60985975-33431.6098597543
10222514182198108.9247360853309.0752639216
10318780972022988.9892132-144891.989213199
10417048721843192.86065965-138320.860659648
10518287491989453.29832023-160704.298320231
10614555971519504.66280727-63907.6628072688
10718409171837299.459589223617.54041078244
10819781451988431.29010591-10286.2901059131
10920900231989048.05974984100974.940250163
11019034471845727.2496072457719.7503927571
11117288701697099.5038514331770.4961485709
11218287491787716.2635278841032.7364721179
11318780971860366.6544626617730.3455373435
11417794011803052.87009453-23651.8700945294
11514062491471319.78386535-65070.783865348
11612436711322317.79775066-78646.7977506588
11713928981475548.46805815-82650.4680581517
1189823971092932.7463629-110535.746362895
11914302471428895.61042341351.38957660343
12017048721567695.69686204137176.303137959







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1211694959.023025581540666.841849321849251.20420185
1221483057.331131641315014.20322281651100.45904049
1231292163.469284721109887.63412751474439.30444194
1241371140.343694761174171.809365931568108.87802359
1251407958.56857311195856.169373011620060.96777319
1261313043.091252561085382.120984211540704.06152091
127961079.037470176717449.324512551204708.7504278
128826893.692748421566898.0171840041086889.36831284
1291008193.02196519731445.8000792781284940.2438511
130643228.973986447349355.153830878937102.794142016
1311094154.04988687782788.1751111171405519.92466262
1321316763.10526403987548.5144017961645977.69612626

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 1694959.02302558 & 1540666.84184932 & 1849251.20420185 \tabularnewline
122 & 1483057.33113164 & 1315014.2032228 & 1651100.45904049 \tabularnewline
123 & 1292163.46928472 & 1109887.6341275 & 1474439.30444194 \tabularnewline
124 & 1371140.34369476 & 1174171.80936593 & 1568108.87802359 \tabularnewline
125 & 1407958.5685731 & 1195856.16937301 & 1620060.96777319 \tabularnewline
126 & 1313043.09125256 & 1085382.12098421 & 1540704.06152091 \tabularnewline
127 & 961079.037470176 & 717449.32451255 & 1204708.7504278 \tabularnewline
128 & 826893.692748421 & 566898.017184004 & 1086889.36831284 \tabularnewline
129 & 1008193.02196519 & 731445.800079278 & 1284940.2438511 \tabularnewline
130 & 643228.973986447 & 349355.153830878 & 937102.794142016 \tabularnewline
131 & 1094154.04988687 & 782788.175111117 & 1405519.92466262 \tabularnewline
132 & 1316763.10526403 & 987548.514401796 & 1645977.69612626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1694959.02302558[/C][C]1540666.84184932[/C][C]1849251.20420185[/C][/ROW]
[ROW][C]122[/C][C]1483057.33113164[/C][C]1315014.2032228[/C][C]1651100.45904049[/C][/ROW]
[ROW][C]123[/C][C]1292163.46928472[/C][C]1109887.6341275[/C][C]1474439.30444194[/C][/ROW]
[ROW][C]124[/C][C]1371140.34369476[/C][C]1174171.80936593[/C][C]1568108.87802359[/C][/ROW]
[ROW][C]125[/C][C]1407958.5685731[/C][C]1195856.16937301[/C][C]1620060.96777319[/C][/ROW]
[ROW][C]126[/C][C]1313043.09125256[/C][C]1085382.12098421[/C][C]1540704.06152091[/C][/ROW]
[ROW][C]127[/C][C]961079.037470176[/C][C]717449.32451255[/C][C]1204708.7504278[/C][/ROW]
[ROW][C]128[/C][C]826893.692748421[/C][C]566898.017184004[/C][C]1086889.36831284[/C][/ROW]
[ROW][C]129[/C][C]1008193.02196519[/C][C]731445.800079278[/C][C]1284940.2438511[/C][/ROW]
[ROW][C]130[/C][C]643228.973986447[/C][C]349355.153830878[/C][C]937102.794142016[/C][/ROW]
[ROW][C]131[/C][C]1094154.04988687[/C][C]782788.175111117[/C][C]1405519.92466262[/C][/ROW]
[ROW][C]132[/C][C]1316763.10526403[/C][C]987548.514401796[/C][C]1645977.69612626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1211694959.023025581540666.841849321849251.20420185
1221483057.331131641315014.20322281651100.45904049
1231292163.469284721109887.63412751474439.30444194
1241371140.343694761174171.809365931568108.87802359
1251407958.56857311195856.169373011620060.96777319
1261313043.091252561085382.120984211540704.06152091
127961079.037470176717449.324512551204708.7504278
128826893.692748421566898.0171840041086889.36831284
1291008193.02196519731445.8000792781284940.2438511
130643228.973986447349355.153830878937102.794142016
1311094154.04988687782788.1751111171405519.92466262
1321316763.10526403987548.5144017961645977.69612626



Parameters (Session):
par1 = 12greygrey0.010.10,010,010,010,10,10,10,010,010,010,010,112DefaultDefaultDefault486060121212additive12 ; par2 = nono0.990.90,990,990,990,990,990,990,990,990,990,990,99grey11111112Triple ; par3 = 0.010.10,010,010,010,10,10,10,010,10,10,10,1FALSE000001additive ; par4 = Unknown00000012 ; par5 = 121212121212 ; par6 = White NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite Noise ; par7 = 0.950.950.950.950.950.95 ; par8 = 480 ;
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')