Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Dec 2016 02:50:19 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/20/t1482198803akelxyije2lupzm.htm/, Retrieved Sun, 28 Apr 2024 03:22:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301553, Retrieved Sun, 28 Apr 2024 03:22:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [triple exponentia...] [2016-12-20 01:50:19] [9b0b4f5f4290a2ed9efd388f9ce31ae7] [Current]
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Dataseries X:
2312
1089
2742
3145
2966
2055
2450
2742
1697
2409
2233
2100
3434
1867
2365
3578
2845
2778
2056
2757
3325
3671
2147
3225
3556
4661
3344
5375
3907
3356
2184
3510
2834
3271
2834
2408
3261
1526
2938
2352
3915
3145
1566
2746
3572
2651
2805
3354
2523
1480
3278
5081
3332
2789
4111
2508
1833
2371
4268
2194
2935
3347
3034
5448
3427
3036
4196
3009
3369
4168
3403
1779
2761
2582
3153
3011
3419
4042
4379
4602
3249
4372
4328
3695
3614
2114
2839
2490
2610
2372
2833
4018
2734
3027
3862
3281
2746
2538
1805
2500
2601
3178
4193
2606
2491
4090
2786
2280
2403
2934
1601
1946
2554
2006
2830
3173
1960
3052
2151
2493
2752
2542
2027
1940
1877




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301553&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301553&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.172907348880291
beta0.0252855840704993
gamma0.285862967573569

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.172907348880291 \tabularnewline
beta & 0.0252855840704993 \tabularnewline
gamma & 0.285862967573569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301553&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]0.172907348880291[/C][/ROW]
[ROW][C]beta[/C][C]0.0252855840704993[/C][/ROW]
[ROW][C]gamma[/C][C]0.285862967573569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301553&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
alpha0.172907348880291
beta0.0252855840704993
gamma0.285862967573569







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1334343245.13382096188188.866179038116
1418671818.3538006028148.6461993971882
1523652283.7505328645881.2494671354216
1635783366.75583574515211.244164254847
1728452694.11654696041150.883453039591
1827782650.47421025548127.525789744517
1920562806.58734898425-750.587348984247
2027572936.15409303797-179.154093037967
2133251808.065400593041516.93459940696
2236712977.16710277055693.832897229445
2321472896.39725143221-749.397251432212
2432252610.7377679269614.262232073104
2535564540.56741211547-984.567412115473
2646612404.870164349942256.12983565006
2733443504.20175159198-160.201751591977
2853755128.99295072574246.00704927426
2939074090.0145757156-183.014575715602
3033563948.66596147-592.665961470001
3121843729.14461041143-1545.14461041143
3235104006.23579464157-496.235794641571
3328342903.46058241424-69.46058241424
3432713723.54802416808-452.548024168077
3528343021.57201582263-187.572015822635
3624083166.91752736859-758.917527368586
3732614543.67161194382-1282.67161194382
3815262980.47474665543-1454.47474665543
3929382822.70412060064115.295879399364
4023524260.38697776795-1908.38697776795
4139153017.47553412683897.524465873173
4231452986.60908855122158.39091144878
4315662696.41847874486-1130.41847874486
4427463118.74718147893-372.74718147893
4535722303.750720332461268.24927966754
4626513157.45385018838-506.453850188381
4728052570.65484087156234.345159128435
4833542631.23668575483722.76331424517
4925234066.17987811655-1543.17987811655
5014802455.28671615871-975.286716158715
5132782724.16403069891553.835969301092
5250813697.030649645331383.96935035467
5333323643.57590474055-311.575904740551
5427893203.98100844915-414.981008449152
5541112468.485096573281642.51490342672
5625083739.57951698751-1231.57951698751
5718333068.58369546386-1235.58369546386
5823713063.2074990841-692.207499084099
5942682613.883275717431654.11672428257
6021943037.95228026783-843.952280267829
6129353624.14413028582-689.144130285818
6233472249.676812135681097.32318786432
6330343387.29135350528-353.291353505282
6454484515.77108049326932.228919506744
6534273914.55169460708-487.551694607082
6630363380.27995974523-344.279959745231
6741963082.519637147151113.48036285285
6830093573.97976385639-564.979763856385
6933692958.41739524008410.582604759924
7041683424.42506261248743.574937387516
7134033802.31830771611-399.318307716107
7217793209.95741803709-1430.95741803709
7327613801.81297008888-1040.81297008888
7425822696.15956102752-114.159561027518
7531533267.70007749484-114.700077494836
7630114727.06357465555-1716.06357465555
7734193421.03170426208-2.03170426207771
7840423025.485163985341016.51483601466
7943793284.804003457931094.19599654207
8046023367.822324872511234.17767512749
8132493270.58967427819-21.5896742781852
8243723752.93816885106619.061831148945
8343283833.70069092486494.299309075145
8436953062.41496641441632.585033585591
8536144292.14054065653-678.140540656534
8621143309.40874730426-1195.40874730426
8728393800.60270310506-961.602703105056
8824904849.20694047692-2359.20694047692
8926103775.7680768442-1165.7680768442
9023723395.78438256001-1023.78438256001
9128333289.36971071669-456.369710716686
9240183116.2129331272901.787066872802
9327342744.48528448096-10.4852844809561
9430273258.43517855344-231.435178553443
9538623152.6806062849709.3193937151
9632812588.3553889567692.644611043299
9727463348.64903096828-602.649030968277
9825382418.5012961576119.498703842397
9918053070.30084240303-1265.30084240303
10025003532.82098151766-1032.82098151766
10126012997.78602949932-396.786029499324
10231782779.48384681326398.516153186739
10341933037.614580311155.38541969
10426063466.49699430429-860.496994304295
10524912606.30550578729-115.305505787291
10640903018.264363024521071.73563697548
10727863356.4218589583-570.421858958301
10822802593.3037604892-313.303760489202
10924032821.92122026699-418.921220266985
11029342161.96508043747772.034919562525
11116012552.35017926479-951.350179264793
11219463059.54675440392-1113.54675440392
11325542669.45320842799-115.453208427991
11420062678.66755972908-672.667559729076
11528302857.82222086666-27.8222208666612
11631732630.34299390388542.657006096117
11719602248.55357544721-288.553575447211
11830522787.92879392821264.071206071789
11921512624.80756318571-473.80756318571
12024932039.88762328524453.112376714763
12127522329.77935170728422.220648292717
12225422112.06160988637429.938390113629
12320272035.07251792627-8.07251792627335
12419402610.8163644162-670.816364416198
12518772531.083568767-654.083568767003

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3434 & 3245.13382096188 & 188.866179038116 \tabularnewline
14 & 1867 & 1818.35380060281 & 48.6461993971882 \tabularnewline
15 & 2365 & 2283.75053286458 & 81.2494671354216 \tabularnewline
16 & 3578 & 3366.75583574515 & 211.244164254847 \tabularnewline
17 & 2845 & 2694.11654696041 & 150.883453039591 \tabularnewline
18 & 2778 & 2650.47421025548 & 127.525789744517 \tabularnewline
19 & 2056 & 2806.58734898425 & -750.587348984247 \tabularnewline
20 & 2757 & 2936.15409303797 & -179.154093037967 \tabularnewline
21 & 3325 & 1808.06540059304 & 1516.93459940696 \tabularnewline
22 & 3671 & 2977.16710277055 & 693.832897229445 \tabularnewline
23 & 2147 & 2896.39725143221 & -749.397251432212 \tabularnewline
24 & 3225 & 2610.7377679269 & 614.262232073104 \tabularnewline
25 & 3556 & 4540.56741211547 & -984.567412115473 \tabularnewline
26 & 4661 & 2404.87016434994 & 2256.12983565006 \tabularnewline
27 & 3344 & 3504.20175159198 & -160.201751591977 \tabularnewline
28 & 5375 & 5128.99295072574 & 246.00704927426 \tabularnewline
29 & 3907 & 4090.0145757156 & -183.014575715602 \tabularnewline
30 & 3356 & 3948.66596147 & -592.665961470001 \tabularnewline
31 & 2184 & 3729.14461041143 & -1545.14461041143 \tabularnewline
32 & 3510 & 4006.23579464157 & -496.235794641571 \tabularnewline
33 & 2834 & 2903.46058241424 & -69.46058241424 \tabularnewline
34 & 3271 & 3723.54802416808 & -452.548024168077 \tabularnewline
35 & 2834 & 3021.57201582263 & -187.572015822635 \tabularnewline
36 & 2408 & 3166.91752736859 & -758.917527368586 \tabularnewline
37 & 3261 & 4543.67161194382 & -1282.67161194382 \tabularnewline
38 & 1526 & 2980.47474665543 & -1454.47474665543 \tabularnewline
39 & 2938 & 2822.70412060064 & 115.295879399364 \tabularnewline
40 & 2352 & 4260.38697776795 & -1908.38697776795 \tabularnewline
41 & 3915 & 3017.47553412683 & 897.524465873173 \tabularnewline
42 & 3145 & 2986.60908855122 & 158.39091144878 \tabularnewline
43 & 1566 & 2696.41847874486 & -1130.41847874486 \tabularnewline
44 & 2746 & 3118.74718147893 & -372.74718147893 \tabularnewline
45 & 3572 & 2303.75072033246 & 1268.24927966754 \tabularnewline
46 & 2651 & 3157.45385018838 & -506.453850188381 \tabularnewline
47 & 2805 & 2570.65484087156 & 234.345159128435 \tabularnewline
48 & 3354 & 2631.23668575483 & 722.76331424517 \tabularnewline
49 & 2523 & 4066.17987811655 & -1543.17987811655 \tabularnewline
50 & 1480 & 2455.28671615871 & -975.286716158715 \tabularnewline
51 & 3278 & 2724.16403069891 & 553.835969301092 \tabularnewline
52 & 5081 & 3697.03064964533 & 1383.96935035467 \tabularnewline
53 & 3332 & 3643.57590474055 & -311.575904740551 \tabularnewline
54 & 2789 & 3203.98100844915 & -414.981008449152 \tabularnewline
55 & 4111 & 2468.48509657328 & 1642.51490342672 \tabularnewline
56 & 2508 & 3739.57951698751 & -1231.57951698751 \tabularnewline
57 & 1833 & 3068.58369546386 & -1235.58369546386 \tabularnewline
58 & 2371 & 3063.2074990841 & -692.207499084099 \tabularnewline
59 & 4268 & 2613.88327571743 & 1654.11672428257 \tabularnewline
60 & 2194 & 3037.95228026783 & -843.952280267829 \tabularnewline
61 & 2935 & 3624.14413028582 & -689.144130285818 \tabularnewline
62 & 3347 & 2249.67681213568 & 1097.32318786432 \tabularnewline
63 & 3034 & 3387.29135350528 & -353.291353505282 \tabularnewline
64 & 5448 & 4515.77108049326 & 932.228919506744 \tabularnewline
65 & 3427 & 3914.55169460708 & -487.551694607082 \tabularnewline
66 & 3036 & 3380.27995974523 & -344.279959745231 \tabularnewline
67 & 4196 & 3082.51963714715 & 1113.48036285285 \tabularnewline
68 & 3009 & 3573.97976385639 & -564.979763856385 \tabularnewline
69 & 3369 & 2958.41739524008 & 410.582604759924 \tabularnewline
70 & 4168 & 3424.42506261248 & 743.574937387516 \tabularnewline
71 & 3403 & 3802.31830771611 & -399.318307716107 \tabularnewline
72 & 1779 & 3209.95741803709 & -1430.95741803709 \tabularnewline
73 & 2761 & 3801.81297008888 & -1040.81297008888 \tabularnewline
74 & 2582 & 2696.15956102752 & -114.159561027518 \tabularnewline
75 & 3153 & 3267.70007749484 & -114.700077494836 \tabularnewline
76 & 3011 & 4727.06357465555 & -1716.06357465555 \tabularnewline
77 & 3419 & 3421.03170426208 & -2.03170426207771 \tabularnewline
78 & 4042 & 3025.48516398534 & 1016.51483601466 \tabularnewline
79 & 4379 & 3284.80400345793 & 1094.19599654207 \tabularnewline
80 & 4602 & 3367.82232487251 & 1234.17767512749 \tabularnewline
81 & 3249 & 3270.58967427819 & -21.5896742781852 \tabularnewline
82 & 4372 & 3752.93816885106 & 619.061831148945 \tabularnewline
83 & 4328 & 3833.70069092486 & 494.299309075145 \tabularnewline
84 & 3695 & 3062.41496641441 & 632.585033585591 \tabularnewline
85 & 3614 & 4292.14054065653 & -678.140540656534 \tabularnewline
86 & 2114 & 3309.40874730426 & -1195.40874730426 \tabularnewline
87 & 2839 & 3800.60270310506 & -961.602703105056 \tabularnewline
88 & 2490 & 4849.20694047692 & -2359.20694047692 \tabularnewline
89 & 2610 & 3775.7680768442 & -1165.7680768442 \tabularnewline
90 & 2372 & 3395.78438256001 & -1023.78438256001 \tabularnewline
91 & 2833 & 3289.36971071669 & -456.369710716686 \tabularnewline
92 & 4018 & 3116.2129331272 & 901.787066872802 \tabularnewline
93 & 2734 & 2744.48528448096 & -10.4852844809561 \tabularnewline
94 & 3027 & 3258.43517855344 & -231.435178553443 \tabularnewline
95 & 3862 & 3152.6806062849 & 709.3193937151 \tabularnewline
96 & 3281 & 2588.3553889567 & 692.644611043299 \tabularnewline
97 & 2746 & 3348.64903096828 & -602.649030968277 \tabularnewline
98 & 2538 & 2418.5012961576 & 119.498703842397 \tabularnewline
99 & 1805 & 3070.30084240303 & -1265.30084240303 \tabularnewline
100 & 2500 & 3532.82098151766 & -1032.82098151766 \tabularnewline
101 & 2601 & 2997.78602949932 & -396.786029499324 \tabularnewline
102 & 3178 & 2779.48384681326 & 398.516153186739 \tabularnewline
103 & 4193 & 3037.61458031 & 1155.38541969 \tabularnewline
104 & 2606 & 3466.49699430429 & -860.496994304295 \tabularnewline
105 & 2491 & 2606.30550578729 & -115.305505787291 \tabularnewline
106 & 4090 & 3018.26436302452 & 1071.73563697548 \tabularnewline
107 & 2786 & 3356.4218589583 & -570.421858958301 \tabularnewline
108 & 2280 & 2593.3037604892 & -313.303760489202 \tabularnewline
109 & 2403 & 2821.92122026699 & -418.921220266985 \tabularnewline
110 & 2934 & 2161.96508043747 & 772.034919562525 \tabularnewline
111 & 1601 & 2552.35017926479 & -951.350179264793 \tabularnewline
112 & 1946 & 3059.54675440392 & -1113.54675440392 \tabularnewline
113 & 2554 & 2669.45320842799 & -115.453208427991 \tabularnewline
114 & 2006 & 2678.66755972908 & -672.667559729076 \tabularnewline
115 & 2830 & 2857.82222086666 & -27.8222208666612 \tabularnewline
116 & 3173 & 2630.34299390388 & 542.657006096117 \tabularnewline
117 & 1960 & 2248.55357544721 & -288.553575447211 \tabularnewline
118 & 3052 & 2787.92879392821 & 264.071206071789 \tabularnewline
119 & 2151 & 2624.80756318571 & -473.80756318571 \tabularnewline
120 & 2493 & 2039.88762328524 & 453.112376714763 \tabularnewline
121 & 2752 & 2329.77935170728 & 422.220648292717 \tabularnewline
122 & 2542 & 2112.06160988637 & 429.938390113629 \tabularnewline
123 & 2027 & 2035.07251792627 & -8.07251792627335 \tabularnewline
124 & 1940 & 2610.8163644162 & -670.816364416198 \tabularnewline
125 & 1877 & 2531.083568767 & -654.083568767003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301553&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]3434[/C][C]3245.13382096188[/C][C]188.866179038116[/C][/ROW]
[ROW][C]14[/C][C]1867[/C][C]1818.35380060281[/C][C]48.6461993971882[/C][/ROW]
[ROW][C]15[/C][C]2365[/C][C]2283.75053286458[/C][C]81.2494671354216[/C][/ROW]
[ROW][C]16[/C][C]3578[/C][C]3366.75583574515[/C][C]211.244164254847[/C][/ROW]
[ROW][C]17[/C][C]2845[/C][C]2694.11654696041[/C][C]150.883453039591[/C][/ROW]
[ROW][C]18[/C][C]2778[/C][C]2650.47421025548[/C][C]127.525789744517[/C][/ROW]
[ROW][C]19[/C][C]2056[/C][C]2806.58734898425[/C][C]-750.587348984247[/C][/ROW]
[ROW][C]20[/C][C]2757[/C][C]2936.15409303797[/C][C]-179.154093037967[/C][/ROW]
[ROW][C]21[/C][C]3325[/C][C]1808.06540059304[/C][C]1516.93459940696[/C][/ROW]
[ROW][C]22[/C][C]3671[/C][C]2977.16710277055[/C][C]693.832897229445[/C][/ROW]
[ROW][C]23[/C][C]2147[/C][C]2896.39725143221[/C][C]-749.397251432212[/C][/ROW]
[ROW][C]24[/C][C]3225[/C][C]2610.7377679269[/C][C]614.262232073104[/C][/ROW]
[ROW][C]25[/C][C]3556[/C][C]4540.56741211547[/C][C]-984.567412115473[/C][/ROW]
[ROW][C]26[/C][C]4661[/C][C]2404.87016434994[/C][C]2256.12983565006[/C][/ROW]
[ROW][C]27[/C][C]3344[/C][C]3504.20175159198[/C][C]-160.201751591977[/C][/ROW]
[ROW][C]28[/C][C]5375[/C][C]5128.99295072574[/C][C]246.00704927426[/C][/ROW]
[ROW][C]29[/C][C]3907[/C][C]4090.0145757156[/C][C]-183.014575715602[/C][/ROW]
[ROW][C]30[/C][C]3356[/C][C]3948.66596147[/C][C]-592.665961470001[/C][/ROW]
[ROW][C]31[/C][C]2184[/C][C]3729.14461041143[/C][C]-1545.14461041143[/C][/ROW]
[ROW][C]32[/C][C]3510[/C][C]4006.23579464157[/C][C]-496.235794641571[/C][/ROW]
[ROW][C]33[/C][C]2834[/C][C]2903.46058241424[/C][C]-69.46058241424[/C][/ROW]
[ROW][C]34[/C][C]3271[/C][C]3723.54802416808[/C][C]-452.548024168077[/C][/ROW]
[ROW][C]35[/C][C]2834[/C][C]3021.57201582263[/C][C]-187.572015822635[/C][/ROW]
[ROW][C]36[/C][C]2408[/C][C]3166.91752736859[/C][C]-758.917527368586[/C][/ROW]
[ROW][C]37[/C][C]3261[/C][C]4543.67161194382[/C][C]-1282.67161194382[/C][/ROW]
[ROW][C]38[/C][C]1526[/C][C]2980.47474665543[/C][C]-1454.47474665543[/C][/ROW]
[ROW][C]39[/C][C]2938[/C][C]2822.70412060064[/C][C]115.295879399364[/C][/ROW]
[ROW][C]40[/C][C]2352[/C][C]4260.38697776795[/C][C]-1908.38697776795[/C][/ROW]
[ROW][C]41[/C][C]3915[/C][C]3017.47553412683[/C][C]897.524465873173[/C][/ROW]
[ROW][C]42[/C][C]3145[/C][C]2986.60908855122[/C][C]158.39091144878[/C][/ROW]
[ROW][C]43[/C][C]1566[/C][C]2696.41847874486[/C][C]-1130.41847874486[/C][/ROW]
[ROW][C]44[/C][C]2746[/C][C]3118.74718147893[/C][C]-372.74718147893[/C][/ROW]
[ROW][C]45[/C][C]3572[/C][C]2303.75072033246[/C][C]1268.24927966754[/C][/ROW]
[ROW][C]46[/C][C]2651[/C][C]3157.45385018838[/C][C]-506.453850188381[/C][/ROW]
[ROW][C]47[/C][C]2805[/C][C]2570.65484087156[/C][C]234.345159128435[/C][/ROW]
[ROW][C]48[/C][C]3354[/C][C]2631.23668575483[/C][C]722.76331424517[/C][/ROW]
[ROW][C]49[/C][C]2523[/C][C]4066.17987811655[/C][C]-1543.17987811655[/C][/ROW]
[ROW][C]50[/C][C]1480[/C][C]2455.28671615871[/C][C]-975.286716158715[/C][/ROW]
[ROW][C]51[/C][C]3278[/C][C]2724.16403069891[/C][C]553.835969301092[/C][/ROW]
[ROW][C]52[/C][C]5081[/C][C]3697.03064964533[/C][C]1383.96935035467[/C][/ROW]
[ROW][C]53[/C][C]3332[/C][C]3643.57590474055[/C][C]-311.575904740551[/C][/ROW]
[ROW][C]54[/C][C]2789[/C][C]3203.98100844915[/C][C]-414.981008449152[/C][/ROW]
[ROW][C]55[/C][C]4111[/C][C]2468.48509657328[/C][C]1642.51490342672[/C][/ROW]
[ROW][C]56[/C][C]2508[/C][C]3739.57951698751[/C][C]-1231.57951698751[/C][/ROW]
[ROW][C]57[/C][C]1833[/C][C]3068.58369546386[/C][C]-1235.58369546386[/C][/ROW]
[ROW][C]58[/C][C]2371[/C][C]3063.2074990841[/C][C]-692.207499084099[/C][/ROW]
[ROW][C]59[/C][C]4268[/C][C]2613.88327571743[/C][C]1654.11672428257[/C][/ROW]
[ROW][C]60[/C][C]2194[/C][C]3037.95228026783[/C][C]-843.952280267829[/C][/ROW]
[ROW][C]61[/C][C]2935[/C][C]3624.14413028582[/C][C]-689.144130285818[/C][/ROW]
[ROW][C]62[/C][C]3347[/C][C]2249.67681213568[/C][C]1097.32318786432[/C][/ROW]
[ROW][C]63[/C][C]3034[/C][C]3387.29135350528[/C][C]-353.291353505282[/C][/ROW]
[ROW][C]64[/C][C]5448[/C][C]4515.77108049326[/C][C]932.228919506744[/C][/ROW]
[ROW][C]65[/C][C]3427[/C][C]3914.55169460708[/C][C]-487.551694607082[/C][/ROW]
[ROW][C]66[/C][C]3036[/C][C]3380.27995974523[/C][C]-344.279959745231[/C][/ROW]
[ROW][C]67[/C][C]4196[/C][C]3082.51963714715[/C][C]1113.48036285285[/C][/ROW]
[ROW][C]68[/C][C]3009[/C][C]3573.97976385639[/C][C]-564.979763856385[/C][/ROW]
[ROW][C]69[/C][C]3369[/C][C]2958.41739524008[/C][C]410.582604759924[/C][/ROW]
[ROW][C]70[/C][C]4168[/C][C]3424.42506261248[/C][C]743.574937387516[/C][/ROW]
[ROW][C]71[/C][C]3403[/C][C]3802.31830771611[/C][C]-399.318307716107[/C][/ROW]
[ROW][C]72[/C][C]1779[/C][C]3209.95741803709[/C][C]-1430.95741803709[/C][/ROW]
[ROW][C]73[/C][C]2761[/C][C]3801.81297008888[/C][C]-1040.81297008888[/C][/ROW]
[ROW][C]74[/C][C]2582[/C][C]2696.15956102752[/C][C]-114.159561027518[/C][/ROW]
[ROW][C]75[/C][C]3153[/C][C]3267.70007749484[/C][C]-114.700077494836[/C][/ROW]
[ROW][C]76[/C][C]3011[/C][C]4727.06357465555[/C][C]-1716.06357465555[/C][/ROW]
[ROW][C]77[/C][C]3419[/C][C]3421.03170426208[/C][C]-2.03170426207771[/C][/ROW]
[ROW][C]78[/C][C]4042[/C][C]3025.48516398534[/C][C]1016.51483601466[/C][/ROW]
[ROW][C]79[/C][C]4379[/C][C]3284.80400345793[/C][C]1094.19599654207[/C][/ROW]
[ROW][C]80[/C][C]4602[/C][C]3367.82232487251[/C][C]1234.17767512749[/C][/ROW]
[ROW][C]81[/C][C]3249[/C][C]3270.58967427819[/C][C]-21.5896742781852[/C][/ROW]
[ROW][C]82[/C][C]4372[/C][C]3752.93816885106[/C][C]619.061831148945[/C][/ROW]
[ROW][C]83[/C][C]4328[/C][C]3833.70069092486[/C][C]494.299309075145[/C][/ROW]
[ROW][C]84[/C][C]3695[/C][C]3062.41496641441[/C][C]632.585033585591[/C][/ROW]
[ROW][C]85[/C][C]3614[/C][C]4292.14054065653[/C][C]-678.140540656534[/C][/ROW]
[ROW][C]86[/C][C]2114[/C][C]3309.40874730426[/C][C]-1195.40874730426[/C][/ROW]
[ROW][C]87[/C][C]2839[/C][C]3800.60270310506[/C][C]-961.602703105056[/C][/ROW]
[ROW][C]88[/C][C]2490[/C][C]4849.20694047692[/C][C]-2359.20694047692[/C][/ROW]
[ROW][C]89[/C][C]2610[/C][C]3775.7680768442[/C][C]-1165.7680768442[/C][/ROW]
[ROW][C]90[/C][C]2372[/C][C]3395.78438256001[/C][C]-1023.78438256001[/C][/ROW]
[ROW][C]91[/C][C]2833[/C][C]3289.36971071669[/C][C]-456.369710716686[/C][/ROW]
[ROW][C]92[/C][C]4018[/C][C]3116.2129331272[/C][C]901.787066872802[/C][/ROW]
[ROW][C]93[/C][C]2734[/C][C]2744.48528448096[/C][C]-10.4852844809561[/C][/ROW]
[ROW][C]94[/C][C]3027[/C][C]3258.43517855344[/C][C]-231.435178553443[/C][/ROW]
[ROW][C]95[/C][C]3862[/C][C]3152.6806062849[/C][C]709.3193937151[/C][/ROW]
[ROW][C]96[/C][C]3281[/C][C]2588.3553889567[/C][C]692.644611043299[/C][/ROW]
[ROW][C]97[/C][C]2746[/C][C]3348.64903096828[/C][C]-602.649030968277[/C][/ROW]
[ROW][C]98[/C][C]2538[/C][C]2418.5012961576[/C][C]119.498703842397[/C][/ROW]
[ROW][C]99[/C][C]1805[/C][C]3070.30084240303[/C][C]-1265.30084240303[/C][/ROW]
[ROW][C]100[/C][C]2500[/C][C]3532.82098151766[/C][C]-1032.82098151766[/C][/ROW]
[ROW][C]101[/C][C]2601[/C][C]2997.78602949932[/C][C]-396.786029499324[/C][/ROW]
[ROW][C]102[/C][C]3178[/C][C]2779.48384681326[/C][C]398.516153186739[/C][/ROW]
[ROW][C]103[/C][C]4193[/C][C]3037.61458031[/C][C]1155.38541969[/C][/ROW]
[ROW][C]104[/C][C]2606[/C][C]3466.49699430429[/C][C]-860.496994304295[/C][/ROW]
[ROW][C]105[/C][C]2491[/C][C]2606.30550578729[/C][C]-115.305505787291[/C][/ROW]
[ROW][C]106[/C][C]4090[/C][C]3018.26436302452[/C][C]1071.73563697548[/C][/ROW]
[ROW][C]107[/C][C]2786[/C][C]3356.4218589583[/C][C]-570.421858958301[/C][/ROW]
[ROW][C]108[/C][C]2280[/C][C]2593.3037604892[/C][C]-313.303760489202[/C][/ROW]
[ROW][C]109[/C][C]2403[/C][C]2821.92122026699[/C][C]-418.921220266985[/C][/ROW]
[ROW][C]110[/C][C]2934[/C][C]2161.96508043747[/C][C]772.034919562525[/C][/ROW]
[ROW][C]111[/C][C]1601[/C][C]2552.35017926479[/C][C]-951.350179264793[/C][/ROW]
[ROW][C]112[/C][C]1946[/C][C]3059.54675440392[/C][C]-1113.54675440392[/C][/ROW]
[ROW][C]113[/C][C]2554[/C][C]2669.45320842799[/C][C]-115.453208427991[/C][/ROW]
[ROW][C]114[/C][C]2006[/C][C]2678.66755972908[/C][C]-672.667559729076[/C][/ROW]
[ROW][C]115[/C][C]2830[/C][C]2857.82222086666[/C][C]-27.8222208666612[/C][/ROW]
[ROW][C]116[/C][C]3173[/C][C]2630.34299390388[/C][C]542.657006096117[/C][/ROW]
[ROW][C]117[/C][C]1960[/C][C]2248.55357544721[/C][C]-288.553575447211[/C][/ROW]
[ROW][C]118[/C][C]3052[/C][C]2787.92879392821[/C][C]264.071206071789[/C][/ROW]
[ROW][C]119[/C][C]2151[/C][C]2624.80756318571[/C][C]-473.80756318571[/C][/ROW]
[ROW][C]120[/C][C]2493[/C][C]2039.88762328524[/C][C]453.112376714763[/C][/ROW]
[ROW][C]121[/C][C]2752[/C][C]2329.77935170728[/C][C]422.220648292717[/C][/ROW]
[ROW][C]122[/C][C]2542[/C][C]2112.06160988637[/C][C]429.938390113629[/C][/ROW]
[ROW][C]123[/C][C]2027[/C][C]2035.07251792627[/C][C]-8.07251792627335[/C][/ROW]
[ROW][C]124[/C][C]1940[/C][C]2610.8163644162[/C][C]-670.816364416198[/C][/ROW]
[ROW][C]125[/C][C]1877[/C][C]2531.083568767[/C][C]-654.083568767003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301553&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301553&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
1334343245.13382096188188.866179038116
1418671818.3538006028148.6461993971882
1523652283.7505328645881.2494671354216
1635783366.75583574515211.244164254847
1728452694.11654696041150.883453039591
1827782650.47421025548127.525789744517
1920562806.58734898425-750.587348984247
2027572936.15409303797-179.154093037967
2133251808.065400593041516.93459940696
2236712977.16710277055693.832897229445
2321472896.39725143221-749.397251432212
2432252610.7377679269614.262232073104
2535564540.56741211547-984.567412115473
2646612404.870164349942256.12983565006
2733443504.20175159198-160.201751591977
2853755128.99295072574246.00704927426
2939074090.0145757156-183.014575715602
3033563948.66596147-592.665961470001
3121843729.14461041143-1545.14461041143
3235104006.23579464157-496.235794641571
3328342903.46058241424-69.46058241424
3432713723.54802416808-452.548024168077
3528343021.57201582263-187.572015822635
3624083166.91752736859-758.917527368586
3732614543.67161194382-1282.67161194382
3815262980.47474665543-1454.47474665543
3929382822.70412060064115.295879399364
4023524260.38697776795-1908.38697776795
4139153017.47553412683897.524465873173
4231452986.60908855122158.39091144878
4315662696.41847874486-1130.41847874486
4427463118.74718147893-372.74718147893
4535722303.750720332461268.24927966754
4626513157.45385018838-506.453850188381
4728052570.65484087156234.345159128435
4833542631.23668575483722.76331424517
4925234066.17987811655-1543.17987811655
5014802455.28671615871-975.286716158715
5132782724.16403069891553.835969301092
5250813697.030649645331383.96935035467
5333323643.57590474055-311.575904740551
5427893203.98100844915-414.981008449152
5541112468.485096573281642.51490342672
5625083739.57951698751-1231.57951698751
5718333068.58369546386-1235.58369546386
5823713063.2074990841-692.207499084099
5942682613.883275717431654.11672428257
6021943037.95228026783-843.952280267829
6129353624.14413028582-689.144130285818
6233472249.676812135681097.32318786432
6330343387.29135350528-353.291353505282
6454484515.77108049326932.228919506744
6534273914.55169460708-487.551694607082
6630363380.27995974523-344.279959745231
6741963082.519637147151113.48036285285
6830093573.97976385639-564.979763856385
6933692958.41739524008410.582604759924
7041683424.42506261248743.574937387516
7134033802.31830771611-399.318307716107
7217793209.95741803709-1430.95741803709
7327613801.81297008888-1040.81297008888
7425822696.15956102752-114.159561027518
7531533267.70007749484-114.700077494836
7630114727.06357465555-1716.06357465555
7734193421.03170426208-2.03170426207771
7840423025.485163985341016.51483601466
7943793284.804003457931094.19599654207
8046023367.822324872511234.17767512749
8132493270.58967427819-21.5896742781852
8243723752.93816885106619.061831148945
8343283833.70069092486494.299309075145
8436953062.41496641441632.585033585591
8536144292.14054065653-678.140540656534
8621143309.40874730426-1195.40874730426
8728393800.60270310506-961.602703105056
8824904849.20694047692-2359.20694047692
8926103775.7680768442-1165.7680768442
9023723395.78438256001-1023.78438256001
9128333289.36971071669-456.369710716686
9240183116.2129331272901.787066872802
9327342744.48528448096-10.4852844809561
9430273258.43517855344-231.435178553443
9538623152.6806062849709.3193937151
9632812588.3553889567692.644611043299
9727463348.64903096828-602.649030968277
9825382418.5012961576119.498703842397
9918053070.30084240303-1265.30084240303
10025003532.82098151766-1032.82098151766
10126012997.78602949932-396.786029499324
10231782779.48384681326398.516153186739
10341933037.614580311155.38541969
10426063466.49699430429-860.496994304295
10524912606.30550578729-115.305505787291
10640903018.264363024521071.73563697548
10727863356.4218589583-570.421858958301
10822802593.3037604892-313.303760489202
10924032821.92122026699-418.921220266985
11029342161.96508043747772.034919562525
11116012552.35017926479-951.350179264793
11219463059.54675440392-1113.54675440392
11325542669.45320842799-115.453208427991
11420062678.66755972908-672.667559729076
11528302857.82222086666-27.8222208666612
11631732630.34299390388542.657006096117
11719602248.55357544721-288.553575447211
11830522787.92879392821264.071206071789
11921512624.80756318571-473.80756318571
12024932039.88762328524453.112376714763
12127522329.77935170728422.220648292717
12225422112.06160988637429.938390113629
12320272035.07251792627-8.07251792627335
12419402610.8163644162-670.816364416198
12518772531.083568767-654.083568767003







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1262313.802952232571628.146981298132999.45892316701
1272745.095035576811973.479529984383516.71054116924
1282656.362958859211833.095371357983479.63054636045
1292027.028420434731220.801649949582833.25519091988
1302710.20711926261725.525921291113694.88831723408
1312346.309798812471380.413957841413312.20563978352
1322068.813402524031109.733948230563027.89285681751
1332253.663747383121186.04134605323321.28614871304
1341986.66942948892943.0448314798613030.29402749797
1351760.33341447775734.0406364588312786.62619249666
1362112.19513030919893.7465897973473330.64367082104
1372138.594882170951047.058326919543230.13143742237

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
126 & 2313.80295223257 & 1628.14698129813 & 2999.45892316701 \tabularnewline
127 & 2745.09503557681 & 1973.47952998438 & 3516.71054116924 \tabularnewline
128 & 2656.36295885921 & 1833.09537135798 & 3479.63054636045 \tabularnewline
129 & 2027.02842043473 & 1220.80164994958 & 2833.25519091988 \tabularnewline
130 & 2710.2071192626 & 1725.52592129111 & 3694.88831723408 \tabularnewline
131 & 2346.30979881247 & 1380.41395784141 & 3312.20563978352 \tabularnewline
132 & 2068.81340252403 & 1109.73394823056 & 3027.89285681751 \tabularnewline
133 & 2253.66374738312 & 1186.0413460532 & 3321.28614871304 \tabularnewline
134 & 1986.66942948892 & 943.044831479861 & 3030.29402749797 \tabularnewline
135 & 1760.33341447775 & 734.040636458831 & 2786.62619249666 \tabularnewline
136 & 2112.19513030919 & 893.746589797347 & 3330.64367082104 \tabularnewline
137 & 2138.59488217095 & 1047.05832691954 & 3230.13143742237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301553&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]126[/C][C]2313.80295223257[/C][C]1628.14698129813[/C][C]2999.45892316701[/C][/ROW]
[ROW][C]127[/C][C]2745.09503557681[/C][C]1973.47952998438[/C][C]3516.71054116924[/C][/ROW]
[ROW][C]128[/C][C]2656.36295885921[/C][C]1833.09537135798[/C][C]3479.63054636045[/C][/ROW]
[ROW][C]129[/C][C]2027.02842043473[/C][C]1220.80164994958[/C][C]2833.25519091988[/C][/ROW]
[ROW][C]130[/C][C]2710.2071192626[/C][C]1725.52592129111[/C][C]3694.88831723408[/C][/ROW]
[ROW][C]131[/C][C]2346.30979881247[/C][C]1380.41395784141[/C][C]3312.20563978352[/C][/ROW]
[ROW][C]132[/C][C]2068.81340252403[/C][C]1109.73394823056[/C][C]3027.89285681751[/C][/ROW]
[ROW][C]133[/C][C]2253.66374738312[/C][C]1186.0413460532[/C][C]3321.28614871304[/C][/ROW]
[ROW][C]134[/C][C]1986.66942948892[/C][C]943.044831479861[/C][C]3030.29402749797[/C][/ROW]
[ROW][C]135[/C][C]1760.33341447775[/C][C]734.040636458831[/C][C]2786.62619249666[/C][/ROW]
[ROW][C]136[/C][C]2112.19513030919[/C][C]893.746589797347[/C][C]3330.64367082104[/C][/ROW]
[ROW][C]137[/C][C]2138.59488217095[/C][C]1047.05832691954[/C][C]3230.13143742237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301553&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301553&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
1262313.802952232571628.146981298132999.45892316701
1272745.095035576811973.479529984383516.71054116924
1282656.362958859211833.095371357983479.63054636045
1292027.028420434731220.801649949582833.25519091988
1302710.20711926261725.525921291113694.88831723408
1312346.309798812471380.413957841413312.20563978352
1322068.813402524031109.733948230563027.89285681751
1332253.663747383121186.04134605323321.28614871304
1341986.66942948892943.0448314798613030.29402749797
1351760.33341447775734.0406364588312786.62619249666
1362112.19513030919893.7465897973473330.64367082104
1372138.594882170951047.058326919543230.13143742237



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; 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')