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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2016 21:49:16 +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/19/t1482180565rcq0j4awd803qf1.htm/, Retrieved Sat, 18 May 2024 21:19:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301496, Retrieved Sat, 18 May 2024 21:19:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-19 20:49:16] [b2e25925e4919b0d6985405fcb461c0d] [Current]
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Dataseries X:
4020
3540
3430
4200
3360
4440
4390
4940
3940
4560
4850
5070
6210
5200
4860
5160
5530
8830
4410
4850
8960
4620
5120
4520
8870
9470
6590
3970
3770
5500
6580
5280
8640
5510
5690
7620
4010
3570
4040
3600
4000
3070
3230
4060
3480
3750
3990
3100
3950
3010
3160
2960
2750
3590
3060
2970
3590
3450
2930
2660
3540
3160
2680
2900
2920
2900
3150
3150
3120
3720
3360
2740
3250
2700
2610
2410
2590
2630
2650
2600
3060
2650
2700
2620
2630
2850
2680
2430
2550
2570
2520
2500
2550
2790
2770
2460
2800
2770
2450
2370
2540
3470
2690
4110
3840
2860
3540
3370




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=301496&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=301496&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301496&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
alpha0.280820311220428
beta0.222942088536615
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.280820311220428 \tabularnewline
beta & 0.222942088536615 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301496&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]0.280820311220428[/C][/ROW]
[ROW][C]beta[/C][C]0.222942088536615[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301496&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301496&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
alpha0.280820311220428
beta0.222942088536615
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
334303060370
442002707.067981825741492.93201817426
533602762.94557972273597.054420277274
644402604.622138847161835.37786115284
743902908.951962027691481.04803797231
849403206.502254848721733.49774515128
939403683.47406854059256.52593145941
1045603761.74243133515798.257568664847
1148504042.11628661946807.883713380539
1250704375.77226522414694.227734775858
1362104720.974620940971489.02537905903
1452005382.59521407787-182.595214077865
1548605563.35911430117-703.359114301172
1651605553.8469643611-393.846964361098
1755305606.59466707026-76.5946670702642
1888305743.637921848773086.36207815123
1944106962.13051609929-2552.13051609929
2048506437.43948065519-1587.43948065519
2189606084.268987564922875.73101243508
2246207164.48735435104-2544.48735435104
2351206563.2964408105-1443.2964408105
2445206180.98232312318-1660.98232312318
2588705633.549021539783236.45097846022
2694706664.037871545542805.96212845446
2765907749.30864442821-1159.30864442821
2839707648.47039490765-3678.47039490765
2937706609.90358867092-2839.90358867092
3055005629.02647654163-129.026476541625
3165805401.340801110171178.65919888983
3252805614.67174763432-334.671747634323
3386405382.075944222363257.92405577764
3455106362.32177786533-852.321777865332
3556906134.96607185534-444.966071855342
3676205994.146279436831625.85372056317
3740106536.6440275718-2526.6440275718
3835705754.85130526253-2184.85130526253
3940404932.25466417584-892.254664175836
4036004416.78432376162-816.784323761622
4140003871.37144391754128.628556082459
4230703599.50270836016-529.502708360158
4332303109.66694672595120.333053274054
4440602809.851917273771250.14808272623
4534802905.57950033849574.42049966151
4637502847.51160598722902.488394012775
4739902938.073629901941051.92637009806
4831003136.45847640106-36.4584764010579
4939503026.92020789874923.079792101262
5030103244.63072345472-234.630723454724
5131603122.5431642312637.456835768739
5229603079.20836570026-119.208365700259
5327502984.41555811763-234.415558117626
5435902842.5942541922747.405745807797
5530603023.2808968056936.7191031943107
5629703006.69115591499-36.6911559149862
5735902967.18921224571622.810787754291
5834503151.88091704611298.119082953894
5929303264.05683831329-334.056838313288
6026603177.79073549337-517.790735493371
6135403007.51127049496532.48872950504
6231603165.50895612852-5.50895612852446
6326803172.08106686647-492.08106686647
6429003011.20629069952-111.20629069952
6529202950.32663253646-30.326632536463
6629002910.26097577521-10.2609757752084
6731502875.18775750025274.81224249975
6831502937.37396756956212.626032430441
6931202995.40883391493124.591166085066
7037203036.52195930218683.478040697817
7133603277.3721526370482.6278473629623
7227403354.66446178166-614.664461781661
7332503197.6608345775852.3391654224197
7427003231.24215423438-531.24215423438
7526103067.6826856025-457.682685602502
7624102896.12622249912-486.126222499117
7725902686.14749413241-96.1474941324109
7826302579.6632395170550.3367604829473
7926502517.46615565733132.533844342669
8026002486.64918468601113.350815313987
8130602457.54174624577602.458253754229
8226502603.5035139741646.4964860258419
8327002596.25091506514103.749084934864
8426202611.571393179528.42860682047922
8526302600.6516319419929.3483680580107
8628502597.44396806265252.556031937347
8726802672.729241131997.27075886801458
8824302679.58862545721-249.588625457211
8925502598.69076565348-48.6907656534777
9025702571.16073882735-1.16073882734509
9125202556.90543893797-36.9054389379685
9225002530.30177472452-30.3017747245194
9325502503.6554604404846.3445395595159
9427902501.43446512855288.565534871445
9527702585.30017136329184.699828636709
9624602651.56171825666-191.561718256661
9728002600.16833980627199.831660193726
9827702671.1969658451998.8030341548051
9924502720.04043030469-270.040430304686
10023702648.39882707095-278.398827070947
10125402556.98039368352-16.9803936835242
10234702537.91048027116932.089519728844
10326902843.71369319729-153.713693197289
10441102834.977807990141275.02219200986
10538403307.28486811232532.715131887679
10628603604.48854729108-744.488547291076
10735403496.4175454584543.5824545415517
10833703612.38143982914-242.381439829137

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3430 & 3060 & 370 \tabularnewline
4 & 4200 & 2707.06798182574 & 1492.93201817426 \tabularnewline
5 & 3360 & 2762.94557972273 & 597.054420277274 \tabularnewline
6 & 4440 & 2604.62213884716 & 1835.37786115284 \tabularnewline
7 & 4390 & 2908.95196202769 & 1481.04803797231 \tabularnewline
8 & 4940 & 3206.50225484872 & 1733.49774515128 \tabularnewline
9 & 3940 & 3683.47406854059 & 256.52593145941 \tabularnewline
10 & 4560 & 3761.74243133515 & 798.257568664847 \tabularnewline
11 & 4850 & 4042.11628661946 & 807.883713380539 \tabularnewline
12 & 5070 & 4375.77226522414 & 694.227734775858 \tabularnewline
13 & 6210 & 4720.97462094097 & 1489.02537905903 \tabularnewline
14 & 5200 & 5382.59521407787 & -182.595214077865 \tabularnewline
15 & 4860 & 5563.35911430117 & -703.359114301172 \tabularnewline
16 & 5160 & 5553.8469643611 & -393.846964361098 \tabularnewline
17 & 5530 & 5606.59466707026 & -76.5946670702642 \tabularnewline
18 & 8830 & 5743.63792184877 & 3086.36207815123 \tabularnewline
19 & 4410 & 6962.13051609929 & -2552.13051609929 \tabularnewline
20 & 4850 & 6437.43948065519 & -1587.43948065519 \tabularnewline
21 & 8960 & 6084.26898756492 & 2875.73101243508 \tabularnewline
22 & 4620 & 7164.48735435104 & -2544.48735435104 \tabularnewline
23 & 5120 & 6563.2964408105 & -1443.2964408105 \tabularnewline
24 & 4520 & 6180.98232312318 & -1660.98232312318 \tabularnewline
25 & 8870 & 5633.54902153978 & 3236.45097846022 \tabularnewline
26 & 9470 & 6664.03787154554 & 2805.96212845446 \tabularnewline
27 & 6590 & 7749.30864442821 & -1159.30864442821 \tabularnewline
28 & 3970 & 7648.47039490765 & -3678.47039490765 \tabularnewline
29 & 3770 & 6609.90358867092 & -2839.90358867092 \tabularnewline
30 & 5500 & 5629.02647654163 & -129.026476541625 \tabularnewline
31 & 6580 & 5401.34080111017 & 1178.65919888983 \tabularnewline
32 & 5280 & 5614.67174763432 & -334.671747634323 \tabularnewline
33 & 8640 & 5382.07594422236 & 3257.92405577764 \tabularnewline
34 & 5510 & 6362.32177786533 & -852.321777865332 \tabularnewline
35 & 5690 & 6134.96607185534 & -444.966071855342 \tabularnewline
36 & 7620 & 5994.14627943683 & 1625.85372056317 \tabularnewline
37 & 4010 & 6536.6440275718 & -2526.6440275718 \tabularnewline
38 & 3570 & 5754.85130526253 & -2184.85130526253 \tabularnewline
39 & 4040 & 4932.25466417584 & -892.254664175836 \tabularnewline
40 & 3600 & 4416.78432376162 & -816.784323761622 \tabularnewline
41 & 4000 & 3871.37144391754 & 128.628556082459 \tabularnewline
42 & 3070 & 3599.50270836016 & -529.502708360158 \tabularnewline
43 & 3230 & 3109.66694672595 & 120.333053274054 \tabularnewline
44 & 4060 & 2809.85191727377 & 1250.14808272623 \tabularnewline
45 & 3480 & 2905.57950033849 & 574.42049966151 \tabularnewline
46 & 3750 & 2847.51160598722 & 902.488394012775 \tabularnewline
47 & 3990 & 2938.07362990194 & 1051.92637009806 \tabularnewline
48 & 3100 & 3136.45847640106 & -36.4584764010579 \tabularnewline
49 & 3950 & 3026.92020789874 & 923.079792101262 \tabularnewline
50 & 3010 & 3244.63072345472 & -234.630723454724 \tabularnewline
51 & 3160 & 3122.54316423126 & 37.456835768739 \tabularnewline
52 & 2960 & 3079.20836570026 & -119.208365700259 \tabularnewline
53 & 2750 & 2984.41555811763 & -234.415558117626 \tabularnewline
54 & 3590 & 2842.5942541922 & 747.405745807797 \tabularnewline
55 & 3060 & 3023.28089680569 & 36.7191031943107 \tabularnewline
56 & 2970 & 3006.69115591499 & -36.6911559149862 \tabularnewline
57 & 3590 & 2967.18921224571 & 622.810787754291 \tabularnewline
58 & 3450 & 3151.88091704611 & 298.119082953894 \tabularnewline
59 & 2930 & 3264.05683831329 & -334.056838313288 \tabularnewline
60 & 2660 & 3177.79073549337 & -517.790735493371 \tabularnewline
61 & 3540 & 3007.51127049496 & 532.48872950504 \tabularnewline
62 & 3160 & 3165.50895612852 & -5.50895612852446 \tabularnewline
63 & 2680 & 3172.08106686647 & -492.08106686647 \tabularnewline
64 & 2900 & 3011.20629069952 & -111.20629069952 \tabularnewline
65 & 2920 & 2950.32663253646 & -30.326632536463 \tabularnewline
66 & 2900 & 2910.26097577521 & -10.2609757752084 \tabularnewline
67 & 3150 & 2875.18775750025 & 274.81224249975 \tabularnewline
68 & 3150 & 2937.37396756956 & 212.626032430441 \tabularnewline
69 & 3120 & 2995.40883391493 & 124.591166085066 \tabularnewline
70 & 3720 & 3036.52195930218 & 683.478040697817 \tabularnewline
71 & 3360 & 3277.37215263704 & 82.6278473629623 \tabularnewline
72 & 2740 & 3354.66446178166 & -614.664461781661 \tabularnewline
73 & 3250 & 3197.66083457758 & 52.3391654224197 \tabularnewline
74 & 2700 & 3231.24215423438 & -531.24215423438 \tabularnewline
75 & 2610 & 3067.6826856025 & -457.682685602502 \tabularnewline
76 & 2410 & 2896.12622249912 & -486.126222499117 \tabularnewline
77 & 2590 & 2686.14749413241 & -96.1474941324109 \tabularnewline
78 & 2630 & 2579.66323951705 & 50.3367604829473 \tabularnewline
79 & 2650 & 2517.46615565733 & 132.533844342669 \tabularnewline
80 & 2600 & 2486.64918468601 & 113.350815313987 \tabularnewline
81 & 3060 & 2457.54174624577 & 602.458253754229 \tabularnewline
82 & 2650 & 2603.50351397416 & 46.4964860258419 \tabularnewline
83 & 2700 & 2596.25091506514 & 103.749084934864 \tabularnewline
84 & 2620 & 2611.57139317952 & 8.42860682047922 \tabularnewline
85 & 2630 & 2600.65163194199 & 29.3483680580107 \tabularnewline
86 & 2850 & 2597.44396806265 & 252.556031937347 \tabularnewline
87 & 2680 & 2672.72924113199 & 7.27075886801458 \tabularnewline
88 & 2430 & 2679.58862545721 & -249.588625457211 \tabularnewline
89 & 2550 & 2598.69076565348 & -48.6907656534777 \tabularnewline
90 & 2570 & 2571.16073882735 & -1.16073882734509 \tabularnewline
91 & 2520 & 2556.90543893797 & -36.9054389379685 \tabularnewline
92 & 2500 & 2530.30177472452 & -30.3017747245194 \tabularnewline
93 & 2550 & 2503.65546044048 & 46.3445395595159 \tabularnewline
94 & 2790 & 2501.43446512855 & 288.565534871445 \tabularnewline
95 & 2770 & 2585.30017136329 & 184.699828636709 \tabularnewline
96 & 2460 & 2651.56171825666 & -191.561718256661 \tabularnewline
97 & 2800 & 2600.16833980627 & 199.831660193726 \tabularnewline
98 & 2770 & 2671.19696584519 & 98.8030341548051 \tabularnewline
99 & 2450 & 2720.04043030469 & -270.040430304686 \tabularnewline
100 & 2370 & 2648.39882707095 & -278.398827070947 \tabularnewline
101 & 2540 & 2556.98039368352 & -16.9803936835242 \tabularnewline
102 & 3470 & 2537.91048027116 & 932.089519728844 \tabularnewline
103 & 2690 & 2843.71369319729 & -153.713693197289 \tabularnewline
104 & 4110 & 2834.97780799014 & 1275.02219200986 \tabularnewline
105 & 3840 & 3307.28486811232 & 532.715131887679 \tabularnewline
106 & 2860 & 3604.48854729108 & -744.488547291076 \tabularnewline
107 & 3540 & 3496.41754545845 & 43.5824545415517 \tabularnewline
108 & 3370 & 3612.38143982914 & -242.381439829137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301496&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]3[/C][C]3430[/C][C]3060[/C][C]370[/C][/ROW]
[ROW][C]4[/C][C]4200[/C][C]2707.06798182574[/C][C]1492.93201817426[/C][/ROW]
[ROW][C]5[/C][C]3360[/C][C]2762.94557972273[/C][C]597.054420277274[/C][/ROW]
[ROW][C]6[/C][C]4440[/C][C]2604.62213884716[/C][C]1835.37786115284[/C][/ROW]
[ROW][C]7[/C][C]4390[/C][C]2908.95196202769[/C][C]1481.04803797231[/C][/ROW]
[ROW][C]8[/C][C]4940[/C][C]3206.50225484872[/C][C]1733.49774515128[/C][/ROW]
[ROW][C]9[/C][C]3940[/C][C]3683.47406854059[/C][C]256.52593145941[/C][/ROW]
[ROW][C]10[/C][C]4560[/C][C]3761.74243133515[/C][C]798.257568664847[/C][/ROW]
[ROW][C]11[/C][C]4850[/C][C]4042.11628661946[/C][C]807.883713380539[/C][/ROW]
[ROW][C]12[/C][C]5070[/C][C]4375.77226522414[/C][C]694.227734775858[/C][/ROW]
[ROW][C]13[/C][C]6210[/C][C]4720.97462094097[/C][C]1489.02537905903[/C][/ROW]
[ROW][C]14[/C][C]5200[/C][C]5382.59521407787[/C][C]-182.595214077865[/C][/ROW]
[ROW][C]15[/C][C]4860[/C][C]5563.35911430117[/C][C]-703.359114301172[/C][/ROW]
[ROW][C]16[/C][C]5160[/C][C]5553.8469643611[/C][C]-393.846964361098[/C][/ROW]
[ROW][C]17[/C][C]5530[/C][C]5606.59466707026[/C][C]-76.5946670702642[/C][/ROW]
[ROW][C]18[/C][C]8830[/C][C]5743.63792184877[/C][C]3086.36207815123[/C][/ROW]
[ROW][C]19[/C][C]4410[/C][C]6962.13051609929[/C][C]-2552.13051609929[/C][/ROW]
[ROW][C]20[/C][C]4850[/C][C]6437.43948065519[/C][C]-1587.43948065519[/C][/ROW]
[ROW][C]21[/C][C]8960[/C][C]6084.26898756492[/C][C]2875.73101243508[/C][/ROW]
[ROW][C]22[/C][C]4620[/C][C]7164.48735435104[/C][C]-2544.48735435104[/C][/ROW]
[ROW][C]23[/C][C]5120[/C][C]6563.2964408105[/C][C]-1443.2964408105[/C][/ROW]
[ROW][C]24[/C][C]4520[/C][C]6180.98232312318[/C][C]-1660.98232312318[/C][/ROW]
[ROW][C]25[/C][C]8870[/C][C]5633.54902153978[/C][C]3236.45097846022[/C][/ROW]
[ROW][C]26[/C][C]9470[/C][C]6664.03787154554[/C][C]2805.96212845446[/C][/ROW]
[ROW][C]27[/C][C]6590[/C][C]7749.30864442821[/C][C]-1159.30864442821[/C][/ROW]
[ROW][C]28[/C][C]3970[/C][C]7648.47039490765[/C][C]-3678.47039490765[/C][/ROW]
[ROW][C]29[/C][C]3770[/C][C]6609.90358867092[/C][C]-2839.90358867092[/C][/ROW]
[ROW][C]30[/C][C]5500[/C][C]5629.02647654163[/C][C]-129.026476541625[/C][/ROW]
[ROW][C]31[/C][C]6580[/C][C]5401.34080111017[/C][C]1178.65919888983[/C][/ROW]
[ROW][C]32[/C][C]5280[/C][C]5614.67174763432[/C][C]-334.671747634323[/C][/ROW]
[ROW][C]33[/C][C]8640[/C][C]5382.07594422236[/C][C]3257.92405577764[/C][/ROW]
[ROW][C]34[/C][C]5510[/C][C]6362.32177786533[/C][C]-852.321777865332[/C][/ROW]
[ROW][C]35[/C][C]5690[/C][C]6134.96607185534[/C][C]-444.966071855342[/C][/ROW]
[ROW][C]36[/C][C]7620[/C][C]5994.14627943683[/C][C]1625.85372056317[/C][/ROW]
[ROW][C]37[/C][C]4010[/C][C]6536.6440275718[/C][C]-2526.6440275718[/C][/ROW]
[ROW][C]38[/C][C]3570[/C][C]5754.85130526253[/C][C]-2184.85130526253[/C][/ROW]
[ROW][C]39[/C][C]4040[/C][C]4932.25466417584[/C][C]-892.254664175836[/C][/ROW]
[ROW][C]40[/C][C]3600[/C][C]4416.78432376162[/C][C]-816.784323761622[/C][/ROW]
[ROW][C]41[/C][C]4000[/C][C]3871.37144391754[/C][C]128.628556082459[/C][/ROW]
[ROW][C]42[/C][C]3070[/C][C]3599.50270836016[/C][C]-529.502708360158[/C][/ROW]
[ROW][C]43[/C][C]3230[/C][C]3109.66694672595[/C][C]120.333053274054[/C][/ROW]
[ROW][C]44[/C][C]4060[/C][C]2809.85191727377[/C][C]1250.14808272623[/C][/ROW]
[ROW][C]45[/C][C]3480[/C][C]2905.57950033849[/C][C]574.42049966151[/C][/ROW]
[ROW][C]46[/C][C]3750[/C][C]2847.51160598722[/C][C]902.488394012775[/C][/ROW]
[ROW][C]47[/C][C]3990[/C][C]2938.07362990194[/C][C]1051.92637009806[/C][/ROW]
[ROW][C]48[/C][C]3100[/C][C]3136.45847640106[/C][C]-36.4584764010579[/C][/ROW]
[ROW][C]49[/C][C]3950[/C][C]3026.92020789874[/C][C]923.079792101262[/C][/ROW]
[ROW][C]50[/C][C]3010[/C][C]3244.63072345472[/C][C]-234.630723454724[/C][/ROW]
[ROW][C]51[/C][C]3160[/C][C]3122.54316423126[/C][C]37.456835768739[/C][/ROW]
[ROW][C]52[/C][C]2960[/C][C]3079.20836570026[/C][C]-119.208365700259[/C][/ROW]
[ROW][C]53[/C][C]2750[/C][C]2984.41555811763[/C][C]-234.415558117626[/C][/ROW]
[ROW][C]54[/C][C]3590[/C][C]2842.5942541922[/C][C]747.405745807797[/C][/ROW]
[ROW][C]55[/C][C]3060[/C][C]3023.28089680569[/C][C]36.7191031943107[/C][/ROW]
[ROW][C]56[/C][C]2970[/C][C]3006.69115591499[/C][C]-36.6911559149862[/C][/ROW]
[ROW][C]57[/C][C]3590[/C][C]2967.18921224571[/C][C]622.810787754291[/C][/ROW]
[ROW][C]58[/C][C]3450[/C][C]3151.88091704611[/C][C]298.119082953894[/C][/ROW]
[ROW][C]59[/C][C]2930[/C][C]3264.05683831329[/C][C]-334.056838313288[/C][/ROW]
[ROW][C]60[/C][C]2660[/C][C]3177.79073549337[/C][C]-517.790735493371[/C][/ROW]
[ROW][C]61[/C][C]3540[/C][C]3007.51127049496[/C][C]532.48872950504[/C][/ROW]
[ROW][C]62[/C][C]3160[/C][C]3165.50895612852[/C][C]-5.50895612852446[/C][/ROW]
[ROW][C]63[/C][C]2680[/C][C]3172.08106686647[/C][C]-492.08106686647[/C][/ROW]
[ROW][C]64[/C][C]2900[/C][C]3011.20629069952[/C][C]-111.20629069952[/C][/ROW]
[ROW][C]65[/C][C]2920[/C][C]2950.32663253646[/C][C]-30.326632536463[/C][/ROW]
[ROW][C]66[/C][C]2900[/C][C]2910.26097577521[/C][C]-10.2609757752084[/C][/ROW]
[ROW][C]67[/C][C]3150[/C][C]2875.18775750025[/C][C]274.81224249975[/C][/ROW]
[ROW][C]68[/C][C]3150[/C][C]2937.37396756956[/C][C]212.626032430441[/C][/ROW]
[ROW][C]69[/C][C]3120[/C][C]2995.40883391493[/C][C]124.591166085066[/C][/ROW]
[ROW][C]70[/C][C]3720[/C][C]3036.52195930218[/C][C]683.478040697817[/C][/ROW]
[ROW][C]71[/C][C]3360[/C][C]3277.37215263704[/C][C]82.6278473629623[/C][/ROW]
[ROW][C]72[/C][C]2740[/C][C]3354.66446178166[/C][C]-614.664461781661[/C][/ROW]
[ROW][C]73[/C][C]3250[/C][C]3197.66083457758[/C][C]52.3391654224197[/C][/ROW]
[ROW][C]74[/C][C]2700[/C][C]3231.24215423438[/C][C]-531.24215423438[/C][/ROW]
[ROW][C]75[/C][C]2610[/C][C]3067.6826856025[/C][C]-457.682685602502[/C][/ROW]
[ROW][C]76[/C][C]2410[/C][C]2896.12622249912[/C][C]-486.126222499117[/C][/ROW]
[ROW][C]77[/C][C]2590[/C][C]2686.14749413241[/C][C]-96.1474941324109[/C][/ROW]
[ROW][C]78[/C][C]2630[/C][C]2579.66323951705[/C][C]50.3367604829473[/C][/ROW]
[ROW][C]79[/C][C]2650[/C][C]2517.46615565733[/C][C]132.533844342669[/C][/ROW]
[ROW][C]80[/C][C]2600[/C][C]2486.64918468601[/C][C]113.350815313987[/C][/ROW]
[ROW][C]81[/C][C]3060[/C][C]2457.54174624577[/C][C]602.458253754229[/C][/ROW]
[ROW][C]82[/C][C]2650[/C][C]2603.50351397416[/C][C]46.4964860258419[/C][/ROW]
[ROW][C]83[/C][C]2700[/C][C]2596.25091506514[/C][C]103.749084934864[/C][/ROW]
[ROW][C]84[/C][C]2620[/C][C]2611.57139317952[/C][C]8.42860682047922[/C][/ROW]
[ROW][C]85[/C][C]2630[/C][C]2600.65163194199[/C][C]29.3483680580107[/C][/ROW]
[ROW][C]86[/C][C]2850[/C][C]2597.44396806265[/C][C]252.556031937347[/C][/ROW]
[ROW][C]87[/C][C]2680[/C][C]2672.72924113199[/C][C]7.27075886801458[/C][/ROW]
[ROW][C]88[/C][C]2430[/C][C]2679.58862545721[/C][C]-249.588625457211[/C][/ROW]
[ROW][C]89[/C][C]2550[/C][C]2598.69076565348[/C][C]-48.6907656534777[/C][/ROW]
[ROW][C]90[/C][C]2570[/C][C]2571.16073882735[/C][C]-1.16073882734509[/C][/ROW]
[ROW][C]91[/C][C]2520[/C][C]2556.90543893797[/C][C]-36.9054389379685[/C][/ROW]
[ROW][C]92[/C][C]2500[/C][C]2530.30177472452[/C][C]-30.3017747245194[/C][/ROW]
[ROW][C]93[/C][C]2550[/C][C]2503.65546044048[/C][C]46.3445395595159[/C][/ROW]
[ROW][C]94[/C][C]2790[/C][C]2501.43446512855[/C][C]288.565534871445[/C][/ROW]
[ROW][C]95[/C][C]2770[/C][C]2585.30017136329[/C][C]184.699828636709[/C][/ROW]
[ROW][C]96[/C][C]2460[/C][C]2651.56171825666[/C][C]-191.561718256661[/C][/ROW]
[ROW][C]97[/C][C]2800[/C][C]2600.16833980627[/C][C]199.831660193726[/C][/ROW]
[ROW][C]98[/C][C]2770[/C][C]2671.19696584519[/C][C]98.8030341548051[/C][/ROW]
[ROW][C]99[/C][C]2450[/C][C]2720.04043030469[/C][C]-270.040430304686[/C][/ROW]
[ROW][C]100[/C][C]2370[/C][C]2648.39882707095[/C][C]-278.398827070947[/C][/ROW]
[ROW][C]101[/C][C]2540[/C][C]2556.98039368352[/C][C]-16.9803936835242[/C][/ROW]
[ROW][C]102[/C][C]3470[/C][C]2537.91048027116[/C][C]932.089519728844[/C][/ROW]
[ROW][C]103[/C][C]2690[/C][C]2843.71369319729[/C][C]-153.713693197289[/C][/ROW]
[ROW][C]104[/C][C]4110[/C][C]2834.97780799014[/C][C]1275.02219200986[/C][/ROW]
[ROW][C]105[/C][C]3840[/C][C]3307.28486811232[/C][C]532.715131887679[/C][/ROW]
[ROW][C]106[/C][C]2860[/C][C]3604.48854729108[/C][C]-744.488547291076[/C][/ROW]
[ROW][C]107[/C][C]3540[/C][C]3496.41754545845[/C][C]43.5824545415517[/C][/ROW]
[ROW][C]108[/C][C]3370[/C][C]3612.38143982914[/C][C]-242.381439829137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301496&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301496&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
334303060370
442002707.067981825741492.93201817426
533602762.94557972273597.054420277274
644402604.622138847161835.37786115284
743902908.951962027691481.04803797231
849403206.502254848721733.49774515128
939403683.47406854059256.52593145941
1045603761.74243133515798.257568664847
1148504042.11628661946807.883713380539
1250704375.77226522414694.227734775858
1362104720.974620940971489.02537905903
1452005382.59521407787-182.595214077865
1548605563.35911430117-703.359114301172
1651605553.8469643611-393.846964361098
1755305606.59466707026-76.5946670702642
1888305743.637921848773086.36207815123
1944106962.13051609929-2552.13051609929
2048506437.43948065519-1587.43948065519
2189606084.268987564922875.73101243508
2246207164.48735435104-2544.48735435104
2351206563.2964408105-1443.2964408105
2445206180.98232312318-1660.98232312318
2588705633.549021539783236.45097846022
2694706664.037871545542805.96212845446
2765907749.30864442821-1159.30864442821
2839707648.47039490765-3678.47039490765
2937706609.90358867092-2839.90358867092
3055005629.02647654163-129.026476541625
3165805401.340801110171178.65919888983
3252805614.67174763432-334.671747634323
3386405382.075944222363257.92405577764
3455106362.32177786533-852.321777865332
3556906134.96607185534-444.966071855342
3676205994.146279436831625.85372056317
3740106536.6440275718-2526.6440275718
3835705754.85130526253-2184.85130526253
3940404932.25466417584-892.254664175836
4036004416.78432376162-816.784323761622
4140003871.37144391754128.628556082459
4230703599.50270836016-529.502708360158
4332303109.66694672595120.333053274054
4440602809.851917273771250.14808272623
4534802905.57950033849574.42049966151
4637502847.51160598722902.488394012775
4739902938.073629901941051.92637009806
4831003136.45847640106-36.4584764010579
4939503026.92020789874923.079792101262
5030103244.63072345472-234.630723454724
5131603122.5431642312637.456835768739
5229603079.20836570026-119.208365700259
5327502984.41555811763-234.415558117626
5435902842.5942541922747.405745807797
5530603023.2808968056936.7191031943107
5629703006.69115591499-36.6911559149862
5735902967.18921224571622.810787754291
5834503151.88091704611298.119082953894
5929303264.05683831329-334.056838313288
6026603177.79073549337-517.790735493371
6135403007.51127049496532.48872950504
6231603165.50895612852-5.50895612852446
6326803172.08106686647-492.08106686647
6429003011.20629069952-111.20629069952
6529202950.32663253646-30.326632536463
6629002910.26097577521-10.2609757752084
6731502875.18775750025274.81224249975
6831502937.37396756956212.626032430441
6931202995.40883391493124.591166085066
7037203036.52195930218683.478040697817
7133603277.3721526370482.6278473629623
7227403354.66446178166-614.664461781661
7332503197.6608345775852.3391654224197
7427003231.24215423438-531.24215423438
7526103067.6826856025-457.682685602502
7624102896.12622249912-486.126222499117
7725902686.14749413241-96.1474941324109
7826302579.6632395170550.3367604829473
7926502517.46615565733132.533844342669
8026002486.64918468601113.350815313987
8130602457.54174624577602.458253754229
8226502603.5035139741646.4964860258419
8327002596.25091506514103.749084934864
8426202611.571393179528.42860682047922
8526302600.6516319419929.3483680580107
8628502597.44396806265252.556031937347
8726802672.729241131997.27075886801458
8824302679.58862545721-249.588625457211
8925502598.69076565348-48.6907656534777
9025702571.16073882735-1.16073882734509
9125202556.90543893797-36.9054389379685
9225002530.30177472452-30.3017747245194
9325502503.6554604404846.3445395595159
9427902501.43446512855288.565534871445
9527702585.30017136329184.699828636709
9624602651.56171825666-191.561718256661
9728002600.16833980627199.831660193726
9827702671.1969658451998.8030341548051
9924502720.04043030469-270.040430304686
10023702648.39882707095-278.398827070947
10125402556.98039368352-16.9803936835242
10234702537.91048027116932.089519728844
10326902843.71369319729-153.713693197289
10441102834.977807990141275.02219200986
10538403307.28486811232532.715131887679
10628603604.48854729108-744.488547291076
10735403496.4175454584543.5824545415517
10833703612.38143982914-242.381439829137







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093632.866170370351401.338661276945864.39367946376
1103721.416532278441361.96044725656080.87261730037
1113809.966894186521282.516524479276337.41726389377
1123898.517256094611163.253280576826633.7812316124
1133987.067618002691005.950230208456968.18500579694
1144075.61797991078813.223476968117338.01248285345
1154164.16834181887587.9724601318127740.36422350592
1164252.71870372695333.0280165336658172.40939092024
1174341.2690656350450.97197575659278631.56615551348
1184429.81942754313-255.9287541254539115.5676092117
1194518.36978945121-585.7239322988589622.46351120128
1204606.9201513593-936.75156907830710150.5918717969

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 3632.86617037035 & 1401.33866127694 & 5864.39367946376 \tabularnewline
110 & 3721.41653227844 & 1361.9604472565 & 6080.87261730037 \tabularnewline
111 & 3809.96689418652 & 1282.51652447927 & 6337.41726389377 \tabularnewline
112 & 3898.51725609461 & 1163.25328057682 & 6633.7812316124 \tabularnewline
113 & 3987.06761800269 & 1005.95023020845 & 6968.18500579694 \tabularnewline
114 & 4075.61797991078 & 813.22347696811 & 7338.01248285345 \tabularnewline
115 & 4164.16834181887 & 587.972460131812 & 7740.36422350592 \tabularnewline
116 & 4252.71870372695 & 333.028016533665 & 8172.40939092024 \tabularnewline
117 & 4341.26906563504 & 50.9719757565927 & 8631.56615551348 \tabularnewline
118 & 4429.81942754313 & -255.928754125453 & 9115.5676092117 \tabularnewline
119 & 4518.36978945121 & -585.723932298858 & 9622.46351120128 \tabularnewline
120 & 4606.9201513593 & -936.751569078307 & 10150.5918717969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301496&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]109[/C][C]3632.86617037035[/C][C]1401.33866127694[/C][C]5864.39367946376[/C][/ROW]
[ROW][C]110[/C][C]3721.41653227844[/C][C]1361.9604472565[/C][C]6080.87261730037[/C][/ROW]
[ROW][C]111[/C][C]3809.96689418652[/C][C]1282.51652447927[/C][C]6337.41726389377[/C][/ROW]
[ROW][C]112[/C][C]3898.51725609461[/C][C]1163.25328057682[/C][C]6633.7812316124[/C][/ROW]
[ROW][C]113[/C][C]3987.06761800269[/C][C]1005.95023020845[/C][C]6968.18500579694[/C][/ROW]
[ROW][C]114[/C][C]4075.61797991078[/C][C]813.22347696811[/C][C]7338.01248285345[/C][/ROW]
[ROW][C]115[/C][C]4164.16834181887[/C][C]587.972460131812[/C][C]7740.36422350592[/C][/ROW]
[ROW][C]116[/C][C]4252.71870372695[/C][C]333.028016533665[/C][C]8172.40939092024[/C][/ROW]
[ROW][C]117[/C][C]4341.26906563504[/C][C]50.9719757565927[/C][C]8631.56615551348[/C][/ROW]
[ROW][C]118[/C][C]4429.81942754313[/C][C]-255.928754125453[/C][C]9115.5676092117[/C][/ROW]
[ROW][C]119[/C][C]4518.36978945121[/C][C]-585.723932298858[/C][C]9622.46351120128[/C][/ROW]
[ROW][C]120[/C][C]4606.9201513593[/C][C]-936.751569078307[/C][C]10150.5918717969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301496&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301496&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
1093632.866170370351401.338661276945864.39367946376
1103721.416532278441361.96044725656080.87261730037
1113809.966894186521282.516524479276337.41726389377
1123898.517256094611163.253280576826633.7812316124
1133987.067618002691005.950230208456968.18500579694
1144075.61797991078813.223476968117338.01248285345
1154164.16834181887587.9724601318127740.36422350592
1164252.71870372695333.0280165336658172.40939092024
1174341.2690656350450.97197575659278631.56615551348
1184429.81942754313-255.9287541254539115.5676092117
1194518.36978945121-585.7239322988589622.46351120128
1204606.9201513593-936.75156907830710150.5918717969



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
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')