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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 computationFri, 16 Dec 2016 15:41:19 +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/16/t1481899737hyafpnbsq68xq30.htm/, Retrieved Fri, 01 Nov 2024 03:39:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300328, Retrieved Fri, 01 Nov 2024 03:39:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-16 14:41:19] [9b171b8beffcb53bb49a1e7c02b89c12] [Current]
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Dataseries X:
2669.94
2778.72
2648.44
2631.32
3057.32
2730.66
2730.62
2738.7
2616.36
2773.54
2872.76
2999.42
2730.62
2907.22
2778.04
2833.94
2914.44
2788.86
2742.8
2726.52
2746.44
2927.42
2879.56
3262.02
2883.14
2903.2
2877.7
2874.3
3026.66
2979.42
3109.68
2966.76
2961.04
3103.84
3359.12
3976.24
3049.42
3089.14
3166.26
3459.04
3457.32
3292.66
3432.86
3388.4
3312.9
3390.04
3757.44
4612.38
3613.34
3525.14
3473.06
3662.22
3717.4
3466.9
3443.4
3383.16
3843.64
3692.4
3558.38
3811.02
3470.54
3354.68
3499.96
3537.36
3414.98
3649
3549.72
3680.78
3484.64
3451.92
3831.14
3906.02
3499.54
3620.62
3473.64
3494.32
3799.66
3476.4
3446.86
3441.94
3514.68
3464.96
3579.48
3944.24
3702.42
3716.28
3538.36
3482.58
3665.5
3484.5
3425.08
3421.44
3602.34
3593.44
3478.5
4365.26
3445.2
3473.48
3472.32
3403.82
3575.4
3512.96
3433.04
3495.2
3478.96
3559.28
3887.1
4083.16
3659.52
3693.48
3779.52
3891.62
3895.86
3745.04
3884.46
3862.98




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=300328&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=300328&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300328&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
alpha0.273142262993391
beta0.0024320185476651
gamma0.27159791932173

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.273142262993391 \tabularnewline
beta & 0.0024320185476651 \tabularnewline
gamma & 0.27159791932173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300328&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]0.273142262993391[/C][/ROW]
[ROW][C]beta[/C][C]0.0024320185476651[/C][/ROW]
[ROW][C]gamma[/C][C]0.27159791932173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300328&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300328&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
alpha0.273142262993391
beta0.0024320185476651
gamma0.27159791932173







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132730.622702.6552136752127.964786324786
142907.222892.056560935915.163439064097
152778.042767.2788921126410.761107887356
162833.942819.4667423872714.4732576127335
172914.442902.4148187027212.0251812972847
182788.862774.0922100855914.767789914411
192742.82794.13020051091-51.3302005109094
202726.522785.48077159802-58.9607715980151
212746.442641.41627768678105.023722313224
222927.422818.64431210359108.775687896408
232879.562950.3627585046-70.8027585046048
243262.023066.44120831525195.578791684754
252883.142859.0094184228824.1305815771179
262903.23045.04863934078-141.848639340781
272877.72876.6232674071.07673259300418
282874.32927.00030801128-52.7003080112795
293026.662991.1741155770235.4858844229757
302979.422869.87358106151109.546418938487
313109.682902.88651292327206.793487076729
322966.762963.542164134083.21783586591846
332961.042869.1822254208991.8577745791113
343103.843043.894294787759.9457052122971
353359.123127.13116819308231.988831806916
363976.243379.01022037077597.229779629234
373049.423248.21521605363-198.795216053631
383089.143341.22446903215-252.084469032152
393166.263171.45809131377-5.19809131376678
403459.043210.05447922474248.985520775263
413457.323374.790504357982.5294956420962
423292.663281.7412971124410.9187028875645
433432.863307.72836744445125.131632555549
443388.43306.5516737856281.8483262143773
453312.93251.8814078137561.018592186254
463390.043412.56333023086-22.523330230857
473757.443507.87639577108249.563604228917
484612.383837.3092778075775.0707221925
493613.343598.7126545544714.6273454455286
503525.143740.40663393681-215.26663393681
513473.063630.36981210358-157.309812103576
523662.223678.43063289913-16.2106328991304
533717.43738.5270333188-21.1270333188008
543466.93603.61632883567-136.71632883567
553443.43612.31546974534-168.915469745335
563383.163522.57237853617-139.412378536174
573843.643403.50240390679440.137596093213
583692.43651.6453294688240.7546705311815
593558.383818.39768351869-260.017683518692
603811.024112.48771448135-301.467714481349
613470.543429.1097428927941.4302571072149
623354.683532.14670569149-177.466705691486
633499.963443.3072316023256.652768397681
643537.363577.23838447626-39.8783844762565
653414.983629.45712735655-214.477127356552
6636493418.34463269646230.65536730354
673549.723520.7051470467429.0148529532553
683680.783490.65413741558190.125862584415
693484.643576.02926937239-91.3892693723869
703451.923599.81681470288-147.896814702881
713831.143655.20924065104175.930759348959
723906.024060.02718672216-154.007186722165
733499.543484.5521554480714.9878445519257
743620.623537.0685996323783.551400367628
753473.643565.83097051144-92.190970511444
763494.323640.03975310901-145.719753109012
773799.663628.80002042147170.859979578526
783476.43610.98965816572-134.589658165719
793446.863573.71254344398-126.852543443978
803441.943532.72212785643-90.7821278564279
813514.683485.4372033093729.2427966906284
823464.963530.74181989839-65.7818198983941
833579.483672.26834058962-92.7883405896191
843944.243938.152411544716.08758845529019
853702.423439.47292660393262.947073396072
863716.283573.12264515012143.157354849885
873538.363583.38146837232-45.0214683723248
883482.583659.84767375941-177.267673759412
893665.53702.40760245696-36.9076024569595
903484.53567.3291325844-82.829132584402
913425.083545.53354043261-120.453540432607
923421.443513.2321125748-91.7921125748007
933602.343489.18551275489113.154487245112
943593.443538.5263084769254.913691523082
953478.53707.64406053881-229.144060538808
964365.263955.66806670357409.59193329643
973445.23618.04317494331-172.843174943306
983473.483608.85570468317-135.375704683169
993472.323505.54499594379-33.2249959437936
1003403.823558.79259961312-154.972599613123
1013575.43634.832385015-59.432385015004
1023512.963484.202192924728.7578070752998
1033433.043485.19854382178-52.1585438217785
1043495.23476.9952561340618.2047438659365
1053478.963523.31139962944-44.3513996294414
1063559.283517.8873786638141.3926213361879
1073887.13626.98045696289260.119543037115
1084083.164134.80807141908-51.6480714190766
1093659.523555.9825750079103.537424992103
1103693.483629.6303154483263.8496845516752
1113779.523600.98212673136178.53787326864
1123891.623688.25698888638203.36301111362
1133895.863881.4927315077414.3672684922603
1143745.043768.93773517951-23.8977351795093
1153884.463740.05020684678144.409793153221
1163862.983800.0317668014762.9482331985346

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2730.62 & 2702.65521367521 & 27.964786324786 \tabularnewline
14 & 2907.22 & 2892.0565609359 & 15.163439064097 \tabularnewline
15 & 2778.04 & 2767.27889211264 & 10.761107887356 \tabularnewline
16 & 2833.94 & 2819.46674238727 & 14.4732576127335 \tabularnewline
17 & 2914.44 & 2902.41481870272 & 12.0251812972847 \tabularnewline
18 & 2788.86 & 2774.09221008559 & 14.767789914411 \tabularnewline
19 & 2742.8 & 2794.13020051091 & -51.3302005109094 \tabularnewline
20 & 2726.52 & 2785.48077159802 & -58.9607715980151 \tabularnewline
21 & 2746.44 & 2641.41627768678 & 105.023722313224 \tabularnewline
22 & 2927.42 & 2818.64431210359 & 108.775687896408 \tabularnewline
23 & 2879.56 & 2950.3627585046 & -70.8027585046048 \tabularnewline
24 & 3262.02 & 3066.44120831525 & 195.578791684754 \tabularnewline
25 & 2883.14 & 2859.00941842288 & 24.1305815771179 \tabularnewline
26 & 2903.2 & 3045.04863934078 & -141.848639340781 \tabularnewline
27 & 2877.7 & 2876.623267407 & 1.07673259300418 \tabularnewline
28 & 2874.3 & 2927.00030801128 & -52.7003080112795 \tabularnewline
29 & 3026.66 & 2991.17411557702 & 35.4858844229757 \tabularnewline
30 & 2979.42 & 2869.87358106151 & 109.546418938487 \tabularnewline
31 & 3109.68 & 2902.88651292327 & 206.793487076729 \tabularnewline
32 & 2966.76 & 2963.54216413408 & 3.21783586591846 \tabularnewline
33 & 2961.04 & 2869.18222542089 & 91.8577745791113 \tabularnewline
34 & 3103.84 & 3043.8942947877 & 59.9457052122971 \tabularnewline
35 & 3359.12 & 3127.13116819308 & 231.988831806916 \tabularnewline
36 & 3976.24 & 3379.01022037077 & 597.229779629234 \tabularnewline
37 & 3049.42 & 3248.21521605363 & -198.795216053631 \tabularnewline
38 & 3089.14 & 3341.22446903215 & -252.084469032152 \tabularnewline
39 & 3166.26 & 3171.45809131377 & -5.19809131376678 \tabularnewline
40 & 3459.04 & 3210.05447922474 & 248.985520775263 \tabularnewline
41 & 3457.32 & 3374.7905043579 & 82.5294956420962 \tabularnewline
42 & 3292.66 & 3281.74129711244 & 10.9187028875645 \tabularnewline
43 & 3432.86 & 3307.72836744445 & 125.131632555549 \tabularnewline
44 & 3388.4 & 3306.55167378562 & 81.8483262143773 \tabularnewline
45 & 3312.9 & 3251.88140781375 & 61.018592186254 \tabularnewline
46 & 3390.04 & 3412.56333023086 & -22.523330230857 \tabularnewline
47 & 3757.44 & 3507.87639577108 & 249.563604228917 \tabularnewline
48 & 4612.38 & 3837.3092778075 & 775.0707221925 \tabularnewline
49 & 3613.34 & 3598.71265455447 & 14.6273454455286 \tabularnewline
50 & 3525.14 & 3740.40663393681 & -215.26663393681 \tabularnewline
51 & 3473.06 & 3630.36981210358 & -157.309812103576 \tabularnewline
52 & 3662.22 & 3678.43063289913 & -16.2106328991304 \tabularnewline
53 & 3717.4 & 3738.5270333188 & -21.1270333188008 \tabularnewline
54 & 3466.9 & 3603.61632883567 & -136.71632883567 \tabularnewline
55 & 3443.4 & 3612.31546974534 & -168.915469745335 \tabularnewline
56 & 3383.16 & 3522.57237853617 & -139.412378536174 \tabularnewline
57 & 3843.64 & 3403.50240390679 & 440.137596093213 \tabularnewline
58 & 3692.4 & 3651.64532946882 & 40.7546705311815 \tabularnewline
59 & 3558.38 & 3818.39768351869 & -260.017683518692 \tabularnewline
60 & 3811.02 & 4112.48771448135 & -301.467714481349 \tabularnewline
61 & 3470.54 & 3429.10974289279 & 41.4302571072149 \tabularnewline
62 & 3354.68 & 3532.14670569149 & -177.466705691486 \tabularnewline
63 & 3499.96 & 3443.30723160232 & 56.652768397681 \tabularnewline
64 & 3537.36 & 3577.23838447626 & -39.8783844762565 \tabularnewline
65 & 3414.98 & 3629.45712735655 & -214.477127356552 \tabularnewline
66 & 3649 & 3418.34463269646 & 230.65536730354 \tabularnewline
67 & 3549.72 & 3520.70514704674 & 29.0148529532553 \tabularnewline
68 & 3680.78 & 3490.65413741558 & 190.125862584415 \tabularnewline
69 & 3484.64 & 3576.02926937239 & -91.3892693723869 \tabularnewline
70 & 3451.92 & 3599.81681470288 & -147.896814702881 \tabularnewline
71 & 3831.14 & 3655.20924065104 & 175.930759348959 \tabularnewline
72 & 3906.02 & 4060.02718672216 & -154.007186722165 \tabularnewline
73 & 3499.54 & 3484.55215544807 & 14.9878445519257 \tabularnewline
74 & 3620.62 & 3537.06859963237 & 83.551400367628 \tabularnewline
75 & 3473.64 & 3565.83097051144 & -92.190970511444 \tabularnewline
76 & 3494.32 & 3640.03975310901 & -145.719753109012 \tabularnewline
77 & 3799.66 & 3628.80002042147 & 170.859979578526 \tabularnewline
78 & 3476.4 & 3610.98965816572 & -134.589658165719 \tabularnewline
79 & 3446.86 & 3573.71254344398 & -126.852543443978 \tabularnewline
80 & 3441.94 & 3532.72212785643 & -90.7821278564279 \tabularnewline
81 & 3514.68 & 3485.43720330937 & 29.2427966906284 \tabularnewline
82 & 3464.96 & 3530.74181989839 & -65.7818198983941 \tabularnewline
83 & 3579.48 & 3672.26834058962 & -92.7883405896191 \tabularnewline
84 & 3944.24 & 3938.15241154471 & 6.08758845529019 \tabularnewline
85 & 3702.42 & 3439.47292660393 & 262.947073396072 \tabularnewline
86 & 3716.28 & 3573.12264515012 & 143.157354849885 \tabularnewline
87 & 3538.36 & 3583.38146837232 & -45.0214683723248 \tabularnewline
88 & 3482.58 & 3659.84767375941 & -177.267673759412 \tabularnewline
89 & 3665.5 & 3702.40760245696 & -36.9076024569595 \tabularnewline
90 & 3484.5 & 3567.3291325844 & -82.829132584402 \tabularnewline
91 & 3425.08 & 3545.53354043261 & -120.453540432607 \tabularnewline
92 & 3421.44 & 3513.2321125748 & -91.7921125748007 \tabularnewline
93 & 3602.34 & 3489.18551275489 & 113.154487245112 \tabularnewline
94 & 3593.44 & 3538.52630847692 & 54.913691523082 \tabularnewline
95 & 3478.5 & 3707.64406053881 & -229.144060538808 \tabularnewline
96 & 4365.26 & 3955.66806670357 & 409.59193329643 \tabularnewline
97 & 3445.2 & 3618.04317494331 & -172.843174943306 \tabularnewline
98 & 3473.48 & 3608.85570468317 & -135.375704683169 \tabularnewline
99 & 3472.32 & 3505.54499594379 & -33.2249959437936 \tabularnewline
100 & 3403.82 & 3558.79259961312 & -154.972599613123 \tabularnewline
101 & 3575.4 & 3634.832385015 & -59.432385015004 \tabularnewline
102 & 3512.96 & 3484.2021929247 & 28.7578070752998 \tabularnewline
103 & 3433.04 & 3485.19854382178 & -52.1585438217785 \tabularnewline
104 & 3495.2 & 3476.99525613406 & 18.2047438659365 \tabularnewline
105 & 3478.96 & 3523.31139962944 & -44.3513996294414 \tabularnewline
106 & 3559.28 & 3517.88737866381 & 41.3926213361879 \tabularnewline
107 & 3887.1 & 3626.98045696289 & 260.119543037115 \tabularnewline
108 & 4083.16 & 4134.80807141908 & -51.6480714190766 \tabularnewline
109 & 3659.52 & 3555.9825750079 & 103.537424992103 \tabularnewline
110 & 3693.48 & 3629.63031544832 & 63.8496845516752 \tabularnewline
111 & 3779.52 & 3600.98212673136 & 178.53787326864 \tabularnewline
112 & 3891.62 & 3688.25698888638 & 203.36301111362 \tabularnewline
113 & 3895.86 & 3881.49273150774 & 14.3672684922603 \tabularnewline
114 & 3745.04 & 3768.93773517951 & -23.8977351795093 \tabularnewline
115 & 3884.46 & 3740.05020684678 & 144.409793153221 \tabularnewline
116 & 3862.98 & 3800.03176680147 & 62.9482331985346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300328&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]2730.62[/C][C]2702.65521367521[/C][C]27.964786324786[/C][/ROW]
[ROW][C]14[/C][C]2907.22[/C][C]2892.0565609359[/C][C]15.163439064097[/C][/ROW]
[ROW][C]15[/C][C]2778.04[/C][C]2767.27889211264[/C][C]10.761107887356[/C][/ROW]
[ROW][C]16[/C][C]2833.94[/C][C]2819.46674238727[/C][C]14.4732576127335[/C][/ROW]
[ROW][C]17[/C][C]2914.44[/C][C]2902.41481870272[/C][C]12.0251812972847[/C][/ROW]
[ROW][C]18[/C][C]2788.86[/C][C]2774.09221008559[/C][C]14.767789914411[/C][/ROW]
[ROW][C]19[/C][C]2742.8[/C][C]2794.13020051091[/C][C]-51.3302005109094[/C][/ROW]
[ROW][C]20[/C][C]2726.52[/C][C]2785.48077159802[/C][C]-58.9607715980151[/C][/ROW]
[ROW][C]21[/C][C]2746.44[/C][C]2641.41627768678[/C][C]105.023722313224[/C][/ROW]
[ROW][C]22[/C][C]2927.42[/C][C]2818.64431210359[/C][C]108.775687896408[/C][/ROW]
[ROW][C]23[/C][C]2879.56[/C][C]2950.3627585046[/C][C]-70.8027585046048[/C][/ROW]
[ROW][C]24[/C][C]3262.02[/C][C]3066.44120831525[/C][C]195.578791684754[/C][/ROW]
[ROW][C]25[/C][C]2883.14[/C][C]2859.00941842288[/C][C]24.1305815771179[/C][/ROW]
[ROW][C]26[/C][C]2903.2[/C][C]3045.04863934078[/C][C]-141.848639340781[/C][/ROW]
[ROW][C]27[/C][C]2877.7[/C][C]2876.623267407[/C][C]1.07673259300418[/C][/ROW]
[ROW][C]28[/C][C]2874.3[/C][C]2927.00030801128[/C][C]-52.7003080112795[/C][/ROW]
[ROW][C]29[/C][C]3026.66[/C][C]2991.17411557702[/C][C]35.4858844229757[/C][/ROW]
[ROW][C]30[/C][C]2979.42[/C][C]2869.87358106151[/C][C]109.546418938487[/C][/ROW]
[ROW][C]31[/C][C]3109.68[/C][C]2902.88651292327[/C][C]206.793487076729[/C][/ROW]
[ROW][C]32[/C][C]2966.76[/C][C]2963.54216413408[/C][C]3.21783586591846[/C][/ROW]
[ROW][C]33[/C][C]2961.04[/C][C]2869.18222542089[/C][C]91.8577745791113[/C][/ROW]
[ROW][C]34[/C][C]3103.84[/C][C]3043.8942947877[/C][C]59.9457052122971[/C][/ROW]
[ROW][C]35[/C][C]3359.12[/C][C]3127.13116819308[/C][C]231.988831806916[/C][/ROW]
[ROW][C]36[/C][C]3976.24[/C][C]3379.01022037077[/C][C]597.229779629234[/C][/ROW]
[ROW][C]37[/C][C]3049.42[/C][C]3248.21521605363[/C][C]-198.795216053631[/C][/ROW]
[ROW][C]38[/C][C]3089.14[/C][C]3341.22446903215[/C][C]-252.084469032152[/C][/ROW]
[ROW][C]39[/C][C]3166.26[/C][C]3171.45809131377[/C][C]-5.19809131376678[/C][/ROW]
[ROW][C]40[/C][C]3459.04[/C][C]3210.05447922474[/C][C]248.985520775263[/C][/ROW]
[ROW][C]41[/C][C]3457.32[/C][C]3374.7905043579[/C][C]82.5294956420962[/C][/ROW]
[ROW][C]42[/C][C]3292.66[/C][C]3281.74129711244[/C][C]10.9187028875645[/C][/ROW]
[ROW][C]43[/C][C]3432.86[/C][C]3307.72836744445[/C][C]125.131632555549[/C][/ROW]
[ROW][C]44[/C][C]3388.4[/C][C]3306.55167378562[/C][C]81.8483262143773[/C][/ROW]
[ROW][C]45[/C][C]3312.9[/C][C]3251.88140781375[/C][C]61.018592186254[/C][/ROW]
[ROW][C]46[/C][C]3390.04[/C][C]3412.56333023086[/C][C]-22.523330230857[/C][/ROW]
[ROW][C]47[/C][C]3757.44[/C][C]3507.87639577108[/C][C]249.563604228917[/C][/ROW]
[ROW][C]48[/C][C]4612.38[/C][C]3837.3092778075[/C][C]775.0707221925[/C][/ROW]
[ROW][C]49[/C][C]3613.34[/C][C]3598.71265455447[/C][C]14.6273454455286[/C][/ROW]
[ROW][C]50[/C][C]3525.14[/C][C]3740.40663393681[/C][C]-215.26663393681[/C][/ROW]
[ROW][C]51[/C][C]3473.06[/C][C]3630.36981210358[/C][C]-157.309812103576[/C][/ROW]
[ROW][C]52[/C][C]3662.22[/C][C]3678.43063289913[/C][C]-16.2106328991304[/C][/ROW]
[ROW][C]53[/C][C]3717.4[/C][C]3738.5270333188[/C][C]-21.1270333188008[/C][/ROW]
[ROW][C]54[/C][C]3466.9[/C][C]3603.61632883567[/C][C]-136.71632883567[/C][/ROW]
[ROW][C]55[/C][C]3443.4[/C][C]3612.31546974534[/C][C]-168.915469745335[/C][/ROW]
[ROW][C]56[/C][C]3383.16[/C][C]3522.57237853617[/C][C]-139.412378536174[/C][/ROW]
[ROW][C]57[/C][C]3843.64[/C][C]3403.50240390679[/C][C]440.137596093213[/C][/ROW]
[ROW][C]58[/C][C]3692.4[/C][C]3651.64532946882[/C][C]40.7546705311815[/C][/ROW]
[ROW][C]59[/C][C]3558.38[/C][C]3818.39768351869[/C][C]-260.017683518692[/C][/ROW]
[ROW][C]60[/C][C]3811.02[/C][C]4112.48771448135[/C][C]-301.467714481349[/C][/ROW]
[ROW][C]61[/C][C]3470.54[/C][C]3429.10974289279[/C][C]41.4302571072149[/C][/ROW]
[ROW][C]62[/C][C]3354.68[/C][C]3532.14670569149[/C][C]-177.466705691486[/C][/ROW]
[ROW][C]63[/C][C]3499.96[/C][C]3443.30723160232[/C][C]56.652768397681[/C][/ROW]
[ROW][C]64[/C][C]3537.36[/C][C]3577.23838447626[/C][C]-39.8783844762565[/C][/ROW]
[ROW][C]65[/C][C]3414.98[/C][C]3629.45712735655[/C][C]-214.477127356552[/C][/ROW]
[ROW][C]66[/C][C]3649[/C][C]3418.34463269646[/C][C]230.65536730354[/C][/ROW]
[ROW][C]67[/C][C]3549.72[/C][C]3520.70514704674[/C][C]29.0148529532553[/C][/ROW]
[ROW][C]68[/C][C]3680.78[/C][C]3490.65413741558[/C][C]190.125862584415[/C][/ROW]
[ROW][C]69[/C][C]3484.64[/C][C]3576.02926937239[/C][C]-91.3892693723869[/C][/ROW]
[ROW][C]70[/C][C]3451.92[/C][C]3599.81681470288[/C][C]-147.896814702881[/C][/ROW]
[ROW][C]71[/C][C]3831.14[/C][C]3655.20924065104[/C][C]175.930759348959[/C][/ROW]
[ROW][C]72[/C][C]3906.02[/C][C]4060.02718672216[/C][C]-154.007186722165[/C][/ROW]
[ROW][C]73[/C][C]3499.54[/C][C]3484.55215544807[/C][C]14.9878445519257[/C][/ROW]
[ROW][C]74[/C][C]3620.62[/C][C]3537.06859963237[/C][C]83.551400367628[/C][/ROW]
[ROW][C]75[/C][C]3473.64[/C][C]3565.83097051144[/C][C]-92.190970511444[/C][/ROW]
[ROW][C]76[/C][C]3494.32[/C][C]3640.03975310901[/C][C]-145.719753109012[/C][/ROW]
[ROW][C]77[/C][C]3799.66[/C][C]3628.80002042147[/C][C]170.859979578526[/C][/ROW]
[ROW][C]78[/C][C]3476.4[/C][C]3610.98965816572[/C][C]-134.589658165719[/C][/ROW]
[ROW][C]79[/C][C]3446.86[/C][C]3573.71254344398[/C][C]-126.852543443978[/C][/ROW]
[ROW][C]80[/C][C]3441.94[/C][C]3532.72212785643[/C][C]-90.7821278564279[/C][/ROW]
[ROW][C]81[/C][C]3514.68[/C][C]3485.43720330937[/C][C]29.2427966906284[/C][/ROW]
[ROW][C]82[/C][C]3464.96[/C][C]3530.74181989839[/C][C]-65.7818198983941[/C][/ROW]
[ROW][C]83[/C][C]3579.48[/C][C]3672.26834058962[/C][C]-92.7883405896191[/C][/ROW]
[ROW][C]84[/C][C]3944.24[/C][C]3938.15241154471[/C][C]6.08758845529019[/C][/ROW]
[ROW][C]85[/C][C]3702.42[/C][C]3439.47292660393[/C][C]262.947073396072[/C][/ROW]
[ROW][C]86[/C][C]3716.28[/C][C]3573.12264515012[/C][C]143.157354849885[/C][/ROW]
[ROW][C]87[/C][C]3538.36[/C][C]3583.38146837232[/C][C]-45.0214683723248[/C][/ROW]
[ROW][C]88[/C][C]3482.58[/C][C]3659.84767375941[/C][C]-177.267673759412[/C][/ROW]
[ROW][C]89[/C][C]3665.5[/C][C]3702.40760245696[/C][C]-36.9076024569595[/C][/ROW]
[ROW][C]90[/C][C]3484.5[/C][C]3567.3291325844[/C][C]-82.829132584402[/C][/ROW]
[ROW][C]91[/C][C]3425.08[/C][C]3545.53354043261[/C][C]-120.453540432607[/C][/ROW]
[ROW][C]92[/C][C]3421.44[/C][C]3513.2321125748[/C][C]-91.7921125748007[/C][/ROW]
[ROW][C]93[/C][C]3602.34[/C][C]3489.18551275489[/C][C]113.154487245112[/C][/ROW]
[ROW][C]94[/C][C]3593.44[/C][C]3538.52630847692[/C][C]54.913691523082[/C][/ROW]
[ROW][C]95[/C][C]3478.5[/C][C]3707.64406053881[/C][C]-229.144060538808[/C][/ROW]
[ROW][C]96[/C][C]4365.26[/C][C]3955.66806670357[/C][C]409.59193329643[/C][/ROW]
[ROW][C]97[/C][C]3445.2[/C][C]3618.04317494331[/C][C]-172.843174943306[/C][/ROW]
[ROW][C]98[/C][C]3473.48[/C][C]3608.85570468317[/C][C]-135.375704683169[/C][/ROW]
[ROW][C]99[/C][C]3472.32[/C][C]3505.54499594379[/C][C]-33.2249959437936[/C][/ROW]
[ROW][C]100[/C][C]3403.82[/C][C]3558.79259961312[/C][C]-154.972599613123[/C][/ROW]
[ROW][C]101[/C][C]3575.4[/C][C]3634.832385015[/C][C]-59.432385015004[/C][/ROW]
[ROW][C]102[/C][C]3512.96[/C][C]3484.2021929247[/C][C]28.7578070752998[/C][/ROW]
[ROW][C]103[/C][C]3433.04[/C][C]3485.19854382178[/C][C]-52.1585438217785[/C][/ROW]
[ROW][C]104[/C][C]3495.2[/C][C]3476.99525613406[/C][C]18.2047438659365[/C][/ROW]
[ROW][C]105[/C][C]3478.96[/C][C]3523.31139962944[/C][C]-44.3513996294414[/C][/ROW]
[ROW][C]106[/C][C]3559.28[/C][C]3517.88737866381[/C][C]41.3926213361879[/C][/ROW]
[ROW][C]107[/C][C]3887.1[/C][C]3626.98045696289[/C][C]260.119543037115[/C][/ROW]
[ROW][C]108[/C][C]4083.16[/C][C]4134.80807141908[/C][C]-51.6480714190766[/C][/ROW]
[ROW][C]109[/C][C]3659.52[/C][C]3555.9825750079[/C][C]103.537424992103[/C][/ROW]
[ROW][C]110[/C][C]3693.48[/C][C]3629.63031544832[/C][C]63.8496845516752[/C][/ROW]
[ROW][C]111[/C][C]3779.52[/C][C]3600.98212673136[/C][C]178.53787326864[/C][/ROW]
[ROW][C]112[/C][C]3891.62[/C][C]3688.25698888638[/C][C]203.36301111362[/C][/ROW]
[ROW][C]113[/C][C]3895.86[/C][C]3881.49273150774[/C][C]14.3672684922603[/C][/ROW]
[ROW][C]114[/C][C]3745.04[/C][C]3768.93773517951[/C][C]-23.8977351795093[/C][/ROW]
[ROW][C]115[/C][C]3884.46[/C][C]3740.05020684678[/C][C]144.409793153221[/C][/ROW]
[ROW][C]116[/C][C]3862.98[/C][C]3800.03176680147[/C][C]62.9482331985346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300328&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300328&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
132730.622702.6552136752127.964786324786
142907.222892.056560935915.163439064097
152778.042767.2788921126410.761107887356
162833.942819.4667423872714.4732576127335
172914.442902.4148187027212.0251812972847
182788.862774.0922100855914.767789914411
192742.82794.13020051091-51.3302005109094
202726.522785.48077159802-58.9607715980151
212746.442641.41627768678105.023722313224
222927.422818.64431210359108.775687896408
232879.562950.3627585046-70.8027585046048
243262.023066.44120831525195.578791684754
252883.142859.0094184228824.1305815771179
262903.23045.04863934078-141.848639340781
272877.72876.6232674071.07673259300418
282874.32927.00030801128-52.7003080112795
293026.662991.1741155770235.4858844229757
302979.422869.87358106151109.546418938487
313109.682902.88651292327206.793487076729
322966.762963.542164134083.21783586591846
332961.042869.1822254208991.8577745791113
343103.843043.894294787759.9457052122971
353359.123127.13116819308231.988831806916
363976.243379.01022037077597.229779629234
373049.423248.21521605363-198.795216053631
383089.143341.22446903215-252.084469032152
393166.263171.45809131377-5.19809131376678
403459.043210.05447922474248.985520775263
413457.323374.790504357982.5294956420962
423292.663281.7412971124410.9187028875645
433432.863307.72836744445125.131632555549
443388.43306.5516737856281.8483262143773
453312.93251.8814078137561.018592186254
463390.043412.56333023086-22.523330230857
473757.443507.87639577108249.563604228917
484612.383837.3092778075775.0707221925
493613.343598.7126545544714.6273454455286
503525.143740.40663393681-215.26663393681
513473.063630.36981210358-157.309812103576
523662.223678.43063289913-16.2106328991304
533717.43738.5270333188-21.1270333188008
543466.93603.61632883567-136.71632883567
553443.43612.31546974534-168.915469745335
563383.163522.57237853617-139.412378536174
573843.643403.50240390679440.137596093213
583692.43651.6453294688240.7546705311815
593558.383818.39768351869-260.017683518692
603811.024112.48771448135-301.467714481349
613470.543429.1097428927941.4302571072149
623354.683532.14670569149-177.466705691486
633499.963443.3072316023256.652768397681
643537.363577.23838447626-39.8783844762565
653414.983629.45712735655-214.477127356552
6636493418.34463269646230.65536730354
673549.723520.7051470467429.0148529532553
683680.783490.65413741558190.125862584415
693484.643576.02926937239-91.3892693723869
703451.923599.81681470288-147.896814702881
713831.143655.20924065104175.930759348959
723906.024060.02718672216-154.007186722165
733499.543484.5521554480714.9878445519257
743620.623537.0685996323783.551400367628
753473.643565.83097051144-92.190970511444
763494.323640.03975310901-145.719753109012
773799.663628.80002042147170.859979578526
783476.43610.98965816572-134.589658165719
793446.863573.71254344398-126.852543443978
803441.943532.72212785643-90.7821278564279
813514.683485.4372033093729.2427966906284
823464.963530.74181989839-65.7818198983941
833579.483672.26834058962-92.7883405896191
843944.243938.152411544716.08758845529019
853702.423439.47292660393262.947073396072
863716.283573.12264515012143.157354849885
873538.363583.38146837232-45.0214683723248
883482.583659.84767375941-177.267673759412
893665.53702.40760245696-36.9076024569595
903484.53567.3291325844-82.829132584402
913425.083545.53354043261-120.453540432607
923421.443513.2321125748-91.7921125748007
933602.343489.18551275489113.154487245112
943593.443538.5263084769254.913691523082
953478.53707.64406053881-229.144060538808
964365.263955.66806670357409.59193329643
973445.23618.04317494331-172.843174943306
983473.483608.85570468317-135.375704683169
993472.323505.54499594379-33.2249959437936
1003403.823558.79259961312-154.972599613123
1013575.43634.832385015-59.432385015004
1023512.963484.202192924728.7578070752998
1033433.043485.19854382178-52.1585438217785
1043495.23476.9952561340618.2047438659365
1053478.963523.31139962944-44.3513996294414
1063559.283517.8873786638141.3926213361879
1073887.13626.98045696289260.119543037115
1084083.164134.80807141908-51.6480714190766
1093659.523555.9825750079103.537424992103
1103693.483629.6303154483263.8496845516752
1113779.523600.98212673136178.53787326864
1123891.623688.25698888638203.36301111362
1133895.863881.4927315077414.3672684922603
1143745.043768.93773517951-23.8977351795093
1153884.463740.05020684678144.409793153221
1163862.983800.0317668014762.9482331985346







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1173846.852667813053515.710435051194177.99490057491
1183871.132157790733527.801369802074214.46294577939
1194012.733494426973657.576037026664367.89095182728
1204388.426462937544021.769070002934755.08385587216
1213854.84017882923476.979623204164232.70073445423
1223892.800115470293504.007389927894281.59284101269
1233869.737930541713470.261657926474269.21420315696
1243913.413865816933503.4831117654323.34461986886
1254013.9237638583593.750380102674434.09714761334
1263890.012318550963459.792912833694320.23172426823
1273901.01611927733460.933724932564341.09851362205
1283905.513502299753455.739003842424355.28800075707

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 3846.85266781305 & 3515.71043505119 & 4177.99490057491 \tabularnewline
118 & 3871.13215779073 & 3527.80136980207 & 4214.46294577939 \tabularnewline
119 & 4012.73349442697 & 3657.57603702666 & 4367.89095182728 \tabularnewline
120 & 4388.42646293754 & 4021.76907000293 & 4755.08385587216 \tabularnewline
121 & 3854.8401788292 & 3476.97962320416 & 4232.70073445423 \tabularnewline
122 & 3892.80011547029 & 3504.00738992789 & 4281.59284101269 \tabularnewline
123 & 3869.73793054171 & 3470.26165792647 & 4269.21420315696 \tabularnewline
124 & 3913.41386581693 & 3503.483111765 & 4323.34461986886 \tabularnewline
125 & 4013.923763858 & 3593.75038010267 & 4434.09714761334 \tabularnewline
126 & 3890.01231855096 & 3459.79291283369 & 4320.23172426823 \tabularnewline
127 & 3901.0161192773 & 3460.93372493256 & 4341.09851362205 \tabularnewline
128 & 3905.51350229975 & 3455.73900384242 & 4355.28800075707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300328&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]117[/C][C]3846.85266781305[/C][C]3515.71043505119[/C][C]4177.99490057491[/C][/ROW]
[ROW][C]118[/C][C]3871.13215779073[/C][C]3527.80136980207[/C][C]4214.46294577939[/C][/ROW]
[ROW][C]119[/C][C]4012.73349442697[/C][C]3657.57603702666[/C][C]4367.89095182728[/C][/ROW]
[ROW][C]120[/C][C]4388.42646293754[/C][C]4021.76907000293[/C][C]4755.08385587216[/C][/ROW]
[ROW][C]121[/C][C]3854.8401788292[/C][C]3476.97962320416[/C][C]4232.70073445423[/C][/ROW]
[ROW][C]122[/C][C]3892.80011547029[/C][C]3504.00738992789[/C][C]4281.59284101269[/C][/ROW]
[ROW][C]123[/C][C]3869.73793054171[/C][C]3470.26165792647[/C][C]4269.21420315696[/C][/ROW]
[ROW][C]124[/C][C]3913.41386581693[/C][C]3503.483111765[/C][C]4323.34461986886[/C][/ROW]
[ROW][C]125[/C][C]4013.923763858[/C][C]3593.75038010267[/C][C]4434.09714761334[/C][/ROW]
[ROW][C]126[/C][C]3890.01231855096[/C][C]3459.79291283369[/C][C]4320.23172426823[/C][/ROW]
[ROW][C]127[/C][C]3901.0161192773[/C][C]3460.93372493256[/C][C]4341.09851362205[/C][/ROW]
[ROW][C]128[/C][C]3905.51350229975[/C][C]3455.73900384242[/C][C]4355.28800075707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300328&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300328&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
1173846.852667813053515.710435051194177.99490057491
1183871.132157790733527.801369802074214.46294577939
1194012.733494426973657.576037026664367.89095182728
1204388.426462937544021.769070002934755.08385587216
1213854.84017882923476.979623204164232.70073445423
1223892.800115470293504.007389927894281.59284101269
1233869.737930541713470.261657926474269.21420315696
1243913.413865816933503.4831117654323.34461986886
1254013.9237638583593.750380102674434.09714761334
1263890.012318550963459.792912833694320.23172426823
1273901.01611927733460.933724932564341.09851362205
1283905.513502299753455.739003842424355.28800075707



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')