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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 computationTue, 06 Dec 2016 13:39:36 +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/06/t1481028314xxoip2haqu2xh4i.htm/, Retrieved Sat, 04 May 2024 19:15:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297818, Retrieved Sat, 04 May 2024 19:15:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [F1:N1809] [2016-12-06 12:39:36] [8d7b5e4c30a3b8052caee801f90adcea] [Current]
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Dataseries X:
3650
3530
3800
4130
3440
4000
3690
4210
4240
4260
4510
4260
3420
3660
3790
3270
3250
3570
3410
4270
4410
4450
3990
4000
4140
3800
3060
3270
3040
3750
3330
3840
4060
3830
3880
3820
3640
2880
3710
2980
3190
3090
3190
3410
3310
3480
3750
3200
3150
3250
3290
2900
2940
3460
3890
3040
3000
3520
2850
2730
2820
3240
3160
3010
2720
2650
2790
3090
3240
3690
3490
2790
3060
3210
3080
2640
2890
3330
2970
2870
3140
3150
2940
2910
3060
2900
2980
2890
2920
2940
3300
3050
2740
3080
3090
2830
3390
3210
2970
2810
2690
2800
2920
2870
2860
3090
3180
3090




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=297818&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=297818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297818&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
alpha0.0289914148667785
beta0.249192098292228
gamma0.383576136510967

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0289914148667785 \tabularnewline
beta & 0.249192098292228 \tabularnewline
gamma & 0.383576136510967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297818&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]0.0289914148667785[/C][/ROW]
[ROW][C]beta[/C][C]0.249192098292228[/C][/ROW]
[ROW][C]gamma[/C][C]0.383576136510967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297818&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
alpha0.0289914148667785
beta0.249192098292228
gamma0.383576136510967







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1334203589.23344017094-169.233440170943
1436603816.41307433463-156.41307433463
1537903914.0843935013-124.0843935013
1632703356.37986099798-86.3798609979826
1732503327.8943908498-77.8943908497981
1835703657.84218379585-87.8421837958481
1934103588.95029964301-178.950299643008
2042704085.70758145701184.292418542988
2144104095.16052489892314.839475101076
2244504141.92274843949308.077251560509
2339904428.21460855354-438.214608553538
2440004171.78789364949-171.787893649494
2541403272.56223321963867.437766780371
2638003537.1222548014262.877745198602
2730603664.570351789-604.570351789002
2832703109.08782407244160.912175927557
2930403094.82740992911-54.8274099291066
3037503425.8007287742324.1992712258
3133303341.95942950812-11.959429508121
3238403987.09491489339-147.094914893393
3340604041.4144569890418.5855430109632
3438304080.77995295541-250.779952955411
3538804072.58237504715-192.582375047148
3638203923.95689006089-103.956890060886
3736403415.70117967857224.298820321427
3828803433.73543090598-553.735430905981
3937103205.8147603971504.185239602902
4029802966.9871128718713.0128871281313
4131902866.41909729749323.580902702509
4230903350.60110083272-260.601100832723
4331903121.4439659524168.5560340475936
4434103716.00598831448-306.005988314485
4533103823.70333038635-513.703330386349
4634803739.74103644207-259.74103644207
4737503745.325684008854.67431599114843
4832003629.21908509238-429.219085092376
4931503225.23551304762-75.2355130476226
5032502934.07979849439315.920201505605
5132903120.96031631696169.039683683045
5229002682.61517022026217.38482977974
5329402698.26029012534241.739709874659
5434602956.5116852743503.488314725696
5538902871.647166736991018.35283326301
5630403360.64324064577-320.643240645767
5730003396.8582856452-396.858285645203
5835203418.01746434078101.982535659222
5928503542.32950813826-692.329508138256
6027303249.13175319896-519.131753198963
6128202978.45717534757-158.457175347571
6232402834.04818467563405.951815324366
6331602972.95403803279187.045961967206
6430102557.38911174213452.610888257874
6527202594.87602293016125.123977069841
6626502952.34498670808-302.344986708078
6727903035.16942712657-245.169427126565
6830902978.97619476583111.02380523417
6932402992.5964383074247.403561692596
7036903216.1615128659473.838487134099
7134903056.02628452134433.973715478665
7227902868.74521204035-78.7452120403473
7330602757.10997930538302.890020694616
7432102851.56303175117358.436968248835
7530802922.4849343897157.515065610298
7626402619.6880074486520.3119925513479
7728902534.25743998426355.742560015742
7833302752.45504136679577.544958633214
7929702901.6967451280568.3032548719498
8028703009.13504324746-139.13504324746
8131403086.3682994857253.6317005142837
8231503407.32279669238-257.322796692377
8329403224.53024084096-284.530240840963
8429102833.6507762330476.3492237669639
8530602877.97179803951182.028201960485
8629002998.05413727173-98.0541372717298
8729802986.05377941083-6.05377941083134
8828902631.37757348215258.622426517848
8929202683.47553697592236.524463024083
9029402985.65366675077-45.6536667507735
9133002927.48097586295372.519024137054
9230502968.9981260201881.0018739798224
9327403128.52169115868-388.521691158677
9430803321.75759897365-241.757598973655
9530903130.31202635246-40.312026352462
9628302883.71804685297-53.7180468529741
9733902965.48294458184424.517055418157
9832102991.88292315395218.117076846045
9929703029.20484724118-59.2048472411839
10028102777.0738691120132.926130887995
10126902818.27352248483-128.273522484834
10228003006.01678327281-206.016783272807
10329203099.02721743333-179.027217433331
10428703012.07389046699-142.073890466994
10528602984.73869903339-124.738699033394
10630903236.67612075218-146.67612075218
10731803120.0945063374359.9054936625676
10830902869.21469561756220.785304382436

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3420 & 3589.23344017094 & -169.233440170943 \tabularnewline
14 & 3660 & 3816.41307433463 & -156.41307433463 \tabularnewline
15 & 3790 & 3914.0843935013 & -124.0843935013 \tabularnewline
16 & 3270 & 3356.37986099798 & -86.3798609979826 \tabularnewline
17 & 3250 & 3327.8943908498 & -77.8943908497981 \tabularnewline
18 & 3570 & 3657.84218379585 & -87.8421837958481 \tabularnewline
19 & 3410 & 3588.95029964301 & -178.950299643008 \tabularnewline
20 & 4270 & 4085.70758145701 & 184.292418542988 \tabularnewline
21 & 4410 & 4095.16052489892 & 314.839475101076 \tabularnewline
22 & 4450 & 4141.92274843949 & 308.077251560509 \tabularnewline
23 & 3990 & 4428.21460855354 & -438.214608553538 \tabularnewline
24 & 4000 & 4171.78789364949 & -171.787893649494 \tabularnewline
25 & 4140 & 3272.56223321963 & 867.437766780371 \tabularnewline
26 & 3800 & 3537.1222548014 & 262.877745198602 \tabularnewline
27 & 3060 & 3664.570351789 & -604.570351789002 \tabularnewline
28 & 3270 & 3109.08782407244 & 160.912175927557 \tabularnewline
29 & 3040 & 3094.82740992911 & -54.8274099291066 \tabularnewline
30 & 3750 & 3425.8007287742 & 324.1992712258 \tabularnewline
31 & 3330 & 3341.95942950812 & -11.959429508121 \tabularnewline
32 & 3840 & 3987.09491489339 & -147.094914893393 \tabularnewline
33 & 4060 & 4041.41445698904 & 18.5855430109632 \tabularnewline
34 & 3830 & 4080.77995295541 & -250.779952955411 \tabularnewline
35 & 3880 & 4072.58237504715 & -192.582375047148 \tabularnewline
36 & 3820 & 3923.95689006089 & -103.956890060886 \tabularnewline
37 & 3640 & 3415.70117967857 & 224.298820321427 \tabularnewline
38 & 2880 & 3433.73543090598 & -553.735430905981 \tabularnewline
39 & 3710 & 3205.8147603971 & 504.185239602902 \tabularnewline
40 & 2980 & 2966.98711287187 & 13.0128871281313 \tabularnewline
41 & 3190 & 2866.41909729749 & 323.580902702509 \tabularnewline
42 & 3090 & 3350.60110083272 & -260.601100832723 \tabularnewline
43 & 3190 & 3121.44396595241 & 68.5560340475936 \tabularnewline
44 & 3410 & 3716.00598831448 & -306.005988314485 \tabularnewline
45 & 3310 & 3823.70333038635 & -513.703330386349 \tabularnewline
46 & 3480 & 3739.74103644207 & -259.74103644207 \tabularnewline
47 & 3750 & 3745.32568400885 & 4.67431599114843 \tabularnewline
48 & 3200 & 3629.21908509238 & -429.219085092376 \tabularnewline
49 & 3150 & 3225.23551304762 & -75.2355130476226 \tabularnewline
50 & 3250 & 2934.07979849439 & 315.920201505605 \tabularnewline
51 & 3290 & 3120.96031631696 & 169.039683683045 \tabularnewline
52 & 2900 & 2682.61517022026 & 217.38482977974 \tabularnewline
53 & 2940 & 2698.26029012534 & 241.739709874659 \tabularnewline
54 & 3460 & 2956.5116852743 & 503.488314725696 \tabularnewline
55 & 3890 & 2871.64716673699 & 1018.35283326301 \tabularnewline
56 & 3040 & 3360.64324064577 & -320.643240645767 \tabularnewline
57 & 3000 & 3396.8582856452 & -396.858285645203 \tabularnewline
58 & 3520 & 3418.01746434078 & 101.982535659222 \tabularnewline
59 & 2850 & 3542.32950813826 & -692.329508138256 \tabularnewline
60 & 2730 & 3249.13175319896 & -519.131753198963 \tabularnewline
61 & 2820 & 2978.45717534757 & -158.457175347571 \tabularnewline
62 & 3240 & 2834.04818467563 & 405.951815324366 \tabularnewline
63 & 3160 & 2972.95403803279 & 187.045961967206 \tabularnewline
64 & 3010 & 2557.38911174213 & 452.610888257874 \tabularnewline
65 & 2720 & 2594.87602293016 & 125.123977069841 \tabularnewline
66 & 2650 & 2952.34498670808 & -302.344986708078 \tabularnewline
67 & 2790 & 3035.16942712657 & -245.169427126565 \tabularnewline
68 & 3090 & 2978.97619476583 & 111.02380523417 \tabularnewline
69 & 3240 & 2992.5964383074 & 247.403561692596 \tabularnewline
70 & 3690 & 3216.1615128659 & 473.838487134099 \tabularnewline
71 & 3490 & 3056.02628452134 & 433.973715478665 \tabularnewline
72 & 2790 & 2868.74521204035 & -78.7452120403473 \tabularnewline
73 & 3060 & 2757.10997930538 & 302.890020694616 \tabularnewline
74 & 3210 & 2851.56303175117 & 358.436968248835 \tabularnewline
75 & 3080 & 2922.4849343897 & 157.515065610298 \tabularnewline
76 & 2640 & 2619.68800744865 & 20.3119925513479 \tabularnewline
77 & 2890 & 2534.25743998426 & 355.742560015742 \tabularnewline
78 & 3330 & 2752.45504136679 & 577.544958633214 \tabularnewline
79 & 2970 & 2901.69674512805 & 68.3032548719498 \tabularnewline
80 & 2870 & 3009.13504324746 & -139.13504324746 \tabularnewline
81 & 3140 & 3086.36829948572 & 53.6317005142837 \tabularnewline
82 & 3150 & 3407.32279669238 & -257.322796692377 \tabularnewline
83 & 2940 & 3224.53024084096 & -284.530240840963 \tabularnewline
84 & 2910 & 2833.65077623304 & 76.3492237669639 \tabularnewline
85 & 3060 & 2877.97179803951 & 182.028201960485 \tabularnewline
86 & 2900 & 2998.05413727173 & -98.0541372717298 \tabularnewline
87 & 2980 & 2986.05377941083 & -6.05377941083134 \tabularnewline
88 & 2890 & 2631.37757348215 & 258.622426517848 \tabularnewline
89 & 2920 & 2683.47553697592 & 236.524463024083 \tabularnewline
90 & 2940 & 2985.65366675077 & -45.6536667507735 \tabularnewline
91 & 3300 & 2927.48097586295 & 372.519024137054 \tabularnewline
92 & 3050 & 2968.99812602018 & 81.0018739798224 \tabularnewline
93 & 2740 & 3128.52169115868 & -388.521691158677 \tabularnewline
94 & 3080 & 3321.75759897365 & -241.757598973655 \tabularnewline
95 & 3090 & 3130.31202635246 & -40.312026352462 \tabularnewline
96 & 2830 & 2883.71804685297 & -53.7180468529741 \tabularnewline
97 & 3390 & 2965.48294458184 & 424.517055418157 \tabularnewline
98 & 3210 & 2991.88292315395 & 218.117076846045 \tabularnewline
99 & 2970 & 3029.20484724118 & -59.2048472411839 \tabularnewline
100 & 2810 & 2777.07386911201 & 32.926130887995 \tabularnewline
101 & 2690 & 2818.27352248483 & -128.273522484834 \tabularnewline
102 & 2800 & 3006.01678327281 & -206.016783272807 \tabularnewline
103 & 2920 & 3099.02721743333 & -179.027217433331 \tabularnewline
104 & 2870 & 3012.07389046699 & -142.073890466994 \tabularnewline
105 & 2860 & 2984.73869903339 & -124.738699033394 \tabularnewline
106 & 3090 & 3236.67612075218 & -146.67612075218 \tabularnewline
107 & 3180 & 3120.09450633743 & 59.9054936625676 \tabularnewline
108 & 3090 & 2869.21469561756 & 220.785304382436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297818&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]3420[/C][C]3589.23344017094[/C][C]-169.233440170943[/C][/ROW]
[ROW][C]14[/C][C]3660[/C][C]3816.41307433463[/C][C]-156.41307433463[/C][/ROW]
[ROW][C]15[/C][C]3790[/C][C]3914.0843935013[/C][C]-124.0843935013[/C][/ROW]
[ROW][C]16[/C][C]3270[/C][C]3356.37986099798[/C][C]-86.3798609979826[/C][/ROW]
[ROW][C]17[/C][C]3250[/C][C]3327.8943908498[/C][C]-77.8943908497981[/C][/ROW]
[ROW][C]18[/C][C]3570[/C][C]3657.84218379585[/C][C]-87.8421837958481[/C][/ROW]
[ROW][C]19[/C][C]3410[/C][C]3588.95029964301[/C][C]-178.950299643008[/C][/ROW]
[ROW][C]20[/C][C]4270[/C][C]4085.70758145701[/C][C]184.292418542988[/C][/ROW]
[ROW][C]21[/C][C]4410[/C][C]4095.16052489892[/C][C]314.839475101076[/C][/ROW]
[ROW][C]22[/C][C]4450[/C][C]4141.92274843949[/C][C]308.077251560509[/C][/ROW]
[ROW][C]23[/C][C]3990[/C][C]4428.21460855354[/C][C]-438.214608553538[/C][/ROW]
[ROW][C]24[/C][C]4000[/C][C]4171.78789364949[/C][C]-171.787893649494[/C][/ROW]
[ROW][C]25[/C][C]4140[/C][C]3272.56223321963[/C][C]867.437766780371[/C][/ROW]
[ROW][C]26[/C][C]3800[/C][C]3537.1222548014[/C][C]262.877745198602[/C][/ROW]
[ROW][C]27[/C][C]3060[/C][C]3664.570351789[/C][C]-604.570351789002[/C][/ROW]
[ROW][C]28[/C][C]3270[/C][C]3109.08782407244[/C][C]160.912175927557[/C][/ROW]
[ROW][C]29[/C][C]3040[/C][C]3094.82740992911[/C][C]-54.8274099291066[/C][/ROW]
[ROW][C]30[/C][C]3750[/C][C]3425.8007287742[/C][C]324.1992712258[/C][/ROW]
[ROW][C]31[/C][C]3330[/C][C]3341.95942950812[/C][C]-11.959429508121[/C][/ROW]
[ROW][C]32[/C][C]3840[/C][C]3987.09491489339[/C][C]-147.094914893393[/C][/ROW]
[ROW][C]33[/C][C]4060[/C][C]4041.41445698904[/C][C]18.5855430109632[/C][/ROW]
[ROW][C]34[/C][C]3830[/C][C]4080.77995295541[/C][C]-250.779952955411[/C][/ROW]
[ROW][C]35[/C][C]3880[/C][C]4072.58237504715[/C][C]-192.582375047148[/C][/ROW]
[ROW][C]36[/C][C]3820[/C][C]3923.95689006089[/C][C]-103.956890060886[/C][/ROW]
[ROW][C]37[/C][C]3640[/C][C]3415.70117967857[/C][C]224.298820321427[/C][/ROW]
[ROW][C]38[/C][C]2880[/C][C]3433.73543090598[/C][C]-553.735430905981[/C][/ROW]
[ROW][C]39[/C][C]3710[/C][C]3205.8147603971[/C][C]504.185239602902[/C][/ROW]
[ROW][C]40[/C][C]2980[/C][C]2966.98711287187[/C][C]13.0128871281313[/C][/ROW]
[ROW][C]41[/C][C]3190[/C][C]2866.41909729749[/C][C]323.580902702509[/C][/ROW]
[ROW][C]42[/C][C]3090[/C][C]3350.60110083272[/C][C]-260.601100832723[/C][/ROW]
[ROW][C]43[/C][C]3190[/C][C]3121.44396595241[/C][C]68.5560340475936[/C][/ROW]
[ROW][C]44[/C][C]3410[/C][C]3716.00598831448[/C][C]-306.005988314485[/C][/ROW]
[ROW][C]45[/C][C]3310[/C][C]3823.70333038635[/C][C]-513.703330386349[/C][/ROW]
[ROW][C]46[/C][C]3480[/C][C]3739.74103644207[/C][C]-259.74103644207[/C][/ROW]
[ROW][C]47[/C][C]3750[/C][C]3745.32568400885[/C][C]4.67431599114843[/C][/ROW]
[ROW][C]48[/C][C]3200[/C][C]3629.21908509238[/C][C]-429.219085092376[/C][/ROW]
[ROW][C]49[/C][C]3150[/C][C]3225.23551304762[/C][C]-75.2355130476226[/C][/ROW]
[ROW][C]50[/C][C]3250[/C][C]2934.07979849439[/C][C]315.920201505605[/C][/ROW]
[ROW][C]51[/C][C]3290[/C][C]3120.96031631696[/C][C]169.039683683045[/C][/ROW]
[ROW][C]52[/C][C]2900[/C][C]2682.61517022026[/C][C]217.38482977974[/C][/ROW]
[ROW][C]53[/C][C]2940[/C][C]2698.26029012534[/C][C]241.739709874659[/C][/ROW]
[ROW][C]54[/C][C]3460[/C][C]2956.5116852743[/C][C]503.488314725696[/C][/ROW]
[ROW][C]55[/C][C]3890[/C][C]2871.64716673699[/C][C]1018.35283326301[/C][/ROW]
[ROW][C]56[/C][C]3040[/C][C]3360.64324064577[/C][C]-320.643240645767[/C][/ROW]
[ROW][C]57[/C][C]3000[/C][C]3396.8582856452[/C][C]-396.858285645203[/C][/ROW]
[ROW][C]58[/C][C]3520[/C][C]3418.01746434078[/C][C]101.982535659222[/C][/ROW]
[ROW][C]59[/C][C]2850[/C][C]3542.32950813826[/C][C]-692.329508138256[/C][/ROW]
[ROW][C]60[/C][C]2730[/C][C]3249.13175319896[/C][C]-519.131753198963[/C][/ROW]
[ROW][C]61[/C][C]2820[/C][C]2978.45717534757[/C][C]-158.457175347571[/C][/ROW]
[ROW][C]62[/C][C]3240[/C][C]2834.04818467563[/C][C]405.951815324366[/C][/ROW]
[ROW][C]63[/C][C]3160[/C][C]2972.95403803279[/C][C]187.045961967206[/C][/ROW]
[ROW][C]64[/C][C]3010[/C][C]2557.38911174213[/C][C]452.610888257874[/C][/ROW]
[ROW][C]65[/C][C]2720[/C][C]2594.87602293016[/C][C]125.123977069841[/C][/ROW]
[ROW][C]66[/C][C]2650[/C][C]2952.34498670808[/C][C]-302.344986708078[/C][/ROW]
[ROW][C]67[/C][C]2790[/C][C]3035.16942712657[/C][C]-245.169427126565[/C][/ROW]
[ROW][C]68[/C][C]3090[/C][C]2978.97619476583[/C][C]111.02380523417[/C][/ROW]
[ROW][C]69[/C][C]3240[/C][C]2992.5964383074[/C][C]247.403561692596[/C][/ROW]
[ROW][C]70[/C][C]3690[/C][C]3216.1615128659[/C][C]473.838487134099[/C][/ROW]
[ROW][C]71[/C][C]3490[/C][C]3056.02628452134[/C][C]433.973715478665[/C][/ROW]
[ROW][C]72[/C][C]2790[/C][C]2868.74521204035[/C][C]-78.7452120403473[/C][/ROW]
[ROW][C]73[/C][C]3060[/C][C]2757.10997930538[/C][C]302.890020694616[/C][/ROW]
[ROW][C]74[/C][C]3210[/C][C]2851.56303175117[/C][C]358.436968248835[/C][/ROW]
[ROW][C]75[/C][C]3080[/C][C]2922.4849343897[/C][C]157.515065610298[/C][/ROW]
[ROW][C]76[/C][C]2640[/C][C]2619.68800744865[/C][C]20.3119925513479[/C][/ROW]
[ROW][C]77[/C][C]2890[/C][C]2534.25743998426[/C][C]355.742560015742[/C][/ROW]
[ROW][C]78[/C][C]3330[/C][C]2752.45504136679[/C][C]577.544958633214[/C][/ROW]
[ROW][C]79[/C][C]2970[/C][C]2901.69674512805[/C][C]68.3032548719498[/C][/ROW]
[ROW][C]80[/C][C]2870[/C][C]3009.13504324746[/C][C]-139.13504324746[/C][/ROW]
[ROW][C]81[/C][C]3140[/C][C]3086.36829948572[/C][C]53.6317005142837[/C][/ROW]
[ROW][C]82[/C][C]3150[/C][C]3407.32279669238[/C][C]-257.322796692377[/C][/ROW]
[ROW][C]83[/C][C]2940[/C][C]3224.53024084096[/C][C]-284.530240840963[/C][/ROW]
[ROW][C]84[/C][C]2910[/C][C]2833.65077623304[/C][C]76.3492237669639[/C][/ROW]
[ROW][C]85[/C][C]3060[/C][C]2877.97179803951[/C][C]182.028201960485[/C][/ROW]
[ROW][C]86[/C][C]2900[/C][C]2998.05413727173[/C][C]-98.0541372717298[/C][/ROW]
[ROW][C]87[/C][C]2980[/C][C]2986.05377941083[/C][C]-6.05377941083134[/C][/ROW]
[ROW][C]88[/C][C]2890[/C][C]2631.37757348215[/C][C]258.622426517848[/C][/ROW]
[ROW][C]89[/C][C]2920[/C][C]2683.47553697592[/C][C]236.524463024083[/C][/ROW]
[ROW][C]90[/C][C]2940[/C][C]2985.65366675077[/C][C]-45.6536667507735[/C][/ROW]
[ROW][C]91[/C][C]3300[/C][C]2927.48097586295[/C][C]372.519024137054[/C][/ROW]
[ROW][C]92[/C][C]3050[/C][C]2968.99812602018[/C][C]81.0018739798224[/C][/ROW]
[ROW][C]93[/C][C]2740[/C][C]3128.52169115868[/C][C]-388.521691158677[/C][/ROW]
[ROW][C]94[/C][C]3080[/C][C]3321.75759897365[/C][C]-241.757598973655[/C][/ROW]
[ROW][C]95[/C][C]3090[/C][C]3130.31202635246[/C][C]-40.312026352462[/C][/ROW]
[ROW][C]96[/C][C]2830[/C][C]2883.71804685297[/C][C]-53.7180468529741[/C][/ROW]
[ROW][C]97[/C][C]3390[/C][C]2965.48294458184[/C][C]424.517055418157[/C][/ROW]
[ROW][C]98[/C][C]3210[/C][C]2991.88292315395[/C][C]218.117076846045[/C][/ROW]
[ROW][C]99[/C][C]2970[/C][C]3029.20484724118[/C][C]-59.2048472411839[/C][/ROW]
[ROW][C]100[/C][C]2810[/C][C]2777.07386911201[/C][C]32.926130887995[/C][/ROW]
[ROW][C]101[/C][C]2690[/C][C]2818.27352248483[/C][C]-128.273522484834[/C][/ROW]
[ROW][C]102[/C][C]2800[/C][C]3006.01678327281[/C][C]-206.016783272807[/C][/ROW]
[ROW][C]103[/C][C]2920[/C][C]3099.02721743333[/C][C]-179.027217433331[/C][/ROW]
[ROW][C]104[/C][C]2870[/C][C]3012.07389046699[/C][C]-142.073890466994[/C][/ROW]
[ROW][C]105[/C][C]2860[/C][C]2984.73869903339[/C][C]-124.738699033394[/C][/ROW]
[ROW][C]106[/C][C]3090[/C][C]3236.67612075218[/C][C]-146.67612075218[/C][/ROW]
[ROW][C]107[/C][C]3180[/C][C]3120.09450633743[/C][C]59.9054936625676[/C][/ROW]
[ROW][C]108[/C][C]3090[/C][C]2869.21469561756[/C][C]220.785304382436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297818&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
1334203589.23344017094-169.233440170943
1436603816.41307433463-156.41307433463
1537903914.0843935013-124.0843935013
1632703356.37986099798-86.3798609979826
1732503327.8943908498-77.8943908497981
1835703657.84218379585-87.8421837958481
1934103588.95029964301-178.950299643008
2042704085.70758145701184.292418542988
2144104095.16052489892314.839475101076
2244504141.92274843949308.077251560509
2339904428.21460855354-438.214608553538
2440004171.78789364949-171.787893649494
2541403272.56223321963867.437766780371
2638003537.1222548014262.877745198602
2730603664.570351789-604.570351789002
2832703109.08782407244160.912175927557
2930403094.82740992911-54.8274099291066
3037503425.8007287742324.1992712258
3133303341.95942950812-11.959429508121
3238403987.09491489339-147.094914893393
3340604041.4144569890418.5855430109632
3438304080.77995295541-250.779952955411
3538804072.58237504715-192.582375047148
3638203923.95689006089-103.956890060886
3736403415.70117967857224.298820321427
3828803433.73543090598-553.735430905981
3937103205.8147603971504.185239602902
4029802966.9871128718713.0128871281313
4131902866.41909729749323.580902702509
4230903350.60110083272-260.601100832723
4331903121.4439659524168.5560340475936
4434103716.00598831448-306.005988314485
4533103823.70333038635-513.703330386349
4634803739.74103644207-259.74103644207
4737503745.325684008854.67431599114843
4832003629.21908509238-429.219085092376
4931503225.23551304762-75.2355130476226
5032502934.07979849439315.920201505605
5132903120.96031631696169.039683683045
5229002682.61517022026217.38482977974
5329402698.26029012534241.739709874659
5434602956.5116852743503.488314725696
5538902871.647166736991018.35283326301
5630403360.64324064577-320.643240645767
5730003396.8582856452-396.858285645203
5835203418.01746434078101.982535659222
5928503542.32950813826-692.329508138256
6027303249.13175319896-519.131753198963
6128202978.45717534757-158.457175347571
6232402834.04818467563405.951815324366
6331602972.95403803279187.045961967206
6430102557.38911174213452.610888257874
6527202594.87602293016125.123977069841
6626502952.34498670808-302.344986708078
6727903035.16942712657-245.169427126565
6830902978.97619476583111.02380523417
6932402992.5964383074247.403561692596
7036903216.1615128659473.838487134099
7134903056.02628452134433.973715478665
7227902868.74521204035-78.7452120403473
7330602757.10997930538302.890020694616
7432102851.56303175117358.436968248835
7530802922.4849343897157.515065610298
7626402619.6880074486520.3119925513479
7728902534.25743998426355.742560015742
7833302752.45504136679577.544958633214
7929702901.6967451280568.3032548719498
8028703009.13504324746-139.13504324746
8131403086.3682994857253.6317005142837
8231503407.32279669238-257.322796692377
8329403224.53024084096-284.530240840963
8429102833.6507762330476.3492237669639
8530602877.97179803951182.028201960485
8629002998.05413727173-98.0541372717298
8729802986.05377941083-6.05377941083134
8828902631.37757348215258.622426517848
8929202683.47553697592236.524463024083
9029402985.65366675077-45.6536667507735
9133002927.48097586295372.519024137054
9230502968.9981260201881.0018739798224
9327403128.52169115868-388.521691158677
9430803321.75759897365-241.757598973655
9530903130.31202635246-40.312026352462
9628302883.71804685297-53.7180468529741
9733902965.48294458184424.517055418157
9832102991.88292315395218.117076846045
9929703029.20484724118-59.2048472411839
10028102777.0738691120132.926130887995
10126902818.27352248483-128.273522484834
10228003006.01678327281-206.016783272807
10329203099.02721743333-179.027217433331
10428703012.07389046699-142.073890466994
10528602984.73869903339-124.738699033394
10630903236.67612075218-146.67612075218
10731803120.0945063374359.9054936625676
10830902869.21469561756220.785304382436







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093136.844234775042538.276342977133735.41212657296
1103070.780116706212471.819816444783669.74041696763
1112993.630715284012394.106284604623593.15514596341
1122773.100935255672172.809984524923373.39188598642
1132748.638463582472147.348277155123349.92865000983
1142907.403519551282304.851504670793509.95553443177
1153014.186330675682410.080585032953618.2920763184
1162945.227344682822339.247352025353551.2073373403
1172928.53468125362320.332142007363536.73722049984
1183176.885915966112566.0857170363787.68611489622
1193143.526985530212529.728310340323757.32566072011
1202952.426084092422335.203660599693569.64850758516

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 3136.84423477504 & 2538.27634297713 & 3735.41212657296 \tabularnewline
110 & 3070.78011670621 & 2471.81981644478 & 3669.74041696763 \tabularnewline
111 & 2993.63071528401 & 2394.10628460462 & 3593.15514596341 \tabularnewline
112 & 2773.10093525567 & 2172.80998452492 & 3373.39188598642 \tabularnewline
113 & 2748.63846358247 & 2147.34827715512 & 3349.92865000983 \tabularnewline
114 & 2907.40351955128 & 2304.85150467079 & 3509.95553443177 \tabularnewline
115 & 3014.18633067568 & 2410.08058503295 & 3618.2920763184 \tabularnewline
116 & 2945.22734468282 & 2339.24735202535 & 3551.2073373403 \tabularnewline
117 & 2928.5346812536 & 2320.33214200736 & 3536.73722049984 \tabularnewline
118 & 3176.88591596611 & 2566.085717036 & 3787.68611489622 \tabularnewline
119 & 3143.52698553021 & 2529.72831034032 & 3757.32566072011 \tabularnewline
120 & 2952.42608409242 & 2335.20366059969 & 3569.64850758516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297818&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]3136.84423477504[/C][C]2538.27634297713[/C][C]3735.41212657296[/C][/ROW]
[ROW][C]110[/C][C]3070.78011670621[/C][C]2471.81981644478[/C][C]3669.74041696763[/C][/ROW]
[ROW][C]111[/C][C]2993.63071528401[/C][C]2394.10628460462[/C][C]3593.15514596341[/C][/ROW]
[ROW][C]112[/C][C]2773.10093525567[/C][C]2172.80998452492[/C][C]3373.39188598642[/C][/ROW]
[ROW][C]113[/C][C]2748.63846358247[/C][C]2147.34827715512[/C][C]3349.92865000983[/C][/ROW]
[ROW][C]114[/C][C]2907.40351955128[/C][C]2304.85150467079[/C][C]3509.95553443177[/C][/ROW]
[ROW][C]115[/C][C]3014.18633067568[/C][C]2410.08058503295[/C][C]3618.2920763184[/C][/ROW]
[ROW][C]116[/C][C]2945.22734468282[/C][C]2339.24735202535[/C][C]3551.2073373403[/C][/ROW]
[ROW][C]117[/C][C]2928.5346812536[/C][C]2320.33214200736[/C][C]3536.73722049984[/C][/ROW]
[ROW][C]118[/C][C]3176.88591596611[/C][C]2566.085717036[/C][C]3787.68611489622[/C][/ROW]
[ROW][C]119[/C][C]3143.52698553021[/C][C]2529.72831034032[/C][C]3757.32566072011[/C][/ROW]
[ROW][C]120[/C][C]2952.42608409242[/C][C]2335.20366059969[/C][C]3569.64850758516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297818&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297818&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
1093136.844234775042538.276342977133735.41212657296
1103070.780116706212471.819816444783669.74041696763
1112993.630715284012394.106284604623593.15514596341
1122773.100935255672172.809984524923373.39188598642
1132748.638463582472147.348277155123349.92865000983
1142907.403519551282304.851504670793509.95553443177
1153014.186330675682410.080585032953618.2920763184
1162945.227344682822339.247352025353551.2073373403
1172928.53468125362320.332142007363536.73722049984
1183176.885915966112566.0857170363787.68611489622
1193143.526985530212529.728310340323757.32566072011
1202952.426084092422335.203660599693569.64850758516



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')