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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, 23 Dec 2016 15:00:45 +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/23/t1482501667ecwbfqffabkoest.htm/, Retrieved Tue, 07 May 2024 13:39:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302957, Retrieved Tue, 07 May 2024 13:39:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ES N2671] [2016-12-23 14:00:45] [11b61e09f442d73f657668491c17a736] [Current]
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Dataseries X:
6258.5
6191
5939.5
5517.5
5382.5
5785
5353.5
5205.5
4915
4691.5
4564.5
4496
4877.5
4703.5
4528.5
4262.5
4077
4291
4357
4191
4025.5
3994.5
3934.5
3989
4565.5
4451
4312.5
4075
4005.5
4376.5
4341
4025.5
3992
3958.5
3907.5
3858.5
4236
4520.5
4333.5
4057.5
4079
4387.5
4235.5
3977.5
4007.5
3921
3936
3730.5
4310
4251.5
4062
3653
3659
3827.5
3726.5
3544
3428.5
3422.5
3401
3263
3801.5
3741
3545
3179.5
3276.5
3409.5
3411.5
3329.5
3184
3091
3162.5
3071
3654.5
3441.5
3189
3114.5
3078
3425
3368
3176
3165
3111
3247.5
3150
3628
3567
3348.5
3228.5
3181.5
3351
3472.5
3418.5
3409
3361
3605.5
3671.5
4297.5
4459.5
4402
4024.5
4116.5
4387
4288
4118.5
4035
4006.5
4143
4279.5
4974.5
5080.5
4845.5
4472.5
4584.5
5047.5
4922.5
4695
4545




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=302957&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=302957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302957&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
alpha0.816405448799803
beta0.0904009090729233
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.816405448799803 \tabularnewline
beta & 0.0904009090729233 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302957&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]0.816405448799803[/C][/ROW]
[ROW][C]beta[/C][C]0.0904009090729233[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302957&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
alpha0.816405448799803
beta0.0904009090729233
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134877.55603.15852553332-725.658525533324
144703.54770.03633885671-66.5363388567139
154528.54468.1121372378360.3878627621707
164262.54174.1966798022488.3033201977551
1740773982.1702029634694.8297970365438
1842914187.80482238373103.195177616272
1943574188.29227107505168.707728924946
2041914190.851980306650.148019693346214
214025.53942.672343267482.8276567326047
223994.53813.57499482331180.925005176691
233934.53852.5284603954281.9715396045831
2439893874.78984865784114.210151342156
254565.54205.85544748418359.644552515818
2644514475.73064964107-24.7306496410747
274312.54334.88217964551-22.3821796455068
2840754077.24374035533-2.24374035532765
294005.53898.49371738734107.006282612655
304376.54196.03289188685180.467108113148
3143414364.79064273677-23.7906427367689
324025.54257.60756013488-232.107560134876
3339923897.6430958095894.3569041904243
343958.53854.64367964528103.856320354717
353907.53865.3918852605642.108114739437
363858.53910.31058070689-51.8105807068937
3742364176.9738444142659.0261555857442
384520.54152.47415093475368.025849065249
394333.54379.43168139662-45.931681396617
404057.54148.1356773677-90.6356773677035
4140793952.51734246117126.482657538829
424387.54321.2261516092266.2738483907824
434235.54390.35271481608-154.852714816077
443977.54158.58974988214-181.089749882141
454007.53924.2984607421383.201539257866
4639213896.4195666636624.5804333363371
4739363848.3756052275887.6243947724233
483730.53933.45498397425-202.954983974246
4943104098.27529571791211.724704282089
504251.54272.0254535878-20.5254535877993
5140624106.5504029239-44.5504029238973
5236533872.4798116777-219.479811677699
5336593600.5392176223958.46078237761
543827.53852.11820230982-24.618202309824
553726.53779.32247060031-52.8224706003098
5635443615.00171697359-71.0017169735879
573428.53506.76207677707-78.2620767770736
583422.53323.7919291299398.7080708700746
5934013333.6343345089567.3656654910515
6032633330.97475133394-67.9747513339412
613801.53615.75867753316185.741322466842
6237413715.4280659085225.5719340914843
6335453589.87566668534-44.8756666853365
643179.53338.85842443059-159.358424430586
653276.53162.73760367208113.762396327922
663409.53418.8102857511-9.31028575110122
673411.53355.9393660656155.5606339343863
683329.53292.0553230941337.4446769058673
6931843287.06955585686-103.069555856862
7030913132.21318962085-41.2131896208502
713162.53028.75510510005133.744894899948
7230713067.073253671813.9267463281908
733654.53445.44870873577209.051291264232
743441.53553.61168570907-112.111685709071
7531893318.58210897316-129.582108973161
763114.52995.58337173473118.916628265273
7730783115.37158803472-37.3715880347204
7834253225.00044631675199.999553683248
7933683369.79286537869-1.79286537869211
8031763276.95009781559-100.950097815588
8131653144.0647630440820.9352369559183
8231113120.69565831187-9.6956583118731
833247.53095.26019785936152.239802140644
8431503145.398447810834.60155218916725
8536283596.3151581834831.6848418165209
8635673512.5499422249654.4500577750387
873348.53427.91716776584-79.4171677658392
883228.53208.0150289426520.4849710573517
893181.53236.99937196109-55.4993719610929
9033513398.82146448367-47.8214644836735
913472.53304.40210885089168.097891149113
923418.53340.7143992999777.7856007000323
9334093399.520708175749.47929182425742
9433613381.91307867623-20.9130786762257
953605.53400.62345967082204.876540329177
963671.53482.45525191586189.044748084141
974297.54203.8952023199493.6047976800646
984459.54203.63380333619255.866196663813
9944024281.0711009471120.928899052901
1004024.54273.09900405517-248.59900405517
1014116.54119.64490520523-3.14490520522577
10243874447.46063380016-60.4606338001604
10342884436.53586151142-148.535861511421
1044118.54201.39654774011-82.8965477401116
10540354132.2657260991-97.2657260991009
1064006.54027.52557261761-21.0255726176051
10741434112.3431260018930.6568739981103
1084279.54031.50863015839247.991369841607
1094974.54866.38738726624108.112612733761
1105080.54897.03969099784183.460309002162
1114845.54861.85109730669-16.351097306685
1124472.54637.97213814129-165.472138141293
1134584.54599.68405315373-15.1840531537264
1145047.54933.34199844124114.15800155876
1154922.55052.69859956349-130.198599563486
11646954832.61238995268-137.612389952682
11745454716.23400739489-171.234007394894

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4877.5 & 5603.15852553332 & -725.658525533324 \tabularnewline
14 & 4703.5 & 4770.03633885671 & -66.5363388567139 \tabularnewline
15 & 4528.5 & 4468.11213723783 & 60.3878627621707 \tabularnewline
16 & 4262.5 & 4174.19667980224 & 88.3033201977551 \tabularnewline
17 & 4077 & 3982.17020296346 & 94.8297970365438 \tabularnewline
18 & 4291 & 4187.80482238373 & 103.195177616272 \tabularnewline
19 & 4357 & 4188.29227107505 & 168.707728924946 \tabularnewline
20 & 4191 & 4190.85198030665 & 0.148019693346214 \tabularnewline
21 & 4025.5 & 3942.6723432674 & 82.8276567326047 \tabularnewline
22 & 3994.5 & 3813.57499482331 & 180.925005176691 \tabularnewline
23 & 3934.5 & 3852.52846039542 & 81.9715396045831 \tabularnewline
24 & 3989 & 3874.78984865784 & 114.210151342156 \tabularnewline
25 & 4565.5 & 4205.85544748418 & 359.644552515818 \tabularnewline
26 & 4451 & 4475.73064964107 & -24.7306496410747 \tabularnewline
27 & 4312.5 & 4334.88217964551 & -22.3821796455068 \tabularnewline
28 & 4075 & 4077.24374035533 & -2.24374035532765 \tabularnewline
29 & 4005.5 & 3898.49371738734 & 107.006282612655 \tabularnewline
30 & 4376.5 & 4196.03289188685 & 180.467108113148 \tabularnewline
31 & 4341 & 4364.79064273677 & -23.7906427367689 \tabularnewline
32 & 4025.5 & 4257.60756013488 & -232.107560134876 \tabularnewline
33 & 3992 & 3897.64309580958 & 94.3569041904243 \tabularnewline
34 & 3958.5 & 3854.64367964528 & 103.856320354717 \tabularnewline
35 & 3907.5 & 3865.39188526056 & 42.108114739437 \tabularnewline
36 & 3858.5 & 3910.31058070689 & -51.8105807068937 \tabularnewline
37 & 4236 & 4176.97384441426 & 59.0261555857442 \tabularnewline
38 & 4520.5 & 4152.47415093475 & 368.025849065249 \tabularnewline
39 & 4333.5 & 4379.43168139662 & -45.931681396617 \tabularnewline
40 & 4057.5 & 4148.1356773677 & -90.6356773677035 \tabularnewline
41 & 4079 & 3952.51734246117 & 126.482657538829 \tabularnewline
42 & 4387.5 & 4321.22615160922 & 66.2738483907824 \tabularnewline
43 & 4235.5 & 4390.35271481608 & -154.852714816077 \tabularnewline
44 & 3977.5 & 4158.58974988214 & -181.089749882141 \tabularnewline
45 & 4007.5 & 3924.29846074213 & 83.201539257866 \tabularnewline
46 & 3921 & 3896.41956666366 & 24.5804333363371 \tabularnewline
47 & 3936 & 3848.37560522758 & 87.6243947724233 \tabularnewline
48 & 3730.5 & 3933.45498397425 & -202.954983974246 \tabularnewline
49 & 4310 & 4098.27529571791 & 211.724704282089 \tabularnewline
50 & 4251.5 & 4272.0254535878 & -20.5254535877993 \tabularnewline
51 & 4062 & 4106.5504029239 & -44.5504029238973 \tabularnewline
52 & 3653 & 3872.4798116777 & -219.479811677699 \tabularnewline
53 & 3659 & 3600.53921762239 & 58.46078237761 \tabularnewline
54 & 3827.5 & 3852.11820230982 & -24.618202309824 \tabularnewline
55 & 3726.5 & 3779.32247060031 & -52.8224706003098 \tabularnewline
56 & 3544 & 3615.00171697359 & -71.0017169735879 \tabularnewline
57 & 3428.5 & 3506.76207677707 & -78.2620767770736 \tabularnewline
58 & 3422.5 & 3323.79192912993 & 98.7080708700746 \tabularnewline
59 & 3401 & 3333.63433450895 & 67.3656654910515 \tabularnewline
60 & 3263 & 3330.97475133394 & -67.9747513339412 \tabularnewline
61 & 3801.5 & 3615.75867753316 & 185.741322466842 \tabularnewline
62 & 3741 & 3715.42806590852 & 25.5719340914843 \tabularnewline
63 & 3545 & 3589.87566668534 & -44.8756666853365 \tabularnewline
64 & 3179.5 & 3338.85842443059 & -159.358424430586 \tabularnewline
65 & 3276.5 & 3162.73760367208 & 113.762396327922 \tabularnewline
66 & 3409.5 & 3418.8102857511 & -9.31028575110122 \tabularnewline
67 & 3411.5 & 3355.93936606561 & 55.5606339343863 \tabularnewline
68 & 3329.5 & 3292.05532309413 & 37.4446769058673 \tabularnewline
69 & 3184 & 3287.06955585686 & -103.069555856862 \tabularnewline
70 & 3091 & 3132.21318962085 & -41.2131896208502 \tabularnewline
71 & 3162.5 & 3028.75510510005 & 133.744894899948 \tabularnewline
72 & 3071 & 3067.07325367181 & 3.9267463281908 \tabularnewline
73 & 3654.5 & 3445.44870873577 & 209.051291264232 \tabularnewline
74 & 3441.5 & 3553.61168570907 & -112.111685709071 \tabularnewline
75 & 3189 & 3318.58210897316 & -129.582108973161 \tabularnewline
76 & 3114.5 & 2995.58337173473 & 118.916628265273 \tabularnewline
77 & 3078 & 3115.37158803472 & -37.3715880347204 \tabularnewline
78 & 3425 & 3225.00044631675 & 199.999553683248 \tabularnewline
79 & 3368 & 3369.79286537869 & -1.79286537869211 \tabularnewline
80 & 3176 & 3276.95009781559 & -100.950097815588 \tabularnewline
81 & 3165 & 3144.06476304408 & 20.9352369559183 \tabularnewline
82 & 3111 & 3120.69565831187 & -9.6956583118731 \tabularnewline
83 & 3247.5 & 3095.26019785936 & 152.239802140644 \tabularnewline
84 & 3150 & 3145.39844781083 & 4.60155218916725 \tabularnewline
85 & 3628 & 3596.31515818348 & 31.6848418165209 \tabularnewline
86 & 3567 & 3512.54994222496 & 54.4500577750387 \tabularnewline
87 & 3348.5 & 3427.91716776584 & -79.4171677658392 \tabularnewline
88 & 3228.5 & 3208.01502894265 & 20.4849710573517 \tabularnewline
89 & 3181.5 & 3236.99937196109 & -55.4993719610929 \tabularnewline
90 & 3351 & 3398.82146448367 & -47.8214644836735 \tabularnewline
91 & 3472.5 & 3304.40210885089 & 168.097891149113 \tabularnewline
92 & 3418.5 & 3340.71439929997 & 77.7856007000323 \tabularnewline
93 & 3409 & 3399.52070817574 & 9.47929182425742 \tabularnewline
94 & 3361 & 3381.91307867623 & -20.9130786762257 \tabularnewline
95 & 3605.5 & 3400.62345967082 & 204.876540329177 \tabularnewline
96 & 3671.5 & 3482.45525191586 & 189.044748084141 \tabularnewline
97 & 4297.5 & 4203.89520231994 & 93.6047976800646 \tabularnewline
98 & 4459.5 & 4203.63380333619 & 255.866196663813 \tabularnewline
99 & 4402 & 4281.0711009471 & 120.928899052901 \tabularnewline
100 & 4024.5 & 4273.09900405517 & -248.59900405517 \tabularnewline
101 & 4116.5 & 4119.64490520523 & -3.14490520522577 \tabularnewline
102 & 4387 & 4447.46063380016 & -60.4606338001604 \tabularnewline
103 & 4288 & 4436.53586151142 & -148.535861511421 \tabularnewline
104 & 4118.5 & 4201.39654774011 & -82.8965477401116 \tabularnewline
105 & 4035 & 4132.2657260991 & -97.2657260991009 \tabularnewline
106 & 4006.5 & 4027.52557261761 & -21.0255726176051 \tabularnewline
107 & 4143 & 4112.34312600189 & 30.6568739981103 \tabularnewline
108 & 4279.5 & 4031.50863015839 & 247.991369841607 \tabularnewline
109 & 4974.5 & 4866.38738726624 & 108.112612733761 \tabularnewline
110 & 5080.5 & 4897.03969099784 & 183.460309002162 \tabularnewline
111 & 4845.5 & 4861.85109730669 & -16.351097306685 \tabularnewline
112 & 4472.5 & 4637.97213814129 & -165.472138141293 \tabularnewline
113 & 4584.5 & 4599.68405315373 & -15.1840531537264 \tabularnewline
114 & 5047.5 & 4933.34199844124 & 114.15800155876 \tabularnewline
115 & 4922.5 & 5052.69859956349 & -130.198599563486 \tabularnewline
116 & 4695 & 4832.61238995268 & -137.612389952682 \tabularnewline
117 & 4545 & 4716.23400739489 & -171.234007394894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302957&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]4877.5[/C][C]5603.15852553332[/C][C]-725.658525533324[/C][/ROW]
[ROW][C]14[/C][C]4703.5[/C][C]4770.03633885671[/C][C]-66.5363388567139[/C][/ROW]
[ROW][C]15[/C][C]4528.5[/C][C]4468.11213723783[/C][C]60.3878627621707[/C][/ROW]
[ROW][C]16[/C][C]4262.5[/C][C]4174.19667980224[/C][C]88.3033201977551[/C][/ROW]
[ROW][C]17[/C][C]4077[/C][C]3982.17020296346[/C][C]94.8297970365438[/C][/ROW]
[ROW][C]18[/C][C]4291[/C][C]4187.80482238373[/C][C]103.195177616272[/C][/ROW]
[ROW][C]19[/C][C]4357[/C][C]4188.29227107505[/C][C]168.707728924946[/C][/ROW]
[ROW][C]20[/C][C]4191[/C][C]4190.85198030665[/C][C]0.148019693346214[/C][/ROW]
[ROW][C]21[/C][C]4025.5[/C][C]3942.6723432674[/C][C]82.8276567326047[/C][/ROW]
[ROW][C]22[/C][C]3994.5[/C][C]3813.57499482331[/C][C]180.925005176691[/C][/ROW]
[ROW][C]23[/C][C]3934.5[/C][C]3852.52846039542[/C][C]81.9715396045831[/C][/ROW]
[ROW][C]24[/C][C]3989[/C][C]3874.78984865784[/C][C]114.210151342156[/C][/ROW]
[ROW][C]25[/C][C]4565.5[/C][C]4205.85544748418[/C][C]359.644552515818[/C][/ROW]
[ROW][C]26[/C][C]4451[/C][C]4475.73064964107[/C][C]-24.7306496410747[/C][/ROW]
[ROW][C]27[/C][C]4312.5[/C][C]4334.88217964551[/C][C]-22.3821796455068[/C][/ROW]
[ROW][C]28[/C][C]4075[/C][C]4077.24374035533[/C][C]-2.24374035532765[/C][/ROW]
[ROW][C]29[/C][C]4005.5[/C][C]3898.49371738734[/C][C]107.006282612655[/C][/ROW]
[ROW][C]30[/C][C]4376.5[/C][C]4196.03289188685[/C][C]180.467108113148[/C][/ROW]
[ROW][C]31[/C][C]4341[/C][C]4364.79064273677[/C][C]-23.7906427367689[/C][/ROW]
[ROW][C]32[/C][C]4025.5[/C][C]4257.60756013488[/C][C]-232.107560134876[/C][/ROW]
[ROW][C]33[/C][C]3992[/C][C]3897.64309580958[/C][C]94.3569041904243[/C][/ROW]
[ROW][C]34[/C][C]3958.5[/C][C]3854.64367964528[/C][C]103.856320354717[/C][/ROW]
[ROW][C]35[/C][C]3907.5[/C][C]3865.39188526056[/C][C]42.108114739437[/C][/ROW]
[ROW][C]36[/C][C]3858.5[/C][C]3910.31058070689[/C][C]-51.8105807068937[/C][/ROW]
[ROW][C]37[/C][C]4236[/C][C]4176.97384441426[/C][C]59.0261555857442[/C][/ROW]
[ROW][C]38[/C][C]4520.5[/C][C]4152.47415093475[/C][C]368.025849065249[/C][/ROW]
[ROW][C]39[/C][C]4333.5[/C][C]4379.43168139662[/C][C]-45.931681396617[/C][/ROW]
[ROW][C]40[/C][C]4057.5[/C][C]4148.1356773677[/C][C]-90.6356773677035[/C][/ROW]
[ROW][C]41[/C][C]4079[/C][C]3952.51734246117[/C][C]126.482657538829[/C][/ROW]
[ROW][C]42[/C][C]4387.5[/C][C]4321.22615160922[/C][C]66.2738483907824[/C][/ROW]
[ROW][C]43[/C][C]4235.5[/C][C]4390.35271481608[/C][C]-154.852714816077[/C][/ROW]
[ROW][C]44[/C][C]3977.5[/C][C]4158.58974988214[/C][C]-181.089749882141[/C][/ROW]
[ROW][C]45[/C][C]4007.5[/C][C]3924.29846074213[/C][C]83.201539257866[/C][/ROW]
[ROW][C]46[/C][C]3921[/C][C]3896.41956666366[/C][C]24.5804333363371[/C][/ROW]
[ROW][C]47[/C][C]3936[/C][C]3848.37560522758[/C][C]87.6243947724233[/C][/ROW]
[ROW][C]48[/C][C]3730.5[/C][C]3933.45498397425[/C][C]-202.954983974246[/C][/ROW]
[ROW][C]49[/C][C]4310[/C][C]4098.27529571791[/C][C]211.724704282089[/C][/ROW]
[ROW][C]50[/C][C]4251.5[/C][C]4272.0254535878[/C][C]-20.5254535877993[/C][/ROW]
[ROW][C]51[/C][C]4062[/C][C]4106.5504029239[/C][C]-44.5504029238973[/C][/ROW]
[ROW][C]52[/C][C]3653[/C][C]3872.4798116777[/C][C]-219.479811677699[/C][/ROW]
[ROW][C]53[/C][C]3659[/C][C]3600.53921762239[/C][C]58.46078237761[/C][/ROW]
[ROW][C]54[/C][C]3827.5[/C][C]3852.11820230982[/C][C]-24.618202309824[/C][/ROW]
[ROW][C]55[/C][C]3726.5[/C][C]3779.32247060031[/C][C]-52.8224706003098[/C][/ROW]
[ROW][C]56[/C][C]3544[/C][C]3615.00171697359[/C][C]-71.0017169735879[/C][/ROW]
[ROW][C]57[/C][C]3428.5[/C][C]3506.76207677707[/C][C]-78.2620767770736[/C][/ROW]
[ROW][C]58[/C][C]3422.5[/C][C]3323.79192912993[/C][C]98.7080708700746[/C][/ROW]
[ROW][C]59[/C][C]3401[/C][C]3333.63433450895[/C][C]67.3656654910515[/C][/ROW]
[ROW][C]60[/C][C]3263[/C][C]3330.97475133394[/C][C]-67.9747513339412[/C][/ROW]
[ROW][C]61[/C][C]3801.5[/C][C]3615.75867753316[/C][C]185.741322466842[/C][/ROW]
[ROW][C]62[/C][C]3741[/C][C]3715.42806590852[/C][C]25.5719340914843[/C][/ROW]
[ROW][C]63[/C][C]3545[/C][C]3589.87566668534[/C][C]-44.8756666853365[/C][/ROW]
[ROW][C]64[/C][C]3179.5[/C][C]3338.85842443059[/C][C]-159.358424430586[/C][/ROW]
[ROW][C]65[/C][C]3276.5[/C][C]3162.73760367208[/C][C]113.762396327922[/C][/ROW]
[ROW][C]66[/C][C]3409.5[/C][C]3418.8102857511[/C][C]-9.31028575110122[/C][/ROW]
[ROW][C]67[/C][C]3411.5[/C][C]3355.93936606561[/C][C]55.5606339343863[/C][/ROW]
[ROW][C]68[/C][C]3329.5[/C][C]3292.05532309413[/C][C]37.4446769058673[/C][/ROW]
[ROW][C]69[/C][C]3184[/C][C]3287.06955585686[/C][C]-103.069555856862[/C][/ROW]
[ROW][C]70[/C][C]3091[/C][C]3132.21318962085[/C][C]-41.2131896208502[/C][/ROW]
[ROW][C]71[/C][C]3162.5[/C][C]3028.75510510005[/C][C]133.744894899948[/C][/ROW]
[ROW][C]72[/C][C]3071[/C][C]3067.07325367181[/C][C]3.9267463281908[/C][/ROW]
[ROW][C]73[/C][C]3654.5[/C][C]3445.44870873577[/C][C]209.051291264232[/C][/ROW]
[ROW][C]74[/C][C]3441.5[/C][C]3553.61168570907[/C][C]-112.111685709071[/C][/ROW]
[ROW][C]75[/C][C]3189[/C][C]3318.58210897316[/C][C]-129.582108973161[/C][/ROW]
[ROW][C]76[/C][C]3114.5[/C][C]2995.58337173473[/C][C]118.916628265273[/C][/ROW]
[ROW][C]77[/C][C]3078[/C][C]3115.37158803472[/C][C]-37.3715880347204[/C][/ROW]
[ROW][C]78[/C][C]3425[/C][C]3225.00044631675[/C][C]199.999553683248[/C][/ROW]
[ROW][C]79[/C][C]3368[/C][C]3369.79286537869[/C][C]-1.79286537869211[/C][/ROW]
[ROW][C]80[/C][C]3176[/C][C]3276.95009781559[/C][C]-100.950097815588[/C][/ROW]
[ROW][C]81[/C][C]3165[/C][C]3144.06476304408[/C][C]20.9352369559183[/C][/ROW]
[ROW][C]82[/C][C]3111[/C][C]3120.69565831187[/C][C]-9.6956583118731[/C][/ROW]
[ROW][C]83[/C][C]3247.5[/C][C]3095.26019785936[/C][C]152.239802140644[/C][/ROW]
[ROW][C]84[/C][C]3150[/C][C]3145.39844781083[/C][C]4.60155218916725[/C][/ROW]
[ROW][C]85[/C][C]3628[/C][C]3596.31515818348[/C][C]31.6848418165209[/C][/ROW]
[ROW][C]86[/C][C]3567[/C][C]3512.54994222496[/C][C]54.4500577750387[/C][/ROW]
[ROW][C]87[/C][C]3348.5[/C][C]3427.91716776584[/C][C]-79.4171677658392[/C][/ROW]
[ROW][C]88[/C][C]3228.5[/C][C]3208.01502894265[/C][C]20.4849710573517[/C][/ROW]
[ROW][C]89[/C][C]3181.5[/C][C]3236.99937196109[/C][C]-55.4993719610929[/C][/ROW]
[ROW][C]90[/C][C]3351[/C][C]3398.82146448367[/C][C]-47.8214644836735[/C][/ROW]
[ROW][C]91[/C][C]3472.5[/C][C]3304.40210885089[/C][C]168.097891149113[/C][/ROW]
[ROW][C]92[/C][C]3418.5[/C][C]3340.71439929997[/C][C]77.7856007000323[/C][/ROW]
[ROW][C]93[/C][C]3409[/C][C]3399.52070817574[/C][C]9.47929182425742[/C][/ROW]
[ROW][C]94[/C][C]3361[/C][C]3381.91307867623[/C][C]-20.9130786762257[/C][/ROW]
[ROW][C]95[/C][C]3605.5[/C][C]3400.62345967082[/C][C]204.876540329177[/C][/ROW]
[ROW][C]96[/C][C]3671.5[/C][C]3482.45525191586[/C][C]189.044748084141[/C][/ROW]
[ROW][C]97[/C][C]4297.5[/C][C]4203.89520231994[/C][C]93.6047976800646[/C][/ROW]
[ROW][C]98[/C][C]4459.5[/C][C]4203.63380333619[/C][C]255.866196663813[/C][/ROW]
[ROW][C]99[/C][C]4402[/C][C]4281.0711009471[/C][C]120.928899052901[/C][/ROW]
[ROW][C]100[/C][C]4024.5[/C][C]4273.09900405517[/C][C]-248.59900405517[/C][/ROW]
[ROW][C]101[/C][C]4116.5[/C][C]4119.64490520523[/C][C]-3.14490520522577[/C][/ROW]
[ROW][C]102[/C][C]4387[/C][C]4447.46063380016[/C][C]-60.4606338001604[/C][/ROW]
[ROW][C]103[/C][C]4288[/C][C]4436.53586151142[/C][C]-148.535861511421[/C][/ROW]
[ROW][C]104[/C][C]4118.5[/C][C]4201.39654774011[/C][C]-82.8965477401116[/C][/ROW]
[ROW][C]105[/C][C]4035[/C][C]4132.2657260991[/C][C]-97.2657260991009[/C][/ROW]
[ROW][C]106[/C][C]4006.5[/C][C]4027.52557261761[/C][C]-21.0255726176051[/C][/ROW]
[ROW][C]107[/C][C]4143[/C][C]4112.34312600189[/C][C]30.6568739981103[/C][/ROW]
[ROW][C]108[/C][C]4279.5[/C][C]4031.50863015839[/C][C]247.991369841607[/C][/ROW]
[ROW][C]109[/C][C]4974.5[/C][C]4866.38738726624[/C][C]108.112612733761[/C][/ROW]
[ROW][C]110[/C][C]5080.5[/C][C]4897.03969099784[/C][C]183.460309002162[/C][/ROW]
[ROW][C]111[/C][C]4845.5[/C][C]4861.85109730669[/C][C]-16.351097306685[/C][/ROW]
[ROW][C]112[/C][C]4472.5[/C][C]4637.97213814129[/C][C]-165.472138141293[/C][/ROW]
[ROW][C]113[/C][C]4584.5[/C][C]4599.68405315373[/C][C]-15.1840531537264[/C][/ROW]
[ROW][C]114[/C][C]5047.5[/C][C]4933.34199844124[/C][C]114.15800155876[/C][/ROW]
[ROW][C]115[/C][C]4922.5[/C][C]5052.69859956349[/C][C]-130.198599563486[/C][/ROW]
[ROW][C]116[/C][C]4695[/C][C]4832.61238995268[/C][C]-137.612389952682[/C][/ROW]
[ROW][C]117[/C][C]4545[/C][C]4716.23400739489[/C][C]-171.234007394894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302957&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
134877.55603.15852553332-725.658525533324
144703.54770.03633885671-66.5363388567139
154528.54468.1121372378360.3878627621707
164262.54174.1966798022488.3033201977551
1740773982.1702029634694.8297970365438
1842914187.80482238373103.195177616272
1943574188.29227107505168.707728924946
2041914190.851980306650.148019693346214
214025.53942.672343267482.8276567326047
223994.53813.57499482331180.925005176691
233934.53852.5284603954281.9715396045831
2439893874.78984865784114.210151342156
254565.54205.85544748418359.644552515818
2644514475.73064964107-24.7306496410747
274312.54334.88217964551-22.3821796455068
2840754077.24374035533-2.24374035532765
294005.53898.49371738734107.006282612655
304376.54196.03289188685180.467108113148
3143414364.79064273677-23.7906427367689
324025.54257.60756013488-232.107560134876
3339923897.6430958095894.3569041904243
343958.53854.64367964528103.856320354717
353907.53865.3918852605642.108114739437
363858.53910.31058070689-51.8105807068937
3742364176.9738444142659.0261555857442
384520.54152.47415093475368.025849065249
394333.54379.43168139662-45.931681396617
404057.54148.1356773677-90.6356773677035
4140793952.51734246117126.482657538829
424387.54321.2261516092266.2738483907824
434235.54390.35271481608-154.852714816077
443977.54158.58974988214-181.089749882141
454007.53924.2984607421383.201539257866
4639213896.4195666636624.5804333363371
4739363848.3756052275887.6243947724233
483730.53933.45498397425-202.954983974246
4943104098.27529571791211.724704282089
504251.54272.0254535878-20.5254535877993
5140624106.5504029239-44.5504029238973
5236533872.4798116777-219.479811677699
5336593600.5392176223958.46078237761
543827.53852.11820230982-24.618202309824
553726.53779.32247060031-52.8224706003098
5635443615.00171697359-71.0017169735879
573428.53506.76207677707-78.2620767770736
583422.53323.7919291299398.7080708700746
5934013333.6343345089567.3656654910515
6032633330.97475133394-67.9747513339412
613801.53615.75867753316185.741322466842
6237413715.4280659085225.5719340914843
6335453589.87566668534-44.8756666853365
643179.53338.85842443059-159.358424430586
653276.53162.73760367208113.762396327922
663409.53418.8102857511-9.31028575110122
673411.53355.9393660656155.5606339343863
683329.53292.0553230941337.4446769058673
6931843287.06955585686-103.069555856862
7030913132.21318962085-41.2131896208502
713162.53028.75510510005133.744894899948
7230713067.073253671813.9267463281908
733654.53445.44870873577209.051291264232
743441.53553.61168570907-112.111685709071
7531893318.58210897316-129.582108973161
763114.52995.58337173473118.916628265273
7730783115.37158803472-37.3715880347204
7834253225.00044631675199.999553683248
7933683369.79286537869-1.79286537869211
8031763276.95009781559-100.950097815588
8131653144.0647630440820.9352369559183
8231113120.69565831187-9.6956583118731
833247.53095.26019785936152.239802140644
8431503145.398447810834.60155218916725
8536283596.3151581834831.6848418165209
8635673512.5499422249654.4500577750387
873348.53427.91716776584-79.4171677658392
883228.53208.0150289426520.4849710573517
893181.53236.99937196109-55.4993719610929
9033513398.82146448367-47.8214644836735
913472.53304.40210885089168.097891149113
923418.53340.7143992999777.7856007000323
9334093399.520708175749.47929182425742
9433613381.91307867623-20.9130786762257
953605.53400.62345967082204.876540329177
963671.53482.45525191586189.044748084141
974297.54203.8952023199493.6047976800646
984459.54203.63380333619255.866196663813
9944024281.0711009471120.928899052901
1004024.54273.09900405517-248.59900405517
1014116.54119.64490520523-3.14490520522577
10243874447.46063380016-60.4606338001604
10342884436.53586151142-148.535861511421
1044118.54201.39654774011-82.8965477401116
10540354132.2657260991-97.2657260991009
1064006.54027.52557261761-21.0255726176051
10741434112.3431260018930.6568739981103
1084279.54031.50863015839247.991369841607
1094974.54866.38738726624108.112612733761
1105080.54897.03969099784183.460309002162
1114845.54861.85109730669-16.351097306685
1124472.54637.97213814129-165.472138141293
1134584.54599.68405315373-15.1840531537264
1145047.54933.34199844124114.15800155876
1154922.55052.69859956349-130.198599563486
11646954832.61238995268-137.612389952682
11745454716.23400739489-171.234007394894







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1184560.501724007684281.910282748834839.09316526652
1194685.919600713374309.298553889025062.54064753772
1204605.117827570014148.680414871765061.55524026826
1215232.497044151774640.3073500345824.68673826954
1225153.687836993484490.193169039335817.18250494763
1234887.871696136914178.094962651855597.64842962196
1244610.026068807173860.976865003115359.07527261124
1254712.0342068713869.104973088425554.96344065358
1265065.087826013534080.748196184266049.4274558428
1275012.463716821953957.39737950066067.53005414329
1284870.931123767493764.667573106485977.1946744285
1294845.389609780083697.25877172435993.52044783585
1304860.264875150223597.555099489416122.97465081103
1314992.248581966463616.574110025216367.92305390771
1324904.533494971943471.638788564346337.42820137955
1335570.870305886423861.784184069537279.95642770332
1345485.178300586633713.50377526227256.85282591107
1355200.588405980013432.83289708226968.34391487782

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
118 & 4560.50172400768 & 4281.91028274883 & 4839.09316526652 \tabularnewline
119 & 4685.91960071337 & 4309.29855388902 & 5062.54064753772 \tabularnewline
120 & 4605.11782757001 & 4148.68041487176 & 5061.55524026826 \tabularnewline
121 & 5232.49704415177 & 4640.307350034 & 5824.68673826954 \tabularnewline
122 & 5153.68783699348 & 4490.19316903933 & 5817.18250494763 \tabularnewline
123 & 4887.87169613691 & 4178.09496265185 & 5597.64842962196 \tabularnewline
124 & 4610.02606880717 & 3860.97686500311 & 5359.07527261124 \tabularnewline
125 & 4712.034206871 & 3869.10497308842 & 5554.96344065358 \tabularnewline
126 & 5065.08782601353 & 4080.74819618426 & 6049.4274558428 \tabularnewline
127 & 5012.46371682195 & 3957.3973795006 & 6067.53005414329 \tabularnewline
128 & 4870.93112376749 & 3764.66757310648 & 5977.1946744285 \tabularnewline
129 & 4845.38960978008 & 3697.2587717243 & 5993.52044783585 \tabularnewline
130 & 4860.26487515022 & 3597.55509948941 & 6122.97465081103 \tabularnewline
131 & 4992.24858196646 & 3616.57411002521 & 6367.92305390771 \tabularnewline
132 & 4904.53349497194 & 3471.63878856434 & 6337.42820137955 \tabularnewline
133 & 5570.87030588642 & 3861.78418406953 & 7279.95642770332 \tabularnewline
134 & 5485.17830058663 & 3713.5037752622 & 7256.85282591107 \tabularnewline
135 & 5200.58840598001 & 3432.8328970822 & 6968.34391487782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302957&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]118[/C][C]4560.50172400768[/C][C]4281.91028274883[/C][C]4839.09316526652[/C][/ROW]
[ROW][C]119[/C][C]4685.91960071337[/C][C]4309.29855388902[/C][C]5062.54064753772[/C][/ROW]
[ROW][C]120[/C][C]4605.11782757001[/C][C]4148.68041487176[/C][C]5061.55524026826[/C][/ROW]
[ROW][C]121[/C][C]5232.49704415177[/C][C]4640.307350034[/C][C]5824.68673826954[/C][/ROW]
[ROW][C]122[/C][C]5153.68783699348[/C][C]4490.19316903933[/C][C]5817.18250494763[/C][/ROW]
[ROW][C]123[/C][C]4887.87169613691[/C][C]4178.09496265185[/C][C]5597.64842962196[/C][/ROW]
[ROW][C]124[/C][C]4610.02606880717[/C][C]3860.97686500311[/C][C]5359.07527261124[/C][/ROW]
[ROW][C]125[/C][C]4712.034206871[/C][C]3869.10497308842[/C][C]5554.96344065358[/C][/ROW]
[ROW][C]126[/C][C]5065.08782601353[/C][C]4080.74819618426[/C][C]6049.4274558428[/C][/ROW]
[ROW][C]127[/C][C]5012.46371682195[/C][C]3957.3973795006[/C][C]6067.53005414329[/C][/ROW]
[ROW][C]128[/C][C]4870.93112376749[/C][C]3764.66757310648[/C][C]5977.1946744285[/C][/ROW]
[ROW][C]129[/C][C]4845.38960978008[/C][C]3697.2587717243[/C][C]5993.52044783585[/C][/ROW]
[ROW][C]130[/C][C]4860.26487515022[/C][C]3597.55509948941[/C][C]6122.97465081103[/C][/ROW]
[ROW][C]131[/C][C]4992.24858196646[/C][C]3616.57411002521[/C][C]6367.92305390771[/C][/ROW]
[ROW][C]132[/C][C]4904.53349497194[/C][C]3471.63878856434[/C][C]6337.42820137955[/C][/ROW]
[ROW][C]133[/C][C]5570.87030588642[/C][C]3861.78418406953[/C][C]7279.95642770332[/C][/ROW]
[ROW][C]134[/C][C]5485.17830058663[/C][C]3713.5037752622[/C][C]7256.85282591107[/C][/ROW]
[ROW][C]135[/C][C]5200.58840598001[/C][C]3432.8328970822[/C][C]6968.34391487782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302957&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302957&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
1184560.501724007684281.910282748834839.09316526652
1194685.919600713374309.298553889025062.54064753772
1204605.117827570014148.680414871765061.55524026826
1215232.497044151774640.3073500345824.68673826954
1225153.687836993484490.193169039335817.18250494763
1234887.871696136914178.094962651855597.64842962196
1244610.026068807173860.976865003115359.07527261124
1254712.0342068713869.104973088425554.96344065358
1265065.087826013534080.748196184266049.4274558428
1275012.463716821953957.39737950066067.53005414329
1284870.931123767493764.667573106485977.1946744285
1294845.389609780083697.25877172435993.52044783585
1304860.264875150223597.555099489416122.97465081103
1314992.248581966463616.574110025216367.92305390771
1324904.533494971943471.638788564346337.42820137955
1335570.870305886423861.784184069537279.95642770332
1345485.178300586633713.50377526227256.85282591107
1355200.588405980013432.83289708226968.34391487782



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'additive'
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')