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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 computationSat, 26 Nov 2011 05:39:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/26/t1322304012xu4xn8v6510dfrz.htm/, Retrieved Sun, 05 Feb 2023 14:56:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147377, Retrieved Sun, 05 Feb 2023 14:56:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
- RM D  [Classical Decomposition] [WS 8: classical d...] [2011-11-26 09:39:36] [10b12745961ee885a66356b3bf31ed40]
- RMP       [Exponential Smoothing] [WS 8: exponential...] [2011-11-26 10:39:49] [080b56dea5ee02335c893a05354948d0] [Current]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147377&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147377&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147377&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.380859354911948
beta0.0316088853012761
gamma0.733581043314601

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380859354911948 \tabularnewline
beta & 0.0316088853012761 \tabularnewline
gamma & 0.733581043314601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147377&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]0.380859354911948[/C][/ROW]
[ROW][C]beta[/C][C]0.0316088853012761[/C][/ROW]
[ROW][C]gamma[/C][C]0.733581043314601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147377&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147377&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
alpha0.380859354911948
beta0.0316088853012761
gamma0.733581043314601







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138065.953525641025614.0464743589744
144232.44671481725939.55328518274065
155447.13530513160876.86469486839134
166660.59089490800925.4091050919908
178179.7238940940241.27610590597605
186369.4231643277678-6.42316432776776
19137111.48776994845825.5122300515416
207280.1890659314046-8.1890659314046
2110786.456323671552120.5436763284479
225868.1223642893233-10.1223642893233
233697.1537646423693-61.1537646423693
2452157.471510088703-105.471510088703
257965.853803915796913.1461960842031
267728.650494978251548.3495050217485
275456.0480501431288-2.0480501431288
288464.494919076742419.5050809232576
294886.335926809279-38.335926809279
309656.191372995916439.8086270040836
3183129.664803267207-46.6648032672074
326653.997391331064212.0026086689358
336179.6754118037333-18.6754118037333
345330.674606122690922.3253938773091
353047.4750331631132-17.4750331631132
3674103.414328539607-29.4143285396072
376994.6690520639605-25.6690520639605
385958.23468268165360.765317318346362
394243.6095578051345-1.60955780513446
406561.00818314122983.99181685877025
417049.478803349944620.5211966500554
4210076.760334137798623.2396658622014
4363103.96583707419-40.9658370741898
4410556.501549428836948.4984505711631
458281.97154136393470.0284586360653378
468158.767430267248722.2325697327513
477557.505438458561917.4945615414381
48102121.811391006708-19.8113910067084
49121119.0110215464261.98897845357396
5098106.036128029629-8.03612802962945
517687.7937238475062-11.7937238475062
5277104.548576897228-27.5485768972279
536388.8253943324135-25.8253943324135
543799.4433230769987-62.4433230769987
553563.5759025308874-28.5759025308874
562360.3350961492407-37.3350961492407
574028.937578654059911.0624213459401
582917.991147653545711.0088523464543
59378.1378362318450628.8621637681549
605157.8014044627004-6.80140446270038
612067.9862803143687-47.9862803143687
622828.9516752372211-0.951675237221107
63139.313210565710753.68678943428925
642222.6070517338621-0.607051733862111
652516.05057370461418.9494262953859
661321.8230856739758-8.82308567397584
671620.946940527163-4.94694052716303
681322.1988348561934-9.1988348561934
691623.3093821664525-7.30938216645249
70174.930823484712412.0691765152876
7193.192179909830055.80782009016995
721727.2017554894769-10.2017554894769
732516.66938856481038.33061143518972
741420.4077763690547-6.40777636905471
7580.6939026255990557.30609737440095
76713.3553977851456-6.35539778514564
77108.820287664652241.17971233534776
7873.338225050029953.66177494997005
79108.904549139226311.09545086077369
80310.5263066432433-7.52630664324327

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80 & 65.9535256410256 & 14.0464743589744 \tabularnewline
14 & 42 & 32.4467148172593 & 9.55328518274065 \tabularnewline
15 & 54 & 47.1353051316087 & 6.86469486839134 \tabularnewline
16 & 66 & 60.5908949080092 & 5.4091050919908 \tabularnewline
17 & 81 & 79.723894094024 & 1.27610590597605 \tabularnewline
18 & 63 & 69.4231643277678 & -6.42316432776776 \tabularnewline
19 & 137 & 111.487769948458 & 25.5122300515416 \tabularnewline
20 & 72 & 80.1890659314046 & -8.1890659314046 \tabularnewline
21 & 107 & 86.4563236715521 & 20.5436763284479 \tabularnewline
22 & 58 & 68.1223642893233 & -10.1223642893233 \tabularnewline
23 & 36 & 97.1537646423693 & -61.1537646423693 \tabularnewline
24 & 52 & 157.471510088703 & -105.471510088703 \tabularnewline
25 & 79 & 65.8538039157969 & 13.1461960842031 \tabularnewline
26 & 77 & 28.6504949782515 & 48.3495050217485 \tabularnewline
27 & 54 & 56.0480501431288 & -2.0480501431288 \tabularnewline
28 & 84 & 64.4949190767424 & 19.5050809232576 \tabularnewline
29 & 48 & 86.335926809279 & -38.335926809279 \tabularnewline
30 & 96 & 56.1913729959164 & 39.8086270040836 \tabularnewline
31 & 83 & 129.664803267207 & -46.6648032672074 \tabularnewline
32 & 66 & 53.9973913310642 & 12.0026086689358 \tabularnewline
33 & 61 & 79.6754118037333 & -18.6754118037333 \tabularnewline
34 & 53 & 30.6746061226909 & 22.3253938773091 \tabularnewline
35 & 30 & 47.4750331631132 & -17.4750331631132 \tabularnewline
36 & 74 & 103.414328539607 & -29.4143285396072 \tabularnewline
37 & 69 & 94.6690520639605 & -25.6690520639605 \tabularnewline
38 & 59 & 58.2346826816536 & 0.765317318346362 \tabularnewline
39 & 42 & 43.6095578051345 & -1.60955780513446 \tabularnewline
40 & 65 & 61.0081831412298 & 3.99181685877025 \tabularnewline
41 & 70 & 49.4788033499446 & 20.5211966500554 \tabularnewline
42 & 100 & 76.7603341377986 & 23.2396658622014 \tabularnewline
43 & 63 & 103.96583707419 & -40.9658370741898 \tabularnewline
44 & 105 & 56.5015494288369 & 48.4984505711631 \tabularnewline
45 & 82 & 81.9715413639347 & 0.0284586360653378 \tabularnewline
46 & 81 & 58.7674302672487 & 22.2325697327513 \tabularnewline
47 & 75 & 57.5054384585619 & 17.4945615414381 \tabularnewline
48 & 102 & 121.811391006708 & -19.8113910067084 \tabularnewline
49 & 121 & 119.011021546426 & 1.98897845357396 \tabularnewline
50 & 98 & 106.036128029629 & -8.03612802962945 \tabularnewline
51 & 76 & 87.7937238475062 & -11.7937238475062 \tabularnewline
52 & 77 & 104.548576897228 & -27.5485768972279 \tabularnewline
53 & 63 & 88.8253943324135 & -25.8253943324135 \tabularnewline
54 & 37 & 99.4433230769987 & -62.4433230769987 \tabularnewline
55 & 35 & 63.5759025308874 & -28.5759025308874 \tabularnewline
56 & 23 & 60.3350961492407 & -37.3350961492407 \tabularnewline
57 & 40 & 28.9375786540599 & 11.0624213459401 \tabularnewline
58 & 29 & 17.9911476535457 & 11.0088523464543 \tabularnewline
59 & 37 & 8.13783623184506 & 28.8621637681549 \tabularnewline
60 & 51 & 57.8014044627004 & -6.80140446270038 \tabularnewline
61 & 20 & 67.9862803143687 & -47.9862803143687 \tabularnewline
62 & 28 & 28.9516752372211 & -0.951675237221107 \tabularnewline
63 & 13 & 9.31321056571075 & 3.68678943428925 \tabularnewline
64 & 22 & 22.6070517338621 & -0.607051733862111 \tabularnewline
65 & 25 & 16.0505737046141 & 8.9494262953859 \tabularnewline
66 & 13 & 21.8230856739758 & -8.82308567397584 \tabularnewline
67 & 16 & 20.946940527163 & -4.94694052716303 \tabularnewline
68 & 13 & 22.1988348561934 & -9.1988348561934 \tabularnewline
69 & 16 & 23.3093821664525 & -7.30938216645249 \tabularnewline
70 & 17 & 4.9308234847124 & 12.0691765152876 \tabularnewline
71 & 9 & 3.19217990983005 & 5.80782009016995 \tabularnewline
72 & 17 & 27.2017554894769 & -10.2017554894769 \tabularnewline
73 & 25 & 16.6693885648103 & 8.33061143518972 \tabularnewline
74 & 14 & 20.4077763690547 & -6.40777636905471 \tabularnewline
75 & 8 & 0.693902625599055 & 7.30609737440095 \tabularnewline
76 & 7 & 13.3553977851456 & -6.35539778514564 \tabularnewline
77 & 10 & 8.82028766465224 & 1.17971233534776 \tabularnewline
78 & 7 & 3.33822505002995 & 3.66177494997005 \tabularnewline
79 & 10 & 8.90454913922631 & 1.09545086077369 \tabularnewline
80 & 3 & 10.5263066432433 & -7.52630664324327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147377&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]80[/C][C]65.9535256410256[/C][C]14.0464743589744[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]32.4467148172593[/C][C]9.55328518274065[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]47.1353051316087[/C][C]6.86469486839134[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]60.5908949080092[/C][C]5.4091050919908[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]79.723894094024[/C][C]1.27610590597605[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]69.4231643277678[/C][C]-6.42316432776776[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]111.487769948458[/C][C]25.5122300515416[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]80.1890659314046[/C][C]-8.1890659314046[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]86.4563236715521[/C][C]20.5436763284479[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]68.1223642893233[/C][C]-10.1223642893233[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]97.1537646423693[/C][C]-61.1537646423693[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]157.471510088703[/C][C]-105.471510088703[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]65.8538039157969[/C][C]13.1461960842031[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]28.6504949782515[/C][C]48.3495050217485[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]56.0480501431288[/C][C]-2.0480501431288[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]64.4949190767424[/C][C]19.5050809232576[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]86.335926809279[/C][C]-38.335926809279[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]56.1913729959164[/C][C]39.8086270040836[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]129.664803267207[/C][C]-46.6648032672074[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]53.9973913310642[/C][C]12.0026086689358[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]79.6754118037333[/C][C]-18.6754118037333[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]30.6746061226909[/C][C]22.3253938773091[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]47.4750331631132[/C][C]-17.4750331631132[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]103.414328539607[/C][C]-29.4143285396072[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]94.6690520639605[/C][C]-25.6690520639605[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]58.2346826816536[/C][C]0.765317318346362[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]43.6095578051345[/C][C]-1.60955780513446[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]61.0081831412298[/C][C]3.99181685877025[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]49.4788033499446[/C][C]20.5211966500554[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]76.7603341377986[/C][C]23.2396658622014[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]103.96583707419[/C][C]-40.9658370741898[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]56.5015494288369[/C][C]48.4984505711631[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]81.9715413639347[/C][C]0.0284586360653378[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]58.7674302672487[/C][C]22.2325697327513[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]57.5054384585619[/C][C]17.4945615414381[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]121.811391006708[/C][C]-19.8113910067084[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]119.011021546426[/C][C]1.98897845357396[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]106.036128029629[/C][C]-8.03612802962945[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]87.7937238475062[/C][C]-11.7937238475062[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]104.548576897228[/C][C]-27.5485768972279[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]88.8253943324135[/C][C]-25.8253943324135[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]99.4433230769987[/C][C]-62.4433230769987[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]63.5759025308874[/C][C]-28.5759025308874[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]60.3350961492407[/C][C]-37.3350961492407[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]28.9375786540599[/C][C]11.0624213459401[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]17.9911476535457[/C][C]11.0088523464543[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]8.13783623184506[/C][C]28.8621637681549[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]57.8014044627004[/C][C]-6.80140446270038[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]67.9862803143687[/C][C]-47.9862803143687[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]28.9516752372211[/C][C]-0.951675237221107[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]9.31321056571075[/C][C]3.68678943428925[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]22.6070517338621[/C][C]-0.607051733862111[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.0505737046141[/C][C]8.9494262953859[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]21.8230856739758[/C][C]-8.82308567397584[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]20.946940527163[/C][C]-4.94694052716303[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]22.1988348561934[/C][C]-9.1988348561934[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]23.3093821664525[/C][C]-7.30938216645249[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]4.9308234847124[/C][C]12.0691765152876[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]3.19217990983005[/C][C]5.80782009016995[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]27.2017554894769[/C][C]-10.2017554894769[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]16.6693885648103[/C][C]8.33061143518972[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]20.4077763690547[/C][C]-6.40777636905471[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]0.693902625599055[/C][C]7.30609737440095[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]13.3553977851456[/C][C]-6.35539778514564[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]8.82028766465224[/C][C]1.17971233534776[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]3.33822505002995[/C][C]3.66177494997005[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]8.90454913922631[/C][C]1.09545086077369[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]10.5263066432433[/C][C]-7.52630664324327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147377&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147377&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
138065.953525641025614.0464743589744
144232.44671481725939.55328518274065
155447.13530513160876.86469486839134
166660.59089490800925.4091050919908
178179.7238940940241.27610590597605
186369.4231643277678-6.42316432776776
19137111.48776994845825.5122300515416
207280.1890659314046-8.1890659314046
2110786.456323671552120.5436763284479
225868.1223642893233-10.1223642893233
233697.1537646423693-61.1537646423693
2452157.471510088703-105.471510088703
257965.853803915796913.1461960842031
267728.650494978251548.3495050217485
275456.0480501431288-2.0480501431288
288464.494919076742419.5050809232576
294886.335926809279-38.335926809279
309656.191372995916439.8086270040836
3183129.664803267207-46.6648032672074
326653.997391331064212.0026086689358
336179.6754118037333-18.6754118037333
345330.674606122690922.3253938773091
353047.4750331631132-17.4750331631132
3674103.414328539607-29.4143285396072
376994.6690520639605-25.6690520639605
385958.23468268165360.765317318346362
394243.6095578051345-1.60955780513446
406561.00818314122983.99181685877025
417049.478803349944620.5211966500554
4210076.760334137798623.2396658622014
4363103.96583707419-40.9658370741898
4410556.501549428836948.4984505711631
458281.97154136393470.0284586360653378
468158.767430267248722.2325697327513
477557.505438458561917.4945615414381
48102121.811391006708-19.8113910067084
49121119.0110215464261.98897845357396
5098106.036128029629-8.03612802962945
517687.7937238475062-11.7937238475062
5277104.548576897228-27.5485768972279
536388.8253943324135-25.8253943324135
543799.4433230769987-62.4433230769987
553563.5759025308874-28.5759025308874
562360.3350961492407-37.3350961492407
574028.937578654059911.0624213459401
582917.991147653545711.0088523464543
59378.1378362318450628.8621637681549
605157.8014044627004-6.80140446270038
612067.9862803143687-47.9862803143687
622828.9516752372211-0.951675237221107
63139.313210565710753.68678943428925
642222.6070517338621-0.607051733862111
652516.05057370461418.9494262953859
661321.8230856739758-8.82308567397584
671620.946940527163-4.94694052716303
681322.1988348561934-9.1988348561934
691623.3093821664525-7.30938216645249
70174.930823484712412.0691765152876
7193.192179909830055.80782009016995
721727.2017554894769-10.2017554894769
732516.66938856481038.33061143518972
741420.4077763690547-6.40777636905471
7580.6939026255990557.30609737440095
76713.3553977851456-6.35539778514564
77108.820287664652241.17971233534776
7873.338225050029953.66177494997005
79108.904549139226311.09545086077369
80310.5263066432433-7.52630664324327







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8113.1518860780303-37.446598918903363.7503710749639
826.46657662735477-47.897222023736660.8303752784461
83-2.75000728511713-60.846725736897955.3467111666637
8411.6688643515536-50.140253426642873.47798212975
8513.4546037022295-52.055546076286478.9647534807455
867.24134529397909-61.965654558537376.4483451464955
87-3.81105338955775-76.716447137438669.0943403583232
88-0.232709452866828-76.84266072626576.3772418205314
891.05592991449233-79.268509091265281.38036892025
90-3.78144524583688-87.833400150122280.2705096584484
91-0.852758842779123-88.647824662597686.9423069770393
92-3.65473445255552-95.210646124490787.9011772193796

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 13.1518860780303 & -37.4465989189033 & 63.7503710749639 \tabularnewline
82 & 6.46657662735477 & -47.8972220237366 & 60.8303752784461 \tabularnewline
83 & -2.75000728511713 & -60.8467257368979 & 55.3467111666637 \tabularnewline
84 & 11.6688643515536 & -50.1402534266428 & 73.47798212975 \tabularnewline
85 & 13.4546037022295 & -52.0555460762864 & 78.9647534807455 \tabularnewline
86 & 7.24134529397909 & -61.9656545585373 & 76.4483451464955 \tabularnewline
87 & -3.81105338955775 & -76.7164471374386 & 69.0943403583232 \tabularnewline
88 & -0.232709452866828 & -76.842660726265 & 76.3772418205314 \tabularnewline
89 & 1.05592991449233 & -79.2685090912652 & 81.38036892025 \tabularnewline
90 & -3.78144524583688 & -87.8334001501222 & 80.2705096584484 \tabularnewline
91 & -0.852758842779123 & -88.6478246625976 & 86.9423069770393 \tabularnewline
92 & -3.65473445255552 & -95.2106461244907 & 87.9011772193796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147377&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]81[/C][C]13.1518860780303[/C][C]-37.4465989189033[/C][C]63.7503710749639[/C][/ROW]
[ROW][C]82[/C][C]6.46657662735477[/C][C]-47.8972220237366[/C][C]60.8303752784461[/C][/ROW]
[ROW][C]83[/C][C]-2.75000728511713[/C][C]-60.8467257368979[/C][C]55.3467111666637[/C][/ROW]
[ROW][C]84[/C][C]11.6688643515536[/C][C]-50.1402534266428[/C][C]73.47798212975[/C][/ROW]
[ROW][C]85[/C][C]13.4546037022295[/C][C]-52.0555460762864[/C][C]78.9647534807455[/C][/ROW]
[ROW][C]86[/C][C]7.24134529397909[/C][C]-61.9656545585373[/C][C]76.4483451464955[/C][/ROW]
[ROW][C]87[/C][C]-3.81105338955775[/C][C]-76.7164471374386[/C][C]69.0943403583232[/C][/ROW]
[ROW][C]88[/C][C]-0.232709452866828[/C][C]-76.842660726265[/C][C]76.3772418205314[/C][/ROW]
[ROW][C]89[/C][C]1.05592991449233[/C][C]-79.2685090912652[/C][C]81.38036892025[/C][/ROW]
[ROW][C]90[/C][C]-3.78144524583688[/C][C]-87.8334001501222[/C][C]80.2705096584484[/C][/ROW]
[ROW][C]91[/C][C]-0.852758842779123[/C][C]-88.6478246625976[/C][C]86.9423069770393[/C][/ROW]
[ROW][C]92[/C][C]-3.65473445255552[/C][C]-95.2106461244907[/C][C]87.9011772193796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147377&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147377&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
8113.1518860780303-37.446598918903363.7503710749639
826.46657662735477-47.897222023736660.8303752784461
83-2.75000728511713-60.846725736897955.3467111666637
8411.6688643515536-50.140253426642873.47798212975
8513.4546037022295-52.055546076286478.9647534807455
867.24134529397909-61.965654558537376.4483451464955
87-3.81105338955775-76.716447137438669.0943403583232
88-0.232709452866828-76.84266072626576.3772418205314
891.05592991449233-79.268509091265281.38036892025
90-3.78144524583688-87.833400150122280.2705096584484
91-0.852758842779123-88.647824662597686.9423069770393
92-3.65473445255552-95.210646124490787.9011772193796



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')