Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 15:33:51 +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/Apr/25/t14615948485uwxvziblgwgpa9.htm/, Retrieved Sun, 05 May 2024 23:31:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294719, Retrieved Sun, 05 May 2024 23:31:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 14:33:51] [c0f67b4e93ea0adf92c2b9d3976edd70] [Current]
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Dataseries X:
87.5
87.3
87.8
88.1
88.0
87.8
87.0
87.2
87.0
89.4
89.1
87.8
87.8
88.0
86.5
84.1
84.3
84.7
85.7
86.4
86.0
86.9
89.1
90.7
89.8
89.4
88.6
86.8
86.8
89.5
88.5
91.2
92.3
92.0
92.8
92.9
92.7
94.2
94.0
94.3
94.8
94.7
95.1
97.0
97.9
97.3
96.5
98.1
99.3
99.9
99.9
99.9
99.8
99.5
99.9
100.1
100.1
100.2
100.6
100.8
100.8
100.5
101.0
100.5
99.0
97.9
97.6
97.2
96.5
96.3
96.3
96.2
95.6
93.5
93.2
93.6
94.6
96.1
98.4
99.6
99.4
99.7
100.1
99.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294719&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294719&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999945056492049
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999945056492049 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294719&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]0.999945056492049[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294719&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
alpha0.999945056492049
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
287.387.5-0.200000000000003
387.887.30001098870160.49998901129841
488.187.79997252884980.300027471150216
58888.0999835154382-0.0999835154382396
687.888.0000054934451-0.200005493445076
78787.8000109890034-0.800010989003425
887.287.00004395541010.199956044589868
98787.1999890137135-0.199989013713477
1089.487.0000109880982.39998901190204
1189.189.3998681361847-0.299868136184656
1287.889.1000164758073-1.30001647580733
1387.887.8000714274656-7.14274655706504e-05
148887.80000000392450.199999996075519
1586.587.9999890112986-1.49998901129862
1684.186.5000824146582-2.40008241465819
1784.384.10013186894720.199868131052767
1884.784.29998901854380.400010981456248
1985.784.69997802199351.00002197800654
2086.485.69994505528450.700054944715504
218686.3999615365256-0.399961536525581
2286.986.00002197528990.899978024710151
2389.186.89995055205032.20004944794974
2490.789.09987912156571.60012087843434
2589.890.6999120837458-0.899912083745804
2689.489.8000494443267-0.400049444326712
2788.689.4000219801198-0.800021980119837
2886.888.600043956014-1.80004395601402
2986.886.8000989007294-9.89007294123212e-05
3089.586.80000000543392.69999999456606
3188.589.4998516525288-0.999851652528832
3291.288.50005493535722.69994506464279
3392.391.19985165554691.10014834445312
349292.2999395539907-0.299939553990683
3592.892.00001647973130.799983520268725
3692.992.79995604609910.100043953900908
3792.792.8999945032342-0.199994503234223
3894.292.70001098839961.49998901160043
399494.1999175853418-0.199917585341822
4094.394.00001098417340.299989015826554
4194.894.29998351755110.500016482448871
4294.794.7999725273404-0.0999725273404124
4395.194.70000549284140.399994507158638
449795.09997802289861.90002197710139
4597.996.99989560612740.90010439387261
4697.397.8999505451071-0.599950545107077
4796.597.3000329633875-0.800032963387537
4898.196.50004395661751.59995604338251
4999.398.09991209280241.2000879071976
5099.999.29993406296050.600065937039474
5199.999.89996703027243.29697275844865e-05
5299.999.89999999818851.81147186140151e-09
5399.899.8999999999999-0.0999999999999091
5499.599.8000054943508-0.300005494350799
5599.999.50001648335430.399983516645747
56100.199.89997802350250.20002197649751
57100.1100.0999890100911.09899090574572e-05
58100.2100.0999999993960.100000000603828
59100.6100.1999945056490.400005494350822
60100.8100.5999780222950.200021977705063
61100.8100.7999890100911.09899091285115e-05
62100.5100.799999999396-0.299999999396164
63101100.5000164830520.499983516947651
64100.5100.999972529152-0.499972529151663
6599100.500027470245-1.50002747024463
6697.999.0000824167712-1.10008241677123
6797.697.900060442387-0.300060442387021
6897.297.6000164863733-0.400016486373289
6996.597.200021978309-0.700021978308996
7096.396.5000384616631-0.200038461663141
7196.396.3000109908148-1.09908148147042e-05
7296.296.3000000006039-0.10000000060387
7395.696.2000054943508-0.600005494350839
7493.595.6000329664066-2.10003296640664
7593.293.500115383178-0.300115383177982
7693.693.20001648939190.399983510608052
7794.693.59997802350281.00002197649719
7896.194.59994505528461.50005494471542
7998.496.09991758171922.30008241828079
8099.698.39987362540341.20012637459662
8199.499.599934060847-0.199934060846985
8299.799.40001098507870.299989014921323
83100.199.69998351755120.400016482448819
8499.9100.099978021691-0.199978021691209

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 87.3 & 87.5 & -0.200000000000003 \tabularnewline
3 & 87.8 & 87.3000109887016 & 0.49998901129841 \tabularnewline
4 & 88.1 & 87.7999725288498 & 0.300027471150216 \tabularnewline
5 & 88 & 88.0999835154382 & -0.0999835154382396 \tabularnewline
6 & 87.8 & 88.0000054934451 & -0.200005493445076 \tabularnewline
7 & 87 & 87.8000109890034 & -0.800010989003425 \tabularnewline
8 & 87.2 & 87.0000439554101 & 0.199956044589868 \tabularnewline
9 & 87 & 87.1999890137135 & -0.199989013713477 \tabularnewline
10 & 89.4 & 87.000010988098 & 2.39998901190204 \tabularnewline
11 & 89.1 & 89.3998681361847 & -0.299868136184656 \tabularnewline
12 & 87.8 & 89.1000164758073 & -1.30001647580733 \tabularnewline
13 & 87.8 & 87.8000714274656 & -7.14274655706504e-05 \tabularnewline
14 & 88 & 87.8000000039245 & 0.199999996075519 \tabularnewline
15 & 86.5 & 87.9999890112986 & -1.49998901129862 \tabularnewline
16 & 84.1 & 86.5000824146582 & -2.40008241465819 \tabularnewline
17 & 84.3 & 84.1001318689472 & 0.199868131052767 \tabularnewline
18 & 84.7 & 84.2999890185438 & 0.400010981456248 \tabularnewline
19 & 85.7 & 84.6999780219935 & 1.00002197800654 \tabularnewline
20 & 86.4 & 85.6999450552845 & 0.700054944715504 \tabularnewline
21 & 86 & 86.3999615365256 & -0.399961536525581 \tabularnewline
22 & 86.9 & 86.0000219752899 & 0.899978024710151 \tabularnewline
23 & 89.1 & 86.8999505520503 & 2.20004944794974 \tabularnewline
24 & 90.7 & 89.0998791215657 & 1.60012087843434 \tabularnewline
25 & 89.8 & 90.6999120837458 & -0.899912083745804 \tabularnewline
26 & 89.4 & 89.8000494443267 & -0.400049444326712 \tabularnewline
27 & 88.6 & 89.4000219801198 & -0.800021980119837 \tabularnewline
28 & 86.8 & 88.600043956014 & -1.80004395601402 \tabularnewline
29 & 86.8 & 86.8000989007294 & -9.89007294123212e-05 \tabularnewline
30 & 89.5 & 86.8000000054339 & 2.69999999456606 \tabularnewline
31 & 88.5 & 89.4998516525288 & -0.999851652528832 \tabularnewline
32 & 91.2 & 88.5000549353572 & 2.69994506464279 \tabularnewline
33 & 92.3 & 91.1998516555469 & 1.10014834445312 \tabularnewline
34 & 92 & 92.2999395539907 & -0.299939553990683 \tabularnewline
35 & 92.8 & 92.0000164797313 & 0.799983520268725 \tabularnewline
36 & 92.9 & 92.7999560460991 & 0.100043953900908 \tabularnewline
37 & 92.7 & 92.8999945032342 & -0.199994503234223 \tabularnewline
38 & 94.2 & 92.7000109883996 & 1.49998901160043 \tabularnewline
39 & 94 & 94.1999175853418 & -0.199917585341822 \tabularnewline
40 & 94.3 & 94.0000109841734 & 0.299989015826554 \tabularnewline
41 & 94.8 & 94.2999835175511 & 0.500016482448871 \tabularnewline
42 & 94.7 & 94.7999725273404 & -0.0999725273404124 \tabularnewline
43 & 95.1 & 94.7000054928414 & 0.399994507158638 \tabularnewline
44 & 97 & 95.0999780228986 & 1.90002197710139 \tabularnewline
45 & 97.9 & 96.9998956061274 & 0.90010439387261 \tabularnewline
46 & 97.3 & 97.8999505451071 & -0.599950545107077 \tabularnewline
47 & 96.5 & 97.3000329633875 & -0.800032963387537 \tabularnewline
48 & 98.1 & 96.5000439566175 & 1.59995604338251 \tabularnewline
49 & 99.3 & 98.0999120928024 & 1.2000879071976 \tabularnewline
50 & 99.9 & 99.2999340629605 & 0.600065937039474 \tabularnewline
51 & 99.9 & 99.8999670302724 & 3.29697275844865e-05 \tabularnewline
52 & 99.9 & 99.8999999981885 & 1.81147186140151e-09 \tabularnewline
53 & 99.8 & 99.8999999999999 & -0.0999999999999091 \tabularnewline
54 & 99.5 & 99.8000054943508 & -0.300005494350799 \tabularnewline
55 & 99.9 & 99.5000164833543 & 0.399983516645747 \tabularnewline
56 & 100.1 & 99.8999780235025 & 0.20002197649751 \tabularnewline
57 & 100.1 & 100.099989010091 & 1.09899090574572e-05 \tabularnewline
58 & 100.2 & 100.099999999396 & 0.100000000603828 \tabularnewline
59 & 100.6 & 100.199994505649 & 0.400005494350822 \tabularnewline
60 & 100.8 & 100.599978022295 & 0.200021977705063 \tabularnewline
61 & 100.8 & 100.799989010091 & 1.09899091285115e-05 \tabularnewline
62 & 100.5 & 100.799999999396 & -0.299999999396164 \tabularnewline
63 & 101 & 100.500016483052 & 0.499983516947651 \tabularnewline
64 & 100.5 & 100.999972529152 & -0.499972529151663 \tabularnewline
65 & 99 & 100.500027470245 & -1.50002747024463 \tabularnewline
66 & 97.9 & 99.0000824167712 & -1.10008241677123 \tabularnewline
67 & 97.6 & 97.900060442387 & -0.300060442387021 \tabularnewline
68 & 97.2 & 97.6000164863733 & -0.400016486373289 \tabularnewline
69 & 96.5 & 97.200021978309 & -0.700021978308996 \tabularnewline
70 & 96.3 & 96.5000384616631 & -0.200038461663141 \tabularnewline
71 & 96.3 & 96.3000109908148 & -1.09908148147042e-05 \tabularnewline
72 & 96.2 & 96.3000000006039 & -0.10000000060387 \tabularnewline
73 & 95.6 & 96.2000054943508 & -0.600005494350839 \tabularnewline
74 & 93.5 & 95.6000329664066 & -2.10003296640664 \tabularnewline
75 & 93.2 & 93.500115383178 & -0.300115383177982 \tabularnewline
76 & 93.6 & 93.2000164893919 & 0.399983510608052 \tabularnewline
77 & 94.6 & 93.5999780235028 & 1.00002197649719 \tabularnewline
78 & 96.1 & 94.5999450552846 & 1.50005494471542 \tabularnewline
79 & 98.4 & 96.0999175817192 & 2.30008241828079 \tabularnewline
80 & 99.6 & 98.3998736254034 & 1.20012637459662 \tabularnewline
81 & 99.4 & 99.599934060847 & -0.199934060846985 \tabularnewline
82 & 99.7 & 99.4000109850787 & 0.299989014921323 \tabularnewline
83 & 100.1 & 99.6999835175512 & 0.400016482448819 \tabularnewline
84 & 99.9 & 100.099978021691 & -0.199978021691209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294719&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]2[/C][C]87.3[/C][C]87.5[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]3[/C][C]87.8[/C][C]87.3000109887016[/C][C]0.49998901129841[/C][/ROW]
[ROW][C]4[/C][C]88.1[/C][C]87.7999725288498[/C][C]0.300027471150216[/C][/ROW]
[ROW][C]5[/C][C]88[/C][C]88.0999835154382[/C][C]-0.0999835154382396[/C][/ROW]
[ROW][C]6[/C][C]87.8[/C][C]88.0000054934451[/C][C]-0.200005493445076[/C][/ROW]
[ROW][C]7[/C][C]87[/C][C]87.8000109890034[/C][C]-0.800010989003425[/C][/ROW]
[ROW][C]8[/C][C]87.2[/C][C]87.0000439554101[/C][C]0.199956044589868[/C][/ROW]
[ROW][C]9[/C][C]87[/C][C]87.1999890137135[/C][C]-0.199989013713477[/C][/ROW]
[ROW][C]10[/C][C]89.4[/C][C]87.000010988098[/C][C]2.39998901190204[/C][/ROW]
[ROW][C]11[/C][C]89.1[/C][C]89.3998681361847[/C][C]-0.299868136184656[/C][/ROW]
[ROW][C]12[/C][C]87.8[/C][C]89.1000164758073[/C][C]-1.30001647580733[/C][/ROW]
[ROW][C]13[/C][C]87.8[/C][C]87.8000714274656[/C][C]-7.14274655706504e-05[/C][/ROW]
[ROW][C]14[/C][C]88[/C][C]87.8000000039245[/C][C]0.199999996075519[/C][/ROW]
[ROW][C]15[/C][C]86.5[/C][C]87.9999890112986[/C][C]-1.49998901129862[/C][/ROW]
[ROW][C]16[/C][C]84.1[/C][C]86.5000824146582[/C][C]-2.40008241465819[/C][/ROW]
[ROW][C]17[/C][C]84.3[/C][C]84.1001318689472[/C][C]0.199868131052767[/C][/ROW]
[ROW][C]18[/C][C]84.7[/C][C]84.2999890185438[/C][C]0.400010981456248[/C][/ROW]
[ROW][C]19[/C][C]85.7[/C][C]84.6999780219935[/C][C]1.00002197800654[/C][/ROW]
[ROW][C]20[/C][C]86.4[/C][C]85.6999450552845[/C][C]0.700054944715504[/C][/ROW]
[ROW][C]21[/C][C]86[/C][C]86.3999615365256[/C][C]-0.399961536525581[/C][/ROW]
[ROW][C]22[/C][C]86.9[/C][C]86.0000219752899[/C][C]0.899978024710151[/C][/ROW]
[ROW][C]23[/C][C]89.1[/C][C]86.8999505520503[/C][C]2.20004944794974[/C][/ROW]
[ROW][C]24[/C][C]90.7[/C][C]89.0998791215657[/C][C]1.60012087843434[/C][/ROW]
[ROW][C]25[/C][C]89.8[/C][C]90.6999120837458[/C][C]-0.899912083745804[/C][/ROW]
[ROW][C]26[/C][C]89.4[/C][C]89.8000494443267[/C][C]-0.400049444326712[/C][/ROW]
[ROW][C]27[/C][C]88.6[/C][C]89.4000219801198[/C][C]-0.800021980119837[/C][/ROW]
[ROW][C]28[/C][C]86.8[/C][C]88.600043956014[/C][C]-1.80004395601402[/C][/ROW]
[ROW][C]29[/C][C]86.8[/C][C]86.8000989007294[/C][C]-9.89007294123212e-05[/C][/ROW]
[ROW][C]30[/C][C]89.5[/C][C]86.8000000054339[/C][C]2.69999999456606[/C][/ROW]
[ROW][C]31[/C][C]88.5[/C][C]89.4998516525288[/C][C]-0.999851652528832[/C][/ROW]
[ROW][C]32[/C][C]91.2[/C][C]88.5000549353572[/C][C]2.69994506464279[/C][/ROW]
[ROW][C]33[/C][C]92.3[/C][C]91.1998516555469[/C][C]1.10014834445312[/C][/ROW]
[ROW][C]34[/C][C]92[/C][C]92.2999395539907[/C][C]-0.299939553990683[/C][/ROW]
[ROW][C]35[/C][C]92.8[/C][C]92.0000164797313[/C][C]0.799983520268725[/C][/ROW]
[ROW][C]36[/C][C]92.9[/C][C]92.7999560460991[/C][C]0.100043953900908[/C][/ROW]
[ROW][C]37[/C][C]92.7[/C][C]92.8999945032342[/C][C]-0.199994503234223[/C][/ROW]
[ROW][C]38[/C][C]94.2[/C][C]92.7000109883996[/C][C]1.49998901160043[/C][/ROW]
[ROW][C]39[/C][C]94[/C][C]94.1999175853418[/C][C]-0.199917585341822[/C][/ROW]
[ROW][C]40[/C][C]94.3[/C][C]94.0000109841734[/C][C]0.299989015826554[/C][/ROW]
[ROW][C]41[/C][C]94.8[/C][C]94.2999835175511[/C][C]0.500016482448871[/C][/ROW]
[ROW][C]42[/C][C]94.7[/C][C]94.7999725273404[/C][C]-0.0999725273404124[/C][/ROW]
[ROW][C]43[/C][C]95.1[/C][C]94.7000054928414[/C][C]0.399994507158638[/C][/ROW]
[ROW][C]44[/C][C]97[/C][C]95.0999780228986[/C][C]1.90002197710139[/C][/ROW]
[ROW][C]45[/C][C]97.9[/C][C]96.9998956061274[/C][C]0.90010439387261[/C][/ROW]
[ROW][C]46[/C][C]97.3[/C][C]97.8999505451071[/C][C]-0.599950545107077[/C][/ROW]
[ROW][C]47[/C][C]96.5[/C][C]97.3000329633875[/C][C]-0.800032963387537[/C][/ROW]
[ROW][C]48[/C][C]98.1[/C][C]96.5000439566175[/C][C]1.59995604338251[/C][/ROW]
[ROW][C]49[/C][C]99.3[/C][C]98.0999120928024[/C][C]1.2000879071976[/C][/ROW]
[ROW][C]50[/C][C]99.9[/C][C]99.2999340629605[/C][C]0.600065937039474[/C][/ROW]
[ROW][C]51[/C][C]99.9[/C][C]99.8999670302724[/C][C]3.29697275844865e-05[/C][/ROW]
[ROW][C]52[/C][C]99.9[/C][C]99.8999999981885[/C][C]1.81147186140151e-09[/C][/ROW]
[ROW][C]53[/C][C]99.8[/C][C]99.8999999999999[/C][C]-0.0999999999999091[/C][/ROW]
[ROW][C]54[/C][C]99.5[/C][C]99.8000054943508[/C][C]-0.300005494350799[/C][/ROW]
[ROW][C]55[/C][C]99.9[/C][C]99.5000164833543[/C][C]0.399983516645747[/C][/ROW]
[ROW][C]56[/C][C]100.1[/C][C]99.8999780235025[/C][C]0.20002197649751[/C][/ROW]
[ROW][C]57[/C][C]100.1[/C][C]100.099989010091[/C][C]1.09899090574572e-05[/C][/ROW]
[ROW][C]58[/C][C]100.2[/C][C]100.099999999396[/C][C]0.100000000603828[/C][/ROW]
[ROW][C]59[/C][C]100.6[/C][C]100.199994505649[/C][C]0.400005494350822[/C][/ROW]
[ROW][C]60[/C][C]100.8[/C][C]100.599978022295[/C][C]0.200021977705063[/C][/ROW]
[ROW][C]61[/C][C]100.8[/C][C]100.799989010091[/C][C]1.09899091285115e-05[/C][/ROW]
[ROW][C]62[/C][C]100.5[/C][C]100.799999999396[/C][C]-0.299999999396164[/C][/ROW]
[ROW][C]63[/C][C]101[/C][C]100.500016483052[/C][C]0.499983516947651[/C][/ROW]
[ROW][C]64[/C][C]100.5[/C][C]100.999972529152[/C][C]-0.499972529151663[/C][/ROW]
[ROW][C]65[/C][C]99[/C][C]100.500027470245[/C][C]-1.50002747024463[/C][/ROW]
[ROW][C]66[/C][C]97.9[/C][C]99.0000824167712[/C][C]-1.10008241677123[/C][/ROW]
[ROW][C]67[/C][C]97.6[/C][C]97.900060442387[/C][C]-0.300060442387021[/C][/ROW]
[ROW][C]68[/C][C]97.2[/C][C]97.6000164863733[/C][C]-0.400016486373289[/C][/ROW]
[ROW][C]69[/C][C]96.5[/C][C]97.200021978309[/C][C]-0.700021978308996[/C][/ROW]
[ROW][C]70[/C][C]96.3[/C][C]96.5000384616631[/C][C]-0.200038461663141[/C][/ROW]
[ROW][C]71[/C][C]96.3[/C][C]96.3000109908148[/C][C]-1.09908148147042e-05[/C][/ROW]
[ROW][C]72[/C][C]96.2[/C][C]96.3000000006039[/C][C]-0.10000000060387[/C][/ROW]
[ROW][C]73[/C][C]95.6[/C][C]96.2000054943508[/C][C]-0.600005494350839[/C][/ROW]
[ROW][C]74[/C][C]93.5[/C][C]95.6000329664066[/C][C]-2.10003296640664[/C][/ROW]
[ROW][C]75[/C][C]93.2[/C][C]93.500115383178[/C][C]-0.300115383177982[/C][/ROW]
[ROW][C]76[/C][C]93.6[/C][C]93.2000164893919[/C][C]0.399983510608052[/C][/ROW]
[ROW][C]77[/C][C]94.6[/C][C]93.5999780235028[/C][C]1.00002197649719[/C][/ROW]
[ROW][C]78[/C][C]96.1[/C][C]94.5999450552846[/C][C]1.50005494471542[/C][/ROW]
[ROW][C]79[/C][C]98.4[/C][C]96.0999175817192[/C][C]2.30008241828079[/C][/ROW]
[ROW][C]80[/C][C]99.6[/C][C]98.3998736254034[/C][C]1.20012637459662[/C][/ROW]
[ROW][C]81[/C][C]99.4[/C][C]99.599934060847[/C][C]-0.199934060846985[/C][/ROW]
[ROW][C]82[/C][C]99.7[/C][C]99.4000109850787[/C][C]0.299989014921323[/C][/ROW]
[ROW][C]83[/C][C]100.1[/C][C]99.6999835175512[/C][C]0.400016482448819[/C][/ROW]
[ROW][C]84[/C][C]99.9[/C][C]100.099978021691[/C][C]-0.199978021691209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294719&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294719&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
287.387.5-0.200000000000003
387.887.30001098870160.49998901129841
488.187.79997252884980.300027471150216
58888.0999835154382-0.0999835154382396
687.888.0000054934451-0.200005493445076
78787.8000109890034-0.800010989003425
887.287.00004395541010.199956044589868
98787.1999890137135-0.199989013713477
1089.487.0000109880982.39998901190204
1189.189.3998681361847-0.299868136184656
1287.889.1000164758073-1.30001647580733
1387.887.8000714274656-7.14274655706504e-05
148887.80000000392450.199999996075519
1586.587.9999890112986-1.49998901129862
1684.186.5000824146582-2.40008241465819
1784.384.10013186894720.199868131052767
1884.784.29998901854380.400010981456248
1985.784.69997802199351.00002197800654
2086.485.69994505528450.700054944715504
218686.3999615365256-0.399961536525581
2286.986.00002197528990.899978024710151
2389.186.89995055205032.20004944794974
2490.789.09987912156571.60012087843434
2589.890.6999120837458-0.899912083745804
2689.489.8000494443267-0.400049444326712
2788.689.4000219801198-0.800021980119837
2886.888.600043956014-1.80004395601402
2986.886.8000989007294-9.89007294123212e-05
3089.586.80000000543392.69999999456606
3188.589.4998516525288-0.999851652528832
3291.288.50005493535722.69994506464279
3392.391.19985165554691.10014834445312
349292.2999395539907-0.299939553990683
3592.892.00001647973130.799983520268725
3692.992.79995604609910.100043953900908
3792.792.8999945032342-0.199994503234223
3894.292.70001098839961.49998901160043
399494.1999175853418-0.199917585341822
4094.394.00001098417340.299989015826554
4194.894.29998351755110.500016482448871
4294.794.7999725273404-0.0999725273404124
4395.194.70000549284140.399994507158638
449795.09997802289861.90002197710139
4597.996.99989560612740.90010439387261
4697.397.8999505451071-0.599950545107077
4796.597.3000329633875-0.800032963387537
4898.196.50004395661751.59995604338251
4999.398.09991209280241.2000879071976
5099.999.29993406296050.600065937039474
5199.999.89996703027243.29697275844865e-05
5299.999.89999999818851.81147186140151e-09
5399.899.8999999999999-0.0999999999999091
5499.599.8000054943508-0.300005494350799
5599.999.50001648335430.399983516645747
56100.199.89997802350250.20002197649751
57100.1100.0999890100911.09899090574572e-05
58100.2100.0999999993960.100000000603828
59100.6100.1999945056490.400005494350822
60100.8100.5999780222950.200021977705063
61100.8100.7999890100911.09899091285115e-05
62100.5100.799999999396-0.299999999396164
63101100.5000164830520.499983516947651
64100.5100.999972529152-0.499972529151663
6599100.500027470245-1.50002747024463
6697.999.0000824167712-1.10008241677123
6797.697.900060442387-0.300060442387021
6897.297.6000164863733-0.400016486373289
6996.597.200021978309-0.700021978308996
7096.396.5000384616631-0.200038461663141
7196.396.3000109908148-1.09908148147042e-05
7296.296.3000000006039-0.10000000060387
7395.696.2000054943508-0.600005494350839
7493.595.6000329664066-2.10003296640664
7593.293.500115383178-0.300115383177982
7693.693.20001648939190.399983510608052
7794.693.59997802350281.00002197649719
7896.194.59994505528461.50005494471542
7998.496.09991758171922.30008241828079
8099.698.39987362540341.20012637459662
8199.499.599934060847-0.199934060846985
8299.799.40001098507870.299989014921323
83100.199.69998351755120.400016482448819
8499.9100.099978021691-0.199978021691209







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8599.90001098749497.9564931874696101.843528787518
8699.90001098749497.1515372624171102.648484712571
8799.90001098749496.5338627144874103.266159260501
8899.90001098749496.0131355618736103.786886413114
8999.90001098749495.5543640905731104.245657884415
9099.90001098749495.1396020417053104.660419933283
9199.90001098749494.7581883816886105.0418335933
9299.90001098749494.4031767997093105.396845175279
9399.90001098749494.0697423430467105.730279631941
9499.90001098749493.7543719771996106.045649997788
9599.90001098749493.4544136355584106.34560833943
9699.90001098749493.1678069203474106.632215054641

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 99.900010987494 & 97.9564931874696 & 101.843528787518 \tabularnewline
86 & 99.900010987494 & 97.1515372624171 & 102.648484712571 \tabularnewline
87 & 99.900010987494 & 96.5338627144874 & 103.266159260501 \tabularnewline
88 & 99.900010987494 & 96.0131355618736 & 103.786886413114 \tabularnewline
89 & 99.900010987494 & 95.5543640905731 & 104.245657884415 \tabularnewline
90 & 99.900010987494 & 95.1396020417053 & 104.660419933283 \tabularnewline
91 & 99.900010987494 & 94.7581883816886 & 105.0418335933 \tabularnewline
92 & 99.900010987494 & 94.4031767997093 & 105.396845175279 \tabularnewline
93 & 99.900010987494 & 94.0697423430467 & 105.730279631941 \tabularnewline
94 & 99.900010987494 & 93.7543719771996 & 106.045649997788 \tabularnewline
95 & 99.900010987494 & 93.4544136355584 & 106.34560833943 \tabularnewline
96 & 99.900010987494 & 93.1678069203474 & 106.632215054641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294719&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]85[/C][C]99.900010987494[/C][C]97.9564931874696[/C][C]101.843528787518[/C][/ROW]
[ROW][C]86[/C][C]99.900010987494[/C][C]97.1515372624171[/C][C]102.648484712571[/C][/ROW]
[ROW][C]87[/C][C]99.900010987494[/C][C]96.5338627144874[/C][C]103.266159260501[/C][/ROW]
[ROW][C]88[/C][C]99.900010987494[/C][C]96.0131355618736[/C][C]103.786886413114[/C][/ROW]
[ROW][C]89[/C][C]99.900010987494[/C][C]95.5543640905731[/C][C]104.245657884415[/C][/ROW]
[ROW][C]90[/C][C]99.900010987494[/C][C]95.1396020417053[/C][C]104.660419933283[/C][/ROW]
[ROW][C]91[/C][C]99.900010987494[/C][C]94.7581883816886[/C][C]105.0418335933[/C][/ROW]
[ROW][C]92[/C][C]99.900010987494[/C][C]94.4031767997093[/C][C]105.396845175279[/C][/ROW]
[ROW][C]93[/C][C]99.900010987494[/C][C]94.0697423430467[/C][C]105.730279631941[/C][/ROW]
[ROW][C]94[/C][C]99.900010987494[/C][C]93.7543719771996[/C][C]106.045649997788[/C][/ROW]
[ROW][C]95[/C][C]99.900010987494[/C][C]93.4544136355584[/C][C]106.34560833943[/C][/ROW]
[ROW][C]96[/C][C]99.900010987494[/C][C]93.1678069203474[/C][C]106.632215054641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294719&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294719&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
8599.90001098749497.9564931874696101.843528787518
8699.90001098749497.1515372624171102.648484712571
8799.90001098749496.5338627144874103.266159260501
8899.90001098749496.0131355618736103.786886413114
8999.90001098749495.5543640905731104.245657884415
9099.90001098749495.1396020417053104.660419933283
9199.90001098749494.7581883816886105.0418335933
9299.90001098749494.4031767997093105.396845175279
9399.90001098749494.0697423430467105.730279631941
9499.90001098749493.7543719771996106.045649997788
9599.90001098749493.4544136355584106.34560833943
9699.90001098749493.1678069203474106.632215054641



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
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')