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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 13:21:44 +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/26/t14616733499ceqk29ixlo7iws.htm/, Retrieved Fri, 03 May 2024 20:38:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294863, Retrieved Fri, 03 May 2024 20:38:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 12:21:44] [b209de2eafe01326572c9c955e85acb1] [Current]
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Dataseries X:
99
99
99
100
101
101
100
101
100
101
100
100
102
102
102
102
102
102
103
103
103
103
103
103
104
104
104
106
106
106
106
107
106
106
106
106
106
106
106
105
105
105
105
105
104
104
104
104
103
104
104
103
103
103
103
103
103
104
104
104
104
104
105
105
104
104
104
104
103




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294863&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294863&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294863&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.794387634816213
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.794387634816213 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294863&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]0.794387634816213[/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=294863&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294863&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
alpha0.794387634816213
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
299990
399990
4100991
510199.79438763481621.20561236518378
6101100.75211119010.24788880990026
7100100.949030995494-0.949030995493814
8101100.1951325076160.804867492383792
9100100.834509291231-0.834509291231427
10101100.1715854291380.828414570862066
11100100.829667720732-0.829667720732331
12100100.170589942376-0.170589942376424
13102100.0350754015291.96492459847141
14102101.59598720590.404012794099515
15102101.9169299738410.0830700261593051
16102101.9829197754460.0170802245544905
17102101.9964880946310.00351190536852641
18102101.9992779088310.000722091169123473
19103101.9998515291271.00014847087317
20103102.7943571073690.205642892631175
21103102.9577172784630.0422827215371342
22103102.9913061496180.00869385038166115
23103102.998212436860.00178756313952988
24103102.9996324549150.000367545085026677
25104102.9999244281861.00007557181425
26104103.7943720963170.205627903683251
27104103.9577203603760.0422796396240983
28106103.9913067832982.00869321670223
29106105.5869878367850.413012163214773
30106105.9150795922720.0849204077282621
31106105.9825393141150.0174606858853821
32107105.9964098670771.00359013292262
33106106.793649459095-0.793649459094667
34106106.163184142411-0.163184142411296
35106106.033552677482-0.0335526774816799
36106106.006898845375-0.00689884537526098
37106106.001418487915-0.00141848791464838
38106106.000291658655-0.000291658655115157
39106106.000059968626-5.99686259050713e-05
40105106.000012330291-1.00001233029101
41105105.205614900444-0.20561490044409
42105105.042276965997-0.0422769659973312
43105105.008692666971-0.0086926669714984
44105105.001787319816-0.00178731981576163
45104105.000367495055-1.00036749505466
46104104.205687926711-0.205687926711178
47104104.042291981101-0.0422919811008455
48104104.008695754262-0.00869575426246172
49103104.001787954601-1.00178795460097
50104103.2059799907580.794020009241862
51104103.8367396678970.163260332103462
52103103.966431656976-0.966431656975516
53103103.198710298779-0.198710298779218
54103103.040857294518-0.0408572945183749
55103103.008400764961-0.008400764960939
56103103.001727301153-0.00172730115298236
57103103.000355154475-0.000355154475457198
58104103.0000730241520.999926975848297
59104103.7944026494850.205597350515234
60104103.9577266424850.0422733575149437
61104103.9913080749770.00869192502290161
62104103.9982128327380.00178716726195205
63105103.9996325363121.0003674636877
64105104.7943120797380.205687920261738
65104104.957708020225-0.957708020225255
66104104.196916611194-0.196916611193998
67104104.040488490172-0.0404884901715832
68104104.008324934227-0.00832493422690561
69103104.001711709416-1.0017117094164

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 99 & 99 & 0 \tabularnewline
3 & 99 & 99 & 0 \tabularnewline
4 & 100 & 99 & 1 \tabularnewline
5 & 101 & 99.7943876348162 & 1.20561236518378 \tabularnewline
6 & 101 & 100.7521111901 & 0.24788880990026 \tabularnewline
7 & 100 & 100.949030995494 & -0.949030995493814 \tabularnewline
8 & 101 & 100.195132507616 & 0.804867492383792 \tabularnewline
9 & 100 & 100.834509291231 & -0.834509291231427 \tabularnewline
10 & 101 & 100.171585429138 & 0.828414570862066 \tabularnewline
11 & 100 & 100.829667720732 & -0.829667720732331 \tabularnewline
12 & 100 & 100.170589942376 & -0.170589942376424 \tabularnewline
13 & 102 & 100.035075401529 & 1.96492459847141 \tabularnewline
14 & 102 & 101.5959872059 & 0.404012794099515 \tabularnewline
15 & 102 & 101.916929973841 & 0.0830700261593051 \tabularnewline
16 & 102 & 101.982919775446 & 0.0170802245544905 \tabularnewline
17 & 102 & 101.996488094631 & 0.00351190536852641 \tabularnewline
18 & 102 & 101.999277908831 & 0.000722091169123473 \tabularnewline
19 & 103 & 101.999851529127 & 1.00014847087317 \tabularnewline
20 & 103 & 102.794357107369 & 0.205642892631175 \tabularnewline
21 & 103 & 102.957717278463 & 0.0422827215371342 \tabularnewline
22 & 103 & 102.991306149618 & 0.00869385038166115 \tabularnewline
23 & 103 & 102.99821243686 & 0.00178756313952988 \tabularnewline
24 & 103 & 102.999632454915 & 0.000367545085026677 \tabularnewline
25 & 104 & 102.999924428186 & 1.00007557181425 \tabularnewline
26 & 104 & 103.794372096317 & 0.205627903683251 \tabularnewline
27 & 104 & 103.957720360376 & 0.0422796396240983 \tabularnewline
28 & 106 & 103.991306783298 & 2.00869321670223 \tabularnewline
29 & 106 & 105.586987836785 & 0.413012163214773 \tabularnewline
30 & 106 & 105.915079592272 & 0.0849204077282621 \tabularnewline
31 & 106 & 105.982539314115 & 0.0174606858853821 \tabularnewline
32 & 107 & 105.996409867077 & 1.00359013292262 \tabularnewline
33 & 106 & 106.793649459095 & -0.793649459094667 \tabularnewline
34 & 106 & 106.163184142411 & -0.163184142411296 \tabularnewline
35 & 106 & 106.033552677482 & -0.0335526774816799 \tabularnewline
36 & 106 & 106.006898845375 & -0.00689884537526098 \tabularnewline
37 & 106 & 106.001418487915 & -0.00141848791464838 \tabularnewline
38 & 106 & 106.000291658655 & -0.000291658655115157 \tabularnewline
39 & 106 & 106.000059968626 & -5.99686259050713e-05 \tabularnewline
40 & 105 & 106.000012330291 & -1.00001233029101 \tabularnewline
41 & 105 & 105.205614900444 & -0.20561490044409 \tabularnewline
42 & 105 & 105.042276965997 & -0.0422769659973312 \tabularnewline
43 & 105 & 105.008692666971 & -0.0086926669714984 \tabularnewline
44 & 105 & 105.001787319816 & -0.00178731981576163 \tabularnewline
45 & 104 & 105.000367495055 & -1.00036749505466 \tabularnewline
46 & 104 & 104.205687926711 & -0.205687926711178 \tabularnewline
47 & 104 & 104.042291981101 & -0.0422919811008455 \tabularnewline
48 & 104 & 104.008695754262 & -0.00869575426246172 \tabularnewline
49 & 103 & 104.001787954601 & -1.00178795460097 \tabularnewline
50 & 104 & 103.205979990758 & 0.794020009241862 \tabularnewline
51 & 104 & 103.836739667897 & 0.163260332103462 \tabularnewline
52 & 103 & 103.966431656976 & -0.966431656975516 \tabularnewline
53 & 103 & 103.198710298779 & -0.198710298779218 \tabularnewline
54 & 103 & 103.040857294518 & -0.0408572945183749 \tabularnewline
55 & 103 & 103.008400764961 & -0.008400764960939 \tabularnewline
56 & 103 & 103.001727301153 & -0.00172730115298236 \tabularnewline
57 & 103 & 103.000355154475 & -0.000355154475457198 \tabularnewline
58 & 104 & 103.000073024152 & 0.999926975848297 \tabularnewline
59 & 104 & 103.794402649485 & 0.205597350515234 \tabularnewline
60 & 104 & 103.957726642485 & 0.0422733575149437 \tabularnewline
61 & 104 & 103.991308074977 & 0.00869192502290161 \tabularnewline
62 & 104 & 103.998212832738 & 0.00178716726195205 \tabularnewline
63 & 105 & 103.999632536312 & 1.0003674636877 \tabularnewline
64 & 105 & 104.794312079738 & 0.205687920261738 \tabularnewline
65 & 104 & 104.957708020225 & -0.957708020225255 \tabularnewline
66 & 104 & 104.196916611194 & -0.196916611193998 \tabularnewline
67 & 104 & 104.040488490172 & -0.0404884901715832 \tabularnewline
68 & 104 & 104.008324934227 & -0.00832493422690561 \tabularnewline
69 & 103 & 104.001711709416 & -1.0017117094164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294863&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]99[/C][C]99[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]99[/C][C]99[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]100[/C][C]99[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]101[/C][C]99.7943876348162[/C][C]1.20561236518378[/C][/ROW]
[ROW][C]6[/C][C]101[/C][C]100.7521111901[/C][C]0.24788880990026[/C][/ROW]
[ROW][C]7[/C][C]100[/C][C]100.949030995494[/C][C]-0.949030995493814[/C][/ROW]
[ROW][C]8[/C][C]101[/C][C]100.195132507616[/C][C]0.804867492383792[/C][/ROW]
[ROW][C]9[/C][C]100[/C][C]100.834509291231[/C][C]-0.834509291231427[/C][/ROW]
[ROW][C]10[/C][C]101[/C][C]100.171585429138[/C][C]0.828414570862066[/C][/ROW]
[ROW][C]11[/C][C]100[/C][C]100.829667720732[/C][C]-0.829667720732331[/C][/ROW]
[ROW][C]12[/C][C]100[/C][C]100.170589942376[/C][C]-0.170589942376424[/C][/ROW]
[ROW][C]13[/C][C]102[/C][C]100.035075401529[/C][C]1.96492459847141[/C][/ROW]
[ROW][C]14[/C][C]102[/C][C]101.5959872059[/C][C]0.404012794099515[/C][/ROW]
[ROW][C]15[/C][C]102[/C][C]101.916929973841[/C][C]0.0830700261593051[/C][/ROW]
[ROW][C]16[/C][C]102[/C][C]101.982919775446[/C][C]0.0170802245544905[/C][/ROW]
[ROW][C]17[/C][C]102[/C][C]101.996488094631[/C][C]0.00351190536852641[/C][/ROW]
[ROW][C]18[/C][C]102[/C][C]101.999277908831[/C][C]0.000722091169123473[/C][/ROW]
[ROW][C]19[/C][C]103[/C][C]101.999851529127[/C][C]1.00014847087317[/C][/ROW]
[ROW][C]20[/C][C]103[/C][C]102.794357107369[/C][C]0.205642892631175[/C][/ROW]
[ROW][C]21[/C][C]103[/C][C]102.957717278463[/C][C]0.0422827215371342[/C][/ROW]
[ROW][C]22[/C][C]103[/C][C]102.991306149618[/C][C]0.00869385038166115[/C][/ROW]
[ROW][C]23[/C][C]103[/C][C]102.99821243686[/C][C]0.00178756313952988[/C][/ROW]
[ROW][C]24[/C][C]103[/C][C]102.999632454915[/C][C]0.000367545085026677[/C][/ROW]
[ROW][C]25[/C][C]104[/C][C]102.999924428186[/C][C]1.00007557181425[/C][/ROW]
[ROW][C]26[/C][C]104[/C][C]103.794372096317[/C][C]0.205627903683251[/C][/ROW]
[ROW][C]27[/C][C]104[/C][C]103.957720360376[/C][C]0.0422796396240983[/C][/ROW]
[ROW][C]28[/C][C]106[/C][C]103.991306783298[/C][C]2.00869321670223[/C][/ROW]
[ROW][C]29[/C][C]106[/C][C]105.586987836785[/C][C]0.413012163214773[/C][/ROW]
[ROW][C]30[/C][C]106[/C][C]105.915079592272[/C][C]0.0849204077282621[/C][/ROW]
[ROW][C]31[/C][C]106[/C][C]105.982539314115[/C][C]0.0174606858853821[/C][/ROW]
[ROW][C]32[/C][C]107[/C][C]105.996409867077[/C][C]1.00359013292262[/C][/ROW]
[ROW][C]33[/C][C]106[/C][C]106.793649459095[/C][C]-0.793649459094667[/C][/ROW]
[ROW][C]34[/C][C]106[/C][C]106.163184142411[/C][C]-0.163184142411296[/C][/ROW]
[ROW][C]35[/C][C]106[/C][C]106.033552677482[/C][C]-0.0335526774816799[/C][/ROW]
[ROW][C]36[/C][C]106[/C][C]106.006898845375[/C][C]-0.00689884537526098[/C][/ROW]
[ROW][C]37[/C][C]106[/C][C]106.001418487915[/C][C]-0.00141848791464838[/C][/ROW]
[ROW][C]38[/C][C]106[/C][C]106.000291658655[/C][C]-0.000291658655115157[/C][/ROW]
[ROW][C]39[/C][C]106[/C][C]106.000059968626[/C][C]-5.99686259050713e-05[/C][/ROW]
[ROW][C]40[/C][C]105[/C][C]106.000012330291[/C][C]-1.00001233029101[/C][/ROW]
[ROW][C]41[/C][C]105[/C][C]105.205614900444[/C][C]-0.20561490044409[/C][/ROW]
[ROW][C]42[/C][C]105[/C][C]105.042276965997[/C][C]-0.0422769659973312[/C][/ROW]
[ROW][C]43[/C][C]105[/C][C]105.008692666971[/C][C]-0.0086926669714984[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]105.001787319816[/C][C]-0.00178731981576163[/C][/ROW]
[ROW][C]45[/C][C]104[/C][C]105.000367495055[/C][C]-1.00036749505466[/C][/ROW]
[ROW][C]46[/C][C]104[/C][C]104.205687926711[/C][C]-0.205687926711178[/C][/ROW]
[ROW][C]47[/C][C]104[/C][C]104.042291981101[/C][C]-0.0422919811008455[/C][/ROW]
[ROW][C]48[/C][C]104[/C][C]104.008695754262[/C][C]-0.00869575426246172[/C][/ROW]
[ROW][C]49[/C][C]103[/C][C]104.001787954601[/C][C]-1.00178795460097[/C][/ROW]
[ROW][C]50[/C][C]104[/C][C]103.205979990758[/C][C]0.794020009241862[/C][/ROW]
[ROW][C]51[/C][C]104[/C][C]103.836739667897[/C][C]0.163260332103462[/C][/ROW]
[ROW][C]52[/C][C]103[/C][C]103.966431656976[/C][C]-0.966431656975516[/C][/ROW]
[ROW][C]53[/C][C]103[/C][C]103.198710298779[/C][C]-0.198710298779218[/C][/ROW]
[ROW][C]54[/C][C]103[/C][C]103.040857294518[/C][C]-0.0408572945183749[/C][/ROW]
[ROW][C]55[/C][C]103[/C][C]103.008400764961[/C][C]-0.008400764960939[/C][/ROW]
[ROW][C]56[/C][C]103[/C][C]103.001727301153[/C][C]-0.00172730115298236[/C][/ROW]
[ROW][C]57[/C][C]103[/C][C]103.000355154475[/C][C]-0.000355154475457198[/C][/ROW]
[ROW][C]58[/C][C]104[/C][C]103.000073024152[/C][C]0.999926975848297[/C][/ROW]
[ROW][C]59[/C][C]104[/C][C]103.794402649485[/C][C]0.205597350515234[/C][/ROW]
[ROW][C]60[/C][C]104[/C][C]103.957726642485[/C][C]0.0422733575149437[/C][/ROW]
[ROW][C]61[/C][C]104[/C][C]103.991308074977[/C][C]0.00869192502290161[/C][/ROW]
[ROW][C]62[/C][C]104[/C][C]103.998212832738[/C][C]0.00178716726195205[/C][/ROW]
[ROW][C]63[/C][C]105[/C][C]103.999632536312[/C][C]1.0003674636877[/C][/ROW]
[ROW][C]64[/C][C]105[/C][C]104.794312079738[/C][C]0.205687920261738[/C][/ROW]
[ROW][C]65[/C][C]104[/C][C]104.957708020225[/C][C]-0.957708020225255[/C][/ROW]
[ROW][C]66[/C][C]104[/C][C]104.196916611194[/C][C]-0.196916611193998[/C][/ROW]
[ROW][C]67[/C][C]104[/C][C]104.040488490172[/C][C]-0.0404884901715832[/C][/ROW]
[ROW][C]68[/C][C]104[/C][C]104.008324934227[/C][C]-0.00832493422690561[/C][/ROW]
[ROW][C]69[/C][C]103[/C][C]104.001711709416[/C][C]-1.0017117094164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294863&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294863&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
299990
399990
4100991
510199.79438763481621.20561236518378
6101100.75211119010.24788880990026
7100100.949030995494-0.949030995493814
8101100.1951325076160.804867492383792
9100100.834509291231-0.834509291231427
10101100.1715854291380.828414570862066
11100100.829667720732-0.829667720732331
12100100.170589942376-0.170589942376424
13102100.0350754015291.96492459847141
14102101.59598720590.404012794099515
15102101.9169299738410.0830700261593051
16102101.9829197754460.0170802245544905
17102101.9964880946310.00351190536852641
18102101.9992779088310.000722091169123473
19103101.9998515291271.00014847087317
20103102.7943571073690.205642892631175
21103102.9577172784630.0422827215371342
22103102.9913061496180.00869385038166115
23103102.998212436860.00178756313952988
24103102.9996324549150.000367545085026677
25104102.9999244281861.00007557181425
26104103.7943720963170.205627903683251
27104103.9577203603760.0422796396240983
28106103.9913067832982.00869321670223
29106105.5869878367850.413012163214773
30106105.9150795922720.0849204077282621
31106105.9825393141150.0174606858853821
32107105.9964098670771.00359013292262
33106106.793649459095-0.793649459094667
34106106.163184142411-0.163184142411296
35106106.033552677482-0.0335526774816799
36106106.006898845375-0.00689884537526098
37106106.001418487915-0.00141848791464838
38106106.000291658655-0.000291658655115157
39106106.000059968626-5.99686259050713e-05
40105106.000012330291-1.00001233029101
41105105.205614900444-0.20561490044409
42105105.042276965997-0.0422769659973312
43105105.008692666971-0.0086926669714984
44105105.001787319816-0.00178731981576163
45104105.000367495055-1.00036749505466
46104104.205687926711-0.205687926711178
47104104.042291981101-0.0422919811008455
48104104.008695754262-0.00869575426246172
49103104.001787954601-1.00178795460097
50104103.2059799907580.794020009241862
51104103.8367396678970.163260332103462
52103103.966431656976-0.966431656975516
53103103.198710298779-0.198710298779218
54103103.040857294518-0.0408572945183749
55103103.008400764961-0.008400764960939
56103103.001727301153-0.00172730115298236
57103103.000355154475-0.000355154475457198
58104103.0000730241520.999926975848297
59104103.7944026494850.205597350515234
60104103.9577266424850.0422733575149437
61104103.9913080749770.00869192502290161
62104103.9982128327380.00178716726195205
63105103.9996325363121.0003674636877
64105104.7943120797380.205687920261738
65104104.957708020225-0.957708020225255
66104104.196916611194-0.196916611193998
67104104.040488490172-0.0404884901715832
68104104.008324934227-0.00832493422690561
69103104.001711709416-1.0017117094164







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
70103.205964313805101.972813266374104.439115361236
71103.205964313805101.631074617367104.780854010243
72103.205964313805101.351269296798105.060659330813
73103.205964313805101.10846350182105.303465125791
74103.205964313805100.890985759596105.520942868014
75103.205964313805100.69225355944105.719675068171
76103.205964313805100.508121136973105.903807490638
77103.205964313805100.335777236811106.0761513908
78103.205964313805100.173211454254106.238717173356
79103.205964313805100.018927138421106.39300148919
80103.20596431380599.8717744560666106.540154171544
81103.20596431380599.7308473290673106.681081298543

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
70 & 103.205964313805 & 101.972813266374 & 104.439115361236 \tabularnewline
71 & 103.205964313805 & 101.631074617367 & 104.780854010243 \tabularnewline
72 & 103.205964313805 & 101.351269296798 & 105.060659330813 \tabularnewline
73 & 103.205964313805 & 101.10846350182 & 105.303465125791 \tabularnewline
74 & 103.205964313805 & 100.890985759596 & 105.520942868014 \tabularnewline
75 & 103.205964313805 & 100.69225355944 & 105.719675068171 \tabularnewline
76 & 103.205964313805 & 100.508121136973 & 105.903807490638 \tabularnewline
77 & 103.205964313805 & 100.335777236811 & 106.0761513908 \tabularnewline
78 & 103.205964313805 & 100.173211454254 & 106.238717173356 \tabularnewline
79 & 103.205964313805 & 100.018927138421 & 106.39300148919 \tabularnewline
80 & 103.205964313805 & 99.8717744560666 & 106.540154171544 \tabularnewline
81 & 103.205964313805 & 99.7308473290673 & 106.681081298543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294863&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]70[/C][C]103.205964313805[/C][C]101.972813266374[/C][C]104.439115361236[/C][/ROW]
[ROW][C]71[/C][C]103.205964313805[/C][C]101.631074617367[/C][C]104.780854010243[/C][/ROW]
[ROW][C]72[/C][C]103.205964313805[/C][C]101.351269296798[/C][C]105.060659330813[/C][/ROW]
[ROW][C]73[/C][C]103.205964313805[/C][C]101.10846350182[/C][C]105.303465125791[/C][/ROW]
[ROW][C]74[/C][C]103.205964313805[/C][C]100.890985759596[/C][C]105.520942868014[/C][/ROW]
[ROW][C]75[/C][C]103.205964313805[/C][C]100.69225355944[/C][C]105.719675068171[/C][/ROW]
[ROW][C]76[/C][C]103.205964313805[/C][C]100.508121136973[/C][C]105.903807490638[/C][/ROW]
[ROW][C]77[/C][C]103.205964313805[/C][C]100.335777236811[/C][C]106.0761513908[/C][/ROW]
[ROW][C]78[/C][C]103.205964313805[/C][C]100.173211454254[/C][C]106.238717173356[/C][/ROW]
[ROW][C]79[/C][C]103.205964313805[/C][C]100.018927138421[/C][C]106.39300148919[/C][/ROW]
[ROW][C]80[/C][C]103.205964313805[/C][C]99.8717744560666[/C][C]106.540154171544[/C][/ROW]
[ROW][C]81[/C][C]103.205964313805[/C][C]99.7308473290673[/C][C]106.681081298543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294863&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294863&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
70103.205964313805101.972813266374104.439115361236
71103.205964313805101.631074617367104.780854010243
72103.205964313805101.351269296798105.060659330813
73103.205964313805101.10846350182105.303465125791
74103.205964313805100.890985759596105.520942868014
75103.205964313805100.69225355944105.719675068171
76103.205964313805100.508121136973105.903807490638
77103.205964313805100.335777236811106.0761513908
78103.205964313805100.173211454254106.238717173356
79103.205964313805100.018927138421106.39300148919
80103.20596431380599.8717744560666106.540154171544
81103.20596431380599.7308473290673106.681081298543



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