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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 19:43:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/27/t1417117578n58z827tbyswfwj.htm/, Retrieved Fri, 17 May 2024 10:06:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260588, Retrieved Fri, 17 May 2024 10:06:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-27 19:43:37] [5f87c1f524450f94c6870e724864065e] [Current]
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Dataseries X:
102.9
103.2
103.1
103.6
104.2
104.9
104.5
103.9
102.8
100.8
99
97.8
96.4
96.1
96
95.6
95.7
95.7
95.5
95.1
95.1
94.6
95
95
95.8
96.1
96.5
96.8
97.7
98.9
100
101.1
102
103.8
104.9
106.3
108.9
110.4
111.3
112.2
112.9
113
113.4
112.4
112.4
112.2
112.6
112.7
113.8
114.1
114.7
115.3
115.6
116.2
117.5
118.5
119.3
120
120.1
119.8
119.9
119.8
119.3
119
118.9
119
119.3
119.2
118.6
117
117.4
117.4




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=260588&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=260588&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260588&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
alpha0.894411253110802
beta0.853567354790621
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.894411253110802 \tabularnewline
beta & 0.853567354790621 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260588&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]0.894411253110802[/C][/ROW]
[ROW][C]beta[/C][C]0.853567354790621[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260588&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260588&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
alpha0.894411253110802
beta0.853567354790621
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3103.1103.5-0.400000000000006
4103.6103.1368593997910.463140600209414
5104.2103.8993016398360.300698360163963
6104.9104.7460189428840.153981057115516
7104.5105.579065975402-1.07906597540151
8103.9104.485459471185-0.585459471185175
9102.8103.386376855417-0.586376855416901
10100.8101.838810029292-1.03881002929175
119999.0935124953949-0.0935124953949469
1297.897.12230851073280.677691489267161
1396.496.3582550066320.0417449933679706
1496.195.05727360828771.04272639171231
159695.44764053124970.552359468750254
1695.695.8211112096447-0.221111209644718
1795.795.3339758127350.366024187264955
1895.795.65141851800570.0485814819943187
1995.595.7220259540978-0.222025954097759
2095.195.3810955048452-0.281095504845183
2195.194.77273296292230.327267037077732
2294.694.958345552223-0.358345552222971
239594.25716310933030.742836890669679
249595.1080022146891-0.108002214689094
2595.895.11538801212490.684611987875101
2696.196.3543572171147-0.254357217114659
2796.596.5593152620718-0.0593152620718342
2896.896.8934373680966-0.0934373680965876
2997.797.12570643109570.574293568904295
3098.998.39364038253050.506359617469542
3110099.98738875497450.0126112450255249
32101.1101.149150958922-0.0491509589219135
33102102.218148532402-0.218148532401912
34103.8102.9694494048630.830550595136685
35104.9105.292794329963-0.392794329962697
36106.3106.2220907871680.077909212831841
37108.9107.6318688186481.26813118135176
38110.4111.074337155315-0.674337155315271
39111.3112.264623828162-0.964623828162402
40112.2112.458842180154-0.258842180154403
41112.9113.086709042306-0.186709042305921
42113113.636551397219-0.63655139721908
43113.4113.2980807315880.101919268411834
44112.4113.697915810882-1.29791581088223
45112.4111.8548414749760.545158525024434
46112.2112.0764295246470.123570475352636
47112.6112.0152831527920.584716847208185
48112.7112.812987659754-0.112987659754083
49113.8112.9003980774260.89960192257405
50114.1114.580272326658-0.480272326657783
51114.7114.659312295610.0406877043902796
52115.3115.2353674098580.0646325901415992
53115.6115.882182219986-0.282182219986126
54116.2116.0033726973480.196627302651592
55117.5116.7029289964390.797071003561086
56118.5118.548044982647-0.0480449826465872
57119.3119.600600247168-0.300600247167651
58120120.197776913999-0.197776913998695
59120.1120.735929070943-0.635929070942709
60119.8120.396699160884-0.596699160883773
61119.9119.6370127688240.262987231176012
62119.8119.847014596804-0.047014596804118
63119.3119.743854465938-0.443854465937761
64119118.9468999271440.0531000728555426
65118.9118.6349658528910.265034147109176
66119118.7149257344090.28507426559085
67119.3119.0304468912650.269553108735181
68119.2119.537873442791-0.33787344279115
69118.6119.244064666435-0.644064666435369
70117118.184690125755-1.1846901257552
71117.4115.7373339678271.66266603217282
72117.4117.1060313661310.293968633868872

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 103.1 & 103.5 & -0.400000000000006 \tabularnewline
4 & 103.6 & 103.136859399791 & 0.463140600209414 \tabularnewline
5 & 104.2 & 103.899301639836 & 0.300698360163963 \tabularnewline
6 & 104.9 & 104.746018942884 & 0.153981057115516 \tabularnewline
7 & 104.5 & 105.579065975402 & -1.07906597540151 \tabularnewline
8 & 103.9 & 104.485459471185 & -0.585459471185175 \tabularnewline
9 & 102.8 & 103.386376855417 & -0.586376855416901 \tabularnewline
10 & 100.8 & 101.838810029292 & -1.03881002929175 \tabularnewline
11 & 99 & 99.0935124953949 & -0.0935124953949469 \tabularnewline
12 & 97.8 & 97.1223085107328 & 0.677691489267161 \tabularnewline
13 & 96.4 & 96.358255006632 & 0.0417449933679706 \tabularnewline
14 & 96.1 & 95.0572736082877 & 1.04272639171231 \tabularnewline
15 & 96 & 95.4476405312497 & 0.552359468750254 \tabularnewline
16 & 95.6 & 95.8211112096447 & -0.221111209644718 \tabularnewline
17 & 95.7 & 95.333975812735 & 0.366024187264955 \tabularnewline
18 & 95.7 & 95.6514185180057 & 0.0485814819943187 \tabularnewline
19 & 95.5 & 95.7220259540978 & -0.222025954097759 \tabularnewline
20 & 95.1 & 95.3810955048452 & -0.281095504845183 \tabularnewline
21 & 95.1 & 94.7727329629223 & 0.327267037077732 \tabularnewline
22 & 94.6 & 94.958345552223 & -0.358345552222971 \tabularnewline
23 & 95 & 94.2571631093303 & 0.742836890669679 \tabularnewline
24 & 95 & 95.1080022146891 & -0.108002214689094 \tabularnewline
25 & 95.8 & 95.1153880121249 & 0.684611987875101 \tabularnewline
26 & 96.1 & 96.3543572171147 & -0.254357217114659 \tabularnewline
27 & 96.5 & 96.5593152620718 & -0.0593152620718342 \tabularnewline
28 & 96.8 & 96.8934373680966 & -0.0934373680965876 \tabularnewline
29 & 97.7 & 97.1257064310957 & 0.574293568904295 \tabularnewline
30 & 98.9 & 98.3936403825305 & 0.506359617469542 \tabularnewline
31 & 100 & 99.9873887549745 & 0.0126112450255249 \tabularnewline
32 & 101.1 & 101.149150958922 & -0.0491509589219135 \tabularnewline
33 & 102 & 102.218148532402 & -0.218148532401912 \tabularnewline
34 & 103.8 & 102.969449404863 & 0.830550595136685 \tabularnewline
35 & 104.9 & 105.292794329963 & -0.392794329962697 \tabularnewline
36 & 106.3 & 106.222090787168 & 0.077909212831841 \tabularnewline
37 & 108.9 & 107.631868818648 & 1.26813118135176 \tabularnewline
38 & 110.4 & 111.074337155315 & -0.674337155315271 \tabularnewline
39 & 111.3 & 112.264623828162 & -0.964623828162402 \tabularnewline
40 & 112.2 & 112.458842180154 & -0.258842180154403 \tabularnewline
41 & 112.9 & 113.086709042306 & -0.186709042305921 \tabularnewline
42 & 113 & 113.636551397219 & -0.63655139721908 \tabularnewline
43 & 113.4 & 113.298080731588 & 0.101919268411834 \tabularnewline
44 & 112.4 & 113.697915810882 & -1.29791581088223 \tabularnewline
45 & 112.4 & 111.854841474976 & 0.545158525024434 \tabularnewline
46 & 112.2 & 112.076429524647 & 0.123570475352636 \tabularnewline
47 & 112.6 & 112.015283152792 & 0.584716847208185 \tabularnewline
48 & 112.7 & 112.812987659754 & -0.112987659754083 \tabularnewline
49 & 113.8 & 112.900398077426 & 0.89960192257405 \tabularnewline
50 & 114.1 & 114.580272326658 & -0.480272326657783 \tabularnewline
51 & 114.7 & 114.65931229561 & 0.0406877043902796 \tabularnewline
52 & 115.3 & 115.235367409858 & 0.0646325901415992 \tabularnewline
53 & 115.6 & 115.882182219986 & -0.282182219986126 \tabularnewline
54 & 116.2 & 116.003372697348 & 0.196627302651592 \tabularnewline
55 & 117.5 & 116.702928996439 & 0.797071003561086 \tabularnewline
56 & 118.5 & 118.548044982647 & -0.0480449826465872 \tabularnewline
57 & 119.3 & 119.600600247168 & -0.300600247167651 \tabularnewline
58 & 120 & 120.197776913999 & -0.197776913998695 \tabularnewline
59 & 120.1 & 120.735929070943 & -0.635929070942709 \tabularnewline
60 & 119.8 & 120.396699160884 & -0.596699160883773 \tabularnewline
61 & 119.9 & 119.637012768824 & 0.262987231176012 \tabularnewline
62 & 119.8 & 119.847014596804 & -0.047014596804118 \tabularnewline
63 & 119.3 & 119.743854465938 & -0.443854465937761 \tabularnewline
64 & 119 & 118.946899927144 & 0.0531000728555426 \tabularnewline
65 & 118.9 & 118.634965852891 & 0.265034147109176 \tabularnewline
66 & 119 & 118.714925734409 & 0.28507426559085 \tabularnewline
67 & 119.3 & 119.030446891265 & 0.269553108735181 \tabularnewline
68 & 119.2 & 119.537873442791 & -0.33787344279115 \tabularnewline
69 & 118.6 & 119.244064666435 & -0.644064666435369 \tabularnewline
70 & 117 & 118.184690125755 & -1.1846901257552 \tabularnewline
71 & 117.4 & 115.737333967827 & 1.66266603217282 \tabularnewline
72 & 117.4 & 117.106031366131 & 0.293968633868872 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260588&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]3[/C][C]103.1[/C][C]103.5[/C][C]-0.400000000000006[/C][/ROW]
[ROW][C]4[/C][C]103.6[/C][C]103.136859399791[/C][C]0.463140600209414[/C][/ROW]
[ROW][C]5[/C][C]104.2[/C][C]103.899301639836[/C][C]0.300698360163963[/C][/ROW]
[ROW][C]6[/C][C]104.9[/C][C]104.746018942884[/C][C]0.153981057115516[/C][/ROW]
[ROW][C]7[/C][C]104.5[/C][C]105.579065975402[/C][C]-1.07906597540151[/C][/ROW]
[ROW][C]8[/C][C]103.9[/C][C]104.485459471185[/C][C]-0.585459471185175[/C][/ROW]
[ROW][C]9[/C][C]102.8[/C][C]103.386376855417[/C][C]-0.586376855416901[/C][/ROW]
[ROW][C]10[/C][C]100.8[/C][C]101.838810029292[/C][C]-1.03881002929175[/C][/ROW]
[ROW][C]11[/C][C]99[/C][C]99.0935124953949[/C][C]-0.0935124953949469[/C][/ROW]
[ROW][C]12[/C][C]97.8[/C][C]97.1223085107328[/C][C]0.677691489267161[/C][/ROW]
[ROW][C]13[/C][C]96.4[/C][C]96.358255006632[/C][C]0.0417449933679706[/C][/ROW]
[ROW][C]14[/C][C]96.1[/C][C]95.0572736082877[/C][C]1.04272639171231[/C][/ROW]
[ROW][C]15[/C][C]96[/C][C]95.4476405312497[/C][C]0.552359468750254[/C][/ROW]
[ROW][C]16[/C][C]95.6[/C][C]95.8211112096447[/C][C]-0.221111209644718[/C][/ROW]
[ROW][C]17[/C][C]95.7[/C][C]95.333975812735[/C][C]0.366024187264955[/C][/ROW]
[ROW][C]18[/C][C]95.7[/C][C]95.6514185180057[/C][C]0.0485814819943187[/C][/ROW]
[ROW][C]19[/C][C]95.5[/C][C]95.7220259540978[/C][C]-0.222025954097759[/C][/ROW]
[ROW][C]20[/C][C]95.1[/C][C]95.3810955048452[/C][C]-0.281095504845183[/C][/ROW]
[ROW][C]21[/C][C]95.1[/C][C]94.7727329629223[/C][C]0.327267037077732[/C][/ROW]
[ROW][C]22[/C][C]94.6[/C][C]94.958345552223[/C][C]-0.358345552222971[/C][/ROW]
[ROW][C]23[/C][C]95[/C][C]94.2571631093303[/C][C]0.742836890669679[/C][/ROW]
[ROW][C]24[/C][C]95[/C][C]95.1080022146891[/C][C]-0.108002214689094[/C][/ROW]
[ROW][C]25[/C][C]95.8[/C][C]95.1153880121249[/C][C]0.684611987875101[/C][/ROW]
[ROW][C]26[/C][C]96.1[/C][C]96.3543572171147[/C][C]-0.254357217114659[/C][/ROW]
[ROW][C]27[/C][C]96.5[/C][C]96.5593152620718[/C][C]-0.0593152620718342[/C][/ROW]
[ROW][C]28[/C][C]96.8[/C][C]96.8934373680966[/C][C]-0.0934373680965876[/C][/ROW]
[ROW][C]29[/C][C]97.7[/C][C]97.1257064310957[/C][C]0.574293568904295[/C][/ROW]
[ROW][C]30[/C][C]98.9[/C][C]98.3936403825305[/C][C]0.506359617469542[/C][/ROW]
[ROW][C]31[/C][C]100[/C][C]99.9873887549745[/C][C]0.0126112450255249[/C][/ROW]
[ROW][C]32[/C][C]101.1[/C][C]101.149150958922[/C][C]-0.0491509589219135[/C][/ROW]
[ROW][C]33[/C][C]102[/C][C]102.218148532402[/C][C]-0.218148532401912[/C][/ROW]
[ROW][C]34[/C][C]103.8[/C][C]102.969449404863[/C][C]0.830550595136685[/C][/ROW]
[ROW][C]35[/C][C]104.9[/C][C]105.292794329963[/C][C]-0.392794329962697[/C][/ROW]
[ROW][C]36[/C][C]106.3[/C][C]106.222090787168[/C][C]0.077909212831841[/C][/ROW]
[ROW][C]37[/C][C]108.9[/C][C]107.631868818648[/C][C]1.26813118135176[/C][/ROW]
[ROW][C]38[/C][C]110.4[/C][C]111.074337155315[/C][C]-0.674337155315271[/C][/ROW]
[ROW][C]39[/C][C]111.3[/C][C]112.264623828162[/C][C]-0.964623828162402[/C][/ROW]
[ROW][C]40[/C][C]112.2[/C][C]112.458842180154[/C][C]-0.258842180154403[/C][/ROW]
[ROW][C]41[/C][C]112.9[/C][C]113.086709042306[/C][C]-0.186709042305921[/C][/ROW]
[ROW][C]42[/C][C]113[/C][C]113.636551397219[/C][C]-0.63655139721908[/C][/ROW]
[ROW][C]43[/C][C]113.4[/C][C]113.298080731588[/C][C]0.101919268411834[/C][/ROW]
[ROW][C]44[/C][C]112.4[/C][C]113.697915810882[/C][C]-1.29791581088223[/C][/ROW]
[ROW][C]45[/C][C]112.4[/C][C]111.854841474976[/C][C]0.545158525024434[/C][/ROW]
[ROW][C]46[/C][C]112.2[/C][C]112.076429524647[/C][C]0.123570475352636[/C][/ROW]
[ROW][C]47[/C][C]112.6[/C][C]112.015283152792[/C][C]0.584716847208185[/C][/ROW]
[ROW][C]48[/C][C]112.7[/C][C]112.812987659754[/C][C]-0.112987659754083[/C][/ROW]
[ROW][C]49[/C][C]113.8[/C][C]112.900398077426[/C][C]0.89960192257405[/C][/ROW]
[ROW][C]50[/C][C]114.1[/C][C]114.580272326658[/C][C]-0.480272326657783[/C][/ROW]
[ROW][C]51[/C][C]114.7[/C][C]114.65931229561[/C][C]0.0406877043902796[/C][/ROW]
[ROW][C]52[/C][C]115.3[/C][C]115.235367409858[/C][C]0.0646325901415992[/C][/ROW]
[ROW][C]53[/C][C]115.6[/C][C]115.882182219986[/C][C]-0.282182219986126[/C][/ROW]
[ROW][C]54[/C][C]116.2[/C][C]116.003372697348[/C][C]0.196627302651592[/C][/ROW]
[ROW][C]55[/C][C]117.5[/C][C]116.702928996439[/C][C]0.797071003561086[/C][/ROW]
[ROW][C]56[/C][C]118.5[/C][C]118.548044982647[/C][C]-0.0480449826465872[/C][/ROW]
[ROW][C]57[/C][C]119.3[/C][C]119.600600247168[/C][C]-0.300600247167651[/C][/ROW]
[ROW][C]58[/C][C]120[/C][C]120.197776913999[/C][C]-0.197776913998695[/C][/ROW]
[ROW][C]59[/C][C]120.1[/C][C]120.735929070943[/C][C]-0.635929070942709[/C][/ROW]
[ROW][C]60[/C][C]119.8[/C][C]120.396699160884[/C][C]-0.596699160883773[/C][/ROW]
[ROW][C]61[/C][C]119.9[/C][C]119.637012768824[/C][C]0.262987231176012[/C][/ROW]
[ROW][C]62[/C][C]119.8[/C][C]119.847014596804[/C][C]-0.047014596804118[/C][/ROW]
[ROW][C]63[/C][C]119.3[/C][C]119.743854465938[/C][C]-0.443854465937761[/C][/ROW]
[ROW][C]64[/C][C]119[/C][C]118.946899927144[/C][C]0.0531000728555426[/C][/ROW]
[ROW][C]65[/C][C]118.9[/C][C]118.634965852891[/C][C]0.265034147109176[/C][/ROW]
[ROW][C]66[/C][C]119[/C][C]118.714925734409[/C][C]0.28507426559085[/C][/ROW]
[ROW][C]67[/C][C]119.3[/C][C]119.030446891265[/C][C]0.269553108735181[/C][/ROW]
[ROW][C]68[/C][C]119.2[/C][C]119.537873442791[/C][C]-0.33787344279115[/C][/ROW]
[ROW][C]69[/C][C]118.6[/C][C]119.244064666435[/C][C]-0.644064666435369[/C][/ROW]
[ROW][C]70[/C][C]117[/C][C]118.184690125755[/C][C]-1.1846901257552[/C][/ROW]
[ROW][C]71[/C][C]117.4[/C][C]115.737333967827[/C][C]1.66266603217282[/C][/ROW]
[ROW][C]72[/C][C]117.4[/C][C]117.106031366131[/C][C]0.293968633868872[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260588&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260588&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
3103.1103.5-0.400000000000006
4103.6103.1368593997910.463140600209414
5104.2103.8993016398360.300698360163963
6104.9104.7460189428840.153981057115516
7104.5105.579065975402-1.07906597540151
8103.9104.485459471185-0.585459471185175
9102.8103.386376855417-0.586376855416901
10100.8101.838810029292-1.03881002929175
119999.0935124953949-0.0935124953949469
1297.897.12230851073280.677691489267161
1396.496.3582550066320.0417449933679706
1496.195.05727360828771.04272639171231
159695.44764053124970.552359468750254
1695.695.8211112096447-0.221111209644718
1795.795.3339758127350.366024187264955
1895.795.65141851800570.0485814819943187
1995.595.7220259540978-0.222025954097759
2095.195.3810955048452-0.281095504845183
2195.194.77273296292230.327267037077732
2294.694.958345552223-0.358345552222971
239594.25716310933030.742836890669679
249595.1080022146891-0.108002214689094
2595.895.11538801212490.684611987875101
2696.196.3543572171147-0.254357217114659
2796.596.5593152620718-0.0593152620718342
2896.896.8934373680966-0.0934373680965876
2997.797.12570643109570.574293568904295
3098.998.39364038253050.506359617469542
3110099.98738875497450.0126112450255249
32101.1101.149150958922-0.0491509589219135
33102102.218148532402-0.218148532401912
34103.8102.9694494048630.830550595136685
35104.9105.292794329963-0.392794329962697
36106.3106.2220907871680.077909212831841
37108.9107.6318688186481.26813118135176
38110.4111.074337155315-0.674337155315271
39111.3112.264623828162-0.964623828162402
40112.2112.458842180154-0.258842180154403
41112.9113.086709042306-0.186709042305921
42113113.636551397219-0.63655139721908
43113.4113.2980807315880.101919268411834
44112.4113.697915810882-1.29791581088223
45112.4111.8548414749760.545158525024434
46112.2112.0764295246470.123570475352636
47112.6112.0152831527920.584716847208185
48112.7112.812987659754-0.112987659754083
49113.8112.9003980774260.89960192257405
50114.1114.580272326658-0.480272326657783
51114.7114.659312295610.0406877043902796
52115.3115.2353674098580.0646325901415992
53115.6115.882182219986-0.282182219986126
54116.2116.0033726973480.196627302651592
55117.5116.7029289964390.797071003561086
56118.5118.548044982647-0.0480449826465872
57119.3119.600600247168-0.300600247167651
58120120.197776913999-0.197776913998695
59120.1120.735929070943-0.635929070942709
60119.8120.396699160884-0.596699160883773
61119.9119.6370127688240.262987231176012
62119.8119.847014596804-0.047014596804118
63119.3119.743854465938-0.443854465937761
64119118.9468999271440.0531000728555426
65118.9118.6349658528910.265034147109176
66119118.7149257344090.28507426559085
67119.3119.0304468912650.269553108735181
68119.2119.537873442791-0.33787344279115
69118.6119.244064666435-0.644064666435369
70117118.184690125755-1.1846901257552
71117.4115.7373339678271.66266603217282
72117.4117.1060313661310.293968633868872







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73117.474977895861116.361806162171118.588149629551
74117.580995571397115.425787116057119.736204026737
75117.687013246933114.235978832997121.138047660868
76117.793030922469112.845531267768122.740530577169
77117.899048598005111.281366011839124.516731184171
78118.005066273541109.561014825088126.449117721993
79118.111083949077107.697292353513128.524875544641
80118.217101624612105.700179846059130.734023403166
81118.323119300148103.577771304531133.068467295766
82118.429136975684101.336817592285135.521456359083
83118.5351546512298.9830685632553138.087240739185
84118.64117232675696.5215021353386140.760842518174

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 117.474977895861 & 116.361806162171 & 118.588149629551 \tabularnewline
74 & 117.580995571397 & 115.425787116057 & 119.736204026737 \tabularnewline
75 & 117.687013246933 & 114.235978832997 & 121.138047660868 \tabularnewline
76 & 117.793030922469 & 112.845531267768 & 122.740530577169 \tabularnewline
77 & 117.899048598005 & 111.281366011839 & 124.516731184171 \tabularnewline
78 & 118.005066273541 & 109.561014825088 & 126.449117721993 \tabularnewline
79 & 118.111083949077 & 107.697292353513 & 128.524875544641 \tabularnewline
80 & 118.217101624612 & 105.700179846059 & 130.734023403166 \tabularnewline
81 & 118.323119300148 & 103.577771304531 & 133.068467295766 \tabularnewline
82 & 118.429136975684 & 101.336817592285 & 135.521456359083 \tabularnewline
83 & 118.53515465122 & 98.9830685632553 & 138.087240739185 \tabularnewline
84 & 118.641172326756 & 96.5215021353386 & 140.760842518174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260588&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]73[/C][C]117.474977895861[/C][C]116.361806162171[/C][C]118.588149629551[/C][/ROW]
[ROW][C]74[/C][C]117.580995571397[/C][C]115.425787116057[/C][C]119.736204026737[/C][/ROW]
[ROW][C]75[/C][C]117.687013246933[/C][C]114.235978832997[/C][C]121.138047660868[/C][/ROW]
[ROW][C]76[/C][C]117.793030922469[/C][C]112.845531267768[/C][C]122.740530577169[/C][/ROW]
[ROW][C]77[/C][C]117.899048598005[/C][C]111.281366011839[/C][C]124.516731184171[/C][/ROW]
[ROW][C]78[/C][C]118.005066273541[/C][C]109.561014825088[/C][C]126.449117721993[/C][/ROW]
[ROW][C]79[/C][C]118.111083949077[/C][C]107.697292353513[/C][C]128.524875544641[/C][/ROW]
[ROW][C]80[/C][C]118.217101624612[/C][C]105.700179846059[/C][C]130.734023403166[/C][/ROW]
[ROW][C]81[/C][C]118.323119300148[/C][C]103.577771304531[/C][C]133.068467295766[/C][/ROW]
[ROW][C]82[/C][C]118.429136975684[/C][C]101.336817592285[/C][C]135.521456359083[/C][/ROW]
[ROW][C]83[/C][C]118.53515465122[/C][C]98.9830685632553[/C][C]138.087240739185[/C][/ROW]
[ROW][C]84[/C][C]118.641172326756[/C][C]96.5215021353386[/C][C]140.760842518174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260588&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260588&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
73117.474977895861116.361806162171118.588149629551
74117.580995571397115.425787116057119.736204026737
75117.687013246933114.235978832997121.138047660868
76117.793030922469112.845531267768122.740530577169
77117.899048598005111.281366011839124.516731184171
78118.005066273541109.561014825088126.449117721993
79118.111083949077107.697292353513128.524875544641
80118.217101624612105.700179846059130.734023403166
81118.323119300148103.577771304531133.068467295766
82118.429136975684101.336817592285135.521456359083
83118.5351546512298.9830685632553138.087240739185
84118.64117232675696.5215021353386140.760842518174



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