Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 08:27:45 +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/2015/Nov/29/t1448785700ij78iwfhchoq98z.htm/, Retrieved Wed, 15 May 2024 12:00:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284396, Retrieved Wed, 15 May 2024 12:00:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-29 08:27:45] [95d8e8f4c3757e497124afd1d843b6c1] [Current]
Feedback Forum

Post a new message
Dataseries X:
94,9
95,8
98,8
100,6
100,6
100,1
99,4
99,9
101
100,4
101,6
106,8
109,3
112,6
118,8
121,9
118,3
117,9
119,2
116,3
119,2
118,7
120,3
120,5
124,3
128,3
131,4
130,3
126,6
121,8
125,1
128,5
129,5
128,5
127,2
126,2
125,9
127,3
125,7
122,5
121,3
121,5
123,4
121,6
121,8
118,9
118,7
119,8
118,5
118,9
117,4
116
115,5
116,5
114,9
113,9
114,3
112
108
97,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284396&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]1 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=284396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284396&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999957915084097
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999957915084097 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284396&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]0.999957915084097[/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=284396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284396&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
alpha0.999957915084097
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
295.894.90.899999999999991
398.895.79996212357573.00003787642432
4100.698.79987374365831.80012625634173
5100.6100.5999242418387.57581621115833e-05
6100.1100.599999996812-0.499999996811724
799.4100.100021042458-0.70002104245782
899.999.40002946032670.499970539673299
910199.89997895878191.1000210412181
10100.4100.999953705707-0.599953705706994
11101.6100.4000252490011.19997475099875
12106.8101.5999494991645.20005050083648
13109.3106.7997811563122.50021884368802
14112.6109.29989477853.30010522149978
15118.8112.5998611153496.20013888465073
16121.9118.7997390676763.10026093232356
17118.3121.899869525779-3.5998695257794
18117.9118.300151500206-0.400151500206249
19119.2117.9000168403421.29998315965777
20116.3119.199945290318-2.89994529031806
21119.2116.3001220439542.89987795604634
22118.7119.19987795888-0.499877958880091
23120.3118.7000210373221.59997896267812
24120.5120.299932665020.200067334980091
25124.3120.4999915801833.80000841981696
26128.3124.2998400769654.0001599230348
27131.4128.2998316536063.10016834639396
28130.3131.399869529676-1.09986952967586
29126.6130.300046287917-3.70004628791668
30121.8126.600155716137-4.80015571613686
31125.1121.800202014153.29979798585036
32128.5125.0998611282793.40013887172073
33129.5128.4998569054421.0001430945585
34128.5129.499957909062-0.999957909061976
35127.2128.500042083145-1.3000420831445
36126.2127.200054712162-1.00005471216174
37125.9126.200042087218-0.300042087218458
38127.3125.9000126272461.39998737275398
39125.7127.299941081649-1.59994108164915
40122.5125.700067333386-3.20006733338587
41121.3122.500134674565-1.20013467456461
42121.5121.3000505075670.199949492433149
43123.4121.4999915851421.90000841485758
44121.6123.399920038306-1.79992003830566
45121.8121.6000757494830.19992425051656
46118.9121.799991586205-2.89999158620472
47118.7118.900122045902-0.20012204590202
48119.8118.7000084221191.09999157788052
49118.5119.799953706947-1.29995370694694
50118.9118.5000547084420.399945291557572
51117.4118.899983168336-1.49998316833603
52116117.400063126666-1.4000631266655
53115.5116.000058921539-0.500058921538951
54116.5115.5000210449380.999978955062346
55114.9116.49995791597-1.59995791596977
56113.9114.900067334094-1.00006733409434
57114.3113.900042087750.399957912250343
58112114.299983167805-2.2999831678049
59108112.000096794598-4.00009679459821
6097.7108.000168343737-10.3001683437372

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 95.8 & 94.9 & 0.899999999999991 \tabularnewline
3 & 98.8 & 95.7999621235757 & 3.00003787642432 \tabularnewline
4 & 100.6 & 98.7998737436583 & 1.80012625634173 \tabularnewline
5 & 100.6 & 100.599924241838 & 7.57581621115833e-05 \tabularnewline
6 & 100.1 & 100.599999996812 & -0.499999996811724 \tabularnewline
7 & 99.4 & 100.100021042458 & -0.70002104245782 \tabularnewline
8 & 99.9 & 99.4000294603267 & 0.499970539673299 \tabularnewline
9 & 101 & 99.8999789587819 & 1.1000210412181 \tabularnewline
10 & 100.4 & 100.999953705707 & -0.599953705706994 \tabularnewline
11 & 101.6 & 100.400025249001 & 1.19997475099875 \tabularnewline
12 & 106.8 & 101.599949499164 & 5.20005050083648 \tabularnewline
13 & 109.3 & 106.799781156312 & 2.50021884368802 \tabularnewline
14 & 112.6 & 109.2998947785 & 3.30010522149978 \tabularnewline
15 & 118.8 & 112.599861115349 & 6.20013888465073 \tabularnewline
16 & 121.9 & 118.799739067676 & 3.10026093232356 \tabularnewline
17 & 118.3 & 121.899869525779 & -3.5998695257794 \tabularnewline
18 & 117.9 & 118.300151500206 & -0.400151500206249 \tabularnewline
19 & 119.2 & 117.900016840342 & 1.29998315965777 \tabularnewline
20 & 116.3 & 119.199945290318 & -2.89994529031806 \tabularnewline
21 & 119.2 & 116.300122043954 & 2.89987795604634 \tabularnewline
22 & 118.7 & 119.19987795888 & -0.499877958880091 \tabularnewline
23 & 120.3 & 118.700021037322 & 1.59997896267812 \tabularnewline
24 & 120.5 & 120.29993266502 & 0.200067334980091 \tabularnewline
25 & 124.3 & 120.499991580183 & 3.80000841981696 \tabularnewline
26 & 128.3 & 124.299840076965 & 4.0001599230348 \tabularnewline
27 & 131.4 & 128.299831653606 & 3.10016834639396 \tabularnewline
28 & 130.3 & 131.399869529676 & -1.09986952967586 \tabularnewline
29 & 126.6 & 130.300046287917 & -3.70004628791668 \tabularnewline
30 & 121.8 & 126.600155716137 & -4.80015571613686 \tabularnewline
31 & 125.1 & 121.80020201415 & 3.29979798585036 \tabularnewline
32 & 128.5 & 125.099861128279 & 3.40013887172073 \tabularnewline
33 & 129.5 & 128.499856905442 & 1.0001430945585 \tabularnewline
34 & 128.5 & 129.499957909062 & -0.999957909061976 \tabularnewline
35 & 127.2 & 128.500042083145 & -1.3000420831445 \tabularnewline
36 & 126.2 & 127.200054712162 & -1.00005471216174 \tabularnewline
37 & 125.9 & 126.200042087218 & -0.300042087218458 \tabularnewline
38 & 127.3 & 125.900012627246 & 1.39998737275398 \tabularnewline
39 & 125.7 & 127.299941081649 & -1.59994108164915 \tabularnewline
40 & 122.5 & 125.700067333386 & -3.20006733338587 \tabularnewline
41 & 121.3 & 122.500134674565 & -1.20013467456461 \tabularnewline
42 & 121.5 & 121.300050507567 & 0.199949492433149 \tabularnewline
43 & 123.4 & 121.499991585142 & 1.90000841485758 \tabularnewline
44 & 121.6 & 123.399920038306 & -1.79992003830566 \tabularnewline
45 & 121.8 & 121.600075749483 & 0.19992425051656 \tabularnewline
46 & 118.9 & 121.799991586205 & -2.89999158620472 \tabularnewline
47 & 118.7 & 118.900122045902 & -0.20012204590202 \tabularnewline
48 & 119.8 & 118.700008422119 & 1.09999157788052 \tabularnewline
49 & 118.5 & 119.799953706947 & -1.29995370694694 \tabularnewline
50 & 118.9 & 118.500054708442 & 0.399945291557572 \tabularnewline
51 & 117.4 & 118.899983168336 & -1.49998316833603 \tabularnewline
52 & 116 & 117.400063126666 & -1.4000631266655 \tabularnewline
53 & 115.5 & 116.000058921539 & -0.500058921538951 \tabularnewline
54 & 116.5 & 115.500021044938 & 0.999978955062346 \tabularnewline
55 & 114.9 & 116.49995791597 & -1.59995791596977 \tabularnewline
56 & 113.9 & 114.900067334094 & -1.00006733409434 \tabularnewline
57 & 114.3 & 113.90004208775 & 0.399957912250343 \tabularnewline
58 & 112 & 114.299983167805 & -2.2999831678049 \tabularnewline
59 & 108 & 112.000096794598 & -4.00009679459821 \tabularnewline
60 & 97.7 & 108.000168343737 & -10.3001683437372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284396&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]95.8[/C][C]94.9[/C][C]0.899999999999991[/C][/ROW]
[ROW][C]3[/C][C]98.8[/C][C]95.7999621235757[/C][C]3.00003787642432[/C][/ROW]
[ROW][C]4[/C][C]100.6[/C][C]98.7998737436583[/C][C]1.80012625634173[/C][/ROW]
[ROW][C]5[/C][C]100.6[/C][C]100.599924241838[/C][C]7.57581621115833e-05[/C][/ROW]
[ROW][C]6[/C][C]100.1[/C][C]100.599999996812[/C][C]-0.499999996811724[/C][/ROW]
[ROW][C]7[/C][C]99.4[/C][C]100.100021042458[/C][C]-0.70002104245782[/C][/ROW]
[ROW][C]8[/C][C]99.9[/C][C]99.4000294603267[/C][C]0.499970539673299[/C][/ROW]
[ROW][C]9[/C][C]101[/C][C]99.8999789587819[/C][C]1.1000210412181[/C][/ROW]
[ROW][C]10[/C][C]100.4[/C][C]100.999953705707[/C][C]-0.599953705706994[/C][/ROW]
[ROW][C]11[/C][C]101.6[/C][C]100.400025249001[/C][C]1.19997475099875[/C][/ROW]
[ROW][C]12[/C][C]106.8[/C][C]101.599949499164[/C][C]5.20005050083648[/C][/ROW]
[ROW][C]13[/C][C]109.3[/C][C]106.799781156312[/C][C]2.50021884368802[/C][/ROW]
[ROW][C]14[/C][C]112.6[/C][C]109.2998947785[/C][C]3.30010522149978[/C][/ROW]
[ROW][C]15[/C][C]118.8[/C][C]112.599861115349[/C][C]6.20013888465073[/C][/ROW]
[ROW][C]16[/C][C]121.9[/C][C]118.799739067676[/C][C]3.10026093232356[/C][/ROW]
[ROW][C]17[/C][C]118.3[/C][C]121.899869525779[/C][C]-3.5998695257794[/C][/ROW]
[ROW][C]18[/C][C]117.9[/C][C]118.300151500206[/C][C]-0.400151500206249[/C][/ROW]
[ROW][C]19[/C][C]119.2[/C][C]117.900016840342[/C][C]1.29998315965777[/C][/ROW]
[ROW][C]20[/C][C]116.3[/C][C]119.199945290318[/C][C]-2.89994529031806[/C][/ROW]
[ROW][C]21[/C][C]119.2[/C][C]116.300122043954[/C][C]2.89987795604634[/C][/ROW]
[ROW][C]22[/C][C]118.7[/C][C]119.19987795888[/C][C]-0.499877958880091[/C][/ROW]
[ROW][C]23[/C][C]120.3[/C][C]118.700021037322[/C][C]1.59997896267812[/C][/ROW]
[ROW][C]24[/C][C]120.5[/C][C]120.29993266502[/C][C]0.200067334980091[/C][/ROW]
[ROW][C]25[/C][C]124.3[/C][C]120.499991580183[/C][C]3.80000841981696[/C][/ROW]
[ROW][C]26[/C][C]128.3[/C][C]124.299840076965[/C][C]4.0001599230348[/C][/ROW]
[ROW][C]27[/C][C]131.4[/C][C]128.299831653606[/C][C]3.10016834639396[/C][/ROW]
[ROW][C]28[/C][C]130.3[/C][C]131.399869529676[/C][C]-1.09986952967586[/C][/ROW]
[ROW][C]29[/C][C]126.6[/C][C]130.300046287917[/C][C]-3.70004628791668[/C][/ROW]
[ROW][C]30[/C][C]121.8[/C][C]126.600155716137[/C][C]-4.80015571613686[/C][/ROW]
[ROW][C]31[/C][C]125.1[/C][C]121.80020201415[/C][C]3.29979798585036[/C][/ROW]
[ROW][C]32[/C][C]128.5[/C][C]125.099861128279[/C][C]3.40013887172073[/C][/ROW]
[ROW][C]33[/C][C]129.5[/C][C]128.499856905442[/C][C]1.0001430945585[/C][/ROW]
[ROW][C]34[/C][C]128.5[/C][C]129.499957909062[/C][C]-0.999957909061976[/C][/ROW]
[ROW][C]35[/C][C]127.2[/C][C]128.500042083145[/C][C]-1.3000420831445[/C][/ROW]
[ROW][C]36[/C][C]126.2[/C][C]127.200054712162[/C][C]-1.00005471216174[/C][/ROW]
[ROW][C]37[/C][C]125.9[/C][C]126.200042087218[/C][C]-0.300042087218458[/C][/ROW]
[ROW][C]38[/C][C]127.3[/C][C]125.900012627246[/C][C]1.39998737275398[/C][/ROW]
[ROW][C]39[/C][C]125.7[/C][C]127.299941081649[/C][C]-1.59994108164915[/C][/ROW]
[ROW][C]40[/C][C]122.5[/C][C]125.700067333386[/C][C]-3.20006733338587[/C][/ROW]
[ROW][C]41[/C][C]121.3[/C][C]122.500134674565[/C][C]-1.20013467456461[/C][/ROW]
[ROW][C]42[/C][C]121.5[/C][C]121.300050507567[/C][C]0.199949492433149[/C][/ROW]
[ROW][C]43[/C][C]123.4[/C][C]121.499991585142[/C][C]1.90000841485758[/C][/ROW]
[ROW][C]44[/C][C]121.6[/C][C]123.399920038306[/C][C]-1.79992003830566[/C][/ROW]
[ROW][C]45[/C][C]121.8[/C][C]121.600075749483[/C][C]0.19992425051656[/C][/ROW]
[ROW][C]46[/C][C]118.9[/C][C]121.799991586205[/C][C]-2.89999158620472[/C][/ROW]
[ROW][C]47[/C][C]118.7[/C][C]118.900122045902[/C][C]-0.20012204590202[/C][/ROW]
[ROW][C]48[/C][C]119.8[/C][C]118.700008422119[/C][C]1.09999157788052[/C][/ROW]
[ROW][C]49[/C][C]118.5[/C][C]119.799953706947[/C][C]-1.29995370694694[/C][/ROW]
[ROW][C]50[/C][C]118.9[/C][C]118.500054708442[/C][C]0.399945291557572[/C][/ROW]
[ROW][C]51[/C][C]117.4[/C][C]118.899983168336[/C][C]-1.49998316833603[/C][/ROW]
[ROW][C]52[/C][C]116[/C][C]117.400063126666[/C][C]-1.4000631266655[/C][/ROW]
[ROW][C]53[/C][C]115.5[/C][C]116.000058921539[/C][C]-0.500058921538951[/C][/ROW]
[ROW][C]54[/C][C]116.5[/C][C]115.500021044938[/C][C]0.999978955062346[/C][/ROW]
[ROW][C]55[/C][C]114.9[/C][C]116.49995791597[/C][C]-1.59995791596977[/C][/ROW]
[ROW][C]56[/C][C]113.9[/C][C]114.900067334094[/C][C]-1.00006733409434[/C][/ROW]
[ROW][C]57[/C][C]114.3[/C][C]113.90004208775[/C][C]0.399957912250343[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]114.299983167805[/C][C]-2.2999831678049[/C][/ROW]
[ROW][C]59[/C][C]108[/C][C]112.000096794598[/C][C]-4.00009679459821[/C][/ROW]
[ROW][C]60[/C][C]97.7[/C][C]108.000168343737[/C][C]-10.3001683437372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284396&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284396&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
295.894.90.899999999999991
398.895.79996212357573.00003787642432
4100.698.79987374365831.80012625634173
5100.6100.5999242418387.57581621115833e-05
6100.1100.599999996812-0.499999996811724
799.4100.100021042458-0.70002104245782
899.999.40002946032670.499970539673299
910199.89997895878191.1000210412181
10100.4100.999953705707-0.599953705706994
11101.6100.4000252490011.19997475099875
12106.8101.5999494991645.20005050083648
13109.3106.7997811563122.50021884368802
14112.6109.29989477853.30010522149978
15118.8112.5998611153496.20013888465073
16121.9118.7997390676763.10026093232356
17118.3121.899869525779-3.5998695257794
18117.9118.300151500206-0.400151500206249
19119.2117.9000168403421.29998315965777
20116.3119.199945290318-2.89994529031806
21119.2116.3001220439542.89987795604634
22118.7119.19987795888-0.499877958880091
23120.3118.7000210373221.59997896267812
24120.5120.299932665020.200067334980091
25124.3120.4999915801833.80000841981696
26128.3124.2998400769654.0001599230348
27131.4128.2998316536063.10016834639396
28130.3131.399869529676-1.09986952967586
29126.6130.300046287917-3.70004628791668
30121.8126.600155716137-4.80015571613686
31125.1121.800202014153.29979798585036
32128.5125.0998611282793.40013887172073
33129.5128.4998569054421.0001430945585
34128.5129.499957909062-0.999957909061976
35127.2128.500042083145-1.3000420831445
36126.2127.200054712162-1.00005471216174
37125.9126.200042087218-0.300042087218458
38127.3125.9000126272461.39998737275398
39125.7127.299941081649-1.59994108164915
40122.5125.700067333386-3.20006733338587
41121.3122.500134674565-1.20013467456461
42121.5121.3000505075670.199949492433149
43123.4121.4999915851421.90000841485758
44121.6123.399920038306-1.79992003830566
45121.8121.6000757494830.19992425051656
46118.9121.799991586205-2.89999158620472
47118.7118.900122045902-0.20012204590202
48119.8118.7000084221191.09999157788052
49118.5119.799953706947-1.29995370694694
50118.9118.5000547084420.399945291557572
51117.4118.899983168336-1.49998316833603
52116117.400063126666-1.4000631266655
53115.5116.000058921539-0.500058921538951
54116.5115.5000210449380.999978955062346
55114.9116.49995791597-1.59995791596977
56113.9114.900067334094-1.00006733409434
57114.3113.900042087750.399957912250343
58112114.299983167805-2.2999831678049
59108112.000096794598-4.00009679459821
6097.7108.000168343737-10.3001683437372







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6197.700433481718592.4258332694178102.975033694019
6297.700433481718590.2411792880809105.159687675356
6397.700433481718588.5648142443051106.836052719132
6497.700433481718587.1515660270248108.249300936412
6597.700433481718585.9064659430828109.494401020354
6697.700433481718584.7808074798526110.620059483584
6797.700433481718583.7456564590002111.655210504437
6897.700433481718582.7821605428195112.618706420618
6997.700433481718581.8772247930491113.523642170388
7097.700433481718581.0213148320152114.379552131422
7197.700433481718580.207232955326115.193634008111
7297.700433481718579.4293872505287115.971479712908

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 97.7004334817185 & 92.4258332694178 & 102.975033694019 \tabularnewline
62 & 97.7004334817185 & 90.2411792880809 & 105.159687675356 \tabularnewline
63 & 97.7004334817185 & 88.5648142443051 & 106.836052719132 \tabularnewline
64 & 97.7004334817185 & 87.1515660270248 & 108.249300936412 \tabularnewline
65 & 97.7004334817185 & 85.9064659430828 & 109.494401020354 \tabularnewline
66 & 97.7004334817185 & 84.7808074798526 & 110.620059483584 \tabularnewline
67 & 97.7004334817185 & 83.7456564590002 & 111.655210504437 \tabularnewline
68 & 97.7004334817185 & 82.7821605428195 & 112.618706420618 \tabularnewline
69 & 97.7004334817185 & 81.8772247930491 & 113.523642170388 \tabularnewline
70 & 97.7004334817185 & 81.0213148320152 & 114.379552131422 \tabularnewline
71 & 97.7004334817185 & 80.207232955326 & 115.193634008111 \tabularnewline
72 & 97.7004334817185 & 79.4293872505287 & 115.971479712908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284396&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]61[/C][C]97.7004334817185[/C][C]92.4258332694178[/C][C]102.975033694019[/C][/ROW]
[ROW][C]62[/C][C]97.7004334817185[/C][C]90.2411792880809[/C][C]105.159687675356[/C][/ROW]
[ROW][C]63[/C][C]97.7004334817185[/C][C]88.5648142443051[/C][C]106.836052719132[/C][/ROW]
[ROW][C]64[/C][C]97.7004334817185[/C][C]87.1515660270248[/C][C]108.249300936412[/C][/ROW]
[ROW][C]65[/C][C]97.7004334817185[/C][C]85.9064659430828[/C][C]109.494401020354[/C][/ROW]
[ROW][C]66[/C][C]97.7004334817185[/C][C]84.7808074798526[/C][C]110.620059483584[/C][/ROW]
[ROW][C]67[/C][C]97.7004334817185[/C][C]83.7456564590002[/C][C]111.655210504437[/C][/ROW]
[ROW][C]68[/C][C]97.7004334817185[/C][C]82.7821605428195[/C][C]112.618706420618[/C][/ROW]
[ROW][C]69[/C][C]97.7004334817185[/C][C]81.8772247930491[/C][C]113.523642170388[/C][/ROW]
[ROW][C]70[/C][C]97.7004334817185[/C][C]81.0213148320152[/C][C]114.379552131422[/C][/ROW]
[ROW][C]71[/C][C]97.7004334817185[/C][C]80.207232955326[/C][C]115.193634008111[/C][/ROW]
[ROW][C]72[/C][C]97.7004334817185[/C][C]79.4293872505287[/C][C]115.971479712908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284396&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284396&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
6197.700433481718592.4258332694178102.975033694019
6297.700433481718590.2411792880809105.159687675356
6397.700433481718588.5648142443051106.836052719132
6497.700433481718587.1515660270248108.249300936412
6597.700433481718585.9064659430828109.494401020354
6697.700433481718584.7808074798526110.620059483584
6797.700433481718583.7456564590002111.655210504437
6897.700433481718582.7821605428195112.618706420618
6997.700433481718581.8772247930491113.523642170388
7097.700433481718581.0213148320152114.379552131422
7197.700433481718580.207232955326115.193634008111
7297.700433481718579.4293872505287115.971479712908



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')