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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 05:17:34 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/06/t1244287196ohmemb4qw55up74.htm/, Retrieved Sun, 28 Apr 2024 20:14:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41963, Retrieved Sun, 28 Apr 2024 20:14:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2009-06-06 11:17:34] [5e28000efa8060aa7512f63d330b190a] [Current]
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Dataseries X:
831581
808744
899237
929532
883165
908232
955613
937590
849396
978630
868513
1156102
1505713
1415151
1545021
1681193
1457973
1638575
1688972
1563924
1596359
1722061
1549332
2264959
1420268
1415099
1597279
1605693
1575400
1654752
1553966
1570959
1642414
1664774
1551560
2304365
1644081
1425600
1569344
1456489
1610786
1601519
1496600
1486452
1637939
1605759
1504221
1993384
1507620
1477037
1679184
1504731
1570141
1734191
1657498
1652164
1610941
1813765
1711573
2165466
1492778
1385488
1470589
1514657
1641395
1606185
1581162
1517847
1630080
1604623
1548973
2125558




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41963&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41963&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.570561730922535
beta0.0317962765371711
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.570561730922535 \tabularnewline
beta & 0.0317962765371711 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41963&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]0.570561730922535[/C][/ROW]
[ROW][C]beta[/C][C]0.0317962765371711[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41963&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
alpha0.570561730922535
beta0.0317962765371711
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315057131167726.14903846337986.850961538
1414151511277413.81662595137737.183374055
1515450211495210.6458979549810.3541020476
1616811931665166.3960219216026.6039780800
1714579731459501.18165776-1528.18165776460
1816385751632388.071209786186.92879022006
1916889721665078.607511323893.3924886987
2015639241675604.82540275-111680.825402748
2115963591537761.6651936258597.3348063775
2217220611709511.5143411412549.4856588582
2315493321618822.22579524-69490.2257952369
2422649591878657.7939676386301.206032401
2514202682606118.88249658-1185850.88249658
2614150991748078.10687168-332979.106871677
2715972791638713.39982424-41434.3998242447
2816056931719615.32194655-113922.321946545
2915754001407424.99918752167975.000812479
3016547521658569.63649736-3817.63649735716
3115539661671206.83851959-117240.838519592
3215709591518477.1421745152481.8578254941
3316424141525891.71588907116522.284110931
3416647741690436.30587636-25662.3058763589
3515515601521540.3015290030019.6984710027
3623043652014518.45271201289846.547287987
3716440811990685.82219720-346604.822197204
3814256001971849.78273390-546249.782733903
3915693441856239.61547470-286895.615474703
4014564891751746.75192061-295257.751920608
4116107861439646.20894040171139.791059598
4216015191601374.97468156144.025318435859
4314966001550188.91024660-53588.9102466037
4414864521490441.37032732-3989.37032732344
4516379391475891.92702859162047.072971410
4616057591588932.5088065816826.4911934154
4715042211452542.5839470151678.4160529862
4819933842054202.50385244-60818.503852441
4915076201535360.10774845-27740.1077484528
5014770371596888.51312674-119851.513126736
5116791841827844.71895860-148660.718958596
5215047311793043.43084426-288312.430844256
5315701411679731.63104864-109590.631048643
5417341911597298.35285094136892.647149056
5516574981592985.8149768764512.1850231325
5616521641615989.7151941036174.2848059025
5716109411690454.69205969-79513.6920596892
5818137651593720.51085287220044.489147129
5917115731582346.31724677129226.682753228
6021654662175449.25655232-9983.2565523237
6114927781696246.30475591-203468.304755910
6213854881611196.41682829-225708.416828286
6314705891760704.17413304-290115.174133042
6415146571573977.59322021-59320.5932202067
6516413951660979.05849022-19584.0584902212
6616061851730291.61965435-124106.619654351
6715811621535787.1486883845374.8513116229
6815178471525162.65604943-7315.65604942641
6916300801513804.12551696116275.874483040
7016046231649644.7213236-45021.7213236007
7115489731435447.48459165113525.515408353
7221255581946939.25114092178618.748859081

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1505713 & 1167726.14903846 & 337986.850961538 \tabularnewline
14 & 1415151 & 1277413.81662595 & 137737.183374055 \tabularnewline
15 & 1545021 & 1495210.64589795 & 49810.3541020476 \tabularnewline
16 & 1681193 & 1665166.39602192 & 16026.6039780800 \tabularnewline
17 & 1457973 & 1459501.18165776 & -1528.18165776460 \tabularnewline
18 & 1638575 & 1632388.07120978 & 6186.92879022006 \tabularnewline
19 & 1688972 & 1665078.6075113 & 23893.3924886987 \tabularnewline
20 & 1563924 & 1675604.82540275 & -111680.825402748 \tabularnewline
21 & 1596359 & 1537761.66519362 & 58597.3348063775 \tabularnewline
22 & 1722061 & 1709511.51434114 & 12549.4856588582 \tabularnewline
23 & 1549332 & 1618822.22579524 & -69490.2257952369 \tabularnewline
24 & 2264959 & 1878657.7939676 & 386301.206032401 \tabularnewline
25 & 1420268 & 2606118.88249658 & -1185850.88249658 \tabularnewline
26 & 1415099 & 1748078.10687168 & -332979.106871677 \tabularnewline
27 & 1597279 & 1638713.39982424 & -41434.3998242447 \tabularnewline
28 & 1605693 & 1719615.32194655 & -113922.321946545 \tabularnewline
29 & 1575400 & 1407424.99918752 & 167975.000812479 \tabularnewline
30 & 1654752 & 1658569.63649736 & -3817.63649735716 \tabularnewline
31 & 1553966 & 1671206.83851959 & -117240.838519592 \tabularnewline
32 & 1570959 & 1518477.14217451 & 52481.8578254941 \tabularnewline
33 & 1642414 & 1525891.71588907 & 116522.284110931 \tabularnewline
34 & 1664774 & 1690436.30587636 & -25662.3058763589 \tabularnewline
35 & 1551560 & 1521540.30152900 & 30019.6984710027 \tabularnewline
36 & 2304365 & 2014518.45271201 & 289846.547287987 \tabularnewline
37 & 1644081 & 1990685.82219720 & -346604.822197204 \tabularnewline
38 & 1425600 & 1971849.78273390 & -546249.782733903 \tabularnewline
39 & 1569344 & 1856239.61547470 & -286895.615474703 \tabularnewline
40 & 1456489 & 1751746.75192061 & -295257.751920608 \tabularnewline
41 & 1610786 & 1439646.20894040 & 171139.791059598 \tabularnewline
42 & 1601519 & 1601374.97468156 & 144.025318435859 \tabularnewline
43 & 1496600 & 1550188.91024660 & -53588.9102466037 \tabularnewline
44 & 1486452 & 1490441.37032732 & -3989.37032732344 \tabularnewline
45 & 1637939 & 1475891.92702859 & 162047.072971410 \tabularnewline
46 & 1605759 & 1588932.50880658 & 16826.4911934154 \tabularnewline
47 & 1504221 & 1452542.58394701 & 51678.4160529862 \tabularnewline
48 & 1993384 & 2054202.50385244 & -60818.503852441 \tabularnewline
49 & 1507620 & 1535360.10774845 & -27740.1077484528 \tabularnewline
50 & 1477037 & 1596888.51312674 & -119851.513126736 \tabularnewline
51 & 1679184 & 1827844.71895860 & -148660.718958596 \tabularnewline
52 & 1504731 & 1793043.43084426 & -288312.430844256 \tabularnewline
53 & 1570141 & 1679731.63104864 & -109590.631048643 \tabularnewline
54 & 1734191 & 1597298.35285094 & 136892.647149056 \tabularnewline
55 & 1657498 & 1592985.81497687 & 64512.1850231325 \tabularnewline
56 & 1652164 & 1615989.71519410 & 36174.2848059025 \tabularnewline
57 & 1610941 & 1690454.69205969 & -79513.6920596892 \tabularnewline
58 & 1813765 & 1593720.51085287 & 220044.489147129 \tabularnewline
59 & 1711573 & 1582346.31724677 & 129226.682753228 \tabularnewline
60 & 2165466 & 2175449.25655232 & -9983.2565523237 \tabularnewline
61 & 1492778 & 1696246.30475591 & -203468.304755910 \tabularnewline
62 & 1385488 & 1611196.41682829 & -225708.416828286 \tabularnewline
63 & 1470589 & 1760704.17413304 & -290115.174133042 \tabularnewline
64 & 1514657 & 1573977.59322021 & -59320.5932202067 \tabularnewline
65 & 1641395 & 1660979.05849022 & -19584.0584902212 \tabularnewline
66 & 1606185 & 1730291.61965435 & -124106.619654351 \tabularnewline
67 & 1581162 & 1535787.14868838 & 45374.8513116229 \tabularnewline
68 & 1517847 & 1525162.65604943 & -7315.65604942641 \tabularnewline
69 & 1630080 & 1513804.12551696 & 116275.874483040 \tabularnewline
70 & 1604623 & 1649644.7213236 & -45021.7213236007 \tabularnewline
71 & 1548973 & 1435447.48459165 & 113525.515408353 \tabularnewline
72 & 2125558 & 1946939.25114092 & 178618.748859081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41963&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1505713[/C][C]1167726.14903846[/C][C]337986.850961538[/C][/ROW]
[ROW][C]14[/C][C]1415151[/C][C]1277413.81662595[/C][C]137737.183374055[/C][/ROW]
[ROW][C]15[/C][C]1545021[/C][C]1495210.64589795[/C][C]49810.3541020476[/C][/ROW]
[ROW][C]16[/C][C]1681193[/C][C]1665166.39602192[/C][C]16026.6039780800[/C][/ROW]
[ROW][C]17[/C][C]1457973[/C][C]1459501.18165776[/C][C]-1528.18165776460[/C][/ROW]
[ROW][C]18[/C][C]1638575[/C][C]1632388.07120978[/C][C]6186.92879022006[/C][/ROW]
[ROW][C]19[/C][C]1688972[/C][C]1665078.6075113[/C][C]23893.3924886987[/C][/ROW]
[ROW][C]20[/C][C]1563924[/C][C]1675604.82540275[/C][C]-111680.825402748[/C][/ROW]
[ROW][C]21[/C][C]1596359[/C][C]1537761.66519362[/C][C]58597.3348063775[/C][/ROW]
[ROW][C]22[/C][C]1722061[/C][C]1709511.51434114[/C][C]12549.4856588582[/C][/ROW]
[ROW][C]23[/C][C]1549332[/C][C]1618822.22579524[/C][C]-69490.2257952369[/C][/ROW]
[ROW][C]24[/C][C]2264959[/C][C]1878657.7939676[/C][C]386301.206032401[/C][/ROW]
[ROW][C]25[/C][C]1420268[/C][C]2606118.88249658[/C][C]-1185850.88249658[/C][/ROW]
[ROW][C]26[/C][C]1415099[/C][C]1748078.10687168[/C][C]-332979.106871677[/C][/ROW]
[ROW][C]27[/C][C]1597279[/C][C]1638713.39982424[/C][C]-41434.3998242447[/C][/ROW]
[ROW][C]28[/C][C]1605693[/C][C]1719615.32194655[/C][C]-113922.321946545[/C][/ROW]
[ROW][C]29[/C][C]1575400[/C][C]1407424.99918752[/C][C]167975.000812479[/C][/ROW]
[ROW][C]30[/C][C]1654752[/C][C]1658569.63649736[/C][C]-3817.63649735716[/C][/ROW]
[ROW][C]31[/C][C]1553966[/C][C]1671206.83851959[/C][C]-117240.838519592[/C][/ROW]
[ROW][C]32[/C][C]1570959[/C][C]1518477.14217451[/C][C]52481.8578254941[/C][/ROW]
[ROW][C]33[/C][C]1642414[/C][C]1525891.71588907[/C][C]116522.284110931[/C][/ROW]
[ROW][C]34[/C][C]1664774[/C][C]1690436.30587636[/C][C]-25662.3058763589[/C][/ROW]
[ROW][C]35[/C][C]1551560[/C][C]1521540.30152900[/C][C]30019.6984710027[/C][/ROW]
[ROW][C]36[/C][C]2304365[/C][C]2014518.45271201[/C][C]289846.547287987[/C][/ROW]
[ROW][C]37[/C][C]1644081[/C][C]1990685.82219720[/C][C]-346604.822197204[/C][/ROW]
[ROW][C]38[/C][C]1425600[/C][C]1971849.78273390[/C][C]-546249.782733903[/C][/ROW]
[ROW][C]39[/C][C]1569344[/C][C]1856239.61547470[/C][C]-286895.615474703[/C][/ROW]
[ROW][C]40[/C][C]1456489[/C][C]1751746.75192061[/C][C]-295257.751920608[/C][/ROW]
[ROW][C]41[/C][C]1610786[/C][C]1439646.20894040[/C][C]171139.791059598[/C][/ROW]
[ROW][C]42[/C][C]1601519[/C][C]1601374.97468156[/C][C]144.025318435859[/C][/ROW]
[ROW][C]43[/C][C]1496600[/C][C]1550188.91024660[/C][C]-53588.9102466037[/C][/ROW]
[ROW][C]44[/C][C]1486452[/C][C]1490441.37032732[/C][C]-3989.37032732344[/C][/ROW]
[ROW][C]45[/C][C]1637939[/C][C]1475891.92702859[/C][C]162047.072971410[/C][/ROW]
[ROW][C]46[/C][C]1605759[/C][C]1588932.50880658[/C][C]16826.4911934154[/C][/ROW]
[ROW][C]47[/C][C]1504221[/C][C]1452542.58394701[/C][C]51678.4160529862[/C][/ROW]
[ROW][C]48[/C][C]1993384[/C][C]2054202.50385244[/C][C]-60818.503852441[/C][/ROW]
[ROW][C]49[/C][C]1507620[/C][C]1535360.10774845[/C][C]-27740.1077484528[/C][/ROW]
[ROW][C]50[/C][C]1477037[/C][C]1596888.51312674[/C][C]-119851.513126736[/C][/ROW]
[ROW][C]51[/C][C]1679184[/C][C]1827844.71895860[/C][C]-148660.718958596[/C][/ROW]
[ROW][C]52[/C][C]1504731[/C][C]1793043.43084426[/C][C]-288312.430844256[/C][/ROW]
[ROW][C]53[/C][C]1570141[/C][C]1679731.63104864[/C][C]-109590.631048643[/C][/ROW]
[ROW][C]54[/C][C]1734191[/C][C]1597298.35285094[/C][C]136892.647149056[/C][/ROW]
[ROW][C]55[/C][C]1657498[/C][C]1592985.81497687[/C][C]64512.1850231325[/C][/ROW]
[ROW][C]56[/C][C]1652164[/C][C]1615989.71519410[/C][C]36174.2848059025[/C][/ROW]
[ROW][C]57[/C][C]1610941[/C][C]1690454.69205969[/C][C]-79513.6920596892[/C][/ROW]
[ROW][C]58[/C][C]1813765[/C][C]1593720.51085287[/C][C]220044.489147129[/C][/ROW]
[ROW][C]59[/C][C]1711573[/C][C]1582346.31724677[/C][C]129226.682753228[/C][/ROW]
[ROW][C]60[/C][C]2165466[/C][C]2175449.25655232[/C][C]-9983.2565523237[/C][/ROW]
[ROW][C]61[/C][C]1492778[/C][C]1696246.30475591[/C][C]-203468.304755910[/C][/ROW]
[ROW][C]62[/C][C]1385488[/C][C]1611196.41682829[/C][C]-225708.416828286[/C][/ROW]
[ROW][C]63[/C][C]1470589[/C][C]1760704.17413304[/C][C]-290115.174133042[/C][/ROW]
[ROW][C]64[/C][C]1514657[/C][C]1573977.59322021[/C][C]-59320.5932202067[/C][/ROW]
[ROW][C]65[/C][C]1641395[/C][C]1660979.05849022[/C][C]-19584.0584902212[/C][/ROW]
[ROW][C]66[/C][C]1606185[/C][C]1730291.61965435[/C][C]-124106.619654351[/C][/ROW]
[ROW][C]67[/C][C]1581162[/C][C]1535787.14868838[/C][C]45374.8513116229[/C][/ROW]
[ROW][C]68[/C][C]1517847[/C][C]1525162.65604943[/C][C]-7315.65604942641[/C][/ROW]
[ROW][C]69[/C][C]1630080[/C][C]1513804.12551696[/C][C]116275.874483040[/C][/ROW]
[ROW][C]70[/C][C]1604623[/C][C]1649644.7213236[/C][C]-45021.7213236007[/C][/ROW]
[ROW][C]71[/C][C]1548973[/C][C]1435447.48459165[/C][C]113525.515408353[/C][/ROW]
[ROW][C]72[/C][C]2125558[/C][C]1946939.25114092[/C][C]178618.748859081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41963&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
1315057131167726.14903846337986.850961538
1414151511277413.81662595137737.183374055
1515450211495210.6458979549810.3541020476
1616811931665166.3960219216026.6039780800
1714579731459501.18165776-1528.18165776460
1816385751632388.071209786186.92879022006
1916889721665078.607511323893.3924886987
2015639241675604.82540275-111680.825402748
2115963591537761.6651936258597.3348063775
2217220611709511.5143411412549.4856588582
2315493321618822.22579524-69490.2257952369
2422649591878657.7939676386301.206032401
2514202682606118.88249658-1185850.88249658
2614150991748078.10687168-332979.106871677
2715972791638713.39982424-41434.3998242447
2816056931719615.32194655-113922.321946545
2915754001407424.99918752167975.000812479
3016547521658569.63649736-3817.63649735716
3115539661671206.83851959-117240.838519592
3215709591518477.1421745152481.8578254941
3316424141525891.71588907116522.284110931
3416647741690436.30587636-25662.3058763589
3515515601521540.3015290030019.6984710027
3623043652014518.45271201289846.547287987
3716440811990685.82219720-346604.822197204
3814256001971849.78273390-546249.782733903
3915693441856239.61547470-286895.615474703
4014564891751746.75192061-295257.751920608
4116107861439646.20894040171139.791059598
4216015191601374.97468156144.025318435859
4314966001550188.91024660-53588.9102466037
4414864521490441.37032732-3989.37032732344
4516379391475891.92702859162047.072971410
4616057591588932.5088065816826.4911934154
4715042211452542.5839470151678.4160529862
4819933842054202.50385244-60818.503852441
4915076201535360.10774845-27740.1077484528
5014770371596888.51312674-119851.513126736
5116791841827844.71895860-148660.718958596
5215047311793043.43084426-288312.430844256
5315701411679731.63104864-109590.631048643
5417341911597298.35285094136892.647149056
5516574981592985.8149768764512.1850231325
5616521641615989.7151941036174.2848059025
5716109411690454.69205969-79513.6920596892
5818137651593720.51085287220044.489147129
5917115731582346.31724677129226.682753228
6021654662175449.25655232-9983.2565523237
6114927781696246.30475591-203468.304755910
6213854881611196.41682829-225708.416828286
6314705891760704.17413304-290115.174133042
6415146571573977.59322021-59320.5932202067
6516413951660979.05849022-19584.0584902212
6616061851730291.61965435-124106.619654351
6715811621535787.1486883845374.8513116229
6815178471525162.65604943-7315.65604942641
6916300801513804.12551696116275.874483040
7016046231649644.7213236-45021.7213236007
7115489731435447.48459165113525.515408353
7221255581946939.25114092178618.748859081







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731482806.45792731037968.422481311927644.49337329
741498539.26782313982340.8516783322014737.68396793
751747505.851742811164983.203384782330028.50010084
761829020.073735941183553.866249062474486.28122281
771971608.328387151265582.106160382677634.55061392
782012240.445326051247386.149128352777094.74152375
791968611.430680871146210.018353882791012.84300785
801915930.424428281036937.110234772794923.73862179
811968413.53930731033540.372091772903286.70652283
821973127.44312561982900.1387582622963354.74749296
831858004.13341973812802.5609127542903205.70592671
842335916.565542401236004.418360643435828.71272416

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1482806.4579273 & 1037968.42248131 & 1927644.49337329 \tabularnewline
74 & 1498539.26782313 & 982340.851678332 & 2014737.68396793 \tabularnewline
75 & 1747505.85174281 & 1164983.20338478 & 2330028.50010084 \tabularnewline
76 & 1829020.07373594 & 1183553.86624906 & 2474486.28122281 \tabularnewline
77 & 1971608.32838715 & 1265582.10616038 & 2677634.55061392 \tabularnewline
78 & 2012240.44532605 & 1247386.14912835 & 2777094.74152375 \tabularnewline
79 & 1968611.43068087 & 1146210.01835388 & 2791012.84300785 \tabularnewline
80 & 1915930.42442828 & 1036937.11023477 & 2794923.73862179 \tabularnewline
81 & 1968413.5393073 & 1033540.37209177 & 2903286.70652283 \tabularnewline
82 & 1973127.44312561 & 982900.138758262 & 2963354.74749296 \tabularnewline
83 & 1858004.13341973 & 812802.560912754 & 2903205.70592671 \tabularnewline
84 & 2335916.56554240 & 1236004.41836064 & 3435828.71272416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41963&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]1482806.4579273[/C][C]1037968.42248131[/C][C]1927644.49337329[/C][/ROW]
[ROW][C]74[/C][C]1498539.26782313[/C][C]982340.851678332[/C][C]2014737.68396793[/C][/ROW]
[ROW][C]75[/C][C]1747505.85174281[/C][C]1164983.20338478[/C][C]2330028.50010084[/C][/ROW]
[ROW][C]76[/C][C]1829020.07373594[/C][C]1183553.86624906[/C][C]2474486.28122281[/C][/ROW]
[ROW][C]77[/C][C]1971608.32838715[/C][C]1265582.10616038[/C][C]2677634.55061392[/C][/ROW]
[ROW][C]78[/C][C]2012240.44532605[/C][C]1247386.14912835[/C][C]2777094.74152375[/C][/ROW]
[ROW][C]79[/C][C]1968611.43068087[/C][C]1146210.01835388[/C][C]2791012.84300785[/C][/ROW]
[ROW][C]80[/C][C]1915930.42442828[/C][C]1036937.11023477[/C][C]2794923.73862179[/C][/ROW]
[ROW][C]81[/C][C]1968413.5393073[/C][C]1033540.37209177[/C][C]2903286.70652283[/C][/ROW]
[ROW][C]82[/C][C]1973127.44312561[/C][C]982900.138758262[/C][C]2963354.74749296[/C][/ROW]
[ROW][C]83[/C][C]1858004.13341973[/C][C]812802.560912754[/C][C]2903205.70592671[/C][/ROW]
[ROW][C]84[/C][C]2335916.56554240[/C][C]1236004.41836064[/C][C]3435828.71272416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41963&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41963&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
731482806.45792731037968.422481311927644.49337329
741498539.26782313982340.8516783322014737.68396793
751747505.851742811164983.203384782330028.50010084
761829020.073735941183553.866249062474486.28122281
771971608.328387151265582.106160382677634.55061392
782012240.445326051247386.149128352777094.74152375
791968611.430680871146210.018353882791012.84300785
801915930.424428281036937.110234772794923.73862179
811968413.53930731033540.372091772903286.70652283
821973127.44312561982900.1387582622963354.74749296
831858004.13341973812802.5609127542903205.70592671
842335916.565542401236004.418360643435828.71272416



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')