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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Aug 2017 00:15:21 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/04/t1501798620fcdd60d2i34u66m.htm/, Retrieved Sat, 11 May 2024 10:11:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306898, Retrieved Sat, 11 May 2024 10:11:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Reeks B stap 28] [2017-08-03 22:15:21] [5e513ceaaef205c0c6f269c0b513af8d] [Current]
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Dataseries X:
1755000
1690000
1787500
1430000
1852500
1820000
1950000
2015000
2242500
1950000
1852500
2307500
1950000
1462500
1722500
1300000
1820000
1495000
1982500
1787500
1885000
2112500
2080000
2470000
1787500
1495000
1657500
1202500
1722500
1332500
1885000
1787500
1592500
2275000
2047500
2340000
1755000
1625000
1462500
1202500
1592500
1430000
1950000
1885000
1625000
2177500
2015000
2600000
2080000
1267500
1267500
1267500
1495000
1495000
2015000
1852500
1657500
2080000
1917500
2762500
2177500
1267500
1332500
1105000
1527500
1755000
2210000
2177500
1755000
2047500
1820000
2600000
1982500
1592500
1430000
1072500
1592500
1917500
2242500
2112500
1560000
2242500
1755000
2697500
2242500
1625000
1495000
1007500
1592500
1527500
2307500
2307500
1755000
2275000
1690000
2632500
2242500
1657500
1267500
877500
1722500
1657500
2177500
2502500
1852500
2080000
1560000
2697500




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306898&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306898&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00926118605786446
beta1
gamma0.929768627342646

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605786446 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627342646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306898&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]0.00926118605786446[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627342646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306898&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
alpha0.00926118605786446
beta1
gamma0.929768627342646







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1319500002016684.02777778-66684.0277777794
1414625001527560.62382535-65060.6238253464
1517225001801599.71597668-79099.7159766767
1613000001376026.23229673-76026.2322967262
1718200001867902.1196384-47902.1196384029
1814950001514594.83917758-19594.8391775836
1919825001893972.4129231788527.5870768272
2017875001950171.1990305-162671.199030504
2118850002175870.39153504-290870.391535042
2221125001873626.0026506238873.997349402
2320800001772145.76498189307854.235018106
2424700002234780.46147776235219.53852224
2517875001822286.03631547-34786.036315467
2614950001335828.30745268159171.692547316
2716575001601963.3443597755536.6556402263
2812025001184666.317062117833.6829379024
2917225001708385.8605341614114.1394658424
3013325001387370.39675598-54870.3967559803
3118850001871334.40552713665.5944729957
3217875001700068.1368966787431.8631033285
3315925001816930.13078642-224430.130786423
3422750002010832.82962868264167.170371316
3520475001980916.3308655666583.669134439
3623400002379961.90758009-39961.9075800888
3717550001719206.0637734935793.9362265116
3816250001415726.17860042209273.821399578
3914625001590983.49783475-128483.497834752
4012025001139670.0976036362829.902396366
4115925001663215.05292888-70715.0529288836
4214300001279917.6832585150082.316741503
4319500001832859.73124498117140.268755025
4418850001735407.90421428149592.095785718
4516250001571052.8886592253947.1113407761
4621775002225668.4843652-48168.4843651955
4720150002016020.73743541-1020.73743541283
4826000002320835.77099683279164.229003171
4920800001740314.8417738339685.158226199
5012675001609762.44046301-342262.440463009
5112675001473986.91774274-206486.917742738
5212675001202661.4026106664838.5973893362
5314950001607708.02310401-112708.023104015
5414950001431521.1265979763478.8734020318
5520150001956624.3904881858375.6095118232
5618525001891285.45150931-38785.4515093092
5716575001638100.9697792619399.0302207374
5820800002199031.33194247-119031.331942474
5919175002032200.8619828-114700.861982802
6027625002593047.88903756169452.11096244
6121775002065234.38141768112265.618582319
6212675001300262.39115224-32762.3911522431
6313325001291158.2156213941341.784378615
6411050001273091.02747346-168091.027473461
6515275001511304.2789909816195.7210090214
6617550001498673.23325776256326.76674224
6722100002022713.68932944187286.310670564
6821775001872113.91023301305386.089766992
6917550001681947.3645795373052.6354204707
7020475002122588.70794084-75088.7079408411
7118200001967291.50841523-147291.508415228
7226000002796421.88902169-196421.88902169
7319825002215989.17478456-233489.174784557
7415925001314466.30137739278033.698622608
7514300001379625.3593942550374.6406057451
7610725001171928.04776496-99428.0477649574
7715925001584377.192530688122.80746932258
7819175001796638.02365151120861.976348492
7922425002258340.23090644-15840.2309064362
8021125002215280.08210665-102780.082106648
8115600001804169.82384697-244169.823846967
8222425002099326.07040959143173.929590413
8317550001875475.75828956-120475.758289557
8426975002655781.6877825741718.3122174293
8522425002041799.11292054200700.88707946
8616250001617901.28900167098.71099840198
8714950001470742.6715543124257.3284456858
8810075001124471.1166193-116971.116619296
8915925001635326.19743343-42826.1974334321
9015275001949990.99373057-422490.993730572
9123075002274729.9424689932770.0575310071
9223075002146477.99171972161022.008280278
9317550001604455.03803464150544.961965363
9422750002260613.541751814386.4582482018
9516900001792056.78035095-102056.780350955
9626325002721459.47665159-88959.476651595
9722425002251024.32990432-8524.32990432344
9816575001643222.6009428914277.3990571068
9912675001508374.68148075-240874.68148075
1008775001023536.97893837-146036.97893837
10117225001596135.84914341126364.150856589
10216575001557917.0361988699582.9638011446
10321775002306974.0334331-129474.033433097
10425025002293972.9561483208527.043851701
10518525001741792.04754738110707.952452624
10620800002270842.30422749-190842.304227488
10715600001689905.78180455-129905.781804552
10826975002627640.8389147569859.1610852536

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1950000 & 2016684.02777778 & -66684.0277777794 \tabularnewline
14 & 1462500 & 1527560.62382535 & -65060.6238253464 \tabularnewline
15 & 1722500 & 1801599.71597668 & -79099.7159766767 \tabularnewline
16 & 1300000 & 1376026.23229673 & -76026.2322967262 \tabularnewline
17 & 1820000 & 1867902.1196384 & -47902.1196384029 \tabularnewline
18 & 1495000 & 1514594.83917758 & -19594.8391775836 \tabularnewline
19 & 1982500 & 1893972.41292317 & 88527.5870768272 \tabularnewline
20 & 1787500 & 1950171.1990305 & -162671.199030504 \tabularnewline
21 & 1885000 & 2175870.39153504 & -290870.391535042 \tabularnewline
22 & 2112500 & 1873626.0026506 & 238873.997349402 \tabularnewline
23 & 2080000 & 1772145.76498189 & 307854.235018106 \tabularnewline
24 & 2470000 & 2234780.46147776 & 235219.53852224 \tabularnewline
25 & 1787500 & 1822286.03631547 & -34786.036315467 \tabularnewline
26 & 1495000 & 1335828.30745268 & 159171.692547316 \tabularnewline
27 & 1657500 & 1601963.34435977 & 55536.6556402263 \tabularnewline
28 & 1202500 & 1184666.3170621 & 17833.6829379024 \tabularnewline
29 & 1722500 & 1708385.86053416 & 14114.1394658424 \tabularnewline
30 & 1332500 & 1387370.39675598 & -54870.3967559803 \tabularnewline
31 & 1885000 & 1871334.405527 & 13665.5944729957 \tabularnewline
32 & 1787500 & 1700068.13689667 & 87431.8631033285 \tabularnewline
33 & 1592500 & 1816930.13078642 & -224430.130786423 \tabularnewline
34 & 2275000 & 2010832.82962868 & 264167.170371316 \tabularnewline
35 & 2047500 & 1980916.33086556 & 66583.669134439 \tabularnewline
36 & 2340000 & 2379961.90758009 & -39961.9075800888 \tabularnewline
37 & 1755000 & 1719206.06377349 & 35793.9362265116 \tabularnewline
38 & 1625000 & 1415726.17860042 & 209273.821399578 \tabularnewline
39 & 1462500 & 1590983.49783475 & -128483.497834752 \tabularnewline
40 & 1202500 & 1139670.09760363 & 62829.902396366 \tabularnewline
41 & 1592500 & 1663215.05292888 & -70715.0529288836 \tabularnewline
42 & 1430000 & 1279917.6832585 & 150082.316741503 \tabularnewline
43 & 1950000 & 1832859.73124498 & 117140.268755025 \tabularnewline
44 & 1885000 & 1735407.90421428 & 149592.095785718 \tabularnewline
45 & 1625000 & 1571052.88865922 & 53947.1113407761 \tabularnewline
46 & 2177500 & 2225668.4843652 & -48168.4843651955 \tabularnewline
47 & 2015000 & 2016020.73743541 & -1020.73743541283 \tabularnewline
48 & 2600000 & 2320835.77099683 & 279164.229003171 \tabularnewline
49 & 2080000 & 1740314.8417738 & 339685.158226199 \tabularnewline
50 & 1267500 & 1609762.44046301 & -342262.440463009 \tabularnewline
51 & 1267500 & 1473986.91774274 & -206486.917742738 \tabularnewline
52 & 1267500 & 1202661.40261066 & 64838.5973893362 \tabularnewline
53 & 1495000 & 1607708.02310401 & -112708.023104015 \tabularnewline
54 & 1495000 & 1431521.12659797 & 63478.8734020318 \tabularnewline
55 & 2015000 & 1956624.39048818 & 58375.6095118232 \tabularnewline
56 & 1852500 & 1891285.45150931 & -38785.4515093092 \tabularnewline
57 & 1657500 & 1638100.96977926 & 19399.0302207374 \tabularnewline
58 & 2080000 & 2199031.33194247 & -119031.331942474 \tabularnewline
59 & 1917500 & 2032200.8619828 & -114700.861982802 \tabularnewline
60 & 2762500 & 2593047.88903756 & 169452.11096244 \tabularnewline
61 & 2177500 & 2065234.38141768 & 112265.618582319 \tabularnewline
62 & 1267500 & 1300262.39115224 & -32762.3911522431 \tabularnewline
63 & 1332500 & 1291158.21562139 & 41341.784378615 \tabularnewline
64 & 1105000 & 1273091.02747346 & -168091.027473461 \tabularnewline
65 & 1527500 & 1511304.27899098 & 16195.7210090214 \tabularnewline
66 & 1755000 & 1498673.23325776 & 256326.76674224 \tabularnewline
67 & 2210000 & 2022713.68932944 & 187286.310670564 \tabularnewline
68 & 2177500 & 1872113.91023301 & 305386.089766992 \tabularnewline
69 & 1755000 & 1681947.36457953 & 73052.6354204707 \tabularnewline
70 & 2047500 & 2122588.70794084 & -75088.7079408411 \tabularnewline
71 & 1820000 & 1967291.50841523 & -147291.508415228 \tabularnewline
72 & 2600000 & 2796421.88902169 & -196421.88902169 \tabularnewline
73 & 1982500 & 2215989.17478456 & -233489.174784557 \tabularnewline
74 & 1592500 & 1314466.30137739 & 278033.698622608 \tabularnewline
75 & 1430000 & 1379625.35939425 & 50374.6406057451 \tabularnewline
76 & 1072500 & 1171928.04776496 & -99428.0477649574 \tabularnewline
77 & 1592500 & 1584377.19253068 & 8122.80746932258 \tabularnewline
78 & 1917500 & 1796638.02365151 & 120861.976348492 \tabularnewline
79 & 2242500 & 2258340.23090644 & -15840.2309064362 \tabularnewline
80 & 2112500 & 2215280.08210665 & -102780.082106648 \tabularnewline
81 & 1560000 & 1804169.82384697 & -244169.823846967 \tabularnewline
82 & 2242500 & 2099326.07040959 & 143173.929590413 \tabularnewline
83 & 1755000 & 1875475.75828956 & -120475.758289557 \tabularnewline
84 & 2697500 & 2655781.68778257 & 41718.3122174293 \tabularnewline
85 & 2242500 & 2041799.11292054 & 200700.88707946 \tabularnewline
86 & 1625000 & 1617901.2890016 & 7098.71099840198 \tabularnewline
87 & 1495000 & 1470742.67155431 & 24257.3284456858 \tabularnewline
88 & 1007500 & 1124471.1166193 & -116971.116619296 \tabularnewline
89 & 1592500 & 1635326.19743343 & -42826.1974334321 \tabularnewline
90 & 1527500 & 1949990.99373057 & -422490.993730572 \tabularnewline
91 & 2307500 & 2274729.94246899 & 32770.0575310071 \tabularnewline
92 & 2307500 & 2146477.99171972 & 161022.008280278 \tabularnewline
93 & 1755000 & 1604455.03803464 & 150544.961965363 \tabularnewline
94 & 2275000 & 2260613.5417518 & 14386.4582482018 \tabularnewline
95 & 1690000 & 1792056.78035095 & -102056.780350955 \tabularnewline
96 & 2632500 & 2721459.47665159 & -88959.476651595 \tabularnewline
97 & 2242500 & 2251024.32990432 & -8524.32990432344 \tabularnewline
98 & 1657500 & 1643222.60094289 & 14277.3990571068 \tabularnewline
99 & 1267500 & 1508374.68148075 & -240874.68148075 \tabularnewline
100 & 877500 & 1023536.97893837 & -146036.97893837 \tabularnewline
101 & 1722500 & 1596135.84914341 & 126364.150856589 \tabularnewline
102 & 1657500 & 1557917.03619886 & 99582.9638011446 \tabularnewline
103 & 2177500 & 2306974.0334331 & -129474.033433097 \tabularnewline
104 & 2502500 & 2293972.9561483 & 208527.043851701 \tabularnewline
105 & 1852500 & 1741792.04754738 & 110707.952452624 \tabularnewline
106 & 2080000 & 2270842.30422749 & -190842.304227488 \tabularnewline
107 & 1560000 & 1689905.78180455 & -129905.781804552 \tabularnewline
108 & 2697500 & 2627640.83891475 & 69859.1610852536 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306898&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]1950000[/C][C]2016684.02777778[/C][C]-66684.0277777794[/C][/ROW]
[ROW][C]14[/C][C]1462500[/C][C]1527560.62382535[/C][C]-65060.6238253464[/C][/ROW]
[ROW][C]15[/C][C]1722500[/C][C]1801599.71597668[/C][C]-79099.7159766767[/C][/ROW]
[ROW][C]16[/C][C]1300000[/C][C]1376026.23229673[/C][C]-76026.2322967262[/C][/ROW]
[ROW][C]17[/C][C]1820000[/C][C]1867902.1196384[/C][C]-47902.1196384029[/C][/ROW]
[ROW][C]18[/C][C]1495000[/C][C]1514594.83917758[/C][C]-19594.8391775836[/C][/ROW]
[ROW][C]19[/C][C]1982500[/C][C]1893972.41292317[/C][C]88527.5870768272[/C][/ROW]
[ROW][C]20[/C][C]1787500[/C][C]1950171.1990305[/C][C]-162671.199030504[/C][/ROW]
[ROW][C]21[/C][C]1885000[/C][C]2175870.39153504[/C][C]-290870.391535042[/C][/ROW]
[ROW][C]22[/C][C]2112500[/C][C]1873626.0026506[/C][C]238873.997349402[/C][/ROW]
[ROW][C]23[/C][C]2080000[/C][C]1772145.76498189[/C][C]307854.235018106[/C][/ROW]
[ROW][C]24[/C][C]2470000[/C][C]2234780.46147776[/C][C]235219.53852224[/C][/ROW]
[ROW][C]25[/C][C]1787500[/C][C]1822286.03631547[/C][C]-34786.036315467[/C][/ROW]
[ROW][C]26[/C][C]1495000[/C][C]1335828.30745268[/C][C]159171.692547316[/C][/ROW]
[ROW][C]27[/C][C]1657500[/C][C]1601963.34435977[/C][C]55536.6556402263[/C][/ROW]
[ROW][C]28[/C][C]1202500[/C][C]1184666.3170621[/C][C]17833.6829379024[/C][/ROW]
[ROW][C]29[/C][C]1722500[/C][C]1708385.86053416[/C][C]14114.1394658424[/C][/ROW]
[ROW][C]30[/C][C]1332500[/C][C]1387370.39675598[/C][C]-54870.3967559803[/C][/ROW]
[ROW][C]31[/C][C]1885000[/C][C]1871334.405527[/C][C]13665.5944729957[/C][/ROW]
[ROW][C]32[/C][C]1787500[/C][C]1700068.13689667[/C][C]87431.8631033285[/C][/ROW]
[ROW][C]33[/C][C]1592500[/C][C]1816930.13078642[/C][C]-224430.130786423[/C][/ROW]
[ROW][C]34[/C][C]2275000[/C][C]2010832.82962868[/C][C]264167.170371316[/C][/ROW]
[ROW][C]35[/C][C]2047500[/C][C]1980916.33086556[/C][C]66583.669134439[/C][/ROW]
[ROW][C]36[/C][C]2340000[/C][C]2379961.90758009[/C][C]-39961.9075800888[/C][/ROW]
[ROW][C]37[/C][C]1755000[/C][C]1719206.06377349[/C][C]35793.9362265116[/C][/ROW]
[ROW][C]38[/C][C]1625000[/C][C]1415726.17860042[/C][C]209273.821399578[/C][/ROW]
[ROW][C]39[/C][C]1462500[/C][C]1590983.49783475[/C][C]-128483.497834752[/C][/ROW]
[ROW][C]40[/C][C]1202500[/C][C]1139670.09760363[/C][C]62829.902396366[/C][/ROW]
[ROW][C]41[/C][C]1592500[/C][C]1663215.05292888[/C][C]-70715.0529288836[/C][/ROW]
[ROW][C]42[/C][C]1430000[/C][C]1279917.6832585[/C][C]150082.316741503[/C][/ROW]
[ROW][C]43[/C][C]1950000[/C][C]1832859.73124498[/C][C]117140.268755025[/C][/ROW]
[ROW][C]44[/C][C]1885000[/C][C]1735407.90421428[/C][C]149592.095785718[/C][/ROW]
[ROW][C]45[/C][C]1625000[/C][C]1571052.88865922[/C][C]53947.1113407761[/C][/ROW]
[ROW][C]46[/C][C]2177500[/C][C]2225668.4843652[/C][C]-48168.4843651955[/C][/ROW]
[ROW][C]47[/C][C]2015000[/C][C]2016020.73743541[/C][C]-1020.73743541283[/C][/ROW]
[ROW][C]48[/C][C]2600000[/C][C]2320835.77099683[/C][C]279164.229003171[/C][/ROW]
[ROW][C]49[/C][C]2080000[/C][C]1740314.8417738[/C][C]339685.158226199[/C][/ROW]
[ROW][C]50[/C][C]1267500[/C][C]1609762.44046301[/C][C]-342262.440463009[/C][/ROW]
[ROW][C]51[/C][C]1267500[/C][C]1473986.91774274[/C][C]-206486.917742738[/C][/ROW]
[ROW][C]52[/C][C]1267500[/C][C]1202661.40261066[/C][C]64838.5973893362[/C][/ROW]
[ROW][C]53[/C][C]1495000[/C][C]1607708.02310401[/C][C]-112708.023104015[/C][/ROW]
[ROW][C]54[/C][C]1495000[/C][C]1431521.12659797[/C][C]63478.8734020318[/C][/ROW]
[ROW][C]55[/C][C]2015000[/C][C]1956624.39048818[/C][C]58375.6095118232[/C][/ROW]
[ROW][C]56[/C][C]1852500[/C][C]1891285.45150931[/C][C]-38785.4515093092[/C][/ROW]
[ROW][C]57[/C][C]1657500[/C][C]1638100.96977926[/C][C]19399.0302207374[/C][/ROW]
[ROW][C]58[/C][C]2080000[/C][C]2199031.33194247[/C][C]-119031.331942474[/C][/ROW]
[ROW][C]59[/C][C]1917500[/C][C]2032200.8619828[/C][C]-114700.861982802[/C][/ROW]
[ROW][C]60[/C][C]2762500[/C][C]2593047.88903756[/C][C]169452.11096244[/C][/ROW]
[ROW][C]61[/C][C]2177500[/C][C]2065234.38141768[/C][C]112265.618582319[/C][/ROW]
[ROW][C]62[/C][C]1267500[/C][C]1300262.39115224[/C][C]-32762.3911522431[/C][/ROW]
[ROW][C]63[/C][C]1332500[/C][C]1291158.21562139[/C][C]41341.784378615[/C][/ROW]
[ROW][C]64[/C][C]1105000[/C][C]1273091.02747346[/C][C]-168091.027473461[/C][/ROW]
[ROW][C]65[/C][C]1527500[/C][C]1511304.27899098[/C][C]16195.7210090214[/C][/ROW]
[ROW][C]66[/C][C]1755000[/C][C]1498673.23325776[/C][C]256326.76674224[/C][/ROW]
[ROW][C]67[/C][C]2210000[/C][C]2022713.68932944[/C][C]187286.310670564[/C][/ROW]
[ROW][C]68[/C][C]2177500[/C][C]1872113.91023301[/C][C]305386.089766992[/C][/ROW]
[ROW][C]69[/C][C]1755000[/C][C]1681947.36457953[/C][C]73052.6354204707[/C][/ROW]
[ROW][C]70[/C][C]2047500[/C][C]2122588.70794084[/C][C]-75088.7079408411[/C][/ROW]
[ROW][C]71[/C][C]1820000[/C][C]1967291.50841523[/C][C]-147291.508415228[/C][/ROW]
[ROW][C]72[/C][C]2600000[/C][C]2796421.88902169[/C][C]-196421.88902169[/C][/ROW]
[ROW][C]73[/C][C]1982500[/C][C]2215989.17478456[/C][C]-233489.174784557[/C][/ROW]
[ROW][C]74[/C][C]1592500[/C][C]1314466.30137739[/C][C]278033.698622608[/C][/ROW]
[ROW][C]75[/C][C]1430000[/C][C]1379625.35939425[/C][C]50374.6406057451[/C][/ROW]
[ROW][C]76[/C][C]1072500[/C][C]1171928.04776496[/C][C]-99428.0477649574[/C][/ROW]
[ROW][C]77[/C][C]1592500[/C][C]1584377.19253068[/C][C]8122.80746932258[/C][/ROW]
[ROW][C]78[/C][C]1917500[/C][C]1796638.02365151[/C][C]120861.976348492[/C][/ROW]
[ROW][C]79[/C][C]2242500[/C][C]2258340.23090644[/C][C]-15840.2309064362[/C][/ROW]
[ROW][C]80[/C][C]2112500[/C][C]2215280.08210665[/C][C]-102780.082106648[/C][/ROW]
[ROW][C]81[/C][C]1560000[/C][C]1804169.82384697[/C][C]-244169.823846967[/C][/ROW]
[ROW][C]82[/C][C]2242500[/C][C]2099326.07040959[/C][C]143173.929590413[/C][/ROW]
[ROW][C]83[/C][C]1755000[/C][C]1875475.75828956[/C][C]-120475.758289557[/C][/ROW]
[ROW][C]84[/C][C]2697500[/C][C]2655781.68778257[/C][C]41718.3122174293[/C][/ROW]
[ROW][C]85[/C][C]2242500[/C][C]2041799.11292054[/C][C]200700.88707946[/C][/ROW]
[ROW][C]86[/C][C]1625000[/C][C]1617901.2890016[/C][C]7098.71099840198[/C][/ROW]
[ROW][C]87[/C][C]1495000[/C][C]1470742.67155431[/C][C]24257.3284456858[/C][/ROW]
[ROW][C]88[/C][C]1007500[/C][C]1124471.1166193[/C][C]-116971.116619296[/C][/ROW]
[ROW][C]89[/C][C]1592500[/C][C]1635326.19743343[/C][C]-42826.1974334321[/C][/ROW]
[ROW][C]90[/C][C]1527500[/C][C]1949990.99373057[/C][C]-422490.993730572[/C][/ROW]
[ROW][C]91[/C][C]2307500[/C][C]2274729.94246899[/C][C]32770.0575310071[/C][/ROW]
[ROW][C]92[/C][C]2307500[/C][C]2146477.99171972[/C][C]161022.008280278[/C][/ROW]
[ROW][C]93[/C][C]1755000[/C][C]1604455.03803464[/C][C]150544.961965363[/C][/ROW]
[ROW][C]94[/C][C]2275000[/C][C]2260613.5417518[/C][C]14386.4582482018[/C][/ROW]
[ROW][C]95[/C][C]1690000[/C][C]1792056.78035095[/C][C]-102056.780350955[/C][/ROW]
[ROW][C]96[/C][C]2632500[/C][C]2721459.47665159[/C][C]-88959.476651595[/C][/ROW]
[ROW][C]97[/C][C]2242500[/C][C]2251024.32990432[/C][C]-8524.32990432344[/C][/ROW]
[ROW][C]98[/C][C]1657500[/C][C]1643222.60094289[/C][C]14277.3990571068[/C][/ROW]
[ROW][C]99[/C][C]1267500[/C][C]1508374.68148075[/C][C]-240874.68148075[/C][/ROW]
[ROW][C]100[/C][C]877500[/C][C]1023536.97893837[/C][C]-146036.97893837[/C][/ROW]
[ROW][C]101[/C][C]1722500[/C][C]1596135.84914341[/C][C]126364.150856589[/C][/ROW]
[ROW][C]102[/C][C]1657500[/C][C]1557917.03619886[/C][C]99582.9638011446[/C][/ROW]
[ROW][C]103[/C][C]2177500[/C][C]2306974.0334331[/C][C]-129474.033433097[/C][/ROW]
[ROW][C]104[/C][C]2502500[/C][C]2293972.9561483[/C][C]208527.043851701[/C][/ROW]
[ROW][C]105[/C][C]1852500[/C][C]1741792.04754738[/C][C]110707.952452624[/C][/ROW]
[ROW][C]106[/C][C]2080000[/C][C]2270842.30422749[/C][C]-190842.304227488[/C][/ROW]
[ROW][C]107[/C][C]1560000[/C][C]1689905.78180455[/C][C]-129905.781804552[/C][/ROW]
[ROW][C]108[/C][C]2697500[/C][C]2627640.83891475[/C][C]69859.1610852536[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306898&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306898&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
1319500002016684.02777778-66684.0277777794
1414625001527560.62382535-65060.6238253464
1517225001801599.71597668-79099.7159766767
1613000001376026.23229673-76026.2322967262
1718200001867902.1196384-47902.1196384029
1814950001514594.83917758-19594.8391775836
1919825001893972.4129231788527.5870768272
2017875001950171.1990305-162671.199030504
2118850002175870.39153504-290870.391535042
2221125001873626.0026506238873.997349402
2320800001772145.76498189307854.235018106
2424700002234780.46147776235219.53852224
2517875001822286.03631547-34786.036315467
2614950001335828.30745268159171.692547316
2716575001601963.3443597755536.6556402263
2812025001184666.317062117833.6829379024
2917225001708385.8605341614114.1394658424
3013325001387370.39675598-54870.3967559803
3118850001871334.40552713665.5944729957
3217875001700068.1368966787431.8631033285
3315925001816930.13078642-224430.130786423
3422750002010832.82962868264167.170371316
3520475001980916.3308655666583.669134439
3623400002379961.90758009-39961.9075800888
3717550001719206.0637734935793.9362265116
3816250001415726.17860042209273.821399578
3914625001590983.49783475-128483.497834752
4012025001139670.0976036362829.902396366
4115925001663215.05292888-70715.0529288836
4214300001279917.6832585150082.316741503
4319500001832859.73124498117140.268755025
4418850001735407.90421428149592.095785718
4516250001571052.8886592253947.1113407761
4621775002225668.4843652-48168.4843651955
4720150002016020.73743541-1020.73743541283
4826000002320835.77099683279164.229003171
4920800001740314.8417738339685.158226199
5012675001609762.44046301-342262.440463009
5112675001473986.91774274-206486.917742738
5212675001202661.4026106664838.5973893362
5314950001607708.02310401-112708.023104015
5414950001431521.1265979763478.8734020318
5520150001956624.3904881858375.6095118232
5618525001891285.45150931-38785.4515093092
5716575001638100.9697792619399.0302207374
5820800002199031.33194247-119031.331942474
5919175002032200.8619828-114700.861982802
6027625002593047.88903756169452.11096244
6121775002065234.38141768112265.618582319
6212675001300262.39115224-32762.3911522431
6313325001291158.2156213941341.784378615
6411050001273091.02747346-168091.027473461
6515275001511304.2789909816195.7210090214
6617550001498673.23325776256326.76674224
6722100002022713.68932944187286.310670564
6821775001872113.91023301305386.089766992
6917550001681947.3645795373052.6354204707
7020475002122588.70794084-75088.7079408411
7118200001967291.50841523-147291.508415228
7226000002796421.88902169-196421.88902169
7319825002215989.17478456-233489.174784557
7415925001314466.30137739278033.698622608
7514300001379625.3593942550374.6406057451
7610725001171928.04776496-99428.0477649574
7715925001584377.192530688122.80746932258
7819175001796638.02365151120861.976348492
7922425002258340.23090644-15840.2309064362
8021125002215280.08210665-102780.082106648
8115600001804169.82384697-244169.823846967
8222425002099326.07040959143173.929590413
8317550001875475.75828956-120475.758289557
8426975002655781.6877825741718.3122174293
8522425002041799.11292054200700.88707946
8616250001617901.28900167098.71099840198
8714950001470742.6715543124257.3284456858
8810075001124471.1166193-116971.116619296
8915925001635326.19743343-42826.1974334321
9015275001949990.99373057-422490.993730572
9123075002274729.9424689932770.0575310071
9223075002146477.99171972161022.008280278
9317550001604455.03803464150544.961965363
9422750002260613.541751814386.4582482018
9516900001792056.78035095-102056.780350955
9626325002721459.47665159-88959.476651595
9722425002251024.32990432-8524.32990432344
9816575001643222.6009428914277.3990571068
9912675001508374.68148075-240874.68148075
1008775001023536.97893837-146036.97893837
10117225001596135.84914341126364.150856589
10216575001557917.0361988699582.9638011446
10321775002306974.0334331-129474.033433097
10425025002293972.9561483208527.043851701
10518525001741792.04754738110707.952452624
10620800002270842.30422749-190842.304227488
10715600001689905.78180455-129905.781804552
10826975002627640.8389147569859.1610852536







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092230766.449544821932862.785823992528670.11326566
1101642123.043616781344168.282141591940077.80509196
1111270050.71217554971981.0127804641568120.41157063
112874978.235873714576704.3117582621173252.15998917
1131701380.446265931402787.70065961999973.19187226
1141637677.789188851338626.537769171936729.04060853
1152174248.757621751874574.556093142473922.95915035
1162474432.080560562173946.174899692774917.98622143
1171828914.896546141527404.810800282130424.982292
1182076840.94600161774071.219158812379610.67284438
1191553247.903762441248960.983122571857534.8244023
1202676848.069889112370765.363647322982930.7761309

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2230766.44954482 & 1932862.78582399 & 2528670.11326566 \tabularnewline
110 & 1642123.04361678 & 1344168.28214159 & 1940077.80509196 \tabularnewline
111 & 1270050.71217554 & 971981.012780464 & 1568120.41157063 \tabularnewline
112 & 874978.235873714 & 576704.311758262 & 1173252.15998917 \tabularnewline
113 & 1701380.44626593 & 1402787.7006596 & 1999973.19187226 \tabularnewline
114 & 1637677.78918885 & 1338626.53776917 & 1936729.04060853 \tabularnewline
115 & 2174248.75762175 & 1874574.55609314 & 2473922.95915035 \tabularnewline
116 & 2474432.08056056 & 2173946.17489969 & 2774917.98622143 \tabularnewline
117 & 1828914.89654614 & 1527404.81080028 & 2130424.982292 \tabularnewline
118 & 2076840.9460016 & 1774071.21915881 & 2379610.67284438 \tabularnewline
119 & 1553247.90376244 & 1248960.98312257 & 1857534.8244023 \tabularnewline
120 & 2676848.06988911 & 2370765.36364732 & 2982930.7761309 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306898&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]109[/C][C]2230766.44954482[/C][C]1932862.78582399[/C][C]2528670.11326566[/C][/ROW]
[ROW][C]110[/C][C]1642123.04361678[/C][C]1344168.28214159[/C][C]1940077.80509196[/C][/ROW]
[ROW][C]111[/C][C]1270050.71217554[/C][C]971981.012780464[/C][C]1568120.41157063[/C][/ROW]
[ROW][C]112[/C][C]874978.235873714[/C][C]576704.311758262[/C][C]1173252.15998917[/C][/ROW]
[ROW][C]113[/C][C]1701380.44626593[/C][C]1402787.7006596[/C][C]1999973.19187226[/C][/ROW]
[ROW][C]114[/C][C]1637677.78918885[/C][C]1338626.53776917[/C][C]1936729.04060853[/C][/ROW]
[ROW][C]115[/C][C]2174248.75762175[/C][C]1874574.55609314[/C][C]2473922.95915035[/C][/ROW]
[ROW][C]116[/C][C]2474432.08056056[/C][C]2173946.17489969[/C][C]2774917.98622143[/C][/ROW]
[ROW][C]117[/C][C]1828914.89654614[/C][C]1527404.81080028[/C][C]2130424.982292[/C][/ROW]
[ROW][C]118[/C][C]2076840.9460016[/C][C]1774071.21915881[/C][C]2379610.67284438[/C][/ROW]
[ROW][C]119[/C][C]1553247.90376244[/C][C]1248960.98312257[/C][C]1857534.8244023[/C][/ROW]
[ROW][C]120[/C][C]2676848.06988911[/C][C]2370765.36364732[/C][C]2982930.7761309[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306898&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306898&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
1092230766.449544821932862.785823992528670.11326566
1101642123.043616781344168.282141591940077.80509196
1111270050.71217554971981.0127804641568120.41157063
112874978.235873714576704.3117582621173252.15998917
1131701380.446265931402787.70065961999973.19187226
1141637677.789188851338626.537769171936729.04060853
1152174248.757621751874574.556093142473922.95915035
1162474432.080560562173946.174899692774917.98622143
1171828914.896546141527404.810800282130424.982292
1182076840.94600161774071.219158812379610.67284438
1191553247.903762441248960.983122571857534.8244023
1202676848.069889112370765.363647322982930.7761309



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')