Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 03 May 2017 18:41:29 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/03/t1493833325rdq090bopadihuf.htm/, Retrieved Fri, 17 May 2024 08:28:19 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 08:28:19 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
83,61
83,89
83,4
82,96
82,76
83,35
87,78
88,99
88,92
88,91
89,79
90,54
93,15
92,79
93,21
95,35
100,91
103,69
104,04
104,16
104,71
105,18
104,92
104,83
104,9
105,05
104,6
103,21
102,52
101,09
101,19
102,34
102,62
102,47
101,82
101,86
101,54
101,98
101,23
100,4
99,94
99,94
100
98,8
99,07
99,46
99,18
98,47
97,12
96,91
96,09
97,17
96,8
97,13
99,9
100,56
100,84
99,81
100,44
100,07
101,32
103,98
104,81
106,23
106,48
107,59
107,16
107,54
107,1
106,38
106,64
106,13




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999923157010773
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999923157010773 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.999923157010773[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.999923157010773
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
283.8983.610.280000000000001
383.483.889978483963-0.489978483963014
482.9683.4000376514114-0.440037651411373
582.7682.9600338138085-0.200033813808489
683.3582.76001537119620.589984628803791
787.7883.34995466381754.43004533618247
888.9987.7796595820741.21034041792603
988.9288.9899069938243-0.06990699382429
1088.9188.9200053718624-0.0100053718623769
1189.7988.91000076884270.879999231157313
1290.5489.78993237822860.750067621771436
1393.1590.53994236256182.61005763743817
1492.7993.1497994353691-0.359799435369084
1593.2192.79002764806420.41997235193584
1695.3593.20996772806912.14003227193092
17100.9195.34983555352325.56016444647682
18103.69100.9095727403432.78042725965666
19104.04103.6897863436580.350213656341964
20104.16104.0399730885360.120026911464208
21104.71104.1599907767730.550009223226652
22105.18104.7099577356470.470042264352827
23104.92105.179963880547-0.259963880547346
24104.83104.920019976402-0.0900199764016776
25104.9104.8300069174040.0699930825959285
26105.05104.8999946215220.150005378477687
27104.6105.049988473138-0.449988473138333
28103.21104.600034578459-1.39003457845939
29102.52103.210106814412-0.690106814412133
30101.09102.52005302987-1.43005302987049
31101.19101.090109889550.0998901104504313
32102.34101.1899923241451.1500076758547
33102.62102.3399116299730.280088370027443
34102.47102.619978477172-0.149978477172411
35101.82102.470011524795-0.650011524794508
36101.86101.8200499488290.0399500511714166
37101.54101.859996930119-0.319996930118634
38101.98101.5400245895210.439975410479335
39101.23101.979966190974-0.749966190974263
40100.4101.230057629644-0.830057629643932
4199.94100.400063784109-0.460063784109494
4299.9499.9400353526764-3.53526764058643e-05
4310099.94000000271660.0599999972833984
4498.899.9999953894209-1.19999538942086
4599.0798.80009221123280.269907788767213
4699.4699.06997925947870.390020740521308
4799.1899.4599700296404-0.279970029640424
4898.4799.180021513734-0.710021513733977
4997.1298.4700545601755-1.35005456017552
5096.9197.120103742228-0.210103742228029
5196.0996.9100161449996-0.820016144999599
5297.1796.09006301249181.0799369875082
5396.897.1699170144137-0.369917014413701
5497.1396.80002842552910.329971574470846
5599.997.12997464399782.77002535600217
56100.5699.89978714297140.660212857028583
57100.84100.5599492672710.280050732729464
5899.81100.839978480065-1.02997848006456
59100.4499.81007914662520.629920853374756
60100.07100.439951594999-0.369951594998653
61101.32100.0700284281861.24997157181357
62103.98101.3199039484482.66009605155203
63104.81103.9797955902680.830204409732232
64106.23104.8099362046111.42006379538851
65106.48106.2298908780530.25010912194692
66107.59106.4799807808671.11001921913257
67107.16107.589914702805-0.429914702805121
68107.54107.1600330359310.379966964069141
69107.1107.539970802203-0.43997080220268
70106.38107.100033808672-0.720033808671616
71106.64106.380055329550.259944670449798
72106.13106.639980025074-0.509980025074498

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 83.89 & 83.61 & 0.280000000000001 \tabularnewline
3 & 83.4 & 83.889978483963 & -0.489978483963014 \tabularnewline
4 & 82.96 & 83.4000376514114 & -0.440037651411373 \tabularnewline
5 & 82.76 & 82.9600338138085 & -0.200033813808489 \tabularnewline
6 & 83.35 & 82.7600153711962 & 0.589984628803791 \tabularnewline
7 & 87.78 & 83.3499546638175 & 4.43004533618247 \tabularnewline
8 & 88.99 & 87.779659582074 & 1.21034041792603 \tabularnewline
9 & 88.92 & 88.9899069938243 & -0.06990699382429 \tabularnewline
10 & 88.91 & 88.9200053718624 & -0.0100053718623769 \tabularnewline
11 & 89.79 & 88.9100007688427 & 0.879999231157313 \tabularnewline
12 & 90.54 & 89.7899323782286 & 0.750067621771436 \tabularnewline
13 & 93.15 & 90.5399423625618 & 2.61005763743817 \tabularnewline
14 & 92.79 & 93.1497994353691 & -0.359799435369084 \tabularnewline
15 & 93.21 & 92.7900276480642 & 0.41997235193584 \tabularnewline
16 & 95.35 & 93.2099677280691 & 2.14003227193092 \tabularnewline
17 & 100.91 & 95.3498355535232 & 5.56016444647682 \tabularnewline
18 & 103.69 & 100.909572740343 & 2.78042725965666 \tabularnewline
19 & 104.04 & 103.689786343658 & 0.350213656341964 \tabularnewline
20 & 104.16 & 104.039973088536 & 0.120026911464208 \tabularnewline
21 & 104.71 & 104.159990776773 & 0.550009223226652 \tabularnewline
22 & 105.18 & 104.709957735647 & 0.470042264352827 \tabularnewline
23 & 104.92 & 105.179963880547 & -0.259963880547346 \tabularnewline
24 & 104.83 & 104.920019976402 & -0.0900199764016776 \tabularnewline
25 & 104.9 & 104.830006917404 & 0.0699930825959285 \tabularnewline
26 & 105.05 & 104.899994621522 & 0.150005378477687 \tabularnewline
27 & 104.6 & 105.049988473138 & -0.449988473138333 \tabularnewline
28 & 103.21 & 104.600034578459 & -1.39003457845939 \tabularnewline
29 & 102.52 & 103.210106814412 & -0.690106814412133 \tabularnewline
30 & 101.09 & 102.52005302987 & -1.43005302987049 \tabularnewline
31 & 101.19 & 101.09010988955 & 0.0998901104504313 \tabularnewline
32 & 102.34 & 101.189992324145 & 1.1500076758547 \tabularnewline
33 & 102.62 & 102.339911629973 & 0.280088370027443 \tabularnewline
34 & 102.47 & 102.619978477172 & -0.149978477172411 \tabularnewline
35 & 101.82 & 102.470011524795 & -0.650011524794508 \tabularnewline
36 & 101.86 & 101.820049948829 & 0.0399500511714166 \tabularnewline
37 & 101.54 & 101.859996930119 & -0.319996930118634 \tabularnewline
38 & 101.98 & 101.540024589521 & 0.439975410479335 \tabularnewline
39 & 101.23 & 101.979966190974 & -0.749966190974263 \tabularnewline
40 & 100.4 & 101.230057629644 & -0.830057629643932 \tabularnewline
41 & 99.94 & 100.400063784109 & -0.460063784109494 \tabularnewline
42 & 99.94 & 99.9400353526764 & -3.53526764058643e-05 \tabularnewline
43 & 100 & 99.9400000027166 & 0.0599999972833984 \tabularnewline
44 & 98.8 & 99.9999953894209 & -1.19999538942086 \tabularnewline
45 & 99.07 & 98.8000922112328 & 0.269907788767213 \tabularnewline
46 & 99.46 & 99.0699792594787 & 0.390020740521308 \tabularnewline
47 & 99.18 & 99.4599700296404 & -0.279970029640424 \tabularnewline
48 & 98.47 & 99.180021513734 & -0.710021513733977 \tabularnewline
49 & 97.12 & 98.4700545601755 & -1.35005456017552 \tabularnewline
50 & 96.91 & 97.120103742228 & -0.210103742228029 \tabularnewline
51 & 96.09 & 96.9100161449996 & -0.820016144999599 \tabularnewline
52 & 97.17 & 96.0900630124918 & 1.0799369875082 \tabularnewline
53 & 96.8 & 97.1699170144137 & -0.369917014413701 \tabularnewline
54 & 97.13 & 96.8000284255291 & 0.329971574470846 \tabularnewline
55 & 99.9 & 97.1299746439978 & 2.77002535600217 \tabularnewline
56 & 100.56 & 99.8997871429714 & 0.660212857028583 \tabularnewline
57 & 100.84 & 100.559949267271 & 0.280050732729464 \tabularnewline
58 & 99.81 & 100.839978480065 & -1.02997848006456 \tabularnewline
59 & 100.44 & 99.8100791466252 & 0.629920853374756 \tabularnewline
60 & 100.07 & 100.439951594999 & -0.369951594998653 \tabularnewline
61 & 101.32 & 100.070028428186 & 1.24997157181357 \tabularnewline
62 & 103.98 & 101.319903948448 & 2.66009605155203 \tabularnewline
63 & 104.81 & 103.979795590268 & 0.830204409732232 \tabularnewline
64 & 106.23 & 104.809936204611 & 1.42006379538851 \tabularnewline
65 & 106.48 & 106.229890878053 & 0.25010912194692 \tabularnewline
66 & 107.59 & 106.479980780867 & 1.11001921913257 \tabularnewline
67 & 107.16 & 107.589914702805 & -0.429914702805121 \tabularnewline
68 & 107.54 & 107.160033035931 & 0.379966964069141 \tabularnewline
69 & 107.1 & 107.539970802203 & -0.43997080220268 \tabularnewline
70 & 106.38 & 107.100033808672 & -0.720033808671616 \tabularnewline
71 & 106.64 & 106.38005532955 & 0.259944670449798 \tabularnewline
72 & 106.13 & 106.639980025074 & -0.509980025074498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]83.89[/C][C]83.61[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]3[/C][C]83.4[/C][C]83.889978483963[/C][C]-0.489978483963014[/C][/ROW]
[ROW][C]4[/C][C]82.96[/C][C]83.4000376514114[/C][C]-0.440037651411373[/C][/ROW]
[ROW][C]5[/C][C]82.76[/C][C]82.9600338138085[/C][C]-0.200033813808489[/C][/ROW]
[ROW][C]6[/C][C]83.35[/C][C]82.7600153711962[/C][C]0.589984628803791[/C][/ROW]
[ROW][C]7[/C][C]87.78[/C][C]83.3499546638175[/C][C]4.43004533618247[/C][/ROW]
[ROW][C]8[/C][C]88.99[/C][C]87.779659582074[/C][C]1.21034041792603[/C][/ROW]
[ROW][C]9[/C][C]88.92[/C][C]88.9899069938243[/C][C]-0.06990699382429[/C][/ROW]
[ROW][C]10[/C][C]88.91[/C][C]88.9200053718624[/C][C]-0.0100053718623769[/C][/ROW]
[ROW][C]11[/C][C]89.79[/C][C]88.9100007688427[/C][C]0.879999231157313[/C][/ROW]
[ROW][C]12[/C][C]90.54[/C][C]89.7899323782286[/C][C]0.750067621771436[/C][/ROW]
[ROW][C]13[/C][C]93.15[/C][C]90.5399423625618[/C][C]2.61005763743817[/C][/ROW]
[ROW][C]14[/C][C]92.79[/C][C]93.1497994353691[/C][C]-0.359799435369084[/C][/ROW]
[ROW][C]15[/C][C]93.21[/C][C]92.7900276480642[/C][C]0.41997235193584[/C][/ROW]
[ROW][C]16[/C][C]95.35[/C][C]93.2099677280691[/C][C]2.14003227193092[/C][/ROW]
[ROW][C]17[/C][C]100.91[/C][C]95.3498355535232[/C][C]5.56016444647682[/C][/ROW]
[ROW][C]18[/C][C]103.69[/C][C]100.909572740343[/C][C]2.78042725965666[/C][/ROW]
[ROW][C]19[/C][C]104.04[/C][C]103.689786343658[/C][C]0.350213656341964[/C][/ROW]
[ROW][C]20[/C][C]104.16[/C][C]104.039973088536[/C][C]0.120026911464208[/C][/ROW]
[ROW][C]21[/C][C]104.71[/C][C]104.159990776773[/C][C]0.550009223226652[/C][/ROW]
[ROW][C]22[/C][C]105.18[/C][C]104.709957735647[/C][C]0.470042264352827[/C][/ROW]
[ROW][C]23[/C][C]104.92[/C][C]105.179963880547[/C][C]-0.259963880547346[/C][/ROW]
[ROW][C]24[/C][C]104.83[/C][C]104.920019976402[/C][C]-0.0900199764016776[/C][/ROW]
[ROW][C]25[/C][C]104.9[/C][C]104.830006917404[/C][C]0.0699930825959285[/C][/ROW]
[ROW][C]26[/C][C]105.05[/C][C]104.899994621522[/C][C]0.150005378477687[/C][/ROW]
[ROW][C]27[/C][C]104.6[/C][C]105.049988473138[/C][C]-0.449988473138333[/C][/ROW]
[ROW][C]28[/C][C]103.21[/C][C]104.600034578459[/C][C]-1.39003457845939[/C][/ROW]
[ROW][C]29[/C][C]102.52[/C][C]103.210106814412[/C][C]-0.690106814412133[/C][/ROW]
[ROW][C]30[/C][C]101.09[/C][C]102.52005302987[/C][C]-1.43005302987049[/C][/ROW]
[ROW][C]31[/C][C]101.19[/C][C]101.09010988955[/C][C]0.0998901104504313[/C][/ROW]
[ROW][C]32[/C][C]102.34[/C][C]101.189992324145[/C][C]1.1500076758547[/C][/ROW]
[ROW][C]33[/C][C]102.62[/C][C]102.339911629973[/C][C]0.280088370027443[/C][/ROW]
[ROW][C]34[/C][C]102.47[/C][C]102.619978477172[/C][C]-0.149978477172411[/C][/ROW]
[ROW][C]35[/C][C]101.82[/C][C]102.470011524795[/C][C]-0.650011524794508[/C][/ROW]
[ROW][C]36[/C][C]101.86[/C][C]101.820049948829[/C][C]0.0399500511714166[/C][/ROW]
[ROW][C]37[/C][C]101.54[/C][C]101.859996930119[/C][C]-0.319996930118634[/C][/ROW]
[ROW][C]38[/C][C]101.98[/C][C]101.540024589521[/C][C]0.439975410479335[/C][/ROW]
[ROW][C]39[/C][C]101.23[/C][C]101.979966190974[/C][C]-0.749966190974263[/C][/ROW]
[ROW][C]40[/C][C]100.4[/C][C]101.230057629644[/C][C]-0.830057629643932[/C][/ROW]
[ROW][C]41[/C][C]99.94[/C][C]100.400063784109[/C][C]-0.460063784109494[/C][/ROW]
[ROW][C]42[/C][C]99.94[/C][C]99.9400353526764[/C][C]-3.53526764058643e-05[/C][/ROW]
[ROW][C]43[/C][C]100[/C][C]99.9400000027166[/C][C]0.0599999972833984[/C][/ROW]
[ROW][C]44[/C][C]98.8[/C][C]99.9999953894209[/C][C]-1.19999538942086[/C][/ROW]
[ROW][C]45[/C][C]99.07[/C][C]98.8000922112328[/C][C]0.269907788767213[/C][/ROW]
[ROW][C]46[/C][C]99.46[/C][C]99.0699792594787[/C][C]0.390020740521308[/C][/ROW]
[ROW][C]47[/C][C]99.18[/C][C]99.4599700296404[/C][C]-0.279970029640424[/C][/ROW]
[ROW][C]48[/C][C]98.47[/C][C]99.180021513734[/C][C]-0.710021513733977[/C][/ROW]
[ROW][C]49[/C][C]97.12[/C][C]98.4700545601755[/C][C]-1.35005456017552[/C][/ROW]
[ROW][C]50[/C][C]96.91[/C][C]97.120103742228[/C][C]-0.210103742228029[/C][/ROW]
[ROW][C]51[/C][C]96.09[/C][C]96.9100161449996[/C][C]-0.820016144999599[/C][/ROW]
[ROW][C]52[/C][C]97.17[/C][C]96.0900630124918[/C][C]1.0799369875082[/C][/ROW]
[ROW][C]53[/C][C]96.8[/C][C]97.1699170144137[/C][C]-0.369917014413701[/C][/ROW]
[ROW][C]54[/C][C]97.13[/C][C]96.8000284255291[/C][C]0.329971574470846[/C][/ROW]
[ROW][C]55[/C][C]99.9[/C][C]97.1299746439978[/C][C]2.77002535600217[/C][/ROW]
[ROW][C]56[/C][C]100.56[/C][C]99.8997871429714[/C][C]0.660212857028583[/C][/ROW]
[ROW][C]57[/C][C]100.84[/C][C]100.559949267271[/C][C]0.280050732729464[/C][/ROW]
[ROW][C]58[/C][C]99.81[/C][C]100.839978480065[/C][C]-1.02997848006456[/C][/ROW]
[ROW][C]59[/C][C]100.44[/C][C]99.8100791466252[/C][C]0.629920853374756[/C][/ROW]
[ROW][C]60[/C][C]100.07[/C][C]100.439951594999[/C][C]-0.369951594998653[/C][/ROW]
[ROW][C]61[/C][C]101.32[/C][C]100.070028428186[/C][C]1.24997157181357[/C][/ROW]
[ROW][C]62[/C][C]103.98[/C][C]101.319903948448[/C][C]2.66009605155203[/C][/ROW]
[ROW][C]63[/C][C]104.81[/C][C]103.979795590268[/C][C]0.830204409732232[/C][/ROW]
[ROW][C]64[/C][C]106.23[/C][C]104.809936204611[/C][C]1.42006379538851[/C][/ROW]
[ROW][C]65[/C][C]106.48[/C][C]106.229890878053[/C][C]0.25010912194692[/C][/ROW]
[ROW][C]66[/C][C]107.59[/C][C]106.479980780867[/C][C]1.11001921913257[/C][/ROW]
[ROW][C]67[/C][C]107.16[/C][C]107.589914702805[/C][C]-0.429914702805121[/C][/ROW]
[ROW][C]68[/C][C]107.54[/C][C]107.160033035931[/C][C]0.379966964069141[/C][/ROW]
[ROW][C]69[/C][C]107.1[/C][C]107.539970802203[/C][C]-0.43997080220268[/C][/ROW]
[ROW][C]70[/C][C]106.38[/C][C]107.100033808672[/C][C]-0.720033808671616[/C][/ROW]
[ROW][C]71[/C][C]106.64[/C][C]106.38005532955[/C][C]0.259944670449798[/C][/ROW]
[ROW][C]72[/C][C]106.13[/C][C]106.639980025074[/C][C]-0.509980025074498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
283.8983.610.280000000000001
383.483.889978483963-0.489978483963014
482.9683.4000376514114-0.440037651411373
582.7682.9600338138085-0.200033813808489
683.3582.76001537119620.589984628803791
787.7883.34995466381754.43004533618247
888.9987.7796595820741.21034041792603
988.9288.9899069938243-0.06990699382429
1088.9188.9200053718624-0.0100053718623769
1189.7988.91000076884270.879999231157313
1290.5489.78993237822860.750067621771436
1393.1590.53994236256182.61005763743817
1492.7993.1497994353691-0.359799435369084
1593.2192.79002764806420.41997235193584
1695.3593.20996772806912.14003227193092
17100.9195.34983555352325.56016444647682
18103.69100.9095727403432.78042725965666
19104.04103.6897863436580.350213656341964
20104.16104.0399730885360.120026911464208
21104.71104.1599907767730.550009223226652
22105.18104.7099577356470.470042264352827
23104.92105.179963880547-0.259963880547346
24104.83104.920019976402-0.0900199764016776
25104.9104.8300069174040.0699930825959285
26105.05104.8999946215220.150005378477687
27104.6105.049988473138-0.449988473138333
28103.21104.600034578459-1.39003457845939
29102.52103.210106814412-0.690106814412133
30101.09102.52005302987-1.43005302987049
31101.19101.090109889550.0998901104504313
32102.34101.1899923241451.1500076758547
33102.62102.3399116299730.280088370027443
34102.47102.619978477172-0.149978477172411
35101.82102.470011524795-0.650011524794508
36101.86101.8200499488290.0399500511714166
37101.54101.859996930119-0.319996930118634
38101.98101.5400245895210.439975410479335
39101.23101.979966190974-0.749966190974263
40100.4101.230057629644-0.830057629643932
4199.94100.400063784109-0.460063784109494
4299.9499.9400353526764-3.53526764058643e-05
4310099.94000000271660.0599999972833984
4498.899.9999953894209-1.19999538942086
4599.0798.80009221123280.269907788767213
4699.4699.06997925947870.390020740521308
4799.1899.4599700296404-0.279970029640424
4898.4799.180021513734-0.710021513733977
4997.1298.4700545601755-1.35005456017552
5096.9197.120103742228-0.210103742228029
5196.0996.9100161449996-0.820016144999599
5297.1796.09006301249181.0799369875082
5396.897.1699170144137-0.369917014413701
5497.1396.80002842552910.329971574470846
5599.997.12997464399782.77002535600217
56100.5699.89978714297140.660212857028583
57100.84100.5599492672710.280050732729464
5899.81100.839978480065-1.02997848006456
59100.4499.81007914662520.629920853374756
60100.07100.439951594999-0.369951594998653
61101.32100.0700284281861.24997157181357
62103.98101.3199039484482.66009605155203
63104.81103.9797955902680.830204409732232
64106.23104.8099362046111.42006379538851
65106.48106.2298908780530.25010912194692
66107.59106.4799807808671.11001921913257
67107.16107.589914702805-0.429914702805121
68107.54107.1600330359310.379966964069141
69107.1107.539970802203-0.43997080220268
70106.38107.100033808672-0.720033808671616
71106.64106.380055329550.259944670449798
72106.13106.639980025074-0.509980025074498







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73106.13003918839103.723181649107108.536896727672
74106.13003918839102.726359390613109.533718986166
75106.13003918839101.961453203049110.298625173731
76106.13003918839101.316601532351110.943476844428
77106.13003918839100.7484729647111.511605412079
78106.13003918839100.234843859026112.025234517753
79106.1300391883999.76251212345112.497566253329
80106.1300391883999.3228757648975112.937202611882
81106.1300391883998.9099597687767113.350118608002
82106.1300391883998.5194137359772113.740664640802
83106.1300391883998.1479534504201114.112124926359
84106.1300391883997.7930273928069114.467050983972

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 106.13003918839 & 103.723181649107 & 108.536896727672 \tabularnewline
74 & 106.13003918839 & 102.726359390613 & 109.533718986166 \tabularnewline
75 & 106.13003918839 & 101.961453203049 & 110.298625173731 \tabularnewline
76 & 106.13003918839 & 101.316601532351 & 110.943476844428 \tabularnewline
77 & 106.13003918839 & 100.7484729647 & 111.511605412079 \tabularnewline
78 & 106.13003918839 & 100.234843859026 & 112.025234517753 \tabularnewline
79 & 106.13003918839 & 99.76251212345 & 112.497566253329 \tabularnewline
80 & 106.13003918839 & 99.3228757648975 & 112.937202611882 \tabularnewline
81 & 106.13003918839 & 98.9099597687767 & 113.350118608002 \tabularnewline
82 & 106.13003918839 & 98.5194137359772 & 113.740664640802 \tabularnewline
83 & 106.13003918839 & 98.1479534504201 & 114.112124926359 \tabularnewline
84 & 106.13003918839 & 97.7930273928069 & 114.467050983972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]106.13003918839[/C][C]103.723181649107[/C][C]108.536896727672[/C][/ROW]
[ROW][C]74[/C][C]106.13003918839[/C][C]102.726359390613[/C][C]109.533718986166[/C][/ROW]
[ROW][C]75[/C][C]106.13003918839[/C][C]101.961453203049[/C][C]110.298625173731[/C][/ROW]
[ROW][C]76[/C][C]106.13003918839[/C][C]101.316601532351[/C][C]110.943476844428[/C][/ROW]
[ROW][C]77[/C][C]106.13003918839[/C][C]100.7484729647[/C][C]111.511605412079[/C][/ROW]
[ROW][C]78[/C][C]106.13003918839[/C][C]100.234843859026[/C][C]112.025234517753[/C][/ROW]
[ROW][C]79[/C][C]106.13003918839[/C][C]99.76251212345[/C][C]112.497566253329[/C][/ROW]
[ROW][C]80[/C][C]106.13003918839[/C][C]99.3228757648975[/C][C]112.937202611882[/C][/ROW]
[ROW][C]81[/C][C]106.13003918839[/C][C]98.9099597687767[/C][C]113.350118608002[/C][/ROW]
[ROW][C]82[/C][C]106.13003918839[/C][C]98.5194137359772[/C][C]113.740664640802[/C][/ROW]
[ROW][C]83[/C][C]106.13003918839[/C][C]98.1479534504201[/C][C]114.112124926359[/C][/ROW]
[ROW][C]84[/C][C]106.13003918839[/C][C]97.7930273928069[/C][C]114.467050983972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73106.13003918839103.723181649107108.536896727672
74106.13003918839102.726359390613109.533718986166
75106.13003918839101.961453203049110.298625173731
76106.13003918839101.316601532351110.943476844428
77106.13003918839100.7484729647111.511605412079
78106.13003918839100.234843859026112.025234517753
79106.1300391883999.76251212345112.497566253329
80106.1300391883999.3228757648975112.937202611882
81106.1300391883998.9099597687767113.350118608002
82106.1300391883998.5194137359772113.740664640802
83106.1300391883998.1479534504201114.112124926359
84106.1300391883997.7930273928069114.467050983972



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')