Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 May 2017 14:30:22 +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/01/t1493645444wg63a0qlzow5x1u.htm/, Retrieved Wed, 15 May 2024 21:39:03 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 21:39:03 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
101.68
101.25
101.24
101.11
101.08
101.09
101.09
101.62
101.66
101.96
102.04
102.02
102.02
101.51
101.62
101.83
102.06
102.14
102.14
102.59
102.92
103.31
103.54
103.58
103.58
102.83
102.86
103.03
103.2
103.28
103.28
103.79
103.92
104.26
104.41
104.45
99.92
99.18
99.18
99.35
99.62
99.67
99.72
100.08
100.39
100.77
101.03
101.07
101.29
101.1
101.2
101.15
101.24
101.16
100.81
101.02
101.15
101.06
101.17
101.22
101.84
101.79
101.88
101.9
101.91
101.96
101.26
101.06
100.98
101.12
101.24
101.25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 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]3 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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999946561509106
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999946561509106 \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]0.999946561509106[/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
alpha0.999946561509106
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2101.25101.68-0.430000000000007
3101.24101.250022978551-0.0100229785510919
4101.11101.240000535613-0.130000535612837
5101.08101.110006947032-0.0300069470324331
6101.09101.0800016035260.00999839647404599
7101.09101.0899994657015.3429921820225e-07
8101.62101.0899999999710.530000000028551
9101.66101.61997167760.0400283224001612
10101.96101.6599978609470.300002139053134
11102.04101.9599839683380.0800160316615859
12102.02102.039995724064-0.0199957240640316
13102.02102.020001068541-1.0685413229794e-06
14101.51102.020000000057-0.51000000005709
15101.62101.510027253630.10997274636965
16101.83101.6199941232220.210005876777601
17102.06101.8299887776030.230011222397138
18102.14102.0599877085470.0800122914526185
19102.14102.1399957242644.27573611716525e-06
20102.59102.1399999997720.450000000228499
21102.92102.5899759526790.330024047320904
22103.31102.9199823640130.39001763598705
23103.54103.3099791580460.230020841953902
24103.58103.5399877080330.0400122919666472
25103.58103.5799978618042.13819649275138e-06
26102.83103.579999999886-0.749999999885745
27102.86102.8300400788680.0299599211318338
28103.03102.8599983989870.17000160101297
29103.2103.0299909153710.170009084629015
30103.28103.1999909149710.0800090850289195
31103.28103.2799957244354.2755647626791e-06
32103.79103.2799999997720.510000000228487
33103.92103.789972746370.130027253630359
34104.26103.919993051540.340006948460214
35104.41104.2599818305420.150018169458207
36104.45104.4099919832550.0400080167445935
3799.92104.449997862032-4.52999786203196
3899.1899.9202420762495-0.740242076249487
3999.1899.1800395574195-3.95574194556048e-05
4099.3599.18000000211390.169999997886094
4199.6299.34999091545670.270009084543346
4299.6799.6199855711220.0500144288780007
4399.7299.66999732730440.050002672695598
44100.0899.71999732793260.360002672067381
45100.39100.0799807620.310019237999512
46100.77100.389983433040.380016566960222
47101.03100.7699796924880.260020307511851
48101.07101.0299861049070.0400138950928266
49101.29101.0699978617180.220002138282183
50101.1101.289988243418-0.189988243417744
51101.2101.1000101526850.0999898473150012
52101.15101.199994656693-0.0499946566934568
53101.24101.1500026716390.0899973283609796
54101.16101.239995190679-0.0799951906785878
55100.81101.160004274822-0.350004274822268
56101.02100.81001870370.209981296299745
57101.15101.0199887789160.130011221083592
58101.06101.149993052397-0.0899930523965509
59101.17101.0600048090930.109995190907085
60101.22101.1699941220230.0500058779770001
61101.84101.2199973277610.620002672238655
62101.79101.839966867993-0.0499668679928362
63101.88101.7900026701540.0899973298459713
64101.9101.8799951906780.0200048093215059
65101.91101.8999989309730.0100010690268135
66101.96101.9099994655580.0500005344420344
67101.26101.959997328047-0.699997328046891
68101.06101.260037406801-0.200037406800845
69100.98101.060010689697-0.0800106896971329
70101.12100.9800042756510.13999572434949
71101.24101.119992518840.120007481160243
72101.25101.2399935869810.0100064130187008

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 101.25 & 101.68 & -0.430000000000007 \tabularnewline
3 & 101.24 & 101.250022978551 & -0.0100229785510919 \tabularnewline
4 & 101.11 & 101.240000535613 & -0.130000535612837 \tabularnewline
5 & 101.08 & 101.110006947032 & -0.0300069470324331 \tabularnewline
6 & 101.09 & 101.080001603526 & 0.00999839647404599 \tabularnewline
7 & 101.09 & 101.089999465701 & 5.3429921820225e-07 \tabularnewline
8 & 101.62 & 101.089999999971 & 0.530000000028551 \tabularnewline
9 & 101.66 & 101.6199716776 & 0.0400283224001612 \tabularnewline
10 & 101.96 & 101.659997860947 & 0.300002139053134 \tabularnewline
11 & 102.04 & 101.959983968338 & 0.0800160316615859 \tabularnewline
12 & 102.02 & 102.039995724064 & -0.0199957240640316 \tabularnewline
13 & 102.02 & 102.020001068541 & -1.0685413229794e-06 \tabularnewline
14 & 101.51 & 102.020000000057 & -0.51000000005709 \tabularnewline
15 & 101.62 & 101.51002725363 & 0.10997274636965 \tabularnewline
16 & 101.83 & 101.619994123222 & 0.210005876777601 \tabularnewline
17 & 102.06 & 101.829988777603 & 0.230011222397138 \tabularnewline
18 & 102.14 & 102.059987708547 & 0.0800122914526185 \tabularnewline
19 & 102.14 & 102.139995724264 & 4.27573611716525e-06 \tabularnewline
20 & 102.59 & 102.139999999772 & 0.450000000228499 \tabularnewline
21 & 102.92 & 102.589975952679 & 0.330024047320904 \tabularnewline
22 & 103.31 & 102.919982364013 & 0.39001763598705 \tabularnewline
23 & 103.54 & 103.309979158046 & 0.230020841953902 \tabularnewline
24 & 103.58 & 103.539987708033 & 0.0400122919666472 \tabularnewline
25 & 103.58 & 103.579997861804 & 2.13819649275138e-06 \tabularnewline
26 & 102.83 & 103.579999999886 & -0.749999999885745 \tabularnewline
27 & 102.86 & 102.830040078868 & 0.0299599211318338 \tabularnewline
28 & 103.03 & 102.859998398987 & 0.17000160101297 \tabularnewline
29 & 103.2 & 103.029990915371 & 0.170009084629015 \tabularnewline
30 & 103.28 & 103.199990914971 & 0.0800090850289195 \tabularnewline
31 & 103.28 & 103.279995724435 & 4.2755647626791e-06 \tabularnewline
32 & 103.79 & 103.279999999772 & 0.510000000228487 \tabularnewline
33 & 103.92 & 103.78997274637 & 0.130027253630359 \tabularnewline
34 & 104.26 & 103.91999305154 & 0.340006948460214 \tabularnewline
35 & 104.41 & 104.259981830542 & 0.150018169458207 \tabularnewline
36 & 104.45 & 104.409991983255 & 0.0400080167445935 \tabularnewline
37 & 99.92 & 104.449997862032 & -4.52999786203196 \tabularnewline
38 & 99.18 & 99.9202420762495 & -0.740242076249487 \tabularnewline
39 & 99.18 & 99.1800395574195 & -3.95574194556048e-05 \tabularnewline
40 & 99.35 & 99.1800000021139 & 0.169999997886094 \tabularnewline
41 & 99.62 & 99.3499909154567 & 0.270009084543346 \tabularnewline
42 & 99.67 & 99.619985571122 & 0.0500144288780007 \tabularnewline
43 & 99.72 & 99.6699973273044 & 0.050002672695598 \tabularnewline
44 & 100.08 & 99.7199973279326 & 0.360002672067381 \tabularnewline
45 & 100.39 & 100.079980762 & 0.310019237999512 \tabularnewline
46 & 100.77 & 100.38998343304 & 0.380016566960222 \tabularnewline
47 & 101.03 & 100.769979692488 & 0.260020307511851 \tabularnewline
48 & 101.07 & 101.029986104907 & 0.0400138950928266 \tabularnewline
49 & 101.29 & 101.069997861718 & 0.220002138282183 \tabularnewline
50 & 101.1 & 101.289988243418 & -0.189988243417744 \tabularnewline
51 & 101.2 & 101.100010152685 & 0.0999898473150012 \tabularnewline
52 & 101.15 & 101.199994656693 & -0.0499946566934568 \tabularnewline
53 & 101.24 & 101.150002671639 & 0.0899973283609796 \tabularnewline
54 & 101.16 & 101.239995190679 & -0.0799951906785878 \tabularnewline
55 & 100.81 & 101.160004274822 & -0.350004274822268 \tabularnewline
56 & 101.02 & 100.8100187037 & 0.209981296299745 \tabularnewline
57 & 101.15 & 101.019988778916 & 0.130011221083592 \tabularnewline
58 & 101.06 & 101.149993052397 & -0.0899930523965509 \tabularnewline
59 & 101.17 & 101.060004809093 & 0.109995190907085 \tabularnewline
60 & 101.22 & 101.169994122023 & 0.0500058779770001 \tabularnewline
61 & 101.84 & 101.219997327761 & 0.620002672238655 \tabularnewline
62 & 101.79 & 101.839966867993 & -0.0499668679928362 \tabularnewline
63 & 101.88 & 101.790002670154 & 0.0899973298459713 \tabularnewline
64 & 101.9 & 101.879995190678 & 0.0200048093215059 \tabularnewline
65 & 101.91 & 101.899998930973 & 0.0100010690268135 \tabularnewline
66 & 101.96 & 101.909999465558 & 0.0500005344420344 \tabularnewline
67 & 101.26 & 101.959997328047 & -0.699997328046891 \tabularnewline
68 & 101.06 & 101.260037406801 & -0.200037406800845 \tabularnewline
69 & 100.98 & 101.060010689697 & -0.0800106896971329 \tabularnewline
70 & 101.12 & 100.980004275651 & 0.13999572434949 \tabularnewline
71 & 101.24 & 101.11999251884 & 0.120007481160243 \tabularnewline
72 & 101.25 & 101.239993586981 & 0.0100064130187008 \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]101.25[/C][C]101.68[/C][C]-0.430000000000007[/C][/ROW]
[ROW][C]3[/C][C]101.24[/C][C]101.250022978551[/C][C]-0.0100229785510919[/C][/ROW]
[ROW][C]4[/C][C]101.11[/C][C]101.240000535613[/C][C]-0.130000535612837[/C][/ROW]
[ROW][C]5[/C][C]101.08[/C][C]101.110006947032[/C][C]-0.0300069470324331[/C][/ROW]
[ROW][C]6[/C][C]101.09[/C][C]101.080001603526[/C][C]0.00999839647404599[/C][/ROW]
[ROW][C]7[/C][C]101.09[/C][C]101.089999465701[/C][C]5.3429921820225e-07[/C][/ROW]
[ROW][C]8[/C][C]101.62[/C][C]101.089999999971[/C][C]0.530000000028551[/C][/ROW]
[ROW][C]9[/C][C]101.66[/C][C]101.6199716776[/C][C]0.0400283224001612[/C][/ROW]
[ROW][C]10[/C][C]101.96[/C][C]101.659997860947[/C][C]0.300002139053134[/C][/ROW]
[ROW][C]11[/C][C]102.04[/C][C]101.959983968338[/C][C]0.0800160316615859[/C][/ROW]
[ROW][C]12[/C][C]102.02[/C][C]102.039995724064[/C][C]-0.0199957240640316[/C][/ROW]
[ROW][C]13[/C][C]102.02[/C][C]102.020001068541[/C][C]-1.0685413229794e-06[/C][/ROW]
[ROW][C]14[/C][C]101.51[/C][C]102.020000000057[/C][C]-0.51000000005709[/C][/ROW]
[ROW][C]15[/C][C]101.62[/C][C]101.51002725363[/C][C]0.10997274636965[/C][/ROW]
[ROW][C]16[/C][C]101.83[/C][C]101.619994123222[/C][C]0.210005876777601[/C][/ROW]
[ROW][C]17[/C][C]102.06[/C][C]101.829988777603[/C][C]0.230011222397138[/C][/ROW]
[ROW][C]18[/C][C]102.14[/C][C]102.059987708547[/C][C]0.0800122914526185[/C][/ROW]
[ROW][C]19[/C][C]102.14[/C][C]102.139995724264[/C][C]4.27573611716525e-06[/C][/ROW]
[ROW][C]20[/C][C]102.59[/C][C]102.139999999772[/C][C]0.450000000228499[/C][/ROW]
[ROW][C]21[/C][C]102.92[/C][C]102.589975952679[/C][C]0.330024047320904[/C][/ROW]
[ROW][C]22[/C][C]103.31[/C][C]102.919982364013[/C][C]0.39001763598705[/C][/ROW]
[ROW][C]23[/C][C]103.54[/C][C]103.309979158046[/C][C]0.230020841953902[/C][/ROW]
[ROW][C]24[/C][C]103.58[/C][C]103.539987708033[/C][C]0.0400122919666472[/C][/ROW]
[ROW][C]25[/C][C]103.58[/C][C]103.579997861804[/C][C]2.13819649275138e-06[/C][/ROW]
[ROW][C]26[/C][C]102.83[/C][C]103.579999999886[/C][C]-0.749999999885745[/C][/ROW]
[ROW][C]27[/C][C]102.86[/C][C]102.830040078868[/C][C]0.0299599211318338[/C][/ROW]
[ROW][C]28[/C][C]103.03[/C][C]102.859998398987[/C][C]0.17000160101297[/C][/ROW]
[ROW][C]29[/C][C]103.2[/C][C]103.029990915371[/C][C]0.170009084629015[/C][/ROW]
[ROW][C]30[/C][C]103.28[/C][C]103.199990914971[/C][C]0.0800090850289195[/C][/ROW]
[ROW][C]31[/C][C]103.28[/C][C]103.279995724435[/C][C]4.2755647626791e-06[/C][/ROW]
[ROW][C]32[/C][C]103.79[/C][C]103.279999999772[/C][C]0.510000000228487[/C][/ROW]
[ROW][C]33[/C][C]103.92[/C][C]103.78997274637[/C][C]0.130027253630359[/C][/ROW]
[ROW][C]34[/C][C]104.26[/C][C]103.91999305154[/C][C]0.340006948460214[/C][/ROW]
[ROW][C]35[/C][C]104.41[/C][C]104.259981830542[/C][C]0.150018169458207[/C][/ROW]
[ROW][C]36[/C][C]104.45[/C][C]104.409991983255[/C][C]0.0400080167445935[/C][/ROW]
[ROW][C]37[/C][C]99.92[/C][C]104.449997862032[/C][C]-4.52999786203196[/C][/ROW]
[ROW][C]38[/C][C]99.18[/C][C]99.9202420762495[/C][C]-0.740242076249487[/C][/ROW]
[ROW][C]39[/C][C]99.18[/C][C]99.1800395574195[/C][C]-3.95574194556048e-05[/C][/ROW]
[ROW][C]40[/C][C]99.35[/C][C]99.1800000021139[/C][C]0.169999997886094[/C][/ROW]
[ROW][C]41[/C][C]99.62[/C][C]99.3499909154567[/C][C]0.270009084543346[/C][/ROW]
[ROW][C]42[/C][C]99.67[/C][C]99.619985571122[/C][C]0.0500144288780007[/C][/ROW]
[ROW][C]43[/C][C]99.72[/C][C]99.6699973273044[/C][C]0.050002672695598[/C][/ROW]
[ROW][C]44[/C][C]100.08[/C][C]99.7199973279326[/C][C]0.360002672067381[/C][/ROW]
[ROW][C]45[/C][C]100.39[/C][C]100.079980762[/C][C]0.310019237999512[/C][/ROW]
[ROW][C]46[/C][C]100.77[/C][C]100.38998343304[/C][C]0.380016566960222[/C][/ROW]
[ROW][C]47[/C][C]101.03[/C][C]100.769979692488[/C][C]0.260020307511851[/C][/ROW]
[ROW][C]48[/C][C]101.07[/C][C]101.029986104907[/C][C]0.0400138950928266[/C][/ROW]
[ROW][C]49[/C][C]101.29[/C][C]101.069997861718[/C][C]0.220002138282183[/C][/ROW]
[ROW][C]50[/C][C]101.1[/C][C]101.289988243418[/C][C]-0.189988243417744[/C][/ROW]
[ROW][C]51[/C][C]101.2[/C][C]101.100010152685[/C][C]0.0999898473150012[/C][/ROW]
[ROW][C]52[/C][C]101.15[/C][C]101.199994656693[/C][C]-0.0499946566934568[/C][/ROW]
[ROW][C]53[/C][C]101.24[/C][C]101.150002671639[/C][C]0.0899973283609796[/C][/ROW]
[ROW][C]54[/C][C]101.16[/C][C]101.239995190679[/C][C]-0.0799951906785878[/C][/ROW]
[ROW][C]55[/C][C]100.81[/C][C]101.160004274822[/C][C]-0.350004274822268[/C][/ROW]
[ROW][C]56[/C][C]101.02[/C][C]100.8100187037[/C][C]0.209981296299745[/C][/ROW]
[ROW][C]57[/C][C]101.15[/C][C]101.019988778916[/C][C]0.130011221083592[/C][/ROW]
[ROW][C]58[/C][C]101.06[/C][C]101.149993052397[/C][C]-0.0899930523965509[/C][/ROW]
[ROW][C]59[/C][C]101.17[/C][C]101.060004809093[/C][C]0.109995190907085[/C][/ROW]
[ROW][C]60[/C][C]101.22[/C][C]101.169994122023[/C][C]0.0500058779770001[/C][/ROW]
[ROW][C]61[/C][C]101.84[/C][C]101.219997327761[/C][C]0.620002672238655[/C][/ROW]
[ROW][C]62[/C][C]101.79[/C][C]101.839966867993[/C][C]-0.0499668679928362[/C][/ROW]
[ROW][C]63[/C][C]101.88[/C][C]101.790002670154[/C][C]0.0899973298459713[/C][/ROW]
[ROW][C]64[/C][C]101.9[/C][C]101.879995190678[/C][C]0.0200048093215059[/C][/ROW]
[ROW][C]65[/C][C]101.91[/C][C]101.899998930973[/C][C]0.0100010690268135[/C][/ROW]
[ROW][C]66[/C][C]101.96[/C][C]101.909999465558[/C][C]0.0500005344420344[/C][/ROW]
[ROW][C]67[/C][C]101.26[/C][C]101.959997328047[/C][C]-0.699997328046891[/C][/ROW]
[ROW][C]68[/C][C]101.06[/C][C]101.260037406801[/C][C]-0.200037406800845[/C][/ROW]
[ROW][C]69[/C][C]100.98[/C][C]101.060010689697[/C][C]-0.0800106896971329[/C][/ROW]
[ROW][C]70[/C][C]101.12[/C][C]100.980004275651[/C][C]0.13999572434949[/C][/ROW]
[ROW][C]71[/C][C]101.24[/C][C]101.11999251884[/C][C]0.120007481160243[/C][/ROW]
[ROW][C]72[/C][C]101.25[/C][C]101.239993586981[/C][C]0.0100064130187008[/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
2101.25101.68-0.430000000000007
3101.24101.250022978551-0.0100229785510919
4101.11101.240000535613-0.130000535612837
5101.08101.110006947032-0.0300069470324331
6101.09101.0800016035260.00999839647404599
7101.09101.0899994657015.3429921820225e-07
8101.62101.0899999999710.530000000028551
9101.66101.61997167760.0400283224001612
10101.96101.6599978609470.300002139053134
11102.04101.9599839683380.0800160316615859
12102.02102.039995724064-0.0199957240640316
13102.02102.020001068541-1.0685413229794e-06
14101.51102.020000000057-0.51000000005709
15101.62101.510027253630.10997274636965
16101.83101.6199941232220.210005876777601
17102.06101.8299887776030.230011222397138
18102.14102.0599877085470.0800122914526185
19102.14102.1399957242644.27573611716525e-06
20102.59102.1399999997720.450000000228499
21102.92102.5899759526790.330024047320904
22103.31102.9199823640130.39001763598705
23103.54103.3099791580460.230020841953902
24103.58103.5399877080330.0400122919666472
25103.58103.5799978618042.13819649275138e-06
26102.83103.579999999886-0.749999999885745
27102.86102.8300400788680.0299599211318338
28103.03102.8599983989870.17000160101297
29103.2103.0299909153710.170009084629015
30103.28103.1999909149710.0800090850289195
31103.28103.2799957244354.2755647626791e-06
32103.79103.2799999997720.510000000228487
33103.92103.789972746370.130027253630359
34104.26103.919993051540.340006948460214
35104.41104.2599818305420.150018169458207
36104.45104.4099919832550.0400080167445935
3799.92104.449997862032-4.52999786203196
3899.1899.9202420762495-0.740242076249487
3999.1899.1800395574195-3.95574194556048e-05
4099.3599.18000000211390.169999997886094
4199.6299.34999091545670.270009084543346
4299.6799.6199855711220.0500144288780007
4399.7299.66999732730440.050002672695598
44100.0899.71999732793260.360002672067381
45100.39100.0799807620.310019237999512
46100.77100.389983433040.380016566960222
47101.03100.7699796924880.260020307511851
48101.07101.0299861049070.0400138950928266
49101.29101.0699978617180.220002138282183
50101.1101.289988243418-0.189988243417744
51101.2101.1000101526850.0999898473150012
52101.15101.199994656693-0.0499946566934568
53101.24101.1500026716390.0899973283609796
54101.16101.239995190679-0.0799951906785878
55100.81101.160004274822-0.350004274822268
56101.02100.81001870370.209981296299745
57101.15101.0199887789160.130011221083592
58101.06101.149993052397-0.0899930523965509
59101.17101.0600048090930.109995190907085
60101.22101.1699941220230.0500058779770001
61101.84101.2199973277610.620002672238655
62101.79101.839966867993-0.0499668679928362
63101.88101.7900026701540.0899973298459713
64101.9101.8799951906780.0200048093215059
65101.91101.8999989309730.0100010690268135
66101.96101.9099994655580.0500005344420344
67101.26101.959997328047-0.699997328046891
68101.06101.260037406801-0.200037406800845
69100.98101.060010689697-0.0800106896971329
70101.12100.9800042756510.13999572434949
71101.24101.119992518840.120007481160243
72101.25101.2399935869810.0100064130187008







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.249999465272100.068927962024102.431070968521
74101.24999946527299.5797567554674102.920242175077
75101.24999946527299.204396492179103.295602438366
76101.24999946527298.8879511301615103.612047800383
77101.24999946527298.6091562000876103.890842730457
78101.24999946527298.357105764297104.142893166248
79101.24999946527298.1253211171836104.374677813361
80101.24999946527297.9095809895591104.590417940986
81101.24999946527297.7069532608378104.793045669707
82101.24999946527297.5153030625336104.984695868011
83101.24999946527297.3330187358711105.166980194674
84101.24999946527297.1588481788528105.341150751692

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.249999465272 & 100.068927962024 & 102.431070968521 \tabularnewline
74 & 101.249999465272 & 99.5797567554674 & 102.920242175077 \tabularnewline
75 & 101.249999465272 & 99.204396492179 & 103.295602438366 \tabularnewline
76 & 101.249999465272 & 98.8879511301615 & 103.612047800383 \tabularnewline
77 & 101.249999465272 & 98.6091562000876 & 103.890842730457 \tabularnewline
78 & 101.249999465272 & 98.357105764297 & 104.142893166248 \tabularnewline
79 & 101.249999465272 & 98.1253211171836 & 104.374677813361 \tabularnewline
80 & 101.249999465272 & 97.9095809895591 & 104.590417940986 \tabularnewline
81 & 101.249999465272 & 97.7069532608378 & 104.793045669707 \tabularnewline
82 & 101.249999465272 & 97.5153030625336 & 104.984695868011 \tabularnewline
83 & 101.249999465272 & 97.3330187358711 & 105.166980194674 \tabularnewline
84 & 101.249999465272 & 97.1588481788528 & 105.341150751692 \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]101.249999465272[/C][C]100.068927962024[/C][C]102.431070968521[/C][/ROW]
[ROW][C]74[/C][C]101.249999465272[/C][C]99.5797567554674[/C][C]102.920242175077[/C][/ROW]
[ROW][C]75[/C][C]101.249999465272[/C][C]99.204396492179[/C][C]103.295602438366[/C][/ROW]
[ROW][C]76[/C][C]101.249999465272[/C][C]98.8879511301615[/C][C]103.612047800383[/C][/ROW]
[ROW][C]77[/C][C]101.249999465272[/C][C]98.6091562000876[/C][C]103.890842730457[/C][/ROW]
[ROW][C]78[/C][C]101.249999465272[/C][C]98.357105764297[/C][C]104.142893166248[/C][/ROW]
[ROW][C]79[/C][C]101.249999465272[/C][C]98.1253211171836[/C][C]104.374677813361[/C][/ROW]
[ROW][C]80[/C][C]101.249999465272[/C][C]97.9095809895591[/C][C]104.590417940986[/C][/ROW]
[ROW][C]81[/C][C]101.249999465272[/C][C]97.7069532608378[/C][C]104.793045669707[/C][/ROW]
[ROW][C]82[/C][C]101.249999465272[/C][C]97.5153030625336[/C][C]104.984695868011[/C][/ROW]
[ROW][C]83[/C][C]101.249999465272[/C][C]97.3330187358711[/C][C]105.166980194674[/C][/ROW]
[ROW][C]84[/C][C]101.249999465272[/C][C]97.1588481788528[/C][C]105.341150751692[/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
73101.249999465272100.068927962024102.431070968521
74101.24999946527299.5797567554674102.920242175077
75101.24999946527299.204396492179103.295602438366
76101.24999946527298.8879511301615103.612047800383
77101.24999946527298.6091562000876103.890842730457
78101.24999946527298.357105764297104.142893166248
79101.24999946527298.1253211171836104.374677813361
80101.24999946527297.9095809895591104.590417940986
81101.24999946527297.7069532608378104.793045669707
82101.24999946527297.5153030625336104.984695868011
83101.24999946527297.3330187358711105.166980194674
84101.24999946527297.1588481788528105.341150751692



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')