Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Apr 2017 17:23:24 +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/Apr/28/t1493396720ct2pv12tcnegsdn.htm/, Retrieved Fri, 10 May 2024 02:56:58 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 02:56:58 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92.61
92.19
92.68
92.66
92.77
92.21
92.58
91.9
93.81
94.05
94.51
94.49
94.36
94.72
95.57
95.87
95.93
96.09
95.82
96.06
97.09
97.67
98.53
98.12
98.84
98.98
100.04
99.47
99.84
99.52
99.81
99.55
100.21
101.44
101
101.32
101.84
101.81
101.83
102.18
101.97
101.8
101.69
101.91
102.27
102.73
102.61
102.89
102.93
103.01
102.54
103.08
103.72
103.83
103.69
103.57
103.95
104.52
104.58
104.75
108.4
107.23
107.76
107.25
108.1
108.49
107.19
106.83
107.24
108.49
109.3
109.15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.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]'Sir Maurice George Kendall' @ kendall.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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.553887318200034
beta0
gamma0.971049904474777

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.553887318200034 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.971049904474777 \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]0.553887318200034[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.971049904474777[/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
alpha0.553887318200034
beta0
gamma0.971049904474777







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1394.3692.75130608974371.60869391025635
1494.7293.9776719564560.74232804354402
1595.5795.21250209000830.357497909991707
1695.8795.70667969292480.163320307075253
1795.9395.8224714507740.107528549226018
1896.0996.00694419482380.0830558051762438
1995.8295.8832784629695-0.0632784629694783
2096.0695.27356003577120.786439964228791
2197.0997.6769898694389-0.586989869438924
2297.6797.62136100246720.0486389975328336
2398.5398.1265489039930.403451096007046
2498.1298.3203460605409-0.200346060540852
2598.8498.76325676098080.0767432390192226
2698.9898.76578689785440.214213102145635
27100.0499.54139334290170.498606657098321
2899.47100.02961200481-0.559612004809651
2999.8499.72081186329020.119188136709838
3099.5299.9011411691093-0.381141169109327
3199.8199.45697095501840.353029044981639
3299.5599.44593602575190.104063974248135
33100.21100.876439838793-0.666439838793423
34101.44101.0521575900010.387842409999081
35101101.898929736829-0.898929736829089
36101.32101.1097911409780.210208859021776
37101.84101.900137445692-0.0601374456924759
38101.81101.886402732568-0.0764027325680274
39101.83102.624239379672-0.794239379671922
40102.18101.9379491512820.242050848718492
41101.97102.367234542289-0.397234542288643
42101.8102.04478238234-0.244782382340333
43101.69101.994180402267-0.30418040226705
44101.91101.5112744044610.398725595539318
45102.27102.77120709073-0.501207090730347
46102.73103.49515778677-0.765157786769947
47102.61103.145871041831-0.535871041831072
48102.89103.038302316147-0.148302316147436
49102.93103.512960436302-0.582960436302074
50103.01103.202594614525-0.192594614524566
51102.54103.56510888371-1.02510888371043
52103.08103.199861484559-0.119861484559053
53103.72103.1517512775090.568248722490708
54103.83103.4301099754070.399890024592992
55103.69103.710852781674-0.020852781674165
56103.57103.689375605242-0.119375605242013
57103.95104.272489857664-0.322489857664138
58104.52104.981086934264-0.461086934263662
59104.58104.899547663647-0.319547663647455
60104.75105.079691585432-0.329691585432073
61108.4105.2655876017123.13441239828815
62107.23107.1833330172280.0466669827723223
63107.76107.3177280033690.442271996631092
64107.25108.157395335273-0.907395335272966
65108.1107.9711678589060.128832141094279
66108.49107.9332066881210.556793311878806
67107.19108.118591429091-0.928591429090758
68106.83107.551649469309-0.721649469308815
69107.24107.713183244017-0.473183244016653
70108.49108.278273233350.21172676664952
71109.3108.6307114224230.669288577576836
72109.15109.354164874645-0.204164874645258

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 94.36 & 92.7513060897437 & 1.60869391025635 \tabularnewline
14 & 94.72 & 93.977671956456 & 0.74232804354402 \tabularnewline
15 & 95.57 & 95.2125020900083 & 0.357497909991707 \tabularnewline
16 & 95.87 & 95.7066796929248 & 0.163320307075253 \tabularnewline
17 & 95.93 & 95.822471450774 & 0.107528549226018 \tabularnewline
18 & 96.09 & 96.0069441948238 & 0.0830558051762438 \tabularnewline
19 & 95.82 & 95.8832784629695 & -0.0632784629694783 \tabularnewline
20 & 96.06 & 95.2735600357712 & 0.786439964228791 \tabularnewline
21 & 97.09 & 97.6769898694389 & -0.586989869438924 \tabularnewline
22 & 97.67 & 97.6213610024672 & 0.0486389975328336 \tabularnewline
23 & 98.53 & 98.126548903993 & 0.403451096007046 \tabularnewline
24 & 98.12 & 98.3203460605409 & -0.200346060540852 \tabularnewline
25 & 98.84 & 98.7632567609808 & 0.0767432390192226 \tabularnewline
26 & 98.98 & 98.7657868978544 & 0.214213102145635 \tabularnewline
27 & 100.04 & 99.5413933429017 & 0.498606657098321 \tabularnewline
28 & 99.47 & 100.02961200481 & -0.559612004809651 \tabularnewline
29 & 99.84 & 99.7208118632902 & 0.119188136709838 \tabularnewline
30 & 99.52 & 99.9011411691093 & -0.381141169109327 \tabularnewline
31 & 99.81 & 99.4569709550184 & 0.353029044981639 \tabularnewline
32 & 99.55 & 99.4459360257519 & 0.104063974248135 \tabularnewline
33 & 100.21 & 100.876439838793 & -0.666439838793423 \tabularnewline
34 & 101.44 & 101.052157590001 & 0.387842409999081 \tabularnewline
35 & 101 & 101.898929736829 & -0.898929736829089 \tabularnewline
36 & 101.32 & 101.109791140978 & 0.210208859021776 \tabularnewline
37 & 101.84 & 101.900137445692 & -0.0601374456924759 \tabularnewline
38 & 101.81 & 101.886402732568 & -0.0764027325680274 \tabularnewline
39 & 101.83 & 102.624239379672 & -0.794239379671922 \tabularnewline
40 & 102.18 & 101.937949151282 & 0.242050848718492 \tabularnewline
41 & 101.97 & 102.367234542289 & -0.397234542288643 \tabularnewline
42 & 101.8 & 102.04478238234 & -0.244782382340333 \tabularnewline
43 & 101.69 & 101.994180402267 & -0.30418040226705 \tabularnewline
44 & 101.91 & 101.511274404461 & 0.398725595539318 \tabularnewline
45 & 102.27 & 102.77120709073 & -0.501207090730347 \tabularnewline
46 & 102.73 & 103.49515778677 & -0.765157786769947 \tabularnewline
47 & 102.61 & 103.145871041831 & -0.535871041831072 \tabularnewline
48 & 102.89 & 103.038302316147 & -0.148302316147436 \tabularnewline
49 & 102.93 & 103.512960436302 & -0.582960436302074 \tabularnewline
50 & 103.01 & 103.202594614525 & -0.192594614524566 \tabularnewline
51 & 102.54 & 103.56510888371 & -1.02510888371043 \tabularnewline
52 & 103.08 & 103.199861484559 & -0.119861484559053 \tabularnewline
53 & 103.72 & 103.151751277509 & 0.568248722490708 \tabularnewline
54 & 103.83 & 103.430109975407 & 0.399890024592992 \tabularnewline
55 & 103.69 & 103.710852781674 & -0.020852781674165 \tabularnewline
56 & 103.57 & 103.689375605242 & -0.119375605242013 \tabularnewline
57 & 103.95 & 104.272489857664 & -0.322489857664138 \tabularnewline
58 & 104.52 & 104.981086934264 & -0.461086934263662 \tabularnewline
59 & 104.58 & 104.899547663647 & -0.319547663647455 \tabularnewline
60 & 104.75 & 105.079691585432 & -0.329691585432073 \tabularnewline
61 & 108.4 & 105.265587601712 & 3.13441239828815 \tabularnewline
62 & 107.23 & 107.183333017228 & 0.0466669827723223 \tabularnewline
63 & 107.76 & 107.317728003369 & 0.442271996631092 \tabularnewline
64 & 107.25 & 108.157395335273 & -0.907395335272966 \tabularnewline
65 & 108.1 & 107.971167858906 & 0.128832141094279 \tabularnewline
66 & 108.49 & 107.933206688121 & 0.556793311878806 \tabularnewline
67 & 107.19 & 108.118591429091 & -0.928591429090758 \tabularnewline
68 & 106.83 & 107.551649469309 & -0.721649469308815 \tabularnewline
69 & 107.24 & 107.713183244017 & -0.473183244016653 \tabularnewline
70 & 108.49 & 108.27827323335 & 0.21172676664952 \tabularnewline
71 & 109.3 & 108.630711422423 & 0.669288577576836 \tabularnewline
72 & 109.15 & 109.354164874645 & -0.204164874645258 \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]13[/C][C]94.36[/C][C]92.7513060897437[/C][C]1.60869391025635[/C][/ROW]
[ROW][C]14[/C][C]94.72[/C][C]93.977671956456[/C][C]0.74232804354402[/C][/ROW]
[ROW][C]15[/C][C]95.57[/C][C]95.2125020900083[/C][C]0.357497909991707[/C][/ROW]
[ROW][C]16[/C][C]95.87[/C][C]95.7066796929248[/C][C]0.163320307075253[/C][/ROW]
[ROW][C]17[/C][C]95.93[/C][C]95.822471450774[/C][C]0.107528549226018[/C][/ROW]
[ROW][C]18[/C][C]96.09[/C][C]96.0069441948238[/C][C]0.0830558051762438[/C][/ROW]
[ROW][C]19[/C][C]95.82[/C][C]95.8832784629695[/C][C]-0.0632784629694783[/C][/ROW]
[ROW][C]20[/C][C]96.06[/C][C]95.2735600357712[/C][C]0.786439964228791[/C][/ROW]
[ROW][C]21[/C][C]97.09[/C][C]97.6769898694389[/C][C]-0.586989869438924[/C][/ROW]
[ROW][C]22[/C][C]97.67[/C][C]97.6213610024672[/C][C]0.0486389975328336[/C][/ROW]
[ROW][C]23[/C][C]98.53[/C][C]98.126548903993[/C][C]0.403451096007046[/C][/ROW]
[ROW][C]24[/C][C]98.12[/C][C]98.3203460605409[/C][C]-0.200346060540852[/C][/ROW]
[ROW][C]25[/C][C]98.84[/C][C]98.7632567609808[/C][C]0.0767432390192226[/C][/ROW]
[ROW][C]26[/C][C]98.98[/C][C]98.7657868978544[/C][C]0.214213102145635[/C][/ROW]
[ROW][C]27[/C][C]100.04[/C][C]99.5413933429017[/C][C]0.498606657098321[/C][/ROW]
[ROW][C]28[/C][C]99.47[/C][C]100.02961200481[/C][C]-0.559612004809651[/C][/ROW]
[ROW][C]29[/C][C]99.84[/C][C]99.7208118632902[/C][C]0.119188136709838[/C][/ROW]
[ROW][C]30[/C][C]99.52[/C][C]99.9011411691093[/C][C]-0.381141169109327[/C][/ROW]
[ROW][C]31[/C][C]99.81[/C][C]99.4569709550184[/C][C]0.353029044981639[/C][/ROW]
[ROW][C]32[/C][C]99.55[/C][C]99.4459360257519[/C][C]0.104063974248135[/C][/ROW]
[ROW][C]33[/C][C]100.21[/C][C]100.876439838793[/C][C]-0.666439838793423[/C][/ROW]
[ROW][C]34[/C][C]101.44[/C][C]101.052157590001[/C][C]0.387842409999081[/C][/ROW]
[ROW][C]35[/C][C]101[/C][C]101.898929736829[/C][C]-0.898929736829089[/C][/ROW]
[ROW][C]36[/C][C]101.32[/C][C]101.109791140978[/C][C]0.210208859021776[/C][/ROW]
[ROW][C]37[/C][C]101.84[/C][C]101.900137445692[/C][C]-0.0601374456924759[/C][/ROW]
[ROW][C]38[/C][C]101.81[/C][C]101.886402732568[/C][C]-0.0764027325680274[/C][/ROW]
[ROW][C]39[/C][C]101.83[/C][C]102.624239379672[/C][C]-0.794239379671922[/C][/ROW]
[ROW][C]40[/C][C]102.18[/C][C]101.937949151282[/C][C]0.242050848718492[/C][/ROW]
[ROW][C]41[/C][C]101.97[/C][C]102.367234542289[/C][C]-0.397234542288643[/C][/ROW]
[ROW][C]42[/C][C]101.8[/C][C]102.04478238234[/C][C]-0.244782382340333[/C][/ROW]
[ROW][C]43[/C][C]101.69[/C][C]101.994180402267[/C][C]-0.30418040226705[/C][/ROW]
[ROW][C]44[/C][C]101.91[/C][C]101.511274404461[/C][C]0.398725595539318[/C][/ROW]
[ROW][C]45[/C][C]102.27[/C][C]102.77120709073[/C][C]-0.501207090730347[/C][/ROW]
[ROW][C]46[/C][C]102.73[/C][C]103.49515778677[/C][C]-0.765157786769947[/C][/ROW]
[ROW][C]47[/C][C]102.61[/C][C]103.145871041831[/C][C]-0.535871041831072[/C][/ROW]
[ROW][C]48[/C][C]102.89[/C][C]103.038302316147[/C][C]-0.148302316147436[/C][/ROW]
[ROW][C]49[/C][C]102.93[/C][C]103.512960436302[/C][C]-0.582960436302074[/C][/ROW]
[ROW][C]50[/C][C]103.01[/C][C]103.202594614525[/C][C]-0.192594614524566[/C][/ROW]
[ROW][C]51[/C][C]102.54[/C][C]103.56510888371[/C][C]-1.02510888371043[/C][/ROW]
[ROW][C]52[/C][C]103.08[/C][C]103.199861484559[/C][C]-0.119861484559053[/C][/ROW]
[ROW][C]53[/C][C]103.72[/C][C]103.151751277509[/C][C]0.568248722490708[/C][/ROW]
[ROW][C]54[/C][C]103.83[/C][C]103.430109975407[/C][C]0.399890024592992[/C][/ROW]
[ROW][C]55[/C][C]103.69[/C][C]103.710852781674[/C][C]-0.020852781674165[/C][/ROW]
[ROW][C]56[/C][C]103.57[/C][C]103.689375605242[/C][C]-0.119375605242013[/C][/ROW]
[ROW][C]57[/C][C]103.95[/C][C]104.272489857664[/C][C]-0.322489857664138[/C][/ROW]
[ROW][C]58[/C][C]104.52[/C][C]104.981086934264[/C][C]-0.461086934263662[/C][/ROW]
[ROW][C]59[/C][C]104.58[/C][C]104.899547663647[/C][C]-0.319547663647455[/C][/ROW]
[ROW][C]60[/C][C]104.75[/C][C]105.079691585432[/C][C]-0.329691585432073[/C][/ROW]
[ROW][C]61[/C][C]108.4[/C][C]105.265587601712[/C][C]3.13441239828815[/C][/ROW]
[ROW][C]62[/C][C]107.23[/C][C]107.183333017228[/C][C]0.0466669827723223[/C][/ROW]
[ROW][C]63[/C][C]107.76[/C][C]107.317728003369[/C][C]0.442271996631092[/C][/ROW]
[ROW][C]64[/C][C]107.25[/C][C]108.157395335273[/C][C]-0.907395335272966[/C][/ROW]
[ROW][C]65[/C][C]108.1[/C][C]107.971167858906[/C][C]0.128832141094279[/C][/ROW]
[ROW][C]66[/C][C]108.49[/C][C]107.933206688121[/C][C]0.556793311878806[/C][/ROW]
[ROW][C]67[/C][C]107.19[/C][C]108.118591429091[/C][C]-0.928591429090758[/C][/ROW]
[ROW][C]68[/C][C]106.83[/C][C]107.551649469309[/C][C]-0.721649469308815[/C][/ROW]
[ROW][C]69[/C][C]107.24[/C][C]107.713183244017[/C][C]-0.473183244016653[/C][/ROW]
[ROW][C]70[/C][C]108.49[/C][C]108.27827323335[/C][C]0.21172676664952[/C][/ROW]
[ROW][C]71[/C][C]109.3[/C][C]108.630711422423[/C][C]0.669288577576836[/C][/ROW]
[ROW][C]72[/C][C]109.15[/C][C]109.354164874645[/C][C]-0.204164874645258[/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
1394.3692.75130608974371.60869391025635
1494.7293.9776719564560.74232804354402
1595.5795.21250209000830.357497909991707
1695.8795.70667969292480.163320307075253
1795.9395.8224714507740.107528549226018
1896.0996.00694419482380.0830558051762438
1995.8295.8832784629695-0.0632784629694783
2096.0695.27356003577120.786439964228791
2197.0997.6769898694389-0.586989869438924
2297.6797.62136100246720.0486389975328336
2398.5398.1265489039930.403451096007046
2498.1298.3203460605409-0.200346060540852
2598.8498.76325676098080.0767432390192226
2698.9898.76578689785440.214213102145635
27100.0499.54139334290170.498606657098321
2899.47100.02961200481-0.559612004809651
2999.8499.72081186329020.119188136709838
3099.5299.9011411691093-0.381141169109327
3199.8199.45697095501840.353029044981639
3299.5599.44593602575190.104063974248135
33100.21100.876439838793-0.666439838793423
34101.44101.0521575900010.387842409999081
35101101.898929736829-0.898929736829089
36101.32101.1097911409780.210208859021776
37101.84101.900137445692-0.0601374456924759
38101.81101.886402732568-0.0764027325680274
39101.83102.624239379672-0.794239379671922
40102.18101.9379491512820.242050848718492
41101.97102.367234542289-0.397234542288643
42101.8102.04478238234-0.244782382340333
43101.69101.994180402267-0.30418040226705
44101.91101.5112744044610.398725595539318
45102.27102.77120709073-0.501207090730347
46102.73103.49515778677-0.765157786769947
47102.61103.145871041831-0.535871041831072
48102.89103.038302316147-0.148302316147436
49102.93103.512960436302-0.582960436302074
50103.01103.202594614525-0.192594614524566
51102.54103.56510888371-1.02510888371043
52103.08103.199861484559-0.119861484559053
53103.72103.1517512775090.568248722490708
54103.83103.4301099754070.399890024592992
55103.69103.710852781674-0.020852781674165
56103.57103.689375605242-0.119375605242013
57103.95104.272489857664-0.322489857664138
58104.52104.981086934264-0.461086934263662
59104.58104.899547663647-0.319547663647455
60104.75105.079691585432-0.329691585432073
61108.4105.2655876017123.13441239828815
62107.23107.1833330172280.0466669827723223
63107.76107.3177280033690.442271996631092
64107.25108.157395335273-0.907395335272966
65108.1107.9711678589060.128832141094279
66108.49107.9332066881210.556793311878806
67107.19108.118591429091-0.928591429090758
68106.83107.551649469309-0.721649469308815
69107.24107.713183244017-0.473183244016653
70108.49108.278273233350.21172676664952
71109.3108.6307114224230.669288577576836
72109.15109.354164874645-0.204164874645258







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73111.110230342922109.836389082937112.384071602906
74109.954260339703108.498069127485111.410451551921
75110.23418224894108.616061691798111.852302806081
76110.244207977748108.478950084876112.00946587062
77111.009466605837109.108425649084112.910507562589
78111.085538730974109.057786771253113.113290690695
79110.319057498326108.172059757048112.466055239605
80110.356097331168108.096137023561112.616057638774
81111.024978586733108.657439382652113.392517790814
82112.148860199719109.678422349102114.619298050336
83112.58224033142110.013021682752115.151458980088
84112.556605321795109.892265674609115.220944968981

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 111.110230342922 & 109.836389082937 & 112.384071602906 \tabularnewline
74 & 109.954260339703 & 108.498069127485 & 111.410451551921 \tabularnewline
75 & 110.23418224894 & 108.616061691798 & 111.852302806081 \tabularnewline
76 & 110.244207977748 & 108.478950084876 & 112.00946587062 \tabularnewline
77 & 111.009466605837 & 109.108425649084 & 112.910507562589 \tabularnewline
78 & 111.085538730974 & 109.057786771253 & 113.113290690695 \tabularnewline
79 & 110.319057498326 & 108.172059757048 & 112.466055239605 \tabularnewline
80 & 110.356097331168 & 108.096137023561 & 112.616057638774 \tabularnewline
81 & 111.024978586733 & 108.657439382652 & 113.392517790814 \tabularnewline
82 & 112.148860199719 & 109.678422349102 & 114.619298050336 \tabularnewline
83 & 112.58224033142 & 110.013021682752 & 115.151458980088 \tabularnewline
84 & 112.556605321795 & 109.892265674609 & 115.220944968981 \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]111.110230342922[/C][C]109.836389082937[/C][C]112.384071602906[/C][/ROW]
[ROW][C]74[/C][C]109.954260339703[/C][C]108.498069127485[/C][C]111.410451551921[/C][/ROW]
[ROW][C]75[/C][C]110.23418224894[/C][C]108.616061691798[/C][C]111.852302806081[/C][/ROW]
[ROW][C]76[/C][C]110.244207977748[/C][C]108.478950084876[/C][C]112.00946587062[/C][/ROW]
[ROW][C]77[/C][C]111.009466605837[/C][C]109.108425649084[/C][C]112.910507562589[/C][/ROW]
[ROW][C]78[/C][C]111.085538730974[/C][C]109.057786771253[/C][C]113.113290690695[/C][/ROW]
[ROW][C]79[/C][C]110.319057498326[/C][C]108.172059757048[/C][C]112.466055239605[/C][/ROW]
[ROW][C]80[/C][C]110.356097331168[/C][C]108.096137023561[/C][C]112.616057638774[/C][/ROW]
[ROW][C]81[/C][C]111.024978586733[/C][C]108.657439382652[/C][C]113.392517790814[/C][/ROW]
[ROW][C]82[/C][C]112.148860199719[/C][C]109.678422349102[/C][C]114.619298050336[/C][/ROW]
[ROW][C]83[/C][C]112.58224033142[/C][C]110.013021682752[/C][C]115.151458980088[/C][/ROW]
[ROW][C]84[/C][C]112.556605321795[/C][C]109.892265674609[/C][C]115.220944968981[/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
73111.110230342922109.836389082937112.384071602906
74109.954260339703108.498069127485111.410451551921
75110.23418224894108.616061691798111.852302806081
76110.244207977748108.478950084876112.00946587062
77111.009466605837109.108425649084112.910507562589
78111.085538730974109.057786771253113.113290690695
79110.319057498326108.172059757048112.466055239605
80110.356097331168108.096137023561112.616057638774
81111.024978586733108.657439382652113.392517790814
82112.148860199719109.678422349102114.619298050336
83112.58224033142110.013021682752115.151458980088
84112.556605321795109.892265674609115.220944968981



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=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')