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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 03:26:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t1355732797wr2hrnm1uud5ses.htm/, Retrieved Thu, 25 Apr 2024 20:44:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200704, Retrieved Thu, 25 Apr 2024 20:44:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 08:26:23] [6e9dcd0648fbf01fc48a73ddbea19f30] [Current]
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Dataseries X:
98.01
99.2
100.7
106.41
107.51
107.1
99.75
98.96
107.26
107.11
107.2
107.65
104.78
105.56
107.95
107.11
107.47
107.06
99.71
99.6
107.19
107.26
113.24
113.52
110.48
111.41
115.5
118.32
118.42
117.5
110.23
109.19
118.41
118.3
116.1
114.11
113.41
114.33
116.61
123.64
123.77
123.39
116.03
114.95
123.4
123.53
114.45
114.26
114.35
112.77
115.31
114.93
116.38
115.07
105
103.43
114.52
115.04
117.16
115
116.22
112.92
116.56
114.32
113.22
111.56
103.87
102.85
112.27
112.76
118.55
122.73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200704&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200704&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200704&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.941725131736059
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.941725131736059 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200704&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]0.941725131736059[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200704&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200704&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
alpha0.941725131736059
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.78103.7908497149840.989150285015697
14105.56105.614037111009-0.0540371110088813
15107.95108.069103444206-0.119103444205763
16107.11107.252552972171-0.142552972170506
17107.47107.3559028122890.114097187710854
18107.06106.6923531058220.367646894178492
1999.71102.036699270851-2.32669927085055
2099.698.66706950209240.932930497907591
21107.19107.453475020569-0.263475020569501
22107.26106.8588583316840.40114166831583
23113.24107.4380168562755.8019831437247
24113.52113.5192117946080.00078820539215485
25110.48110.693926844879-0.213926844878543
26111.41111.3611794877670.0488205122330356
27115.5114.0401472575941.45985274240644
28118.32114.6507433516743.66925664832605
29118.42118.3703580131510.0496419868489539
30117.5117.569718917193-0.0697189171925885
31110.23111.825842497473-1.59584249747313
32109.19109.214873198194-0.0248731981941717
33118.41117.7708820363470.639117963653277
34118.3118.0182721372820.2817278627181
35116.1118.820357978662-2.72035797866249
36114.11116.541503362267-2.43150336226712
37113.41111.3939595484352.0160404515654
38114.33114.1955542876370.134445712363146
39116.61117.103653357213-0.493653357213276
40123.64115.9893805318687.65061946813211
41123.77123.2438708769740.52612912302645
42123.39122.8404174283620.549582571638069
43116.03117.295430711571-1.2654307115712
44114.95115.026084125287-0.076084125286755
45123.4124.019954786072-0.619954786071744
46123.53123.0389403020830.491059697916626
47114.45123.869343813906-9.4193438139056
48114.26115.294386882796-1.03438688279613
49114.35111.7147106728382.63528932716223
50112.77114.994360348226-2.22436034822555
51115.31115.61180977227-0.301809772269877
52114.93115.130479456671-0.200479456671331
53116.38114.6116055139671.76839448603272
54115.07115.441961003818-0.371961003818257
55105109.346304625988-4.34630462598807
56103.43104.350630591449-0.920630591449154
57114.52111.630132442622.88986755738046
58115.04114.0536360357610.986363964238649
59117.16114.7576455181692.40235448183077
60115117.818059500949-2.81805950094861
61116.22112.7491326502013.47086734979895
62112.92116.53554185632-3.61554185631958
63116.56115.963458514980.596541485020069
64114.32116.330525638085-2.01052563808499
65113.22114.221872904957-1.00187290495687
66111.56112.347860495145-0.787860495144784
67103.87105.803250085783-1.93325008578299
68102.85103.287263454452-0.437263454452051
69112.27111.1959183190961.0740816809037
70112.76111.8091390543660.950860945633693
71118.55112.5652902266035.98470977339736
72122.73118.6944116585534.03558834144697

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.78 & 103.790849714984 & 0.989150285015697 \tabularnewline
14 & 105.56 & 105.614037111009 & -0.0540371110088813 \tabularnewline
15 & 107.95 & 108.069103444206 & -0.119103444205763 \tabularnewline
16 & 107.11 & 107.252552972171 & -0.142552972170506 \tabularnewline
17 & 107.47 & 107.355902812289 & 0.114097187710854 \tabularnewline
18 & 107.06 & 106.692353105822 & 0.367646894178492 \tabularnewline
19 & 99.71 & 102.036699270851 & -2.32669927085055 \tabularnewline
20 & 99.6 & 98.6670695020924 & 0.932930497907591 \tabularnewline
21 & 107.19 & 107.453475020569 & -0.263475020569501 \tabularnewline
22 & 107.26 & 106.858858331684 & 0.40114166831583 \tabularnewline
23 & 113.24 & 107.438016856275 & 5.8019831437247 \tabularnewline
24 & 113.52 & 113.519211794608 & 0.00078820539215485 \tabularnewline
25 & 110.48 & 110.693926844879 & -0.213926844878543 \tabularnewline
26 & 111.41 & 111.361179487767 & 0.0488205122330356 \tabularnewline
27 & 115.5 & 114.040147257594 & 1.45985274240644 \tabularnewline
28 & 118.32 & 114.650743351674 & 3.66925664832605 \tabularnewline
29 & 118.42 & 118.370358013151 & 0.0496419868489539 \tabularnewline
30 & 117.5 & 117.569718917193 & -0.0697189171925885 \tabularnewline
31 & 110.23 & 111.825842497473 & -1.59584249747313 \tabularnewline
32 & 109.19 & 109.214873198194 & -0.0248731981941717 \tabularnewline
33 & 118.41 & 117.770882036347 & 0.639117963653277 \tabularnewline
34 & 118.3 & 118.018272137282 & 0.2817278627181 \tabularnewline
35 & 116.1 & 118.820357978662 & -2.72035797866249 \tabularnewline
36 & 114.11 & 116.541503362267 & -2.43150336226712 \tabularnewline
37 & 113.41 & 111.393959548435 & 2.0160404515654 \tabularnewline
38 & 114.33 & 114.195554287637 & 0.134445712363146 \tabularnewline
39 & 116.61 & 117.103653357213 & -0.493653357213276 \tabularnewline
40 & 123.64 & 115.989380531868 & 7.65061946813211 \tabularnewline
41 & 123.77 & 123.243870876974 & 0.52612912302645 \tabularnewline
42 & 123.39 & 122.840417428362 & 0.549582571638069 \tabularnewline
43 & 116.03 & 117.295430711571 & -1.2654307115712 \tabularnewline
44 & 114.95 & 115.026084125287 & -0.076084125286755 \tabularnewline
45 & 123.4 & 124.019954786072 & -0.619954786071744 \tabularnewline
46 & 123.53 & 123.038940302083 & 0.491059697916626 \tabularnewline
47 & 114.45 & 123.869343813906 & -9.4193438139056 \tabularnewline
48 & 114.26 & 115.294386882796 & -1.03438688279613 \tabularnewline
49 & 114.35 & 111.714710672838 & 2.63528932716223 \tabularnewline
50 & 112.77 & 114.994360348226 & -2.22436034822555 \tabularnewline
51 & 115.31 & 115.61180977227 & -0.301809772269877 \tabularnewline
52 & 114.93 & 115.130479456671 & -0.200479456671331 \tabularnewline
53 & 116.38 & 114.611605513967 & 1.76839448603272 \tabularnewline
54 & 115.07 & 115.441961003818 & -0.371961003818257 \tabularnewline
55 & 105 & 109.346304625988 & -4.34630462598807 \tabularnewline
56 & 103.43 & 104.350630591449 & -0.920630591449154 \tabularnewline
57 & 114.52 & 111.63013244262 & 2.88986755738046 \tabularnewline
58 & 115.04 & 114.053636035761 & 0.986363964238649 \tabularnewline
59 & 117.16 & 114.757645518169 & 2.40235448183077 \tabularnewline
60 & 115 & 117.818059500949 & -2.81805950094861 \tabularnewline
61 & 116.22 & 112.749132650201 & 3.47086734979895 \tabularnewline
62 & 112.92 & 116.53554185632 & -3.61554185631958 \tabularnewline
63 & 116.56 & 115.96345851498 & 0.596541485020069 \tabularnewline
64 & 114.32 & 116.330525638085 & -2.01052563808499 \tabularnewline
65 & 113.22 & 114.221872904957 & -1.00187290495687 \tabularnewline
66 & 111.56 & 112.347860495145 & -0.787860495144784 \tabularnewline
67 & 103.87 & 105.803250085783 & -1.93325008578299 \tabularnewline
68 & 102.85 & 103.287263454452 & -0.437263454452051 \tabularnewline
69 & 112.27 & 111.195918319096 & 1.0740816809037 \tabularnewline
70 & 112.76 & 111.809139054366 & 0.950860945633693 \tabularnewline
71 & 118.55 & 112.565290226603 & 5.98470977339736 \tabularnewline
72 & 122.73 & 118.694411658553 & 4.03558834144697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200704&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]104.78[/C][C]103.790849714984[/C][C]0.989150285015697[/C][/ROW]
[ROW][C]14[/C][C]105.56[/C][C]105.614037111009[/C][C]-0.0540371110088813[/C][/ROW]
[ROW][C]15[/C][C]107.95[/C][C]108.069103444206[/C][C]-0.119103444205763[/C][/ROW]
[ROW][C]16[/C][C]107.11[/C][C]107.252552972171[/C][C]-0.142552972170506[/C][/ROW]
[ROW][C]17[/C][C]107.47[/C][C]107.355902812289[/C][C]0.114097187710854[/C][/ROW]
[ROW][C]18[/C][C]107.06[/C][C]106.692353105822[/C][C]0.367646894178492[/C][/ROW]
[ROW][C]19[/C][C]99.71[/C][C]102.036699270851[/C][C]-2.32669927085055[/C][/ROW]
[ROW][C]20[/C][C]99.6[/C][C]98.6670695020924[/C][C]0.932930497907591[/C][/ROW]
[ROW][C]21[/C][C]107.19[/C][C]107.453475020569[/C][C]-0.263475020569501[/C][/ROW]
[ROW][C]22[/C][C]107.26[/C][C]106.858858331684[/C][C]0.40114166831583[/C][/ROW]
[ROW][C]23[/C][C]113.24[/C][C]107.438016856275[/C][C]5.8019831437247[/C][/ROW]
[ROW][C]24[/C][C]113.52[/C][C]113.519211794608[/C][C]0.00078820539215485[/C][/ROW]
[ROW][C]25[/C][C]110.48[/C][C]110.693926844879[/C][C]-0.213926844878543[/C][/ROW]
[ROW][C]26[/C][C]111.41[/C][C]111.361179487767[/C][C]0.0488205122330356[/C][/ROW]
[ROW][C]27[/C][C]115.5[/C][C]114.040147257594[/C][C]1.45985274240644[/C][/ROW]
[ROW][C]28[/C][C]118.32[/C][C]114.650743351674[/C][C]3.66925664832605[/C][/ROW]
[ROW][C]29[/C][C]118.42[/C][C]118.370358013151[/C][C]0.0496419868489539[/C][/ROW]
[ROW][C]30[/C][C]117.5[/C][C]117.569718917193[/C][C]-0.0697189171925885[/C][/ROW]
[ROW][C]31[/C][C]110.23[/C][C]111.825842497473[/C][C]-1.59584249747313[/C][/ROW]
[ROW][C]32[/C][C]109.19[/C][C]109.214873198194[/C][C]-0.0248731981941717[/C][/ROW]
[ROW][C]33[/C][C]118.41[/C][C]117.770882036347[/C][C]0.639117963653277[/C][/ROW]
[ROW][C]34[/C][C]118.3[/C][C]118.018272137282[/C][C]0.2817278627181[/C][/ROW]
[ROW][C]35[/C][C]116.1[/C][C]118.820357978662[/C][C]-2.72035797866249[/C][/ROW]
[ROW][C]36[/C][C]114.11[/C][C]116.541503362267[/C][C]-2.43150336226712[/C][/ROW]
[ROW][C]37[/C][C]113.41[/C][C]111.393959548435[/C][C]2.0160404515654[/C][/ROW]
[ROW][C]38[/C][C]114.33[/C][C]114.195554287637[/C][C]0.134445712363146[/C][/ROW]
[ROW][C]39[/C][C]116.61[/C][C]117.103653357213[/C][C]-0.493653357213276[/C][/ROW]
[ROW][C]40[/C][C]123.64[/C][C]115.989380531868[/C][C]7.65061946813211[/C][/ROW]
[ROW][C]41[/C][C]123.77[/C][C]123.243870876974[/C][C]0.52612912302645[/C][/ROW]
[ROW][C]42[/C][C]123.39[/C][C]122.840417428362[/C][C]0.549582571638069[/C][/ROW]
[ROW][C]43[/C][C]116.03[/C][C]117.295430711571[/C][C]-1.2654307115712[/C][/ROW]
[ROW][C]44[/C][C]114.95[/C][C]115.026084125287[/C][C]-0.076084125286755[/C][/ROW]
[ROW][C]45[/C][C]123.4[/C][C]124.019954786072[/C][C]-0.619954786071744[/C][/ROW]
[ROW][C]46[/C][C]123.53[/C][C]123.038940302083[/C][C]0.491059697916626[/C][/ROW]
[ROW][C]47[/C][C]114.45[/C][C]123.869343813906[/C][C]-9.4193438139056[/C][/ROW]
[ROW][C]48[/C][C]114.26[/C][C]115.294386882796[/C][C]-1.03438688279613[/C][/ROW]
[ROW][C]49[/C][C]114.35[/C][C]111.714710672838[/C][C]2.63528932716223[/C][/ROW]
[ROW][C]50[/C][C]112.77[/C][C]114.994360348226[/C][C]-2.22436034822555[/C][/ROW]
[ROW][C]51[/C][C]115.31[/C][C]115.61180977227[/C][C]-0.301809772269877[/C][/ROW]
[ROW][C]52[/C][C]114.93[/C][C]115.130479456671[/C][C]-0.200479456671331[/C][/ROW]
[ROW][C]53[/C][C]116.38[/C][C]114.611605513967[/C][C]1.76839448603272[/C][/ROW]
[ROW][C]54[/C][C]115.07[/C][C]115.441961003818[/C][C]-0.371961003818257[/C][/ROW]
[ROW][C]55[/C][C]105[/C][C]109.346304625988[/C][C]-4.34630462598807[/C][/ROW]
[ROW][C]56[/C][C]103.43[/C][C]104.350630591449[/C][C]-0.920630591449154[/C][/ROW]
[ROW][C]57[/C][C]114.52[/C][C]111.63013244262[/C][C]2.88986755738046[/C][/ROW]
[ROW][C]58[/C][C]115.04[/C][C]114.053636035761[/C][C]0.986363964238649[/C][/ROW]
[ROW][C]59[/C][C]117.16[/C][C]114.757645518169[/C][C]2.40235448183077[/C][/ROW]
[ROW][C]60[/C][C]115[/C][C]117.818059500949[/C][C]-2.81805950094861[/C][/ROW]
[ROW][C]61[/C][C]116.22[/C][C]112.749132650201[/C][C]3.47086734979895[/C][/ROW]
[ROW][C]62[/C][C]112.92[/C][C]116.53554185632[/C][C]-3.61554185631958[/C][/ROW]
[ROW][C]63[/C][C]116.56[/C][C]115.96345851498[/C][C]0.596541485020069[/C][/ROW]
[ROW][C]64[/C][C]114.32[/C][C]116.330525638085[/C][C]-2.01052563808499[/C][/ROW]
[ROW][C]65[/C][C]113.22[/C][C]114.221872904957[/C][C]-1.00187290495687[/C][/ROW]
[ROW][C]66[/C][C]111.56[/C][C]112.347860495145[/C][C]-0.787860495144784[/C][/ROW]
[ROW][C]67[/C][C]103.87[/C][C]105.803250085783[/C][C]-1.93325008578299[/C][/ROW]
[ROW][C]68[/C][C]102.85[/C][C]103.287263454452[/C][C]-0.437263454452051[/C][/ROW]
[ROW][C]69[/C][C]112.27[/C][C]111.195918319096[/C][C]1.0740816809037[/C][/ROW]
[ROW][C]70[/C][C]112.76[/C][C]111.809139054366[/C][C]0.950860945633693[/C][/ROW]
[ROW][C]71[/C][C]118.55[/C][C]112.565290226603[/C][C]5.98470977339736[/C][/ROW]
[ROW][C]72[/C][C]122.73[/C][C]118.694411658553[/C][C]4.03558834144697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200704&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200704&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
13104.78103.7908497149840.989150285015697
14105.56105.614037111009-0.0540371110088813
15107.95108.069103444206-0.119103444205763
16107.11107.252552972171-0.142552972170506
17107.47107.3559028122890.114097187710854
18107.06106.6923531058220.367646894178492
1999.71102.036699270851-2.32669927085055
2099.698.66706950209240.932930497907591
21107.19107.453475020569-0.263475020569501
22107.26106.8588583316840.40114166831583
23113.24107.4380168562755.8019831437247
24113.52113.5192117946080.00078820539215485
25110.48110.693926844879-0.213926844878543
26111.41111.3611794877670.0488205122330356
27115.5114.0401472575941.45985274240644
28118.32114.6507433516743.66925664832605
29118.42118.3703580131510.0496419868489539
30117.5117.569718917193-0.0697189171925885
31110.23111.825842497473-1.59584249747313
32109.19109.214873198194-0.0248731981941717
33118.41117.7708820363470.639117963653277
34118.3118.0182721372820.2817278627181
35116.1118.820357978662-2.72035797866249
36114.11116.541503362267-2.43150336226712
37113.41111.3939595484352.0160404515654
38114.33114.1955542876370.134445712363146
39116.61117.103653357213-0.493653357213276
40123.64115.9893805318687.65061946813211
41123.77123.2438708769740.52612912302645
42123.39122.8404174283620.549582571638069
43116.03117.295430711571-1.2654307115712
44114.95115.026084125287-0.076084125286755
45123.4124.019954786072-0.619954786071744
46123.53123.0389403020830.491059697916626
47114.45123.869343813906-9.4193438139056
48114.26115.294386882796-1.03438688279613
49114.35111.7147106728382.63528932716223
50112.77114.994360348226-2.22436034822555
51115.31115.61180977227-0.301809772269877
52114.93115.130479456671-0.200479456671331
53116.38114.6116055139671.76839448603272
54115.07115.441961003818-0.371961003818257
55105109.346304625988-4.34630462598807
56103.43104.350630591449-0.920630591449154
57114.52111.630132442622.88986755738046
58115.04114.0536360357610.986363964238649
59117.16114.7576455181692.40235448183077
60115117.818059500949-2.81805950094861
61116.22112.7491326502013.47086734979895
62112.92116.53554185632-3.61554185631958
63116.56115.963458514980.596541485020069
64114.32116.330525638085-2.01052563808499
65113.22114.221872904957-1.00187290495687
66111.56112.347860495145-0.787860495144784
67103.87105.803250085783-1.93325008578299
68102.85103.287263454452-0.437263454452051
69112.27111.1959183190961.0740816809037
70112.76111.8091390543660.950860945633693
71118.55112.5652902266035.98470977339736
72122.73118.6944116585534.03558834144697







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73120.297731771146115.358288679007125.237174863285
74120.394898370523113.611001754639127.178794986408
75123.667426802851115.304478099103132.0303755066
76123.289081638014113.748918979928132.829244296101
77123.108840329135112.516615526644133.701065131626
78122.098221553074110.617799328792133.578643777355
79115.659882715473103.830837407131127.488928023814
80114.967801954042102.333656848712127.601947059371
81124.349873882593109.945287081089138.754460684097
82123.885316927206108.813962773139138.956671081274
83124.02254494628108.249930618765139.795159273795
84124.40557372383984.6225348340652164.188612613614

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 120.297731771146 & 115.358288679007 & 125.237174863285 \tabularnewline
74 & 120.394898370523 & 113.611001754639 & 127.178794986408 \tabularnewline
75 & 123.667426802851 & 115.304478099103 & 132.0303755066 \tabularnewline
76 & 123.289081638014 & 113.748918979928 & 132.829244296101 \tabularnewline
77 & 123.108840329135 & 112.516615526644 & 133.701065131626 \tabularnewline
78 & 122.098221553074 & 110.617799328792 & 133.578643777355 \tabularnewline
79 & 115.659882715473 & 103.830837407131 & 127.488928023814 \tabularnewline
80 & 114.967801954042 & 102.333656848712 & 127.601947059371 \tabularnewline
81 & 124.349873882593 & 109.945287081089 & 138.754460684097 \tabularnewline
82 & 123.885316927206 & 108.813962773139 & 138.956671081274 \tabularnewline
83 & 124.02254494628 & 108.249930618765 & 139.795159273795 \tabularnewline
84 & 124.405573723839 & 84.6225348340652 & 164.188612613614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200704&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]120.297731771146[/C][C]115.358288679007[/C][C]125.237174863285[/C][/ROW]
[ROW][C]74[/C][C]120.394898370523[/C][C]113.611001754639[/C][C]127.178794986408[/C][/ROW]
[ROW][C]75[/C][C]123.667426802851[/C][C]115.304478099103[/C][C]132.0303755066[/C][/ROW]
[ROW][C]76[/C][C]123.289081638014[/C][C]113.748918979928[/C][C]132.829244296101[/C][/ROW]
[ROW][C]77[/C][C]123.108840329135[/C][C]112.516615526644[/C][C]133.701065131626[/C][/ROW]
[ROW][C]78[/C][C]122.098221553074[/C][C]110.617799328792[/C][C]133.578643777355[/C][/ROW]
[ROW][C]79[/C][C]115.659882715473[/C][C]103.830837407131[/C][C]127.488928023814[/C][/ROW]
[ROW][C]80[/C][C]114.967801954042[/C][C]102.333656848712[/C][C]127.601947059371[/C][/ROW]
[ROW][C]81[/C][C]124.349873882593[/C][C]109.945287081089[/C][C]138.754460684097[/C][/ROW]
[ROW][C]82[/C][C]123.885316927206[/C][C]108.813962773139[/C][C]138.956671081274[/C][/ROW]
[ROW][C]83[/C][C]124.02254494628[/C][C]108.249930618765[/C][C]139.795159273795[/C][/ROW]
[ROW][C]84[/C][C]124.405573723839[/C][C]84.6225348340652[/C][C]164.188612613614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200704&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200704&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
73120.297731771146115.358288679007125.237174863285
74120.394898370523113.611001754639127.178794986408
75123.667426802851115.304478099103132.0303755066
76123.289081638014113.748918979928132.829244296101
77123.108840329135112.516615526644133.701065131626
78122.098221553074110.617799328792133.578643777355
79115.659882715473103.830837407131127.488928023814
80114.967801954042102.333656848712127.601947059371
81124.349873882593109.945287081089138.754460684097
82123.885316927206108.813962773139138.956671081274
83124.02254494628108.249930618765139.795159273795
84124.40557372383984.6225348340652164.188612613614



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')