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 12:21:56 +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/t1493637737r0tvc387kjeoi1f.htm/, Retrieved Wed, 15 May 2024 21:11:36 +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 21:11:36 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
78,46
78,59
81,37
83,61
83,85
84,08
84,56
84,65
85,41
85,75
86,21
86,38
86,65
87,30
87,87
88,23
88,33
88,62
88,67
88,85
88,87
89,20
89,38
89,65
90,37
90,38
91,43
92,09
92,21
92,31
92,62
93,13
93,17
93,42
93,50
95,75
97,29
98,01
98,02
98,20
98,29
98,39
98,42
98,70
98,90
99,04
99,31
99,34
99,35
99,51
99,88
99,91
100,30
100,74
101,16
101,30
101,37
101,68
101,68
101,89
101,93
102,66
102,68
103,13
103,14
104,01
104,17
104,41
104,71
105,51
105,98
106,25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.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]'Gertrude Mary Cox' @ cox.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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.863244205086227
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.863244205086227 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \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]0.863244205086227[/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=&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
alpha0.863244205086227
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1386.6584.01590862831742.63409137168263
1487.386.97531205328220.324687946717816
1587.8787.8895732869056-0.0195732869056258
1688.2388.3282409486638-0.0982409486637579
1788.3388.4508986712291-0.120898671229071
1888.6288.7515777878929-0.131577787892923
1988.6789.4119440289267-0.741944028926682
2088.8588.5095925996470.340407400353016
2188.8789.3183821386634-0.448382138663433
2289.289.18586479958630.0141352004137474
2389.3889.6651357065552-0.285135706555224
2489.6589.58850620699510.0614937930048711
2590.3790.30616742354620.0638325764538195
2690.3890.7302370146284-0.350237014628377
2791.4391.02204079925470.407959200745353
2892.0991.82139193183360.268608068166429
2992.2192.2498231542379-0.0398231542378795
3092.3192.6198596957692-0.309859695769148
3192.6293.0549362321681-0.434936232168113
3293.1392.54298275764080.587017242359167
3393.1793.4576229620219-0.287622962021885
3493.4293.5239408910519-0.103940891051863
3593.593.862276082765-0.36227608276495
3695.7593.75872400464821.99127599535176
3797.2996.16084415892421.12915584107576
3898.0197.44242077926520.5675792207348
3998.0298.6561329955435-0.636132995543548
4098.298.5381689077998-0.338168907799798
4198.2998.3852669047352-0.0952669047352401
4298.3998.6692911413893-0.279291141389294
4398.4299.1332917753678-0.713291775367765
4498.798.49612087744340.203879122556643
4598.998.9546441449038-0.0546441449037758
4699.0499.2445145661648-0.204514566164818
4799.3199.4611064255111-0.151106425511131
4899.3499.8656863858667-0.52568638586672
4999.3599.9824604788274-0.632460478827397
5099.5199.6627434653036-0.152743465303629
5199.88100.092242139932-0.212242139931519
5299.91100.382485822148-0.472485822148002
53100.3100.1430156252250.156984374775348
54100.74100.6186676302660.121332369733835
55101.16101.374715062886-0.214715062885617
56101.3101.2854428758420.0145571241575055
57101.37101.541595247792-0.171595247791686
58101.68101.708286638911-0.0282866389106999
59101.68102.084746607318-0.40474660731789
60101.89102.221262062142-0.331262062142159
61101.93102.49527282405-0.565272824050012
62102.66102.2966732256670.36332677433299
63102.68103.168734815211-0.488734815211416
64103.13103.185965987602-0.0559659876021215
65103.14103.387920727592-0.247920727591506
66104.01103.5077534761430.502246523857309
67104.17104.553621231009-0.383621231009244
68104.41104.3421355193040.0678644806959312
69104.71104.6137612730670.0962387269330094
70105.51105.029662872290.480337127710143
71105.98105.7922710412910.187728958708931
72106.25106.454892093007-0.204892093007388

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 86.65 & 84.0159086283174 & 2.63409137168263 \tabularnewline
14 & 87.3 & 86.9753120532822 & 0.324687946717816 \tabularnewline
15 & 87.87 & 87.8895732869056 & -0.0195732869056258 \tabularnewline
16 & 88.23 & 88.3282409486638 & -0.0982409486637579 \tabularnewline
17 & 88.33 & 88.4508986712291 & -0.120898671229071 \tabularnewline
18 & 88.62 & 88.7515777878929 & -0.131577787892923 \tabularnewline
19 & 88.67 & 89.4119440289267 & -0.741944028926682 \tabularnewline
20 & 88.85 & 88.509592599647 & 0.340407400353016 \tabularnewline
21 & 88.87 & 89.3183821386634 & -0.448382138663433 \tabularnewline
22 & 89.2 & 89.1858647995863 & 0.0141352004137474 \tabularnewline
23 & 89.38 & 89.6651357065552 & -0.285135706555224 \tabularnewline
24 & 89.65 & 89.5885062069951 & 0.0614937930048711 \tabularnewline
25 & 90.37 & 90.3061674235462 & 0.0638325764538195 \tabularnewline
26 & 90.38 & 90.7302370146284 & -0.350237014628377 \tabularnewline
27 & 91.43 & 91.0220407992547 & 0.407959200745353 \tabularnewline
28 & 92.09 & 91.8213919318336 & 0.268608068166429 \tabularnewline
29 & 92.21 & 92.2498231542379 & -0.0398231542378795 \tabularnewline
30 & 92.31 & 92.6198596957692 & -0.309859695769148 \tabularnewline
31 & 92.62 & 93.0549362321681 & -0.434936232168113 \tabularnewline
32 & 93.13 & 92.5429827576408 & 0.587017242359167 \tabularnewline
33 & 93.17 & 93.4576229620219 & -0.287622962021885 \tabularnewline
34 & 93.42 & 93.5239408910519 & -0.103940891051863 \tabularnewline
35 & 93.5 & 93.862276082765 & -0.36227608276495 \tabularnewline
36 & 95.75 & 93.7587240046482 & 1.99127599535176 \tabularnewline
37 & 97.29 & 96.1608441589242 & 1.12915584107576 \tabularnewline
38 & 98.01 & 97.4424207792652 & 0.5675792207348 \tabularnewline
39 & 98.02 & 98.6561329955435 & -0.636132995543548 \tabularnewline
40 & 98.2 & 98.5381689077998 & -0.338168907799798 \tabularnewline
41 & 98.29 & 98.3852669047352 & -0.0952669047352401 \tabularnewline
42 & 98.39 & 98.6692911413893 & -0.279291141389294 \tabularnewline
43 & 98.42 & 99.1332917753678 & -0.713291775367765 \tabularnewline
44 & 98.7 & 98.4961208774434 & 0.203879122556643 \tabularnewline
45 & 98.9 & 98.9546441449038 & -0.0546441449037758 \tabularnewline
46 & 99.04 & 99.2445145661648 & -0.204514566164818 \tabularnewline
47 & 99.31 & 99.4611064255111 & -0.151106425511131 \tabularnewline
48 & 99.34 & 99.8656863858667 & -0.52568638586672 \tabularnewline
49 & 99.35 & 99.9824604788274 & -0.632460478827397 \tabularnewline
50 & 99.51 & 99.6627434653036 & -0.152743465303629 \tabularnewline
51 & 99.88 & 100.092242139932 & -0.212242139931519 \tabularnewline
52 & 99.91 & 100.382485822148 & -0.472485822148002 \tabularnewline
53 & 100.3 & 100.143015625225 & 0.156984374775348 \tabularnewline
54 & 100.74 & 100.618667630266 & 0.121332369733835 \tabularnewline
55 & 101.16 & 101.374715062886 & -0.214715062885617 \tabularnewline
56 & 101.3 & 101.285442875842 & 0.0145571241575055 \tabularnewline
57 & 101.37 & 101.541595247792 & -0.171595247791686 \tabularnewline
58 & 101.68 & 101.708286638911 & -0.0282866389106999 \tabularnewline
59 & 101.68 & 102.084746607318 & -0.40474660731789 \tabularnewline
60 & 101.89 & 102.221262062142 & -0.331262062142159 \tabularnewline
61 & 101.93 & 102.49527282405 & -0.565272824050012 \tabularnewline
62 & 102.66 & 102.296673225667 & 0.36332677433299 \tabularnewline
63 & 102.68 & 103.168734815211 & -0.488734815211416 \tabularnewline
64 & 103.13 & 103.185965987602 & -0.0559659876021215 \tabularnewline
65 & 103.14 & 103.387920727592 & -0.247920727591506 \tabularnewline
66 & 104.01 & 103.507753476143 & 0.502246523857309 \tabularnewline
67 & 104.17 & 104.553621231009 & -0.383621231009244 \tabularnewline
68 & 104.41 & 104.342135519304 & 0.0678644806959312 \tabularnewline
69 & 104.71 & 104.613761273067 & 0.0962387269330094 \tabularnewline
70 & 105.51 & 105.02966287229 & 0.480337127710143 \tabularnewline
71 & 105.98 & 105.792271041291 & 0.187728958708931 \tabularnewline
72 & 106.25 & 106.454892093007 & -0.204892093007388 \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]86.65[/C][C]84.0159086283174[/C][C]2.63409137168263[/C][/ROW]
[ROW][C]14[/C][C]87.3[/C][C]86.9753120532822[/C][C]0.324687946717816[/C][/ROW]
[ROW][C]15[/C][C]87.87[/C][C]87.8895732869056[/C][C]-0.0195732869056258[/C][/ROW]
[ROW][C]16[/C][C]88.23[/C][C]88.3282409486638[/C][C]-0.0982409486637579[/C][/ROW]
[ROW][C]17[/C][C]88.33[/C][C]88.4508986712291[/C][C]-0.120898671229071[/C][/ROW]
[ROW][C]18[/C][C]88.62[/C][C]88.7515777878929[/C][C]-0.131577787892923[/C][/ROW]
[ROW][C]19[/C][C]88.67[/C][C]89.4119440289267[/C][C]-0.741944028926682[/C][/ROW]
[ROW][C]20[/C][C]88.85[/C][C]88.509592599647[/C][C]0.340407400353016[/C][/ROW]
[ROW][C]21[/C][C]88.87[/C][C]89.3183821386634[/C][C]-0.448382138663433[/C][/ROW]
[ROW][C]22[/C][C]89.2[/C][C]89.1858647995863[/C][C]0.0141352004137474[/C][/ROW]
[ROW][C]23[/C][C]89.38[/C][C]89.6651357065552[/C][C]-0.285135706555224[/C][/ROW]
[ROW][C]24[/C][C]89.65[/C][C]89.5885062069951[/C][C]0.0614937930048711[/C][/ROW]
[ROW][C]25[/C][C]90.37[/C][C]90.3061674235462[/C][C]0.0638325764538195[/C][/ROW]
[ROW][C]26[/C][C]90.38[/C][C]90.7302370146284[/C][C]-0.350237014628377[/C][/ROW]
[ROW][C]27[/C][C]91.43[/C][C]91.0220407992547[/C][C]0.407959200745353[/C][/ROW]
[ROW][C]28[/C][C]92.09[/C][C]91.8213919318336[/C][C]0.268608068166429[/C][/ROW]
[ROW][C]29[/C][C]92.21[/C][C]92.2498231542379[/C][C]-0.0398231542378795[/C][/ROW]
[ROW][C]30[/C][C]92.31[/C][C]92.6198596957692[/C][C]-0.309859695769148[/C][/ROW]
[ROW][C]31[/C][C]92.62[/C][C]93.0549362321681[/C][C]-0.434936232168113[/C][/ROW]
[ROW][C]32[/C][C]93.13[/C][C]92.5429827576408[/C][C]0.587017242359167[/C][/ROW]
[ROW][C]33[/C][C]93.17[/C][C]93.4576229620219[/C][C]-0.287622962021885[/C][/ROW]
[ROW][C]34[/C][C]93.42[/C][C]93.5239408910519[/C][C]-0.103940891051863[/C][/ROW]
[ROW][C]35[/C][C]93.5[/C][C]93.862276082765[/C][C]-0.36227608276495[/C][/ROW]
[ROW][C]36[/C][C]95.75[/C][C]93.7587240046482[/C][C]1.99127599535176[/C][/ROW]
[ROW][C]37[/C][C]97.29[/C][C]96.1608441589242[/C][C]1.12915584107576[/C][/ROW]
[ROW][C]38[/C][C]98.01[/C][C]97.4424207792652[/C][C]0.5675792207348[/C][/ROW]
[ROW][C]39[/C][C]98.02[/C][C]98.6561329955435[/C][C]-0.636132995543548[/C][/ROW]
[ROW][C]40[/C][C]98.2[/C][C]98.5381689077998[/C][C]-0.338168907799798[/C][/ROW]
[ROW][C]41[/C][C]98.29[/C][C]98.3852669047352[/C][C]-0.0952669047352401[/C][/ROW]
[ROW][C]42[/C][C]98.39[/C][C]98.6692911413893[/C][C]-0.279291141389294[/C][/ROW]
[ROW][C]43[/C][C]98.42[/C][C]99.1332917753678[/C][C]-0.713291775367765[/C][/ROW]
[ROW][C]44[/C][C]98.7[/C][C]98.4961208774434[/C][C]0.203879122556643[/C][/ROW]
[ROW][C]45[/C][C]98.9[/C][C]98.9546441449038[/C][C]-0.0546441449037758[/C][/ROW]
[ROW][C]46[/C][C]99.04[/C][C]99.2445145661648[/C][C]-0.204514566164818[/C][/ROW]
[ROW][C]47[/C][C]99.31[/C][C]99.4611064255111[/C][C]-0.151106425511131[/C][/ROW]
[ROW][C]48[/C][C]99.34[/C][C]99.8656863858667[/C][C]-0.52568638586672[/C][/ROW]
[ROW][C]49[/C][C]99.35[/C][C]99.9824604788274[/C][C]-0.632460478827397[/C][/ROW]
[ROW][C]50[/C][C]99.51[/C][C]99.6627434653036[/C][C]-0.152743465303629[/C][/ROW]
[ROW][C]51[/C][C]99.88[/C][C]100.092242139932[/C][C]-0.212242139931519[/C][/ROW]
[ROW][C]52[/C][C]99.91[/C][C]100.382485822148[/C][C]-0.472485822148002[/C][/ROW]
[ROW][C]53[/C][C]100.3[/C][C]100.143015625225[/C][C]0.156984374775348[/C][/ROW]
[ROW][C]54[/C][C]100.74[/C][C]100.618667630266[/C][C]0.121332369733835[/C][/ROW]
[ROW][C]55[/C][C]101.16[/C][C]101.374715062886[/C][C]-0.214715062885617[/C][/ROW]
[ROW][C]56[/C][C]101.3[/C][C]101.285442875842[/C][C]0.0145571241575055[/C][/ROW]
[ROW][C]57[/C][C]101.37[/C][C]101.541595247792[/C][C]-0.171595247791686[/C][/ROW]
[ROW][C]58[/C][C]101.68[/C][C]101.708286638911[/C][C]-0.0282866389106999[/C][/ROW]
[ROW][C]59[/C][C]101.68[/C][C]102.084746607318[/C][C]-0.40474660731789[/C][/ROW]
[ROW][C]60[/C][C]101.89[/C][C]102.221262062142[/C][C]-0.331262062142159[/C][/ROW]
[ROW][C]61[/C][C]101.93[/C][C]102.49527282405[/C][C]-0.565272824050012[/C][/ROW]
[ROW][C]62[/C][C]102.66[/C][C]102.296673225667[/C][C]0.36332677433299[/C][/ROW]
[ROW][C]63[/C][C]102.68[/C][C]103.168734815211[/C][C]-0.488734815211416[/C][/ROW]
[ROW][C]64[/C][C]103.13[/C][C]103.185965987602[/C][C]-0.0559659876021215[/C][/ROW]
[ROW][C]65[/C][C]103.14[/C][C]103.387920727592[/C][C]-0.247920727591506[/C][/ROW]
[ROW][C]66[/C][C]104.01[/C][C]103.507753476143[/C][C]0.502246523857309[/C][/ROW]
[ROW][C]67[/C][C]104.17[/C][C]104.553621231009[/C][C]-0.383621231009244[/C][/ROW]
[ROW][C]68[/C][C]104.41[/C][C]104.342135519304[/C][C]0.0678644806959312[/C][/ROW]
[ROW][C]69[/C][C]104.71[/C][C]104.613761273067[/C][C]0.0962387269330094[/C][/ROW]
[ROW][C]70[/C][C]105.51[/C][C]105.02966287229[/C][C]0.480337127710143[/C][/ROW]
[ROW][C]71[/C][C]105.98[/C][C]105.792271041291[/C][C]0.187728958708931[/C][/ROW]
[ROW][C]72[/C][C]106.25[/C][C]106.454892093007[/C][C]-0.204892093007388[/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
1386.6584.01590862831742.63409137168263
1487.386.97531205328220.324687946717816
1587.8787.8895732869056-0.0195732869056258
1688.2388.3282409486638-0.0982409486637579
1788.3388.4508986712291-0.120898671229071
1888.6288.7515777878929-0.131577787892923
1988.6789.4119440289267-0.741944028926682
2088.8588.5095925996470.340407400353016
2188.8789.3183821386634-0.448382138663433
2289.289.18586479958630.0141352004137474
2389.3889.6651357065552-0.285135706555224
2489.6589.58850620699510.0614937930048711
2590.3790.30616742354620.0638325764538195
2690.3890.7302370146284-0.350237014628377
2791.4391.02204079925470.407959200745353
2892.0991.82139193183360.268608068166429
2992.2192.2498231542379-0.0398231542378795
3092.3192.6198596957692-0.309859695769148
3192.6293.0549362321681-0.434936232168113
3293.1392.54298275764080.587017242359167
3393.1793.4576229620219-0.287622962021885
3493.4293.5239408910519-0.103940891051863
3593.593.862276082765-0.36227608276495
3695.7593.75872400464821.99127599535176
3797.2996.16084415892421.12915584107576
3898.0197.44242077926520.5675792207348
3998.0298.6561329955435-0.636132995543548
4098.298.5381689077998-0.338168907799798
4198.2998.3852669047352-0.0952669047352401
4298.3998.6692911413893-0.279291141389294
4398.4299.1332917753678-0.713291775367765
4498.798.49612087744340.203879122556643
4598.998.9546441449038-0.0546441449037758
4699.0499.2445145661648-0.204514566164818
4799.3199.4611064255111-0.151106425511131
4899.3499.8656863858667-0.52568638586672
4999.3599.9824604788274-0.632460478827397
5099.5199.6627434653036-0.152743465303629
5199.88100.092242139932-0.212242139931519
5299.91100.382485822148-0.472485822148002
53100.3100.1430156252250.156984374775348
54100.74100.6186676302660.121332369733835
55101.16101.374715062886-0.214715062885617
56101.3101.2854428758420.0145571241575055
57101.37101.541595247792-0.171595247791686
58101.68101.708286638911-0.0282866389106999
59101.68102.084746607318-0.40474660731789
60101.89102.221262062142-0.331262062142159
61101.93102.49527282405-0.565272824050012
62102.66102.2966732256670.36332677433299
63102.68103.168734815211-0.488734815211416
64103.13103.185965987602-0.0559659876021215
65103.14103.387920727592-0.247920727591506
66104.01103.5077534761430.502246523857309
67104.17104.553621231009-0.383621231009244
68104.41104.3421355193040.0678644806959312
69104.71104.6137612730670.0962387269330094
70105.51105.029662872290.480337127710143
71105.98105.7922710412910.187728958708931
72106.25106.454892093007-0.204892093007388







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73106.811811614053105.703336655676107.920286572429
74107.229566202017105.765009976237108.694122427797
75107.67374793894105.923717922049109.423777955831
76108.177588487368106.181510310134110.173666664602
77108.393702155674106.182690618861110.604713692487
78108.832502509095106.422354370257111.242650647932
79109.328429654461106.733107737745111.923751571176
80109.499818276648106.738226227364112.261410325932
81109.708624206705106.789935664557112.627312748854
82110.093807871306107.022217545968113.165398196643
83110.398453207105107.183281754199113.61362466001
84110.847932736386106.564268509168115.131596963604

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 106.811811614053 & 105.703336655676 & 107.920286572429 \tabularnewline
74 & 107.229566202017 & 105.765009976237 & 108.694122427797 \tabularnewline
75 & 107.67374793894 & 105.923717922049 & 109.423777955831 \tabularnewline
76 & 108.177588487368 & 106.181510310134 & 110.173666664602 \tabularnewline
77 & 108.393702155674 & 106.182690618861 & 110.604713692487 \tabularnewline
78 & 108.832502509095 & 106.422354370257 & 111.242650647932 \tabularnewline
79 & 109.328429654461 & 106.733107737745 & 111.923751571176 \tabularnewline
80 & 109.499818276648 & 106.738226227364 & 112.261410325932 \tabularnewline
81 & 109.708624206705 & 106.789935664557 & 112.627312748854 \tabularnewline
82 & 110.093807871306 & 107.022217545968 & 113.165398196643 \tabularnewline
83 & 110.398453207105 & 107.183281754199 & 113.61362466001 \tabularnewline
84 & 110.847932736386 & 106.564268509168 & 115.131596963604 \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]106.811811614053[/C][C]105.703336655676[/C][C]107.920286572429[/C][/ROW]
[ROW][C]74[/C][C]107.229566202017[/C][C]105.765009976237[/C][C]108.694122427797[/C][/ROW]
[ROW][C]75[/C][C]107.67374793894[/C][C]105.923717922049[/C][C]109.423777955831[/C][/ROW]
[ROW][C]76[/C][C]108.177588487368[/C][C]106.181510310134[/C][C]110.173666664602[/C][/ROW]
[ROW][C]77[/C][C]108.393702155674[/C][C]106.182690618861[/C][C]110.604713692487[/C][/ROW]
[ROW][C]78[/C][C]108.832502509095[/C][C]106.422354370257[/C][C]111.242650647932[/C][/ROW]
[ROW][C]79[/C][C]109.328429654461[/C][C]106.733107737745[/C][C]111.923751571176[/C][/ROW]
[ROW][C]80[/C][C]109.499818276648[/C][C]106.738226227364[/C][C]112.261410325932[/C][/ROW]
[ROW][C]81[/C][C]109.708624206705[/C][C]106.789935664557[/C][C]112.627312748854[/C][/ROW]
[ROW][C]82[/C][C]110.093807871306[/C][C]107.022217545968[/C][C]113.165398196643[/C][/ROW]
[ROW][C]83[/C][C]110.398453207105[/C][C]107.183281754199[/C][C]113.61362466001[/C][/ROW]
[ROW][C]84[/C][C]110.847932736386[/C][C]106.564268509168[/C][C]115.131596963604[/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
73106.811811614053105.703336655676107.920286572429
74107.229566202017105.765009976237108.694122427797
75107.67374793894105.923717922049109.423777955831
76108.177588487368106.181510310134110.173666664602
77108.393702155674106.182690618861110.604713692487
78108.832502509095106.422354370257111.242650647932
79109.328429654461106.733107737745111.923751571176
80109.499818276648106.738226227364112.261410325932
81109.708624206705106.789935664557112.627312748854
82110.093807871306107.022217545968113.165398196643
83110.398453207105107.183281754199113.61362466001
84110.847932736386106.564268509168115.131596963604



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')