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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 Dec 2013 03:48:50 -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/2013/Dec/18/t13873565437sslassnvfwbu9h.htm/, Retrieved Wed, 24 Apr 2024 17:00:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232428, Retrieved Wed, 24 Apr 2024 17:00:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-18 08:48:50] [43b132fa6864a311b34d1147ccf52151] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9
13
12
5
13
11
8
8
8
8
0
3
0
-1
-1
-4
1
-1
0
-1
6
0
-3
-3
4
1
0
-4
-2
3
2
5
6
6
3
4
7
5
6
1
3
6
0
3
4
7
6
6
6
6
2
2
2
3
-1
-4
4
5
3
-1
-4
0
-1
-1
3
2
-4
-3
-1
3
-2
-10

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232428&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]4 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=232428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232428&T=0

As an alternative you can also use a QR Code:  
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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.638240333271957
beta0.0182302317487774
gamma0.715496229916317

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.638240333271957 \tabularnewline
beta & 0.0182302317487774 \tabularnewline
gamma & 0.715496229916317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232428&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]0.638240333271957[/C][/ROW]
[ROW][C]beta[/C][C]0.0182302317487774[/C][/ROW]
[ROW][C]gamma[/C][C]0.715496229916317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232428&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.638240333271957
beta0.0182302317487774
gamma0.715496229916317






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1305.72088675213675-5.72088675213675
14-10.960335547306137-1.96033554730614
15-1-0.67288923505681-0.32711076494319
16-4-4.309196776487140.309196776487145
1710.5058770737813130.494122926218687
18-1-1.63860582859020.638605828590198
190-1.183443564481.18344356448
20-1-0.283440864462724-0.716559135537276
216-0.4377672126857786.43776721268578
2203.84065789306667-3.84065789306667
23-3-6.527376221294713.52737622129471
24-3-1.02679181508847-1.97320818491153
254-6.7073087497414910.7073087497415
2610.1591274714558820.840872528544118
2700.93755769799308-0.93755769799308
28-4-2.72969312229872-1.27030687770128
29-21.30073390307596-3.30073390307596
303-3.096945989943546.09694598994354
3121.177918987107990.822081012892012
3251.546234029725793.45376597027421
3366.14465022384395-0.144650223843946
3463.724142787436812.27585721256319
353-0.5991171076342233.59911710763422
3643.758174197303350.241825802696648
3773.034026830066223.96597316993378
3853.226078073301171.77392192669883
3964.332562317497561.66743768250244
4012.4649754231565-1.4649754231565
4136.06651992538445-3.06651992538445
4264.474437431436141.52556256856386
4304.63677700551988-4.63677700551988
4432.309142303579410.690857696420587
4544.28754052132147-0.287540521321473
4672.47547790254034.52452209745969
4760.02920461753976985.97079538246023
4865.158086751814680.841913248185317
4965.914754812077970.0852451879220277
5063.15129592729682.8487040727032
5125.01740517737731-3.01740517737731
522-0.6043155014548882.60431550145489
5325.27393024985562-3.27393024985562
5434.82971652761799-1.82971652761799
55-11.30813885110121-2.30813885110121
56-41.925424728845-5.925424728845
574-0.5694867089348484.56948670893485
5852.02317224992812.9768277500719
593-0.9953320267238673.99533202672387
60-11.56341667442649-2.56341667442649
61-4-0.0705754056961404-3.92942459430386
620-4.749169985959144.74916998595914
63-1-3.234463196652232.23446319665223
64-1-4.033995990119993.03399599011999
6530.6170976874773392.38290231252266
6624.2430583477622-2.2430583477622
67-40.414964940406587-4.41496494040659
68-3-1.19208451864613-1.80791548135387
69-11.76196727511312-2.76196727511312
703-0.717622733893863.71762273389386
71-2-2.971854329935840.971854329935836
72-10-4.04780113922337-5.95219886077663

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0 & 5.72088675213675 & -5.72088675213675 \tabularnewline
14 & -1 & 0.960335547306137 & -1.96033554730614 \tabularnewline
15 & -1 & -0.67288923505681 & -0.32711076494319 \tabularnewline
16 & -4 & -4.30919677648714 & 0.309196776487145 \tabularnewline
17 & 1 & 0.505877073781313 & 0.494122926218687 \tabularnewline
18 & -1 & -1.6386058285902 & 0.638605828590198 \tabularnewline
19 & 0 & -1.18344356448 & 1.18344356448 \tabularnewline
20 & -1 & -0.283440864462724 & -0.716559135537276 \tabularnewline
21 & 6 & -0.437767212685778 & 6.43776721268578 \tabularnewline
22 & 0 & 3.84065789306667 & -3.84065789306667 \tabularnewline
23 & -3 & -6.52737622129471 & 3.52737622129471 \tabularnewline
24 & -3 & -1.02679181508847 & -1.97320818491153 \tabularnewline
25 & 4 & -6.70730874974149 & 10.7073087497415 \tabularnewline
26 & 1 & 0.159127471455882 & 0.840872528544118 \tabularnewline
27 & 0 & 0.93755769799308 & -0.93755769799308 \tabularnewline
28 & -4 & -2.72969312229872 & -1.27030687770128 \tabularnewline
29 & -2 & 1.30073390307596 & -3.30073390307596 \tabularnewline
30 & 3 & -3.09694598994354 & 6.09694598994354 \tabularnewline
31 & 2 & 1.17791898710799 & 0.822081012892012 \tabularnewline
32 & 5 & 1.54623402972579 & 3.45376597027421 \tabularnewline
33 & 6 & 6.14465022384395 & -0.144650223843946 \tabularnewline
34 & 6 & 3.72414278743681 & 2.27585721256319 \tabularnewline
35 & 3 & -0.599117107634223 & 3.59911710763422 \tabularnewline
36 & 4 & 3.75817419730335 & 0.241825802696648 \tabularnewline
37 & 7 & 3.03402683006622 & 3.96597316993378 \tabularnewline
38 & 5 & 3.22607807330117 & 1.77392192669883 \tabularnewline
39 & 6 & 4.33256231749756 & 1.66743768250244 \tabularnewline
40 & 1 & 2.4649754231565 & -1.4649754231565 \tabularnewline
41 & 3 & 6.06651992538445 & -3.06651992538445 \tabularnewline
42 & 6 & 4.47443743143614 & 1.52556256856386 \tabularnewline
43 & 0 & 4.63677700551988 & -4.63677700551988 \tabularnewline
44 & 3 & 2.30914230357941 & 0.690857696420587 \tabularnewline
45 & 4 & 4.28754052132147 & -0.287540521321473 \tabularnewline
46 & 7 & 2.4754779025403 & 4.52452209745969 \tabularnewline
47 & 6 & 0.0292046175397698 & 5.97079538246023 \tabularnewline
48 & 6 & 5.15808675181468 & 0.841913248185317 \tabularnewline
49 & 6 & 5.91475481207797 & 0.0852451879220277 \tabularnewline
50 & 6 & 3.1512959272968 & 2.8487040727032 \tabularnewline
51 & 2 & 5.01740517737731 & -3.01740517737731 \tabularnewline
52 & 2 & -0.604315501454888 & 2.60431550145489 \tabularnewline
53 & 2 & 5.27393024985562 & -3.27393024985562 \tabularnewline
54 & 3 & 4.82971652761799 & -1.82971652761799 \tabularnewline
55 & -1 & 1.30813885110121 & -2.30813885110121 \tabularnewline
56 & -4 & 1.925424728845 & -5.925424728845 \tabularnewline
57 & 4 & -0.569486708934848 & 4.56948670893485 \tabularnewline
58 & 5 & 2.0231722499281 & 2.9768277500719 \tabularnewline
59 & 3 & -0.995332026723867 & 3.99533202672387 \tabularnewline
60 & -1 & 1.56341667442649 & -2.56341667442649 \tabularnewline
61 & -4 & -0.0705754056961404 & -3.92942459430386 \tabularnewline
62 & 0 & -4.74916998595914 & 4.74916998595914 \tabularnewline
63 & -1 & -3.23446319665223 & 2.23446319665223 \tabularnewline
64 & -1 & -4.03399599011999 & 3.03399599011999 \tabularnewline
65 & 3 & 0.617097687477339 & 2.38290231252266 \tabularnewline
66 & 2 & 4.2430583477622 & -2.2430583477622 \tabularnewline
67 & -4 & 0.414964940406587 & -4.41496494040659 \tabularnewline
68 & -3 & -1.19208451864613 & -1.80791548135387 \tabularnewline
69 & -1 & 1.76196727511312 & -2.76196727511312 \tabularnewline
70 & 3 & -0.71762273389386 & 3.71762273389386 \tabularnewline
71 & -2 & -2.97185432993584 & 0.971854329935836 \tabularnewline
72 & -10 & -4.04780113922337 & -5.95219886077663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232428&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]0[/C][C]5.72088675213675[/C][C]-5.72088675213675[/C][/ROW]
[ROW][C]14[/C][C]-1[/C][C]0.960335547306137[/C][C]-1.96033554730614[/C][/ROW]
[ROW][C]15[/C][C]-1[/C][C]-0.67288923505681[/C][C]-0.32711076494319[/C][/ROW]
[ROW][C]16[/C][C]-4[/C][C]-4.30919677648714[/C][C]0.309196776487145[/C][/ROW]
[ROW][C]17[/C][C]1[/C][C]0.505877073781313[/C][C]0.494122926218687[/C][/ROW]
[ROW][C]18[/C][C]-1[/C][C]-1.6386058285902[/C][C]0.638605828590198[/C][/ROW]
[ROW][C]19[/C][C]0[/C][C]-1.18344356448[/C][C]1.18344356448[/C][/ROW]
[ROW][C]20[/C][C]-1[/C][C]-0.283440864462724[/C][C]-0.716559135537276[/C][/ROW]
[ROW][C]21[/C][C]6[/C][C]-0.437767212685778[/C][C]6.43776721268578[/C][/ROW]
[ROW][C]22[/C][C]0[/C][C]3.84065789306667[/C][C]-3.84065789306667[/C][/ROW]
[ROW][C]23[/C][C]-3[/C][C]-6.52737622129471[/C][C]3.52737622129471[/C][/ROW]
[ROW][C]24[/C][C]-3[/C][C]-1.02679181508847[/C][C]-1.97320818491153[/C][/ROW]
[ROW][C]25[/C][C]4[/C][C]-6.70730874974149[/C][C]10.7073087497415[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]0.159127471455882[/C][C]0.840872528544118[/C][/ROW]
[ROW][C]27[/C][C]0[/C][C]0.93755769799308[/C][C]-0.93755769799308[/C][/ROW]
[ROW][C]28[/C][C]-4[/C][C]-2.72969312229872[/C][C]-1.27030687770128[/C][/ROW]
[ROW][C]29[/C][C]-2[/C][C]1.30073390307596[/C][C]-3.30073390307596[/C][/ROW]
[ROW][C]30[/C][C]3[/C][C]-3.09694598994354[/C][C]6.09694598994354[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]1.17791898710799[/C][C]0.822081012892012[/C][/ROW]
[ROW][C]32[/C][C]5[/C][C]1.54623402972579[/C][C]3.45376597027421[/C][/ROW]
[ROW][C]33[/C][C]6[/C][C]6.14465022384395[/C][C]-0.144650223843946[/C][/ROW]
[ROW][C]34[/C][C]6[/C][C]3.72414278743681[/C][C]2.27585721256319[/C][/ROW]
[ROW][C]35[/C][C]3[/C][C]-0.599117107634223[/C][C]3.59911710763422[/C][/ROW]
[ROW][C]36[/C][C]4[/C][C]3.75817419730335[/C][C]0.241825802696648[/C][/ROW]
[ROW][C]37[/C][C]7[/C][C]3.03402683006622[/C][C]3.96597316993378[/C][/ROW]
[ROW][C]38[/C][C]5[/C][C]3.22607807330117[/C][C]1.77392192669883[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]4.33256231749756[/C][C]1.66743768250244[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]2.4649754231565[/C][C]-1.4649754231565[/C][/ROW]
[ROW][C]41[/C][C]3[/C][C]6.06651992538445[/C][C]-3.06651992538445[/C][/ROW]
[ROW][C]42[/C][C]6[/C][C]4.47443743143614[/C][C]1.52556256856386[/C][/ROW]
[ROW][C]43[/C][C]0[/C][C]4.63677700551988[/C][C]-4.63677700551988[/C][/ROW]
[ROW][C]44[/C][C]3[/C][C]2.30914230357941[/C][C]0.690857696420587[/C][/ROW]
[ROW][C]45[/C][C]4[/C][C]4.28754052132147[/C][C]-0.287540521321473[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]2.4754779025403[/C][C]4.52452209745969[/C][/ROW]
[ROW][C]47[/C][C]6[/C][C]0.0292046175397698[/C][C]5.97079538246023[/C][/ROW]
[ROW][C]48[/C][C]6[/C][C]5.15808675181468[/C][C]0.841913248185317[/C][/ROW]
[ROW][C]49[/C][C]6[/C][C]5.91475481207797[/C][C]0.0852451879220277[/C][/ROW]
[ROW][C]50[/C][C]6[/C][C]3.1512959272968[/C][C]2.8487040727032[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]5.01740517737731[/C][C]-3.01740517737731[/C][/ROW]
[ROW][C]52[/C][C]2[/C][C]-0.604315501454888[/C][C]2.60431550145489[/C][/ROW]
[ROW][C]53[/C][C]2[/C][C]5.27393024985562[/C][C]-3.27393024985562[/C][/ROW]
[ROW][C]54[/C][C]3[/C][C]4.82971652761799[/C][C]-1.82971652761799[/C][/ROW]
[ROW][C]55[/C][C]-1[/C][C]1.30813885110121[/C][C]-2.30813885110121[/C][/ROW]
[ROW][C]56[/C][C]-4[/C][C]1.925424728845[/C][C]-5.925424728845[/C][/ROW]
[ROW][C]57[/C][C]4[/C][C]-0.569486708934848[/C][C]4.56948670893485[/C][/ROW]
[ROW][C]58[/C][C]5[/C][C]2.0231722499281[/C][C]2.9768277500719[/C][/ROW]
[ROW][C]59[/C][C]3[/C][C]-0.995332026723867[/C][C]3.99533202672387[/C][/ROW]
[ROW][C]60[/C][C]-1[/C][C]1.56341667442649[/C][C]-2.56341667442649[/C][/ROW]
[ROW][C]61[/C][C]-4[/C][C]-0.0705754056961404[/C][C]-3.92942459430386[/C][/ROW]
[ROW][C]62[/C][C]0[/C][C]-4.74916998595914[/C][C]4.74916998595914[/C][/ROW]
[ROW][C]63[/C][C]-1[/C][C]-3.23446319665223[/C][C]2.23446319665223[/C][/ROW]
[ROW][C]64[/C][C]-1[/C][C]-4.03399599011999[/C][C]3.03399599011999[/C][/ROW]
[ROW][C]65[/C][C]3[/C][C]0.617097687477339[/C][C]2.38290231252266[/C][/ROW]
[ROW][C]66[/C][C]2[/C][C]4.2430583477622[/C][C]-2.2430583477622[/C][/ROW]
[ROW][C]67[/C][C]-4[/C][C]0.414964940406587[/C][C]-4.41496494040659[/C][/ROW]
[ROW][C]68[/C][C]-3[/C][C]-1.19208451864613[/C][C]-1.80791548135387[/C][/ROW]
[ROW][C]69[/C][C]-1[/C][C]1.76196727511312[/C][C]-2.76196727511312[/C][/ROW]
[ROW][C]70[/C][C]3[/C][C]-0.71762273389386[/C][C]3.71762273389386[/C][/ROW]
[ROW][C]71[/C][C]-2[/C][C]-2.97185432993584[/C][C]0.971854329935836[/C][/ROW]
[ROW][C]72[/C][C]-10[/C][C]-4.04780113922337[/C][C]-5.95219886077663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232428&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232428&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1305.72088675213675-5.72088675213675
14-10.960335547306137-1.96033554730614
15-1-0.67288923505681-0.32711076494319
16-4-4.309196776487140.309196776487145
1710.5058770737813130.494122926218687
18-1-1.63860582859020.638605828590198
190-1.183443564481.18344356448
20-1-0.283440864462724-0.716559135537276
216-0.4377672126857786.43776721268578
2203.84065789306667-3.84065789306667
23-3-6.527376221294713.52737622129471
24-3-1.02679181508847-1.97320818491153
254-6.7073087497414910.7073087497415
2610.1591274714558820.840872528544118
2700.93755769799308-0.93755769799308
28-4-2.72969312229872-1.27030687770128
29-21.30073390307596-3.30073390307596
303-3.096945989943546.09694598994354
3121.177918987107990.822081012892012
3251.546234029725793.45376597027421
3366.14465022384395-0.144650223843946
3463.724142787436812.27585721256319
353-0.5991171076342233.59911710763422
3643.758174197303350.241825802696648
3773.034026830066223.96597316993378
3853.226078073301171.77392192669883
3964.332562317497561.66743768250244
4012.4649754231565-1.4649754231565
4136.06651992538445-3.06651992538445
4264.474437431436141.52556256856386
4304.63677700551988-4.63677700551988
4432.309142303579410.690857696420587
4544.28754052132147-0.287540521321473
4672.47547790254034.52452209745969
4760.02920461753976985.97079538246023
4865.158086751814680.841913248185317
4965.914754812077970.0852451879220277
5063.15129592729682.8487040727032
5125.01740517737731-3.01740517737731
522-0.6043155014548882.60431550145489
5325.27393024985562-3.27393024985562
5434.82971652761799-1.82971652761799
55-11.30813885110121-2.30813885110121
56-41.925424728845-5.925424728845
574-0.5694867089348484.56948670893485
5852.02317224992812.9768277500719
593-0.9953320267238673.99533202672387
60-11.56341667442649-2.56341667442649
61-4-0.0705754056961404-3.92942459430386
620-4.749169985959144.74916998595914
63-1-3.234463196652232.23446319665223
64-1-4.033995990119993.03399599011999
6530.6170976874773392.38290231252266
6624.2430583477622-2.2430583477622
67-40.414964940406587-4.41496494040659
68-3-1.19208451864613-1.80791548135387
69-11.76196727511312-2.76196727511312
703-0.717622733893863.71762273389386
71-2-2.971854329935840.971854329935836
72-10-4.04780113922337-5.95219886077663






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-8.24499321728457-14.9279988535843-1.5619875809848
74-8.17037156359181-16.1406460739383-0.200097053245278
75-10.3939836408381-19.5082287306958-1.27973855098053
76-12.4949965054725-22.6590124680847-2.33098054286034
77-10.066455122615-21.21323220620661.0803219609767
78-9.30406356002588-21.38345977579012.77533265573833
79-12.3819511481073-25.35510936177750.591207065562832
80-10.5642532086737-24.40028571225153.27177929490404
81-6.75008972699769-21.42397094285627.92379148886081
82-5.80441089961802-21.29556677380619.68674497457003
83-11.2000352347068-27.49135959382925.09128912441571
84-14.7577199594385-31.83486550237522.31942558349814

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & -8.24499321728457 & -14.9279988535843 & -1.5619875809848 \tabularnewline
74 & -8.17037156359181 & -16.1406460739383 & -0.200097053245278 \tabularnewline
75 & -10.3939836408381 & -19.5082287306958 & -1.27973855098053 \tabularnewline
76 & -12.4949965054725 & -22.6590124680847 & -2.33098054286034 \tabularnewline
77 & -10.066455122615 & -21.2132322062066 & 1.0803219609767 \tabularnewline
78 & -9.30406356002588 & -21.3834597757901 & 2.77533265573833 \tabularnewline
79 & -12.3819511481073 & -25.3551093617775 & 0.591207065562832 \tabularnewline
80 & -10.5642532086737 & -24.4002857122515 & 3.27177929490404 \tabularnewline
81 & -6.75008972699769 & -21.4239709428562 & 7.92379148886081 \tabularnewline
82 & -5.80441089961802 & -21.2955667738061 & 9.68674497457003 \tabularnewline
83 & -11.2000352347068 & -27.4913595938292 & 5.09128912441571 \tabularnewline
84 & -14.7577199594385 & -31.8348655023752 & 2.31942558349814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232428&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]-8.24499321728457[/C][C]-14.9279988535843[/C][C]-1.5619875809848[/C][/ROW]
[ROW][C]74[/C][C]-8.17037156359181[/C][C]-16.1406460739383[/C][C]-0.200097053245278[/C][/ROW]
[ROW][C]75[/C][C]-10.3939836408381[/C][C]-19.5082287306958[/C][C]-1.27973855098053[/C][/ROW]
[ROW][C]76[/C][C]-12.4949965054725[/C][C]-22.6590124680847[/C][C]-2.33098054286034[/C][/ROW]
[ROW][C]77[/C][C]-10.066455122615[/C][C]-21.2132322062066[/C][C]1.0803219609767[/C][/ROW]
[ROW][C]78[/C][C]-9.30406356002588[/C][C]-21.3834597757901[/C][C]2.77533265573833[/C][/ROW]
[ROW][C]79[/C][C]-12.3819511481073[/C][C]-25.3551093617775[/C][C]0.591207065562832[/C][/ROW]
[ROW][C]80[/C][C]-10.5642532086737[/C][C]-24.4002857122515[/C][C]3.27177929490404[/C][/ROW]
[ROW][C]81[/C][C]-6.75008972699769[/C][C]-21.4239709428562[/C][C]7.92379148886081[/C][/ROW]
[ROW][C]82[/C][C]-5.80441089961802[/C][C]-21.2955667738061[/C][C]9.68674497457003[/C][/ROW]
[ROW][C]83[/C][C]-11.2000352347068[/C][C]-27.4913595938292[/C][C]5.09128912441571[/C][/ROW]
[ROW][C]84[/C][C]-14.7577199594385[/C][C]-31.8348655023752[/C][C]2.31942558349814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232428&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232428&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-8.24499321728457-14.9279988535843-1.5619875809848
74-8.17037156359181-16.1406460739383-0.200097053245278
75-10.3939836408381-19.5082287306958-1.27973855098053
76-12.4949965054725-22.6590124680847-2.33098054286034
77-10.066455122615-21.21323220620661.0803219609767
78-9.30406356002588-21.38345977579012.77533265573833
79-12.3819511481073-25.35510936177750.591207065562832
80-10.5642532086737-24.40028571225153.27177929490404
81-6.75008972699769-21.42397094285627.92379148886081
82-5.80441089961802-21.29556677380619.68674497457003
83-11.2000352347068-27.49135959382925.09128912441571
84-14.7577199594385-31.83486550237522.31942558349814


Figures (Output of Computation)

Input Parameters & R Code

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')