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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 08:38:48 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243953632glao4q35rkrjviz.htm/, Retrieved Fri, 10 May 2024 04:53:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41243, Retrieved Fri, 10 May 2024 04:53:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2009-06-02 14:38:48] [497dd3403aa93022e6ec9f5d7facee10] [Current]
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Dataseries X:
310.95
312.97
315.07
315.43
315.73
315.77
315.77
315.77
313.99
314.57
314.63
314.65
314.65
314.93
315.27
316.26
316.98
317.01
317.07
317.07
317
317.08
317.04
317
317.05
321.59
325.59
326.23
326.28
326.35
326.35
326.35
326.39
326.74
326.9
326.9
326.91
336.93
348.5
349.43
349.26
349.26
349.28
349.61
349.66
349.68
349.91
349.91
350.89
355.52
356.36
357.04
360.28
360.63
360.79
360.97
361
361.01
361
361
361.58
363.19
363.61
364.14
365.51
365.51
365.5
365.5
364.59
364.63
364.54
363.67
365.22
369.05
370.45
370.46
370.46
370.58
370.58
370.22
370.21
370.29
370.29
370.2
370.2
372.55
374.51
375.58
375.75
375.75
375.75
375.69
375.76
377.5
377.51
377.74




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41243&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41243&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.936452106375678
beta0.0510905500579434
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.936452106375678 \tabularnewline
beta & 0.0510905500579434 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41243&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]0.936452106375678[/C][/ROW]
[ROW][C]beta[/C][C]0.0510905500579434[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41243&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
alpha0.936452106375678
beta0.0510905500579434
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13314.65314.0628472222220.58715277777776
14314.93314.944605086629-0.0146050866285918
15315.27315.2508967677630.0191032322372280
16316.26316.1892519806740.0707480193264018
17316.98316.9343549210890.0456450789106384
18317.01316.9748006631990.0351993368010994
19317.07317.521731873344-0.451731873343817
20317.07317.0089793993130.0610206006868452
21317315.3451478536341.65485214636630
22317.08317.660121052635-0.580121052634752
23317.04317.290643665247-0.250643665247367
24317317.160630979219-0.160630979218752
25317.05317.12245464656-0.0724546465602316
26321.59317.3653319498594.22466805014091
27325.59321.8635157893393.72648421066077
28326.23326.674186844677-0.444186844676494
29326.28327.308095438622-1.02809543862173
30326.35326.663611653322-0.313611653322425
31326.35327.157507009326-0.807507009326116
32326.35326.631703231131-0.281703231131246
33326.39325.0193453717041.37065462829599
34326.74327.183689765782-0.443689765782096
35326.9327.226975135375-0.326975135375335
36326.9327.291613605373-0.391613605373038
37326.91327.292097232676-0.382097232676358
38336.93327.7526283921169.17737160788408
39348.5337.32862601102211.1713739889783
40349.43349.673737268367-0.243737268367397
41349.26351.295536257096-2.03553625709628
42349.26350.542121612269-1.28212161226890
43349.28350.840415796707-1.56041579670750
44349.61350.349688692796-0.73968869279588
45349.66349.0982674269510.561732573048914
46349.68351.035909528238-1.35590952823844
47349.91350.834829874594-0.924829874593968
48349.91350.909362827614-0.99936282761422
49350.89350.8861105479450.00388945205457958
50355.52352.8788383375112.64116166248863
51356.36356.711240044503-0.351240044503186
52357.04357.239819596813-0.199819596812972
53360.28358.4902322741391.78976772586083
54360.63361.251278741752-0.621278741752121
55360.79362.066722110706-1.27672211070580
56360.97361.823375530047-0.853375530047117
57361360.4723148445370.527685155463473
58361.01362.178702372381-1.16870237238078
59361362.111775488561-1.11177548856091
60361361.929010247339-0.92901024733942
61361.58361.961264129234-0.381264129234182
62363.19363.668349669231-0.47834966923125
63363.61364.147510690169-0.537510690168517
64364.14364.260560345816-0.120560345815932
65365.51365.4647028585210.0452971414790682
66365.51366.108530313146-0.598530313145659
67365.5366.574323887690-1.07432388769041
68365.5366.227799280841-0.727799280841396
69364.59364.768489235643-0.178489235642758
70364.63365.358381309089-0.728381309088775
71364.54365.381083148135-0.841083148135226
72363.67365.150045182103-1.48004518210251
73365.22364.3613482328720.858651767128322
74369.05366.9429672804992.10703271950075
75370.45369.6827314187250.767268581274834
76370.46370.949842247384-0.489842247384161
77370.46371.706743530168-1.24674353016763
78370.58370.925940384150-0.345940384150424
79370.58371.43633901222-0.85633901222036
80370.22371.164699308334-0.944699308333838
81370.21369.3755345370740.834465462926005
82370.29370.765883609822-0.47588360982212
83370.29370.916773870737-0.626773870736827
84370.2370.7549733532-0.554973353200239
85370.2370.934591898066-0.73459189806573
86372.55371.9807303897820.569269610218157
87374.51372.9989251741571.51107482584308
88375.58374.7218860767320.858113923267638
89375.75376.596673584464-0.846673584463588
90375.75376.170591123898-0.420591123898419
91375.75376.497906772331-0.747906772331476
92375.69376.246639993924-0.556639993924477
93375.76374.8769490482790.883050951721032
94377.5376.174863387471.32513661252989
95377.51378.034239024749-0.524239024749477
96377.74378.009430867254-0.269430867253845

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 314.65 & 314.062847222222 & 0.58715277777776 \tabularnewline
14 & 314.93 & 314.944605086629 & -0.0146050866285918 \tabularnewline
15 & 315.27 & 315.250896767763 & 0.0191032322372280 \tabularnewline
16 & 316.26 & 316.189251980674 & 0.0707480193264018 \tabularnewline
17 & 316.98 & 316.934354921089 & 0.0456450789106384 \tabularnewline
18 & 317.01 & 316.974800663199 & 0.0351993368010994 \tabularnewline
19 & 317.07 & 317.521731873344 & -0.451731873343817 \tabularnewline
20 & 317.07 & 317.008979399313 & 0.0610206006868452 \tabularnewline
21 & 317 & 315.345147853634 & 1.65485214636630 \tabularnewline
22 & 317.08 & 317.660121052635 & -0.580121052634752 \tabularnewline
23 & 317.04 & 317.290643665247 & -0.250643665247367 \tabularnewline
24 & 317 & 317.160630979219 & -0.160630979218752 \tabularnewline
25 & 317.05 & 317.12245464656 & -0.0724546465602316 \tabularnewline
26 & 321.59 & 317.365331949859 & 4.22466805014091 \tabularnewline
27 & 325.59 & 321.863515789339 & 3.72648421066077 \tabularnewline
28 & 326.23 & 326.674186844677 & -0.444186844676494 \tabularnewline
29 & 326.28 & 327.308095438622 & -1.02809543862173 \tabularnewline
30 & 326.35 & 326.663611653322 & -0.313611653322425 \tabularnewline
31 & 326.35 & 327.157507009326 & -0.807507009326116 \tabularnewline
32 & 326.35 & 326.631703231131 & -0.281703231131246 \tabularnewline
33 & 326.39 & 325.019345371704 & 1.37065462829599 \tabularnewline
34 & 326.74 & 327.183689765782 & -0.443689765782096 \tabularnewline
35 & 326.9 & 327.226975135375 & -0.326975135375335 \tabularnewline
36 & 326.9 & 327.291613605373 & -0.391613605373038 \tabularnewline
37 & 326.91 & 327.292097232676 & -0.382097232676358 \tabularnewline
38 & 336.93 & 327.752628392116 & 9.17737160788408 \tabularnewline
39 & 348.5 & 337.328626011022 & 11.1713739889783 \tabularnewline
40 & 349.43 & 349.673737268367 & -0.243737268367397 \tabularnewline
41 & 349.26 & 351.295536257096 & -2.03553625709628 \tabularnewline
42 & 349.26 & 350.542121612269 & -1.28212161226890 \tabularnewline
43 & 349.28 & 350.840415796707 & -1.56041579670750 \tabularnewline
44 & 349.61 & 350.349688692796 & -0.73968869279588 \tabularnewline
45 & 349.66 & 349.098267426951 & 0.561732573048914 \tabularnewline
46 & 349.68 & 351.035909528238 & -1.35590952823844 \tabularnewline
47 & 349.91 & 350.834829874594 & -0.924829874593968 \tabularnewline
48 & 349.91 & 350.909362827614 & -0.99936282761422 \tabularnewline
49 & 350.89 & 350.886110547945 & 0.00388945205457958 \tabularnewline
50 & 355.52 & 352.878838337511 & 2.64116166248863 \tabularnewline
51 & 356.36 & 356.711240044503 & -0.351240044503186 \tabularnewline
52 & 357.04 & 357.239819596813 & -0.199819596812972 \tabularnewline
53 & 360.28 & 358.490232274139 & 1.78976772586083 \tabularnewline
54 & 360.63 & 361.251278741752 & -0.621278741752121 \tabularnewline
55 & 360.79 & 362.066722110706 & -1.27672211070580 \tabularnewline
56 & 360.97 & 361.823375530047 & -0.853375530047117 \tabularnewline
57 & 361 & 360.472314844537 & 0.527685155463473 \tabularnewline
58 & 361.01 & 362.178702372381 & -1.16870237238078 \tabularnewline
59 & 361 & 362.111775488561 & -1.11177548856091 \tabularnewline
60 & 361 & 361.929010247339 & -0.92901024733942 \tabularnewline
61 & 361.58 & 361.961264129234 & -0.381264129234182 \tabularnewline
62 & 363.19 & 363.668349669231 & -0.47834966923125 \tabularnewline
63 & 363.61 & 364.147510690169 & -0.537510690168517 \tabularnewline
64 & 364.14 & 364.260560345816 & -0.120560345815932 \tabularnewline
65 & 365.51 & 365.464702858521 & 0.0452971414790682 \tabularnewline
66 & 365.51 & 366.108530313146 & -0.598530313145659 \tabularnewline
67 & 365.5 & 366.574323887690 & -1.07432388769041 \tabularnewline
68 & 365.5 & 366.227799280841 & -0.727799280841396 \tabularnewline
69 & 364.59 & 364.768489235643 & -0.178489235642758 \tabularnewline
70 & 364.63 & 365.358381309089 & -0.728381309088775 \tabularnewline
71 & 364.54 & 365.381083148135 & -0.841083148135226 \tabularnewline
72 & 363.67 & 365.150045182103 & -1.48004518210251 \tabularnewline
73 & 365.22 & 364.361348232872 & 0.858651767128322 \tabularnewline
74 & 369.05 & 366.942967280499 & 2.10703271950075 \tabularnewline
75 & 370.45 & 369.682731418725 & 0.767268581274834 \tabularnewline
76 & 370.46 & 370.949842247384 & -0.489842247384161 \tabularnewline
77 & 370.46 & 371.706743530168 & -1.24674353016763 \tabularnewline
78 & 370.58 & 370.925940384150 & -0.345940384150424 \tabularnewline
79 & 370.58 & 371.43633901222 & -0.85633901222036 \tabularnewline
80 & 370.22 & 371.164699308334 & -0.944699308333838 \tabularnewline
81 & 370.21 & 369.375534537074 & 0.834465462926005 \tabularnewline
82 & 370.29 & 370.765883609822 & -0.47588360982212 \tabularnewline
83 & 370.29 & 370.916773870737 & -0.626773870736827 \tabularnewline
84 & 370.2 & 370.7549733532 & -0.554973353200239 \tabularnewline
85 & 370.2 & 370.934591898066 & -0.73459189806573 \tabularnewline
86 & 372.55 & 371.980730389782 & 0.569269610218157 \tabularnewline
87 & 374.51 & 372.998925174157 & 1.51107482584308 \tabularnewline
88 & 375.58 & 374.721886076732 & 0.858113923267638 \tabularnewline
89 & 375.75 & 376.596673584464 & -0.846673584463588 \tabularnewline
90 & 375.75 & 376.170591123898 & -0.420591123898419 \tabularnewline
91 & 375.75 & 376.497906772331 & -0.747906772331476 \tabularnewline
92 & 375.69 & 376.246639993924 & -0.556639993924477 \tabularnewline
93 & 375.76 & 374.876949048279 & 0.883050951721032 \tabularnewline
94 & 377.5 & 376.17486338747 & 1.32513661252989 \tabularnewline
95 & 377.51 & 378.034239024749 & -0.524239024749477 \tabularnewline
96 & 377.74 & 378.009430867254 & -0.269430867253845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41243&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]314.65[/C][C]314.062847222222[/C][C]0.58715277777776[/C][/ROW]
[ROW][C]14[/C][C]314.93[/C][C]314.944605086629[/C][C]-0.0146050866285918[/C][/ROW]
[ROW][C]15[/C][C]315.27[/C][C]315.250896767763[/C][C]0.0191032322372280[/C][/ROW]
[ROW][C]16[/C][C]316.26[/C][C]316.189251980674[/C][C]0.0707480193264018[/C][/ROW]
[ROW][C]17[/C][C]316.98[/C][C]316.934354921089[/C][C]0.0456450789106384[/C][/ROW]
[ROW][C]18[/C][C]317.01[/C][C]316.974800663199[/C][C]0.0351993368010994[/C][/ROW]
[ROW][C]19[/C][C]317.07[/C][C]317.521731873344[/C][C]-0.451731873343817[/C][/ROW]
[ROW][C]20[/C][C]317.07[/C][C]317.008979399313[/C][C]0.0610206006868452[/C][/ROW]
[ROW][C]21[/C][C]317[/C][C]315.345147853634[/C][C]1.65485214636630[/C][/ROW]
[ROW][C]22[/C][C]317.08[/C][C]317.660121052635[/C][C]-0.580121052634752[/C][/ROW]
[ROW][C]23[/C][C]317.04[/C][C]317.290643665247[/C][C]-0.250643665247367[/C][/ROW]
[ROW][C]24[/C][C]317[/C][C]317.160630979219[/C][C]-0.160630979218752[/C][/ROW]
[ROW][C]25[/C][C]317.05[/C][C]317.12245464656[/C][C]-0.0724546465602316[/C][/ROW]
[ROW][C]26[/C][C]321.59[/C][C]317.365331949859[/C][C]4.22466805014091[/C][/ROW]
[ROW][C]27[/C][C]325.59[/C][C]321.863515789339[/C][C]3.72648421066077[/C][/ROW]
[ROW][C]28[/C][C]326.23[/C][C]326.674186844677[/C][C]-0.444186844676494[/C][/ROW]
[ROW][C]29[/C][C]326.28[/C][C]327.308095438622[/C][C]-1.02809543862173[/C][/ROW]
[ROW][C]30[/C][C]326.35[/C][C]326.663611653322[/C][C]-0.313611653322425[/C][/ROW]
[ROW][C]31[/C][C]326.35[/C][C]327.157507009326[/C][C]-0.807507009326116[/C][/ROW]
[ROW][C]32[/C][C]326.35[/C][C]326.631703231131[/C][C]-0.281703231131246[/C][/ROW]
[ROW][C]33[/C][C]326.39[/C][C]325.019345371704[/C][C]1.37065462829599[/C][/ROW]
[ROW][C]34[/C][C]326.74[/C][C]327.183689765782[/C][C]-0.443689765782096[/C][/ROW]
[ROW][C]35[/C][C]326.9[/C][C]327.226975135375[/C][C]-0.326975135375335[/C][/ROW]
[ROW][C]36[/C][C]326.9[/C][C]327.291613605373[/C][C]-0.391613605373038[/C][/ROW]
[ROW][C]37[/C][C]326.91[/C][C]327.292097232676[/C][C]-0.382097232676358[/C][/ROW]
[ROW][C]38[/C][C]336.93[/C][C]327.752628392116[/C][C]9.17737160788408[/C][/ROW]
[ROW][C]39[/C][C]348.5[/C][C]337.328626011022[/C][C]11.1713739889783[/C][/ROW]
[ROW][C]40[/C][C]349.43[/C][C]349.673737268367[/C][C]-0.243737268367397[/C][/ROW]
[ROW][C]41[/C][C]349.26[/C][C]351.295536257096[/C][C]-2.03553625709628[/C][/ROW]
[ROW][C]42[/C][C]349.26[/C][C]350.542121612269[/C][C]-1.28212161226890[/C][/ROW]
[ROW][C]43[/C][C]349.28[/C][C]350.840415796707[/C][C]-1.56041579670750[/C][/ROW]
[ROW][C]44[/C][C]349.61[/C][C]350.349688692796[/C][C]-0.73968869279588[/C][/ROW]
[ROW][C]45[/C][C]349.66[/C][C]349.098267426951[/C][C]0.561732573048914[/C][/ROW]
[ROW][C]46[/C][C]349.68[/C][C]351.035909528238[/C][C]-1.35590952823844[/C][/ROW]
[ROW][C]47[/C][C]349.91[/C][C]350.834829874594[/C][C]-0.924829874593968[/C][/ROW]
[ROW][C]48[/C][C]349.91[/C][C]350.909362827614[/C][C]-0.99936282761422[/C][/ROW]
[ROW][C]49[/C][C]350.89[/C][C]350.886110547945[/C][C]0.00388945205457958[/C][/ROW]
[ROW][C]50[/C][C]355.52[/C][C]352.878838337511[/C][C]2.64116166248863[/C][/ROW]
[ROW][C]51[/C][C]356.36[/C][C]356.711240044503[/C][C]-0.351240044503186[/C][/ROW]
[ROW][C]52[/C][C]357.04[/C][C]357.239819596813[/C][C]-0.199819596812972[/C][/ROW]
[ROW][C]53[/C][C]360.28[/C][C]358.490232274139[/C][C]1.78976772586083[/C][/ROW]
[ROW][C]54[/C][C]360.63[/C][C]361.251278741752[/C][C]-0.621278741752121[/C][/ROW]
[ROW][C]55[/C][C]360.79[/C][C]362.066722110706[/C][C]-1.27672211070580[/C][/ROW]
[ROW][C]56[/C][C]360.97[/C][C]361.823375530047[/C][C]-0.853375530047117[/C][/ROW]
[ROW][C]57[/C][C]361[/C][C]360.472314844537[/C][C]0.527685155463473[/C][/ROW]
[ROW][C]58[/C][C]361.01[/C][C]362.178702372381[/C][C]-1.16870237238078[/C][/ROW]
[ROW][C]59[/C][C]361[/C][C]362.111775488561[/C][C]-1.11177548856091[/C][/ROW]
[ROW][C]60[/C][C]361[/C][C]361.929010247339[/C][C]-0.92901024733942[/C][/ROW]
[ROW][C]61[/C][C]361.58[/C][C]361.961264129234[/C][C]-0.381264129234182[/C][/ROW]
[ROW][C]62[/C][C]363.19[/C][C]363.668349669231[/C][C]-0.47834966923125[/C][/ROW]
[ROW][C]63[/C][C]363.61[/C][C]364.147510690169[/C][C]-0.537510690168517[/C][/ROW]
[ROW][C]64[/C][C]364.14[/C][C]364.260560345816[/C][C]-0.120560345815932[/C][/ROW]
[ROW][C]65[/C][C]365.51[/C][C]365.464702858521[/C][C]0.0452971414790682[/C][/ROW]
[ROW][C]66[/C][C]365.51[/C][C]366.108530313146[/C][C]-0.598530313145659[/C][/ROW]
[ROW][C]67[/C][C]365.5[/C][C]366.574323887690[/C][C]-1.07432388769041[/C][/ROW]
[ROW][C]68[/C][C]365.5[/C][C]366.227799280841[/C][C]-0.727799280841396[/C][/ROW]
[ROW][C]69[/C][C]364.59[/C][C]364.768489235643[/C][C]-0.178489235642758[/C][/ROW]
[ROW][C]70[/C][C]364.63[/C][C]365.358381309089[/C][C]-0.728381309088775[/C][/ROW]
[ROW][C]71[/C][C]364.54[/C][C]365.381083148135[/C][C]-0.841083148135226[/C][/ROW]
[ROW][C]72[/C][C]363.67[/C][C]365.150045182103[/C][C]-1.48004518210251[/C][/ROW]
[ROW][C]73[/C][C]365.22[/C][C]364.361348232872[/C][C]0.858651767128322[/C][/ROW]
[ROW][C]74[/C][C]369.05[/C][C]366.942967280499[/C][C]2.10703271950075[/C][/ROW]
[ROW][C]75[/C][C]370.45[/C][C]369.682731418725[/C][C]0.767268581274834[/C][/ROW]
[ROW][C]76[/C][C]370.46[/C][C]370.949842247384[/C][C]-0.489842247384161[/C][/ROW]
[ROW][C]77[/C][C]370.46[/C][C]371.706743530168[/C][C]-1.24674353016763[/C][/ROW]
[ROW][C]78[/C][C]370.58[/C][C]370.925940384150[/C][C]-0.345940384150424[/C][/ROW]
[ROW][C]79[/C][C]370.58[/C][C]371.43633901222[/C][C]-0.85633901222036[/C][/ROW]
[ROW][C]80[/C][C]370.22[/C][C]371.164699308334[/C][C]-0.944699308333838[/C][/ROW]
[ROW][C]81[/C][C]370.21[/C][C]369.375534537074[/C][C]0.834465462926005[/C][/ROW]
[ROW][C]82[/C][C]370.29[/C][C]370.765883609822[/C][C]-0.47588360982212[/C][/ROW]
[ROW][C]83[/C][C]370.29[/C][C]370.916773870737[/C][C]-0.626773870736827[/C][/ROW]
[ROW][C]84[/C][C]370.2[/C][C]370.7549733532[/C][C]-0.554973353200239[/C][/ROW]
[ROW][C]85[/C][C]370.2[/C][C]370.934591898066[/C][C]-0.73459189806573[/C][/ROW]
[ROW][C]86[/C][C]372.55[/C][C]371.980730389782[/C][C]0.569269610218157[/C][/ROW]
[ROW][C]87[/C][C]374.51[/C][C]372.998925174157[/C][C]1.51107482584308[/C][/ROW]
[ROW][C]88[/C][C]375.58[/C][C]374.721886076732[/C][C]0.858113923267638[/C][/ROW]
[ROW][C]89[/C][C]375.75[/C][C]376.596673584464[/C][C]-0.846673584463588[/C][/ROW]
[ROW][C]90[/C][C]375.75[/C][C]376.170591123898[/C][C]-0.420591123898419[/C][/ROW]
[ROW][C]91[/C][C]375.75[/C][C]376.497906772331[/C][C]-0.747906772331476[/C][/ROW]
[ROW][C]92[/C][C]375.69[/C][C]376.246639993924[/C][C]-0.556639993924477[/C][/ROW]
[ROW][C]93[/C][C]375.76[/C][C]374.876949048279[/C][C]0.883050951721032[/C][/ROW]
[ROW][C]94[/C][C]377.5[/C][C]376.17486338747[/C][C]1.32513661252989[/C][/ROW]
[ROW][C]95[/C][C]377.51[/C][C]378.034239024749[/C][C]-0.524239024749477[/C][/ROW]
[ROW][C]96[/C][C]377.74[/C][C]378.009430867254[/C][C]-0.269430867253845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41243&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
13314.65314.0628472222220.58715277777776
14314.93314.944605086629-0.0146050866285918
15315.27315.2508967677630.0191032322372280
16316.26316.1892519806740.0707480193264018
17316.98316.9343549210890.0456450789106384
18317.01316.9748006631990.0351993368010994
19317.07317.521731873344-0.451731873343817
20317.07317.0089793993130.0610206006868452
21317315.3451478536341.65485214636630
22317.08317.660121052635-0.580121052634752
23317.04317.290643665247-0.250643665247367
24317317.160630979219-0.160630979218752
25317.05317.12245464656-0.0724546465602316
26321.59317.3653319498594.22466805014091
27325.59321.8635157893393.72648421066077
28326.23326.674186844677-0.444186844676494
29326.28327.308095438622-1.02809543862173
30326.35326.663611653322-0.313611653322425
31326.35327.157507009326-0.807507009326116
32326.35326.631703231131-0.281703231131246
33326.39325.0193453717041.37065462829599
34326.74327.183689765782-0.443689765782096
35326.9327.226975135375-0.326975135375335
36326.9327.291613605373-0.391613605373038
37326.91327.292097232676-0.382097232676358
38336.93327.7526283921169.17737160788408
39348.5337.32862601102211.1713739889783
40349.43349.673737268367-0.243737268367397
41349.26351.295536257096-2.03553625709628
42349.26350.542121612269-1.28212161226890
43349.28350.840415796707-1.56041579670750
44349.61350.349688692796-0.73968869279588
45349.66349.0982674269510.561732573048914
46349.68351.035909528238-1.35590952823844
47349.91350.834829874594-0.924829874593968
48349.91350.909362827614-0.99936282761422
49350.89350.8861105479450.00388945205457958
50355.52352.8788383375112.64116166248863
51356.36356.711240044503-0.351240044503186
52357.04357.239819596813-0.199819596812972
53360.28358.4902322741391.78976772586083
54360.63361.251278741752-0.621278741752121
55360.79362.066722110706-1.27672211070580
56360.97361.823375530047-0.853375530047117
57361360.4723148445370.527685155463473
58361.01362.178702372381-1.16870237238078
59361362.111775488561-1.11177548856091
60361361.929010247339-0.92901024733942
61361.58361.961264129234-0.381264129234182
62363.19363.668349669231-0.47834966923125
63363.61364.147510690169-0.537510690168517
64364.14364.260560345816-0.120560345815932
65365.51365.4647028585210.0452971414790682
66365.51366.108530313146-0.598530313145659
67365.5366.574323887690-1.07432388769041
68365.5366.227799280841-0.727799280841396
69364.59364.768489235643-0.178489235642758
70364.63365.358381309089-0.728381309088775
71364.54365.381083148135-0.841083148135226
72363.67365.150045182103-1.48004518210251
73365.22364.3613482328720.858651767128322
74369.05366.9429672804992.10703271950075
75370.45369.6827314187250.767268581274834
76370.46370.949842247384-0.489842247384161
77370.46371.706743530168-1.24674353016763
78370.58370.925940384150-0.345940384150424
79370.58371.43633901222-0.85633901222036
80370.22371.164699308334-0.944699308333838
81370.21369.3755345370740.834465462926005
82370.29370.765883609822-0.47588360982212
83370.29370.916773870737-0.626773870736827
84370.2370.7549733532-0.554973353200239
85370.2370.934591898066-0.73459189806573
86372.55371.9807303897820.569269610218157
87374.51372.9989251741571.51107482584308
88375.58374.7218860767320.858113923267638
89375.75376.596673584464-0.846673584463588
90375.75376.170591123898-0.420591123898419
91375.75376.497906772331-0.747906772331476
92375.69376.246639993924-0.556639993924477
93375.76374.8769490482790.883050951721032
94377.5376.174863387471.32513661252989
95377.51378.034239024749-0.524239024749477
96377.74378.009430867254-0.269430867253845







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97378.495103963035374.747881657762382.242326268308
98380.397228013070375.139301533829385.655154492312
99381.000160533465374.472943356632387.527377710299
100381.25226402429373.572271941374388.932256107205
101382.159763891063373.39373756367390.925790218457
102382.538766066849372.727972757363392.349559376335
103383.244406371056372.415191001902394.073621740209
104383.746717239580371.915900624742395.577533854417
105383.057458291688370.235410955174395.879505628202
106383.581958735416369.774489103352397.38942836748
107384.044911248571369.254493244106398.835329253035
108384.514329740868368.740936860126400.287722621609

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 378.495103963035 & 374.747881657762 & 382.242326268308 \tabularnewline
98 & 380.397228013070 & 375.139301533829 & 385.655154492312 \tabularnewline
99 & 381.000160533465 & 374.472943356632 & 387.527377710299 \tabularnewline
100 & 381.25226402429 & 373.572271941374 & 388.932256107205 \tabularnewline
101 & 382.159763891063 & 373.39373756367 & 390.925790218457 \tabularnewline
102 & 382.538766066849 & 372.727972757363 & 392.349559376335 \tabularnewline
103 & 383.244406371056 & 372.415191001902 & 394.073621740209 \tabularnewline
104 & 383.746717239580 & 371.915900624742 & 395.577533854417 \tabularnewline
105 & 383.057458291688 & 370.235410955174 & 395.879505628202 \tabularnewline
106 & 383.581958735416 & 369.774489103352 & 397.38942836748 \tabularnewline
107 & 384.044911248571 & 369.254493244106 & 398.835329253035 \tabularnewline
108 & 384.514329740868 & 368.740936860126 & 400.287722621609 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41243&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]97[/C][C]378.495103963035[/C][C]374.747881657762[/C][C]382.242326268308[/C][/ROW]
[ROW][C]98[/C][C]380.397228013070[/C][C]375.139301533829[/C][C]385.655154492312[/C][/ROW]
[ROW][C]99[/C][C]381.000160533465[/C][C]374.472943356632[/C][C]387.527377710299[/C][/ROW]
[ROW][C]100[/C][C]381.25226402429[/C][C]373.572271941374[/C][C]388.932256107205[/C][/ROW]
[ROW][C]101[/C][C]382.159763891063[/C][C]373.39373756367[/C][C]390.925790218457[/C][/ROW]
[ROW][C]102[/C][C]382.538766066849[/C][C]372.727972757363[/C][C]392.349559376335[/C][/ROW]
[ROW][C]103[/C][C]383.244406371056[/C][C]372.415191001902[/C][C]394.073621740209[/C][/ROW]
[ROW][C]104[/C][C]383.746717239580[/C][C]371.915900624742[/C][C]395.577533854417[/C][/ROW]
[ROW][C]105[/C][C]383.057458291688[/C][C]370.235410955174[/C][C]395.879505628202[/C][/ROW]
[ROW][C]106[/C][C]383.581958735416[/C][C]369.774489103352[/C][C]397.38942836748[/C][/ROW]
[ROW][C]107[/C][C]384.044911248571[/C][C]369.254493244106[/C][C]398.835329253035[/C][/ROW]
[ROW][C]108[/C][C]384.514329740868[/C][C]368.740936860126[/C][C]400.287722621609[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41243&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41243&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
97378.495103963035374.747881657762382.242326268308
98380.397228013070375.139301533829385.655154492312
99381.000160533465374.472943356632387.527377710299
100381.25226402429373.572271941374388.932256107205
101382.159763891063373.39373756367390.925790218457
102382.538766066849372.727972757363392.349559376335
103383.244406371056372.415191001902394.073621740209
104383.746717239580371.915900624742395.577533854417
105383.057458291688370.235410955174395.879505628202
106383.581958735416369.774489103352397.38942836748
107384.044911248571369.254493244106398.835329253035
108384.514329740868368.740936860126400.287722621609



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')