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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 17:33:22 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/18/t1313703423oli9k9c0vmddesk.htm/, Retrieved Wed, 15 May 2024 12:32:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124166, Retrieved Wed, 15 May 2024 12:32:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVoorspellen van tijdsreeksen - Willem-Jan Carpels
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Voorspellen van t...] [2011-08-18 21:33:22] [49802af8bc65831d925aaf5d22a63767] [Current]
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Dataseries X:
510
460
570
520
470
500
520
500
580
460
530
610
460
380
570
480
530
530
580
420
580
460
520
640
380
360
610
440
520
540
580
360
500
530
470
660
410
360
610
360
540
560
580
480
560
560
390
630
380
440
620
310
500
660
420
550
570
560
290
560
320
440
610
250
510
670
350
590
500
530
300
620
280
450
620
320
560
680
370
670
510
480
280
570
240
460
600
320
570
680
390
700
570
450
270
640
230
490
590
310
570
660
370
600
540
510
330
590




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'AstonUniversity' @ aston.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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124166&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124166&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 time1 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124166&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[/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=124166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124166&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
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13460455.256410256414.74358974358961
14380376.0431235431243.95687645687633
15570569.3298368298370.67016317016305
16480479.2832167832170.716783216783028
17530529.6532634032640.346736596736378
18530528.773310023311.22668997668984
19580512.89335664335767.106643356643
20420498.263403263403-78.2634032634035
21580581.550116550117-1.55011655011674
22460463.170163170163-3.17016317016339
23520532.29020979021-12.29020979021
24640608.4935897435931.5064102564099
25380459.44055944056-79.4405594405596
26360379.44055944056-19.4405594405596
27610569.4405594405640.5594405594404
28440479.44055944056-39.4405594405596
29520529.44055944056-9.44055944055958
30540529.4405594405610.5594405594404
31580579.440559440560.559440559440418
32360419.44055944056-59.4405594405596
33500579.44055944056-79.4405594405596
34530459.4405594405670.5594405594404
35470519.44055944056-49.4405594405596
36660639.4405594405620.5594405594404
37410379.4405594405630.5594405594404
38360359.440559440560.559440559440418
39610609.440559440560.559440559440418
40360439.44055944056-79.4405594405596
41540519.4405594405620.5594405594404
42560539.4405594405620.5594405594404
43580579.440559440560.559440559440418
44480359.44055944056120.55944055944
45560499.4405594405660.5594405594404
46560529.4405594405630.5594405594404
47390469.44055944056-79.4405594405596
48630659.44055944056-29.4405594405596
49380409.44055944056-29.4405594405596
50440359.4405594405680.5594405594404
51620609.4405594405610.5594405594404
52310359.44055944056-49.4405594405596
53500539.44055944056-39.4405594405596
54660559.44055944056100.55944055944
55420579.44055944056-159.44055944056
56550479.4405594405670.5594405594404
57570559.4405594405610.5594405594404
58560559.440559440560.559440559440418
59290389.44055944056-99.4405594405596
60560629.44055944056-69.4405594405596
61320379.44055944056-59.4405594405596
62440439.440559440560.559440559440418
63610619.44055944056-9.44055944055958
64250309.44055944056-59.4405594405596
65510499.4405594405610.5594405594404
66670659.4405594405610.5594405594404
67350419.44055944056-69.4405594405596
68590549.4405594405640.5594405594404
69500569.44055944056-69.4405594405596
70530559.44055944056-29.4405594405596
71300289.4405594405610.5594405594404
72620559.4405594405660.5594405594404
73280319.44055944056-39.4405594405596
74450439.4405594405610.5594405594404
75620609.4405594405610.5594405594404
76320249.4405594405670.5594405594404
77560509.4405594405650.5594405594404
78680669.4405594405610.5594405594404
79370349.4405594405620.5594405594404
80670589.4405594405680.5594405594404
81510499.4405594405610.5594405594404
82480529.44055944056-49.4405594405596
83280299.44055944056-19.4405594405596
84570619.44055944056-49.4405594405596
85240279.44055944056-39.4405594405596
86460449.4405594405610.5594405594404
87600619.44055944056-19.4405594405596
88320319.440559440560.559440559440418
89570559.4405594405610.5594405594404
90680679.440559440560.559440559440418
91390369.4405594405620.5594405594404
92700669.4405594405630.5594405594404
93570509.4405594405660.5594405594404
94450479.44055944056-29.4405594405596
95270279.44055944056-9.44055944055958
96640569.4405594405670.5594405594404
97230239.44055944056-9.44055944055958
98490459.4405594405630.5594405594404
99590599.44055944056-9.44055944055958
100310319.44055944056-9.44055944055958
101570569.440559440560.559440559440418
102660679.44055944056-19.4405594405596
103370389.44055944056-19.4405594405596
104600699.44055944056-99.4405594405596
105540569.44055944056-29.4405594405596
106510449.4405594405660.5594405594404
107330269.4405594405660.5594405594404
108590639.44055944056-49.4405594405596

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 460 & 455.25641025641 & 4.74358974358961 \tabularnewline
14 & 380 & 376.043123543124 & 3.95687645687633 \tabularnewline
15 & 570 & 569.329836829837 & 0.67016317016305 \tabularnewline
16 & 480 & 479.283216783217 & 0.716783216783028 \tabularnewline
17 & 530 & 529.653263403264 & 0.346736596736378 \tabularnewline
18 & 530 & 528.77331002331 & 1.22668997668984 \tabularnewline
19 & 580 & 512.893356643357 & 67.106643356643 \tabularnewline
20 & 420 & 498.263403263403 & -78.2634032634035 \tabularnewline
21 & 580 & 581.550116550117 & -1.55011655011674 \tabularnewline
22 & 460 & 463.170163170163 & -3.17016317016339 \tabularnewline
23 & 520 & 532.29020979021 & -12.29020979021 \tabularnewline
24 & 640 & 608.49358974359 & 31.5064102564099 \tabularnewline
25 & 380 & 459.44055944056 & -79.4405594405596 \tabularnewline
26 & 360 & 379.44055944056 & -19.4405594405596 \tabularnewline
27 & 610 & 569.44055944056 & 40.5594405594404 \tabularnewline
28 & 440 & 479.44055944056 & -39.4405594405596 \tabularnewline
29 & 520 & 529.44055944056 & -9.44055944055958 \tabularnewline
30 & 540 & 529.44055944056 & 10.5594405594404 \tabularnewline
31 & 580 & 579.44055944056 & 0.559440559440418 \tabularnewline
32 & 360 & 419.44055944056 & -59.4405594405596 \tabularnewline
33 & 500 & 579.44055944056 & -79.4405594405596 \tabularnewline
34 & 530 & 459.44055944056 & 70.5594405594404 \tabularnewline
35 & 470 & 519.44055944056 & -49.4405594405596 \tabularnewline
36 & 660 & 639.44055944056 & 20.5594405594404 \tabularnewline
37 & 410 & 379.44055944056 & 30.5594405594404 \tabularnewline
38 & 360 & 359.44055944056 & 0.559440559440418 \tabularnewline
39 & 610 & 609.44055944056 & 0.559440559440418 \tabularnewline
40 & 360 & 439.44055944056 & -79.4405594405596 \tabularnewline
41 & 540 & 519.44055944056 & 20.5594405594404 \tabularnewline
42 & 560 & 539.44055944056 & 20.5594405594404 \tabularnewline
43 & 580 & 579.44055944056 & 0.559440559440418 \tabularnewline
44 & 480 & 359.44055944056 & 120.55944055944 \tabularnewline
45 & 560 & 499.44055944056 & 60.5594405594404 \tabularnewline
46 & 560 & 529.44055944056 & 30.5594405594404 \tabularnewline
47 & 390 & 469.44055944056 & -79.4405594405596 \tabularnewline
48 & 630 & 659.44055944056 & -29.4405594405596 \tabularnewline
49 & 380 & 409.44055944056 & -29.4405594405596 \tabularnewline
50 & 440 & 359.44055944056 & 80.5594405594404 \tabularnewline
51 & 620 & 609.44055944056 & 10.5594405594404 \tabularnewline
52 & 310 & 359.44055944056 & -49.4405594405596 \tabularnewline
53 & 500 & 539.44055944056 & -39.4405594405596 \tabularnewline
54 & 660 & 559.44055944056 & 100.55944055944 \tabularnewline
55 & 420 & 579.44055944056 & -159.44055944056 \tabularnewline
56 & 550 & 479.44055944056 & 70.5594405594404 \tabularnewline
57 & 570 & 559.44055944056 & 10.5594405594404 \tabularnewline
58 & 560 & 559.44055944056 & 0.559440559440418 \tabularnewline
59 & 290 & 389.44055944056 & -99.4405594405596 \tabularnewline
60 & 560 & 629.44055944056 & -69.4405594405596 \tabularnewline
61 & 320 & 379.44055944056 & -59.4405594405596 \tabularnewline
62 & 440 & 439.44055944056 & 0.559440559440418 \tabularnewline
63 & 610 & 619.44055944056 & -9.44055944055958 \tabularnewline
64 & 250 & 309.44055944056 & -59.4405594405596 \tabularnewline
65 & 510 & 499.44055944056 & 10.5594405594404 \tabularnewline
66 & 670 & 659.44055944056 & 10.5594405594404 \tabularnewline
67 & 350 & 419.44055944056 & -69.4405594405596 \tabularnewline
68 & 590 & 549.44055944056 & 40.5594405594404 \tabularnewline
69 & 500 & 569.44055944056 & -69.4405594405596 \tabularnewline
70 & 530 & 559.44055944056 & -29.4405594405596 \tabularnewline
71 & 300 & 289.44055944056 & 10.5594405594404 \tabularnewline
72 & 620 & 559.44055944056 & 60.5594405594404 \tabularnewline
73 & 280 & 319.44055944056 & -39.4405594405596 \tabularnewline
74 & 450 & 439.44055944056 & 10.5594405594404 \tabularnewline
75 & 620 & 609.44055944056 & 10.5594405594404 \tabularnewline
76 & 320 & 249.44055944056 & 70.5594405594404 \tabularnewline
77 & 560 & 509.44055944056 & 50.5594405594404 \tabularnewline
78 & 680 & 669.44055944056 & 10.5594405594404 \tabularnewline
79 & 370 & 349.44055944056 & 20.5594405594404 \tabularnewline
80 & 670 & 589.44055944056 & 80.5594405594404 \tabularnewline
81 & 510 & 499.44055944056 & 10.5594405594404 \tabularnewline
82 & 480 & 529.44055944056 & -49.4405594405596 \tabularnewline
83 & 280 & 299.44055944056 & -19.4405594405596 \tabularnewline
84 & 570 & 619.44055944056 & -49.4405594405596 \tabularnewline
85 & 240 & 279.44055944056 & -39.4405594405596 \tabularnewline
86 & 460 & 449.44055944056 & 10.5594405594404 \tabularnewline
87 & 600 & 619.44055944056 & -19.4405594405596 \tabularnewline
88 & 320 & 319.44055944056 & 0.559440559440418 \tabularnewline
89 & 570 & 559.44055944056 & 10.5594405594404 \tabularnewline
90 & 680 & 679.44055944056 & 0.559440559440418 \tabularnewline
91 & 390 & 369.44055944056 & 20.5594405594404 \tabularnewline
92 & 700 & 669.44055944056 & 30.5594405594404 \tabularnewline
93 & 570 & 509.44055944056 & 60.5594405594404 \tabularnewline
94 & 450 & 479.44055944056 & -29.4405594405596 \tabularnewline
95 & 270 & 279.44055944056 & -9.44055944055958 \tabularnewline
96 & 640 & 569.44055944056 & 70.5594405594404 \tabularnewline
97 & 230 & 239.44055944056 & -9.44055944055958 \tabularnewline
98 & 490 & 459.44055944056 & 30.5594405594404 \tabularnewline
99 & 590 & 599.44055944056 & -9.44055944055958 \tabularnewline
100 & 310 & 319.44055944056 & -9.44055944055958 \tabularnewline
101 & 570 & 569.44055944056 & 0.559440559440418 \tabularnewline
102 & 660 & 679.44055944056 & -19.4405594405596 \tabularnewline
103 & 370 & 389.44055944056 & -19.4405594405596 \tabularnewline
104 & 600 & 699.44055944056 & -99.4405594405596 \tabularnewline
105 & 540 & 569.44055944056 & -29.4405594405596 \tabularnewline
106 & 510 & 449.44055944056 & 60.5594405594404 \tabularnewline
107 & 330 & 269.44055944056 & 60.5594405594404 \tabularnewline
108 & 590 & 639.44055944056 & -49.4405594405596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124166&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]460[/C][C]455.25641025641[/C][C]4.74358974358961[/C][/ROW]
[ROW][C]14[/C][C]380[/C][C]376.043123543124[/C][C]3.95687645687633[/C][/ROW]
[ROW][C]15[/C][C]570[/C][C]569.329836829837[/C][C]0.67016317016305[/C][/ROW]
[ROW][C]16[/C][C]480[/C][C]479.283216783217[/C][C]0.716783216783028[/C][/ROW]
[ROW][C]17[/C][C]530[/C][C]529.653263403264[/C][C]0.346736596736378[/C][/ROW]
[ROW][C]18[/C][C]530[/C][C]528.77331002331[/C][C]1.22668997668984[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]512.893356643357[/C][C]67.106643356643[/C][/ROW]
[ROW][C]20[/C][C]420[/C][C]498.263403263403[/C][C]-78.2634032634035[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]581.550116550117[/C][C]-1.55011655011674[/C][/ROW]
[ROW][C]22[/C][C]460[/C][C]463.170163170163[/C][C]-3.17016317016339[/C][/ROW]
[ROW][C]23[/C][C]520[/C][C]532.29020979021[/C][C]-12.29020979021[/C][/ROW]
[ROW][C]24[/C][C]640[/C][C]608.49358974359[/C][C]31.5064102564099[/C][/ROW]
[ROW][C]25[/C][C]380[/C][C]459.44055944056[/C][C]-79.4405594405596[/C][/ROW]
[ROW][C]26[/C][C]360[/C][C]379.44055944056[/C][C]-19.4405594405596[/C][/ROW]
[ROW][C]27[/C][C]610[/C][C]569.44055944056[/C][C]40.5594405594404[/C][/ROW]
[ROW][C]28[/C][C]440[/C][C]479.44055944056[/C][C]-39.4405594405596[/C][/ROW]
[ROW][C]29[/C][C]520[/C][C]529.44055944056[/C][C]-9.44055944055958[/C][/ROW]
[ROW][C]30[/C][C]540[/C][C]529.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]579.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]32[/C][C]360[/C][C]419.44055944056[/C][C]-59.4405594405596[/C][/ROW]
[ROW][C]33[/C][C]500[/C][C]579.44055944056[/C][C]-79.4405594405596[/C][/ROW]
[ROW][C]34[/C][C]530[/C][C]459.44055944056[/C][C]70.5594405594404[/C][/ROW]
[ROW][C]35[/C][C]470[/C][C]519.44055944056[/C][C]-49.4405594405596[/C][/ROW]
[ROW][C]36[/C][C]660[/C][C]639.44055944056[/C][C]20.5594405594404[/C][/ROW]
[ROW][C]37[/C][C]410[/C][C]379.44055944056[/C][C]30.5594405594404[/C][/ROW]
[ROW][C]38[/C][C]360[/C][C]359.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]39[/C][C]610[/C][C]609.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]40[/C][C]360[/C][C]439.44055944056[/C][C]-79.4405594405596[/C][/ROW]
[ROW][C]41[/C][C]540[/C][C]519.44055944056[/C][C]20.5594405594404[/C][/ROW]
[ROW][C]42[/C][C]560[/C][C]539.44055944056[/C][C]20.5594405594404[/C][/ROW]
[ROW][C]43[/C][C]580[/C][C]579.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]44[/C][C]480[/C][C]359.44055944056[/C][C]120.55944055944[/C][/ROW]
[ROW][C]45[/C][C]560[/C][C]499.44055944056[/C][C]60.5594405594404[/C][/ROW]
[ROW][C]46[/C][C]560[/C][C]529.44055944056[/C][C]30.5594405594404[/C][/ROW]
[ROW][C]47[/C][C]390[/C][C]469.44055944056[/C][C]-79.4405594405596[/C][/ROW]
[ROW][C]48[/C][C]630[/C][C]659.44055944056[/C][C]-29.4405594405596[/C][/ROW]
[ROW][C]49[/C][C]380[/C][C]409.44055944056[/C][C]-29.4405594405596[/C][/ROW]
[ROW][C]50[/C][C]440[/C][C]359.44055944056[/C][C]80.5594405594404[/C][/ROW]
[ROW][C]51[/C][C]620[/C][C]609.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]52[/C][C]310[/C][C]359.44055944056[/C][C]-49.4405594405596[/C][/ROW]
[ROW][C]53[/C][C]500[/C][C]539.44055944056[/C][C]-39.4405594405596[/C][/ROW]
[ROW][C]54[/C][C]660[/C][C]559.44055944056[/C][C]100.55944055944[/C][/ROW]
[ROW][C]55[/C][C]420[/C][C]579.44055944056[/C][C]-159.44055944056[/C][/ROW]
[ROW][C]56[/C][C]550[/C][C]479.44055944056[/C][C]70.5594405594404[/C][/ROW]
[ROW][C]57[/C][C]570[/C][C]559.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]58[/C][C]560[/C][C]559.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]59[/C][C]290[/C][C]389.44055944056[/C][C]-99.4405594405596[/C][/ROW]
[ROW][C]60[/C][C]560[/C][C]629.44055944056[/C][C]-69.4405594405596[/C][/ROW]
[ROW][C]61[/C][C]320[/C][C]379.44055944056[/C][C]-59.4405594405596[/C][/ROW]
[ROW][C]62[/C][C]440[/C][C]439.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]63[/C][C]610[/C][C]619.44055944056[/C][C]-9.44055944055958[/C][/ROW]
[ROW][C]64[/C][C]250[/C][C]309.44055944056[/C][C]-59.4405594405596[/C][/ROW]
[ROW][C]65[/C][C]510[/C][C]499.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]66[/C][C]670[/C][C]659.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]67[/C][C]350[/C][C]419.44055944056[/C][C]-69.4405594405596[/C][/ROW]
[ROW][C]68[/C][C]590[/C][C]549.44055944056[/C][C]40.5594405594404[/C][/ROW]
[ROW][C]69[/C][C]500[/C][C]569.44055944056[/C][C]-69.4405594405596[/C][/ROW]
[ROW][C]70[/C][C]530[/C][C]559.44055944056[/C][C]-29.4405594405596[/C][/ROW]
[ROW][C]71[/C][C]300[/C][C]289.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]72[/C][C]620[/C][C]559.44055944056[/C][C]60.5594405594404[/C][/ROW]
[ROW][C]73[/C][C]280[/C][C]319.44055944056[/C][C]-39.4405594405596[/C][/ROW]
[ROW][C]74[/C][C]450[/C][C]439.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]75[/C][C]620[/C][C]609.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]76[/C][C]320[/C][C]249.44055944056[/C][C]70.5594405594404[/C][/ROW]
[ROW][C]77[/C][C]560[/C][C]509.44055944056[/C][C]50.5594405594404[/C][/ROW]
[ROW][C]78[/C][C]680[/C][C]669.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]79[/C][C]370[/C][C]349.44055944056[/C][C]20.5594405594404[/C][/ROW]
[ROW][C]80[/C][C]670[/C][C]589.44055944056[/C][C]80.5594405594404[/C][/ROW]
[ROW][C]81[/C][C]510[/C][C]499.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]82[/C][C]480[/C][C]529.44055944056[/C][C]-49.4405594405596[/C][/ROW]
[ROW][C]83[/C][C]280[/C][C]299.44055944056[/C][C]-19.4405594405596[/C][/ROW]
[ROW][C]84[/C][C]570[/C][C]619.44055944056[/C][C]-49.4405594405596[/C][/ROW]
[ROW][C]85[/C][C]240[/C][C]279.44055944056[/C][C]-39.4405594405596[/C][/ROW]
[ROW][C]86[/C][C]460[/C][C]449.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]87[/C][C]600[/C][C]619.44055944056[/C][C]-19.4405594405596[/C][/ROW]
[ROW][C]88[/C][C]320[/C][C]319.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]89[/C][C]570[/C][C]559.44055944056[/C][C]10.5594405594404[/C][/ROW]
[ROW][C]90[/C][C]680[/C][C]679.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]91[/C][C]390[/C][C]369.44055944056[/C][C]20.5594405594404[/C][/ROW]
[ROW][C]92[/C][C]700[/C][C]669.44055944056[/C][C]30.5594405594404[/C][/ROW]
[ROW][C]93[/C][C]570[/C][C]509.44055944056[/C][C]60.5594405594404[/C][/ROW]
[ROW][C]94[/C][C]450[/C][C]479.44055944056[/C][C]-29.4405594405596[/C][/ROW]
[ROW][C]95[/C][C]270[/C][C]279.44055944056[/C][C]-9.44055944055958[/C][/ROW]
[ROW][C]96[/C][C]640[/C][C]569.44055944056[/C][C]70.5594405594404[/C][/ROW]
[ROW][C]97[/C][C]230[/C][C]239.44055944056[/C][C]-9.44055944055958[/C][/ROW]
[ROW][C]98[/C][C]490[/C][C]459.44055944056[/C][C]30.5594405594404[/C][/ROW]
[ROW][C]99[/C][C]590[/C][C]599.44055944056[/C][C]-9.44055944055958[/C][/ROW]
[ROW][C]100[/C][C]310[/C][C]319.44055944056[/C][C]-9.44055944055958[/C][/ROW]
[ROW][C]101[/C][C]570[/C][C]569.44055944056[/C][C]0.559440559440418[/C][/ROW]
[ROW][C]102[/C][C]660[/C][C]679.44055944056[/C][C]-19.4405594405596[/C][/ROW]
[ROW][C]103[/C][C]370[/C][C]389.44055944056[/C][C]-19.4405594405596[/C][/ROW]
[ROW][C]104[/C][C]600[/C][C]699.44055944056[/C][C]-99.4405594405596[/C][/ROW]
[ROW][C]105[/C][C]540[/C][C]569.44055944056[/C][C]-29.4405594405596[/C][/ROW]
[ROW][C]106[/C][C]510[/C][C]449.44055944056[/C][C]60.5594405594404[/C][/ROW]
[ROW][C]107[/C][C]330[/C][C]269.44055944056[/C][C]60.5594405594404[/C][/ROW]
[ROW][C]108[/C][C]590[/C][C]639.44055944056[/C][C]-49.4405594405596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124166&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124166&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
13460455.256410256414.74358974358961
14380376.0431235431243.95687645687633
15570569.3298368298370.67016317016305
16480479.2832167832170.716783216783028
17530529.6532634032640.346736596736378
18530528.773310023311.22668997668984
19580512.89335664335767.106643356643
20420498.263403263403-78.2634032634035
21580581.550116550117-1.55011655011674
22460463.170163170163-3.17016317016339
23520532.29020979021-12.29020979021
24640608.4935897435931.5064102564099
25380459.44055944056-79.4405594405596
26360379.44055944056-19.4405594405596
27610569.4405594405640.5594405594404
28440479.44055944056-39.4405594405596
29520529.44055944056-9.44055944055958
30540529.4405594405610.5594405594404
31580579.440559440560.559440559440418
32360419.44055944056-59.4405594405596
33500579.44055944056-79.4405594405596
34530459.4405594405670.5594405594404
35470519.44055944056-49.4405594405596
36660639.4405594405620.5594405594404
37410379.4405594405630.5594405594404
38360359.440559440560.559440559440418
39610609.440559440560.559440559440418
40360439.44055944056-79.4405594405596
41540519.4405594405620.5594405594404
42560539.4405594405620.5594405594404
43580579.440559440560.559440559440418
44480359.44055944056120.55944055944
45560499.4405594405660.5594405594404
46560529.4405594405630.5594405594404
47390469.44055944056-79.4405594405596
48630659.44055944056-29.4405594405596
49380409.44055944056-29.4405594405596
50440359.4405594405680.5594405594404
51620609.4405594405610.5594405594404
52310359.44055944056-49.4405594405596
53500539.44055944056-39.4405594405596
54660559.44055944056100.55944055944
55420579.44055944056-159.44055944056
56550479.4405594405670.5594405594404
57570559.4405594405610.5594405594404
58560559.440559440560.559440559440418
59290389.44055944056-99.4405594405596
60560629.44055944056-69.4405594405596
61320379.44055944056-59.4405594405596
62440439.440559440560.559440559440418
63610619.44055944056-9.44055944055958
64250309.44055944056-59.4405594405596
65510499.4405594405610.5594405594404
66670659.4405594405610.5594405594404
67350419.44055944056-69.4405594405596
68590549.4405594405640.5594405594404
69500569.44055944056-69.4405594405596
70530559.44055944056-29.4405594405596
71300289.4405594405610.5594405594404
72620559.4405594405660.5594405594404
73280319.44055944056-39.4405594405596
74450439.4405594405610.5594405594404
75620609.4405594405610.5594405594404
76320249.4405594405670.5594405594404
77560509.4405594405650.5594405594404
78680669.4405594405610.5594405594404
79370349.4405594405620.5594405594404
80670589.4405594405680.5594405594404
81510499.4405594405610.5594405594404
82480529.44055944056-49.4405594405596
83280299.44055944056-19.4405594405596
84570619.44055944056-49.4405594405596
85240279.44055944056-39.4405594405596
86460449.4405594405610.5594405594404
87600619.44055944056-19.4405594405596
88320319.440559440560.559440559440418
89570559.4405594405610.5594405594404
90680679.440559440560.559440559440418
91390369.4405594405620.5594405594404
92700669.4405594405630.5594405594404
93570509.4405594405660.5594405594404
94450479.44055944056-29.4405594405596
95270279.44055944056-9.44055944055958
96640569.4405594405670.5594405594404
97230239.44055944056-9.44055944055958
98490459.4405594405630.5594405594404
99590599.44055944056-9.44055944055958
100310319.44055944056-9.44055944055958
101570569.440559440560.559440559440418
102660679.44055944056-19.4405594405596
103370389.44055944056-19.4405594405596
104600699.44055944056-99.4405594405596
105540569.44055944056-29.4405594405596
106510449.4405594405660.5594405594404
107330269.4405594405660.5594405594404
108590639.44055944056-49.4405594405596







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109229.44055944056135.009688703307323.871430177812
110489.44055944056395.009688703307583.871430177812
111589.44055944056495.009688703307683.871430177812
112309.440559440559215.009688703307403.871430177812
113569.44055944056475.009688703307663.871430177812
114659.44055944056565.009688703307753.871430177812
115369.440559440559275.009688703307463.871430177812
116599.440559440559505.009688703307693.871430177812
117539.440559440559445.009688703307633.871430177812
118509.440559440559415.009688703307603.871430177812
119329.440559440559235.009688703307423.871430177812
120589.440559440559495.009688703307683.871430177812

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 229.44055944056 & 135.009688703307 & 323.871430177812 \tabularnewline
110 & 489.44055944056 & 395.009688703307 & 583.871430177812 \tabularnewline
111 & 589.44055944056 & 495.009688703307 & 683.871430177812 \tabularnewline
112 & 309.440559440559 & 215.009688703307 & 403.871430177812 \tabularnewline
113 & 569.44055944056 & 475.009688703307 & 663.871430177812 \tabularnewline
114 & 659.44055944056 & 565.009688703307 & 753.871430177812 \tabularnewline
115 & 369.440559440559 & 275.009688703307 & 463.871430177812 \tabularnewline
116 & 599.440559440559 & 505.009688703307 & 693.871430177812 \tabularnewline
117 & 539.440559440559 & 445.009688703307 & 633.871430177812 \tabularnewline
118 & 509.440559440559 & 415.009688703307 & 603.871430177812 \tabularnewline
119 & 329.440559440559 & 235.009688703307 & 423.871430177812 \tabularnewline
120 & 589.440559440559 & 495.009688703307 & 683.871430177812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124166&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]109[/C][C]229.44055944056[/C][C]135.009688703307[/C][C]323.871430177812[/C][/ROW]
[ROW][C]110[/C][C]489.44055944056[/C][C]395.009688703307[/C][C]583.871430177812[/C][/ROW]
[ROW][C]111[/C][C]589.44055944056[/C][C]495.009688703307[/C][C]683.871430177812[/C][/ROW]
[ROW][C]112[/C][C]309.440559440559[/C][C]215.009688703307[/C][C]403.871430177812[/C][/ROW]
[ROW][C]113[/C][C]569.44055944056[/C][C]475.009688703307[/C][C]663.871430177812[/C][/ROW]
[ROW][C]114[/C][C]659.44055944056[/C][C]565.009688703307[/C][C]753.871430177812[/C][/ROW]
[ROW][C]115[/C][C]369.440559440559[/C][C]275.009688703307[/C][C]463.871430177812[/C][/ROW]
[ROW][C]116[/C][C]599.440559440559[/C][C]505.009688703307[/C][C]693.871430177812[/C][/ROW]
[ROW][C]117[/C][C]539.440559440559[/C][C]445.009688703307[/C][C]633.871430177812[/C][/ROW]
[ROW][C]118[/C][C]509.440559440559[/C][C]415.009688703307[/C][C]603.871430177812[/C][/ROW]
[ROW][C]119[/C][C]329.440559440559[/C][C]235.009688703307[/C][C]423.871430177812[/C][/ROW]
[ROW][C]120[/C][C]589.440559440559[/C][C]495.009688703307[/C][C]683.871430177812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124166&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124166&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
109229.44055944056135.009688703307323.871430177812
110489.44055944056395.009688703307583.871430177812
111589.44055944056495.009688703307683.871430177812
112309.440559440559215.009688703307403.871430177812
113569.44055944056475.009688703307663.871430177812
114659.44055944056565.009688703307753.871430177812
115369.440559440559275.009688703307463.871430177812
116599.440559440559505.009688703307693.871430177812
117539.440559440559445.009688703307633.871430177812
118509.440559440559415.009688703307603.871430177812
119329.440559440559235.009688703307423.871430177812
120589.440559440559495.009688703307683.871430177812



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')