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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, 16 Aug 2012 18:05:21 -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/2012/Aug/16/t13451547946xachocffggybdq.htm/, Retrieved Fri, 03 May 2024 11:15:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169425, Retrieved Fri, 03 May 2024 11:15:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVerbraken Frederik
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2012-08-16 22:05:21] [31886bd2f92a612f059dd2285dd41f3c] [Current]
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Dataseries X:
500
510
590
490
540
530
550
510
390
480
530
690
570
460
540
510
520
520
580
480
410
530
540
670
570
400
510
570
470
640
650
500
340
450
600
680
630
480
400
520
470
610
670
500
290
470
660
650
570
500
400
500
340
530
680
480
340
460
630
650
550
470
240
430
390
570
700
620
280
480
560
560
560
550
140
380
390
500
750
680
280
360
590
580
490
610
170
320
440
510
770
660
300
350
580
620
490
640
150
290
370
560
780
690
310
280
590
590




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=169425&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=169425&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169425&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
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=169425&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=169425&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169425&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
13570575.486111111111-5.48611111111109
14460465.448232323232-5.44823232323239
15540545.82702020202-5.82702020202032
16510512.872474747475-2.87247474747483
17520520.334595959596-0.334595959596072
18520520.713383838384-0.713383838384061
19580550.25883838383929.7411616161614
20480509.387626262627-29.3876262626266
21410393.51641414141416.4835858585855
22530484.72853535353645.2714646464643
23540534.6906565656575.30934343434296
24670695.902777777778-25.9027777777783
25570569.5454545454550.454545454545041
26400459.545454545455-59.545454545455
27510539.545454545455-29.545454545455
28570509.54545454545560.454545454545
29470519.545454545455-49.545454545455
30640519.545454545455120.454545454545
31650579.54545454545570.454545454545
32500479.54545454545520.454545454545
33340409.545454545455-69.545454545455
34450529.545454545455-79.545454545455
35600539.54545454545560.454545454545
36680669.54545454545510.454545454545
37630569.54545454545560.454545454545
38480399.54545454545580.454545454545
39400509.545454545455-109.545454545455
40520569.545454545455-49.545454545455
41470469.5454545454550.454545454545041
42610639.545454545455-29.545454545455
43670649.54545454545520.454545454545
44500499.5454545454550.454545454545041
45290339.545454545455-49.545454545455
46470449.54545454545520.454545454545
47660599.54545454545560.454545454545
48650679.545454545455-29.545454545455
49570629.545454545455-59.545454545455
50500479.54545454545520.454545454545
51400399.5454545454550.454545454545041
52500519.545454545455-19.545454545455
53340469.545454545455-129.545454545455
54530609.545454545455-79.545454545455
55680669.54545454545510.454545454545
56480499.545454545455-19.545454545455
57340289.54545454545550.454545454545
58460469.545454545455-9.54545454545496
59630659.545454545455-29.545454545455
60650649.5454545454550.454545454545041
61550569.545454545455-19.545454545455
62470499.545454545455-29.545454545455
63240399.545454545455-159.545454545455
64430499.545454545455-69.545454545455
65390339.54545454545550.454545454545
66570529.54545454545540.454545454545
67700679.54545454545520.454545454545
68620479.545454545455140.454545454545
69280339.545454545455-59.545454545455
70480459.54545454545520.454545454545
71560629.545454545455-69.545454545455
72560649.545454545455-89.545454545455
73560549.54545454545510.454545454545
74550469.54545454545580.454545454545
75140239.545454545455-99.545454545455
76380429.545454545455-49.545454545455
77390389.5454545454550.454545454545041
78500569.545454545455-69.545454545455
79750699.54545454545550.454545454545
80680619.54545454545560.454545454545
81280279.5454545454550.454545454545041
82360479.545454545455-119.545454545455
83590559.54545454545530.454545454545
84580559.54545454545520.454545454545
85490559.545454545455-69.545454545455
86610549.54545454545560.454545454545
87170139.54545454545530.454545454545
88320379.545454545455-59.545454545455
89440389.54545454545550.454545454545
90510499.54545454545510.454545454545
91770749.54545454545520.454545454545
92660679.545454545455-19.545454545455
93300279.54545454545520.454545454545
94350359.545454545455-9.54545454545496
95580589.545454545455-9.54545454545496
96620579.54545454545540.454545454545
97490489.5454545454550.454545454545041
98640609.54545454545530.454545454545
99150169.545454545455-19.545454545455
100290319.545454545455-29.545454545455
101370439.545454545455-69.545454545455
102560509.54545454545550.454545454545
103780769.54545454545510.454545454545
104690659.54545454545530.454545454545
105310299.54545454545510.454545454545
106280349.545454545455-69.545454545455
107590579.54545454545510.454545454545
108590619.545454545455-29.545454545455

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 570 & 575.486111111111 & -5.48611111111109 \tabularnewline
14 & 460 & 465.448232323232 & -5.44823232323239 \tabularnewline
15 & 540 & 545.82702020202 & -5.82702020202032 \tabularnewline
16 & 510 & 512.872474747475 & -2.87247474747483 \tabularnewline
17 & 520 & 520.334595959596 & -0.334595959596072 \tabularnewline
18 & 520 & 520.713383838384 & -0.713383838384061 \tabularnewline
19 & 580 & 550.258838383839 & 29.7411616161614 \tabularnewline
20 & 480 & 509.387626262627 & -29.3876262626266 \tabularnewline
21 & 410 & 393.516414141414 & 16.4835858585855 \tabularnewline
22 & 530 & 484.728535353536 & 45.2714646464643 \tabularnewline
23 & 540 & 534.690656565657 & 5.30934343434296 \tabularnewline
24 & 670 & 695.902777777778 & -25.9027777777783 \tabularnewline
25 & 570 & 569.545454545455 & 0.454545454545041 \tabularnewline
26 & 400 & 459.545454545455 & -59.545454545455 \tabularnewline
27 & 510 & 539.545454545455 & -29.545454545455 \tabularnewline
28 & 570 & 509.545454545455 & 60.454545454545 \tabularnewline
29 & 470 & 519.545454545455 & -49.545454545455 \tabularnewline
30 & 640 & 519.545454545455 & 120.454545454545 \tabularnewline
31 & 650 & 579.545454545455 & 70.454545454545 \tabularnewline
32 & 500 & 479.545454545455 & 20.454545454545 \tabularnewline
33 & 340 & 409.545454545455 & -69.545454545455 \tabularnewline
34 & 450 & 529.545454545455 & -79.545454545455 \tabularnewline
35 & 600 & 539.545454545455 & 60.454545454545 \tabularnewline
36 & 680 & 669.545454545455 & 10.454545454545 \tabularnewline
37 & 630 & 569.545454545455 & 60.454545454545 \tabularnewline
38 & 480 & 399.545454545455 & 80.454545454545 \tabularnewline
39 & 400 & 509.545454545455 & -109.545454545455 \tabularnewline
40 & 520 & 569.545454545455 & -49.545454545455 \tabularnewline
41 & 470 & 469.545454545455 & 0.454545454545041 \tabularnewline
42 & 610 & 639.545454545455 & -29.545454545455 \tabularnewline
43 & 670 & 649.545454545455 & 20.454545454545 \tabularnewline
44 & 500 & 499.545454545455 & 0.454545454545041 \tabularnewline
45 & 290 & 339.545454545455 & -49.545454545455 \tabularnewline
46 & 470 & 449.545454545455 & 20.454545454545 \tabularnewline
47 & 660 & 599.545454545455 & 60.454545454545 \tabularnewline
48 & 650 & 679.545454545455 & -29.545454545455 \tabularnewline
49 & 570 & 629.545454545455 & -59.545454545455 \tabularnewline
50 & 500 & 479.545454545455 & 20.454545454545 \tabularnewline
51 & 400 & 399.545454545455 & 0.454545454545041 \tabularnewline
52 & 500 & 519.545454545455 & -19.545454545455 \tabularnewline
53 & 340 & 469.545454545455 & -129.545454545455 \tabularnewline
54 & 530 & 609.545454545455 & -79.545454545455 \tabularnewline
55 & 680 & 669.545454545455 & 10.454545454545 \tabularnewline
56 & 480 & 499.545454545455 & -19.545454545455 \tabularnewline
57 & 340 & 289.545454545455 & 50.454545454545 \tabularnewline
58 & 460 & 469.545454545455 & -9.54545454545496 \tabularnewline
59 & 630 & 659.545454545455 & -29.545454545455 \tabularnewline
60 & 650 & 649.545454545455 & 0.454545454545041 \tabularnewline
61 & 550 & 569.545454545455 & -19.545454545455 \tabularnewline
62 & 470 & 499.545454545455 & -29.545454545455 \tabularnewline
63 & 240 & 399.545454545455 & -159.545454545455 \tabularnewline
64 & 430 & 499.545454545455 & -69.545454545455 \tabularnewline
65 & 390 & 339.545454545455 & 50.454545454545 \tabularnewline
66 & 570 & 529.545454545455 & 40.454545454545 \tabularnewline
67 & 700 & 679.545454545455 & 20.454545454545 \tabularnewline
68 & 620 & 479.545454545455 & 140.454545454545 \tabularnewline
69 & 280 & 339.545454545455 & -59.545454545455 \tabularnewline
70 & 480 & 459.545454545455 & 20.454545454545 \tabularnewline
71 & 560 & 629.545454545455 & -69.545454545455 \tabularnewline
72 & 560 & 649.545454545455 & -89.545454545455 \tabularnewline
73 & 560 & 549.545454545455 & 10.454545454545 \tabularnewline
74 & 550 & 469.545454545455 & 80.454545454545 \tabularnewline
75 & 140 & 239.545454545455 & -99.545454545455 \tabularnewline
76 & 380 & 429.545454545455 & -49.545454545455 \tabularnewline
77 & 390 & 389.545454545455 & 0.454545454545041 \tabularnewline
78 & 500 & 569.545454545455 & -69.545454545455 \tabularnewline
79 & 750 & 699.545454545455 & 50.454545454545 \tabularnewline
80 & 680 & 619.545454545455 & 60.454545454545 \tabularnewline
81 & 280 & 279.545454545455 & 0.454545454545041 \tabularnewline
82 & 360 & 479.545454545455 & -119.545454545455 \tabularnewline
83 & 590 & 559.545454545455 & 30.454545454545 \tabularnewline
84 & 580 & 559.545454545455 & 20.454545454545 \tabularnewline
85 & 490 & 559.545454545455 & -69.545454545455 \tabularnewline
86 & 610 & 549.545454545455 & 60.454545454545 \tabularnewline
87 & 170 & 139.545454545455 & 30.454545454545 \tabularnewline
88 & 320 & 379.545454545455 & -59.545454545455 \tabularnewline
89 & 440 & 389.545454545455 & 50.454545454545 \tabularnewline
90 & 510 & 499.545454545455 & 10.454545454545 \tabularnewline
91 & 770 & 749.545454545455 & 20.454545454545 \tabularnewline
92 & 660 & 679.545454545455 & -19.545454545455 \tabularnewline
93 & 300 & 279.545454545455 & 20.454545454545 \tabularnewline
94 & 350 & 359.545454545455 & -9.54545454545496 \tabularnewline
95 & 580 & 589.545454545455 & -9.54545454545496 \tabularnewline
96 & 620 & 579.545454545455 & 40.454545454545 \tabularnewline
97 & 490 & 489.545454545455 & 0.454545454545041 \tabularnewline
98 & 640 & 609.545454545455 & 30.454545454545 \tabularnewline
99 & 150 & 169.545454545455 & -19.545454545455 \tabularnewline
100 & 290 & 319.545454545455 & -29.545454545455 \tabularnewline
101 & 370 & 439.545454545455 & -69.545454545455 \tabularnewline
102 & 560 & 509.545454545455 & 50.454545454545 \tabularnewline
103 & 780 & 769.545454545455 & 10.454545454545 \tabularnewline
104 & 690 & 659.545454545455 & 30.454545454545 \tabularnewline
105 & 310 & 299.545454545455 & 10.454545454545 \tabularnewline
106 & 280 & 349.545454545455 & -69.545454545455 \tabularnewline
107 & 590 & 579.545454545455 & 10.454545454545 \tabularnewline
108 & 590 & 619.545454545455 & -29.545454545455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169425&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]570[/C][C]575.486111111111[/C][C]-5.48611111111109[/C][/ROW]
[ROW][C]14[/C][C]460[/C][C]465.448232323232[/C][C]-5.44823232323239[/C][/ROW]
[ROW][C]15[/C][C]540[/C][C]545.82702020202[/C][C]-5.82702020202032[/C][/ROW]
[ROW][C]16[/C][C]510[/C][C]512.872474747475[/C][C]-2.87247474747483[/C][/ROW]
[ROW][C]17[/C][C]520[/C][C]520.334595959596[/C][C]-0.334595959596072[/C][/ROW]
[ROW][C]18[/C][C]520[/C][C]520.713383838384[/C][C]-0.713383838384061[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]550.258838383839[/C][C]29.7411616161614[/C][/ROW]
[ROW][C]20[/C][C]480[/C][C]509.387626262627[/C][C]-29.3876262626266[/C][/ROW]
[ROW][C]21[/C][C]410[/C][C]393.516414141414[/C][C]16.4835858585855[/C][/ROW]
[ROW][C]22[/C][C]530[/C][C]484.728535353536[/C][C]45.2714646464643[/C][/ROW]
[ROW][C]23[/C][C]540[/C][C]534.690656565657[/C][C]5.30934343434296[/C][/ROW]
[ROW][C]24[/C][C]670[/C][C]695.902777777778[/C][C]-25.9027777777783[/C][/ROW]
[ROW][C]25[/C][C]570[/C][C]569.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]26[/C][C]400[/C][C]459.545454545455[/C][C]-59.545454545455[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]539.545454545455[/C][C]-29.545454545455[/C][/ROW]
[ROW][C]28[/C][C]570[/C][C]509.545454545455[/C][C]60.454545454545[/C][/ROW]
[ROW][C]29[/C][C]470[/C][C]519.545454545455[/C][C]-49.545454545455[/C][/ROW]
[ROW][C]30[/C][C]640[/C][C]519.545454545455[/C][C]120.454545454545[/C][/ROW]
[ROW][C]31[/C][C]650[/C][C]579.545454545455[/C][C]70.454545454545[/C][/ROW]
[ROW][C]32[/C][C]500[/C][C]479.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]33[/C][C]340[/C][C]409.545454545455[/C][C]-69.545454545455[/C][/ROW]
[ROW][C]34[/C][C]450[/C][C]529.545454545455[/C][C]-79.545454545455[/C][/ROW]
[ROW][C]35[/C][C]600[/C][C]539.545454545455[/C][C]60.454545454545[/C][/ROW]
[ROW][C]36[/C][C]680[/C][C]669.545454545455[/C][C]10.454545454545[/C][/ROW]
[ROW][C]37[/C][C]630[/C][C]569.545454545455[/C][C]60.454545454545[/C][/ROW]
[ROW][C]38[/C][C]480[/C][C]399.545454545455[/C][C]80.454545454545[/C][/ROW]
[ROW][C]39[/C][C]400[/C][C]509.545454545455[/C][C]-109.545454545455[/C][/ROW]
[ROW][C]40[/C][C]520[/C][C]569.545454545455[/C][C]-49.545454545455[/C][/ROW]
[ROW][C]41[/C][C]470[/C][C]469.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]42[/C][C]610[/C][C]639.545454545455[/C][C]-29.545454545455[/C][/ROW]
[ROW][C]43[/C][C]670[/C][C]649.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]44[/C][C]500[/C][C]499.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]45[/C][C]290[/C][C]339.545454545455[/C][C]-49.545454545455[/C][/ROW]
[ROW][C]46[/C][C]470[/C][C]449.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]47[/C][C]660[/C][C]599.545454545455[/C][C]60.454545454545[/C][/ROW]
[ROW][C]48[/C][C]650[/C][C]679.545454545455[/C][C]-29.545454545455[/C][/ROW]
[ROW][C]49[/C][C]570[/C][C]629.545454545455[/C][C]-59.545454545455[/C][/ROW]
[ROW][C]50[/C][C]500[/C][C]479.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]51[/C][C]400[/C][C]399.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]52[/C][C]500[/C][C]519.545454545455[/C][C]-19.545454545455[/C][/ROW]
[ROW][C]53[/C][C]340[/C][C]469.545454545455[/C][C]-129.545454545455[/C][/ROW]
[ROW][C]54[/C][C]530[/C][C]609.545454545455[/C][C]-79.545454545455[/C][/ROW]
[ROW][C]55[/C][C]680[/C][C]669.545454545455[/C][C]10.454545454545[/C][/ROW]
[ROW][C]56[/C][C]480[/C][C]499.545454545455[/C][C]-19.545454545455[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]289.545454545455[/C][C]50.454545454545[/C][/ROW]
[ROW][C]58[/C][C]460[/C][C]469.545454545455[/C][C]-9.54545454545496[/C][/ROW]
[ROW][C]59[/C][C]630[/C][C]659.545454545455[/C][C]-29.545454545455[/C][/ROW]
[ROW][C]60[/C][C]650[/C][C]649.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]61[/C][C]550[/C][C]569.545454545455[/C][C]-19.545454545455[/C][/ROW]
[ROW][C]62[/C][C]470[/C][C]499.545454545455[/C][C]-29.545454545455[/C][/ROW]
[ROW][C]63[/C][C]240[/C][C]399.545454545455[/C][C]-159.545454545455[/C][/ROW]
[ROW][C]64[/C][C]430[/C][C]499.545454545455[/C][C]-69.545454545455[/C][/ROW]
[ROW][C]65[/C][C]390[/C][C]339.545454545455[/C][C]50.454545454545[/C][/ROW]
[ROW][C]66[/C][C]570[/C][C]529.545454545455[/C][C]40.454545454545[/C][/ROW]
[ROW][C]67[/C][C]700[/C][C]679.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]68[/C][C]620[/C][C]479.545454545455[/C][C]140.454545454545[/C][/ROW]
[ROW][C]69[/C][C]280[/C][C]339.545454545455[/C][C]-59.545454545455[/C][/ROW]
[ROW][C]70[/C][C]480[/C][C]459.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]629.545454545455[/C][C]-69.545454545455[/C][/ROW]
[ROW][C]72[/C][C]560[/C][C]649.545454545455[/C][C]-89.545454545455[/C][/ROW]
[ROW][C]73[/C][C]560[/C][C]549.545454545455[/C][C]10.454545454545[/C][/ROW]
[ROW][C]74[/C][C]550[/C][C]469.545454545455[/C][C]80.454545454545[/C][/ROW]
[ROW][C]75[/C][C]140[/C][C]239.545454545455[/C][C]-99.545454545455[/C][/ROW]
[ROW][C]76[/C][C]380[/C][C]429.545454545455[/C][C]-49.545454545455[/C][/ROW]
[ROW][C]77[/C][C]390[/C][C]389.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]78[/C][C]500[/C][C]569.545454545455[/C][C]-69.545454545455[/C][/ROW]
[ROW][C]79[/C][C]750[/C][C]699.545454545455[/C][C]50.454545454545[/C][/ROW]
[ROW][C]80[/C][C]680[/C][C]619.545454545455[/C][C]60.454545454545[/C][/ROW]
[ROW][C]81[/C][C]280[/C][C]279.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]82[/C][C]360[/C][C]479.545454545455[/C][C]-119.545454545455[/C][/ROW]
[ROW][C]83[/C][C]590[/C][C]559.545454545455[/C][C]30.454545454545[/C][/ROW]
[ROW][C]84[/C][C]580[/C][C]559.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]85[/C][C]490[/C][C]559.545454545455[/C][C]-69.545454545455[/C][/ROW]
[ROW][C]86[/C][C]610[/C][C]549.545454545455[/C][C]60.454545454545[/C][/ROW]
[ROW][C]87[/C][C]170[/C][C]139.545454545455[/C][C]30.454545454545[/C][/ROW]
[ROW][C]88[/C][C]320[/C][C]379.545454545455[/C][C]-59.545454545455[/C][/ROW]
[ROW][C]89[/C][C]440[/C][C]389.545454545455[/C][C]50.454545454545[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]499.545454545455[/C][C]10.454545454545[/C][/ROW]
[ROW][C]91[/C][C]770[/C][C]749.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]92[/C][C]660[/C][C]679.545454545455[/C][C]-19.545454545455[/C][/ROW]
[ROW][C]93[/C][C]300[/C][C]279.545454545455[/C][C]20.454545454545[/C][/ROW]
[ROW][C]94[/C][C]350[/C][C]359.545454545455[/C][C]-9.54545454545496[/C][/ROW]
[ROW][C]95[/C][C]580[/C][C]589.545454545455[/C][C]-9.54545454545496[/C][/ROW]
[ROW][C]96[/C][C]620[/C][C]579.545454545455[/C][C]40.454545454545[/C][/ROW]
[ROW][C]97[/C][C]490[/C][C]489.545454545455[/C][C]0.454545454545041[/C][/ROW]
[ROW][C]98[/C][C]640[/C][C]609.545454545455[/C][C]30.454545454545[/C][/ROW]
[ROW][C]99[/C][C]150[/C][C]169.545454545455[/C][C]-19.545454545455[/C][/ROW]
[ROW][C]100[/C][C]290[/C][C]319.545454545455[/C][C]-29.545454545455[/C][/ROW]
[ROW][C]101[/C][C]370[/C][C]439.545454545455[/C][C]-69.545454545455[/C][/ROW]
[ROW][C]102[/C][C]560[/C][C]509.545454545455[/C][C]50.454545454545[/C][/ROW]
[ROW][C]103[/C][C]780[/C][C]769.545454545455[/C][C]10.454545454545[/C][/ROW]
[ROW][C]104[/C][C]690[/C][C]659.545454545455[/C][C]30.454545454545[/C][/ROW]
[ROW][C]105[/C][C]310[/C][C]299.545454545455[/C][C]10.454545454545[/C][/ROW]
[ROW][C]106[/C][C]280[/C][C]349.545454545455[/C][C]-69.545454545455[/C][/ROW]
[ROW][C]107[/C][C]590[/C][C]579.545454545455[/C][C]10.454545454545[/C][/ROW]
[ROW][C]108[/C][C]590[/C][C]619.545454545455[/C][C]-29.545454545455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169425&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169425&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
13570575.486111111111-5.48611111111109
14460465.448232323232-5.44823232323239
15540545.82702020202-5.82702020202032
16510512.872474747475-2.87247474747483
17520520.334595959596-0.334595959596072
18520520.713383838384-0.713383838384061
19580550.25883838383929.7411616161614
20480509.387626262627-29.3876262626266
21410393.51641414141416.4835858585855
22530484.72853535353645.2714646464643
23540534.6906565656575.30934343434296
24670695.902777777778-25.9027777777783
25570569.5454545454550.454545454545041
26400459.545454545455-59.545454545455
27510539.545454545455-29.545454545455
28570509.54545454545560.454545454545
29470519.545454545455-49.545454545455
30640519.545454545455120.454545454545
31650579.54545454545570.454545454545
32500479.54545454545520.454545454545
33340409.545454545455-69.545454545455
34450529.545454545455-79.545454545455
35600539.54545454545560.454545454545
36680669.54545454545510.454545454545
37630569.54545454545560.454545454545
38480399.54545454545580.454545454545
39400509.545454545455-109.545454545455
40520569.545454545455-49.545454545455
41470469.5454545454550.454545454545041
42610639.545454545455-29.545454545455
43670649.54545454545520.454545454545
44500499.5454545454550.454545454545041
45290339.545454545455-49.545454545455
46470449.54545454545520.454545454545
47660599.54545454545560.454545454545
48650679.545454545455-29.545454545455
49570629.545454545455-59.545454545455
50500479.54545454545520.454545454545
51400399.5454545454550.454545454545041
52500519.545454545455-19.545454545455
53340469.545454545455-129.545454545455
54530609.545454545455-79.545454545455
55680669.54545454545510.454545454545
56480499.545454545455-19.545454545455
57340289.54545454545550.454545454545
58460469.545454545455-9.54545454545496
59630659.545454545455-29.545454545455
60650649.5454545454550.454545454545041
61550569.545454545455-19.545454545455
62470499.545454545455-29.545454545455
63240399.545454545455-159.545454545455
64430499.545454545455-69.545454545455
65390339.54545454545550.454545454545
66570529.54545454545540.454545454545
67700679.54545454545520.454545454545
68620479.545454545455140.454545454545
69280339.545454545455-59.545454545455
70480459.54545454545520.454545454545
71560629.545454545455-69.545454545455
72560649.545454545455-89.545454545455
73560549.54545454545510.454545454545
74550469.54545454545580.454545454545
75140239.545454545455-99.545454545455
76380429.545454545455-49.545454545455
77390389.5454545454550.454545454545041
78500569.545454545455-69.545454545455
79750699.54545454545550.454545454545
80680619.54545454545560.454545454545
81280279.5454545454550.454545454545041
82360479.545454545455-119.545454545455
83590559.54545454545530.454545454545
84580559.54545454545520.454545454545
85490559.545454545455-69.545454545455
86610549.54545454545560.454545454545
87170139.54545454545530.454545454545
88320379.545454545455-59.545454545455
89440389.54545454545550.454545454545
90510499.54545454545510.454545454545
91770749.54545454545520.454545454545
92660679.545454545455-19.545454545455
93300279.54545454545520.454545454545
94350359.545454545455-9.54545454545496
95580589.545454545455-9.54545454545496
96620579.54545454545540.454545454545
97490489.5454545454550.454545454545041
98640609.54545454545530.454545454545
99150169.545454545455-19.545454545455
100290319.545454545455-29.545454545455
101370439.545454545455-69.545454545455
102560509.54545454545550.454545454545
103780769.54545454545510.454545454545
104690659.54545454545530.454545454545
105310299.54545454545510.454545454545
106280349.545454545455-69.545454545455
107590579.54545454545510.454545454545
108590619.545454545455-29.545454545455







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109489.545454545455385.928462316055593.162446774855
110639.545454545455535.928462316055743.162446774855
111149.54545454545545.9284623160549253.162446774855
112289.545454545455185.928462316055393.162446774855
113369.545454545455265.928462316055473.162446774855
114559.545454545455455.928462316055663.162446774855
115779.545454545455675.928462316055883.162446774855
116689.545454545455585.928462316055793.162446774855
117309.545454545455205.928462316055413.162446774855
118279.545454545455175.928462316055383.162446774855
119589.545454545455485.928462316055693.162446774855
120589.545454545455485.928462316055693.162446774855

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 489.545454545455 & 385.928462316055 & 593.162446774855 \tabularnewline
110 & 639.545454545455 & 535.928462316055 & 743.162446774855 \tabularnewline
111 & 149.545454545455 & 45.9284623160549 & 253.162446774855 \tabularnewline
112 & 289.545454545455 & 185.928462316055 & 393.162446774855 \tabularnewline
113 & 369.545454545455 & 265.928462316055 & 473.162446774855 \tabularnewline
114 & 559.545454545455 & 455.928462316055 & 663.162446774855 \tabularnewline
115 & 779.545454545455 & 675.928462316055 & 883.162446774855 \tabularnewline
116 & 689.545454545455 & 585.928462316055 & 793.162446774855 \tabularnewline
117 & 309.545454545455 & 205.928462316055 & 413.162446774855 \tabularnewline
118 & 279.545454545455 & 175.928462316055 & 383.162446774855 \tabularnewline
119 & 589.545454545455 & 485.928462316055 & 693.162446774855 \tabularnewline
120 & 589.545454545455 & 485.928462316055 & 693.162446774855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169425&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]489.545454545455[/C][C]385.928462316055[/C][C]593.162446774855[/C][/ROW]
[ROW][C]110[/C][C]639.545454545455[/C][C]535.928462316055[/C][C]743.162446774855[/C][/ROW]
[ROW][C]111[/C][C]149.545454545455[/C][C]45.9284623160549[/C][C]253.162446774855[/C][/ROW]
[ROW][C]112[/C][C]289.545454545455[/C][C]185.928462316055[/C][C]393.162446774855[/C][/ROW]
[ROW][C]113[/C][C]369.545454545455[/C][C]265.928462316055[/C][C]473.162446774855[/C][/ROW]
[ROW][C]114[/C][C]559.545454545455[/C][C]455.928462316055[/C][C]663.162446774855[/C][/ROW]
[ROW][C]115[/C][C]779.545454545455[/C][C]675.928462316055[/C][C]883.162446774855[/C][/ROW]
[ROW][C]116[/C][C]689.545454545455[/C][C]585.928462316055[/C][C]793.162446774855[/C][/ROW]
[ROW][C]117[/C][C]309.545454545455[/C][C]205.928462316055[/C][C]413.162446774855[/C][/ROW]
[ROW][C]118[/C][C]279.545454545455[/C][C]175.928462316055[/C][C]383.162446774855[/C][/ROW]
[ROW][C]119[/C][C]589.545454545455[/C][C]485.928462316055[/C][C]693.162446774855[/C][/ROW]
[ROW][C]120[/C][C]589.545454545455[/C][C]485.928462316055[/C][C]693.162446774855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169425&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169425&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
109489.545454545455385.928462316055593.162446774855
110639.545454545455535.928462316055743.162446774855
111149.54545454545545.9284623160549253.162446774855
112289.545454545455185.928462316055393.162446774855
113369.545454545455265.928462316055473.162446774855
114559.545454545455455.928462316055663.162446774855
115779.545454545455675.928462316055883.162446774855
116689.545454545455585.928462316055793.162446774855
117309.545454545455205.928462316055413.162446774855
118279.545454545455175.928462316055383.162446774855
119589.545454545455485.928462316055693.162446774855
120589.545454545455485.928462316055693.162446774855



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')