Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Aug 2011 16:28:46 -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/17/t13136130504n7brt2npyyg4zg.htm/, Retrieved Wed, 15 May 2024 02:18:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123983, Retrieved Wed, 15 May 2024 02:18:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPeeters Marin
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2011-08-17 20:28:46] [3f8170910ab21fde7eba151af40022ac] [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=123983&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=123983&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123983&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
alpha0.0371942900326046
beta0.345015689980917
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0371942900326046 \tabularnewline
beta & 0.345015689980917 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123983&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]0.0371942900326046[/C][/ROW]
[ROW][C]beta[/C][C]0.345015689980917[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123983&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123983&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
alpha0.0371942900326046
beta0.345015689980917
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
359052070
4490533.501883257009-43.5018832570088
5540542.223901688506-2.22390168850563
6530552.452686867282-22.4526868672823
7550561.640950087388-11.6409500873882
8510571.08196436618-61.0819643661799
9390577.900213971361-187.900213971361
10480577.590297970729-97.5902979707289
11530579.387056589876-49.3870565898765
12690582.342935533472107.657064466528
13570592.521480577358-22.5214805773577
14460597.569117602032-137.569117602032
15540596.572268112807-56.572268112807
16510597.862068875841-87.8620688758406
17520596.860567730829-76.8605677308291
18520595.281937640439-75.2819376404392
19580592.795959555754-12.7959595557542
20480592.469897457803-112.469897457803
21410586.993251264743-176.993251264743
22530576.84541872613-46.84541872613
23540570.937193258805-30.9371932588053
24670565.223657895253104.776342104747
25570565.9024454440954.09755455590516
26400562.889139303195-162.889139303195
27510551.574588248655-41.5745882486545
28570544.23873516301925.7612648369811
29470539.737975685147-69.7379756851468
30640530.790269259471109.209730740529
31650529.899842007469120.100157992531
32500530.955675390751-30.9556753907508
33340525.995852073836-185.995852073836
34450512.882606550554-62.8826065505541
35600503.54152259364796.4584774063533
36680501.364831500299178.635168499701
37630504.537000189083125.462999810917
38480507.34148601655-27.3414860165501
39400504.111654753503-104.111654753503
40520496.69038692783723.3096130721625
41470494.307585952631-24.3075859526307
42610489.84176720733120.15823279267
43670492.291196201207177.708803798793
44500499.1616462440170.838353755982723
45290499.464283739581-209.464283739581
46470489.256889717124-19.2568897171245
47660485.877008448657174.122991551343
48650491.924207646796158.075792353204
49570499.40306823268870.5969317673121
50500504.534157855691-4.53415785569143
51400506.812614844851-106.812614844851
52500503.916212222599-3.91621222259937
53340504.79671300441-164.79671300441
54530497.57860523259732.4213947674026
55680498.111936193617181.888063806383
56480506.538673041443-26.5386730414431
57340506.872564850771-166.872564850771
58460499.845426035068-39.8454260350679
59630497.031650504901132.968349495099
60650502.351892118711147.648107881289
61550510.11284804650939.887151953491
62470514.377568135515-44.3775681355147
63240514.938641599894-274.938641599894
64430503.395978265542-73.3959782655423
65390498.407688973457-108.407688973457
66570490.72600997067779.2739900293234
67700491.042310256196208.957689743804
68620498.863576980766121.136423019234
69280504.972890953962-224.972890953962
70480495.321924531404-15.3219245314042
71560493.27215662186666.7278433781344
72560495.13046421009464.8695357899056
73560497.75209905664762.2479009433534
74550501.07502731899848.9249726810019
75140504.530253995188-364.530253995188
76380487.929431145658-107.929431145658
77390479.487677033636-89.4876770336358
78500470.58349008794629.4165099120541
79750466.479350663913283.520649336087
80680475.464745251697204.535254748303
81280484.137056064572-204.137056064572
82360474.989478450909-114.989478450909
83590467.682066145208122.317933854792
84580470.770793345965109.229206654035
85490474.7743908381415.2256091618601
86610475.476975620874134.523024379126
87170482.34302506274-312.34302506274
88320468.58003169249-148.58003169249
89440459.001416453088-19.0014164530882
90510453.99854797498856.0014520250115
91770452.504002937398317.495997062602
92660464.809865312096195.190134687904
93300475.071447553527-175.071447553527
94350469.314788871473-119.314788871473
95580464.100838936688115.899161063312
96620469.122794030495150.877205969505
97490477.38188156244812.6181184375522
98640480.660443931853159.339556068147
99150491.440948966916-341.440948966916
100290479.213698876422-189.213698876422
101370470.220326983782-100.220326983782
102560463.25091164134496.7490883586557
103780464.849177531533315.150822468467
104690478.61494960656211.38505039344
105310491.233850140321-181.233850140321
106280486.923865438197-206.923865438197
107590479.002984838295110.997015161705
108590484.331327489494105.668672510506

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 590 & 520 & 70 \tabularnewline
4 & 490 & 533.501883257009 & -43.5018832570088 \tabularnewline
5 & 540 & 542.223901688506 & -2.22390168850563 \tabularnewline
6 & 530 & 552.452686867282 & -22.4526868672823 \tabularnewline
7 & 550 & 561.640950087388 & -11.6409500873882 \tabularnewline
8 & 510 & 571.08196436618 & -61.0819643661799 \tabularnewline
9 & 390 & 577.900213971361 & -187.900213971361 \tabularnewline
10 & 480 & 577.590297970729 & -97.5902979707289 \tabularnewline
11 & 530 & 579.387056589876 & -49.3870565898765 \tabularnewline
12 & 690 & 582.342935533472 & 107.657064466528 \tabularnewline
13 & 570 & 592.521480577358 & -22.5214805773577 \tabularnewline
14 & 460 & 597.569117602032 & -137.569117602032 \tabularnewline
15 & 540 & 596.572268112807 & -56.572268112807 \tabularnewline
16 & 510 & 597.862068875841 & -87.8620688758406 \tabularnewline
17 & 520 & 596.860567730829 & -76.8605677308291 \tabularnewline
18 & 520 & 595.281937640439 & -75.2819376404392 \tabularnewline
19 & 580 & 592.795959555754 & -12.7959595557542 \tabularnewline
20 & 480 & 592.469897457803 & -112.469897457803 \tabularnewline
21 & 410 & 586.993251264743 & -176.993251264743 \tabularnewline
22 & 530 & 576.84541872613 & -46.84541872613 \tabularnewline
23 & 540 & 570.937193258805 & -30.9371932588053 \tabularnewline
24 & 670 & 565.223657895253 & 104.776342104747 \tabularnewline
25 & 570 & 565.902445444095 & 4.09755455590516 \tabularnewline
26 & 400 & 562.889139303195 & -162.889139303195 \tabularnewline
27 & 510 & 551.574588248655 & -41.5745882486545 \tabularnewline
28 & 570 & 544.238735163019 & 25.7612648369811 \tabularnewline
29 & 470 & 539.737975685147 & -69.7379756851468 \tabularnewline
30 & 640 & 530.790269259471 & 109.209730740529 \tabularnewline
31 & 650 & 529.899842007469 & 120.100157992531 \tabularnewline
32 & 500 & 530.955675390751 & -30.9556753907508 \tabularnewline
33 & 340 & 525.995852073836 & -185.995852073836 \tabularnewline
34 & 450 & 512.882606550554 & -62.8826065505541 \tabularnewline
35 & 600 & 503.541522593647 & 96.4584774063533 \tabularnewline
36 & 680 & 501.364831500299 & 178.635168499701 \tabularnewline
37 & 630 & 504.537000189083 & 125.462999810917 \tabularnewline
38 & 480 & 507.34148601655 & -27.3414860165501 \tabularnewline
39 & 400 & 504.111654753503 & -104.111654753503 \tabularnewline
40 & 520 & 496.690386927837 & 23.3096130721625 \tabularnewline
41 & 470 & 494.307585952631 & -24.3075859526307 \tabularnewline
42 & 610 & 489.84176720733 & 120.15823279267 \tabularnewline
43 & 670 & 492.291196201207 & 177.708803798793 \tabularnewline
44 & 500 & 499.161646244017 & 0.838353755982723 \tabularnewline
45 & 290 & 499.464283739581 & -209.464283739581 \tabularnewline
46 & 470 & 489.256889717124 & -19.2568897171245 \tabularnewline
47 & 660 & 485.877008448657 & 174.122991551343 \tabularnewline
48 & 650 & 491.924207646796 & 158.075792353204 \tabularnewline
49 & 570 & 499.403068232688 & 70.5969317673121 \tabularnewline
50 & 500 & 504.534157855691 & -4.53415785569143 \tabularnewline
51 & 400 & 506.812614844851 & -106.812614844851 \tabularnewline
52 & 500 & 503.916212222599 & -3.91621222259937 \tabularnewline
53 & 340 & 504.79671300441 & -164.79671300441 \tabularnewline
54 & 530 & 497.578605232597 & 32.4213947674026 \tabularnewline
55 & 680 & 498.111936193617 & 181.888063806383 \tabularnewline
56 & 480 & 506.538673041443 & -26.5386730414431 \tabularnewline
57 & 340 & 506.872564850771 & -166.872564850771 \tabularnewline
58 & 460 & 499.845426035068 & -39.8454260350679 \tabularnewline
59 & 630 & 497.031650504901 & 132.968349495099 \tabularnewline
60 & 650 & 502.351892118711 & 147.648107881289 \tabularnewline
61 & 550 & 510.112848046509 & 39.887151953491 \tabularnewline
62 & 470 & 514.377568135515 & -44.3775681355147 \tabularnewline
63 & 240 & 514.938641599894 & -274.938641599894 \tabularnewline
64 & 430 & 503.395978265542 & -73.3959782655423 \tabularnewline
65 & 390 & 498.407688973457 & -108.407688973457 \tabularnewline
66 & 570 & 490.726009970677 & 79.2739900293234 \tabularnewline
67 & 700 & 491.042310256196 & 208.957689743804 \tabularnewline
68 & 620 & 498.863576980766 & 121.136423019234 \tabularnewline
69 & 280 & 504.972890953962 & -224.972890953962 \tabularnewline
70 & 480 & 495.321924531404 & -15.3219245314042 \tabularnewline
71 & 560 & 493.272156621866 & 66.7278433781344 \tabularnewline
72 & 560 & 495.130464210094 & 64.8695357899056 \tabularnewline
73 & 560 & 497.752099056647 & 62.2479009433534 \tabularnewline
74 & 550 & 501.075027318998 & 48.9249726810019 \tabularnewline
75 & 140 & 504.530253995188 & -364.530253995188 \tabularnewline
76 & 380 & 487.929431145658 & -107.929431145658 \tabularnewline
77 & 390 & 479.487677033636 & -89.4876770336358 \tabularnewline
78 & 500 & 470.583490087946 & 29.4165099120541 \tabularnewline
79 & 750 & 466.479350663913 & 283.520649336087 \tabularnewline
80 & 680 & 475.464745251697 & 204.535254748303 \tabularnewline
81 & 280 & 484.137056064572 & -204.137056064572 \tabularnewline
82 & 360 & 474.989478450909 & -114.989478450909 \tabularnewline
83 & 590 & 467.682066145208 & 122.317933854792 \tabularnewline
84 & 580 & 470.770793345965 & 109.229206654035 \tabularnewline
85 & 490 & 474.77439083814 & 15.2256091618601 \tabularnewline
86 & 610 & 475.476975620874 & 134.523024379126 \tabularnewline
87 & 170 & 482.34302506274 & -312.34302506274 \tabularnewline
88 & 320 & 468.58003169249 & -148.58003169249 \tabularnewline
89 & 440 & 459.001416453088 & -19.0014164530882 \tabularnewline
90 & 510 & 453.998547974988 & 56.0014520250115 \tabularnewline
91 & 770 & 452.504002937398 & 317.495997062602 \tabularnewline
92 & 660 & 464.809865312096 & 195.190134687904 \tabularnewline
93 & 300 & 475.071447553527 & -175.071447553527 \tabularnewline
94 & 350 & 469.314788871473 & -119.314788871473 \tabularnewline
95 & 580 & 464.100838936688 & 115.899161063312 \tabularnewline
96 & 620 & 469.122794030495 & 150.877205969505 \tabularnewline
97 & 490 & 477.381881562448 & 12.6181184375522 \tabularnewline
98 & 640 & 480.660443931853 & 159.339556068147 \tabularnewline
99 & 150 & 491.440948966916 & -341.440948966916 \tabularnewline
100 & 290 & 479.213698876422 & -189.213698876422 \tabularnewline
101 & 370 & 470.220326983782 & -100.220326983782 \tabularnewline
102 & 560 & 463.250911641344 & 96.7490883586557 \tabularnewline
103 & 780 & 464.849177531533 & 315.150822468467 \tabularnewline
104 & 690 & 478.61494960656 & 211.38505039344 \tabularnewline
105 & 310 & 491.233850140321 & -181.233850140321 \tabularnewline
106 & 280 & 486.923865438197 & -206.923865438197 \tabularnewline
107 & 590 & 479.002984838295 & 110.997015161705 \tabularnewline
108 & 590 & 484.331327489494 & 105.668672510506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123983&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]3[/C][C]590[/C][C]520[/C][C]70[/C][/ROW]
[ROW][C]4[/C][C]490[/C][C]533.501883257009[/C][C]-43.5018832570088[/C][/ROW]
[ROW][C]5[/C][C]540[/C][C]542.223901688506[/C][C]-2.22390168850563[/C][/ROW]
[ROW][C]6[/C][C]530[/C][C]552.452686867282[/C][C]-22.4526868672823[/C][/ROW]
[ROW][C]7[/C][C]550[/C][C]561.640950087388[/C][C]-11.6409500873882[/C][/ROW]
[ROW][C]8[/C][C]510[/C][C]571.08196436618[/C][C]-61.0819643661799[/C][/ROW]
[ROW][C]9[/C][C]390[/C][C]577.900213971361[/C][C]-187.900213971361[/C][/ROW]
[ROW][C]10[/C][C]480[/C][C]577.590297970729[/C][C]-97.5902979707289[/C][/ROW]
[ROW][C]11[/C][C]530[/C][C]579.387056589876[/C][C]-49.3870565898765[/C][/ROW]
[ROW][C]12[/C][C]690[/C][C]582.342935533472[/C][C]107.657064466528[/C][/ROW]
[ROW][C]13[/C][C]570[/C][C]592.521480577358[/C][C]-22.5214805773577[/C][/ROW]
[ROW][C]14[/C][C]460[/C][C]597.569117602032[/C][C]-137.569117602032[/C][/ROW]
[ROW][C]15[/C][C]540[/C][C]596.572268112807[/C][C]-56.572268112807[/C][/ROW]
[ROW][C]16[/C][C]510[/C][C]597.862068875841[/C][C]-87.8620688758406[/C][/ROW]
[ROW][C]17[/C][C]520[/C][C]596.860567730829[/C][C]-76.8605677308291[/C][/ROW]
[ROW][C]18[/C][C]520[/C][C]595.281937640439[/C][C]-75.2819376404392[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]592.795959555754[/C][C]-12.7959595557542[/C][/ROW]
[ROW][C]20[/C][C]480[/C][C]592.469897457803[/C][C]-112.469897457803[/C][/ROW]
[ROW][C]21[/C][C]410[/C][C]586.993251264743[/C][C]-176.993251264743[/C][/ROW]
[ROW][C]22[/C][C]530[/C][C]576.84541872613[/C][C]-46.84541872613[/C][/ROW]
[ROW][C]23[/C][C]540[/C][C]570.937193258805[/C][C]-30.9371932588053[/C][/ROW]
[ROW][C]24[/C][C]670[/C][C]565.223657895253[/C][C]104.776342104747[/C][/ROW]
[ROW][C]25[/C][C]570[/C][C]565.902445444095[/C][C]4.09755455590516[/C][/ROW]
[ROW][C]26[/C][C]400[/C][C]562.889139303195[/C][C]-162.889139303195[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]551.574588248655[/C][C]-41.5745882486545[/C][/ROW]
[ROW][C]28[/C][C]570[/C][C]544.238735163019[/C][C]25.7612648369811[/C][/ROW]
[ROW][C]29[/C][C]470[/C][C]539.737975685147[/C][C]-69.7379756851468[/C][/ROW]
[ROW][C]30[/C][C]640[/C][C]530.790269259471[/C][C]109.209730740529[/C][/ROW]
[ROW][C]31[/C][C]650[/C][C]529.899842007469[/C][C]120.100157992531[/C][/ROW]
[ROW][C]32[/C][C]500[/C][C]530.955675390751[/C][C]-30.9556753907508[/C][/ROW]
[ROW][C]33[/C][C]340[/C][C]525.995852073836[/C][C]-185.995852073836[/C][/ROW]
[ROW][C]34[/C][C]450[/C][C]512.882606550554[/C][C]-62.8826065505541[/C][/ROW]
[ROW][C]35[/C][C]600[/C][C]503.541522593647[/C][C]96.4584774063533[/C][/ROW]
[ROW][C]36[/C][C]680[/C][C]501.364831500299[/C][C]178.635168499701[/C][/ROW]
[ROW][C]37[/C][C]630[/C][C]504.537000189083[/C][C]125.462999810917[/C][/ROW]
[ROW][C]38[/C][C]480[/C][C]507.34148601655[/C][C]-27.3414860165501[/C][/ROW]
[ROW][C]39[/C][C]400[/C][C]504.111654753503[/C][C]-104.111654753503[/C][/ROW]
[ROW][C]40[/C][C]520[/C][C]496.690386927837[/C][C]23.3096130721625[/C][/ROW]
[ROW][C]41[/C][C]470[/C][C]494.307585952631[/C][C]-24.3075859526307[/C][/ROW]
[ROW][C]42[/C][C]610[/C][C]489.84176720733[/C][C]120.15823279267[/C][/ROW]
[ROW][C]43[/C][C]670[/C][C]492.291196201207[/C][C]177.708803798793[/C][/ROW]
[ROW][C]44[/C][C]500[/C][C]499.161646244017[/C][C]0.838353755982723[/C][/ROW]
[ROW][C]45[/C][C]290[/C][C]499.464283739581[/C][C]-209.464283739581[/C][/ROW]
[ROW][C]46[/C][C]470[/C][C]489.256889717124[/C][C]-19.2568897171245[/C][/ROW]
[ROW][C]47[/C][C]660[/C][C]485.877008448657[/C][C]174.122991551343[/C][/ROW]
[ROW][C]48[/C][C]650[/C][C]491.924207646796[/C][C]158.075792353204[/C][/ROW]
[ROW][C]49[/C][C]570[/C][C]499.403068232688[/C][C]70.5969317673121[/C][/ROW]
[ROW][C]50[/C][C]500[/C][C]504.534157855691[/C][C]-4.53415785569143[/C][/ROW]
[ROW][C]51[/C][C]400[/C][C]506.812614844851[/C][C]-106.812614844851[/C][/ROW]
[ROW][C]52[/C][C]500[/C][C]503.916212222599[/C][C]-3.91621222259937[/C][/ROW]
[ROW][C]53[/C][C]340[/C][C]504.79671300441[/C][C]-164.79671300441[/C][/ROW]
[ROW][C]54[/C][C]530[/C][C]497.578605232597[/C][C]32.4213947674026[/C][/ROW]
[ROW][C]55[/C][C]680[/C][C]498.111936193617[/C][C]181.888063806383[/C][/ROW]
[ROW][C]56[/C][C]480[/C][C]506.538673041443[/C][C]-26.5386730414431[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]506.872564850771[/C][C]-166.872564850771[/C][/ROW]
[ROW][C]58[/C][C]460[/C][C]499.845426035068[/C][C]-39.8454260350679[/C][/ROW]
[ROW][C]59[/C][C]630[/C][C]497.031650504901[/C][C]132.968349495099[/C][/ROW]
[ROW][C]60[/C][C]650[/C][C]502.351892118711[/C][C]147.648107881289[/C][/ROW]
[ROW][C]61[/C][C]550[/C][C]510.112848046509[/C][C]39.887151953491[/C][/ROW]
[ROW][C]62[/C][C]470[/C][C]514.377568135515[/C][C]-44.3775681355147[/C][/ROW]
[ROW][C]63[/C][C]240[/C][C]514.938641599894[/C][C]-274.938641599894[/C][/ROW]
[ROW][C]64[/C][C]430[/C][C]503.395978265542[/C][C]-73.3959782655423[/C][/ROW]
[ROW][C]65[/C][C]390[/C][C]498.407688973457[/C][C]-108.407688973457[/C][/ROW]
[ROW][C]66[/C][C]570[/C][C]490.726009970677[/C][C]79.2739900293234[/C][/ROW]
[ROW][C]67[/C][C]700[/C][C]491.042310256196[/C][C]208.957689743804[/C][/ROW]
[ROW][C]68[/C][C]620[/C][C]498.863576980766[/C][C]121.136423019234[/C][/ROW]
[ROW][C]69[/C][C]280[/C][C]504.972890953962[/C][C]-224.972890953962[/C][/ROW]
[ROW][C]70[/C][C]480[/C][C]495.321924531404[/C][C]-15.3219245314042[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]493.272156621866[/C][C]66.7278433781344[/C][/ROW]
[ROW][C]72[/C][C]560[/C][C]495.130464210094[/C][C]64.8695357899056[/C][/ROW]
[ROW][C]73[/C][C]560[/C][C]497.752099056647[/C][C]62.2479009433534[/C][/ROW]
[ROW][C]74[/C][C]550[/C][C]501.075027318998[/C][C]48.9249726810019[/C][/ROW]
[ROW][C]75[/C][C]140[/C][C]504.530253995188[/C][C]-364.530253995188[/C][/ROW]
[ROW][C]76[/C][C]380[/C][C]487.929431145658[/C][C]-107.929431145658[/C][/ROW]
[ROW][C]77[/C][C]390[/C][C]479.487677033636[/C][C]-89.4876770336358[/C][/ROW]
[ROW][C]78[/C][C]500[/C][C]470.583490087946[/C][C]29.4165099120541[/C][/ROW]
[ROW][C]79[/C][C]750[/C][C]466.479350663913[/C][C]283.520649336087[/C][/ROW]
[ROW][C]80[/C][C]680[/C][C]475.464745251697[/C][C]204.535254748303[/C][/ROW]
[ROW][C]81[/C][C]280[/C][C]484.137056064572[/C][C]-204.137056064572[/C][/ROW]
[ROW][C]82[/C][C]360[/C][C]474.989478450909[/C][C]-114.989478450909[/C][/ROW]
[ROW][C]83[/C][C]590[/C][C]467.682066145208[/C][C]122.317933854792[/C][/ROW]
[ROW][C]84[/C][C]580[/C][C]470.770793345965[/C][C]109.229206654035[/C][/ROW]
[ROW][C]85[/C][C]490[/C][C]474.77439083814[/C][C]15.2256091618601[/C][/ROW]
[ROW][C]86[/C][C]610[/C][C]475.476975620874[/C][C]134.523024379126[/C][/ROW]
[ROW][C]87[/C][C]170[/C][C]482.34302506274[/C][C]-312.34302506274[/C][/ROW]
[ROW][C]88[/C][C]320[/C][C]468.58003169249[/C][C]-148.58003169249[/C][/ROW]
[ROW][C]89[/C][C]440[/C][C]459.001416453088[/C][C]-19.0014164530882[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]453.998547974988[/C][C]56.0014520250115[/C][/ROW]
[ROW][C]91[/C][C]770[/C][C]452.504002937398[/C][C]317.495997062602[/C][/ROW]
[ROW][C]92[/C][C]660[/C][C]464.809865312096[/C][C]195.190134687904[/C][/ROW]
[ROW][C]93[/C][C]300[/C][C]475.071447553527[/C][C]-175.071447553527[/C][/ROW]
[ROW][C]94[/C][C]350[/C][C]469.314788871473[/C][C]-119.314788871473[/C][/ROW]
[ROW][C]95[/C][C]580[/C][C]464.100838936688[/C][C]115.899161063312[/C][/ROW]
[ROW][C]96[/C][C]620[/C][C]469.122794030495[/C][C]150.877205969505[/C][/ROW]
[ROW][C]97[/C][C]490[/C][C]477.381881562448[/C][C]12.6181184375522[/C][/ROW]
[ROW][C]98[/C][C]640[/C][C]480.660443931853[/C][C]159.339556068147[/C][/ROW]
[ROW][C]99[/C][C]150[/C][C]491.440948966916[/C][C]-341.440948966916[/C][/ROW]
[ROW][C]100[/C][C]290[/C][C]479.213698876422[/C][C]-189.213698876422[/C][/ROW]
[ROW][C]101[/C][C]370[/C][C]470.220326983782[/C][C]-100.220326983782[/C][/ROW]
[ROW][C]102[/C][C]560[/C][C]463.250911641344[/C][C]96.7490883586557[/C][/ROW]
[ROW][C]103[/C][C]780[/C][C]464.849177531533[/C][C]315.150822468467[/C][/ROW]
[ROW][C]104[/C][C]690[/C][C]478.61494960656[/C][C]211.38505039344[/C][/ROW]
[ROW][C]105[/C][C]310[/C][C]491.233850140321[/C][C]-181.233850140321[/C][/ROW]
[ROW][C]106[/C][C]280[/C][C]486.923865438197[/C][C]-206.923865438197[/C][/ROW]
[ROW][C]107[/C][C]590[/C][C]479.002984838295[/C][C]110.997015161705[/C][/ROW]
[ROW][C]108[/C][C]590[/C][C]484.331327489494[/C][C]105.668672510506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123983&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123983&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
359052070
4490533.501883257009-43.5018832570088
5540542.223901688506-2.22390168850563
6530552.452686867282-22.4526868672823
7550561.640950087388-11.6409500873882
8510571.08196436618-61.0819643661799
9390577.900213971361-187.900213971361
10480577.590297970729-97.5902979707289
11530579.387056589876-49.3870565898765
12690582.342935533472107.657064466528
13570592.521480577358-22.5214805773577
14460597.569117602032-137.569117602032
15540596.572268112807-56.572268112807
16510597.862068875841-87.8620688758406
17520596.860567730829-76.8605677308291
18520595.281937640439-75.2819376404392
19580592.795959555754-12.7959595557542
20480592.469897457803-112.469897457803
21410586.993251264743-176.993251264743
22530576.84541872613-46.84541872613
23540570.937193258805-30.9371932588053
24670565.223657895253104.776342104747
25570565.9024454440954.09755455590516
26400562.889139303195-162.889139303195
27510551.574588248655-41.5745882486545
28570544.23873516301925.7612648369811
29470539.737975685147-69.7379756851468
30640530.790269259471109.209730740529
31650529.899842007469120.100157992531
32500530.955675390751-30.9556753907508
33340525.995852073836-185.995852073836
34450512.882606550554-62.8826065505541
35600503.54152259364796.4584774063533
36680501.364831500299178.635168499701
37630504.537000189083125.462999810917
38480507.34148601655-27.3414860165501
39400504.111654753503-104.111654753503
40520496.69038692783723.3096130721625
41470494.307585952631-24.3075859526307
42610489.84176720733120.15823279267
43670492.291196201207177.708803798793
44500499.1616462440170.838353755982723
45290499.464283739581-209.464283739581
46470489.256889717124-19.2568897171245
47660485.877008448657174.122991551343
48650491.924207646796158.075792353204
49570499.40306823268870.5969317673121
50500504.534157855691-4.53415785569143
51400506.812614844851-106.812614844851
52500503.916212222599-3.91621222259937
53340504.79671300441-164.79671300441
54530497.57860523259732.4213947674026
55680498.111936193617181.888063806383
56480506.538673041443-26.5386730414431
57340506.872564850771-166.872564850771
58460499.845426035068-39.8454260350679
59630497.031650504901132.968349495099
60650502.351892118711147.648107881289
61550510.11284804650939.887151953491
62470514.377568135515-44.3775681355147
63240514.938641599894-274.938641599894
64430503.395978265542-73.3959782655423
65390498.407688973457-108.407688973457
66570490.72600997067779.2739900293234
67700491.042310256196208.957689743804
68620498.863576980766121.136423019234
69280504.972890953962-224.972890953962
70480495.321924531404-15.3219245314042
71560493.27215662186666.7278433781344
72560495.13046421009464.8695357899056
73560497.75209905664762.2479009433534
74550501.07502731899848.9249726810019
75140504.530253995188-364.530253995188
76380487.929431145658-107.929431145658
77390479.487677033636-89.4876770336358
78500470.58349008794629.4165099120541
79750466.479350663913283.520649336087
80680475.464745251697204.535254748303
81280484.137056064572-204.137056064572
82360474.989478450909-114.989478450909
83590467.682066145208122.317933854792
84580470.770793345965109.229206654035
85490474.7743908381415.2256091618601
86610475.476975620874134.523024379126
87170482.34302506274-312.34302506274
88320468.58003169249-148.58003169249
89440459.001416453088-19.0014164530882
90510453.99854797498856.0014520250115
91770452.504002937398317.495997062602
92660464.809865312096195.190134687904
93300475.071447553527-175.071447553527
94350469.314788871473-119.314788871473
95580464.100838936688115.899161063312
96620469.122794030495150.877205969505
97490477.38188156244812.6181184375522
98640480.660443931853159.339556068147
99150491.440948966916-341.440948966916
100290479.213698876422-189.213698876422
101370470.220326983782-100.220326983782
102560463.25091164134496.7490883586557
103780464.849177531533315.150822468467
104690478.61494960656211.38505039344
105310491.233850140321-181.233850140321
106280486.923865438197-206.923865438197
107590479.002984838295110.997015161705
108590484.331327489494105.668672510506







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109490.817491466799219.281649260459762.353333673139
110493.373384191388221.497969147178765.248799235598
111495.929276915977223.518596471603768.33995736035
112498.485169640566225.300232592144771.670106688987
113501.041062365154226.800624029119775.281500701189
114503.596955089743227.978945755689779.214964423797
115506.152847814332228.796216984895783.509478643769
116508.708740538921229.215730806229788.201750271613
117511.26463326351229.20347637419793.32579015283
118513.820525988099228.728531085938798.912520890259
119516.376418712688227.763400698213804.989436727162
120518.932311437277226.284287798881811.580335075672

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 490.817491466799 & 219.281649260459 & 762.353333673139 \tabularnewline
110 & 493.373384191388 & 221.497969147178 & 765.248799235598 \tabularnewline
111 & 495.929276915977 & 223.518596471603 & 768.33995736035 \tabularnewline
112 & 498.485169640566 & 225.300232592144 & 771.670106688987 \tabularnewline
113 & 501.041062365154 & 226.800624029119 & 775.281500701189 \tabularnewline
114 & 503.596955089743 & 227.978945755689 & 779.214964423797 \tabularnewline
115 & 506.152847814332 & 228.796216984895 & 783.509478643769 \tabularnewline
116 & 508.708740538921 & 229.215730806229 & 788.201750271613 \tabularnewline
117 & 511.26463326351 & 229.20347637419 & 793.32579015283 \tabularnewline
118 & 513.820525988099 & 228.728531085938 & 798.912520890259 \tabularnewline
119 & 516.376418712688 & 227.763400698213 & 804.989436727162 \tabularnewline
120 & 518.932311437277 & 226.284287798881 & 811.580335075672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123983&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]490.817491466799[/C][C]219.281649260459[/C][C]762.353333673139[/C][/ROW]
[ROW][C]110[/C][C]493.373384191388[/C][C]221.497969147178[/C][C]765.248799235598[/C][/ROW]
[ROW][C]111[/C][C]495.929276915977[/C][C]223.518596471603[/C][C]768.33995736035[/C][/ROW]
[ROW][C]112[/C][C]498.485169640566[/C][C]225.300232592144[/C][C]771.670106688987[/C][/ROW]
[ROW][C]113[/C][C]501.041062365154[/C][C]226.800624029119[/C][C]775.281500701189[/C][/ROW]
[ROW][C]114[/C][C]503.596955089743[/C][C]227.978945755689[/C][C]779.214964423797[/C][/ROW]
[ROW][C]115[/C][C]506.152847814332[/C][C]228.796216984895[/C][C]783.509478643769[/C][/ROW]
[ROW][C]116[/C][C]508.708740538921[/C][C]229.215730806229[/C][C]788.201750271613[/C][/ROW]
[ROW][C]117[/C][C]511.26463326351[/C][C]229.20347637419[/C][C]793.32579015283[/C][/ROW]
[ROW][C]118[/C][C]513.820525988099[/C][C]228.728531085938[/C][C]798.912520890259[/C][/ROW]
[ROW][C]119[/C][C]516.376418712688[/C][C]227.763400698213[/C][C]804.989436727162[/C][/ROW]
[ROW][C]120[/C][C]518.932311437277[/C][C]226.284287798881[/C][C]811.580335075672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123983&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123983&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
109490.817491466799219.281649260459762.353333673139
110493.373384191388221.497969147178765.248799235598
111495.929276915977223.518596471603768.33995736035
112498.485169640566225.300232592144771.670106688987
113501.041062365154226.800624029119775.281500701189
114503.596955089743227.978945755689779.214964423797
115506.152847814332228.796216984895783.509478643769
116508.708740538921229.215730806229788.201750271613
117511.26463326351229.20347637419793.32579015283
118513.820525988099228.728531085938798.912520890259
119516.376418712688227.763400698213804.989436727162
120518.932311437277226.284287798881811.580335075672



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')