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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 computationWed, 16 Aug 2017 00:04:42 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t1502834692z24yac0pteroel6.htm/, Retrieved Sun, 12 May 2024 11:30:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307343, Retrieved Sun, 12 May 2024 11:30:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-15 22:04:42] [1a8cec710a8245ea2c14b5d40c333c7c] [Current]
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Dataseries X:
70 200
67 600
71 500
57 200
74 100
72 800
78 000
80 600
89 700
78 000
74 100
92 300
78 000
58 500
68 900
52 000
72 800
59 800
79 300
71 500
75 400
84 500
83 200
98 800
71 500
59 800
66 300
48 100
68 900
53 300
75 400
71 500
63 700
91 000
81 900
93 600
70 200
65 000
58 500
48 100
63 700
57 200
78 000
75 400
65 000
87 100
80 600
104 000
83 200
50 700
50 700
50 700
59 800
59 800
80 600
74 100
66 300
83 200
76 700
110 500
87 100
50 700
53 300
44 200
61 100
70 200
88 400
87 100
70 200
81 900
72 800
104 000
79 300
63 700
57 200
42 900
63 700
76 700
89 700
84 500
62 400
89 700
70 200
107 900
89 700
65 000
59 800
40 300
63 700
61 100
92 300
92 300
70 200
91 000
67 600
105 300
89 700
66 300
50 700
35 100
68 900
66 300
87 100
100 100
74 100
83 200
62 400
107 900




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307343&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307343&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307343&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.548594506058805
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.548594506058805 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307343&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]0.548594506058805[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307343&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307343&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
alpha0.548594506058805
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26760070200-2600
37150068773.65428424712726.34571575289
45720070269.3125655261-13069.3125655261
57410063099.559494113211000.4405058868
67280069134.34071986943665.65928013057
77800071145.30126203256854.69873796747
88060074905.75133036975694.24866963029
98970078029.584866661511670.4151333385
107800084431.9104922366-6431.91049223655
117410080903.3997327336-6803.3997327336
129230077171.09201683415128.907983166
137800085470.7278190681-7470.72781906807
145850081372.3275812666-22872.3275812666
156890068824.694329406575.3056705935014
165200068866.0066065692-16866.0066065692
177280059613.408043053813186.5919569462
185980066847.4999442737-7047.49994427372
197930062981.280193395416318.7198066046
207150071933.6402252117-433.640225211697
217540071695.74758005453704.25241994554
228450073727.880106691610772.1198933084
238320079637.40589876733562.59410123265
249880081591.825450021117208.1745499789
257150091032.1354674405-19532.1354674405
265980080316.9132584063-20516.9132584063
276630069061.4473635596-2761.44736355956
284810067546.5325111402-19446.5325111402
296890056878.271613634812021.7283863652
305330063473.3257597259-10173.3257597259
317540057892.295139593817507.7048604062
327150067496.92583971174003.07416028835
336370069692.9903313918-5992.9903313918
349100066405.268760726724594.7312392733
358190079897.80319658492002.19680341509
369360080996.197362986912603.8026370131
377020087910.5742451018-17710.5742451018
386500078194.6505150924-13194.6505150924
395850070956.1377331467-12456.1377331467
404810064122.7690060307-16022.7690060307
416370055332.76595747298367.23404252705
425720059922.9845841115-2722.98458411149
437800058429.170201185119570.8297988149
447540069165.61990782696234.3800921731
456500072585.7665750755-7585.76657507545
468710068424.256707744518675.7432922555
478060078669.66687444051930.33312555954
4810400079728.637021985724271.3629780143
498320093043.7734062834-9843.77340628344
505070087643.5333967086-36943.5333967086
515070067376.5139408743-16676.5139408743
525070058227.8700126976-7527.87001269759
535980054098.12188140695701.87811859313
545980057226.1408914842573.85910851603
558060058638.145857785321961.8541422147
567410070686.29838306913413.70161693092
576630072559.0363354414-6259.03633544144
588320069125.363388595814074.6366114042
597670076846.6317083863-146.631708386267
6011050076766.190358751533733.8096412485
618710095272.372996374-8172.37299637398
625070090789.0540690999-40089.0540690999
635330068796.4192536973-15496.4192536973
644420060295.1687875351-16095.1687875351
656110051465.44761660429634.55238339581
667020056750.910122470913449.0898775291
678840064129.006940774424270.9930592256
688710077443.9403896579656.05961034304
697020082741.2016420675-12541.2016420675
708190075861.16732185366038.8326781464
717280079174.0377520931-6374.03775209309
7210400075677.275659883428322.7243401166
737930091214.9666294894-11914.9666294894
746370084678.4813966775-20978.4813966775
755720073169.8017570034-15969.8017570034
764290064408.8562502631-21508.8562502631
776370052609.215879760211090.7841202398
787670058693.55911600818006.440883992
798970068571.793658638621128.2063413614
808450080162.61158038634337.38841961371
816240082542.0790380294-20142.0790380294
828970071492.245137164318207.7548628357
837020081480.9194225814-11280.9194225814
8410790075292.269004061232607.7309959388
858970093180.6910834766-3480.69108347662
866500091271.2030777935-26271.2030777935
875980076858.9654017608-17058.9654017608
884030067500.5107033076-27200.5107033076
896370052578.459969479311121.5400305207
906110058679.6757291362420.32427086395
919230060007.452327012832292.5476729872
929230077722.966567055614577.0334329444
937020085719.8470230044-15519.8470230044
949100077205.744211311113794.2557886889
956760084773.1971521557-17173.1971521557
9610530075352.075543018429947.9244569816
978970091781.3423679826-2081.34236798261
986630090639.5293796799-24339.5293796799
995070077286.9972819307-26586.9972819307
1003510062701.5166404631-27601.5166404631
1016890047559.476252614421340.5237473856
1026630059266.77033684767033.22966315242
1038710063125.161489902823974.8385100972
10410010076277.626180189223822.3738198108
1057410089346.4495790165-15246.4495790165
1068320080982.33110306552217.66889693451
1076240082198.9320761813-19798.9320761813
10810790071337.346713356836562.6532866432

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 67600 & 70200 & -2600 \tabularnewline
3 & 71500 & 68773.6542842471 & 2726.34571575289 \tabularnewline
4 & 57200 & 70269.3125655261 & -13069.3125655261 \tabularnewline
5 & 74100 & 63099.5594941132 & 11000.4405058868 \tabularnewline
6 & 72800 & 69134.3407198694 & 3665.65928013057 \tabularnewline
7 & 78000 & 71145.3012620325 & 6854.69873796747 \tabularnewline
8 & 80600 & 74905.7513303697 & 5694.24866963029 \tabularnewline
9 & 89700 & 78029.5848666615 & 11670.4151333385 \tabularnewline
10 & 78000 & 84431.9104922366 & -6431.91049223655 \tabularnewline
11 & 74100 & 80903.3997327336 & -6803.3997327336 \tabularnewline
12 & 92300 & 77171.092016834 & 15128.907983166 \tabularnewline
13 & 78000 & 85470.7278190681 & -7470.72781906807 \tabularnewline
14 & 58500 & 81372.3275812666 & -22872.3275812666 \tabularnewline
15 & 68900 & 68824.6943294065 & 75.3056705935014 \tabularnewline
16 & 52000 & 68866.0066065692 & -16866.0066065692 \tabularnewline
17 & 72800 & 59613.4080430538 & 13186.5919569462 \tabularnewline
18 & 59800 & 66847.4999442737 & -7047.49994427372 \tabularnewline
19 & 79300 & 62981.2801933954 & 16318.7198066046 \tabularnewline
20 & 71500 & 71933.6402252117 & -433.640225211697 \tabularnewline
21 & 75400 & 71695.7475800545 & 3704.25241994554 \tabularnewline
22 & 84500 & 73727.8801066916 & 10772.1198933084 \tabularnewline
23 & 83200 & 79637.4058987673 & 3562.59410123265 \tabularnewline
24 & 98800 & 81591.8254500211 & 17208.1745499789 \tabularnewline
25 & 71500 & 91032.1354674405 & -19532.1354674405 \tabularnewline
26 & 59800 & 80316.9132584063 & -20516.9132584063 \tabularnewline
27 & 66300 & 69061.4473635596 & -2761.44736355956 \tabularnewline
28 & 48100 & 67546.5325111402 & -19446.5325111402 \tabularnewline
29 & 68900 & 56878.2716136348 & 12021.7283863652 \tabularnewline
30 & 53300 & 63473.3257597259 & -10173.3257597259 \tabularnewline
31 & 75400 & 57892.2951395938 & 17507.7048604062 \tabularnewline
32 & 71500 & 67496.9258397117 & 4003.07416028835 \tabularnewline
33 & 63700 & 69692.9903313918 & -5992.9903313918 \tabularnewline
34 & 91000 & 66405.2687607267 & 24594.7312392733 \tabularnewline
35 & 81900 & 79897.8031965849 & 2002.19680341509 \tabularnewline
36 & 93600 & 80996.1973629869 & 12603.8026370131 \tabularnewline
37 & 70200 & 87910.5742451018 & -17710.5742451018 \tabularnewline
38 & 65000 & 78194.6505150924 & -13194.6505150924 \tabularnewline
39 & 58500 & 70956.1377331467 & -12456.1377331467 \tabularnewline
40 & 48100 & 64122.7690060307 & -16022.7690060307 \tabularnewline
41 & 63700 & 55332.7659574729 & 8367.23404252705 \tabularnewline
42 & 57200 & 59922.9845841115 & -2722.98458411149 \tabularnewline
43 & 78000 & 58429.1702011851 & 19570.8297988149 \tabularnewline
44 & 75400 & 69165.6199078269 & 6234.3800921731 \tabularnewline
45 & 65000 & 72585.7665750755 & -7585.76657507545 \tabularnewline
46 & 87100 & 68424.2567077445 & 18675.7432922555 \tabularnewline
47 & 80600 & 78669.6668744405 & 1930.33312555954 \tabularnewline
48 & 104000 & 79728.6370219857 & 24271.3629780143 \tabularnewline
49 & 83200 & 93043.7734062834 & -9843.77340628344 \tabularnewline
50 & 50700 & 87643.5333967086 & -36943.5333967086 \tabularnewline
51 & 50700 & 67376.5139408743 & -16676.5139408743 \tabularnewline
52 & 50700 & 58227.8700126976 & -7527.87001269759 \tabularnewline
53 & 59800 & 54098.1218814069 & 5701.87811859313 \tabularnewline
54 & 59800 & 57226.140891484 & 2573.85910851603 \tabularnewline
55 & 80600 & 58638.1458577853 & 21961.8541422147 \tabularnewline
56 & 74100 & 70686.2983830691 & 3413.70161693092 \tabularnewline
57 & 66300 & 72559.0363354414 & -6259.03633544144 \tabularnewline
58 & 83200 & 69125.3633885958 & 14074.6366114042 \tabularnewline
59 & 76700 & 76846.6317083863 & -146.631708386267 \tabularnewline
60 & 110500 & 76766.1903587515 & 33733.8096412485 \tabularnewline
61 & 87100 & 95272.372996374 & -8172.37299637398 \tabularnewline
62 & 50700 & 90789.0540690999 & -40089.0540690999 \tabularnewline
63 & 53300 & 68796.4192536973 & -15496.4192536973 \tabularnewline
64 & 44200 & 60295.1687875351 & -16095.1687875351 \tabularnewline
65 & 61100 & 51465.4476166042 & 9634.55238339581 \tabularnewline
66 & 70200 & 56750.9101224709 & 13449.0898775291 \tabularnewline
67 & 88400 & 64129.0069407744 & 24270.9930592256 \tabularnewline
68 & 87100 & 77443.940389657 & 9656.05961034304 \tabularnewline
69 & 70200 & 82741.2016420675 & -12541.2016420675 \tabularnewline
70 & 81900 & 75861.1673218536 & 6038.8326781464 \tabularnewline
71 & 72800 & 79174.0377520931 & -6374.03775209309 \tabularnewline
72 & 104000 & 75677.2756598834 & 28322.7243401166 \tabularnewline
73 & 79300 & 91214.9666294894 & -11914.9666294894 \tabularnewline
74 & 63700 & 84678.4813966775 & -20978.4813966775 \tabularnewline
75 & 57200 & 73169.8017570034 & -15969.8017570034 \tabularnewline
76 & 42900 & 64408.8562502631 & -21508.8562502631 \tabularnewline
77 & 63700 & 52609.2158797602 & 11090.7841202398 \tabularnewline
78 & 76700 & 58693.559116008 & 18006.440883992 \tabularnewline
79 & 89700 & 68571.7936586386 & 21128.2063413614 \tabularnewline
80 & 84500 & 80162.6115803863 & 4337.38841961371 \tabularnewline
81 & 62400 & 82542.0790380294 & -20142.0790380294 \tabularnewline
82 & 89700 & 71492.2451371643 & 18207.7548628357 \tabularnewline
83 & 70200 & 81480.9194225814 & -11280.9194225814 \tabularnewline
84 & 107900 & 75292.2690040612 & 32607.7309959388 \tabularnewline
85 & 89700 & 93180.6910834766 & -3480.69108347662 \tabularnewline
86 & 65000 & 91271.2030777935 & -26271.2030777935 \tabularnewline
87 & 59800 & 76858.9654017608 & -17058.9654017608 \tabularnewline
88 & 40300 & 67500.5107033076 & -27200.5107033076 \tabularnewline
89 & 63700 & 52578.4599694793 & 11121.5400305207 \tabularnewline
90 & 61100 & 58679.675729136 & 2420.32427086395 \tabularnewline
91 & 92300 & 60007.4523270128 & 32292.5476729872 \tabularnewline
92 & 92300 & 77722.9665670556 & 14577.0334329444 \tabularnewline
93 & 70200 & 85719.8470230044 & -15519.8470230044 \tabularnewline
94 & 91000 & 77205.7442113111 & 13794.2557886889 \tabularnewline
95 & 67600 & 84773.1971521557 & -17173.1971521557 \tabularnewline
96 & 105300 & 75352.0755430184 & 29947.9244569816 \tabularnewline
97 & 89700 & 91781.3423679826 & -2081.34236798261 \tabularnewline
98 & 66300 & 90639.5293796799 & -24339.5293796799 \tabularnewline
99 & 50700 & 77286.9972819307 & -26586.9972819307 \tabularnewline
100 & 35100 & 62701.5166404631 & -27601.5166404631 \tabularnewline
101 & 68900 & 47559.4762526144 & 21340.5237473856 \tabularnewline
102 & 66300 & 59266.7703368476 & 7033.22966315242 \tabularnewline
103 & 87100 & 63125.1614899028 & 23974.8385100972 \tabularnewline
104 & 100100 & 76277.6261801892 & 23822.3738198108 \tabularnewline
105 & 74100 & 89346.4495790165 & -15246.4495790165 \tabularnewline
106 & 83200 & 80982.3311030655 & 2217.66889693451 \tabularnewline
107 & 62400 & 82198.9320761813 & -19798.9320761813 \tabularnewline
108 & 107900 & 71337.3467133568 & 36562.6532866432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307343&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]2[/C][C]67600[/C][C]70200[/C][C]-2600[/C][/ROW]
[ROW][C]3[/C][C]71500[/C][C]68773.6542842471[/C][C]2726.34571575289[/C][/ROW]
[ROW][C]4[/C][C]57200[/C][C]70269.3125655261[/C][C]-13069.3125655261[/C][/ROW]
[ROW][C]5[/C][C]74100[/C][C]63099.5594941132[/C][C]11000.4405058868[/C][/ROW]
[ROW][C]6[/C][C]72800[/C][C]69134.3407198694[/C][C]3665.65928013057[/C][/ROW]
[ROW][C]7[/C][C]78000[/C][C]71145.3012620325[/C][C]6854.69873796747[/C][/ROW]
[ROW][C]8[/C][C]80600[/C][C]74905.7513303697[/C][C]5694.24866963029[/C][/ROW]
[ROW][C]9[/C][C]89700[/C][C]78029.5848666615[/C][C]11670.4151333385[/C][/ROW]
[ROW][C]10[/C][C]78000[/C][C]84431.9104922366[/C][C]-6431.91049223655[/C][/ROW]
[ROW][C]11[/C][C]74100[/C][C]80903.3997327336[/C][C]-6803.3997327336[/C][/ROW]
[ROW][C]12[/C][C]92300[/C][C]77171.092016834[/C][C]15128.907983166[/C][/ROW]
[ROW][C]13[/C][C]78000[/C][C]85470.7278190681[/C][C]-7470.72781906807[/C][/ROW]
[ROW][C]14[/C][C]58500[/C][C]81372.3275812666[/C][C]-22872.3275812666[/C][/ROW]
[ROW][C]15[/C][C]68900[/C][C]68824.6943294065[/C][C]75.3056705935014[/C][/ROW]
[ROW][C]16[/C][C]52000[/C][C]68866.0066065692[/C][C]-16866.0066065692[/C][/ROW]
[ROW][C]17[/C][C]72800[/C][C]59613.4080430538[/C][C]13186.5919569462[/C][/ROW]
[ROW][C]18[/C][C]59800[/C][C]66847.4999442737[/C][C]-7047.49994427372[/C][/ROW]
[ROW][C]19[/C][C]79300[/C][C]62981.2801933954[/C][C]16318.7198066046[/C][/ROW]
[ROW][C]20[/C][C]71500[/C][C]71933.6402252117[/C][C]-433.640225211697[/C][/ROW]
[ROW][C]21[/C][C]75400[/C][C]71695.7475800545[/C][C]3704.25241994554[/C][/ROW]
[ROW][C]22[/C][C]84500[/C][C]73727.8801066916[/C][C]10772.1198933084[/C][/ROW]
[ROW][C]23[/C][C]83200[/C][C]79637.4058987673[/C][C]3562.59410123265[/C][/ROW]
[ROW][C]24[/C][C]98800[/C][C]81591.8254500211[/C][C]17208.1745499789[/C][/ROW]
[ROW][C]25[/C][C]71500[/C][C]91032.1354674405[/C][C]-19532.1354674405[/C][/ROW]
[ROW][C]26[/C][C]59800[/C][C]80316.9132584063[/C][C]-20516.9132584063[/C][/ROW]
[ROW][C]27[/C][C]66300[/C][C]69061.4473635596[/C][C]-2761.44736355956[/C][/ROW]
[ROW][C]28[/C][C]48100[/C][C]67546.5325111402[/C][C]-19446.5325111402[/C][/ROW]
[ROW][C]29[/C][C]68900[/C][C]56878.2716136348[/C][C]12021.7283863652[/C][/ROW]
[ROW][C]30[/C][C]53300[/C][C]63473.3257597259[/C][C]-10173.3257597259[/C][/ROW]
[ROW][C]31[/C][C]75400[/C][C]57892.2951395938[/C][C]17507.7048604062[/C][/ROW]
[ROW][C]32[/C][C]71500[/C][C]67496.9258397117[/C][C]4003.07416028835[/C][/ROW]
[ROW][C]33[/C][C]63700[/C][C]69692.9903313918[/C][C]-5992.9903313918[/C][/ROW]
[ROW][C]34[/C][C]91000[/C][C]66405.2687607267[/C][C]24594.7312392733[/C][/ROW]
[ROW][C]35[/C][C]81900[/C][C]79897.8031965849[/C][C]2002.19680341509[/C][/ROW]
[ROW][C]36[/C][C]93600[/C][C]80996.1973629869[/C][C]12603.8026370131[/C][/ROW]
[ROW][C]37[/C][C]70200[/C][C]87910.5742451018[/C][C]-17710.5742451018[/C][/ROW]
[ROW][C]38[/C][C]65000[/C][C]78194.6505150924[/C][C]-13194.6505150924[/C][/ROW]
[ROW][C]39[/C][C]58500[/C][C]70956.1377331467[/C][C]-12456.1377331467[/C][/ROW]
[ROW][C]40[/C][C]48100[/C][C]64122.7690060307[/C][C]-16022.7690060307[/C][/ROW]
[ROW][C]41[/C][C]63700[/C][C]55332.7659574729[/C][C]8367.23404252705[/C][/ROW]
[ROW][C]42[/C][C]57200[/C][C]59922.9845841115[/C][C]-2722.98458411149[/C][/ROW]
[ROW][C]43[/C][C]78000[/C][C]58429.1702011851[/C][C]19570.8297988149[/C][/ROW]
[ROW][C]44[/C][C]75400[/C][C]69165.6199078269[/C][C]6234.3800921731[/C][/ROW]
[ROW][C]45[/C][C]65000[/C][C]72585.7665750755[/C][C]-7585.76657507545[/C][/ROW]
[ROW][C]46[/C][C]87100[/C][C]68424.2567077445[/C][C]18675.7432922555[/C][/ROW]
[ROW][C]47[/C][C]80600[/C][C]78669.6668744405[/C][C]1930.33312555954[/C][/ROW]
[ROW][C]48[/C][C]104000[/C][C]79728.6370219857[/C][C]24271.3629780143[/C][/ROW]
[ROW][C]49[/C][C]83200[/C][C]93043.7734062834[/C][C]-9843.77340628344[/C][/ROW]
[ROW][C]50[/C][C]50700[/C][C]87643.5333967086[/C][C]-36943.5333967086[/C][/ROW]
[ROW][C]51[/C][C]50700[/C][C]67376.5139408743[/C][C]-16676.5139408743[/C][/ROW]
[ROW][C]52[/C][C]50700[/C][C]58227.8700126976[/C][C]-7527.87001269759[/C][/ROW]
[ROW][C]53[/C][C]59800[/C][C]54098.1218814069[/C][C]5701.87811859313[/C][/ROW]
[ROW][C]54[/C][C]59800[/C][C]57226.140891484[/C][C]2573.85910851603[/C][/ROW]
[ROW][C]55[/C][C]80600[/C][C]58638.1458577853[/C][C]21961.8541422147[/C][/ROW]
[ROW][C]56[/C][C]74100[/C][C]70686.2983830691[/C][C]3413.70161693092[/C][/ROW]
[ROW][C]57[/C][C]66300[/C][C]72559.0363354414[/C][C]-6259.03633544144[/C][/ROW]
[ROW][C]58[/C][C]83200[/C][C]69125.3633885958[/C][C]14074.6366114042[/C][/ROW]
[ROW][C]59[/C][C]76700[/C][C]76846.6317083863[/C][C]-146.631708386267[/C][/ROW]
[ROW][C]60[/C][C]110500[/C][C]76766.1903587515[/C][C]33733.8096412485[/C][/ROW]
[ROW][C]61[/C][C]87100[/C][C]95272.372996374[/C][C]-8172.37299637398[/C][/ROW]
[ROW][C]62[/C][C]50700[/C][C]90789.0540690999[/C][C]-40089.0540690999[/C][/ROW]
[ROW][C]63[/C][C]53300[/C][C]68796.4192536973[/C][C]-15496.4192536973[/C][/ROW]
[ROW][C]64[/C][C]44200[/C][C]60295.1687875351[/C][C]-16095.1687875351[/C][/ROW]
[ROW][C]65[/C][C]61100[/C][C]51465.4476166042[/C][C]9634.55238339581[/C][/ROW]
[ROW][C]66[/C][C]70200[/C][C]56750.9101224709[/C][C]13449.0898775291[/C][/ROW]
[ROW][C]67[/C][C]88400[/C][C]64129.0069407744[/C][C]24270.9930592256[/C][/ROW]
[ROW][C]68[/C][C]87100[/C][C]77443.940389657[/C][C]9656.05961034304[/C][/ROW]
[ROW][C]69[/C][C]70200[/C][C]82741.2016420675[/C][C]-12541.2016420675[/C][/ROW]
[ROW][C]70[/C][C]81900[/C][C]75861.1673218536[/C][C]6038.8326781464[/C][/ROW]
[ROW][C]71[/C][C]72800[/C][C]79174.0377520931[/C][C]-6374.03775209309[/C][/ROW]
[ROW][C]72[/C][C]104000[/C][C]75677.2756598834[/C][C]28322.7243401166[/C][/ROW]
[ROW][C]73[/C][C]79300[/C][C]91214.9666294894[/C][C]-11914.9666294894[/C][/ROW]
[ROW][C]74[/C][C]63700[/C][C]84678.4813966775[/C][C]-20978.4813966775[/C][/ROW]
[ROW][C]75[/C][C]57200[/C][C]73169.8017570034[/C][C]-15969.8017570034[/C][/ROW]
[ROW][C]76[/C][C]42900[/C][C]64408.8562502631[/C][C]-21508.8562502631[/C][/ROW]
[ROW][C]77[/C][C]63700[/C][C]52609.2158797602[/C][C]11090.7841202398[/C][/ROW]
[ROW][C]78[/C][C]76700[/C][C]58693.559116008[/C][C]18006.440883992[/C][/ROW]
[ROW][C]79[/C][C]89700[/C][C]68571.7936586386[/C][C]21128.2063413614[/C][/ROW]
[ROW][C]80[/C][C]84500[/C][C]80162.6115803863[/C][C]4337.38841961371[/C][/ROW]
[ROW][C]81[/C][C]62400[/C][C]82542.0790380294[/C][C]-20142.0790380294[/C][/ROW]
[ROW][C]82[/C][C]89700[/C][C]71492.2451371643[/C][C]18207.7548628357[/C][/ROW]
[ROW][C]83[/C][C]70200[/C][C]81480.9194225814[/C][C]-11280.9194225814[/C][/ROW]
[ROW][C]84[/C][C]107900[/C][C]75292.2690040612[/C][C]32607.7309959388[/C][/ROW]
[ROW][C]85[/C][C]89700[/C][C]93180.6910834766[/C][C]-3480.69108347662[/C][/ROW]
[ROW][C]86[/C][C]65000[/C][C]91271.2030777935[/C][C]-26271.2030777935[/C][/ROW]
[ROW][C]87[/C][C]59800[/C][C]76858.9654017608[/C][C]-17058.9654017608[/C][/ROW]
[ROW][C]88[/C][C]40300[/C][C]67500.5107033076[/C][C]-27200.5107033076[/C][/ROW]
[ROW][C]89[/C][C]63700[/C][C]52578.4599694793[/C][C]11121.5400305207[/C][/ROW]
[ROW][C]90[/C][C]61100[/C][C]58679.675729136[/C][C]2420.32427086395[/C][/ROW]
[ROW][C]91[/C][C]92300[/C][C]60007.4523270128[/C][C]32292.5476729872[/C][/ROW]
[ROW][C]92[/C][C]92300[/C][C]77722.9665670556[/C][C]14577.0334329444[/C][/ROW]
[ROW][C]93[/C][C]70200[/C][C]85719.8470230044[/C][C]-15519.8470230044[/C][/ROW]
[ROW][C]94[/C][C]91000[/C][C]77205.7442113111[/C][C]13794.2557886889[/C][/ROW]
[ROW][C]95[/C][C]67600[/C][C]84773.1971521557[/C][C]-17173.1971521557[/C][/ROW]
[ROW][C]96[/C][C]105300[/C][C]75352.0755430184[/C][C]29947.9244569816[/C][/ROW]
[ROW][C]97[/C][C]89700[/C][C]91781.3423679826[/C][C]-2081.34236798261[/C][/ROW]
[ROW][C]98[/C][C]66300[/C][C]90639.5293796799[/C][C]-24339.5293796799[/C][/ROW]
[ROW][C]99[/C][C]50700[/C][C]77286.9972819307[/C][C]-26586.9972819307[/C][/ROW]
[ROW][C]100[/C][C]35100[/C][C]62701.5166404631[/C][C]-27601.5166404631[/C][/ROW]
[ROW][C]101[/C][C]68900[/C][C]47559.4762526144[/C][C]21340.5237473856[/C][/ROW]
[ROW][C]102[/C][C]66300[/C][C]59266.7703368476[/C][C]7033.22966315242[/C][/ROW]
[ROW][C]103[/C][C]87100[/C][C]63125.1614899028[/C][C]23974.8385100972[/C][/ROW]
[ROW][C]104[/C][C]100100[/C][C]76277.6261801892[/C][C]23822.3738198108[/C][/ROW]
[ROW][C]105[/C][C]74100[/C][C]89346.4495790165[/C][C]-15246.4495790165[/C][/ROW]
[ROW][C]106[/C][C]83200[/C][C]80982.3311030655[/C][C]2217.66889693451[/C][/ROW]
[ROW][C]107[/C][C]62400[/C][C]82198.9320761813[/C][C]-19798.9320761813[/C][/ROW]
[ROW][C]108[/C][C]107900[/C][C]71337.3467133568[/C][C]36562.6532866432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307343&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307343&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
26760070200-2600
37150068773.65428424712726.34571575289
45720070269.3125655261-13069.3125655261
57410063099.559494113211000.4405058868
67280069134.34071986943665.65928013057
77800071145.30126203256854.69873796747
88060074905.75133036975694.24866963029
98970078029.584866661511670.4151333385
107800084431.9104922366-6431.91049223655
117410080903.3997327336-6803.3997327336
129230077171.09201683415128.907983166
137800085470.7278190681-7470.72781906807
145850081372.3275812666-22872.3275812666
156890068824.694329406575.3056705935014
165200068866.0066065692-16866.0066065692
177280059613.408043053813186.5919569462
185980066847.4999442737-7047.49994427372
197930062981.280193395416318.7198066046
207150071933.6402252117-433.640225211697
217540071695.74758005453704.25241994554
228450073727.880106691610772.1198933084
238320079637.40589876733562.59410123265
249880081591.825450021117208.1745499789
257150091032.1354674405-19532.1354674405
265980080316.9132584063-20516.9132584063
276630069061.4473635596-2761.44736355956
284810067546.5325111402-19446.5325111402
296890056878.271613634812021.7283863652
305330063473.3257597259-10173.3257597259
317540057892.295139593817507.7048604062
327150067496.92583971174003.07416028835
336370069692.9903313918-5992.9903313918
349100066405.268760726724594.7312392733
358190079897.80319658492002.19680341509
369360080996.197362986912603.8026370131
377020087910.5742451018-17710.5742451018
386500078194.6505150924-13194.6505150924
395850070956.1377331467-12456.1377331467
404810064122.7690060307-16022.7690060307
416370055332.76595747298367.23404252705
425720059922.9845841115-2722.98458411149
437800058429.170201185119570.8297988149
447540069165.61990782696234.3800921731
456500072585.7665750755-7585.76657507545
468710068424.256707744518675.7432922555
478060078669.66687444051930.33312555954
4810400079728.637021985724271.3629780143
498320093043.7734062834-9843.77340628344
505070087643.5333967086-36943.5333967086
515070067376.5139408743-16676.5139408743
525070058227.8700126976-7527.87001269759
535980054098.12188140695701.87811859313
545980057226.1408914842573.85910851603
558060058638.145857785321961.8541422147
567410070686.29838306913413.70161693092
576630072559.0363354414-6259.03633544144
588320069125.363388595814074.6366114042
597670076846.6317083863-146.631708386267
6011050076766.190358751533733.8096412485
618710095272.372996374-8172.37299637398
625070090789.0540690999-40089.0540690999
635330068796.4192536973-15496.4192536973
644420060295.1687875351-16095.1687875351
656110051465.44761660429634.55238339581
667020056750.910122470913449.0898775291
678840064129.006940774424270.9930592256
688710077443.9403896579656.05961034304
697020082741.2016420675-12541.2016420675
708190075861.16732185366038.8326781464
717280079174.0377520931-6374.03775209309
7210400075677.275659883428322.7243401166
737930091214.9666294894-11914.9666294894
746370084678.4813966775-20978.4813966775
755720073169.8017570034-15969.8017570034
764290064408.8562502631-21508.8562502631
776370052609.215879760211090.7841202398
787670058693.55911600818006.440883992
798970068571.793658638621128.2063413614
808450080162.61158038634337.38841961371
816240082542.0790380294-20142.0790380294
828970071492.245137164318207.7548628357
837020081480.9194225814-11280.9194225814
8410790075292.269004061232607.7309959388
858970093180.6910834766-3480.69108347662
866500091271.2030777935-26271.2030777935
875980076858.9654017608-17058.9654017608
884030067500.5107033076-27200.5107033076
896370052578.459969479311121.5400305207
906110058679.6757291362420.32427086395
919230060007.452327012832292.5476729872
929230077722.966567055614577.0334329444
937020085719.8470230044-15519.8470230044
949100077205.744211311113794.2557886889
956760084773.1971521557-17173.1971521557
9610530075352.075543018429947.9244569816
978970091781.3423679826-2081.34236798261
986630090639.5293796799-24339.5293796799
995070077286.9972819307-26586.9972819307
1003510062701.5166404631-27601.5166404631
1016890047559.476252614421340.5237473856
1026630059266.77033684767033.22966315242
1038710063125.161489902823974.8385100972
10410010076277.626180189223822.3738198108
1057410089346.4495790165-15246.4495790165
1068320080982.33110306552217.66889693451
1076240082198.9320761813-19798.9320761813
10810790071337.346713356836562.6532866432







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10991395.417433342258411.3196805245124379.51518616
11091395.417433342253773.9352334695129016.899633215
11191395.417433342249648.5475954341133142.28727125
11291395.417433342245895.6772185767136895.157648108
11391395.417433342242429.5969259817140361.237940703
11491395.417433342239193.1493187578143597.685547926
11591395.417433342236145.9648147428146644.870051941
11691395.417433342233258.2758369173149532.559029767
11791395.417433342230507.3853469735152283.449519711
11891395.417433342227875.5176404539154915.31722623
11991395.417433342225348.4425741825157442.392292502
12091395.417433342222914.5580170471159876.276849637

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 91395.4174333422 & 58411.3196805245 & 124379.51518616 \tabularnewline
110 & 91395.4174333422 & 53773.9352334695 & 129016.899633215 \tabularnewline
111 & 91395.4174333422 & 49648.5475954341 & 133142.28727125 \tabularnewline
112 & 91395.4174333422 & 45895.6772185767 & 136895.157648108 \tabularnewline
113 & 91395.4174333422 & 42429.5969259817 & 140361.237940703 \tabularnewline
114 & 91395.4174333422 & 39193.1493187578 & 143597.685547926 \tabularnewline
115 & 91395.4174333422 & 36145.9648147428 & 146644.870051941 \tabularnewline
116 & 91395.4174333422 & 33258.2758369173 & 149532.559029767 \tabularnewline
117 & 91395.4174333422 & 30507.3853469735 & 152283.449519711 \tabularnewline
118 & 91395.4174333422 & 27875.5176404539 & 154915.31722623 \tabularnewline
119 & 91395.4174333422 & 25348.4425741825 & 157442.392292502 \tabularnewline
120 & 91395.4174333422 & 22914.5580170471 & 159876.276849637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307343&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]91395.4174333422[/C][C]58411.3196805245[/C][C]124379.51518616[/C][/ROW]
[ROW][C]110[/C][C]91395.4174333422[/C][C]53773.9352334695[/C][C]129016.899633215[/C][/ROW]
[ROW][C]111[/C][C]91395.4174333422[/C][C]49648.5475954341[/C][C]133142.28727125[/C][/ROW]
[ROW][C]112[/C][C]91395.4174333422[/C][C]45895.6772185767[/C][C]136895.157648108[/C][/ROW]
[ROW][C]113[/C][C]91395.4174333422[/C][C]42429.5969259817[/C][C]140361.237940703[/C][/ROW]
[ROW][C]114[/C][C]91395.4174333422[/C][C]39193.1493187578[/C][C]143597.685547926[/C][/ROW]
[ROW][C]115[/C][C]91395.4174333422[/C][C]36145.9648147428[/C][C]146644.870051941[/C][/ROW]
[ROW][C]116[/C][C]91395.4174333422[/C][C]33258.2758369173[/C][C]149532.559029767[/C][/ROW]
[ROW][C]117[/C][C]91395.4174333422[/C][C]30507.3853469735[/C][C]152283.449519711[/C][/ROW]
[ROW][C]118[/C][C]91395.4174333422[/C][C]27875.5176404539[/C][C]154915.31722623[/C][/ROW]
[ROW][C]119[/C][C]91395.4174333422[/C][C]25348.4425741825[/C][C]157442.392292502[/C][/ROW]
[ROW][C]120[/C][C]91395.4174333422[/C][C]22914.5580170471[/C][C]159876.276849637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307343&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307343&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
10991395.417433342258411.3196805245124379.51518616
11091395.417433342253773.9352334695129016.899633215
11191395.417433342249648.5475954341133142.28727125
11291395.417433342245895.6772185767136895.157648108
11391395.417433342242429.5969259817140361.237940703
11491395.417433342239193.1493187578143597.685547926
11591395.417433342236145.9648147428146644.870051941
11691395.417433342233258.2758369173149532.559029767
11791395.417433342230507.3853469735152283.449519711
11891395.417433342227875.5176404539154915.31722623
11991395.417433342225348.4425741825157442.392292502
12091395.417433342222914.5580170471159876.276849637



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')