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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 computationMon, 30 Mar 2015 15:04:27 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/30/t142772429894fydws3th03uxo.htm/, Retrieved Sun, 19 May 2024 13:00:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278466, Retrieved Sun, 19 May 2024 13:00:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-03-30 14:04:27] [9d11e60232d68c92754922ab1f7d0739] [Current]
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Dataseries X:
78.7
75.7
77.1
86.1
86.8
86.3
91.5
90.7
78.2
73
73.7
77.3
67.5
72.7
76.6
82.4
82.3
86.3
93
88.8
96.9
103.9
115.7
112.8
114.7
118
129.3
137
156
166.2
167.8
144.3
126
90.4
67.5
52.4
54.6
52.9
59.1
63.3
73.8
87.6
81.8
90.7
86.3
93.6
98
94.3
97.6
94.2
100.2
106.7
95.7
94.6
94.7
96.2
96.3
103.3
106.8
113.7
117.4
123.6
137.6
147.4
137.2
133.8
136.7
127.3
128.7
127
133.7
132
135.1
142.6
149.3
143.5
131.4
114.7
122.3
133.4
134.6
130.9
127.9
128
133.3
136.3
129.5
124.6
125.5
126.2
133.3
137
137.8
133.5
129.9
133.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278466&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278466&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278466&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.613489252289332
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.613489252289332 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278466&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.613489252289332[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278466&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278466&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
alpha1
beta0.613489252289332
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
377.172.74.39999999999999
486.176.79935271007319.30064728992694
586.891.5051998617771-4.70519986177713
686.389.3186103167036-3.01861031670362
791.586.96672533055624.53327466944376
890.794.9478406179355-4.24784061793547
978.291.541836053394-13.341836053394
107370.85676302883052.14323697116953
1173.766.97161587575216.7283841242479
1277.371.79940722125245.50059277874763
1367.578.7739617722343-11.2739617722343
1472.762.057507394247810.6424926057522
1576.673.78656222544552.81343777455453
1682.479.41257606211952.98742393788054
1782.387.0453285400411-4.74532854004107
1886.384.0341204821442.26587951785596
199389.42421321333123.5757867866688
2088.898.3179199754307-9.51791997543071
2196.988.2787783663548.62122163364597
22103.9101.66780518022.23219481979989
23115.7110.0372327111635.66276728883673
24112.8125.31127958108-12.5112795810802
25114.7114.735744025701-0.0357440257005095
26118116.61381545011.38618454990029
27129.3120.7642247731538.53577522684695
28137137.300831134781-0.30083113478122
29156144.81627446683911.1837255331611
30166.2170.677369881987-4.47736988198704
31167.8178.130551580864-10.330551580864
32144.3173.392869215783-29.0928692157834
33126132.044706633641-6.04470663364114
3490.4110.03634408066-19.6363440806603
3567.562.389658032925.11034196708004
3652.442.62479790524679.77520209475332
3754.633.52177932933421.078220670666
3852.948.65304116817044.24695883182957
3959.149.55850476641319.54149523358688
4063.361.61210954298861.68789045701143
4173.866.84761219740686.95238780259319
4287.681.61282739204525.98717260795482
4381.899.0858934386265-17.2858934386265
4490.782.68118359781058.01881640218953
4586.396.5006412766352-10.2006412766352
4693.685.84265748696067.75734251303943
479897.90170374503740.0982962549626336
4894.3102.362007440997-8.06200744099725
4997.693.71605252406883.88394747593118
5094.299.3988125570089-5.19881255700886
51100.292.80939692861717.39060307138288
52106.7103.3434524808473.35654751915295
5395.7111.902658308646-16.2026583086458
5494.690.96250157777523.63749842222484
5594.792.09406776502952.60593223497051
5696.293.79277918337822.40722081662177
5796.396.7695832822628-0.469583282262832
58103.396.58149898553986.71850101446017
59106.8107.703227149406-0.903227149406121
60113.7110.649107000873.05089299913047
61117.4119.420797065721-2.02079706572084
62123.6121.8810597848431.71894021515669
63137.6129.135611132178.46438886783017
64147.4148.328422729781-0.92842272978109
65137.2157.558845363479-20.3588453634793
66133.8134.868912543964-1.06891254396422
67136.7130.8131461866055.88685381339502
68127.3137.324667730921-10.0246677309213
69128.7121.7746418202296.9253581797706
70127127.423274631773-0.423274631772657
71133.7125.4636001944138.23639980558657
72132137.216542952699-5.21654295269872
73135.1132.3162499171122.78375008288759
74142.6137.1240506740235.47594932597653
75149.3147.9834867315911.31651326840893
76143.5155.491153472256-11.9911534722563
77131.4142.334709694475-10.9347096944751
78114.7123.526382820011-8.82638282001068
79122.3101.41149182334320.8885081766571
80133.4121.8263670860811.5736329139202
81134.6140.026666488712-5.42666648871193
82130.9137.897464922128-6.99746492212844
83127.9129.904595399131-2.00459539913106
84128125.6747976665762.32520233342449
85133.3127.201284307536.09871569247051
86136.3136.2427808376280.0572191623715526
87129.5139.277884178768-9.7778841787684
88124.6126.479257324964-1.87925732496409
89125.5120.4263531538135.07364684618739
90126.2124.438980963861.76101903613976
91133.3126.2193472156097.08065278439111
92137137.663251598025-0.663251598025397
93137.8140.956353871073-3.15635387107307
94133.5139.819964694748-6.31996469474794
95129.9131.642734279672-1.74273427967202
96133.3126.9735855294976.32641447050295

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 77.1 & 72.7 & 4.39999999999999 \tabularnewline
4 & 86.1 & 76.7993527100731 & 9.30064728992694 \tabularnewline
5 & 86.8 & 91.5051998617771 & -4.70519986177713 \tabularnewline
6 & 86.3 & 89.3186103167036 & -3.01861031670362 \tabularnewline
7 & 91.5 & 86.9667253305562 & 4.53327466944376 \tabularnewline
8 & 90.7 & 94.9478406179355 & -4.24784061793547 \tabularnewline
9 & 78.2 & 91.541836053394 & -13.341836053394 \tabularnewline
10 & 73 & 70.8567630288305 & 2.14323697116953 \tabularnewline
11 & 73.7 & 66.9716158757521 & 6.7283841242479 \tabularnewline
12 & 77.3 & 71.7994072212524 & 5.50059277874763 \tabularnewline
13 & 67.5 & 78.7739617722343 & -11.2739617722343 \tabularnewline
14 & 72.7 & 62.0575073942478 & 10.6424926057522 \tabularnewline
15 & 76.6 & 73.7865622254455 & 2.81343777455453 \tabularnewline
16 & 82.4 & 79.4125760621195 & 2.98742393788054 \tabularnewline
17 & 82.3 & 87.0453285400411 & -4.74532854004107 \tabularnewline
18 & 86.3 & 84.034120482144 & 2.26587951785596 \tabularnewline
19 & 93 & 89.4242132133312 & 3.5757867866688 \tabularnewline
20 & 88.8 & 98.3179199754307 & -9.51791997543071 \tabularnewline
21 & 96.9 & 88.278778366354 & 8.62122163364597 \tabularnewline
22 & 103.9 & 101.6678051802 & 2.23219481979989 \tabularnewline
23 & 115.7 & 110.037232711163 & 5.66276728883673 \tabularnewline
24 & 112.8 & 125.31127958108 & -12.5112795810802 \tabularnewline
25 & 114.7 & 114.735744025701 & -0.0357440257005095 \tabularnewline
26 & 118 & 116.6138154501 & 1.38618454990029 \tabularnewline
27 & 129.3 & 120.764224773153 & 8.53577522684695 \tabularnewline
28 & 137 & 137.300831134781 & -0.30083113478122 \tabularnewline
29 & 156 & 144.816274466839 & 11.1837255331611 \tabularnewline
30 & 166.2 & 170.677369881987 & -4.47736988198704 \tabularnewline
31 & 167.8 & 178.130551580864 & -10.330551580864 \tabularnewline
32 & 144.3 & 173.392869215783 & -29.0928692157834 \tabularnewline
33 & 126 & 132.044706633641 & -6.04470663364114 \tabularnewline
34 & 90.4 & 110.03634408066 & -19.6363440806603 \tabularnewline
35 & 67.5 & 62.38965803292 & 5.11034196708004 \tabularnewline
36 & 52.4 & 42.6247979052467 & 9.77520209475332 \tabularnewline
37 & 54.6 & 33.521779329334 & 21.078220670666 \tabularnewline
38 & 52.9 & 48.6530411681704 & 4.24695883182957 \tabularnewline
39 & 59.1 & 49.5585047664131 & 9.54149523358688 \tabularnewline
40 & 63.3 & 61.6121095429886 & 1.68789045701143 \tabularnewline
41 & 73.8 & 66.8476121974068 & 6.95238780259319 \tabularnewline
42 & 87.6 & 81.6128273920452 & 5.98717260795482 \tabularnewline
43 & 81.8 & 99.0858934386265 & -17.2858934386265 \tabularnewline
44 & 90.7 & 82.6811835978105 & 8.01881640218953 \tabularnewline
45 & 86.3 & 96.5006412766352 & -10.2006412766352 \tabularnewline
46 & 93.6 & 85.8426574869606 & 7.75734251303943 \tabularnewline
47 & 98 & 97.9017037450374 & 0.0982962549626336 \tabularnewline
48 & 94.3 & 102.362007440997 & -8.06200744099725 \tabularnewline
49 & 97.6 & 93.7160525240688 & 3.88394747593118 \tabularnewline
50 & 94.2 & 99.3988125570089 & -5.19881255700886 \tabularnewline
51 & 100.2 & 92.8093969286171 & 7.39060307138288 \tabularnewline
52 & 106.7 & 103.343452480847 & 3.35654751915295 \tabularnewline
53 & 95.7 & 111.902658308646 & -16.2026583086458 \tabularnewline
54 & 94.6 & 90.9625015777752 & 3.63749842222484 \tabularnewline
55 & 94.7 & 92.0940677650295 & 2.60593223497051 \tabularnewline
56 & 96.2 & 93.7927791833782 & 2.40722081662177 \tabularnewline
57 & 96.3 & 96.7695832822628 & -0.469583282262832 \tabularnewline
58 & 103.3 & 96.5814989855398 & 6.71850101446017 \tabularnewline
59 & 106.8 & 107.703227149406 & -0.903227149406121 \tabularnewline
60 & 113.7 & 110.64910700087 & 3.05089299913047 \tabularnewline
61 & 117.4 & 119.420797065721 & -2.02079706572084 \tabularnewline
62 & 123.6 & 121.881059784843 & 1.71894021515669 \tabularnewline
63 & 137.6 & 129.13561113217 & 8.46438886783017 \tabularnewline
64 & 147.4 & 148.328422729781 & -0.92842272978109 \tabularnewline
65 & 137.2 & 157.558845363479 & -20.3588453634793 \tabularnewline
66 & 133.8 & 134.868912543964 & -1.06891254396422 \tabularnewline
67 & 136.7 & 130.813146186605 & 5.88685381339502 \tabularnewline
68 & 127.3 & 137.324667730921 & -10.0246677309213 \tabularnewline
69 & 128.7 & 121.774641820229 & 6.9253581797706 \tabularnewline
70 & 127 & 127.423274631773 & -0.423274631772657 \tabularnewline
71 & 133.7 & 125.463600194413 & 8.23639980558657 \tabularnewline
72 & 132 & 137.216542952699 & -5.21654295269872 \tabularnewline
73 & 135.1 & 132.316249917112 & 2.78375008288759 \tabularnewline
74 & 142.6 & 137.124050674023 & 5.47594932597653 \tabularnewline
75 & 149.3 & 147.983486731591 & 1.31651326840893 \tabularnewline
76 & 143.5 & 155.491153472256 & -11.9911534722563 \tabularnewline
77 & 131.4 & 142.334709694475 & -10.9347096944751 \tabularnewline
78 & 114.7 & 123.526382820011 & -8.82638282001068 \tabularnewline
79 & 122.3 & 101.411491823343 & 20.8885081766571 \tabularnewline
80 & 133.4 & 121.82636708608 & 11.5736329139202 \tabularnewline
81 & 134.6 & 140.026666488712 & -5.42666648871193 \tabularnewline
82 & 130.9 & 137.897464922128 & -6.99746492212844 \tabularnewline
83 & 127.9 & 129.904595399131 & -2.00459539913106 \tabularnewline
84 & 128 & 125.674797666576 & 2.32520233342449 \tabularnewline
85 & 133.3 & 127.20128430753 & 6.09871569247051 \tabularnewline
86 & 136.3 & 136.242780837628 & 0.0572191623715526 \tabularnewline
87 & 129.5 & 139.277884178768 & -9.7778841787684 \tabularnewline
88 & 124.6 & 126.479257324964 & -1.87925732496409 \tabularnewline
89 & 125.5 & 120.426353153813 & 5.07364684618739 \tabularnewline
90 & 126.2 & 124.43898096386 & 1.76101903613976 \tabularnewline
91 & 133.3 & 126.219347215609 & 7.08065278439111 \tabularnewline
92 & 137 & 137.663251598025 & -0.663251598025397 \tabularnewline
93 & 137.8 & 140.956353871073 & -3.15635387107307 \tabularnewline
94 & 133.5 & 139.819964694748 & -6.31996469474794 \tabularnewline
95 & 129.9 & 131.642734279672 & -1.74273427967202 \tabularnewline
96 & 133.3 & 126.973585529497 & 6.32641447050295 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278466&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]77.1[/C][C]72.7[/C][C]4.39999999999999[/C][/ROW]
[ROW][C]4[/C][C]86.1[/C][C]76.7993527100731[/C][C]9.30064728992694[/C][/ROW]
[ROW][C]5[/C][C]86.8[/C][C]91.5051998617771[/C][C]-4.70519986177713[/C][/ROW]
[ROW][C]6[/C][C]86.3[/C][C]89.3186103167036[/C][C]-3.01861031670362[/C][/ROW]
[ROW][C]7[/C][C]91.5[/C][C]86.9667253305562[/C][C]4.53327466944376[/C][/ROW]
[ROW][C]8[/C][C]90.7[/C][C]94.9478406179355[/C][C]-4.24784061793547[/C][/ROW]
[ROW][C]9[/C][C]78.2[/C][C]91.541836053394[/C][C]-13.341836053394[/C][/ROW]
[ROW][C]10[/C][C]73[/C][C]70.8567630288305[/C][C]2.14323697116953[/C][/ROW]
[ROW][C]11[/C][C]73.7[/C][C]66.9716158757521[/C][C]6.7283841242479[/C][/ROW]
[ROW][C]12[/C][C]77.3[/C][C]71.7994072212524[/C][C]5.50059277874763[/C][/ROW]
[ROW][C]13[/C][C]67.5[/C][C]78.7739617722343[/C][C]-11.2739617722343[/C][/ROW]
[ROW][C]14[/C][C]72.7[/C][C]62.0575073942478[/C][C]10.6424926057522[/C][/ROW]
[ROW][C]15[/C][C]76.6[/C][C]73.7865622254455[/C][C]2.81343777455453[/C][/ROW]
[ROW][C]16[/C][C]82.4[/C][C]79.4125760621195[/C][C]2.98742393788054[/C][/ROW]
[ROW][C]17[/C][C]82.3[/C][C]87.0453285400411[/C][C]-4.74532854004107[/C][/ROW]
[ROW][C]18[/C][C]86.3[/C][C]84.034120482144[/C][C]2.26587951785596[/C][/ROW]
[ROW][C]19[/C][C]93[/C][C]89.4242132133312[/C][C]3.5757867866688[/C][/ROW]
[ROW][C]20[/C][C]88.8[/C][C]98.3179199754307[/C][C]-9.51791997543071[/C][/ROW]
[ROW][C]21[/C][C]96.9[/C][C]88.278778366354[/C][C]8.62122163364597[/C][/ROW]
[ROW][C]22[/C][C]103.9[/C][C]101.6678051802[/C][C]2.23219481979989[/C][/ROW]
[ROW][C]23[/C][C]115.7[/C][C]110.037232711163[/C][C]5.66276728883673[/C][/ROW]
[ROW][C]24[/C][C]112.8[/C][C]125.31127958108[/C][C]-12.5112795810802[/C][/ROW]
[ROW][C]25[/C][C]114.7[/C][C]114.735744025701[/C][C]-0.0357440257005095[/C][/ROW]
[ROW][C]26[/C][C]118[/C][C]116.6138154501[/C][C]1.38618454990029[/C][/ROW]
[ROW][C]27[/C][C]129.3[/C][C]120.764224773153[/C][C]8.53577522684695[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]137.300831134781[/C][C]-0.30083113478122[/C][/ROW]
[ROW][C]29[/C][C]156[/C][C]144.816274466839[/C][C]11.1837255331611[/C][/ROW]
[ROW][C]30[/C][C]166.2[/C][C]170.677369881987[/C][C]-4.47736988198704[/C][/ROW]
[ROW][C]31[/C][C]167.8[/C][C]178.130551580864[/C][C]-10.330551580864[/C][/ROW]
[ROW][C]32[/C][C]144.3[/C][C]173.392869215783[/C][C]-29.0928692157834[/C][/ROW]
[ROW][C]33[/C][C]126[/C][C]132.044706633641[/C][C]-6.04470663364114[/C][/ROW]
[ROW][C]34[/C][C]90.4[/C][C]110.03634408066[/C][C]-19.6363440806603[/C][/ROW]
[ROW][C]35[/C][C]67.5[/C][C]62.38965803292[/C][C]5.11034196708004[/C][/ROW]
[ROW][C]36[/C][C]52.4[/C][C]42.6247979052467[/C][C]9.77520209475332[/C][/ROW]
[ROW][C]37[/C][C]54.6[/C][C]33.521779329334[/C][C]21.078220670666[/C][/ROW]
[ROW][C]38[/C][C]52.9[/C][C]48.6530411681704[/C][C]4.24695883182957[/C][/ROW]
[ROW][C]39[/C][C]59.1[/C][C]49.5585047664131[/C][C]9.54149523358688[/C][/ROW]
[ROW][C]40[/C][C]63.3[/C][C]61.6121095429886[/C][C]1.68789045701143[/C][/ROW]
[ROW][C]41[/C][C]73.8[/C][C]66.8476121974068[/C][C]6.95238780259319[/C][/ROW]
[ROW][C]42[/C][C]87.6[/C][C]81.6128273920452[/C][C]5.98717260795482[/C][/ROW]
[ROW][C]43[/C][C]81.8[/C][C]99.0858934386265[/C][C]-17.2858934386265[/C][/ROW]
[ROW][C]44[/C][C]90.7[/C][C]82.6811835978105[/C][C]8.01881640218953[/C][/ROW]
[ROW][C]45[/C][C]86.3[/C][C]96.5006412766352[/C][C]-10.2006412766352[/C][/ROW]
[ROW][C]46[/C][C]93.6[/C][C]85.8426574869606[/C][C]7.75734251303943[/C][/ROW]
[ROW][C]47[/C][C]98[/C][C]97.9017037450374[/C][C]0.0982962549626336[/C][/ROW]
[ROW][C]48[/C][C]94.3[/C][C]102.362007440997[/C][C]-8.06200744099725[/C][/ROW]
[ROW][C]49[/C][C]97.6[/C][C]93.7160525240688[/C][C]3.88394747593118[/C][/ROW]
[ROW][C]50[/C][C]94.2[/C][C]99.3988125570089[/C][C]-5.19881255700886[/C][/ROW]
[ROW][C]51[/C][C]100.2[/C][C]92.8093969286171[/C][C]7.39060307138288[/C][/ROW]
[ROW][C]52[/C][C]106.7[/C][C]103.343452480847[/C][C]3.35654751915295[/C][/ROW]
[ROW][C]53[/C][C]95.7[/C][C]111.902658308646[/C][C]-16.2026583086458[/C][/ROW]
[ROW][C]54[/C][C]94.6[/C][C]90.9625015777752[/C][C]3.63749842222484[/C][/ROW]
[ROW][C]55[/C][C]94.7[/C][C]92.0940677650295[/C][C]2.60593223497051[/C][/ROW]
[ROW][C]56[/C][C]96.2[/C][C]93.7927791833782[/C][C]2.40722081662177[/C][/ROW]
[ROW][C]57[/C][C]96.3[/C][C]96.7695832822628[/C][C]-0.469583282262832[/C][/ROW]
[ROW][C]58[/C][C]103.3[/C][C]96.5814989855398[/C][C]6.71850101446017[/C][/ROW]
[ROW][C]59[/C][C]106.8[/C][C]107.703227149406[/C][C]-0.903227149406121[/C][/ROW]
[ROW][C]60[/C][C]113.7[/C][C]110.64910700087[/C][C]3.05089299913047[/C][/ROW]
[ROW][C]61[/C][C]117.4[/C][C]119.420797065721[/C][C]-2.02079706572084[/C][/ROW]
[ROW][C]62[/C][C]123.6[/C][C]121.881059784843[/C][C]1.71894021515669[/C][/ROW]
[ROW][C]63[/C][C]137.6[/C][C]129.13561113217[/C][C]8.46438886783017[/C][/ROW]
[ROW][C]64[/C][C]147.4[/C][C]148.328422729781[/C][C]-0.92842272978109[/C][/ROW]
[ROW][C]65[/C][C]137.2[/C][C]157.558845363479[/C][C]-20.3588453634793[/C][/ROW]
[ROW][C]66[/C][C]133.8[/C][C]134.868912543964[/C][C]-1.06891254396422[/C][/ROW]
[ROW][C]67[/C][C]136.7[/C][C]130.813146186605[/C][C]5.88685381339502[/C][/ROW]
[ROW][C]68[/C][C]127.3[/C][C]137.324667730921[/C][C]-10.0246677309213[/C][/ROW]
[ROW][C]69[/C][C]128.7[/C][C]121.774641820229[/C][C]6.9253581797706[/C][/ROW]
[ROW][C]70[/C][C]127[/C][C]127.423274631773[/C][C]-0.423274631772657[/C][/ROW]
[ROW][C]71[/C][C]133.7[/C][C]125.463600194413[/C][C]8.23639980558657[/C][/ROW]
[ROW][C]72[/C][C]132[/C][C]137.216542952699[/C][C]-5.21654295269872[/C][/ROW]
[ROW][C]73[/C][C]135.1[/C][C]132.316249917112[/C][C]2.78375008288759[/C][/ROW]
[ROW][C]74[/C][C]142.6[/C][C]137.124050674023[/C][C]5.47594932597653[/C][/ROW]
[ROW][C]75[/C][C]149.3[/C][C]147.983486731591[/C][C]1.31651326840893[/C][/ROW]
[ROW][C]76[/C][C]143.5[/C][C]155.491153472256[/C][C]-11.9911534722563[/C][/ROW]
[ROW][C]77[/C][C]131.4[/C][C]142.334709694475[/C][C]-10.9347096944751[/C][/ROW]
[ROW][C]78[/C][C]114.7[/C][C]123.526382820011[/C][C]-8.82638282001068[/C][/ROW]
[ROW][C]79[/C][C]122.3[/C][C]101.411491823343[/C][C]20.8885081766571[/C][/ROW]
[ROW][C]80[/C][C]133.4[/C][C]121.82636708608[/C][C]11.5736329139202[/C][/ROW]
[ROW][C]81[/C][C]134.6[/C][C]140.026666488712[/C][C]-5.42666648871193[/C][/ROW]
[ROW][C]82[/C][C]130.9[/C][C]137.897464922128[/C][C]-6.99746492212844[/C][/ROW]
[ROW][C]83[/C][C]127.9[/C][C]129.904595399131[/C][C]-2.00459539913106[/C][/ROW]
[ROW][C]84[/C][C]128[/C][C]125.674797666576[/C][C]2.32520233342449[/C][/ROW]
[ROW][C]85[/C][C]133.3[/C][C]127.20128430753[/C][C]6.09871569247051[/C][/ROW]
[ROW][C]86[/C][C]136.3[/C][C]136.242780837628[/C][C]0.0572191623715526[/C][/ROW]
[ROW][C]87[/C][C]129.5[/C][C]139.277884178768[/C][C]-9.7778841787684[/C][/ROW]
[ROW][C]88[/C][C]124.6[/C][C]126.479257324964[/C][C]-1.87925732496409[/C][/ROW]
[ROW][C]89[/C][C]125.5[/C][C]120.426353153813[/C][C]5.07364684618739[/C][/ROW]
[ROW][C]90[/C][C]126.2[/C][C]124.43898096386[/C][C]1.76101903613976[/C][/ROW]
[ROW][C]91[/C][C]133.3[/C][C]126.219347215609[/C][C]7.08065278439111[/C][/ROW]
[ROW][C]92[/C][C]137[/C][C]137.663251598025[/C][C]-0.663251598025397[/C][/ROW]
[ROW][C]93[/C][C]137.8[/C][C]140.956353871073[/C][C]-3.15635387107307[/C][/ROW]
[ROW][C]94[/C][C]133.5[/C][C]139.819964694748[/C][C]-6.31996469474794[/C][/ROW]
[ROW][C]95[/C][C]129.9[/C][C]131.642734279672[/C][C]-1.74273427967202[/C][/ROW]
[ROW][C]96[/C][C]133.3[/C][C]126.973585529497[/C][C]6.32641447050295[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278466&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278466&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
377.172.74.39999999999999
486.176.79935271007319.30064728992694
586.891.5051998617771-4.70519986177713
686.389.3186103167036-3.01861031670362
791.586.96672533055624.53327466944376
890.794.9478406179355-4.24784061793547
978.291.541836053394-13.341836053394
107370.85676302883052.14323697116953
1173.766.97161587575216.7283841242479
1277.371.79940722125245.50059277874763
1367.578.7739617722343-11.2739617722343
1472.762.057507394247810.6424926057522
1576.673.78656222544552.81343777455453
1682.479.41257606211952.98742393788054
1782.387.0453285400411-4.74532854004107
1886.384.0341204821442.26587951785596
199389.42421321333123.5757867866688
2088.898.3179199754307-9.51791997543071
2196.988.2787783663548.62122163364597
22103.9101.66780518022.23219481979989
23115.7110.0372327111635.66276728883673
24112.8125.31127958108-12.5112795810802
25114.7114.735744025701-0.0357440257005095
26118116.61381545011.38618454990029
27129.3120.7642247731538.53577522684695
28137137.300831134781-0.30083113478122
29156144.81627446683911.1837255331611
30166.2170.677369881987-4.47736988198704
31167.8178.130551580864-10.330551580864
32144.3173.392869215783-29.0928692157834
33126132.044706633641-6.04470663364114
3490.4110.03634408066-19.6363440806603
3567.562.389658032925.11034196708004
3652.442.62479790524679.77520209475332
3754.633.52177932933421.078220670666
3852.948.65304116817044.24695883182957
3959.149.55850476641319.54149523358688
4063.361.61210954298861.68789045701143
4173.866.84761219740686.95238780259319
4287.681.61282739204525.98717260795482
4381.899.0858934386265-17.2858934386265
4490.782.68118359781058.01881640218953
4586.396.5006412766352-10.2006412766352
4693.685.84265748696067.75734251303943
479897.90170374503740.0982962549626336
4894.3102.362007440997-8.06200744099725
4997.693.71605252406883.88394747593118
5094.299.3988125570089-5.19881255700886
51100.292.80939692861717.39060307138288
52106.7103.3434524808473.35654751915295
5395.7111.902658308646-16.2026583086458
5494.690.96250157777523.63749842222484
5594.792.09406776502952.60593223497051
5696.293.79277918337822.40722081662177
5796.396.7695832822628-0.469583282262832
58103.396.58149898553986.71850101446017
59106.8107.703227149406-0.903227149406121
60113.7110.649107000873.05089299913047
61117.4119.420797065721-2.02079706572084
62123.6121.8810597848431.71894021515669
63137.6129.135611132178.46438886783017
64147.4148.328422729781-0.92842272978109
65137.2157.558845363479-20.3588453634793
66133.8134.868912543964-1.06891254396422
67136.7130.8131461866055.88685381339502
68127.3137.324667730921-10.0246677309213
69128.7121.7746418202296.9253581797706
70127127.423274631773-0.423274631772657
71133.7125.4636001944138.23639980558657
72132137.216542952699-5.21654295269872
73135.1132.3162499171122.78375008288759
74142.6137.1240506740235.47594932597653
75149.3147.9834867315911.31651326840893
76143.5155.491153472256-11.9911534722563
77131.4142.334709694475-10.9347096944751
78114.7123.526382820011-8.82638282001068
79122.3101.41149182334320.8885081766571
80133.4121.8263670860811.5736329139202
81134.6140.026666488712-5.42666648871193
82130.9137.897464922128-6.99746492212844
83127.9129.904595399131-2.00459539913106
84128125.6747976665762.32520233342449
85133.3127.201284307536.09871569247051
86136.3136.2427808376280.0572191623715526
87129.5139.277884178768-9.7778841787684
88124.6126.479257324964-1.87925732496409
89125.5120.4263531538135.07364684618739
90126.2124.438980963861.76101903613976
91133.3126.2193472156097.08065278439111
92137137.663251598025-0.663251598025397
93137.8140.956353871073-3.15635387107307
94133.5139.819964694748-6.31996469474794
95129.9131.642734279672-1.74273427967202
96133.3126.9735855294976.32641447050295







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97134.254772812678117.728473283179150.781072342177
98135.209545625357103.838521464499166.580569786214
99136.16431843803587.8046812672723184.523955608798
100137.11909125071369.7229089233773204.515273578049
101138.07386406339249.753421486733226.39430664005
102139.0286368760728.0376154995617250.019658252578
103139.9834096887484.69353236937485275.273287008122
104140.938182501427-20.1801577910719302.056522793925
105141.892955314105-46.499984075236330.285894703446
106142.847728126783-74.1943824636073359.889838717174
107143.802500939462-103.201225382504390.806227261427
108144.75727375214-133.465973872806422.980521377085

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 134.254772812678 & 117.728473283179 & 150.781072342177 \tabularnewline
98 & 135.209545625357 & 103.838521464499 & 166.580569786214 \tabularnewline
99 & 136.164318438035 & 87.8046812672723 & 184.523955608798 \tabularnewline
100 & 137.119091250713 & 69.7229089233773 & 204.515273578049 \tabularnewline
101 & 138.073864063392 & 49.753421486733 & 226.39430664005 \tabularnewline
102 & 139.02863687607 & 28.0376154995617 & 250.019658252578 \tabularnewline
103 & 139.983409688748 & 4.69353236937485 & 275.273287008122 \tabularnewline
104 & 140.938182501427 & -20.1801577910719 & 302.056522793925 \tabularnewline
105 & 141.892955314105 & -46.499984075236 & 330.285894703446 \tabularnewline
106 & 142.847728126783 & -74.1943824636073 & 359.889838717174 \tabularnewline
107 & 143.802500939462 & -103.201225382504 & 390.806227261427 \tabularnewline
108 & 144.75727375214 & -133.465973872806 & 422.980521377085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278466&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]97[/C][C]134.254772812678[/C][C]117.728473283179[/C][C]150.781072342177[/C][/ROW]
[ROW][C]98[/C][C]135.209545625357[/C][C]103.838521464499[/C][C]166.580569786214[/C][/ROW]
[ROW][C]99[/C][C]136.164318438035[/C][C]87.8046812672723[/C][C]184.523955608798[/C][/ROW]
[ROW][C]100[/C][C]137.119091250713[/C][C]69.7229089233773[/C][C]204.515273578049[/C][/ROW]
[ROW][C]101[/C][C]138.073864063392[/C][C]49.753421486733[/C][C]226.39430664005[/C][/ROW]
[ROW][C]102[/C][C]139.02863687607[/C][C]28.0376154995617[/C][C]250.019658252578[/C][/ROW]
[ROW][C]103[/C][C]139.983409688748[/C][C]4.69353236937485[/C][C]275.273287008122[/C][/ROW]
[ROW][C]104[/C][C]140.938182501427[/C][C]-20.1801577910719[/C][C]302.056522793925[/C][/ROW]
[ROW][C]105[/C][C]141.892955314105[/C][C]-46.499984075236[/C][C]330.285894703446[/C][/ROW]
[ROW][C]106[/C][C]142.847728126783[/C][C]-74.1943824636073[/C][C]359.889838717174[/C][/ROW]
[ROW][C]107[/C][C]143.802500939462[/C][C]-103.201225382504[/C][C]390.806227261427[/C][/ROW]
[ROW][C]108[/C][C]144.75727375214[/C][C]-133.465973872806[/C][C]422.980521377085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278466&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278466&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
97134.254772812678117.728473283179150.781072342177
98135.209545625357103.838521464499166.580569786214
99136.16431843803587.8046812672723184.523955608798
100137.11909125071369.7229089233773204.515273578049
101138.07386406339249.753421486733226.39430664005
102139.0286368760728.0376154995617250.019658252578
103139.9834096887484.69353236937485275.273287008122
104140.938182501427-20.1801577910719302.056522793925
105141.892955314105-46.499984075236330.285894703446
106142.847728126783-74.1943824636073359.889838717174
107143.802500939462-103.201225382504390.806227261427
108144.75727375214-133.465973872806422.980521377085



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')