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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 11 Dec 2015 14:55:32 +0000
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/Dec/11/t1449846197z9wgvu1yn5yam3h.htm/, Retrieved Thu, 31 Oct 2024 22:58:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285975, Retrieved Thu, 31 Oct 2024 22:58:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Decomposition by Loess] [HPC Retail Sales] [2008-03-06 11:35:25] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [] [2015-12-11 14:55:32] [09da0ac04f7f2be6cb42b66305b85db6] [Current]
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Dataseries X:
87.29
88.19
89.1
89.1
103.65
127.75
125.47
125.47
109.11
100.01
95.01
85.01
86.83
86.83
86.83
86.83
100.47
111.38
105.47
102.74
105.01
96.38
94.1
86.83
92.74
93.2
95.47
96.38
99.56
120.47
123.2
114.11
120.93
102.74
101.83
95.47
100.01
100.01
98.2
100.01
103.65
114.56
134.11
131.84
113.65
107.29
102.29
94.56
97.29
98.2
95.47
100.47
116.38
117.29
140.93
120.02
111.38
108.65
105.92
99.1
101.83
102.74
102.74
105.47
108.65
139.57
110.47
118.65
120.02
109.11
108.2
101.38
106.38
108.65
107.74
105.92
129.56
139.11
125.93
123.65
118.65
110.47
110.02
100.47
104.1
106.6
105.5
107.5
117.9
136.3
156.8
135.8
130
117.5
115.8
105.5
111.6
113.2
113.1
112.5
120
147.6
149.9
131.2
134.6
122.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285975&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285975&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.25971692091122
beta0.0432717723966238
gamma0.184165056033786

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.25971692091122 \tabularnewline
beta & 0.0432717723966238 \tabularnewline
gamma & 0.184165056033786 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285975&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]0.25971692091122[/C][/ROW]
[ROW][C]beta[/C][C]0.0432717723966238[/C][/ROW]
[ROW][C]gamma[/C][C]0.184165056033786[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285975&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
alpha0.25971692091122
beta0.0432717723966238
gamma0.184165056033786







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1386.8390.0810630341881-3.25106303418806
1486.8390.2482470921818-3.41824709218176
1586.8389.6710949540142-2.84109495401415
1686.8388.4160762645622-1.58607626456222
17100.47100.97626552044-0.506265520439712
18111.38110.8541269443730.525873055627343
19105.47117.878878865692-12.4088788656924
20102.74113.735634091777-10.9956340917772
21105.0193.551276105195511.4587238948045
2296.3886.62538935686499.75461064313509
2394.183.504458556918110.5955414430819
2486.8376.308508769721410.5214912302786
2592.7481.289173749617911.4508262503821
2693.285.50533026033327.69466973966676
2795.4788.27140376790047.19859623209962
2896.3890.2861224894456.09387751055502
2999.56105.565609054364-6.00560905436355
30120.47114.6715780344485.79842196555211
31123.2121.8771694377171.32283056228268
32114.11122.22219759343-8.11219759343035
33120.93106.60966264945814.3203373505419
34102.74100.988463464721.75153653528002
35101.8396.60751192264585.22248807735421
3695.4788.64947442494676.82052557505334
37100.0193.39752398907956.61247601092049
38100.0196.3924986013413.61750139865903
3998.298.5337221856774-0.333722185677416
40100.0198.85859954709751.15140045290254
41103.65111.566361084767-7.91636108476681
42114.56122.12539024285-7.56539024285011
43134.11125.4398297628898.67017023711134
44131.84126.6791738448555.16082615514452
45113.65117.993764054622-4.34376405462234
46107.29106.023441638561.26655836144003
47102.29102.1961103960520.093889603947531
4894.5693.2726867539361.28731324606399
4997.2996.64184902221680.648150977783246
5098.297.69898613036640.501013869633596
5195.4798.4766099190823-3.00660991908232
52100.4798.26421916524842.20578083475162
53116.38109.9758769359686.40412306403189
54117.29124.429269491485-7.13926949148451
55140.93130.19987405756610.7301259424335
56120.02131.650961155676-11.6309611556757
57111.38117.275107183455-5.89510718345549
58108.65105.6157878398483.03421216015201
59105.92102.0565707708693.8634292291313
6099.194.28612805385184.81387194614823
61101.8398.53495363634243.29504636365759
62102.74100.3401174041732.39988259582691
63102.74101.2346834254951.50531657450546
64105.47103.0574339667132.41256603328729
65108.65115.550189358249-6.90018935824945
66139.57124.70729298025414.8627070197462
67110.47138.881156197187-28.4111561971868
68118.65126.930883581475-8.28088358147457
69120.02114.0576206392085.96237936079166
70109.11106.6790484865192.43095151348081
71108.2103.0532104554565.14678954454412
72101.3895.73708430567275.64291569432726
73106.3899.99490398746596.38509601253405
74108.65102.5160370759526.13396292404786
75107.74104.335884707543.40411529246003
76105.92106.874251858226-0.954251858226144
77129.56117.28387949272712.2761205072734
78139.11134.6648747936854.44512520631534
79125.93140.392778742896-14.4627787428959
80123.65135.1257132553-11.4757132553004
81118.65123.644770466557-4.99477046655676
82110.47113.096072041934-2.62607204193448
83110.02108.6273539182891.39264608171068
84100.47100.4619142633920.00808573660756906
85104.1103.3521934132830.747806586716806
86106.6104.3063703632422.29362963675787
87105.5104.6448687763510.855131223649167
88107.5105.7866023920191.7133976079806
89117.9118.582372678701-0.682372678701356
90136.3131.2741178119275.02588218807261
91156.8134.32550843741822.4744915625818
92135.8139.224482343237-3.42448234323712
93130130.974204013202-0.974204013201557
94117.5122.093883212127-4.59388321212668
95115.8117.941098881699-2.14109888169894
96105.5108.908527785636-3.40852778563564
97111.6111.2133115390350.386688460965232
98113.2112.4813979134390.718602086561134
99113.1112.3939668230220.70603317697848
100112.5113.791561092966-1.29156109296579
101120125.62406900633-5.62406900633006
102147.6137.898867808229.70113219177986
103149.9144.6841508924925.21584910750806
104131.2141.516693190135-10.3166931901345
105134.6131.6798381914992.92016180850106
106122.2123.230620429538-1.03062042953846

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 86.83 & 90.0810630341881 & -3.25106303418806 \tabularnewline
14 & 86.83 & 90.2482470921818 & -3.41824709218176 \tabularnewline
15 & 86.83 & 89.6710949540142 & -2.84109495401415 \tabularnewline
16 & 86.83 & 88.4160762645622 & -1.58607626456222 \tabularnewline
17 & 100.47 & 100.97626552044 & -0.506265520439712 \tabularnewline
18 & 111.38 & 110.854126944373 & 0.525873055627343 \tabularnewline
19 & 105.47 & 117.878878865692 & -12.4088788656924 \tabularnewline
20 & 102.74 & 113.735634091777 & -10.9956340917772 \tabularnewline
21 & 105.01 & 93.5512761051955 & 11.4587238948045 \tabularnewline
22 & 96.38 & 86.6253893568649 & 9.75461064313509 \tabularnewline
23 & 94.1 & 83.5044585569181 & 10.5955414430819 \tabularnewline
24 & 86.83 & 76.3085087697214 & 10.5214912302786 \tabularnewline
25 & 92.74 & 81.2891737496179 & 11.4508262503821 \tabularnewline
26 & 93.2 & 85.5053302603332 & 7.69466973966676 \tabularnewline
27 & 95.47 & 88.2714037679004 & 7.19859623209962 \tabularnewline
28 & 96.38 & 90.286122489445 & 6.09387751055502 \tabularnewline
29 & 99.56 & 105.565609054364 & -6.00560905436355 \tabularnewline
30 & 120.47 & 114.671578034448 & 5.79842196555211 \tabularnewline
31 & 123.2 & 121.877169437717 & 1.32283056228268 \tabularnewline
32 & 114.11 & 122.22219759343 & -8.11219759343035 \tabularnewline
33 & 120.93 & 106.609662649458 & 14.3203373505419 \tabularnewline
34 & 102.74 & 100.98846346472 & 1.75153653528002 \tabularnewline
35 & 101.83 & 96.6075119226458 & 5.22248807735421 \tabularnewline
36 & 95.47 & 88.6494744249467 & 6.82052557505334 \tabularnewline
37 & 100.01 & 93.3975239890795 & 6.61247601092049 \tabularnewline
38 & 100.01 & 96.392498601341 & 3.61750139865903 \tabularnewline
39 & 98.2 & 98.5337221856774 & -0.333722185677416 \tabularnewline
40 & 100.01 & 98.8585995470975 & 1.15140045290254 \tabularnewline
41 & 103.65 & 111.566361084767 & -7.91636108476681 \tabularnewline
42 & 114.56 & 122.12539024285 & -7.56539024285011 \tabularnewline
43 & 134.11 & 125.439829762889 & 8.67017023711134 \tabularnewline
44 & 131.84 & 126.679173844855 & 5.16082615514452 \tabularnewline
45 & 113.65 & 117.993764054622 & -4.34376405462234 \tabularnewline
46 & 107.29 & 106.02344163856 & 1.26655836144003 \tabularnewline
47 & 102.29 & 102.196110396052 & 0.093889603947531 \tabularnewline
48 & 94.56 & 93.272686753936 & 1.28731324606399 \tabularnewline
49 & 97.29 & 96.6418490222168 & 0.648150977783246 \tabularnewline
50 & 98.2 & 97.6989861303664 & 0.501013869633596 \tabularnewline
51 & 95.47 & 98.4766099190823 & -3.00660991908232 \tabularnewline
52 & 100.47 & 98.2642191652484 & 2.20578083475162 \tabularnewline
53 & 116.38 & 109.975876935968 & 6.40412306403189 \tabularnewline
54 & 117.29 & 124.429269491485 & -7.13926949148451 \tabularnewline
55 & 140.93 & 130.199874057566 & 10.7301259424335 \tabularnewline
56 & 120.02 & 131.650961155676 & -11.6309611556757 \tabularnewline
57 & 111.38 & 117.275107183455 & -5.89510718345549 \tabularnewline
58 & 108.65 & 105.615787839848 & 3.03421216015201 \tabularnewline
59 & 105.92 & 102.056570770869 & 3.8634292291313 \tabularnewline
60 & 99.1 & 94.2861280538518 & 4.81387194614823 \tabularnewline
61 & 101.83 & 98.5349536363424 & 3.29504636365759 \tabularnewline
62 & 102.74 & 100.340117404173 & 2.39988259582691 \tabularnewline
63 & 102.74 & 101.234683425495 & 1.50531657450546 \tabularnewline
64 & 105.47 & 103.057433966713 & 2.41256603328729 \tabularnewline
65 & 108.65 & 115.550189358249 & -6.90018935824945 \tabularnewline
66 & 139.57 & 124.707292980254 & 14.8627070197462 \tabularnewline
67 & 110.47 & 138.881156197187 & -28.4111561971868 \tabularnewline
68 & 118.65 & 126.930883581475 & -8.28088358147457 \tabularnewline
69 & 120.02 & 114.057620639208 & 5.96237936079166 \tabularnewline
70 & 109.11 & 106.679048486519 & 2.43095151348081 \tabularnewline
71 & 108.2 & 103.053210455456 & 5.14678954454412 \tabularnewline
72 & 101.38 & 95.7370843056727 & 5.64291569432726 \tabularnewline
73 & 106.38 & 99.9949039874659 & 6.38509601253405 \tabularnewline
74 & 108.65 & 102.516037075952 & 6.13396292404786 \tabularnewline
75 & 107.74 & 104.33588470754 & 3.40411529246003 \tabularnewline
76 & 105.92 & 106.874251858226 & -0.954251858226144 \tabularnewline
77 & 129.56 & 117.283879492727 & 12.2761205072734 \tabularnewline
78 & 139.11 & 134.664874793685 & 4.44512520631534 \tabularnewline
79 & 125.93 & 140.392778742896 & -14.4627787428959 \tabularnewline
80 & 123.65 & 135.1257132553 & -11.4757132553004 \tabularnewline
81 & 118.65 & 123.644770466557 & -4.99477046655676 \tabularnewline
82 & 110.47 & 113.096072041934 & -2.62607204193448 \tabularnewline
83 & 110.02 & 108.627353918289 & 1.39264608171068 \tabularnewline
84 & 100.47 & 100.461914263392 & 0.00808573660756906 \tabularnewline
85 & 104.1 & 103.352193413283 & 0.747806586716806 \tabularnewline
86 & 106.6 & 104.306370363242 & 2.29362963675787 \tabularnewline
87 & 105.5 & 104.644868776351 & 0.855131223649167 \tabularnewline
88 & 107.5 & 105.786602392019 & 1.7133976079806 \tabularnewline
89 & 117.9 & 118.582372678701 & -0.682372678701356 \tabularnewline
90 & 136.3 & 131.274117811927 & 5.02588218807261 \tabularnewline
91 & 156.8 & 134.325508437418 & 22.4744915625818 \tabularnewline
92 & 135.8 & 139.224482343237 & -3.42448234323712 \tabularnewline
93 & 130 & 130.974204013202 & -0.974204013201557 \tabularnewline
94 & 117.5 & 122.093883212127 & -4.59388321212668 \tabularnewline
95 & 115.8 & 117.941098881699 & -2.14109888169894 \tabularnewline
96 & 105.5 & 108.908527785636 & -3.40852778563564 \tabularnewline
97 & 111.6 & 111.213311539035 & 0.386688460965232 \tabularnewline
98 & 113.2 & 112.481397913439 & 0.718602086561134 \tabularnewline
99 & 113.1 & 112.393966823022 & 0.70603317697848 \tabularnewline
100 & 112.5 & 113.791561092966 & -1.29156109296579 \tabularnewline
101 & 120 & 125.62406900633 & -5.62406900633006 \tabularnewline
102 & 147.6 & 137.89886780822 & 9.70113219177986 \tabularnewline
103 & 149.9 & 144.684150892492 & 5.21584910750806 \tabularnewline
104 & 131.2 & 141.516693190135 & -10.3166931901345 \tabularnewline
105 & 134.6 & 131.679838191499 & 2.92016180850106 \tabularnewline
106 & 122.2 & 123.230620429538 & -1.03062042953846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285975&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]86.83[/C][C]90.0810630341881[/C][C]-3.25106303418806[/C][/ROW]
[ROW][C]14[/C][C]86.83[/C][C]90.2482470921818[/C][C]-3.41824709218176[/C][/ROW]
[ROW][C]15[/C][C]86.83[/C][C]89.6710949540142[/C][C]-2.84109495401415[/C][/ROW]
[ROW][C]16[/C][C]86.83[/C][C]88.4160762645622[/C][C]-1.58607626456222[/C][/ROW]
[ROW][C]17[/C][C]100.47[/C][C]100.97626552044[/C][C]-0.506265520439712[/C][/ROW]
[ROW][C]18[/C][C]111.38[/C][C]110.854126944373[/C][C]0.525873055627343[/C][/ROW]
[ROW][C]19[/C][C]105.47[/C][C]117.878878865692[/C][C]-12.4088788656924[/C][/ROW]
[ROW][C]20[/C][C]102.74[/C][C]113.735634091777[/C][C]-10.9956340917772[/C][/ROW]
[ROW][C]21[/C][C]105.01[/C][C]93.5512761051955[/C][C]11.4587238948045[/C][/ROW]
[ROW][C]22[/C][C]96.38[/C][C]86.6253893568649[/C][C]9.75461064313509[/C][/ROW]
[ROW][C]23[/C][C]94.1[/C][C]83.5044585569181[/C][C]10.5955414430819[/C][/ROW]
[ROW][C]24[/C][C]86.83[/C][C]76.3085087697214[/C][C]10.5214912302786[/C][/ROW]
[ROW][C]25[/C][C]92.74[/C][C]81.2891737496179[/C][C]11.4508262503821[/C][/ROW]
[ROW][C]26[/C][C]93.2[/C][C]85.5053302603332[/C][C]7.69466973966676[/C][/ROW]
[ROW][C]27[/C][C]95.47[/C][C]88.2714037679004[/C][C]7.19859623209962[/C][/ROW]
[ROW][C]28[/C][C]96.38[/C][C]90.286122489445[/C][C]6.09387751055502[/C][/ROW]
[ROW][C]29[/C][C]99.56[/C][C]105.565609054364[/C][C]-6.00560905436355[/C][/ROW]
[ROW][C]30[/C][C]120.47[/C][C]114.671578034448[/C][C]5.79842196555211[/C][/ROW]
[ROW][C]31[/C][C]123.2[/C][C]121.877169437717[/C][C]1.32283056228268[/C][/ROW]
[ROW][C]32[/C][C]114.11[/C][C]122.22219759343[/C][C]-8.11219759343035[/C][/ROW]
[ROW][C]33[/C][C]120.93[/C][C]106.609662649458[/C][C]14.3203373505419[/C][/ROW]
[ROW][C]34[/C][C]102.74[/C][C]100.98846346472[/C][C]1.75153653528002[/C][/ROW]
[ROW][C]35[/C][C]101.83[/C][C]96.6075119226458[/C][C]5.22248807735421[/C][/ROW]
[ROW][C]36[/C][C]95.47[/C][C]88.6494744249467[/C][C]6.82052557505334[/C][/ROW]
[ROW][C]37[/C][C]100.01[/C][C]93.3975239890795[/C][C]6.61247601092049[/C][/ROW]
[ROW][C]38[/C][C]100.01[/C][C]96.392498601341[/C][C]3.61750139865903[/C][/ROW]
[ROW][C]39[/C][C]98.2[/C][C]98.5337221856774[/C][C]-0.333722185677416[/C][/ROW]
[ROW][C]40[/C][C]100.01[/C][C]98.8585995470975[/C][C]1.15140045290254[/C][/ROW]
[ROW][C]41[/C][C]103.65[/C][C]111.566361084767[/C][C]-7.91636108476681[/C][/ROW]
[ROW][C]42[/C][C]114.56[/C][C]122.12539024285[/C][C]-7.56539024285011[/C][/ROW]
[ROW][C]43[/C][C]134.11[/C][C]125.439829762889[/C][C]8.67017023711134[/C][/ROW]
[ROW][C]44[/C][C]131.84[/C][C]126.679173844855[/C][C]5.16082615514452[/C][/ROW]
[ROW][C]45[/C][C]113.65[/C][C]117.993764054622[/C][C]-4.34376405462234[/C][/ROW]
[ROW][C]46[/C][C]107.29[/C][C]106.02344163856[/C][C]1.26655836144003[/C][/ROW]
[ROW][C]47[/C][C]102.29[/C][C]102.196110396052[/C][C]0.093889603947531[/C][/ROW]
[ROW][C]48[/C][C]94.56[/C][C]93.272686753936[/C][C]1.28731324606399[/C][/ROW]
[ROW][C]49[/C][C]97.29[/C][C]96.6418490222168[/C][C]0.648150977783246[/C][/ROW]
[ROW][C]50[/C][C]98.2[/C][C]97.6989861303664[/C][C]0.501013869633596[/C][/ROW]
[ROW][C]51[/C][C]95.47[/C][C]98.4766099190823[/C][C]-3.00660991908232[/C][/ROW]
[ROW][C]52[/C][C]100.47[/C][C]98.2642191652484[/C][C]2.20578083475162[/C][/ROW]
[ROW][C]53[/C][C]116.38[/C][C]109.975876935968[/C][C]6.40412306403189[/C][/ROW]
[ROW][C]54[/C][C]117.29[/C][C]124.429269491485[/C][C]-7.13926949148451[/C][/ROW]
[ROW][C]55[/C][C]140.93[/C][C]130.199874057566[/C][C]10.7301259424335[/C][/ROW]
[ROW][C]56[/C][C]120.02[/C][C]131.650961155676[/C][C]-11.6309611556757[/C][/ROW]
[ROW][C]57[/C][C]111.38[/C][C]117.275107183455[/C][C]-5.89510718345549[/C][/ROW]
[ROW][C]58[/C][C]108.65[/C][C]105.615787839848[/C][C]3.03421216015201[/C][/ROW]
[ROW][C]59[/C][C]105.92[/C][C]102.056570770869[/C][C]3.8634292291313[/C][/ROW]
[ROW][C]60[/C][C]99.1[/C][C]94.2861280538518[/C][C]4.81387194614823[/C][/ROW]
[ROW][C]61[/C][C]101.83[/C][C]98.5349536363424[/C][C]3.29504636365759[/C][/ROW]
[ROW][C]62[/C][C]102.74[/C][C]100.340117404173[/C][C]2.39988259582691[/C][/ROW]
[ROW][C]63[/C][C]102.74[/C][C]101.234683425495[/C][C]1.50531657450546[/C][/ROW]
[ROW][C]64[/C][C]105.47[/C][C]103.057433966713[/C][C]2.41256603328729[/C][/ROW]
[ROW][C]65[/C][C]108.65[/C][C]115.550189358249[/C][C]-6.90018935824945[/C][/ROW]
[ROW][C]66[/C][C]139.57[/C][C]124.707292980254[/C][C]14.8627070197462[/C][/ROW]
[ROW][C]67[/C][C]110.47[/C][C]138.881156197187[/C][C]-28.4111561971868[/C][/ROW]
[ROW][C]68[/C][C]118.65[/C][C]126.930883581475[/C][C]-8.28088358147457[/C][/ROW]
[ROW][C]69[/C][C]120.02[/C][C]114.057620639208[/C][C]5.96237936079166[/C][/ROW]
[ROW][C]70[/C][C]109.11[/C][C]106.679048486519[/C][C]2.43095151348081[/C][/ROW]
[ROW][C]71[/C][C]108.2[/C][C]103.053210455456[/C][C]5.14678954454412[/C][/ROW]
[ROW][C]72[/C][C]101.38[/C][C]95.7370843056727[/C][C]5.64291569432726[/C][/ROW]
[ROW][C]73[/C][C]106.38[/C][C]99.9949039874659[/C][C]6.38509601253405[/C][/ROW]
[ROW][C]74[/C][C]108.65[/C][C]102.516037075952[/C][C]6.13396292404786[/C][/ROW]
[ROW][C]75[/C][C]107.74[/C][C]104.33588470754[/C][C]3.40411529246003[/C][/ROW]
[ROW][C]76[/C][C]105.92[/C][C]106.874251858226[/C][C]-0.954251858226144[/C][/ROW]
[ROW][C]77[/C][C]129.56[/C][C]117.283879492727[/C][C]12.2761205072734[/C][/ROW]
[ROW][C]78[/C][C]139.11[/C][C]134.664874793685[/C][C]4.44512520631534[/C][/ROW]
[ROW][C]79[/C][C]125.93[/C][C]140.392778742896[/C][C]-14.4627787428959[/C][/ROW]
[ROW][C]80[/C][C]123.65[/C][C]135.1257132553[/C][C]-11.4757132553004[/C][/ROW]
[ROW][C]81[/C][C]118.65[/C][C]123.644770466557[/C][C]-4.99477046655676[/C][/ROW]
[ROW][C]82[/C][C]110.47[/C][C]113.096072041934[/C][C]-2.62607204193448[/C][/ROW]
[ROW][C]83[/C][C]110.02[/C][C]108.627353918289[/C][C]1.39264608171068[/C][/ROW]
[ROW][C]84[/C][C]100.47[/C][C]100.461914263392[/C][C]0.00808573660756906[/C][/ROW]
[ROW][C]85[/C][C]104.1[/C][C]103.352193413283[/C][C]0.747806586716806[/C][/ROW]
[ROW][C]86[/C][C]106.6[/C][C]104.306370363242[/C][C]2.29362963675787[/C][/ROW]
[ROW][C]87[/C][C]105.5[/C][C]104.644868776351[/C][C]0.855131223649167[/C][/ROW]
[ROW][C]88[/C][C]107.5[/C][C]105.786602392019[/C][C]1.7133976079806[/C][/ROW]
[ROW][C]89[/C][C]117.9[/C][C]118.582372678701[/C][C]-0.682372678701356[/C][/ROW]
[ROW][C]90[/C][C]136.3[/C][C]131.274117811927[/C][C]5.02588218807261[/C][/ROW]
[ROW][C]91[/C][C]156.8[/C][C]134.325508437418[/C][C]22.4744915625818[/C][/ROW]
[ROW][C]92[/C][C]135.8[/C][C]139.224482343237[/C][C]-3.42448234323712[/C][/ROW]
[ROW][C]93[/C][C]130[/C][C]130.974204013202[/C][C]-0.974204013201557[/C][/ROW]
[ROW][C]94[/C][C]117.5[/C][C]122.093883212127[/C][C]-4.59388321212668[/C][/ROW]
[ROW][C]95[/C][C]115.8[/C][C]117.941098881699[/C][C]-2.14109888169894[/C][/ROW]
[ROW][C]96[/C][C]105.5[/C][C]108.908527785636[/C][C]-3.40852778563564[/C][/ROW]
[ROW][C]97[/C][C]111.6[/C][C]111.213311539035[/C][C]0.386688460965232[/C][/ROW]
[ROW][C]98[/C][C]113.2[/C][C]112.481397913439[/C][C]0.718602086561134[/C][/ROW]
[ROW][C]99[/C][C]113.1[/C][C]112.393966823022[/C][C]0.70603317697848[/C][/ROW]
[ROW][C]100[/C][C]112.5[/C][C]113.791561092966[/C][C]-1.29156109296579[/C][/ROW]
[ROW][C]101[/C][C]120[/C][C]125.62406900633[/C][C]-5.62406900633006[/C][/ROW]
[ROW][C]102[/C][C]147.6[/C][C]137.89886780822[/C][C]9.70113219177986[/C][/ROW]
[ROW][C]103[/C][C]149.9[/C][C]144.684150892492[/C][C]5.21584910750806[/C][/ROW]
[ROW][C]104[/C][C]131.2[/C][C]141.516693190135[/C][C]-10.3166931901345[/C][/ROW]
[ROW][C]105[/C][C]134.6[/C][C]131.679838191499[/C][C]2.92016180850106[/C][/ROW]
[ROW][C]106[/C][C]122.2[/C][C]123.230620429538[/C][C]-1.03062042953846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285975&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285975&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
1386.8390.0810630341881-3.25106303418806
1486.8390.2482470921818-3.41824709218176
1586.8389.6710949540142-2.84109495401415
1686.8388.4160762645622-1.58607626456222
17100.47100.97626552044-0.506265520439712
18111.38110.8541269443730.525873055627343
19105.47117.878878865692-12.4088788656924
20102.74113.735634091777-10.9956340917772
21105.0193.551276105195511.4587238948045
2296.3886.62538935686499.75461064313509
2394.183.504458556918110.5955414430819
2486.8376.308508769721410.5214912302786
2592.7481.289173749617911.4508262503821
2693.285.50533026033327.69466973966676
2795.4788.27140376790047.19859623209962
2896.3890.2861224894456.09387751055502
2999.56105.565609054364-6.00560905436355
30120.47114.6715780344485.79842196555211
31123.2121.8771694377171.32283056228268
32114.11122.22219759343-8.11219759343035
33120.93106.60966264945814.3203373505419
34102.74100.988463464721.75153653528002
35101.8396.60751192264585.22248807735421
3695.4788.64947442494676.82052557505334
37100.0193.39752398907956.61247601092049
38100.0196.3924986013413.61750139865903
3998.298.5337221856774-0.333722185677416
40100.0198.85859954709751.15140045290254
41103.65111.566361084767-7.91636108476681
42114.56122.12539024285-7.56539024285011
43134.11125.4398297628898.67017023711134
44131.84126.6791738448555.16082615514452
45113.65117.993764054622-4.34376405462234
46107.29106.023441638561.26655836144003
47102.29102.1961103960520.093889603947531
4894.5693.2726867539361.28731324606399
4997.2996.64184902221680.648150977783246
5098.297.69898613036640.501013869633596
5195.4798.4766099190823-3.00660991908232
52100.4798.26421916524842.20578083475162
53116.38109.9758769359686.40412306403189
54117.29124.429269491485-7.13926949148451
55140.93130.19987405756610.7301259424335
56120.02131.650961155676-11.6309611556757
57111.38117.275107183455-5.89510718345549
58108.65105.6157878398483.03421216015201
59105.92102.0565707708693.8634292291313
6099.194.28612805385184.81387194614823
61101.8398.53495363634243.29504636365759
62102.74100.3401174041732.39988259582691
63102.74101.2346834254951.50531657450546
64105.47103.0574339667132.41256603328729
65108.65115.550189358249-6.90018935824945
66139.57124.70729298025414.8627070197462
67110.47138.881156197187-28.4111561971868
68118.65126.930883581475-8.28088358147457
69120.02114.0576206392085.96237936079166
70109.11106.6790484865192.43095151348081
71108.2103.0532104554565.14678954454412
72101.3895.73708430567275.64291569432726
73106.3899.99490398746596.38509601253405
74108.65102.5160370759526.13396292404786
75107.74104.335884707543.40411529246003
76105.92106.874251858226-0.954251858226144
77129.56117.28387949272712.2761205072734
78139.11134.6648747936854.44512520631534
79125.93140.392778742896-14.4627787428959
80123.65135.1257132553-11.4757132553004
81118.65123.644770466557-4.99477046655676
82110.47113.096072041934-2.62607204193448
83110.02108.6273539182891.39264608171068
84100.47100.4619142633920.00808573660756906
85104.1103.3521934132830.747806586716806
86106.6104.3063703632422.29362963675787
87105.5104.6448687763510.855131223649167
88107.5105.7866023920191.7133976079806
89117.9118.582372678701-0.682372678701356
90136.3131.2741178119275.02588218807261
91156.8134.32550843741822.4744915625818
92135.8139.224482343237-3.42448234323712
93130130.974204013202-0.974204013201557
94117.5122.093883212127-4.59388321212668
95115.8117.941098881699-2.14109888169894
96105.5108.908527785636-3.40852778563564
97111.6111.2133115390350.386688460965232
98113.2112.4813979134390.718602086561134
99113.1112.3939668230220.70603317697848
100112.5113.791561092966-1.29156109296579
101120125.62406900633-5.62406900633006
102147.6137.898867808229.70113219177986
103149.9144.6841508924925.21584910750806
104131.2141.516693190135-10.3166931901345
105134.6131.6798381914992.92016180850106
106122.2123.230620429538-1.03062042953846







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
107120.290876400964106.103237141523134.478515660405
108111.61885555446696.9196342028612126.31807690607
109115.341880782532100.107169558556130.576592006508
110116.566014138758100.772727357657132.359300919858
111116.29338572277399.9192476217769132.66752382377
112117.230485341431100.254009085451134.20696159741
113128.817493973395111.217954311839146.41703363495
114144.715244225492126.472645846213162.95784260477
115148.333391370058129.428434600803167.238348139313
116141.598963708788122.013008864857161.184918552719
117136.267400969117115.982432344008156.552369594225
118126.50955820613105.508148449702147.510967962557

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
107 & 120.290876400964 & 106.103237141523 & 134.478515660405 \tabularnewline
108 & 111.618855554466 & 96.9196342028612 & 126.31807690607 \tabularnewline
109 & 115.341880782532 & 100.107169558556 & 130.576592006508 \tabularnewline
110 & 116.566014138758 & 100.772727357657 & 132.359300919858 \tabularnewline
111 & 116.293385722773 & 99.9192476217769 & 132.66752382377 \tabularnewline
112 & 117.230485341431 & 100.254009085451 & 134.20696159741 \tabularnewline
113 & 128.817493973395 & 111.217954311839 & 146.41703363495 \tabularnewline
114 & 144.715244225492 & 126.472645846213 & 162.95784260477 \tabularnewline
115 & 148.333391370058 & 129.428434600803 & 167.238348139313 \tabularnewline
116 & 141.598963708788 & 122.013008864857 & 161.184918552719 \tabularnewline
117 & 136.267400969117 & 115.982432344008 & 156.552369594225 \tabularnewline
118 & 126.50955820613 & 105.508148449702 & 147.510967962557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285975&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]107[/C][C]120.290876400964[/C][C]106.103237141523[/C][C]134.478515660405[/C][/ROW]
[ROW][C]108[/C][C]111.618855554466[/C][C]96.9196342028612[/C][C]126.31807690607[/C][/ROW]
[ROW][C]109[/C][C]115.341880782532[/C][C]100.107169558556[/C][C]130.576592006508[/C][/ROW]
[ROW][C]110[/C][C]116.566014138758[/C][C]100.772727357657[/C][C]132.359300919858[/C][/ROW]
[ROW][C]111[/C][C]116.293385722773[/C][C]99.9192476217769[/C][C]132.66752382377[/C][/ROW]
[ROW][C]112[/C][C]117.230485341431[/C][C]100.254009085451[/C][C]134.20696159741[/C][/ROW]
[ROW][C]113[/C][C]128.817493973395[/C][C]111.217954311839[/C][C]146.41703363495[/C][/ROW]
[ROW][C]114[/C][C]144.715244225492[/C][C]126.472645846213[/C][C]162.95784260477[/C][/ROW]
[ROW][C]115[/C][C]148.333391370058[/C][C]129.428434600803[/C][C]167.238348139313[/C][/ROW]
[ROW][C]116[/C][C]141.598963708788[/C][C]122.013008864857[/C][C]161.184918552719[/C][/ROW]
[ROW][C]117[/C][C]136.267400969117[/C][C]115.982432344008[/C][C]156.552369594225[/C][/ROW]
[ROW][C]118[/C][C]126.50955820613[/C][C]105.508148449702[/C][C]147.510967962557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285975&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285975&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
107120.290876400964106.103237141523134.478515660405
108111.61885555446696.9196342028612126.31807690607
109115.341880782532100.107169558556130.576592006508
110116.566014138758100.772727357657132.359300919858
111116.29338572277399.9192476217769132.66752382377
112117.230485341431100.254009085451134.20696159741
113128.817493973395111.217954311839146.41703363495
114144.715244225492126.472645846213162.95784260477
115148.333391370058129.428434600803167.238348139313
116141.598963708788122.013008864857161.184918552719
117136.267400969117115.982432344008156.552369594225
118126.50955820613105.508148449702147.510967962557



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
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')