Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 02 Jan 2012 09:29:30 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/02/t1325514755dt8myktxglfy9b3.htm/, Retrieved Sat, 04 May 2024 09:50:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160933, Retrieved Sat, 04 May 2024 09:50:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-01-02 14:29:30] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
98.6
100.1
98.8
98.3
102.8
103.6
105.2
100.1
98.2
98.4
97.4
98.4
100.3
101.1
104.1
107.3
110.1
112.6
114.3
115.3
109.9
108.2
103.2
101.8
105.6
108.2
109.8
114.6
117.2
116.5
116.1
112.1
106.8
106.9
104.5
103
105.9
107.7
107.1
112.5
114.5
114.6
113.1
112.8
111.9
112
112.4
110
112.3
109.6
111.9
110.8
110.4
110.8
114
108.4
110.5
105.1
102.3
104.3
103.4
102.4
104.5
107.3
110.1
111.8
111.8
105.7
106
106.4
107.1
111.5
109.6
109.9
109.3
111.4
112.9
115.5
118.4
116.2
113.3
113.8
114.1
117.1
115.5
115.2
114.2
115.3
118.8
118
118.1
111.8
112
114.3
115
118.5
117.6
119.1
120.6
123.6
122.7
123.8
123.1
124.5
120.7
118.7
119
122.3
118.6
118.1
118.2
120.8
119.7
119.7
117.1
114.5
116.5
116.4
114.9
115.5




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=160933&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=160933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160933&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
alpha0.959702211416699
beta0.0188108560999103
gamma0.434955331866694

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.959702211416699 \tabularnewline
beta & 0.0188108560999103 \tabularnewline
gamma & 0.434955331866694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160933&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]0.959702211416699[/C][/ROW]
[ROW][C]beta[/C][C]0.0188108560999103[/C][/ROW]
[ROW][C]gamma[/C][C]0.434955331866694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160933&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
alpha0.959702211416699
beta0.0188108560999103
gamma0.434955331866694







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13100.396.82272970085473.4772702991453
14101.1100.7372024279320.362797572068388
15104.1103.7609249774390.339075022560792
16107.3107.193002204140.106997795860266
17110.1110.25011934846-0.150119348459839
18112.6113.024437189844-0.424437189843559
19114.3113.1569959706131.14300402938657
20115.3109.8561326686395.44386733136137
21109.9113.831094546683-3.93109454668328
22108.2110.504584102056-2.30458410205638
23103.2107.414101752272-4.21410175227196
24101.8104.414974669608-2.61497466960778
25105.6103.7892743997631.81072560023725
26108.2105.9697454915392.23025450846077
27109.8110.738942313951-0.938942313950875
28114.6112.8710513945151.72894860548482
29117.2117.440148128804-0.240148128803909
30116.5120.081528199067-3.58152819906732
31116.1117.112970279057-1.01297027905701
32112.1111.6807534775140.419246522486105
33106.8110.440900608947-3.6409006089474
34106.9107.198284626843-0.298284626842786
35104.5105.81288780858-1.3128878085804
36103105.491571351183-2.49157135118259
37105.9104.929581918840.970418081159877
38107.7106.1634993836121.53650061638758
39107.1110.051363960287-2.95136396028722
40112.5110.1025934937432.3974065062574
41114.5115.094448356382-0.59444835638206
42114.6117.146594176385-2.5465941763851
43113.1115.044324510823-1.94432451082275
44112.8108.5546137177544.24538628224605
45111.9110.795848259211.10415174078994
46112112.131617401107-0.131617401106695
47112.4110.8573559961421.5426440038585
48110113.276358686901-3.27635868690116
49112.3112.0282389413820.271761058618466
50109.6112.59531411801-2.99531411801043
51111.9111.967250176317-0.0672501763172164
52110.8114.844114539668-4.04411453966785
53110.4113.449291946263-3.04929194626317
54110.8112.914690378754-2.11469037875366
55114111.0486613842692.95133861573137
56108.4109.26538669186-0.865386691859527
57110.5106.3540442490214.1459557509794
58105.1110.449594206372-5.3495942063721
59102.3103.964990758408-1.66499075840817
60104.3102.9312620250371.36873797496268
61103.4105.997208393558-2.59720839355776
62102.4103.495835877118-1.09583587711796
63104.5104.518491752953-0.0184917529525563
64107.3107.1497884850010.150211514999214
65110.1109.6507705241770.449229475822762
66111.8112.406310984473-0.606310984473154
67111.8112.020125392204-0.220125392204196
68105.7107.012489580137-1.31248958013667
69106103.6380259994572.36197400054344
70106.4105.7009703074980.699029692502421
71107.1105.0409431684892.05905683151148
72111.5107.6567109198383.84328908016235
73109.6113.094993388389-3.49499338838889
74109.9109.8091407410670.0908592589330368
75109.3112.061787612635-2.76178761263463
76111.4112.086003645189-0.686003645189246
77112.9113.797322629388-0.897322629387787
78115.5115.2253771318380.274622868161984
79118.4115.6906023183422.70939768165793
80116.2113.5273834110842.67261658891626
81113.3114.165876279392-0.865876279391799
82113.8113.1676622936370.632337706362776
83114.1112.5320293391181.56797066088222
84117.1114.7634691032722.33653089672755
85115.5118.655582625373-3.15558262537289
86115.2115.792936151897-0.592936151897064
87114.2117.361619201208-3.16161920120808
88115.3117.053558276441-1.7535582764408
89118.8117.7324249095051.06757509049473
90118121.097995730895-3.09799573089464
91118.1118.339560285812-0.239560285812118
92111.8113.26271099964-1.46271099964008
93112109.7129805281282.28701947187184
94114.3111.6662679973322.63373200266781
95115112.9033080434512.09669195654909
96118.5115.6007097764822.89929022351801
97117.6119.891875584767-2.29187558476663
98119.1117.8738756547621.22612434523796
99120.6121.146958645041-0.546958645041428
100123.6123.4237421206950.176257879305467
101122.7126.089813056245-3.38981305624483
102123.8125.109844538946-1.309844538946
103123.1124.155123783555-1.05512378355536
104124.5118.296934247456.20306575255016
105120.7122.330976767582-1.63097676758157
106118.7120.620686583256-1.92068658325644
107119117.4856627590751.51433724092487
108122.3119.6359667864252.66403321357537
109118.6123.603841145862-5.00384114586195
110118.1118.989340442095-0.889340442095317
111118.2120.107454949665-1.90745494966484
112120.8120.973008553726-0.173008553726334
113119.7123.116842410753-3.41684241075281
114119.7122.022362796018-2.32236279601818
115117.1119.957083789464-2.85708378946433
116114.5112.3209315159892.17906848401113
117116.5112.107340035374.3926599646295
118116.4116.0331311382630.366868861736791
119114.9115.055246110449-0.155246110449312
120115.5115.4948167645210.00518323547899513

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100.3 & 96.8227297008547 & 3.4772702991453 \tabularnewline
14 & 101.1 & 100.737202427932 & 0.362797572068388 \tabularnewline
15 & 104.1 & 103.760924977439 & 0.339075022560792 \tabularnewline
16 & 107.3 & 107.19300220414 & 0.106997795860266 \tabularnewline
17 & 110.1 & 110.25011934846 & -0.150119348459839 \tabularnewline
18 & 112.6 & 113.024437189844 & -0.424437189843559 \tabularnewline
19 & 114.3 & 113.156995970613 & 1.14300402938657 \tabularnewline
20 & 115.3 & 109.856132668639 & 5.44386733136137 \tabularnewline
21 & 109.9 & 113.831094546683 & -3.93109454668328 \tabularnewline
22 & 108.2 & 110.504584102056 & -2.30458410205638 \tabularnewline
23 & 103.2 & 107.414101752272 & -4.21410175227196 \tabularnewline
24 & 101.8 & 104.414974669608 & -2.61497466960778 \tabularnewline
25 & 105.6 & 103.789274399763 & 1.81072560023725 \tabularnewline
26 & 108.2 & 105.969745491539 & 2.23025450846077 \tabularnewline
27 & 109.8 & 110.738942313951 & -0.938942313950875 \tabularnewline
28 & 114.6 & 112.871051394515 & 1.72894860548482 \tabularnewline
29 & 117.2 & 117.440148128804 & -0.240148128803909 \tabularnewline
30 & 116.5 & 120.081528199067 & -3.58152819906732 \tabularnewline
31 & 116.1 & 117.112970279057 & -1.01297027905701 \tabularnewline
32 & 112.1 & 111.680753477514 & 0.419246522486105 \tabularnewline
33 & 106.8 & 110.440900608947 & -3.6409006089474 \tabularnewline
34 & 106.9 & 107.198284626843 & -0.298284626842786 \tabularnewline
35 & 104.5 & 105.81288780858 & -1.3128878085804 \tabularnewline
36 & 103 & 105.491571351183 & -2.49157135118259 \tabularnewline
37 & 105.9 & 104.92958191884 & 0.970418081159877 \tabularnewline
38 & 107.7 & 106.163499383612 & 1.53650061638758 \tabularnewline
39 & 107.1 & 110.051363960287 & -2.95136396028722 \tabularnewline
40 & 112.5 & 110.102593493743 & 2.3974065062574 \tabularnewline
41 & 114.5 & 115.094448356382 & -0.59444835638206 \tabularnewline
42 & 114.6 & 117.146594176385 & -2.5465941763851 \tabularnewline
43 & 113.1 & 115.044324510823 & -1.94432451082275 \tabularnewline
44 & 112.8 & 108.554613717754 & 4.24538628224605 \tabularnewline
45 & 111.9 & 110.79584825921 & 1.10415174078994 \tabularnewline
46 & 112 & 112.131617401107 & -0.131617401106695 \tabularnewline
47 & 112.4 & 110.857355996142 & 1.5426440038585 \tabularnewline
48 & 110 & 113.276358686901 & -3.27635868690116 \tabularnewline
49 & 112.3 & 112.028238941382 & 0.271761058618466 \tabularnewline
50 & 109.6 & 112.59531411801 & -2.99531411801043 \tabularnewline
51 & 111.9 & 111.967250176317 & -0.0672501763172164 \tabularnewline
52 & 110.8 & 114.844114539668 & -4.04411453966785 \tabularnewline
53 & 110.4 & 113.449291946263 & -3.04929194626317 \tabularnewline
54 & 110.8 & 112.914690378754 & -2.11469037875366 \tabularnewline
55 & 114 & 111.048661384269 & 2.95133861573137 \tabularnewline
56 & 108.4 & 109.26538669186 & -0.865386691859527 \tabularnewline
57 & 110.5 & 106.354044249021 & 4.1459557509794 \tabularnewline
58 & 105.1 & 110.449594206372 & -5.3495942063721 \tabularnewline
59 & 102.3 & 103.964990758408 & -1.66499075840817 \tabularnewline
60 & 104.3 & 102.931262025037 & 1.36873797496268 \tabularnewline
61 & 103.4 & 105.997208393558 & -2.59720839355776 \tabularnewline
62 & 102.4 & 103.495835877118 & -1.09583587711796 \tabularnewline
63 & 104.5 & 104.518491752953 & -0.0184917529525563 \tabularnewline
64 & 107.3 & 107.149788485001 & 0.150211514999214 \tabularnewline
65 & 110.1 & 109.650770524177 & 0.449229475822762 \tabularnewline
66 & 111.8 & 112.406310984473 & -0.606310984473154 \tabularnewline
67 & 111.8 & 112.020125392204 & -0.220125392204196 \tabularnewline
68 & 105.7 & 107.012489580137 & -1.31248958013667 \tabularnewline
69 & 106 & 103.638025999457 & 2.36197400054344 \tabularnewline
70 & 106.4 & 105.700970307498 & 0.699029692502421 \tabularnewline
71 & 107.1 & 105.040943168489 & 2.05905683151148 \tabularnewline
72 & 111.5 & 107.656710919838 & 3.84328908016235 \tabularnewline
73 & 109.6 & 113.094993388389 & -3.49499338838889 \tabularnewline
74 & 109.9 & 109.809140741067 & 0.0908592589330368 \tabularnewline
75 & 109.3 & 112.061787612635 & -2.76178761263463 \tabularnewline
76 & 111.4 & 112.086003645189 & -0.686003645189246 \tabularnewline
77 & 112.9 & 113.797322629388 & -0.897322629387787 \tabularnewline
78 & 115.5 & 115.225377131838 & 0.274622868161984 \tabularnewline
79 & 118.4 & 115.690602318342 & 2.70939768165793 \tabularnewline
80 & 116.2 & 113.527383411084 & 2.67261658891626 \tabularnewline
81 & 113.3 & 114.165876279392 & -0.865876279391799 \tabularnewline
82 & 113.8 & 113.167662293637 & 0.632337706362776 \tabularnewline
83 & 114.1 & 112.532029339118 & 1.56797066088222 \tabularnewline
84 & 117.1 & 114.763469103272 & 2.33653089672755 \tabularnewline
85 & 115.5 & 118.655582625373 & -3.15558262537289 \tabularnewline
86 & 115.2 & 115.792936151897 & -0.592936151897064 \tabularnewline
87 & 114.2 & 117.361619201208 & -3.16161920120808 \tabularnewline
88 & 115.3 & 117.053558276441 & -1.7535582764408 \tabularnewline
89 & 118.8 & 117.732424909505 & 1.06757509049473 \tabularnewline
90 & 118 & 121.097995730895 & -3.09799573089464 \tabularnewline
91 & 118.1 & 118.339560285812 & -0.239560285812118 \tabularnewline
92 & 111.8 & 113.26271099964 & -1.46271099964008 \tabularnewline
93 & 112 & 109.712980528128 & 2.28701947187184 \tabularnewline
94 & 114.3 & 111.666267997332 & 2.63373200266781 \tabularnewline
95 & 115 & 112.903308043451 & 2.09669195654909 \tabularnewline
96 & 118.5 & 115.600709776482 & 2.89929022351801 \tabularnewline
97 & 117.6 & 119.891875584767 & -2.29187558476663 \tabularnewline
98 & 119.1 & 117.873875654762 & 1.22612434523796 \tabularnewline
99 & 120.6 & 121.146958645041 & -0.546958645041428 \tabularnewline
100 & 123.6 & 123.423742120695 & 0.176257879305467 \tabularnewline
101 & 122.7 & 126.089813056245 & -3.38981305624483 \tabularnewline
102 & 123.8 & 125.109844538946 & -1.309844538946 \tabularnewline
103 & 123.1 & 124.155123783555 & -1.05512378355536 \tabularnewline
104 & 124.5 & 118.29693424745 & 6.20306575255016 \tabularnewline
105 & 120.7 & 122.330976767582 & -1.63097676758157 \tabularnewline
106 & 118.7 & 120.620686583256 & -1.92068658325644 \tabularnewline
107 & 119 & 117.485662759075 & 1.51433724092487 \tabularnewline
108 & 122.3 & 119.635966786425 & 2.66403321357537 \tabularnewline
109 & 118.6 & 123.603841145862 & -5.00384114586195 \tabularnewline
110 & 118.1 & 118.989340442095 & -0.889340442095317 \tabularnewline
111 & 118.2 & 120.107454949665 & -1.90745494966484 \tabularnewline
112 & 120.8 & 120.973008553726 & -0.173008553726334 \tabularnewline
113 & 119.7 & 123.116842410753 & -3.41684241075281 \tabularnewline
114 & 119.7 & 122.022362796018 & -2.32236279601818 \tabularnewline
115 & 117.1 & 119.957083789464 & -2.85708378946433 \tabularnewline
116 & 114.5 & 112.320931515989 & 2.17906848401113 \tabularnewline
117 & 116.5 & 112.10734003537 & 4.3926599646295 \tabularnewline
118 & 116.4 & 116.033131138263 & 0.366868861736791 \tabularnewline
119 & 114.9 & 115.055246110449 & -0.155246110449312 \tabularnewline
120 & 115.5 & 115.494816764521 & 0.00518323547899513 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160933&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]100.3[/C][C]96.8227297008547[/C][C]3.4772702991453[/C][/ROW]
[ROW][C]14[/C][C]101.1[/C][C]100.737202427932[/C][C]0.362797572068388[/C][/ROW]
[ROW][C]15[/C][C]104.1[/C][C]103.760924977439[/C][C]0.339075022560792[/C][/ROW]
[ROW][C]16[/C][C]107.3[/C][C]107.19300220414[/C][C]0.106997795860266[/C][/ROW]
[ROW][C]17[/C][C]110.1[/C][C]110.25011934846[/C][C]-0.150119348459839[/C][/ROW]
[ROW][C]18[/C][C]112.6[/C][C]113.024437189844[/C][C]-0.424437189843559[/C][/ROW]
[ROW][C]19[/C][C]114.3[/C][C]113.156995970613[/C][C]1.14300402938657[/C][/ROW]
[ROW][C]20[/C][C]115.3[/C][C]109.856132668639[/C][C]5.44386733136137[/C][/ROW]
[ROW][C]21[/C][C]109.9[/C][C]113.831094546683[/C][C]-3.93109454668328[/C][/ROW]
[ROW][C]22[/C][C]108.2[/C][C]110.504584102056[/C][C]-2.30458410205638[/C][/ROW]
[ROW][C]23[/C][C]103.2[/C][C]107.414101752272[/C][C]-4.21410175227196[/C][/ROW]
[ROW][C]24[/C][C]101.8[/C][C]104.414974669608[/C][C]-2.61497466960778[/C][/ROW]
[ROW][C]25[/C][C]105.6[/C][C]103.789274399763[/C][C]1.81072560023725[/C][/ROW]
[ROW][C]26[/C][C]108.2[/C][C]105.969745491539[/C][C]2.23025450846077[/C][/ROW]
[ROW][C]27[/C][C]109.8[/C][C]110.738942313951[/C][C]-0.938942313950875[/C][/ROW]
[ROW][C]28[/C][C]114.6[/C][C]112.871051394515[/C][C]1.72894860548482[/C][/ROW]
[ROW][C]29[/C][C]117.2[/C][C]117.440148128804[/C][C]-0.240148128803909[/C][/ROW]
[ROW][C]30[/C][C]116.5[/C][C]120.081528199067[/C][C]-3.58152819906732[/C][/ROW]
[ROW][C]31[/C][C]116.1[/C][C]117.112970279057[/C][C]-1.01297027905701[/C][/ROW]
[ROW][C]32[/C][C]112.1[/C][C]111.680753477514[/C][C]0.419246522486105[/C][/ROW]
[ROW][C]33[/C][C]106.8[/C][C]110.440900608947[/C][C]-3.6409006089474[/C][/ROW]
[ROW][C]34[/C][C]106.9[/C][C]107.198284626843[/C][C]-0.298284626842786[/C][/ROW]
[ROW][C]35[/C][C]104.5[/C][C]105.81288780858[/C][C]-1.3128878085804[/C][/ROW]
[ROW][C]36[/C][C]103[/C][C]105.491571351183[/C][C]-2.49157135118259[/C][/ROW]
[ROW][C]37[/C][C]105.9[/C][C]104.92958191884[/C][C]0.970418081159877[/C][/ROW]
[ROW][C]38[/C][C]107.7[/C][C]106.163499383612[/C][C]1.53650061638758[/C][/ROW]
[ROW][C]39[/C][C]107.1[/C][C]110.051363960287[/C][C]-2.95136396028722[/C][/ROW]
[ROW][C]40[/C][C]112.5[/C][C]110.102593493743[/C][C]2.3974065062574[/C][/ROW]
[ROW][C]41[/C][C]114.5[/C][C]115.094448356382[/C][C]-0.59444835638206[/C][/ROW]
[ROW][C]42[/C][C]114.6[/C][C]117.146594176385[/C][C]-2.5465941763851[/C][/ROW]
[ROW][C]43[/C][C]113.1[/C][C]115.044324510823[/C][C]-1.94432451082275[/C][/ROW]
[ROW][C]44[/C][C]112.8[/C][C]108.554613717754[/C][C]4.24538628224605[/C][/ROW]
[ROW][C]45[/C][C]111.9[/C][C]110.79584825921[/C][C]1.10415174078994[/C][/ROW]
[ROW][C]46[/C][C]112[/C][C]112.131617401107[/C][C]-0.131617401106695[/C][/ROW]
[ROW][C]47[/C][C]112.4[/C][C]110.857355996142[/C][C]1.5426440038585[/C][/ROW]
[ROW][C]48[/C][C]110[/C][C]113.276358686901[/C][C]-3.27635868690116[/C][/ROW]
[ROW][C]49[/C][C]112.3[/C][C]112.028238941382[/C][C]0.271761058618466[/C][/ROW]
[ROW][C]50[/C][C]109.6[/C][C]112.59531411801[/C][C]-2.99531411801043[/C][/ROW]
[ROW][C]51[/C][C]111.9[/C][C]111.967250176317[/C][C]-0.0672501763172164[/C][/ROW]
[ROW][C]52[/C][C]110.8[/C][C]114.844114539668[/C][C]-4.04411453966785[/C][/ROW]
[ROW][C]53[/C][C]110.4[/C][C]113.449291946263[/C][C]-3.04929194626317[/C][/ROW]
[ROW][C]54[/C][C]110.8[/C][C]112.914690378754[/C][C]-2.11469037875366[/C][/ROW]
[ROW][C]55[/C][C]114[/C][C]111.048661384269[/C][C]2.95133861573137[/C][/ROW]
[ROW][C]56[/C][C]108.4[/C][C]109.26538669186[/C][C]-0.865386691859527[/C][/ROW]
[ROW][C]57[/C][C]110.5[/C][C]106.354044249021[/C][C]4.1459557509794[/C][/ROW]
[ROW][C]58[/C][C]105.1[/C][C]110.449594206372[/C][C]-5.3495942063721[/C][/ROW]
[ROW][C]59[/C][C]102.3[/C][C]103.964990758408[/C][C]-1.66499075840817[/C][/ROW]
[ROW][C]60[/C][C]104.3[/C][C]102.931262025037[/C][C]1.36873797496268[/C][/ROW]
[ROW][C]61[/C][C]103.4[/C][C]105.997208393558[/C][C]-2.59720839355776[/C][/ROW]
[ROW][C]62[/C][C]102.4[/C][C]103.495835877118[/C][C]-1.09583587711796[/C][/ROW]
[ROW][C]63[/C][C]104.5[/C][C]104.518491752953[/C][C]-0.0184917529525563[/C][/ROW]
[ROW][C]64[/C][C]107.3[/C][C]107.149788485001[/C][C]0.150211514999214[/C][/ROW]
[ROW][C]65[/C][C]110.1[/C][C]109.650770524177[/C][C]0.449229475822762[/C][/ROW]
[ROW][C]66[/C][C]111.8[/C][C]112.406310984473[/C][C]-0.606310984473154[/C][/ROW]
[ROW][C]67[/C][C]111.8[/C][C]112.020125392204[/C][C]-0.220125392204196[/C][/ROW]
[ROW][C]68[/C][C]105.7[/C][C]107.012489580137[/C][C]-1.31248958013667[/C][/ROW]
[ROW][C]69[/C][C]106[/C][C]103.638025999457[/C][C]2.36197400054344[/C][/ROW]
[ROW][C]70[/C][C]106.4[/C][C]105.700970307498[/C][C]0.699029692502421[/C][/ROW]
[ROW][C]71[/C][C]107.1[/C][C]105.040943168489[/C][C]2.05905683151148[/C][/ROW]
[ROW][C]72[/C][C]111.5[/C][C]107.656710919838[/C][C]3.84328908016235[/C][/ROW]
[ROW][C]73[/C][C]109.6[/C][C]113.094993388389[/C][C]-3.49499338838889[/C][/ROW]
[ROW][C]74[/C][C]109.9[/C][C]109.809140741067[/C][C]0.0908592589330368[/C][/ROW]
[ROW][C]75[/C][C]109.3[/C][C]112.061787612635[/C][C]-2.76178761263463[/C][/ROW]
[ROW][C]76[/C][C]111.4[/C][C]112.086003645189[/C][C]-0.686003645189246[/C][/ROW]
[ROW][C]77[/C][C]112.9[/C][C]113.797322629388[/C][C]-0.897322629387787[/C][/ROW]
[ROW][C]78[/C][C]115.5[/C][C]115.225377131838[/C][C]0.274622868161984[/C][/ROW]
[ROW][C]79[/C][C]118.4[/C][C]115.690602318342[/C][C]2.70939768165793[/C][/ROW]
[ROW][C]80[/C][C]116.2[/C][C]113.527383411084[/C][C]2.67261658891626[/C][/ROW]
[ROW][C]81[/C][C]113.3[/C][C]114.165876279392[/C][C]-0.865876279391799[/C][/ROW]
[ROW][C]82[/C][C]113.8[/C][C]113.167662293637[/C][C]0.632337706362776[/C][/ROW]
[ROW][C]83[/C][C]114.1[/C][C]112.532029339118[/C][C]1.56797066088222[/C][/ROW]
[ROW][C]84[/C][C]117.1[/C][C]114.763469103272[/C][C]2.33653089672755[/C][/ROW]
[ROW][C]85[/C][C]115.5[/C][C]118.655582625373[/C][C]-3.15558262537289[/C][/ROW]
[ROW][C]86[/C][C]115.2[/C][C]115.792936151897[/C][C]-0.592936151897064[/C][/ROW]
[ROW][C]87[/C][C]114.2[/C][C]117.361619201208[/C][C]-3.16161920120808[/C][/ROW]
[ROW][C]88[/C][C]115.3[/C][C]117.053558276441[/C][C]-1.7535582764408[/C][/ROW]
[ROW][C]89[/C][C]118.8[/C][C]117.732424909505[/C][C]1.06757509049473[/C][/ROW]
[ROW][C]90[/C][C]118[/C][C]121.097995730895[/C][C]-3.09799573089464[/C][/ROW]
[ROW][C]91[/C][C]118.1[/C][C]118.339560285812[/C][C]-0.239560285812118[/C][/ROW]
[ROW][C]92[/C][C]111.8[/C][C]113.26271099964[/C][C]-1.46271099964008[/C][/ROW]
[ROW][C]93[/C][C]112[/C][C]109.712980528128[/C][C]2.28701947187184[/C][/ROW]
[ROW][C]94[/C][C]114.3[/C][C]111.666267997332[/C][C]2.63373200266781[/C][/ROW]
[ROW][C]95[/C][C]115[/C][C]112.903308043451[/C][C]2.09669195654909[/C][/ROW]
[ROW][C]96[/C][C]118.5[/C][C]115.600709776482[/C][C]2.89929022351801[/C][/ROW]
[ROW][C]97[/C][C]117.6[/C][C]119.891875584767[/C][C]-2.29187558476663[/C][/ROW]
[ROW][C]98[/C][C]119.1[/C][C]117.873875654762[/C][C]1.22612434523796[/C][/ROW]
[ROW][C]99[/C][C]120.6[/C][C]121.146958645041[/C][C]-0.546958645041428[/C][/ROW]
[ROW][C]100[/C][C]123.6[/C][C]123.423742120695[/C][C]0.176257879305467[/C][/ROW]
[ROW][C]101[/C][C]122.7[/C][C]126.089813056245[/C][C]-3.38981305624483[/C][/ROW]
[ROW][C]102[/C][C]123.8[/C][C]125.109844538946[/C][C]-1.309844538946[/C][/ROW]
[ROW][C]103[/C][C]123.1[/C][C]124.155123783555[/C][C]-1.05512378355536[/C][/ROW]
[ROW][C]104[/C][C]124.5[/C][C]118.29693424745[/C][C]6.20306575255016[/C][/ROW]
[ROW][C]105[/C][C]120.7[/C][C]122.330976767582[/C][C]-1.63097676758157[/C][/ROW]
[ROW][C]106[/C][C]118.7[/C][C]120.620686583256[/C][C]-1.92068658325644[/C][/ROW]
[ROW][C]107[/C][C]119[/C][C]117.485662759075[/C][C]1.51433724092487[/C][/ROW]
[ROW][C]108[/C][C]122.3[/C][C]119.635966786425[/C][C]2.66403321357537[/C][/ROW]
[ROW][C]109[/C][C]118.6[/C][C]123.603841145862[/C][C]-5.00384114586195[/C][/ROW]
[ROW][C]110[/C][C]118.1[/C][C]118.989340442095[/C][C]-0.889340442095317[/C][/ROW]
[ROW][C]111[/C][C]118.2[/C][C]120.107454949665[/C][C]-1.90745494966484[/C][/ROW]
[ROW][C]112[/C][C]120.8[/C][C]120.973008553726[/C][C]-0.173008553726334[/C][/ROW]
[ROW][C]113[/C][C]119.7[/C][C]123.116842410753[/C][C]-3.41684241075281[/C][/ROW]
[ROW][C]114[/C][C]119.7[/C][C]122.022362796018[/C][C]-2.32236279601818[/C][/ROW]
[ROW][C]115[/C][C]117.1[/C][C]119.957083789464[/C][C]-2.85708378946433[/C][/ROW]
[ROW][C]116[/C][C]114.5[/C][C]112.320931515989[/C][C]2.17906848401113[/C][/ROW]
[ROW][C]117[/C][C]116.5[/C][C]112.10734003537[/C][C]4.3926599646295[/C][/ROW]
[ROW][C]118[/C][C]116.4[/C][C]116.033131138263[/C][C]0.366868861736791[/C][/ROW]
[ROW][C]119[/C][C]114.9[/C][C]115.055246110449[/C][C]-0.155246110449312[/C][/ROW]
[ROW][C]120[/C][C]115.5[/C][C]115.494816764521[/C][C]0.00518323547899513[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160933&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160933&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
13100.396.82272970085473.4772702991453
14101.1100.7372024279320.362797572068388
15104.1103.7609249774390.339075022560792
16107.3107.193002204140.106997795860266
17110.1110.25011934846-0.150119348459839
18112.6113.024437189844-0.424437189843559
19114.3113.1569959706131.14300402938657
20115.3109.8561326686395.44386733136137
21109.9113.831094546683-3.93109454668328
22108.2110.504584102056-2.30458410205638
23103.2107.414101752272-4.21410175227196
24101.8104.414974669608-2.61497466960778
25105.6103.7892743997631.81072560023725
26108.2105.9697454915392.23025450846077
27109.8110.738942313951-0.938942313950875
28114.6112.8710513945151.72894860548482
29117.2117.440148128804-0.240148128803909
30116.5120.081528199067-3.58152819906732
31116.1117.112970279057-1.01297027905701
32112.1111.6807534775140.419246522486105
33106.8110.440900608947-3.6409006089474
34106.9107.198284626843-0.298284626842786
35104.5105.81288780858-1.3128878085804
36103105.491571351183-2.49157135118259
37105.9104.929581918840.970418081159877
38107.7106.1634993836121.53650061638758
39107.1110.051363960287-2.95136396028722
40112.5110.1025934937432.3974065062574
41114.5115.094448356382-0.59444835638206
42114.6117.146594176385-2.5465941763851
43113.1115.044324510823-1.94432451082275
44112.8108.5546137177544.24538628224605
45111.9110.795848259211.10415174078994
46112112.131617401107-0.131617401106695
47112.4110.8573559961421.5426440038585
48110113.276358686901-3.27635868690116
49112.3112.0282389413820.271761058618466
50109.6112.59531411801-2.99531411801043
51111.9111.967250176317-0.0672501763172164
52110.8114.844114539668-4.04411453966785
53110.4113.449291946263-3.04929194626317
54110.8112.914690378754-2.11469037875366
55114111.0486613842692.95133861573137
56108.4109.26538669186-0.865386691859527
57110.5106.3540442490214.1459557509794
58105.1110.449594206372-5.3495942063721
59102.3103.964990758408-1.66499075840817
60104.3102.9312620250371.36873797496268
61103.4105.997208393558-2.59720839355776
62102.4103.495835877118-1.09583587711796
63104.5104.518491752953-0.0184917529525563
64107.3107.1497884850010.150211514999214
65110.1109.6507705241770.449229475822762
66111.8112.406310984473-0.606310984473154
67111.8112.020125392204-0.220125392204196
68105.7107.012489580137-1.31248958013667
69106103.6380259994572.36197400054344
70106.4105.7009703074980.699029692502421
71107.1105.0409431684892.05905683151148
72111.5107.6567109198383.84328908016235
73109.6113.094993388389-3.49499338838889
74109.9109.8091407410670.0908592589330368
75109.3112.061787612635-2.76178761263463
76111.4112.086003645189-0.686003645189246
77112.9113.797322629388-0.897322629387787
78115.5115.2253771318380.274622868161984
79118.4115.6906023183422.70939768165793
80116.2113.5273834110842.67261658891626
81113.3114.165876279392-0.865876279391799
82113.8113.1676622936370.632337706362776
83114.1112.5320293391181.56797066088222
84117.1114.7634691032722.33653089672755
85115.5118.655582625373-3.15558262537289
86115.2115.792936151897-0.592936151897064
87114.2117.361619201208-3.16161920120808
88115.3117.053558276441-1.7535582764408
89118.8117.7324249095051.06757509049473
90118121.097995730895-3.09799573089464
91118.1118.339560285812-0.239560285812118
92111.8113.26271099964-1.46271099964008
93112109.7129805281282.28701947187184
94114.3111.6662679973322.63373200266781
95115112.9033080434512.09669195654909
96118.5115.6007097764822.89929022351801
97117.6119.891875584767-2.29187558476663
98119.1117.8738756547621.22612434523796
99120.6121.146958645041-0.546958645041428
100123.6123.4237421206950.176257879305467
101122.7126.089813056245-3.38981305624483
102123.8125.109844538946-1.309844538946
103123.1124.155123783555-1.05512378355536
104124.5118.296934247456.20306575255016
105120.7122.330976767582-1.63097676758157
106118.7120.620686583256-1.92068658325644
107119117.4856627590751.51433724092487
108122.3119.6359667864252.66403321357537
109118.6123.603841145862-5.00384114586195
110118.1118.989340442095-0.889340442095317
111118.2120.107454949665-1.90745494966484
112120.8120.973008553726-0.173008553726334
113119.7123.116842410753-3.41684241075281
114119.7122.022362796018-2.32236279601818
115117.1119.957083789464-2.85708378946433
116114.5112.3209315159892.17906848401113
117116.5112.107340035374.3926599646295
118116.4116.0331311382630.366868861736791
119114.9115.055246110449-0.155246110449312
120115.5115.4948167645210.00518323547899513







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121116.60000457811112.018545995502121.181463160719
122116.773570773271110.366069012352123.18107253419
123118.657148723869110.791385820948126.52291162679
124121.347933622955112.213061662217130.482805583693
125123.568312033555113.282557845985133.854066221126
126125.80121596206114.446196465922137.156235458198
127126.026314988704113.661900214874138.390729762535
128121.342936895361108.014873444857134.671000345865
129119.160101683363104.904375921752133.415827444974
130118.803598251974103.649134917474133.958061586475
131117.46176781371101.432198806759133.491336820661
132118.053234038856101.168111324628134.938356753083

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 116.60000457811 & 112.018545995502 & 121.181463160719 \tabularnewline
122 & 116.773570773271 & 110.366069012352 & 123.18107253419 \tabularnewline
123 & 118.657148723869 & 110.791385820948 & 126.52291162679 \tabularnewline
124 & 121.347933622955 & 112.213061662217 & 130.482805583693 \tabularnewline
125 & 123.568312033555 & 113.282557845985 & 133.854066221126 \tabularnewline
126 & 125.80121596206 & 114.446196465922 & 137.156235458198 \tabularnewline
127 & 126.026314988704 & 113.661900214874 & 138.390729762535 \tabularnewline
128 & 121.342936895361 & 108.014873444857 & 134.671000345865 \tabularnewline
129 & 119.160101683363 & 104.904375921752 & 133.415827444974 \tabularnewline
130 & 118.803598251974 & 103.649134917474 & 133.958061586475 \tabularnewline
131 & 117.46176781371 & 101.432198806759 & 133.491336820661 \tabularnewline
132 & 118.053234038856 & 101.168111324628 & 134.938356753083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160933&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]121[/C][C]116.60000457811[/C][C]112.018545995502[/C][C]121.181463160719[/C][/ROW]
[ROW][C]122[/C][C]116.773570773271[/C][C]110.366069012352[/C][C]123.18107253419[/C][/ROW]
[ROW][C]123[/C][C]118.657148723869[/C][C]110.791385820948[/C][C]126.52291162679[/C][/ROW]
[ROW][C]124[/C][C]121.347933622955[/C][C]112.213061662217[/C][C]130.482805583693[/C][/ROW]
[ROW][C]125[/C][C]123.568312033555[/C][C]113.282557845985[/C][C]133.854066221126[/C][/ROW]
[ROW][C]126[/C][C]125.80121596206[/C][C]114.446196465922[/C][C]137.156235458198[/C][/ROW]
[ROW][C]127[/C][C]126.026314988704[/C][C]113.661900214874[/C][C]138.390729762535[/C][/ROW]
[ROW][C]128[/C][C]121.342936895361[/C][C]108.014873444857[/C][C]134.671000345865[/C][/ROW]
[ROW][C]129[/C][C]119.160101683363[/C][C]104.904375921752[/C][C]133.415827444974[/C][/ROW]
[ROW][C]130[/C][C]118.803598251974[/C][C]103.649134917474[/C][C]133.958061586475[/C][/ROW]
[ROW][C]131[/C][C]117.46176781371[/C][C]101.432198806759[/C][C]133.491336820661[/C][/ROW]
[ROW][C]132[/C][C]118.053234038856[/C][C]101.168111324628[/C][C]134.938356753083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160933&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160933&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
121116.60000457811112.018545995502121.181463160719
122116.773570773271110.366069012352123.18107253419
123118.657148723869110.791385820948126.52291162679
124121.347933622955112.213061662217130.482805583693
125123.568312033555113.282557845985133.854066221126
126125.80121596206114.446196465922137.156235458198
127126.026314988704113.661900214874138.390729762535
128121.342936895361108.014873444857134.671000345865
129119.160101683363104.904375921752133.415827444974
130118.803598251974103.649134917474133.958061586475
131117.46176781371101.432198806759133.491336820661
132118.053234038856101.168111324628134.938356753083



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