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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 10 Jan 2014 07:43:38 -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/2014/Jan/10/t1389357855ukslc6t4362uz2q.htm/, Retrieved Mon, 06 May 2024 12:05:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232859, Retrieved Mon, 06 May 2024 12:05:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2013-12-14 09:37:21] [2f0f353a58a70fd7baf0f5141860d820]
- R PD    [Exponential Smoothing] [] [2014-01-10 12:43:38] [998078bdc1a977f0c7d195eebcf8b96b] [Current]
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Dataseries X:
55.7
59.2
59.8
61.6
65.8
64.2
67
62.8
65.5
75.2
80.9
83.2
83.7
86.4
85.9
80.4
81.8
87.5
83.7
87
99.7
101.4
101.9
115.7
123.2
136.9
146.8
149.6
146.5
157
147.9
133.6
128.7
100.8
91.8
89.3
96.7
91.6
93.3
93.3
101
100.4
86.9
83.9
80.3
87.7
92.7
95.5
92
87.4
86.8
83.7
85
81.7
90.9
101.5
113.8
120.1
122.1
132.5
140
149.4
144.3
154.4
151.4
145.5
136.8
146.6
145.1
133.6
131.4
127.5
130.1
131.1
132.3
128.6
125.1
128.7
156.1
163.2
159.8
157.4
156.2
152.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232859&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232859&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232859&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.272905598557063
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.272905598557063 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232859&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]0.272905598557063[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232859&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232859&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
beta0.272905598557063
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
359.862.7-2.90000000000001
461.662.5085737641845-0.90857376418451
565.864.06061889723651.7393811027635
664.268.735305738205-4.53530573820501
76765.89759541108091.1024045889191
862.868.9984477952719-6.19844779527192
965.563.10685668957852.39314331042148
1075.266.45995889714198.74004110285807
1180.978.54516504573082.35483495426925
1283.284.8878126884287-1.68781268842869
1383.786.7271991564409-3.02719915644086
1486.486.4010595587009-0.00105955870091634
1585.989.1007703991994-3.20077039919944
1680.487.7272622375622-7.32726223756219
1781.880.22761135083571.57238864916428
1887.582.05672501630025.44327498369978
1983.789.2422252338375-5.5422252338375
208783.9297209390593.07027906094098
2199.788.067617283922311.6323827160777
22101.4103.942159651698-2.54215965169834
23101.9104.948390050324-3.048390050324
24115.7104.61646733900511.0835326609951
25123.2121.4412254539811.75877454601945
26136.9129.4212048741897.4787951258111
27146.8145.1622099344841.63779006551596
28149.6155.509172012625-5.90917201262451
29146.5156.696525887543-10.1965258875425
30157150.8138368876.18616311299985
31147.9163.002075434125-15.102075434125
32133.6149.780634498321-16.1806344983212
33128.7131.064848755524-2.36484875552378
34100.8125.519468290401-24.7194682904006
3591.890.87338700059650.926612999403488
3689.382.12626487582957.17373512417052
3796.781.584017353781115.1159826462189
3891.693.1092536456256-1.50925364562563
3993.387.59736987609175.70263012390828
4093.390.85364956340642.44635043659355
4110191.52127229358539.47872770641466
42100.4101.808070151864-1.40807015186385
4386.9100.823799924259-13.9237999242591
4483.983.52391697174040.3760830282596
4580.380.6265521356747-0.326552135674746
4687.776.937434229628310.7625657703717
4792.787.27459868320145.42540131679863
4895.593.75522107697461.74477892302542
499297.0313810133126-5.03138101331258
5087.492.1582889663059-4.75828896630586
5186.886.25972526784870.540274732151289
5283.785.8071692670117-2.1071692670117
538582.13211097693682.86788902306317
5481.784.2147739473711-2.51477394737111
5590.980.228478058028110.6715219419719
56101.592.34079614111689.15920385888323
57113.8105.4403941525318.35960584746854
58120.1120.0217773900360.0782226099640155
59122.1126.343124778229-4.24312477822892
60132.5127.1851522708745.31484772912596
61140139.0356039716310.96439602836918
62149.4146.7987930469992.60120695300105
63144.3156.908676987479-12.6086769874785
64154.4148.3676984471986.03230155280198
65151.4160.113947313142-8.71394731314214
66145.5154.735862305854-9.23586230585437
67136.8146.315343775085-9.51534377508455
68146.6135.01855318666911.5814468133311
69145.1147.979194861418-2.8791948614178
70133.6145.6934464644-12.0934464644002
71131.4130.8930772184150.506922781584791
72127.5128.831419283546-1.33141928354584
73130.1124.5680675070395.53193249296065
74131.1128.6777628552082.42223714479195
75132.3130.3388049330551.96119506694538
76128.6132.074026046687-3.47402604668653
77125.1127.425944889013-2.3259448890127
78128.7123.2911815068665.40881849313404
79156.1128.36727835522127.7327216447788
80163.2163.335693355306-0.135693355305989
81159.8170.398661878956-10.598661878956
82157.4164.106227714976-6.7062277149756
83156.2159.87606062636-3.67606062636023
84152.5157.672843100791-5.17284310079131

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 59.8 & 62.7 & -2.90000000000001 \tabularnewline
4 & 61.6 & 62.5085737641845 & -0.90857376418451 \tabularnewline
5 & 65.8 & 64.0606188972365 & 1.7393811027635 \tabularnewline
6 & 64.2 & 68.735305738205 & -4.53530573820501 \tabularnewline
7 & 67 & 65.8975954110809 & 1.1024045889191 \tabularnewline
8 & 62.8 & 68.9984477952719 & -6.19844779527192 \tabularnewline
9 & 65.5 & 63.1068566895785 & 2.39314331042148 \tabularnewline
10 & 75.2 & 66.4599588971419 & 8.74004110285807 \tabularnewline
11 & 80.9 & 78.5451650457308 & 2.35483495426925 \tabularnewline
12 & 83.2 & 84.8878126884287 & -1.68781268842869 \tabularnewline
13 & 83.7 & 86.7271991564409 & -3.02719915644086 \tabularnewline
14 & 86.4 & 86.4010595587009 & -0.00105955870091634 \tabularnewline
15 & 85.9 & 89.1007703991994 & -3.20077039919944 \tabularnewline
16 & 80.4 & 87.7272622375622 & -7.32726223756219 \tabularnewline
17 & 81.8 & 80.2276113508357 & 1.57238864916428 \tabularnewline
18 & 87.5 & 82.0567250163002 & 5.44327498369978 \tabularnewline
19 & 83.7 & 89.2422252338375 & -5.5422252338375 \tabularnewline
20 & 87 & 83.929720939059 & 3.07027906094098 \tabularnewline
21 & 99.7 & 88.0676172839223 & 11.6323827160777 \tabularnewline
22 & 101.4 & 103.942159651698 & -2.54215965169834 \tabularnewline
23 & 101.9 & 104.948390050324 & -3.048390050324 \tabularnewline
24 & 115.7 & 104.616467339005 & 11.0835326609951 \tabularnewline
25 & 123.2 & 121.441225453981 & 1.75877454601945 \tabularnewline
26 & 136.9 & 129.421204874189 & 7.4787951258111 \tabularnewline
27 & 146.8 & 145.162209934484 & 1.63779006551596 \tabularnewline
28 & 149.6 & 155.509172012625 & -5.90917201262451 \tabularnewline
29 & 146.5 & 156.696525887543 & -10.1965258875425 \tabularnewline
30 & 157 & 150.813836887 & 6.18616311299985 \tabularnewline
31 & 147.9 & 163.002075434125 & -15.102075434125 \tabularnewline
32 & 133.6 & 149.780634498321 & -16.1806344983212 \tabularnewline
33 & 128.7 & 131.064848755524 & -2.36484875552378 \tabularnewline
34 & 100.8 & 125.519468290401 & -24.7194682904006 \tabularnewline
35 & 91.8 & 90.8733870005965 & 0.926612999403488 \tabularnewline
36 & 89.3 & 82.1262648758295 & 7.17373512417052 \tabularnewline
37 & 96.7 & 81.5840173537811 & 15.1159826462189 \tabularnewline
38 & 91.6 & 93.1092536456256 & -1.50925364562563 \tabularnewline
39 & 93.3 & 87.5973698760917 & 5.70263012390828 \tabularnewline
40 & 93.3 & 90.8536495634064 & 2.44635043659355 \tabularnewline
41 & 101 & 91.5212722935853 & 9.47872770641466 \tabularnewline
42 & 100.4 & 101.808070151864 & -1.40807015186385 \tabularnewline
43 & 86.9 & 100.823799924259 & -13.9237999242591 \tabularnewline
44 & 83.9 & 83.5239169717404 & 0.3760830282596 \tabularnewline
45 & 80.3 & 80.6265521356747 & -0.326552135674746 \tabularnewline
46 & 87.7 & 76.9374342296283 & 10.7625657703717 \tabularnewline
47 & 92.7 & 87.2745986832014 & 5.42540131679863 \tabularnewline
48 & 95.5 & 93.7552210769746 & 1.74477892302542 \tabularnewline
49 & 92 & 97.0313810133126 & -5.03138101331258 \tabularnewline
50 & 87.4 & 92.1582889663059 & -4.75828896630586 \tabularnewline
51 & 86.8 & 86.2597252678487 & 0.540274732151289 \tabularnewline
52 & 83.7 & 85.8071692670117 & -2.1071692670117 \tabularnewline
53 & 85 & 82.1321109769368 & 2.86788902306317 \tabularnewline
54 & 81.7 & 84.2147739473711 & -2.51477394737111 \tabularnewline
55 & 90.9 & 80.2284780580281 & 10.6715219419719 \tabularnewline
56 & 101.5 & 92.3407961411168 & 9.15920385888323 \tabularnewline
57 & 113.8 & 105.440394152531 & 8.35960584746854 \tabularnewline
58 & 120.1 & 120.021777390036 & 0.0782226099640155 \tabularnewline
59 & 122.1 & 126.343124778229 & -4.24312477822892 \tabularnewline
60 & 132.5 & 127.185152270874 & 5.31484772912596 \tabularnewline
61 & 140 & 139.035603971631 & 0.96439602836918 \tabularnewline
62 & 149.4 & 146.798793046999 & 2.60120695300105 \tabularnewline
63 & 144.3 & 156.908676987479 & -12.6086769874785 \tabularnewline
64 & 154.4 & 148.367698447198 & 6.03230155280198 \tabularnewline
65 & 151.4 & 160.113947313142 & -8.71394731314214 \tabularnewline
66 & 145.5 & 154.735862305854 & -9.23586230585437 \tabularnewline
67 & 136.8 & 146.315343775085 & -9.51534377508455 \tabularnewline
68 & 146.6 & 135.018553186669 & 11.5814468133311 \tabularnewline
69 & 145.1 & 147.979194861418 & -2.8791948614178 \tabularnewline
70 & 133.6 & 145.6934464644 & -12.0934464644002 \tabularnewline
71 & 131.4 & 130.893077218415 & 0.506922781584791 \tabularnewline
72 & 127.5 & 128.831419283546 & -1.33141928354584 \tabularnewline
73 & 130.1 & 124.568067507039 & 5.53193249296065 \tabularnewline
74 & 131.1 & 128.677762855208 & 2.42223714479195 \tabularnewline
75 & 132.3 & 130.338804933055 & 1.96119506694538 \tabularnewline
76 & 128.6 & 132.074026046687 & -3.47402604668653 \tabularnewline
77 & 125.1 & 127.425944889013 & -2.3259448890127 \tabularnewline
78 & 128.7 & 123.291181506866 & 5.40881849313404 \tabularnewline
79 & 156.1 & 128.367278355221 & 27.7327216447788 \tabularnewline
80 & 163.2 & 163.335693355306 & -0.135693355305989 \tabularnewline
81 & 159.8 & 170.398661878956 & -10.598661878956 \tabularnewline
82 & 157.4 & 164.106227714976 & -6.7062277149756 \tabularnewline
83 & 156.2 & 159.87606062636 & -3.67606062636023 \tabularnewline
84 & 152.5 & 157.672843100791 & -5.17284310079131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232859&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]59.8[/C][C]62.7[/C][C]-2.90000000000001[/C][/ROW]
[ROW][C]4[/C][C]61.6[/C][C]62.5085737641845[/C][C]-0.90857376418451[/C][/ROW]
[ROW][C]5[/C][C]65.8[/C][C]64.0606188972365[/C][C]1.7393811027635[/C][/ROW]
[ROW][C]6[/C][C]64.2[/C][C]68.735305738205[/C][C]-4.53530573820501[/C][/ROW]
[ROW][C]7[/C][C]67[/C][C]65.8975954110809[/C][C]1.1024045889191[/C][/ROW]
[ROW][C]8[/C][C]62.8[/C][C]68.9984477952719[/C][C]-6.19844779527192[/C][/ROW]
[ROW][C]9[/C][C]65.5[/C][C]63.1068566895785[/C][C]2.39314331042148[/C][/ROW]
[ROW][C]10[/C][C]75.2[/C][C]66.4599588971419[/C][C]8.74004110285807[/C][/ROW]
[ROW][C]11[/C][C]80.9[/C][C]78.5451650457308[/C][C]2.35483495426925[/C][/ROW]
[ROW][C]12[/C][C]83.2[/C][C]84.8878126884287[/C][C]-1.68781268842869[/C][/ROW]
[ROW][C]13[/C][C]83.7[/C][C]86.7271991564409[/C][C]-3.02719915644086[/C][/ROW]
[ROW][C]14[/C][C]86.4[/C][C]86.4010595587009[/C][C]-0.00105955870091634[/C][/ROW]
[ROW][C]15[/C][C]85.9[/C][C]89.1007703991994[/C][C]-3.20077039919944[/C][/ROW]
[ROW][C]16[/C][C]80.4[/C][C]87.7272622375622[/C][C]-7.32726223756219[/C][/ROW]
[ROW][C]17[/C][C]81.8[/C][C]80.2276113508357[/C][C]1.57238864916428[/C][/ROW]
[ROW][C]18[/C][C]87.5[/C][C]82.0567250163002[/C][C]5.44327498369978[/C][/ROW]
[ROW][C]19[/C][C]83.7[/C][C]89.2422252338375[/C][C]-5.5422252338375[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]83.929720939059[/C][C]3.07027906094098[/C][/ROW]
[ROW][C]21[/C][C]99.7[/C][C]88.0676172839223[/C][C]11.6323827160777[/C][/ROW]
[ROW][C]22[/C][C]101.4[/C][C]103.942159651698[/C][C]-2.54215965169834[/C][/ROW]
[ROW][C]23[/C][C]101.9[/C][C]104.948390050324[/C][C]-3.048390050324[/C][/ROW]
[ROW][C]24[/C][C]115.7[/C][C]104.616467339005[/C][C]11.0835326609951[/C][/ROW]
[ROW][C]25[/C][C]123.2[/C][C]121.441225453981[/C][C]1.75877454601945[/C][/ROW]
[ROW][C]26[/C][C]136.9[/C][C]129.421204874189[/C][C]7.4787951258111[/C][/ROW]
[ROW][C]27[/C][C]146.8[/C][C]145.162209934484[/C][C]1.63779006551596[/C][/ROW]
[ROW][C]28[/C][C]149.6[/C][C]155.509172012625[/C][C]-5.90917201262451[/C][/ROW]
[ROW][C]29[/C][C]146.5[/C][C]156.696525887543[/C][C]-10.1965258875425[/C][/ROW]
[ROW][C]30[/C][C]157[/C][C]150.813836887[/C][C]6.18616311299985[/C][/ROW]
[ROW][C]31[/C][C]147.9[/C][C]163.002075434125[/C][C]-15.102075434125[/C][/ROW]
[ROW][C]32[/C][C]133.6[/C][C]149.780634498321[/C][C]-16.1806344983212[/C][/ROW]
[ROW][C]33[/C][C]128.7[/C][C]131.064848755524[/C][C]-2.36484875552378[/C][/ROW]
[ROW][C]34[/C][C]100.8[/C][C]125.519468290401[/C][C]-24.7194682904006[/C][/ROW]
[ROW][C]35[/C][C]91.8[/C][C]90.8733870005965[/C][C]0.926612999403488[/C][/ROW]
[ROW][C]36[/C][C]89.3[/C][C]82.1262648758295[/C][C]7.17373512417052[/C][/ROW]
[ROW][C]37[/C][C]96.7[/C][C]81.5840173537811[/C][C]15.1159826462189[/C][/ROW]
[ROW][C]38[/C][C]91.6[/C][C]93.1092536456256[/C][C]-1.50925364562563[/C][/ROW]
[ROW][C]39[/C][C]93.3[/C][C]87.5973698760917[/C][C]5.70263012390828[/C][/ROW]
[ROW][C]40[/C][C]93.3[/C][C]90.8536495634064[/C][C]2.44635043659355[/C][/ROW]
[ROW][C]41[/C][C]101[/C][C]91.5212722935853[/C][C]9.47872770641466[/C][/ROW]
[ROW][C]42[/C][C]100.4[/C][C]101.808070151864[/C][C]-1.40807015186385[/C][/ROW]
[ROW][C]43[/C][C]86.9[/C][C]100.823799924259[/C][C]-13.9237999242591[/C][/ROW]
[ROW][C]44[/C][C]83.9[/C][C]83.5239169717404[/C][C]0.3760830282596[/C][/ROW]
[ROW][C]45[/C][C]80.3[/C][C]80.6265521356747[/C][C]-0.326552135674746[/C][/ROW]
[ROW][C]46[/C][C]87.7[/C][C]76.9374342296283[/C][C]10.7625657703717[/C][/ROW]
[ROW][C]47[/C][C]92.7[/C][C]87.2745986832014[/C][C]5.42540131679863[/C][/ROW]
[ROW][C]48[/C][C]95.5[/C][C]93.7552210769746[/C][C]1.74477892302542[/C][/ROW]
[ROW][C]49[/C][C]92[/C][C]97.0313810133126[/C][C]-5.03138101331258[/C][/ROW]
[ROW][C]50[/C][C]87.4[/C][C]92.1582889663059[/C][C]-4.75828896630586[/C][/ROW]
[ROW][C]51[/C][C]86.8[/C][C]86.2597252678487[/C][C]0.540274732151289[/C][/ROW]
[ROW][C]52[/C][C]83.7[/C][C]85.8071692670117[/C][C]-2.1071692670117[/C][/ROW]
[ROW][C]53[/C][C]85[/C][C]82.1321109769368[/C][C]2.86788902306317[/C][/ROW]
[ROW][C]54[/C][C]81.7[/C][C]84.2147739473711[/C][C]-2.51477394737111[/C][/ROW]
[ROW][C]55[/C][C]90.9[/C][C]80.2284780580281[/C][C]10.6715219419719[/C][/ROW]
[ROW][C]56[/C][C]101.5[/C][C]92.3407961411168[/C][C]9.15920385888323[/C][/ROW]
[ROW][C]57[/C][C]113.8[/C][C]105.440394152531[/C][C]8.35960584746854[/C][/ROW]
[ROW][C]58[/C][C]120.1[/C][C]120.021777390036[/C][C]0.0782226099640155[/C][/ROW]
[ROW][C]59[/C][C]122.1[/C][C]126.343124778229[/C][C]-4.24312477822892[/C][/ROW]
[ROW][C]60[/C][C]132.5[/C][C]127.185152270874[/C][C]5.31484772912596[/C][/ROW]
[ROW][C]61[/C][C]140[/C][C]139.035603971631[/C][C]0.96439602836918[/C][/ROW]
[ROW][C]62[/C][C]149.4[/C][C]146.798793046999[/C][C]2.60120695300105[/C][/ROW]
[ROW][C]63[/C][C]144.3[/C][C]156.908676987479[/C][C]-12.6086769874785[/C][/ROW]
[ROW][C]64[/C][C]154.4[/C][C]148.367698447198[/C][C]6.03230155280198[/C][/ROW]
[ROW][C]65[/C][C]151.4[/C][C]160.113947313142[/C][C]-8.71394731314214[/C][/ROW]
[ROW][C]66[/C][C]145.5[/C][C]154.735862305854[/C][C]-9.23586230585437[/C][/ROW]
[ROW][C]67[/C][C]136.8[/C][C]146.315343775085[/C][C]-9.51534377508455[/C][/ROW]
[ROW][C]68[/C][C]146.6[/C][C]135.018553186669[/C][C]11.5814468133311[/C][/ROW]
[ROW][C]69[/C][C]145.1[/C][C]147.979194861418[/C][C]-2.8791948614178[/C][/ROW]
[ROW][C]70[/C][C]133.6[/C][C]145.6934464644[/C][C]-12.0934464644002[/C][/ROW]
[ROW][C]71[/C][C]131.4[/C][C]130.893077218415[/C][C]0.506922781584791[/C][/ROW]
[ROW][C]72[/C][C]127.5[/C][C]128.831419283546[/C][C]-1.33141928354584[/C][/ROW]
[ROW][C]73[/C][C]130.1[/C][C]124.568067507039[/C][C]5.53193249296065[/C][/ROW]
[ROW][C]74[/C][C]131.1[/C][C]128.677762855208[/C][C]2.42223714479195[/C][/ROW]
[ROW][C]75[/C][C]132.3[/C][C]130.338804933055[/C][C]1.96119506694538[/C][/ROW]
[ROW][C]76[/C][C]128.6[/C][C]132.074026046687[/C][C]-3.47402604668653[/C][/ROW]
[ROW][C]77[/C][C]125.1[/C][C]127.425944889013[/C][C]-2.3259448890127[/C][/ROW]
[ROW][C]78[/C][C]128.7[/C][C]123.291181506866[/C][C]5.40881849313404[/C][/ROW]
[ROW][C]79[/C][C]156.1[/C][C]128.367278355221[/C][C]27.7327216447788[/C][/ROW]
[ROW][C]80[/C][C]163.2[/C][C]163.335693355306[/C][C]-0.135693355305989[/C][/ROW]
[ROW][C]81[/C][C]159.8[/C][C]170.398661878956[/C][C]-10.598661878956[/C][/ROW]
[ROW][C]82[/C][C]157.4[/C][C]164.106227714976[/C][C]-6.7062277149756[/C][/ROW]
[ROW][C]83[/C][C]156.2[/C][C]159.87606062636[/C][C]-3.67606062636023[/C][/ROW]
[ROW][C]84[/C][C]152.5[/C][C]157.672843100791[/C][C]-5.17284310079131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232859&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232859&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
359.862.7-2.90000000000001
461.662.5085737641845-0.90857376418451
565.864.06061889723651.7393811027635
664.268.735305738205-4.53530573820501
76765.89759541108091.1024045889191
862.868.9984477952719-6.19844779527192
965.563.10685668957852.39314331042148
1075.266.45995889714198.74004110285807
1180.978.54516504573082.35483495426925
1283.284.8878126884287-1.68781268842869
1383.786.7271991564409-3.02719915644086
1486.486.4010595587009-0.00105955870091634
1585.989.1007703991994-3.20077039919944
1680.487.7272622375622-7.32726223756219
1781.880.22761135083571.57238864916428
1887.582.05672501630025.44327498369978
1983.789.2422252338375-5.5422252338375
208783.9297209390593.07027906094098
2199.788.067617283922311.6323827160777
22101.4103.942159651698-2.54215965169834
23101.9104.948390050324-3.048390050324
24115.7104.61646733900511.0835326609951
25123.2121.4412254539811.75877454601945
26136.9129.4212048741897.4787951258111
27146.8145.1622099344841.63779006551596
28149.6155.509172012625-5.90917201262451
29146.5156.696525887543-10.1965258875425
30157150.8138368876.18616311299985
31147.9163.002075434125-15.102075434125
32133.6149.780634498321-16.1806344983212
33128.7131.064848755524-2.36484875552378
34100.8125.519468290401-24.7194682904006
3591.890.87338700059650.926612999403488
3689.382.12626487582957.17373512417052
3796.781.584017353781115.1159826462189
3891.693.1092536456256-1.50925364562563
3993.387.59736987609175.70263012390828
4093.390.85364956340642.44635043659355
4110191.52127229358539.47872770641466
42100.4101.808070151864-1.40807015186385
4386.9100.823799924259-13.9237999242591
4483.983.52391697174040.3760830282596
4580.380.6265521356747-0.326552135674746
4687.776.937434229628310.7625657703717
4792.787.27459868320145.42540131679863
4895.593.75522107697461.74477892302542
499297.0313810133126-5.03138101331258
5087.492.1582889663059-4.75828896630586
5186.886.25972526784870.540274732151289
5283.785.8071692670117-2.1071692670117
538582.13211097693682.86788902306317
5481.784.2147739473711-2.51477394737111
5590.980.228478058028110.6715219419719
56101.592.34079614111689.15920385888323
57113.8105.4403941525318.35960584746854
58120.1120.0217773900360.0782226099640155
59122.1126.343124778229-4.24312477822892
60132.5127.1851522708745.31484772912596
61140139.0356039716310.96439602836918
62149.4146.7987930469992.60120695300105
63144.3156.908676987479-12.6086769874785
64154.4148.3676984471986.03230155280198
65151.4160.113947313142-8.71394731314214
66145.5154.735862305854-9.23586230585437
67136.8146.315343775085-9.51534377508455
68146.6135.01855318666911.5814468133311
69145.1147.979194861418-2.8791948614178
70133.6145.6934464644-12.0934464644002
71131.4130.8930772184150.506922781584791
72127.5128.831419283546-1.33141928354584
73130.1124.5680675070395.53193249296065
74131.1128.6777628552082.42223714479195
75132.3130.3388049330551.96119506694538
76128.6132.074026046687-3.47402604668653
77125.1127.425944889013-2.3259448890127
78128.7123.2911815068665.40881849313404
79156.1128.36727835522127.7327216447788
80163.2163.335693355306-0.135693355305989
81159.8170.398661878956-10.598661878956
82157.4164.106227714976-6.7062277149756
83156.2159.87606062636-3.67606062636023
84152.5157.672843100791-5.17284310079131







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85152.561145258128137.376229026137167.746061490119
86152.622290516256128.042002387136177.202578645376
87152.683435774384118.695600758069186.6712707907
88152.744581032512108.951030671619196.538131393405
89152.8057262906498.7072677604726206.904184820808
90152.86687154876987.9374968870389217.796246210498
91152.92801680689776.6406471605174229.215386453276
92152.98916206502564.8256394798717241.152684650178
93153.05030732315352.5052835098181253.595331136488
94153.11145258128139.6936658675145266.529239295047
95153.17259783940926.4049734971457279.940222181672
96153.23374309753712.652959179173293.814527015901

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 152.561145258128 & 137.376229026137 & 167.746061490119 \tabularnewline
86 & 152.622290516256 & 128.042002387136 & 177.202578645376 \tabularnewline
87 & 152.683435774384 & 118.695600758069 & 186.6712707907 \tabularnewline
88 & 152.744581032512 & 108.951030671619 & 196.538131393405 \tabularnewline
89 & 152.80572629064 & 98.7072677604726 & 206.904184820808 \tabularnewline
90 & 152.866871548769 & 87.9374968870389 & 217.796246210498 \tabularnewline
91 & 152.928016806897 & 76.6406471605174 & 229.215386453276 \tabularnewline
92 & 152.989162065025 & 64.8256394798717 & 241.152684650178 \tabularnewline
93 & 153.050307323153 & 52.5052835098181 & 253.595331136488 \tabularnewline
94 & 153.111452581281 & 39.6936658675145 & 266.529239295047 \tabularnewline
95 & 153.172597839409 & 26.4049734971457 & 279.940222181672 \tabularnewline
96 & 153.233743097537 & 12.652959179173 & 293.814527015901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232859&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]85[/C][C]152.561145258128[/C][C]137.376229026137[/C][C]167.746061490119[/C][/ROW]
[ROW][C]86[/C][C]152.622290516256[/C][C]128.042002387136[/C][C]177.202578645376[/C][/ROW]
[ROW][C]87[/C][C]152.683435774384[/C][C]118.695600758069[/C][C]186.6712707907[/C][/ROW]
[ROW][C]88[/C][C]152.744581032512[/C][C]108.951030671619[/C][C]196.538131393405[/C][/ROW]
[ROW][C]89[/C][C]152.80572629064[/C][C]98.7072677604726[/C][C]206.904184820808[/C][/ROW]
[ROW][C]90[/C][C]152.866871548769[/C][C]87.9374968870389[/C][C]217.796246210498[/C][/ROW]
[ROW][C]91[/C][C]152.928016806897[/C][C]76.6406471605174[/C][C]229.215386453276[/C][/ROW]
[ROW][C]92[/C][C]152.989162065025[/C][C]64.8256394798717[/C][C]241.152684650178[/C][/ROW]
[ROW][C]93[/C][C]153.050307323153[/C][C]52.5052835098181[/C][C]253.595331136488[/C][/ROW]
[ROW][C]94[/C][C]153.111452581281[/C][C]39.6936658675145[/C][C]266.529239295047[/C][/ROW]
[ROW][C]95[/C][C]153.172597839409[/C][C]26.4049734971457[/C][C]279.940222181672[/C][/ROW]
[ROW][C]96[/C][C]153.233743097537[/C][C]12.652959179173[/C][C]293.814527015901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232859&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232859&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
85152.561145258128137.376229026137167.746061490119
86152.622290516256128.042002387136177.202578645376
87152.683435774384118.695600758069186.6712707907
88152.744581032512108.951030671619196.538131393405
89152.8057262906498.7072677604726206.904184820808
90152.86687154876987.9374968870389217.796246210498
91152.92801680689776.6406471605174229.215386453276
92152.98916206502564.8256394798717241.152684650178
93153.05030732315352.5052835098181253.595331136488
94153.11145258128139.6936658675145266.529239295047
95153.17259783940926.4049734971457279.940222181672
96153.23374309753712.652959179173293.814527015901



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')