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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Jan 2009 07:07:31 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/16/t1232114947ew5hztryhjohrfo.htm/, Retrieved Sun, 05 May 2024 08:15:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36920, Retrieved Sun, 05 May 2024 08:15:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10-2 - Con...] [2009-01-16 14:07:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105,6
110,2
104,9
102,9
102,6
103,6
107,8
106,6
106
105,2
107,9
107,5
107,5
113,3
107,8
104,5
105,1
104,2
106,6
103,8
107,7
106,4
110
113,2
113,9
112
113,9
113,1
111,7
110,7
113,5
114
112,7
112,2
115,8
118,4
118,8
123,9
118
120,2
118,7
119,8
124,8
121,3
120,2
118,3
129,6
130,2
127,19
133,1
129,12
123,28
123,36
124,13
126,96
127,14
123,7
123,67
130,19
134,01
124,96
129,96
128,32
132,38
126,25
128,91
131,42
129,44
126,86
126,71
131,63
132,78
126,61
132,84
123,14
128,13
125,49
126,48
130,86
127,32
126,56
126,64
129,26
126,47
135,38
135,5
132,22
122,62
125,16
128,5
133,86
128,87
125,07
125,25
132,16
130,24

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36920&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36920&T=0

As an alternative you can also use a QR Code:  
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' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.208653452026953
beta0.135928514801665
gamma0.144824151716476

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.208653452026953 \tabularnewline
beta & 0.135928514801665 \tabularnewline
gamma & 0.144824151716476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36920&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]0.208653452026953[/C][/ROW]
[ROW][C]beta[/C][C]0.135928514801665[/C][/ROW]
[ROW][C]gamma[/C][C]0.144824151716476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36920&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.208653452026953
beta0.135928514801665
gamma0.144824151716476






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13107.5106.5763087606840.923691239316184
14113.3112.8448735955540.455126404446062
15107.8107.6077457008720.192254299128066
16104.5104.3545546748650.145445325135029
17105.1104.9790552417800.120944758220134
18104.2103.9143739104810.285626089518516
19106.6109.008821488077-2.40882148807660
20103.8107.172744393442-3.37274439344178
21107.7105.5982171696392.10178283036056
22106.4105.0880796169201.31192038307984
23110107.9670098299662.03299017003442
24113.2107.9957199832425.20428001675758
25113.9109.4937615703374.40623842966316
26112116.732364194594-4.73236419459447
27113.9110.5326870464083.36731295359249
28113.1108.1766345546094.92336544539111
29111.7110.1707840629691.52921593703110
30110.7109.8342855096650.86571449033454
31113.5115.172891517895-1.67289151789539
32114113.8326908178590.167309182141238
33112.7114.177418506156-1.47741850615607
34112.2113.281628386918-1.08162838691824
35115.8116.127572854054-0.327572854054125
36118.4116.3440398185162.05596018148393
37118.8117.3212679713731.47873202862695
38123.9123.0462217353550.853778264645186
39118119.243343752074-1.24334375207384
40120.2116.2757865943173.92421340568275
41118.7117.8163231398090.883676860191187
42119.8117.3946343439262.40536565607441
43124.8122.9327667054501.86723329454969
44121.3122.811740874061-1.51174087406100
45120.2122.839629412424-2.63962941242441
46118.3121.935733616598-3.63573361659770
47129.6124.4517688362185.14823116378203
48130.2126.3558473873623.84415261263807
49127.19127.9626496001-0.772649600100024
50133.1133.404983124011-0.30498312401059
51129.12129.345879697500-0.225879697500488
52123.28127.437607809812-4.15760780981222
53123.36126.968918556119-3.60891855611925
54124.13125.682348349915-1.55234834991494
55126.96130.118887597700-3.15888759769963
56127.14128.205213479842-1.06521347984237
57123.7127.852993205802-4.15299320580236
58123.67126.132231869226-2.46223186922607
59130.19129.5461636116340.643836388366424
60134.01129.8795213116874.13047868831259
61124.96130.543665569088-5.58366556908798
62129.96134.42602440002-4.46602440002013
63128.32128.780018790534-0.460018790534349
64132.38125.6379000435356.7420999564651
65126.25127.081099647821-0.83109964782112
66128.91126.2633548680172.64664513198268
67131.42131.1645295212250.255470478774669
68129.44130.072678784374-0.632678784374292
69126.86129.338555499994-2.47855549999376
70126.71128.090158747334-1.38015874733365
71131.63132.045748662242-0.415748662241555
72132.78132.4874643656550.292535634345285
73126.61131.058510508721-4.44851050872084
74132.84135.159009132355-2.31900913235461
75123.14130.334189151014-7.19418915101356
76128.13126.3354658017791.79453419822060
77125.49125.4611778877890.0288221122108894
78126.48124.8285925238271.65140747617325
79130.86128.8270003686892.03299963131099
80127.32127.633600256416-0.313600256415839
81126.56126.3929051286360.167094871364441
82126.64125.5358512703261.10414872967354
83129.26129.904223453292-0.64422345329163
84126.47130.156856472641-3.68685647264132
85135.38127.0187882815878.36121171841295
86135.5134.0639945886301.43600541136965
87132.22129.5983066605672.62169333943251
88122.62129.090621782214-6.47062178221364
89125.16126.467761450972-1.30776145097161
90128.5125.8826856319612.61731436803927
91133.86130.2941952276503.56580477234968
92128.87129.362988061814-0.49298806181406
93125.07128.346168357144-3.27616835714363
94125.25126.986614866068-1.73661486606794
95132.16130.5898652531571.57013474684348
96130.24131.046618437654-0.806618437653555

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 107.5 & 106.576308760684 & 0.923691239316184 \tabularnewline
14 & 113.3 & 112.844873595554 & 0.455126404446062 \tabularnewline
15 & 107.8 & 107.607745700872 & 0.192254299128066 \tabularnewline
16 & 104.5 & 104.354554674865 & 0.145445325135029 \tabularnewline
17 & 105.1 & 104.979055241780 & 0.120944758220134 \tabularnewline
18 & 104.2 & 103.914373910481 & 0.285626089518516 \tabularnewline
19 & 106.6 & 109.008821488077 & -2.40882148807660 \tabularnewline
20 & 103.8 & 107.172744393442 & -3.37274439344178 \tabularnewline
21 & 107.7 & 105.598217169639 & 2.10178283036056 \tabularnewline
22 & 106.4 & 105.088079616920 & 1.31192038307984 \tabularnewline
23 & 110 & 107.967009829966 & 2.03299017003442 \tabularnewline
24 & 113.2 & 107.995719983242 & 5.20428001675758 \tabularnewline
25 & 113.9 & 109.493761570337 & 4.40623842966316 \tabularnewline
26 & 112 & 116.732364194594 & -4.73236419459447 \tabularnewline
27 & 113.9 & 110.532687046408 & 3.36731295359249 \tabularnewline
28 & 113.1 & 108.176634554609 & 4.92336544539111 \tabularnewline
29 & 111.7 & 110.170784062969 & 1.52921593703110 \tabularnewline
30 & 110.7 & 109.834285509665 & 0.86571449033454 \tabularnewline
31 & 113.5 & 115.172891517895 & -1.67289151789539 \tabularnewline
32 & 114 & 113.832690817859 & 0.167309182141238 \tabularnewline
33 & 112.7 & 114.177418506156 & -1.47741850615607 \tabularnewline
34 & 112.2 & 113.281628386918 & -1.08162838691824 \tabularnewline
35 & 115.8 & 116.127572854054 & -0.327572854054125 \tabularnewline
36 & 118.4 & 116.344039818516 & 2.05596018148393 \tabularnewline
37 & 118.8 & 117.321267971373 & 1.47873202862695 \tabularnewline
38 & 123.9 & 123.046221735355 & 0.853778264645186 \tabularnewline
39 & 118 & 119.243343752074 & -1.24334375207384 \tabularnewline
40 & 120.2 & 116.275786594317 & 3.92421340568275 \tabularnewline
41 & 118.7 & 117.816323139809 & 0.883676860191187 \tabularnewline
42 & 119.8 & 117.394634343926 & 2.40536565607441 \tabularnewline
43 & 124.8 & 122.932766705450 & 1.86723329454969 \tabularnewline
44 & 121.3 & 122.811740874061 & -1.51174087406100 \tabularnewline
45 & 120.2 & 122.839629412424 & -2.63962941242441 \tabularnewline
46 & 118.3 & 121.935733616598 & -3.63573361659770 \tabularnewline
47 & 129.6 & 124.451768836218 & 5.14823116378203 \tabularnewline
48 & 130.2 & 126.355847387362 & 3.84415261263807 \tabularnewline
49 & 127.19 & 127.9626496001 & -0.772649600100024 \tabularnewline
50 & 133.1 & 133.404983124011 & -0.30498312401059 \tabularnewline
51 & 129.12 & 129.345879697500 & -0.225879697500488 \tabularnewline
52 & 123.28 & 127.437607809812 & -4.15760780981222 \tabularnewline
53 & 123.36 & 126.968918556119 & -3.60891855611925 \tabularnewline
54 & 124.13 & 125.682348349915 & -1.55234834991494 \tabularnewline
55 & 126.96 & 130.118887597700 & -3.15888759769963 \tabularnewline
56 & 127.14 & 128.205213479842 & -1.06521347984237 \tabularnewline
57 & 123.7 & 127.852993205802 & -4.15299320580236 \tabularnewline
58 & 123.67 & 126.132231869226 & -2.46223186922607 \tabularnewline
59 & 130.19 & 129.546163611634 & 0.643836388366424 \tabularnewline
60 & 134.01 & 129.879521311687 & 4.13047868831259 \tabularnewline
61 & 124.96 & 130.543665569088 & -5.58366556908798 \tabularnewline
62 & 129.96 & 134.42602440002 & -4.46602440002013 \tabularnewline
63 & 128.32 & 128.780018790534 & -0.460018790534349 \tabularnewline
64 & 132.38 & 125.637900043535 & 6.7420999564651 \tabularnewline
65 & 126.25 & 127.081099647821 & -0.83109964782112 \tabularnewline
66 & 128.91 & 126.263354868017 & 2.64664513198268 \tabularnewline
67 & 131.42 & 131.164529521225 & 0.255470478774669 \tabularnewline
68 & 129.44 & 130.072678784374 & -0.632678784374292 \tabularnewline
69 & 126.86 & 129.338555499994 & -2.47855549999376 \tabularnewline
70 & 126.71 & 128.090158747334 & -1.38015874733365 \tabularnewline
71 & 131.63 & 132.045748662242 & -0.415748662241555 \tabularnewline
72 & 132.78 & 132.487464365655 & 0.292535634345285 \tabularnewline
73 & 126.61 & 131.058510508721 & -4.44851050872084 \tabularnewline
74 & 132.84 & 135.159009132355 & -2.31900913235461 \tabularnewline
75 & 123.14 & 130.334189151014 & -7.19418915101356 \tabularnewline
76 & 128.13 & 126.335465801779 & 1.79453419822060 \tabularnewline
77 & 125.49 & 125.461177887789 & 0.0288221122108894 \tabularnewline
78 & 126.48 & 124.828592523827 & 1.65140747617325 \tabularnewline
79 & 130.86 & 128.827000368689 & 2.03299963131099 \tabularnewline
80 & 127.32 & 127.633600256416 & -0.313600256415839 \tabularnewline
81 & 126.56 & 126.392905128636 & 0.167094871364441 \tabularnewline
82 & 126.64 & 125.535851270326 & 1.10414872967354 \tabularnewline
83 & 129.26 & 129.904223453292 & -0.64422345329163 \tabularnewline
84 & 126.47 & 130.156856472641 & -3.68685647264132 \tabularnewline
85 & 135.38 & 127.018788281587 & 8.36121171841295 \tabularnewline
86 & 135.5 & 134.063994588630 & 1.43600541136965 \tabularnewline
87 & 132.22 & 129.598306660567 & 2.62169333943251 \tabularnewline
88 & 122.62 & 129.090621782214 & -6.47062178221364 \tabularnewline
89 & 125.16 & 126.467761450972 & -1.30776145097161 \tabularnewline
90 & 128.5 & 125.882685631961 & 2.61731436803927 \tabularnewline
91 & 133.86 & 130.294195227650 & 3.56580477234968 \tabularnewline
92 & 128.87 & 129.362988061814 & -0.49298806181406 \tabularnewline
93 & 125.07 & 128.346168357144 & -3.27616835714363 \tabularnewline
94 & 125.25 & 126.986614866068 & -1.73661486606794 \tabularnewline
95 & 132.16 & 130.589865253157 & 1.57013474684348 \tabularnewline
96 & 130.24 & 131.046618437654 & -0.806618437653555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36920&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]107.5[/C][C]106.576308760684[/C][C]0.923691239316184[/C][/ROW]
[ROW][C]14[/C][C]113.3[/C][C]112.844873595554[/C][C]0.455126404446062[/C][/ROW]
[ROW][C]15[/C][C]107.8[/C][C]107.607745700872[/C][C]0.192254299128066[/C][/ROW]
[ROW][C]16[/C][C]104.5[/C][C]104.354554674865[/C][C]0.145445325135029[/C][/ROW]
[ROW][C]17[/C][C]105.1[/C][C]104.979055241780[/C][C]0.120944758220134[/C][/ROW]
[ROW][C]18[/C][C]104.2[/C][C]103.914373910481[/C][C]0.285626089518516[/C][/ROW]
[ROW][C]19[/C][C]106.6[/C][C]109.008821488077[/C][C]-2.40882148807660[/C][/ROW]
[ROW][C]20[/C][C]103.8[/C][C]107.172744393442[/C][C]-3.37274439344178[/C][/ROW]
[ROW][C]21[/C][C]107.7[/C][C]105.598217169639[/C][C]2.10178283036056[/C][/ROW]
[ROW][C]22[/C][C]106.4[/C][C]105.088079616920[/C][C]1.31192038307984[/C][/ROW]
[ROW][C]23[/C][C]110[/C][C]107.967009829966[/C][C]2.03299017003442[/C][/ROW]
[ROW][C]24[/C][C]113.2[/C][C]107.995719983242[/C][C]5.20428001675758[/C][/ROW]
[ROW][C]25[/C][C]113.9[/C][C]109.493761570337[/C][C]4.40623842966316[/C][/ROW]
[ROW][C]26[/C][C]112[/C][C]116.732364194594[/C][C]-4.73236419459447[/C][/ROW]
[ROW][C]27[/C][C]113.9[/C][C]110.532687046408[/C][C]3.36731295359249[/C][/ROW]
[ROW][C]28[/C][C]113.1[/C][C]108.176634554609[/C][C]4.92336544539111[/C][/ROW]
[ROW][C]29[/C][C]111.7[/C][C]110.170784062969[/C][C]1.52921593703110[/C][/ROW]
[ROW][C]30[/C][C]110.7[/C][C]109.834285509665[/C][C]0.86571449033454[/C][/ROW]
[ROW][C]31[/C][C]113.5[/C][C]115.172891517895[/C][C]-1.67289151789539[/C][/ROW]
[ROW][C]32[/C][C]114[/C][C]113.832690817859[/C][C]0.167309182141238[/C][/ROW]
[ROW][C]33[/C][C]112.7[/C][C]114.177418506156[/C][C]-1.47741850615607[/C][/ROW]
[ROW][C]34[/C][C]112.2[/C][C]113.281628386918[/C][C]-1.08162838691824[/C][/ROW]
[ROW][C]35[/C][C]115.8[/C][C]116.127572854054[/C][C]-0.327572854054125[/C][/ROW]
[ROW][C]36[/C][C]118.4[/C][C]116.344039818516[/C][C]2.05596018148393[/C][/ROW]
[ROW][C]37[/C][C]118.8[/C][C]117.321267971373[/C][C]1.47873202862695[/C][/ROW]
[ROW][C]38[/C][C]123.9[/C][C]123.046221735355[/C][C]0.853778264645186[/C][/ROW]
[ROW][C]39[/C][C]118[/C][C]119.243343752074[/C][C]-1.24334375207384[/C][/ROW]
[ROW][C]40[/C][C]120.2[/C][C]116.275786594317[/C][C]3.92421340568275[/C][/ROW]
[ROW][C]41[/C][C]118.7[/C][C]117.816323139809[/C][C]0.883676860191187[/C][/ROW]
[ROW][C]42[/C][C]119.8[/C][C]117.394634343926[/C][C]2.40536565607441[/C][/ROW]
[ROW][C]43[/C][C]124.8[/C][C]122.932766705450[/C][C]1.86723329454969[/C][/ROW]
[ROW][C]44[/C][C]121.3[/C][C]122.811740874061[/C][C]-1.51174087406100[/C][/ROW]
[ROW][C]45[/C][C]120.2[/C][C]122.839629412424[/C][C]-2.63962941242441[/C][/ROW]
[ROW][C]46[/C][C]118.3[/C][C]121.935733616598[/C][C]-3.63573361659770[/C][/ROW]
[ROW][C]47[/C][C]129.6[/C][C]124.451768836218[/C][C]5.14823116378203[/C][/ROW]
[ROW][C]48[/C][C]130.2[/C][C]126.355847387362[/C][C]3.84415261263807[/C][/ROW]
[ROW][C]49[/C][C]127.19[/C][C]127.9626496001[/C][C]-0.772649600100024[/C][/ROW]
[ROW][C]50[/C][C]133.1[/C][C]133.404983124011[/C][C]-0.30498312401059[/C][/ROW]
[ROW][C]51[/C][C]129.12[/C][C]129.345879697500[/C][C]-0.225879697500488[/C][/ROW]
[ROW][C]52[/C][C]123.28[/C][C]127.437607809812[/C][C]-4.15760780981222[/C][/ROW]
[ROW][C]53[/C][C]123.36[/C][C]126.968918556119[/C][C]-3.60891855611925[/C][/ROW]
[ROW][C]54[/C][C]124.13[/C][C]125.682348349915[/C][C]-1.55234834991494[/C][/ROW]
[ROW][C]55[/C][C]126.96[/C][C]130.118887597700[/C][C]-3.15888759769963[/C][/ROW]
[ROW][C]56[/C][C]127.14[/C][C]128.205213479842[/C][C]-1.06521347984237[/C][/ROW]
[ROW][C]57[/C][C]123.7[/C][C]127.852993205802[/C][C]-4.15299320580236[/C][/ROW]
[ROW][C]58[/C][C]123.67[/C][C]126.132231869226[/C][C]-2.46223186922607[/C][/ROW]
[ROW][C]59[/C][C]130.19[/C][C]129.546163611634[/C][C]0.643836388366424[/C][/ROW]
[ROW][C]60[/C][C]134.01[/C][C]129.879521311687[/C][C]4.13047868831259[/C][/ROW]
[ROW][C]61[/C][C]124.96[/C][C]130.543665569088[/C][C]-5.58366556908798[/C][/ROW]
[ROW][C]62[/C][C]129.96[/C][C]134.42602440002[/C][C]-4.46602440002013[/C][/ROW]
[ROW][C]63[/C][C]128.32[/C][C]128.780018790534[/C][C]-0.460018790534349[/C][/ROW]
[ROW][C]64[/C][C]132.38[/C][C]125.637900043535[/C][C]6.7420999564651[/C][/ROW]
[ROW][C]65[/C][C]126.25[/C][C]127.081099647821[/C][C]-0.83109964782112[/C][/ROW]
[ROW][C]66[/C][C]128.91[/C][C]126.263354868017[/C][C]2.64664513198268[/C][/ROW]
[ROW][C]67[/C][C]131.42[/C][C]131.164529521225[/C][C]0.255470478774669[/C][/ROW]
[ROW][C]68[/C][C]129.44[/C][C]130.072678784374[/C][C]-0.632678784374292[/C][/ROW]
[ROW][C]69[/C][C]126.86[/C][C]129.338555499994[/C][C]-2.47855549999376[/C][/ROW]
[ROW][C]70[/C][C]126.71[/C][C]128.090158747334[/C][C]-1.38015874733365[/C][/ROW]
[ROW][C]71[/C][C]131.63[/C][C]132.045748662242[/C][C]-0.415748662241555[/C][/ROW]
[ROW][C]72[/C][C]132.78[/C][C]132.487464365655[/C][C]0.292535634345285[/C][/ROW]
[ROW][C]73[/C][C]126.61[/C][C]131.058510508721[/C][C]-4.44851050872084[/C][/ROW]
[ROW][C]74[/C][C]132.84[/C][C]135.159009132355[/C][C]-2.31900913235461[/C][/ROW]
[ROW][C]75[/C][C]123.14[/C][C]130.334189151014[/C][C]-7.19418915101356[/C][/ROW]
[ROW][C]76[/C][C]128.13[/C][C]126.335465801779[/C][C]1.79453419822060[/C][/ROW]
[ROW][C]77[/C][C]125.49[/C][C]125.461177887789[/C][C]0.0288221122108894[/C][/ROW]
[ROW][C]78[/C][C]126.48[/C][C]124.828592523827[/C][C]1.65140747617325[/C][/ROW]
[ROW][C]79[/C][C]130.86[/C][C]128.827000368689[/C][C]2.03299963131099[/C][/ROW]
[ROW][C]80[/C][C]127.32[/C][C]127.633600256416[/C][C]-0.313600256415839[/C][/ROW]
[ROW][C]81[/C][C]126.56[/C][C]126.392905128636[/C][C]0.167094871364441[/C][/ROW]
[ROW][C]82[/C][C]126.64[/C][C]125.535851270326[/C][C]1.10414872967354[/C][/ROW]
[ROW][C]83[/C][C]129.26[/C][C]129.904223453292[/C][C]-0.64422345329163[/C][/ROW]
[ROW][C]84[/C][C]126.47[/C][C]130.156856472641[/C][C]-3.68685647264132[/C][/ROW]
[ROW][C]85[/C][C]135.38[/C][C]127.018788281587[/C][C]8.36121171841295[/C][/ROW]
[ROW][C]86[/C][C]135.5[/C][C]134.063994588630[/C][C]1.43600541136965[/C][/ROW]
[ROW][C]87[/C][C]132.22[/C][C]129.598306660567[/C][C]2.62169333943251[/C][/ROW]
[ROW][C]88[/C][C]122.62[/C][C]129.090621782214[/C][C]-6.47062178221364[/C][/ROW]
[ROW][C]89[/C][C]125.16[/C][C]126.467761450972[/C][C]-1.30776145097161[/C][/ROW]
[ROW][C]90[/C][C]128.5[/C][C]125.882685631961[/C][C]2.61731436803927[/C][/ROW]
[ROW][C]91[/C][C]133.86[/C][C]130.294195227650[/C][C]3.56580477234968[/C][/ROW]
[ROW][C]92[/C][C]128.87[/C][C]129.362988061814[/C][C]-0.49298806181406[/C][/ROW]
[ROW][C]93[/C][C]125.07[/C][C]128.346168357144[/C][C]-3.27616835714363[/C][/ROW]
[ROW][C]94[/C][C]125.25[/C][C]126.986614866068[/C][C]-1.73661486606794[/C][/ROW]
[ROW][C]95[/C][C]132.16[/C][C]130.589865253157[/C][C]1.57013474684348[/C][/ROW]
[ROW][C]96[/C][C]130.24[/C][C]131.046618437654[/C][C]-0.806618437653555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36920&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36920&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13107.5106.5763087606840.923691239316184
14113.3112.8448735955540.455126404446062
15107.8107.6077457008720.192254299128066
16104.5104.3545546748650.145445325135029
17105.1104.9790552417800.120944758220134
18104.2103.9143739104810.285626089518516
19106.6109.008821488077-2.40882148807660
20103.8107.172744393442-3.37274439344178
21107.7105.5982171696392.10178283036056
22106.4105.0880796169201.31192038307984
23110107.9670098299662.03299017003442
24113.2107.9957199832425.20428001675758
25113.9109.4937615703374.40623842966316
26112116.732364194594-4.73236419459447
27113.9110.5326870464083.36731295359249
28113.1108.1766345546094.92336544539111
29111.7110.1707840629691.52921593703110
30110.7109.8342855096650.86571449033454
31113.5115.172891517895-1.67289151789539
32114113.8326908178590.167309182141238
33112.7114.177418506156-1.47741850615607
34112.2113.281628386918-1.08162838691824
35115.8116.127572854054-0.327572854054125
36118.4116.3440398185162.05596018148393
37118.8117.3212679713731.47873202862695
38123.9123.0462217353550.853778264645186
39118119.243343752074-1.24334375207384
40120.2116.2757865943173.92421340568275
41118.7117.8163231398090.883676860191187
42119.8117.3946343439262.40536565607441
43124.8122.9327667054501.86723329454969
44121.3122.811740874061-1.51174087406100
45120.2122.839629412424-2.63962941242441
46118.3121.935733616598-3.63573361659770
47129.6124.4517688362185.14823116378203
48130.2126.3558473873623.84415261263807
49127.19127.9626496001-0.772649600100024
50133.1133.404983124011-0.30498312401059
51129.12129.345879697500-0.225879697500488
52123.28127.437607809812-4.15760780981222
53123.36126.968918556119-3.60891855611925
54124.13125.682348349915-1.55234834991494
55126.96130.118887597700-3.15888759769963
56127.14128.205213479842-1.06521347984237
57123.7127.852993205802-4.15299320580236
58123.67126.132231869226-2.46223186922607
59130.19129.5461636116340.643836388366424
60134.01129.8795213116874.13047868831259
61124.96130.543665569088-5.58366556908798
62129.96134.42602440002-4.46602440002013
63128.32128.780018790534-0.460018790534349
64132.38125.6379000435356.7420999564651
65126.25127.081099647821-0.83109964782112
66128.91126.2633548680172.64664513198268
67131.42131.1645295212250.255470478774669
68129.44130.072678784374-0.632678784374292
69126.86129.338555499994-2.47855549999376
70126.71128.090158747334-1.38015874733365
71131.63132.045748662242-0.415748662241555
72132.78132.4874643656550.292535634345285
73126.61131.058510508721-4.44851050872084
74132.84135.159009132355-2.31900913235461
75123.14130.334189151014-7.19418915101356
76128.13126.3354658017791.79453419822060
77125.49125.4611778877890.0288221122108894
78126.48124.8285925238271.65140747617325
79130.86128.8270003686892.03299963131099
80127.32127.633600256416-0.313600256415839
81126.56126.3929051286360.167094871364441
82126.64125.5358512703261.10414872967354
83129.26129.904223453292-0.64422345329163
84126.47130.156856472641-3.68685647264132
85135.38127.0187882815878.36121171841295
86135.5134.0639945886301.43600541136965
87132.22129.5983066605672.62169333943251
88122.62129.090621782214-6.47062178221364
89125.16126.467761450972-1.30776145097161
90128.5125.8826856319612.61731436803927
91133.86130.2941952276503.56580477234968
92128.87129.362988061814-0.49298806181406
93125.07128.346168357144-3.27616835714363
94125.25126.986614866068-1.73661486606794
95132.16130.5898652531571.57013474684348
96130.24131.046618437654-0.806618437653555






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97130.062784015298124.369193041398135.756374989198
98134.505063640771128.653735231408140.356392050133
99129.770247209067123.726985301821135.813509116313
100127.493757833897121.223347830058133.764167837736
101126.816485376104120.283394375182133.349576377026
102126.994981823671120.163958754473133.82600489287
103130.935716094095123.772268005701138.099164182490
104128.660829449433121.131568694351136.190090204515
105127.307386475152119.380258013804135.234514936500
106126.780260054706118.424666996682135.135853112730
107131.146489594850122.333338676713139.959640512988
108130.980361074005121.682049433254140.278672714757

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 130.062784015298 & 124.369193041398 & 135.756374989198 \tabularnewline
98 & 134.505063640771 & 128.653735231408 & 140.356392050133 \tabularnewline
99 & 129.770247209067 & 123.726985301821 & 135.813509116313 \tabularnewline
100 & 127.493757833897 & 121.223347830058 & 133.764167837736 \tabularnewline
101 & 126.816485376104 & 120.283394375182 & 133.349576377026 \tabularnewline
102 & 126.994981823671 & 120.163958754473 & 133.82600489287 \tabularnewline
103 & 130.935716094095 & 123.772268005701 & 138.099164182490 \tabularnewline
104 & 128.660829449433 & 121.131568694351 & 136.190090204515 \tabularnewline
105 & 127.307386475152 & 119.380258013804 & 135.234514936500 \tabularnewline
106 & 126.780260054706 & 118.424666996682 & 135.135853112730 \tabularnewline
107 & 131.146489594850 & 122.333338676713 & 139.959640512988 \tabularnewline
108 & 130.980361074005 & 121.682049433254 & 140.278672714757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36920&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]97[/C][C]130.062784015298[/C][C]124.369193041398[/C][C]135.756374989198[/C][/ROW]
[ROW][C]98[/C][C]134.505063640771[/C][C]128.653735231408[/C][C]140.356392050133[/C][/ROW]
[ROW][C]99[/C][C]129.770247209067[/C][C]123.726985301821[/C][C]135.813509116313[/C][/ROW]
[ROW][C]100[/C][C]127.493757833897[/C][C]121.223347830058[/C][C]133.764167837736[/C][/ROW]
[ROW][C]101[/C][C]126.816485376104[/C][C]120.283394375182[/C][C]133.349576377026[/C][/ROW]
[ROW][C]102[/C][C]126.994981823671[/C][C]120.163958754473[/C][C]133.82600489287[/C][/ROW]
[ROW][C]103[/C][C]130.935716094095[/C][C]123.772268005701[/C][C]138.099164182490[/C][/ROW]
[ROW][C]104[/C][C]128.660829449433[/C][C]121.131568694351[/C][C]136.190090204515[/C][/ROW]
[ROW][C]105[/C][C]127.307386475152[/C][C]119.380258013804[/C][C]135.234514936500[/C][/ROW]
[ROW][C]106[/C][C]126.780260054706[/C][C]118.424666996682[/C][C]135.135853112730[/C][/ROW]
[ROW][C]107[/C][C]131.146489594850[/C][C]122.333338676713[/C][C]139.959640512988[/C][/ROW]
[ROW][C]108[/C][C]130.980361074005[/C][C]121.682049433254[/C][C]140.278672714757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36920&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36920&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97130.062784015298124.369193041398135.756374989198
98134.505063640771128.653735231408140.356392050133
99129.770247209067123.726985301821135.813509116313
100127.493757833897121.223347830058133.764167837736
101126.816485376104120.283394375182133.349576377026
102126.994981823671120.163958754473133.82600489287
103130.935716094095123.772268005701138.099164182490
104128.660829449433121.131568694351136.190090204515
105127.307386475152119.380258013804135.234514936500
106126.780260054706118.424666996682135.135853112730
107131.146489594850122.333338676713139.959640512988
108130.980361074005121.682049433254140.278672714757


Figures (Output of Computation)

Input Parameters & R Code

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')