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Author's title

Exponential Smoothing – Vooruitzichten kledingprijs (additief) - Matthias S...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 15:06:52 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211836379im75deul9yf0ijr.htm/, Retrieved Mon, 20 May 2024 04:11:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13301, Retrieved Mon, 20 May 2024 04:11:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-26 21:06:52] [314f9a525820ae2bc37b608258bd4c0b] [Current]
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Dataseries X:
8
5
2
5
-4
-4
-1
5
16
5
11
16
22
12
8
4
17
5
11
9
4
7
-5
9
11
11
-4
-7
9
-3
14
11
8
-14
-8
-2
15
-8
-4
-17
-13
0
9
-7
-14
-21
-10
-1
7
-14
-12
-16
-15
-15
-24
-14
-8
-14
-13
0
-6
-37
-12
-36
-32
-18
-22
-13
-17
-18
-19
-24
-14
-3
-6
-25
-19
-11
-13
-11
-22
-10
-4
5
-8
-7
5
-13
-15
3
3
7
16
16
18
10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 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 & 12 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13301&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]12 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=13301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13301&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 time12 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0294665928016946
beta0.872429013811499
gamma0.295401379572641

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0294665928016946 \tabularnewline
beta & 0.872429013811499 \tabularnewline
gamma & 0.295401379572641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13301&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]0.0294665928016946[/C][/ROW]
[ROW][C]beta[/C][C]0.872429013811499[/C][/ROW]
[ROW][C]gamma[/C][C]0.295401379572641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13301&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
alpha0.0294665928016946
beta0.872429013811499
gamma0.295401379572641







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132221.14944444444450.850555555555545
141210.28996004105091.71003995894914
1586.499762584788781.50023741521122
1642.825283664836541.17471633516346
171716.33807844695560.661921553044351
1855.2277792693132-0.227779269313201
191111.8770746685325-0.877074668532503
20910.2346901383658-1.23469013836584
2145.59169375574241-1.59169375574241
2279.31392587562775-2.31392587562775
23-5-2.21127566467869-2.78872433532131
24912.0528409420129-3.05284094201288
251118.9745456389925-7.9745456389925
26117.715445291770463.28455470822954
27-43.56598873356366-7.56598873356366
28-7-1.04754191787462-5.95245808212538
29911.3464256781728-2.34642567817278
30-3-0.946727796177753-2.05327220382225
31144.576562604797499.42343739520251
32112.513909383706228.48609061629378
338-2.3163659067508510.3163659067509
34-141.48445564884403-15.4844556488440
35-8-10.96878010594432.96878010594427
36-23.13345990457096-5.13345990457096
37158.273521579416686.72647842058332
38-80.744189547425426-8.74418954742543
39-4-7.111129461610423.11112946161042
40-17-10.9135645365030-6.08643546349696
41-132.54073235050789-15.5407323505079
420-10.365920158982810.3659201589828
439-1.1758287740398810.1758287740399
44-7-3.45519134772467-3.54480865227533
45-14-8.39467179203912-5.60532820796088
46-21-13.1487609903597-7.85123900964026
47-10-20.579092167378410.5790921673784
48-1-8.872353098397787.87235309839778
4970.08863653239000516.91136346761
50-14-11.8284039746170-2.17159602538298
51-12-15.87996647894783.87996647894783
52-16-22.06569380901746.06569380901745
53-15-10.4204656082173-4.5795343917827
54-15-14.7516195454207-0.248380454579340
55-24-5.3765090315148-18.6234909684852
56-14-12.6262275502268-1.37377244977323
57-8-18.224741402525610.2247414025256
58-14-22.88157824951838.88157824951826
59-13-23.830082470379410.8300824703794
600-12.180660064124712.1806600641247
61-6-2.54617498650440-3.45382501349560
62-37-16.8171047952368-20.1828952047632
63-12-19.57186644277207.57186644277202
64-36-24.8346870163289-11.1653129836711
65-32-17.0046403904448-14.9953596095552
66-18-20.92423821523982.9242382152398
67-22-17.1654221152343-4.83457788476569
68-13-19.15060208484846.15060208484844
69-17-21.09592195821254.0959219582125
70-18-26.36977339798838.36977339798826
71-19-26.83922430215677.83922430215669
72-24-15.0321090664354-8.96789093356457
73-14-11.1882180369779-2.81178196302213
74-3-30.904956170665527.9049561706655
75-6-23.717863867189817.7178638671898
76-25-33.22511504023848.22511504023835
77-19-24.59478863745825.59478863745824
78-11-20.9138777646179.913877764617
79-13-17.13754924594454.13754924594448
80-11-13.44230288457032.44230288457030
81-22-13.9146640894396-8.08533591056042
82-10-16.46400546965316.46400546965314
83-4-15.332561960878311.3325619608783
845-6.3420952273741811.3420952273742
85-82.28628118007011-10.2862811800701
86-7-6.61538003449939-0.384619965500612
875-1.680816470596396.68081647059639
88-13-13.01689202846970.0168920284697158
89-15-4.37561188717197-10.6243881128280
9030.6556184965625472.34438150343745
9132.948225216314880.0517747836851212
9276.327401733943790.672598266056214
93163.0295030764864112.9704969235136
94166.058000768309599.94199923169041
95189.563283795050278.43671620494973
961019.2722627961366-9.27226279613664

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 22 & 21.1494444444445 & 0.850555555555545 \tabularnewline
14 & 12 & 10.2899600410509 & 1.71003995894914 \tabularnewline
15 & 8 & 6.49976258478878 & 1.50023741521122 \tabularnewline
16 & 4 & 2.82528366483654 & 1.17471633516346 \tabularnewline
17 & 17 & 16.3380784469556 & 0.661921553044351 \tabularnewline
18 & 5 & 5.2277792693132 & -0.227779269313201 \tabularnewline
19 & 11 & 11.8770746685325 & -0.877074668532503 \tabularnewline
20 & 9 & 10.2346901383658 & -1.23469013836584 \tabularnewline
21 & 4 & 5.59169375574241 & -1.59169375574241 \tabularnewline
22 & 7 & 9.31392587562775 & -2.31392587562775 \tabularnewline
23 & -5 & -2.21127566467869 & -2.78872433532131 \tabularnewline
24 & 9 & 12.0528409420129 & -3.05284094201288 \tabularnewline
25 & 11 & 18.9745456389925 & -7.9745456389925 \tabularnewline
26 & 11 & 7.71544529177046 & 3.28455470822954 \tabularnewline
27 & -4 & 3.56598873356366 & -7.56598873356366 \tabularnewline
28 & -7 & -1.04754191787462 & -5.95245808212538 \tabularnewline
29 & 9 & 11.3464256781728 & -2.34642567817278 \tabularnewline
30 & -3 & -0.946727796177753 & -2.05327220382225 \tabularnewline
31 & 14 & 4.57656260479749 & 9.42343739520251 \tabularnewline
32 & 11 & 2.51390938370622 & 8.48609061629378 \tabularnewline
33 & 8 & -2.31636590675085 & 10.3163659067509 \tabularnewline
34 & -14 & 1.48445564884403 & -15.4844556488440 \tabularnewline
35 & -8 & -10.9687801059443 & 2.96878010594427 \tabularnewline
36 & -2 & 3.13345990457096 & -5.13345990457096 \tabularnewline
37 & 15 & 8.27352157941668 & 6.72647842058332 \tabularnewline
38 & -8 & 0.744189547425426 & -8.74418954742543 \tabularnewline
39 & -4 & -7.11112946161042 & 3.11112946161042 \tabularnewline
40 & -17 & -10.9135645365030 & -6.08643546349696 \tabularnewline
41 & -13 & 2.54073235050789 & -15.5407323505079 \tabularnewline
42 & 0 & -10.3659201589828 & 10.3659201589828 \tabularnewline
43 & 9 & -1.17582877403988 & 10.1758287740399 \tabularnewline
44 & -7 & -3.45519134772467 & -3.54480865227533 \tabularnewline
45 & -14 & -8.39467179203912 & -5.60532820796088 \tabularnewline
46 & -21 & -13.1487609903597 & -7.85123900964026 \tabularnewline
47 & -10 & -20.5790921673784 & 10.5790921673784 \tabularnewline
48 & -1 & -8.87235309839778 & 7.87235309839778 \tabularnewline
49 & 7 & 0.0886365323900051 & 6.91136346761 \tabularnewline
50 & -14 & -11.8284039746170 & -2.17159602538298 \tabularnewline
51 & -12 & -15.8799664789478 & 3.87996647894783 \tabularnewline
52 & -16 & -22.0656938090174 & 6.06569380901745 \tabularnewline
53 & -15 & -10.4204656082173 & -4.5795343917827 \tabularnewline
54 & -15 & -14.7516195454207 & -0.248380454579340 \tabularnewline
55 & -24 & -5.3765090315148 & -18.6234909684852 \tabularnewline
56 & -14 & -12.6262275502268 & -1.37377244977323 \tabularnewline
57 & -8 & -18.2247414025256 & 10.2247414025256 \tabularnewline
58 & -14 & -22.8815782495183 & 8.88157824951826 \tabularnewline
59 & -13 & -23.8300824703794 & 10.8300824703794 \tabularnewline
60 & 0 & -12.1806600641247 & 12.1806600641247 \tabularnewline
61 & -6 & -2.54617498650440 & -3.45382501349560 \tabularnewline
62 & -37 & -16.8171047952368 & -20.1828952047632 \tabularnewline
63 & -12 & -19.5718664427720 & 7.57186644277202 \tabularnewline
64 & -36 & -24.8346870163289 & -11.1653129836711 \tabularnewline
65 & -32 & -17.0046403904448 & -14.9953596095552 \tabularnewline
66 & -18 & -20.9242382152398 & 2.9242382152398 \tabularnewline
67 & -22 & -17.1654221152343 & -4.83457788476569 \tabularnewline
68 & -13 & -19.1506020848484 & 6.15060208484844 \tabularnewline
69 & -17 & -21.0959219582125 & 4.0959219582125 \tabularnewline
70 & -18 & -26.3697733979883 & 8.36977339798826 \tabularnewline
71 & -19 & -26.8392243021567 & 7.83922430215669 \tabularnewline
72 & -24 & -15.0321090664354 & -8.96789093356457 \tabularnewline
73 & -14 & -11.1882180369779 & -2.81178196302213 \tabularnewline
74 & -3 & -30.9049561706655 & 27.9049561706655 \tabularnewline
75 & -6 & -23.7178638671898 & 17.7178638671898 \tabularnewline
76 & -25 & -33.2251150402384 & 8.22511504023835 \tabularnewline
77 & -19 & -24.5947886374582 & 5.59478863745824 \tabularnewline
78 & -11 & -20.913877764617 & 9.913877764617 \tabularnewline
79 & -13 & -17.1375492459445 & 4.13754924594448 \tabularnewline
80 & -11 & -13.4423028845703 & 2.44230288457030 \tabularnewline
81 & -22 & -13.9146640894396 & -8.08533591056042 \tabularnewline
82 & -10 & -16.4640054696531 & 6.46400546965314 \tabularnewline
83 & -4 & -15.3325619608783 & 11.3325619608783 \tabularnewline
84 & 5 & -6.34209522737418 & 11.3420952273742 \tabularnewline
85 & -8 & 2.28628118007011 & -10.2862811800701 \tabularnewline
86 & -7 & -6.61538003449939 & -0.384619965500612 \tabularnewline
87 & 5 & -1.68081647059639 & 6.68081647059639 \tabularnewline
88 & -13 & -13.0168920284697 & 0.0168920284697158 \tabularnewline
89 & -15 & -4.37561188717197 & -10.6243881128280 \tabularnewline
90 & 3 & 0.655618496562547 & 2.34438150343745 \tabularnewline
91 & 3 & 2.94822521631488 & 0.0517747836851212 \tabularnewline
92 & 7 & 6.32740173394379 & 0.672598266056214 \tabularnewline
93 & 16 & 3.02950307648641 & 12.9704969235136 \tabularnewline
94 & 16 & 6.05800076830959 & 9.94199923169041 \tabularnewline
95 & 18 & 9.56328379505027 & 8.43671620494973 \tabularnewline
96 & 10 & 19.2722627961366 & -9.27226279613664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13301&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]22[/C][C]21.1494444444445[/C][C]0.850555555555545[/C][/ROW]
[ROW][C]14[/C][C]12[/C][C]10.2899600410509[/C][C]1.71003995894914[/C][/ROW]
[ROW][C]15[/C][C]8[/C][C]6.49976258478878[/C][C]1.50023741521122[/C][/ROW]
[ROW][C]16[/C][C]4[/C][C]2.82528366483654[/C][C]1.17471633516346[/C][/ROW]
[ROW][C]17[/C][C]17[/C][C]16.3380784469556[/C][C]0.661921553044351[/C][/ROW]
[ROW][C]18[/C][C]5[/C][C]5.2277792693132[/C][C]-0.227779269313201[/C][/ROW]
[ROW][C]19[/C][C]11[/C][C]11.8770746685325[/C][C]-0.877074668532503[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]10.2346901383658[/C][C]-1.23469013836584[/C][/ROW]
[ROW][C]21[/C][C]4[/C][C]5.59169375574241[/C][C]-1.59169375574241[/C][/ROW]
[ROW][C]22[/C][C]7[/C][C]9.31392587562775[/C][C]-2.31392587562775[/C][/ROW]
[ROW][C]23[/C][C]-5[/C][C]-2.21127566467869[/C][C]-2.78872433532131[/C][/ROW]
[ROW][C]24[/C][C]9[/C][C]12.0528409420129[/C][C]-3.05284094201288[/C][/ROW]
[ROW][C]25[/C][C]11[/C][C]18.9745456389925[/C][C]-7.9745456389925[/C][/ROW]
[ROW][C]26[/C][C]11[/C][C]7.71544529177046[/C][C]3.28455470822954[/C][/ROW]
[ROW][C]27[/C][C]-4[/C][C]3.56598873356366[/C][C]-7.56598873356366[/C][/ROW]
[ROW][C]28[/C][C]-7[/C][C]-1.04754191787462[/C][C]-5.95245808212538[/C][/ROW]
[ROW][C]29[/C][C]9[/C][C]11.3464256781728[/C][C]-2.34642567817278[/C][/ROW]
[ROW][C]30[/C][C]-3[/C][C]-0.946727796177753[/C][C]-2.05327220382225[/C][/ROW]
[ROW][C]31[/C][C]14[/C][C]4.57656260479749[/C][C]9.42343739520251[/C][/ROW]
[ROW][C]32[/C][C]11[/C][C]2.51390938370622[/C][C]8.48609061629378[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]-2.31636590675085[/C][C]10.3163659067509[/C][/ROW]
[ROW][C]34[/C][C]-14[/C][C]1.48445564884403[/C][C]-15.4844556488440[/C][/ROW]
[ROW][C]35[/C][C]-8[/C][C]-10.9687801059443[/C][C]2.96878010594427[/C][/ROW]
[ROW][C]36[/C][C]-2[/C][C]3.13345990457096[/C][C]-5.13345990457096[/C][/ROW]
[ROW][C]37[/C][C]15[/C][C]8.27352157941668[/C][C]6.72647842058332[/C][/ROW]
[ROW][C]38[/C][C]-8[/C][C]0.744189547425426[/C][C]-8.74418954742543[/C][/ROW]
[ROW][C]39[/C][C]-4[/C][C]-7.11112946161042[/C][C]3.11112946161042[/C][/ROW]
[ROW][C]40[/C][C]-17[/C][C]-10.9135645365030[/C][C]-6.08643546349696[/C][/ROW]
[ROW][C]41[/C][C]-13[/C][C]2.54073235050789[/C][C]-15.5407323505079[/C][/ROW]
[ROW][C]42[/C][C]0[/C][C]-10.3659201589828[/C][C]10.3659201589828[/C][/ROW]
[ROW][C]43[/C][C]9[/C][C]-1.17582877403988[/C][C]10.1758287740399[/C][/ROW]
[ROW][C]44[/C][C]-7[/C][C]-3.45519134772467[/C][C]-3.54480865227533[/C][/ROW]
[ROW][C]45[/C][C]-14[/C][C]-8.39467179203912[/C][C]-5.60532820796088[/C][/ROW]
[ROW][C]46[/C][C]-21[/C][C]-13.1487609903597[/C][C]-7.85123900964026[/C][/ROW]
[ROW][C]47[/C][C]-10[/C][C]-20.5790921673784[/C][C]10.5790921673784[/C][/ROW]
[ROW][C]48[/C][C]-1[/C][C]-8.87235309839778[/C][C]7.87235309839778[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]0.0886365323900051[/C][C]6.91136346761[/C][/ROW]
[ROW][C]50[/C][C]-14[/C][C]-11.8284039746170[/C][C]-2.17159602538298[/C][/ROW]
[ROW][C]51[/C][C]-12[/C][C]-15.8799664789478[/C][C]3.87996647894783[/C][/ROW]
[ROW][C]52[/C][C]-16[/C][C]-22.0656938090174[/C][C]6.06569380901745[/C][/ROW]
[ROW][C]53[/C][C]-15[/C][C]-10.4204656082173[/C][C]-4.5795343917827[/C][/ROW]
[ROW][C]54[/C][C]-15[/C][C]-14.7516195454207[/C][C]-0.248380454579340[/C][/ROW]
[ROW][C]55[/C][C]-24[/C][C]-5.3765090315148[/C][C]-18.6234909684852[/C][/ROW]
[ROW][C]56[/C][C]-14[/C][C]-12.6262275502268[/C][C]-1.37377244977323[/C][/ROW]
[ROW][C]57[/C][C]-8[/C][C]-18.2247414025256[/C][C]10.2247414025256[/C][/ROW]
[ROW][C]58[/C][C]-14[/C][C]-22.8815782495183[/C][C]8.88157824951826[/C][/ROW]
[ROW][C]59[/C][C]-13[/C][C]-23.8300824703794[/C][C]10.8300824703794[/C][/ROW]
[ROW][C]60[/C][C]0[/C][C]-12.1806600641247[/C][C]12.1806600641247[/C][/ROW]
[ROW][C]61[/C][C]-6[/C][C]-2.54617498650440[/C][C]-3.45382501349560[/C][/ROW]
[ROW][C]62[/C][C]-37[/C][C]-16.8171047952368[/C][C]-20.1828952047632[/C][/ROW]
[ROW][C]63[/C][C]-12[/C][C]-19.5718664427720[/C][C]7.57186644277202[/C][/ROW]
[ROW][C]64[/C][C]-36[/C][C]-24.8346870163289[/C][C]-11.1653129836711[/C][/ROW]
[ROW][C]65[/C][C]-32[/C][C]-17.0046403904448[/C][C]-14.9953596095552[/C][/ROW]
[ROW][C]66[/C][C]-18[/C][C]-20.9242382152398[/C][C]2.9242382152398[/C][/ROW]
[ROW][C]67[/C][C]-22[/C][C]-17.1654221152343[/C][C]-4.83457788476569[/C][/ROW]
[ROW][C]68[/C][C]-13[/C][C]-19.1506020848484[/C][C]6.15060208484844[/C][/ROW]
[ROW][C]69[/C][C]-17[/C][C]-21.0959219582125[/C][C]4.0959219582125[/C][/ROW]
[ROW][C]70[/C][C]-18[/C][C]-26.3697733979883[/C][C]8.36977339798826[/C][/ROW]
[ROW][C]71[/C][C]-19[/C][C]-26.8392243021567[/C][C]7.83922430215669[/C][/ROW]
[ROW][C]72[/C][C]-24[/C][C]-15.0321090664354[/C][C]-8.96789093356457[/C][/ROW]
[ROW][C]73[/C][C]-14[/C][C]-11.1882180369779[/C][C]-2.81178196302213[/C][/ROW]
[ROW][C]74[/C][C]-3[/C][C]-30.9049561706655[/C][C]27.9049561706655[/C][/ROW]
[ROW][C]75[/C][C]-6[/C][C]-23.7178638671898[/C][C]17.7178638671898[/C][/ROW]
[ROW][C]76[/C][C]-25[/C][C]-33.2251150402384[/C][C]8.22511504023835[/C][/ROW]
[ROW][C]77[/C][C]-19[/C][C]-24.5947886374582[/C][C]5.59478863745824[/C][/ROW]
[ROW][C]78[/C][C]-11[/C][C]-20.913877764617[/C][C]9.913877764617[/C][/ROW]
[ROW][C]79[/C][C]-13[/C][C]-17.1375492459445[/C][C]4.13754924594448[/C][/ROW]
[ROW][C]80[/C][C]-11[/C][C]-13.4423028845703[/C][C]2.44230288457030[/C][/ROW]
[ROW][C]81[/C][C]-22[/C][C]-13.9146640894396[/C][C]-8.08533591056042[/C][/ROW]
[ROW][C]82[/C][C]-10[/C][C]-16.4640054696531[/C][C]6.46400546965314[/C][/ROW]
[ROW][C]83[/C][C]-4[/C][C]-15.3325619608783[/C][C]11.3325619608783[/C][/ROW]
[ROW][C]84[/C][C]5[/C][C]-6.34209522737418[/C][C]11.3420952273742[/C][/ROW]
[ROW][C]85[/C][C]-8[/C][C]2.28628118007011[/C][C]-10.2862811800701[/C][/ROW]
[ROW][C]86[/C][C]-7[/C][C]-6.61538003449939[/C][C]-0.384619965500612[/C][/ROW]
[ROW][C]87[/C][C]5[/C][C]-1.68081647059639[/C][C]6.68081647059639[/C][/ROW]
[ROW][C]88[/C][C]-13[/C][C]-13.0168920284697[/C][C]0.0168920284697158[/C][/ROW]
[ROW][C]89[/C][C]-15[/C][C]-4.37561188717197[/C][C]-10.6243881128280[/C][/ROW]
[ROW][C]90[/C][C]3[/C][C]0.655618496562547[/C][C]2.34438150343745[/C][/ROW]
[ROW][C]91[/C][C]3[/C][C]2.94822521631488[/C][C]0.0517747836851212[/C][/ROW]
[ROW][C]92[/C][C]7[/C][C]6.32740173394379[/C][C]0.672598266056214[/C][/ROW]
[ROW][C]93[/C][C]16[/C][C]3.02950307648641[/C][C]12.9704969235136[/C][/ROW]
[ROW][C]94[/C][C]16[/C][C]6.05800076830959[/C][C]9.94199923169041[/C][/ROW]
[ROW][C]95[/C][C]18[/C][C]9.56328379505027[/C][C]8.43671620494973[/C][/ROW]
[ROW][C]96[/C][C]10[/C][C]19.2722627961366[/C][C]-9.27226279613664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13301&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
132221.14944444444450.850555555555545
141210.28996004105091.71003995894914
1586.499762584788781.50023741521122
1642.825283664836541.17471633516346
171716.33807844695560.661921553044351
1855.2277792693132-0.227779269313201
191111.8770746685325-0.877074668532503
20910.2346901383658-1.23469013836584
2145.59169375574241-1.59169375574241
2279.31392587562775-2.31392587562775
23-5-2.21127566467869-2.78872433532131
24912.0528409420129-3.05284094201288
251118.9745456389925-7.9745456389925
26117.715445291770463.28455470822954
27-43.56598873356366-7.56598873356366
28-7-1.04754191787462-5.95245808212538
29911.3464256781728-2.34642567817278
30-3-0.946727796177753-2.05327220382225
31144.576562604797499.42343739520251
32112.513909383706228.48609061629378
338-2.3163659067508510.3163659067509
34-141.48445564884403-15.4844556488440
35-8-10.96878010594432.96878010594427
36-23.13345990457096-5.13345990457096
37158.273521579416686.72647842058332
38-80.744189547425426-8.74418954742543
39-4-7.111129461610423.11112946161042
40-17-10.9135645365030-6.08643546349696
41-132.54073235050789-15.5407323505079
420-10.365920158982810.3659201589828
439-1.1758287740398810.1758287740399
44-7-3.45519134772467-3.54480865227533
45-14-8.39467179203912-5.60532820796088
46-21-13.1487609903597-7.85123900964026
47-10-20.579092167378410.5790921673784
48-1-8.872353098397787.87235309839778
4970.08863653239000516.91136346761
50-14-11.8284039746170-2.17159602538298
51-12-15.87996647894783.87996647894783
52-16-22.06569380901746.06569380901745
53-15-10.4204656082173-4.5795343917827
54-15-14.7516195454207-0.248380454579340
55-24-5.3765090315148-18.6234909684852
56-14-12.6262275502268-1.37377244977323
57-8-18.224741402525610.2247414025256
58-14-22.88157824951838.88157824951826
59-13-23.830082470379410.8300824703794
600-12.180660064124712.1806600641247
61-6-2.54617498650440-3.45382501349560
62-37-16.8171047952368-20.1828952047632
63-12-19.57186644277207.57186644277202
64-36-24.8346870163289-11.1653129836711
65-32-17.0046403904448-14.9953596095552
66-18-20.92423821523982.9242382152398
67-22-17.1654221152343-4.83457788476569
68-13-19.15060208484846.15060208484844
69-17-21.09592195821254.0959219582125
70-18-26.36977339798838.36977339798826
71-19-26.83922430215677.83922430215669
72-24-15.0321090664354-8.96789093356457
73-14-11.1882180369779-2.81178196302213
74-3-30.904956170665527.9049561706655
75-6-23.717863867189817.7178638671898
76-25-33.22511504023848.22511504023835
77-19-24.59478863745825.59478863745824
78-11-20.9138777646179.913877764617
79-13-17.13754924594454.13754924594448
80-11-13.44230288457032.44230288457030
81-22-13.9146640894396-8.08533591056042
82-10-16.46400546965316.46400546965314
83-4-15.332561960878311.3325619608783
845-6.3420952273741811.3420952273742
85-82.28628118007011-10.2862811800701
86-7-6.61538003449939-0.384619965500612
875-1.680816470596396.68081647059639
88-13-13.01689202846970.0168920284697158
89-15-4.37561188717197-10.6243881128280
9030.6556184965625472.34438150343745
9132.948225216314880.0517747836851212
9276.327401733943790.672598266056214
93163.0295030764864112.9704969235136
94166.058000768309599.94199923169041
95189.563283795050278.43671620494973
961019.2722627961366-9.27226279613664







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9721.36358167352994.7308798794046437.9962834676551
9816.1393984397394-0.5186005996663132.7973974791451
9923.65642251445116.9441901789009640.3686548500013
10010.5867006649311-6.219303035155127.3927043650173
10116.5499678319675-0.39947884513261733.4994145090677
10226.25880232843809.1068253290256543.4107793278504
10328.411210097071510.989179910375345.8332402837676
10432.551683400348714.784864223959450.3185025767381
10533.327278489061815.135133015732451.5194239623911
10635.339423134125716.637132522325154.0417137459262
10738.098709506566718.798707596301857.3987114168316
10842.243610920523422.257040073576062.2301817674707

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 21.3635816735299 & 4.73087987940464 & 37.9962834676551 \tabularnewline
98 & 16.1393984397394 & -0.51860059966631 & 32.7973974791451 \tabularnewline
99 & 23.6564225144511 & 6.94419017890096 & 40.3686548500013 \tabularnewline
100 & 10.5867006649311 & -6.2193030351551 & 27.3927043650173 \tabularnewline
101 & 16.5499678319675 & -0.399478845132617 & 33.4994145090677 \tabularnewline
102 & 26.2588023284380 & 9.10682532902565 & 43.4107793278504 \tabularnewline
103 & 28.4112100970715 & 10.9891799103753 & 45.8332402837676 \tabularnewline
104 & 32.5516834003487 & 14.7848642239594 & 50.3185025767381 \tabularnewline
105 & 33.3272784890618 & 15.1351330157324 & 51.5194239623911 \tabularnewline
106 & 35.3394231341257 & 16.6371325223251 & 54.0417137459262 \tabularnewline
107 & 38.0987095065667 & 18.7987075963018 & 57.3987114168316 \tabularnewline
108 & 42.2436109205234 & 22.2570400735760 & 62.2301817674707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13301&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]21.3635816735299[/C][C]4.73087987940464[/C][C]37.9962834676551[/C][/ROW]
[ROW][C]98[/C][C]16.1393984397394[/C][C]-0.51860059966631[/C][C]32.7973974791451[/C][/ROW]
[ROW][C]99[/C][C]23.6564225144511[/C][C]6.94419017890096[/C][C]40.3686548500013[/C][/ROW]
[ROW][C]100[/C][C]10.5867006649311[/C][C]-6.2193030351551[/C][C]27.3927043650173[/C][/ROW]
[ROW][C]101[/C][C]16.5499678319675[/C][C]-0.399478845132617[/C][C]33.4994145090677[/C][/ROW]
[ROW][C]102[/C][C]26.2588023284380[/C][C]9.10682532902565[/C][C]43.4107793278504[/C][/ROW]
[ROW][C]103[/C][C]28.4112100970715[/C][C]10.9891799103753[/C][C]45.8332402837676[/C][/ROW]
[ROW][C]104[/C][C]32.5516834003487[/C][C]14.7848642239594[/C][C]50.3185025767381[/C][/ROW]
[ROW][C]105[/C][C]33.3272784890618[/C][C]15.1351330157324[/C][C]51.5194239623911[/C][/ROW]
[ROW][C]106[/C][C]35.3394231341257[/C][C]16.6371325223251[/C][C]54.0417137459262[/C][/ROW]
[ROW][C]107[/C][C]38.0987095065667[/C][C]18.7987075963018[/C][C]57.3987114168316[/C][/ROW]
[ROW][C]108[/C][C]42.2436109205234[/C][C]22.2570400735760[/C][C]62.2301817674707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13301&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13301&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
9721.36358167352994.7308798794046437.9962834676551
9816.1393984397394-0.5186005996663132.7973974791451
9923.65642251445116.9441901789009640.3686548500013
10010.5867006649311-6.219303035155127.3927043650173
10116.5499678319675-0.39947884513261733.4994145090677
10226.25880232843809.1068253290256543.4107793278504
10328.411210097071510.989179910375345.8332402837676
10432.551683400348714.784864223959450.3185025767381
10533.327278489061815.135133015732451.5194239623911
10635.339423134125716.637132522325154.0417137459262
10738.098709506566718.798707596301857.3987114168316
10842.243610920523422.257040073576062.2301817674707



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')