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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 May 2013 12:12:57 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/21/t1369152910w50v6cu0h3fay0t.htm/, Retrieved Wed, 01 May 2024 23:37:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209245, Retrieved Wed, 01 May 2024 23:37:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [OPGAVE 10 - OEF2] [2013-05-21 16:12:57] [7c11a516588a95ad0530ec4511c20064] [Current]
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Dataseries X:
-5.3
-7.1
-8
-8.9
-7.7
-1.1
4
9.6
10.9
13
14.9
20.1
10.8
11
3.8
10.8
7.6
10.2
2.2
-0.1
-1.7
-4.8
-9.9
-13.5
-18.1
-18
-15.7
-15.2
-15.1
-17.9
-14.5
-9.4
-4.2
-2.2
4.5
12.4
15.8
11.5
14.1
18.8
26.1
27.9
25.4
23.4
11.5
9.9
8.1
12.6
8.2
5.4
1
-2.9
-3.7
-7
-7.2
-11.8
-2.1
1.2
2.5
4.8
-6.6
-16
-22.7
-17.7
-18.2
-18.9
-16
-12.2
-17.1
-18.6
-17.5
-24.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209245&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209245&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209245&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999936568776778
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999936568776778 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209245&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]0.999936568776778[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209245&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209245&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
alpha0.999936568776778
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2-7.1-5.3-1.8
3-8-7.0998858237982-0.900114176201799
4-8.9-7.99994290465676-0.900057095343236
5-7.7-8.899942908277471.19994290827747
6-1.1-7.700076113846476.60007611384647
74-1.100418650901265.10041865090126
89.63.999676474206035.60032352579397
910.99.599644764628321.30035523537168
101310.89991751687682.1000824831232
1114.912.99986678919921.90013321080077
1220.114.89987947222625.20012052777385
1310.820.099670149994-9.29967014999403
141110.80058988945320.199410110546827
153.810.9999873511728-7.19998735117276
1610.83.800456704004866.99954329599514
177.610.7995560104067-3.19955601040674
1810.27.600202951751512.59979704824849
192.210.1998350916931-7.9998350916931
20-0.12.20050743932544-2.30050743932544
21-1.7-0.0998540759990932-1.60014592400091
22-4.8-1.69989850078671-3.10010149921329
23-9.9-4.79980335676979-5.10019664323021
24-13.5-9.89967648828825-3.60032351171175
25-18.1-13.4997716270757-4.60022837292434
26-18-18.09970820188720.0997082018872071
27-15.7-18.00000632461322.30000632461321
28-15.2-15.70014589221460.500145892214588
29-15.1-15.20003172486570.100031724865731
30-17.9-15.1000063451347-2.79999365486533
31-14.5-17.89982239297753.39982239297746
32-9.4-14.50021565489315.10021565489312
33-4.2-9.400323512917685.20032351291768
34-2.2-4.200329862881572.00032986288157
354.5-2.200126883370056.70012688337005
3612.44.499575002756057.90042499724395
3715.812.39949886637853.40050113362155
3811.515.7997843020535-4.29978430205353
3914.111.50027274057792.59972725942213
4018.814.09983509611994.70016490388011
4126.118.79970186279087.3002981372092
4227.926.09953693315931.80046306684072
4325.427.8998857944253-2.4998857944253
4423.425.4001585708139-2.00015857081386
4511.523.4001268725048-11.9001268725048
469.911.500754839604-1.60075483960401
478.19.90010153783756-1.80010153783756
4812.68.100114182642474.49988581735753
498.212.5997145667382-4.39971456673825
505.48.20027907927679-2.80027907927679
5115.40017762512736-4.40017762512736
52-2.91.00027910864915-3.90027910864915
53-3.7-2.89975260052523-0.800247399474768
54-7-3.69994923932857-3.30005076067143
55-7.2-6.99979067374356-0.200209326256443
56-11.8-7.19998730047754-4.60001269952247
57-2.1-11.79970821556769.69970821556764
581.2-2.100615264357013.30061526435701
592.51.19979063793641.3002093620636
604.82.499917526129722.30008247387028
61-6.64.79985410295517-11.3998541029552
62-16-6.5992768933097-9.4007231066903
63-22.7-15.9994037006342-6.70059629936582
64-17.7-22.69957497298044.99957497298042
65-18.2-17.7003171291561-0.499682870843877
66-18.9-18.1999683045043-0.700031695495721
67-16-18.89995559613332.89995559613326
68-12.2-16.00018394773083.80018394773075
69-17.1-12.2002410503163-4.89975894968373
70-18.6-17.0996892022963-1.50031079770367
71-17.5-18.59990483345091.09990483345089
72-24.9-17.500069768309-7.39993023169098

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & -7.1 & -5.3 & -1.8 \tabularnewline
3 & -8 & -7.0998858237982 & -0.900114176201799 \tabularnewline
4 & -8.9 & -7.99994290465676 & -0.900057095343236 \tabularnewline
5 & -7.7 & -8.89994290827747 & 1.19994290827747 \tabularnewline
6 & -1.1 & -7.70007611384647 & 6.60007611384647 \tabularnewline
7 & 4 & -1.10041865090126 & 5.10041865090126 \tabularnewline
8 & 9.6 & 3.99967647420603 & 5.60032352579397 \tabularnewline
9 & 10.9 & 9.59964476462832 & 1.30035523537168 \tabularnewline
10 & 13 & 10.8999175168768 & 2.1000824831232 \tabularnewline
11 & 14.9 & 12.9998667891992 & 1.90013321080077 \tabularnewline
12 & 20.1 & 14.8998794722262 & 5.20012052777385 \tabularnewline
13 & 10.8 & 20.099670149994 & -9.29967014999403 \tabularnewline
14 & 11 & 10.8005898894532 & 0.199410110546827 \tabularnewline
15 & 3.8 & 10.9999873511728 & -7.19998735117276 \tabularnewline
16 & 10.8 & 3.80045670400486 & 6.99954329599514 \tabularnewline
17 & 7.6 & 10.7995560104067 & -3.19955601040674 \tabularnewline
18 & 10.2 & 7.60020295175151 & 2.59979704824849 \tabularnewline
19 & 2.2 & 10.1998350916931 & -7.9998350916931 \tabularnewline
20 & -0.1 & 2.20050743932544 & -2.30050743932544 \tabularnewline
21 & -1.7 & -0.0998540759990932 & -1.60014592400091 \tabularnewline
22 & -4.8 & -1.69989850078671 & -3.10010149921329 \tabularnewline
23 & -9.9 & -4.79980335676979 & -5.10019664323021 \tabularnewline
24 & -13.5 & -9.89967648828825 & -3.60032351171175 \tabularnewline
25 & -18.1 & -13.4997716270757 & -4.60022837292434 \tabularnewline
26 & -18 & -18.0997082018872 & 0.0997082018872071 \tabularnewline
27 & -15.7 & -18.0000063246132 & 2.30000632461321 \tabularnewline
28 & -15.2 & -15.7001458922146 & 0.500145892214588 \tabularnewline
29 & -15.1 & -15.2000317248657 & 0.100031724865731 \tabularnewline
30 & -17.9 & -15.1000063451347 & -2.79999365486533 \tabularnewline
31 & -14.5 & -17.8998223929775 & 3.39982239297746 \tabularnewline
32 & -9.4 & -14.5002156548931 & 5.10021565489312 \tabularnewline
33 & -4.2 & -9.40032351291768 & 5.20032351291768 \tabularnewline
34 & -2.2 & -4.20032986288157 & 2.00032986288157 \tabularnewline
35 & 4.5 & -2.20012688337005 & 6.70012688337005 \tabularnewline
36 & 12.4 & 4.49957500275605 & 7.90042499724395 \tabularnewline
37 & 15.8 & 12.3994988663785 & 3.40050113362155 \tabularnewline
38 & 11.5 & 15.7997843020535 & -4.29978430205353 \tabularnewline
39 & 14.1 & 11.5002727405779 & 2.59972725942213 \tabularnewline
40 & 18.8 & 14.0998350961199 & 4.70016490388011 \tabularnewline
41 & 26.1 & 18.7997018627908 & 7.3002981372092 \tabularnewline
42 & 27.9 & 26.0995369331593 & 1.80046306684072 \tabularnewline
43 & 25.4 & 27.8998857944253 & -2.4998857944253 \tabularnewline
44 & 23.4 & 25.4001585708139 & -2.00015857081386 \tabularnewline
45 & 11.5 & 23.4001268725048 & -11.9001268725048 \tabularnewline
46 & 9.9 & 11.500754839604 & -1.60075483960401 \tabularnewline
47 & 8.1 & 9.90010153783756 & -1.80010153783756 \tabularnewline
48 & 12.6 & 8.10011418264247 & 4.49988581735753 \tabularnewline
49 & 8.2 & 12.5997145667382 & -4.39971456673825 \tabularnewline
50 & 5.4 & 8.20027907927679 & -2.80027907927679 \tabularnewline
51 & 1 & 5.40017762512736 & -4.40017762512736 \tabularnewline
52 & -2.9 & 1.00027910864915 & -3.90027910864915 \tabularnewline
53 & -3.7 & -2.89975260052523 & -0.800247399474768 \tabularnewline
54 & -7 & -3.69994923932857 & -3.30005076067143 \tabularnewline
55 & -7.2 & -6.99979067374356 & -0.200209326256443 \tabularnewline
56 & -11.8 & -7.19998730047754 & -4.60001269952247 \tabularnewline
57 & -2.1 & -11.7997082155676 & 9.69970821556764 \tabularnewline
58 & 1.2 & -2.10061526435701 & 3.30061526435701 \tabularnewline
59 & 2.5 & 1.1997906379364 & 1.3002093620636 \tabularnewline
60 & 4.8 & 2.49991752612972 & 2.30008247387028 \tabularnewline
61 & -6.6 & 4.79985410295517 & -11.3998541029552 \tabularnewline
62 & -16 & -6.5992768933097 & -9.4007231066903 \tabularnewline
63 & -22.7 & -15.9994037006342 & -6.70059629936582 \tabularnewline
64 & -17.7 & -22.6995749729804 & 4.99957497298042 \tabularnewline
65 & -18.2 & -17.7003171291561 & -0.499682870843877 \tabularnewline
66 & -18.9 & -18.1999683045043 & -0.700031695495721 \tabularnewline
67 & -16 & -18.8999555961333 & 2.89995559613326 \tabularnewline
68 & -12.2 & -16.0001839477308 & 3.80018394773075 \tabularnewline
69 & -17.1 & -12.2002410503163 & -4.89975894968373 \tabularnewline
70 & -18.6 & -17.0996892022963 & -1.50031079770367 \tabularnewline
71 & -17.5 & -18.5999048334509 & 1.09990483345089 \tabularnewline
72 & -24.9 & -17.500069768309 & -7.39993023169098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209245&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]2[/C][C]-7.1[/C][C]-5.3[/C][C]-1.8[/C][/ROW]
[ROW][C]3[/C][C]-8[/C][C]-7.0998858237982[/C][C]-0.900114176201799[/C][/ROW]
[ROW][C]4[/C][C]-8.9[/C][C]-7.99994290465676[/C][C]-0.900057095343236[/C][/ROW]
[ROW][C]5[/C][C]-7.7[/C][C]-8.89994290827747[/C][C]1.19994290827747[/C][/ROW]
[ROW][C]6[/C][C]-1.1[/C][C]-7.70007611384647[/C][C]6.60007611384647[/C][/ROW]
[ROW][C]7[/C][C]4[/C][C]-1.10041865090126[/C][C]5.10041865090126[/C][/ROW]
[ROW][C]8[/C][C]9.6[/C][C]3.99967647420603[/C][C]5.60032352579397[/C][/ROW]
[ROW][C]9[/C][C]10.9[/C][C]9.59964476462832[/C][C]1.30035523537168[/C][/ROW]
[ROW][C]10[/C][C]13[/C][C]10.8999175168768[/C][C]2.1000824831232[/C][/ROW]
[ROW][C]11[/C][C]14.9[/C][C]12.9998667891992[/C][C]1.90013321080077[/C][/ROW]
[ROW][C]12[/C][C]20.1[/C][C]14.8998794722262[/C][C]5.20012052777385[/C][/ROW]
[ROW][C]13[/C][C]10.8[/C][C]20.099670149994[/C][C]-9.29967014999403[/C][/ROW]
[ROW][C]14[/C][C]11[/C][C]10.8005898894532[/C][C]0.199410110546827[/C][/ROW]
[ROW][C]15[/C][C]3.8[/C][C]10.9999873511728[/C][C]-7.19998735117276[/C][/ROW]
[ROW][C]16[/C][C]10.8[/C][C]3.80045670400486[/C][C]6.99954329599514[/C][/ROW]
[ROW][C]17[/C][C]7.6[/C][C]10.7995560104067[/C][C]-3.19955601040674[/C][/ROW]
[ROW][C]18[/C][C]10.2[/C][C]7.60020295175151[/C][C]2.59979704824849[/C][/ROW]
[ROW][C]19[/C][C]2.2[/C][C]10.1998350916931[/C][C]-7.9998350916931[/C][/ROW]
[ROW][C]20[/C][C]-0.1[/C][C]2.20050743932544[/C][C]-2.30050743932544[/C][/ROW]
[ROW][C]21[/C][C]-1.7[/C][C]-0.0998540759990932[/C][C]-1.60014592400091[/C][/ROW]
[ROW][C]22[/C][C]-4.8[/C][C]-1.69989850078671[/C][C]-3.10010149921329[/C][/ROW]
[ROW][C]23[/C][C]-9.9[/C][C]-4.79980335676979[/C][C]-5.10019664323021[/C][/ROW]
[ROW][C]24[/C][C]-13.5[/C][C]-9.89967648828825[/C][C]-3.60032351171175[/C][/ROW]
[ROW][C]25[/C][C]-18.1[/C][C]-13.4997716270757[/C][C]-4.60022837292434[/C][/ROW]
[ROW][C]26[/C][C]-18[/C][C]-18.0997082018872[/C][C]0.0997082018872071[/C][/ROW]
[ROW][C]27[/C][C]-15.7[/C][C]-18.0000063246132[/C][C]2.30000632461321[/C][/ROW]
[ROW][C]28[/C][C]-15.2[/C][C]-15.7001458922146[/C][C]0.500145892214588[/C][/ROW]
[ROW][C]29[/C][C]-15.1[/C][C]-15.2000317248657[/C][C]0.100031724865731[/C][/ROW]
[ROW][C]30[/C][C]-17.9[/C][C]-15.1000063451347[/C][C]-2.79999365486533[/C][/ROW]
[ROW][C]31[/C][C]-14.5[/C][C]-17.8998223929775[/C][C]3.39982239297746[/C][/ROW]
[ROW][C]32[/C][C]-9.4[/C][C]-14.5002156548931[/C][C]5.10021565489312[/C][/ROW]
[ROW][C]33[/C][C]-4.2[/C][C]-9.40032351291768[/C][C]5.20032351291768[/C][/ROW]
[ROW][C]34[/C][C]-2.2[/C][C]-4.20032986288157[/C][C]2.00032986288157[/C][/ROW]
[ROW][C]35[/C][C]4.5[/C][C]-2.20012688337005[/C][C]6.70012688337005[/C][/ROW]
[ROW][C]36[/C][C]12.4[/C][C]4.49957500275605[/C][C]7.90042499724395[/C][/ROW]
[ROW][C]37[/C][C]15.8[/C][C]12.3994988663785[/C][C]3.40050113362155[/C][/ROW]
[ROW][C]38[/C][C]11.5[/C][C]15.7997843020535[/C][C]-4.29978430205353[/C][/ROW]
[ROW][C]39[/C][C]14.1[/C][C]11.5002727405779[/C][C]2.59972725942213[/C][/ROW]
[ROW][C]40[/C][C]18.8[/C][C]14.0998350961199[/C][C]4.70016490388011[/C][/ROW]
[ROW][C]41[/C][C]26.1[/C][C]18.7997018627908[/C][C]7.3002981372092[/C][/ROW]
[ROW][C]42[/C][C]27.9[/C][C]26.0995369331593[/C][C]1.80046306684072[/C][/ROW]
[ROW][C]43[/C][C]25.4[/C][C]27.8998857944253[/C][C]-2.4998857944253[/C][/ROW]
[ROW][C]44[/C][C]23.4[/C][C]25.4001585708139[/C][C]-2.00015857081386[/C][/ROW]
[ROW][C]45[/C][C]11.5[/C][C]23.4001268725048[/C][C]-11.9001268725048[/C][/ROW]
[ROW][C]46[/C][C]9.9[/C][C]11.500754839604[/C][C]-1.60075483960401[/C][/ROW]
[ROW][C]47[/C][C]8.1[/C][C]9.90010153783756[/C][C]-1.80010153783756[/C][/ROW]
[ROW][C]48[/C][C]12.6[/C][C]8.10011418264247[/C][C]4.49988581735753[/C][/ROW]
[ROW][C]49[/C][C]8.2[/C][C]12.5997145667382[/C][C]-4.39971456673825[/C][/ROW]
[ROW][C]50[/C][C]5.4[/C][C]8.20027907927679[/C][C]-2.80027907927679[/C][/ROW]
[ROW][C]51[/C][C]1[/C][C]5.40017762512736[/C][C]-4.40017762512736[/C][/ROW]
[ROW][C]52[/C][C]-2.9[/C][C]1.00027910864915[/C][C]-3.90027910864915[/C][/ROW]
[ROW][C]53[/C][C]-3.7[/C][C]-2.89975260052523[/C][C]-0.800247399474768[/C][/ROW]
[ROW][C]54[/C][C]-7[/C][C]-3.69994923932857[/C][C]-3.30005076067143[/C][/ROW]
[ROW][C]55[/C][C]-7.2[/C][C]-6.99979067374356[/C][C]-0.200209326256443[/C][/ROW]
[ROW][C]56[/C][C]-11.8[/C][C]-7.19998730047754[/C][C]-4.60001269952247[/C][/ROW]
[ROW][C]57[/C][C]-2.1[/C][C]-11.7997082155676[/C][C]9.69970821556764[/C][/ROW]
[ROW][C]58[/C][C]1.2[/C][C]-2.10061526435701[/C][C]3.30061526435701[/C][/ROW]
[ROW][C]59[/C][C]2.5[/C][C]1.1997906379364[/C][C]1.3002093620636[/C][/ROW]
[ROW][C]60[/C][C]4.8[/C][C]2.49991752612972[/C][C]2.30008247387028[/C][/ROW]
[ROW][C]61[/C][C]-6.6[/C][C]4.79985410295517[/C][C]-11.3998541029552[/C][/ROW]
[ROW][C]62[/C][C]-16[/C][C]-6.5992768933097[/C][C]-9.4007231066903[/C][/ROW]
[ROW][C]63[/C][C]-22.7[/C][C]-15.9994037006342[/C][C]-6.70059629936582[/C][/ROW]
[ROW][C]64[/C][C]-17.7[/C][C]-22.6995749729804[/C][C]4.99957497298042[/C][/ROW]
[ROW][C]65[/C][C]-18.2[/C][C]-17.7003171291561[/C][C]-0.499682870843877[/C][/ROW]
[ROW][C]66[/C][C]-18.9[/C][C]-18.1999683045043[/C][C]-0.700031695495721[/C][/ROW]
[ROW][C]67[/C][C]-16[/C][C]-18.8999555961333[/C][C]2.89995559613326[/C][/ROW]
[ROW][C]68[/C][C]-12.2[/C][C]-16.0001839477308[/C][C]3.80018394773075[/C][/ROW]
[ROW][C]69[/C][C]-17.1[/C][C]-12.2002410503163[/C][C]-4.89975894968373[/C][/ROW]
[ROW][C]70[/C][C]-18.6[/C][C]-17.0996892022963[/C][C]-1.50031079770367[/C][/ROW]
[ROW][C]71[/C][C]-17.5[/C][C]-18.5999048334509[/C][C]1.09990483345089[/C][/ROW]
[ROW][C]72[/C][C]-24.9[/C][C]-17.500069768309[/C][C]-7.39993023169098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209245&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209245&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
2-7.1-5.3-1.8
3-8-7.0998858237982-0.900114176201799
4-8.9-7.99994290465676-0.900057095343236
5-7.7-8.899942908277471.19994290827747
6-1.1-7.700076113846476.60007611384647
74-1.100418650901265.10041865090126
89.63.999676474206035.60032352579397
910.99.599644764628321.30035523537168
101310.89991751687682.1000824831232
1114.912.99986678919921.90013321080077
1220.114.89987947222625.20012052777385
1310.820.099670149994-9.29967014999403
141110.80058988945320.199410110546827
153.810.9999873511728-7.19998735117276
1610.83.800456704004866.99954329599514
177.610.7995560104067-3.19955601040674
1810.27.600202951751512.59979704824849
192.210.1998350916931-7.9998350916931
20-0.12.20050743932544-2.30050743932544
21-1.7-0.0998540759990932-1.60014592400091
22-4.8-1.69989850078671-3.10010149921329
23-9.9-4.79980335676979-5.10019664323021
24-13.5-9.89967648828825-3.60032351171175
25-18.1-13.4997716270757-4.60022837292434
26-18-18.09970820188720.0997082018872071
27-15.7-18.00000632461322.30000632461321
28-15.2-15.70014589221460.500145892214588
29-15.1-15.20003172486570.100031724865731
30-17.9-15.1000063451347-2.79999365486533
31-14.5-17.89982239297753.39982239297746
32-9.4-14.50021565489315.10021565489312
33-4.2-9.400323512917685.20032351291768
34-2.2-4.200329862881572.00032986288157
354.5-2.200126883370056.70012688337005
3612.44.499575002756057.90042499724395
3715.812.39949886637853.40050113362155
3811.515.7997843020535-4.29978430205353
3914.111.50027274057792.59972725942213
4018.814.09983509611994.70016490388011
4126.118.79970186279087.3002981372092
4227.926.09953693315931.80046306684072
4325.427.8998857944253-2.4998857944253
4423.425.4001585708139-2.00015857081386
4511.523.4001268725048-11.9001268725048
469.911.500754839604-1.60075483960401
478.19.90010153783756-1.80010153783756
4812.68.100114182642474.49988581735753
498.212.5997145667382-4.39971456673825
505.48.20027907927679-2.80027907927679
5115.40017762512736-4.40017762512736
52-2.91.00027910864915-3.90027910864915
53-3.7-2.89975260052523-0.800247399474768
54-7-3.69994923932857-3.30005076067143
55-7.2-6.99979067374356-0.200209326256443
56-11.8-7.19998730047754-4.60001269952247
57-2.1-11.79970821556769.69970821556764
581.2-2.100615264357013.30061526435701
592.51.19979063793641.3002093620636
604.82.499917526129722.30008247387028
61-6.64.79985410295517-11.3998541029552
62-16-6.5992768933097-9.4007231066903
63-22.7-15.9994037006342-6.70059629936582
64-17.7-22.69957497298044.99957497298042
65-18.2-17.7003171291561-0.499682870843877
66-18.9-18.1999683045043-0.700031695495721
67-16-18.89995559613332.89995559613326
68-12.2-16.00018394773083.80018394773075
69-17.1-12.2002410503163-4.89975894968373
70-18.6-17.0996892022963-1.50031079770367
71-17.5-18.59990483345091.09990483345089
72-24.9-17.500069768309-7.39993023169098







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-24.8995306133736-34.1749252453349-15.6241359814124
74-24.8995306133736-38.0165034788422-11.7825577479051
75-24.8995306133736-40.9643060157332-8.83475521101406
76-24.8995306133736-43.449437359853-6.34962386689434
77-24.8995306133736-45.638891063443-4.16017016330434
78-24.8995306133736-47.6183136673297-2.18074755941762
79-24.8995306133736-49.4385838760311-0.36047735071617
80-24.8995306133736-51.13285229787181.33379107112451
81-24.8995306133736-52.7241455824472.92508435569972
82-24.8995306133736-54.22922938018684.43016815343953
83-24.8995306133736-55.66076045430855.86169922756125
84-24.8995306133736-57.02857188294237.22951065619498

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & -24.8995306133736 & -34.1749252453349 & -15.6241359814124 \tabularnewline
74 & -24.8995306133736 & -38.0165034788422 & -11.7825577479051 \tabularnewline
75 & -24.8995306133736 & -40.9643060157332 & -8.83475521101406 \tabularnewline
76 & -24.8995306133736 & -43.449437359853 & -6.34962386689434 \tabularnewline
77 & -24.8995306133736 & -45.638891063443 & -4.16017016330434 \tabularnewline
78 & -24.8995306133736 & -47.6183136673297 & -2.18074755941762 \tabularnewline
79 & -24.8995306133736 & -49.4385838760311 & -0.36047735071617 \tabularnewline
80 & -24.8995306133736 & -51.1328522978718 & 1.33379107112451 \tabularnewline
81 & -24.8995306133736 & -52.724145582447 & 2.92508435569972 \tabularnewline
82 & -24.8995306133736 & -54.2292293801868 & 4.43016815343953 \tabularnewline
83 & -24.8995306133736 & -55.6607604543085 & 5.86169922756125 \tabularnewline
84 & -24.8995306133736 & -57.0285718829423 & 7.22951065619498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209245&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]73[/C][C]-24.8995306133736[/C][C]-34.1749252453349[/C][C]-15.6241359814124[/C][/ROW]
[ROW][C]74[/C][C]-24.8995306133736[/C][C]-38.0165034788422[/C][C]-11.7825577479051[/C][/ROW]
[ROW][C]75[/C][C]-24.8995306133736[/C][C]-40.9643060157332[/C][C]-8.83475521101406[/C][/ROW]
[ROW][C]76[/C][C]-24.8995306133736[/C][C]-43.449437359853[/C][C]-6.34962386689434[/C][/ROW]
[ROW][C]77[/C][C]-24.8995306133736[/C][C]-45.638891063443[/C][C]-4.16017016330434[/C][/ROW]
[ROW][C]78[/C][C]-24.8995306133736[/C][C]-47.6183136673297[/C][C]-2.18074755941762[/C][/ROW]
[ROW][C]79[/C][C]-24.8995306133736[/C][C]-49.4385838760311[/C][C]-0.36047735071617[/C][/ROW]
[ROW][C]80[/C][C]-24.8995306133736[/C][C]-51.1328522978718[/C][C]1.33379107112451[/C][/ROW]
[ROW][C]81[/C][C]-24.8995306133736[/C][C]-52.724145582447[/C][C]2.92508435569972[/C][/ROW]
[ROW][C]82[/C][C]-24.8995306133736[/C][C]-54.2292293801868[/C][C]4.43016815343953[/C][/ROW]
[ROW][C]83[/C][C]-24.8995306133736[/C][C]-55.6607604543085[/C][C]5.86169922756125[/C][/ROW]
[ROW][C]84[/C][C]-24.8995306133736[/C][C]-57.0285718829423[/C][C]7.22951065619498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209245&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209245&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
73-24.8995306133736-34.1749252453349-15.6241359814124
74-24.8995306133736-38.0165034788422-11.7825577479051
75-24.8995306133736-40.9643060157332-8.83475521101406
76-24.8995306133736-43.449437359853-6.34962386689434
77-24.8995306133736-45.638891063443-4.16017016330434
78-24.8995306133736-47.6183136673297-2.18074755941762
79-24.8995306133736-49.4385838760311-0.36047735071617
80-24.8995306133736-51.13285229787181.33379107112451
81-24.8995306133736-52.7241455824472.92508435569972
82-24.8995306133736-54.22922938018684.43016815343953
83-24.8995306133736-55.66076045430855.86169922756125
84-24.8995306133736-57.02857188294237.22951065619498



Parameters (Session):
par1 = 750 ; par2 = 5 ; par3 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')