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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 24 May 2015 20:17:44 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/24/t1432495087pvm766xoqoi5nvr.htm/, Retrieved Thu, 02 May 2024 17:56:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279312, Retrieved Thu, 02 May 2024 17:56:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [double consumente...] [2015-05-24 19:17:44] [e6344a6a1a33122c0bdf1792ef294740] [Current]
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Dataseries X:
-5
-6
-6
-7
-12
-16
-18
-19
-20
-24
-17
-23
-25
-24
-17
-14
-16
-13
-10
-10
-12
-12
-20
-16
-12
-14
-7
-9
-9
-4
-3
1
-1
-2
1
-3
-2
0
-2
-4
-4
-7
-9
-13
-8
-13
-15
-15
-15
-10
-12
-11
-11
-17
-18
-19
-22
-24
-24
-20
-25
-22
-17
-9
-11
-13
-11
-9
-7
-3
-3
-6
-4
-8
-1
-2
-2
-1
1
2
2
-1
1
-1
-8
1
2
-2
-2
-2
-2
-6
-4
-5
-2
-1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279312&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279312&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279312&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.845253755054203
beta0.0375954877050928
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.845253755054203 \tabularnewline
beta & 0.0375954877050928 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279312&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]0.845253755054203[/C][/ROW]
[ROW][C]beta[/C][C]0.0375954877050928[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279312&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279312&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
alpha0.845253755054203
beta0.0375954877050928
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3-6-71
4-7-7.122968517789970.122968517789973
5-12-7.98334352921164-4.01665647078836
6-16-12.4703923201527-3.52960767984726
7-18-16.6579242014736-1.34207579852644
8-19-19.03908466435520.0390846643551725
9-20-20.25157203785380.251572037853844
10-24-21.2764592734222-2.72354072657779
11-17-24.90261967894317.90261967894306
12-23-19.2958508079154-3.70414919208458
13-25-23.6174563515407-1.38254364845934
14-24-26.02065018650382.02065018650377
15-17-25.48306998298298.48306998298292
16-14-19.21353249638855.21353249638846
17-16-15.5419096344402-0.458090365559812
18-13-16.67880436445443.67880436445443
19-10-14.20206924830694.20206924830691
20-10-11.14951031413251.1495103141325
21-12-10.640609456468-1.35939054353204
22-12-12.29556481159370.295564811593652
23-20-12.5422705604126-7.45772943958739
24-16-19.57946708041573.57946708041567
25-12-17.17368446837035.17368446837025
26-14-13.2559756893573-0.74402431064267
27-7-14.36387587866327.36387587866321
28-9-8.38453574887209-0.615464251127905
29-9-9.169320881688120.169320881688119
30-4-9.285382801300625.28538280130062
31-3-4.909116719697021.90911671969702
321-3.325984831403854.32598483140385
33-10.437483869432859-1.43748386943286
34-2-0.716320961443765-1.28367903855624
351-1.780914083719342.78091408371934
36-30.678476522372228-3.67847652237223
37-2-2.4388506599740.438850659973996
380-2.062045904120532.06204590412053
39-2-0.24770214084215-1.75229785915785
40-4-1.71313080980646-2.28686919019354
41-4-3.70307940884003-0.296920591159965
42-7-4.02045194370846-2.97954805629154
43-9-6.70000868207138-2.29999131792862
44-13-8.87825603212256-4.12174396787744
45-8-12.72732630554034.72732630554029
46-13-8.94646301609916-4.05353698390084
47-15-12.7164695869662-2.28353041303381
48-15-15.06293686375470.0629368637546559
49-15-15.42404387324140.424043873241425
50-10-15.46644867647715.46644867647714
51-12-11.0730305707221-0.926969429277884
52-11-12.11313010809341.11313010809344
53-11-11.39345510595340.393455105953382
54-17-11.2695849927858-5.7304150072142
55-18-16.5040386528262-1.49596134717379
56-19-18.2068427076406-0.7931572923594
57-22-19.3408037320841-2.65919626791595
58-24-22.1365444211498-1.86345557885021
59-24-24.3188986876850.318898687685
60-20-24.64647594008524.64647594008516
61-25-21.1684978249468-3.8315021750532
62-22-24.97831897761232.97831897761229
63-17-22.93746902188615.93746902188615
64-9-18.20670710889519.20670710889506
65-11-10.4200412001834-0.579958799816573
66-13-10.9240211727734-2.07597882722655
67-11-12.75848757992091.75848757992092
68-9-11.29597611927622.29597611927615
69-7-9.306189549768142.30618954976814
70-3-7.234484577502644.23448457750264
71-3-3.398318696642780.398318696642783
72-6-2.79202876872756-3.20797123127244
73-4-5.335910978707941.33591097870794
74-8-3.99660747359256-4.00339252640744
75-1-7.297589020951866.29758902095186
76-2-1.69150416901434-0.308495830985662
77-2-1.67904064072947-0.320959359270533
78-1-1.687311315475610.687311315475615
791-0.8214962248272521.82149622482725
8021.060875929424320.939124070575683
8122.2272629354197-0.227262935419701
82-12.40053504519666-3.40053504519666
831-0.2164742864742071.21647428647421
84-11.10771764453768-2.10771764453768
85-8-0.444854612888752-7.55514538711125
861-6.841970973846147.84197097384614
8720.02458310027299081.97541689972701
88-21.99518457327292-3.99518457327292
89-2-1.20784515401912-0.792154845980878
90-2-1.72867485732807-0.271325142671931
91-2-1.8178933945257-0.182106605474295
92-6-1.83748656215863-4.16251343784137
93-4-5.353808767803411.35380876780341
94-5-4.16441794939363-0.835582050606368
95-2-4.852170839946392.85217083994639
96-1-2.332201245293821.33220124529382

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -6 & -7 & 1 \tabularnewline
4 & -7 & -7.12296851778997 & 0.122968517789973 \tabularnewline
5 & -12 & -7.98334352921164 & -4.01665647078836 \tabularnewline
6 & -16 & -12.4703923201527 & -3.52960767984726 \tabularnewline
7 & -18 & -16.6579242014736 & -1.34207579852644 \tabularnewline
8 & -19 & -19.0390846643552 & 0.0390846643551725 \tabularnewline
9 & -20 & -20.2515720378538 & 0.251572037853844 \tabularnewline
10 & -24 & -21.2764592734222 & -2.72354072657779 \tabularnewline
11 & -17 & -24.9026196789431 & 7.90261967894306 \tabularnewline
12 & -23 & -19.2958508079154 & -3.70414919208458 \tabularnewline
13 & -25 & -23.6174563515407 & -1.38254364845934 \tabularnewline
14 & -24 & -26.0206501865038 & 2.02065018650377 \tabularnewline
15 & -17 & -25.4830699829829 & 8.48306998298292 \tabularnewline
16 & -14 & -19.2135324963885 & 5.21353249638846 \tabularnewline
17 & -16 & -15.5419096344402 & -0.458090365559812 \tabularnewline
18 & -13 & -16.6788043644544 & 3.67880436445443 \tabularnewline
19 & -10 & -14.2020692483069 & 4.20206924830691 \tabularnewline
20 & -10 & -11.1495103141325 & 1.1495103141325 \tabularnewline
21 & -12 & -10.640609456468 & -1.35939054353204 \tabularnewline
22 & -12 & -12.2955648115937 & 0.295564811593652 \tabularnewline
23 & -20 & -12.5422705604126 & -7.45772943958739 \tabularnewline
24 & -16 & -19.5794670804157 & 3.57946708041567 \tabularnewline
25 & -12 & -17.1736844683703 & 5.17368446837025 \tabularnewline
26 & -14 & -13.2559756893573 & -0.74402431064267 \tabularnewline
27 & -7 & -14.3638758786632 & 7.36387587866321 \tabularnewline
28 & -9 & -8.38453574887209 & -0.615464251127905 \tabularnewline
29 & -9 & -9.16932088168812 & 0.169320881688119 \tabularnewline
30 & -4 & -9.28538280130062 & 5.28538280130062 \tabularnewline
31 & -3 & -4.90911671969702 & 1.90911671969702 \tabularnewline
32 & 1 & -3.32598483140385 & 4.32598483140385 \tabularnewline
33 & -1 & 0.437483869432859 & -1.43748386943286 \tabularnewline
34 & -2 & -0.716320961443765 & -1.28367903855624 \tabularnewline
35 & 1 & -1.78091408371934 & 2.78091408371934 \tabularnewline
36 & -3 & 0.678476522372228 & -3.67847652237223 \tabularnewline
37 & -2 & -2.438850659974 & 0.438850659973996 \tabularnewline
38 & 0 & -2.06204590412053 & 2.06204590412053 \tabularnewline
39 & -2 & -0.24770214084215 & -1.75229785915785 \tabularnewline
40 & -4 & -1.71313080980646 & -2.28686919019354 \tabularnewline
41 & -4 & -3.70307940884003 & -0.296920591159965 \tabularnewline
42 & -7 & -4.02045194370846 & -2.97954805629154 \tabularnewline
43 & -9 & -6.70000868207138 & -2.29999131792862 \tabularnewline
44 & -13 & -8.87825603212256 & -4.12174396787744 \tabularnewline
45 & -8 & -12.7273263055403 & 4.72732630554029 \tabularnewline
46 & -13 & -8.94646301609916 & -4.05353698390084 \tabularnewline
47 & -15 & -12.7164695869662 & -2.28353041303381 \tabularnewline
48 & -15 & -15.0629368637547 & 0.0629368637546559 \tabularnewline
49 & -15 & -15.4240438732414 & 0.424043873241425 \tabularnewline
50 & -10 & -15.4664486764771 & 5.46644867647714 \tabularnewline
51 & -12 & -11.0730305707221 & -0.926969429277884 \tabularnewline
52 & -11 & -12.1131301080934 & 1.11313010809344 \tabularnewline
53 & -11 & -11.3934551059534 & 0.393455105953382 \tabularnewline
54 & -17 & -11.2695849927858 & -5.7304150072142 \tabularnewline
55 & -18 & -16.5040386528262 & -1.49596134717379 \tabularnewline
56 & -19 & -18.2068427076406 & -0.7931572923594 \tabularnewline
57 & -22 & -19.3408037320841 & -2.65919626791595 \tabularnewline
58 & -24 & -22.1365444211498 & -1.86345557885021 \tabularnewline
59 & -24 & -24.318898687685 & 0.318898687685 \tabularnewline
60 & -20 & -24.6464759400852 & 4.64647594008516 \tabularnewline
61 & -25 & -21.1684978249468 & -3.8315021750532 \tabularnewline
62 & -22 & -24.9783189776123 & 2.97831897761229 \tabularnewline
63 & -17 & -22.9374690218861 & 5.93746902188615 \tabularnewline
64 & -9 & -18.2067071088951 & 9.20670710889506 \tabularnewline
65 & -11 & -10.4200412001834 & -0.579958799816573 \tabularnewline
66 & -13 & -10.9240211727734 & -2.07597882722655 \tabularnewline
67 & -11 & -12.7584875799209 & 1.75848757992092 \tabularnewline
68 & -9 & -11.2959761192762 & 2.29597611927615 \tabularnewline
69 & -7 & -9.30618954976814 & 2.30618954976814 \tabularnewline
70 & -3 & -7.23448457750264 & 4.23448457750264 \tabularnewline
71 & -3 & -3.39831869664278 & 0.398318696642783 \tabularnewline
72 & -6 & -2.79202876872756 & -3.20797123127244 \tabularnewline
73 & -4 & -5.33591097870794 & 1.33591097870794 \tabularnewline
74 & -8 & -3.99660747359256 & -4.00339252640744 \tabularnewline
75 & -1 & -7.29758902095186 & 6.29758902095186 \tabularnewline
76 & -2 & -1.69150416901434 & -0.308495830985662 \tabularnewline
77 & -2 & -1.67904064072947 & -0.320959359270533 \tabularnewline
78 & -1 & -1.68731131547561 & 0.687311315475615 \tabularnewline
79 & 1 & -0.821496224827252 & 1.82149622482725 \tabularnewline
80 & 2 & 1.06087592942432 & 0.939124070575683 \tabularnewline
81 & 2 & 2.2272629354197 & -0.227262935419701 \tabularnewline
82 & -1 & 2.40053504519666 & -3.40053504519666 \tabularnewline
83 & 1 & -0.216474286474207 & 1.21647428647421 \tabularnewline
84 & -1 & 1.10771764453768 & -2.10771764453768 \tabularnewline
85 & -8 & -0.444854612888752 & -7.55514538711125 \tabularnewline
86 & 1 & -6.84197097384614 & 7.84197097384614 \tabularnewline
87 & 2 & 0.0245831002729908 & 1.97541689972701 \tabularnewline
88 & -2 & 1.99518457327292 & -3.99518457327292 \tabularnewline
89 & -2 & -1.20784515401912 & -0.792154845980878 \tabularnewline
90 & -2 & -1.72867485732807 & -0.271325142671931 \tabularnewline
91 & -2 & -1.8178933945257 & -0.182106605474295 \tabularnewline
92 & -6 & -1.83748656215863 & -4.16251343784137 \tabularnewline
93 & -4 & -5.35380876780341 & 1.35380876780341 \tabularnewline
94 & -5 & -4.16441794939363 & -0.835582050606368 \tabularnewline
95 & -2 & -4.85217083994639 & 2.85217083994639 \tabularnewline
96 & -1 & -2.33220124529382 & 1.33220124529382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279312&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]-6[/C][C]-7[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]-7[/C][C]-7.12296851778997[/C][C]0.122968517789973[/C][/ROW]
[ROW][C]5[/C][C]-12[/C][C]-7.98334352921164[/C][C]-4.01665647078836[/C][/ROW]
[ROW][C]6[/C][C]-16[/C][C]-12.4703923201527[/C][C]-3.52960767984726[/C][/ROW]
[ROW][C]7[/C][C]-18[/C][C]-16.6579242014736[/C][C]-1.34207579852644[/C][/ROW]
[ROW][C]8[/C][C]-19[/C][C]-19.0390846643552[/C][C]0.0390846643551725[/C][/ROW]
[ROW][C]9[/C][C]-20[/C][C]-20.2515720378538[/C][C]0.251572037853844[/C][/ROW]
[ROW][C]10[/C][C]-24[/C][C]-21.2764592734222[/C][C]-2.72354072657779[/C][/ROW]
[ROW][C]11[/C][C]-17[/C][C]-24.9026196789431[/C][C]7.90261967894306[/C][/ROW]
[ROW][C]12[/C][C]-23[/C][C]-19.2958508079154[/C][C]-3.70414919208458[/C][/ROW]
[ROW][C]13[/C][C]-25[/C][C]-23.6174563515407[/C][C]-1.38254364845934[/C][/ROW]
[ROW][C]14[/C][C]-24[/C][C]-26.0206501865038[/C][C]2.02065018650377[/C][/ROW]
[ROW][C]15[/C][C]-17[/C][C]-25.4830699829829[/C][C]8.48306998298292[/C][/ROW]
[ROW][C]16[/C][C]-14[/C][C]-19.2135324963885[/C][C]5.21353249638846[/C][/ROW]
[ROW][C]17[/C][C]-16[/C][C]-15.5419096344402[/C][C]-0.458090365559812[/C][/ROW]
[ROW][C]18[/C][C]-13[/C][C]-16.6788043644544[/C][C]3.67880436445443[/C][/ROW]
[ROW][C]19[/C][C]-10[/C][C]-14.2020692483069[/C][C]4.20206924830691[/C][/ROW]
[ROW][C]20[/C][C]-10[/C][C]-11.1495103141325[/C][C]1.1495103141325[/C][/ROW]
[ROW][C]21[/C][C]-12[/C][C]-10.640609456468[/C][C]-1.35939054353204[/C][/ROW]
[ROW][C]22[/C][C]-12[/C][C]-12.2955648115937[/C][C]0.295564811593652[/C][/ROW]
[ROW][C]23[/C][C]-20[/C][C]-12.5422705604126[/C][C]-7.45772943958739[/C][/ROW]
[ROW][C]24[/C][C]-16[/C][C]-19.5794670804157[/C][C]3.57946708041567[/C][/ROW]
[ROW][C]25[/C][C]-12[/C][C]-17.1736844683703[/C][C]5.17368446837025[/C][/ROW]
[ROW][C]26[/C][C]-14[/C][C]-13.2559756893573[/C][C]-0.74402431064267[/C][/ROW]
[ROW][C]27[/C][C]-7[/C][C]-14.3638758786632[/C][C]7.36387587866321[/C][/ROW]
[ROW][C]28[/C][C]-9[/C][C]-8.38453574887209[/C][C]-0.615464251127905[/C][/ROW]
[ROW][C]29[/C][C]-9[/C][C]-9.16932088168812[/C][C]0.169320881688119[/C][/ROW]
[ROW][C]30[/C][C]-4[/C][C]-9.28538280130062[/C][C]5.28538280130062[/C][/ROW]
[ROW][C]31[/C][C]-3[/C][C]-4.90911671969702[/C][C]1.90911671969702[/C][/ROW]
[ROW][C]32[/C][C]1[/C][C]-3.32598483140385[/C][C]4.32598483140385[/C][/ROW]
[ROW][C]33[/C][C]-1[/C][C]0.437483869432859[/C][C]-1.43748386943286[/C][/ROW]
[ROW][C]34[/C][C]-2[/C][C]-0.716320961443765[/C][C]-1.28367903855624[/C][/ROW]
[ROW][C]35[/C][C]1[/C][C]-1.78091408371934[/C][C]2.78091408371934[/C][/ROW]
[ROW][C]36[/C][C]-3[/C][C]0.678476522372228[/C][C]-3.67847652237223[/C][/ROW]
[ROW][C]37[/C][C]-2[/C][C]-2.438850659974[/C][C]0.438850659973996[/C][/ROW]
[ROW][C]38[/C][C]0[/C][C]-2.06204590412053[/C][C]2.06204590412053[/C][/ROW]
[ROW][C]39[/C][C]-2[/C][C]-0.24770214084215[/C][C]-1.75229785915785[/C][/ROW]
[ROW][C]40[/C][C]-4[/C][C]-1.71313080980646[/C][C]-2.28686919019354[/C][/ROW]
[ROW][C]41[/C][C]-4[/C][C]-3.70307940884003[/C][C]-0.296920591159965[/C][/ROW]
[ROW][C]42[/C][C]-7[/C][C]-4.02045194370846[/C][C]-2.97954805629154[/C][/ROW]
[ROW][C]43[/C][C]-9[/C][C]-6.70000868207138[/C][C]-2.29999131792862[/C][/ROW]
[ROW][C]44[/C][C]-13[/C][C]-8.87825603212256[/C][C]-4.12174396787744[/C][/ROW]
[ROW][C]45[/C][C]-8[/C][C]-12.7273263055403[/C][C]4.72732630554029[/C][/ROW]
[ROW][C]46[/C][C]-13[/C][C]-8.94646301609916[/C][C]-4.05353698390084[/C][/ROW]
[ROW][C]47[/C][C]-15[/C][C]-12.7164695869662[/C][C]-2.28353041303381[/C][/ROW]
[ROW][C]48[/C][C]-15[/C][C]-15.0629368637547[/C][C]0.0629368637546559[/C][/ROW]
[ROW][C]49[/C][C]-15[/C][C]-15.4240438732414[/C][C]0.424043873241425[/C][/ROW]
[ROW][C]50[/C][C]-10[/C][C]-15.4664486764771[/C][C]5.46644867647714[/C][/ROW]
[ROW][C]51[/C][C]-12[/C][C]-11.0730305707221[/C][C]-0.926969429277884[/C][/ROW]
[ROW][C]52[/C][C]-11[/C][C]-12.1131301080934[/C][C]1.11313010809344[/C][/ROW]
[ROW][C]53[/C][C]-11[/C][C]-11.3934551059534[/C][C]0.393455105953382[/C][/ROW]
[ROW][C]54[/C][C]-17[/C][C]-11.2695849927858[/C][C]-5.7304150072142[/C][/ROW]
[ROW][C]55[/C][C]-18[/C][C]-16.5040386528262[/C][C]-1.49596134717379[/C][/ROW]
[ROW][C]56[/C][C]-19[/C][C]-18.2068427076406[/C][C]-0.7931572923594[/C][/ROW]
[ROW][C]57[/C][C]-22[/C][C]-19.3408037320841[/C][C]-2.65919626791595[/C][/ROW]
[ROW][C]58[/C][C]-24[/C][C]-22.1365444211498[/C][C]-1.86345557885021[/C][/ROW]
[ROW][C]59[/C][C]-24[/C][C]-24.318898687685[/C][C]0.318898687685[/C][/ROW]
[ROW][C]60[/C][C]-20[/C][C]-24.6464759400852[/C][C]4.64647594008516[/C][/ROW]
[ROW][C]61[/C][C]-25[/C][C]-21.1684978249468[/C][C]-3.8315021750532[/C][/ROW]
[ROW][C]62[/C][C]-22[/C][C]-24.9783189776123[/C][C]2.97831897761229[/C][/ROW]
[ROW][C]63[/C][C]-17[/C][C]-22.9374690218861[/C][C]5.93746902188615[/C][/ROW]
[ROW][C]64[/C][C]-9[/C][C]-18.2067071088951[/C][C]9.20670710889506[/C][/ROW]
[ROW][C]65[/C][C]-11[/C][C]-10.4200412001834[/C][C]-0.579958799816573[/C][/ROW]
[ROW][C]66[/C][C]-13[/C][C]-10.9240211727734[/C][C]-2.07597882722655[/C][/ROW]
[ROW][C]67[/C][C]-11[/C][C]-12.7584875799209[/C][C]1.75848757992092[/C][/ROW]
[ROW][C]68[/C][C]-9[/C][C]-11.2959761192762[/C][C]2.29597611927615[/C][/ROW]
[ROW][C]69[/C][C]-7[/C][C]-9.30618954976814[/C][C]2.30618954976814[/C][/ROW]
[ROW][C]70[/C][C]-3[/C][C]-7.23448457750264[/C][C]4.23448457750264[/C][/ROW]
[ROW][C]71[/C][C]-3[/C][C]-3.39831869664278[/C][C]0.398318696642783[/C][/ROW]
[ROW][C]72[/C][C]-6[/C][C]-2.79202876872756[/C][C]-3.20797123127244[/C][/ROW]
[ROW][C]73[/C][C]-4[/C][C]-5.33591097870794[/C][C]1.33591097870794[/C][/ROW]
[ROW][C]74[/C][C]-8[/C][C]-3.99660747359256[/C][C]-4.00339252640744[/C][/ROW]
[ROW][C]75[/C][C]-1[/C][C]-7.29758902095186[/C][C]6.29758902095186[/C][/ROW]
[ROW][C]76[/C][C]-2[/C][C]-1.69150416901434[/C][C]-0.308495830985662[/C][/ROW]
[ROW][C]77[/C][C]-2[/C][C]-1.67904064072947[/C][C]-0.320959359270533[/C][/ROW]
[ROW][C]78[/C][C]-1[/C][C]-1.68731131547561[/C][C]0.687311315475615[/C][/ROW]
[ROW][C]79[/C][C]1[/C][C]-0.821496224827252[/C][C]1.82149622482725[/C][/ROW]
[ROW][C]80[/C][C]2[/C][C]1.06087592942432[/C][C]0.939124070575683[/C][/ROW]
[ROW][C]81[/C][C]2[/C][C]2.2272629354197[/C][C]-0.227262935419701[/C][/ROW]
[ROW][C]82[/C][C]-1[/C][C]2.40053504519666[/C][C]-3.40053504519666[/C][/ROW]
[ROW][C]83[/C][C]1[/C][C]-0.216474286474207[/C][C]1.21647428647421[/C][/ROW]
[ROW][C]84[/C][C]-1[/C][C]1.10771764453768[/C][C]-2.10771764453768[/C][/ROW]
[ROW][C]85[/C][C]-8[/C][C]-0.444854612888752[/C][C]-7.55514538711125[/C][/ROW]
[ROW][C]86[/C][C]1[/C][C]-6.84197097384614[/C][C]7.84197097384614[/C][/ROW]
[ROW][C]87[/C][C]2[/C][C]0.0245831002729908[/C][C]1.97541689972701[/C][/ROW]
[ROW][C]88[/C][C]-2[/C][C]1.99518457327292[/C][C]-3.99518457327292[/C][/ROW]
[ROW][C]89[/C][C]-2[/C][C]-1.20784515401912[/C][C]-0.792154845980878[/C][/ROW]
[ROW][C]90[/C][C]-2[/C][C]-1.72867485732807[/C][C]-0.271325142671931[/C][/ROW]
[ROW][C]91[/C][C]-2[/C][C]-1.8178933945257[/C][C]-0.182106605474295[/C][/ROW]
[ROW][C]92[/C][C]-6[/C][C]-1.83748656215863[/C][C]-4.16251343784137[/C][/ROW]
[ROW][C]93[/C][C]-4[/C][C]-5.35380876780341[/C][C]1.35380876780341[/C][/ROW]
[ROW][C]94[/C][C]-5[/C][C]-4.16441794939363[/C][C]-0.835582050606368[/C][/ROW]
[ROW][C]95[/C][C]-2[/C][C]-4.85217083994639[/C][C]2.85217083994639[/C][/ROW]
[ROW][C]96[/C][C]-1[/C][C]-2.33220124529382[/C][C]1.33220124529382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279312&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279312&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
3-6-71
4-7-7.122968517789970.122968517789973
5-12-7.98334352921164-4.01665647078836
6-16-12.4703923201527-3.52960767984726
7-18-16.6579242014736-1.34207579852644
8-19-19.03908466435520.0390846643551725
9-20-20.25157203785380.251572037853844
10-24-21.2764592734222-2.72354072657779
11-17-24.90261967894317.90261967894306
12-23-19.2958508079154-3.70414919208458
13-25-23.6174563515407-1.38254364845934
14-24-26.02065018650382.02065018650377
15-17-25.48306998298298.48306998298292
16-14-19.21353249638855.21353249638846
17-16-15.5419096344402-0.458090365559812
18-13-16.67880436445443.67880436445443
19-10-14.20206924830694.20206924830691
20-10-11.14951031413251.1495103141325
21-12-10.640609456468-1.35939054353204
22-12-12.29556481159370.295564811593652
23-20-12.5422705604126-7.45772943958739
24-16-19.57946708041573.57946708041567
25-12-17.17368446837035.17368446837025
26-14-13.2559756893573-0.74402431064267
27-7-14.36387587866327.36387587866321
28-9-8.38453574887209-0.615464251127905
29-9-9.169320881688120.169320881688119
30-4-9.285382801300625.28538280130062
31-3-4.909116719697021.90911671969702
321-3.325984831403854.32598483140385
33-10.437483869432859-1.43748386943286
34-2-0.716320961443765-1.28367903855624
351-1.780914083719342.78091408371934
36-30.678476522372228-3.67847652237223
37-2-2.4388506599740.438850659973996
380-2.062045904120532.06204590412053
39-2-0.24770214084215-1.75229785915785
40-4-1.71313080980646-2.28686919019354
41-4-3.70307940884003-0.296920591159965
42-7-4.02045194370846-2.97954805629154
43-9-6.70000868207138-2.29999131792862
44-13-8.87825603212256-4.12174396787744
45-8-12.72732630554034.72732630554029
46-13-8.94646301609916-4.05353698390084
47-15-12.7164695869662-2.28353041303381
48-15-15.06293686375470.0629368637546559
49-15-15.42404387324140.424043873241425
50-10-15.46644867647715.46644867647714
51-12-11.0730305707221-0.926969429277884
52-11-12.11313010809341.11313010809344
53-11-11.39345510595340.393455105953382
54-17-11.2695849927858-5.7304150072142
55-18-16.5040386528262-1.49596134717379
56-19-18.2068427076406-0.7931572923594
57-22-19.3408037320841-2.65919626791595
58-24-22.1365444211498-1.86345557885021
59-24-24.3188986876850.318898687685
60-20-24.64647594008524.64647594008516
61-25-21.1684978249468-3.8315021750532
62-22-24.97831897761232.97831897761229
63-17-22.93746902188615.93746902188615
64-9-18.20670710889519.20670710889506
65-11-10.4200412001834-0.579958799816573
66-13-10.9240211727734-2.07597882722655
67-11-12.75848757992091.75848757992092
68-9-11.29597611927622.29597611927615
69-7-9.306189549768142.30618954976814
70-3-7.234484577502644.23448457750264
71-3-3.398318696642780.398318696642783
72-6-2.79202876872756-3.20797123127244
73-4-5.335910978707941.33591097870794
74-8-3.99660747359256-4.00339252640744
75-1-7.297589020951866.29758902095186
76-2-1.69150416901434-0.308495830985662
77-2-1.67904064072947-0.320959359270533
78-1-1.687311315475610.687311315475615
791-0.8214962248272521.82149622482725
8021.060875929424320.939124070575683
8122.2272629354197-0.227262935419701
82-12.40053504519666-3.40053504519666
831-0.2164742864742071.21647428647421
84-11.10771764453768-2.10771764453768
85-8-0.444854612888752-7.55514538711125
861-6.841970973846147.84197097384614
8720.02458310027299081.97541689972701
88-21.99518457327292-3.99518457327292
89-2-1.20784515401912-0.792154845980878
90-2-1.72867485732807-0.271325142671931
91-2-1.8178933945257-0.182106605474295
92-6-1.83748656215863-4.16251343784137
93-4-5.353808767803411.35380876780341
94-5-4.16441794939363-0.835582050606368
95-2-4.852170839946392.85217083994639
96-1-2.332201245293821.33220124529382







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97-1.05465733039996-7.776570173749075.66725551294916
98-0.903161520578579-9.844023809234668.0377007680775
99-0.751665710757202-11.580244617544110.0769131960297
100-0.600169900935825-13.139415344654811.9390755427832
101-0.448674091114448-14.589181151807613.6918329695787
102-0.297178281293071-15.966038100833915.3716815382478
103-0.145682471471694-17.292157812701517.0007928697581
1040.00581333834968323-18.582100521987218.5937271986866
1050.15730914817106-19.84597056284120.1605888591831
1060.308804957992437-21.091074601885721.7086845178706
1070.460300767813814-22.322867045663623.2434685812912
1080.611796577635191-23.545523772792524.7691169280628

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & -1.05465733039996 & -7.77657017374907 & 5.66725551294916 \tabularnewline
98 & -0.903161520578579 & -9.84402380923466 & 8.0377007680775 \tabularnewline
99 & -0.751665710757202 & -11.5802446175441 & 10.0769131960297 \tabularnewline
100 & -0.600169900935825 & -13.1394153446548 & 11.9390755427832 \tabularnewline
101 & -0.448674091114448 & -14.5891811518076 & 13.6918329695787 \tabularnewline
102 & -0.297178281293071 & -15.9660381008339 & 15.3716815382478 \tabularnewline
103 & -0.145682471471694 & -17.2921578127015 & 17.0007928697581 \tabularnewline
104 & 0.00581333834968323 & -18.5821005219872 & 18.5937271986866 \tabularnewline
105 & 0.15730914817106 & -19.845970562841 & 20.1605888591831 \tabularnewline
106 & 0.308804957992437 & -21.0910746018857 & 21.7086845178706 \tabularnewline
107 & 0.460300767813814 & -22.3228670456636 & 23.2434685812912 \tabularnewline
108 & 0.611796577635191 & -23.5455237727925 & 24.7691169280628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279312&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]-1.05465733039996[/C][C]-7.77657017374907[/C][C]5.66725551294916[/C][/ROW]
[ROW][C]98[/C][C]-0.903161520578579[/C][C]-9.84402380923466[/C][C]8.0377007680775[/C][/ROW]
[ROW][C]99[/C][C]-0.751665710757202[/C][C]-11.5802446175441[/C][C]10.0769131960297[/C][/ROW]
[ROW][C]100[/C][C]-0.600169900935825[/C][C]-13.1394153446548[/C][C]11.9390755427832[/C][/ROW]
[ROW][C]101[/C][C]-0.448674091114448[/C][C]-14.5891811518076[/C][C]13.6918329695787[/C][/ROW]
[ROW][C]102[/C][C]-0.297178281293071[/C][C]-15.9660381008339[/C][C]15.3716815382478[/C][/ROW]
[ROW][C]103[/C][C]-0.145682471471694[/C][C]-17.2921578127015[/C][C]17.0007928697581[/C][/ROW]
[ROW][C]104[/C][C]0.00581333834968323[/C][C]-18.5821005219872[/C][C]18.5937271986866[/C][/ROW]
[ROW][C]105[/C][C]0.15730914817106[/C][C]-19.845970562841[/C][C]20.1605888591831[/C][/ROW]
[ROW][C]106[/C][C]0.308804957992437[/C][C]-21.0910746018857[/C][C]21.7086845178706[/C][/ROW]
[ROW][C]107[/C][C]0.460300767813814[/C][C]-22.3228670456636[/C][C]23.2434685812912[/C][/ROW]
[ROW][C]108[/C][C]0.611796577635191[/C][C]-23.5455237727925[/C][C]24.7691169280628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279312&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279312&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
97-1.05465733039996-7.776570173749075.66725551294916
98-0.903161520578579-9.844023809234668.0377007680775
99-0.751665710757202-11.580244617544110.0769131960297
100-0.600169900935825-13.139415344654811.9390755427832
101-0.448674091114448-14.589181151807613.6918329695787
102-0.297178281293071-15.966038100833915.3716815382478
103-0.145682471471694-17.292157812701517.0007928697581
1040.00581333834968323-18.582100521987218.5937271986866
1050.15730914817106-19.84597056284120.1605888591831
1060.308804957992437-21.091074601885721.7086845178706
1070.460300767813814-22.322867045663623.2434685812912
1080.611796577635191-23.545523772792524.7691169280628



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
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')