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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 14 Dec 2013 12:14:55 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/14/t13870413154i9tnrdd21j7fd8.htm/, Retrieved Thu, 28 Mar 2024 10:12:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232329, Retrieved Thu, 28 Mar 2024 10:12:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-14 17:14:55] [cbeaf4c3f774367e9472b81246022ded] [Current]
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Dataseries X:
86.5
86.6
98.8
84.4
91.4
95.7
78.5
81.7
94.3
98.5
95.4
91.7
92.8
90.6
102.2
91.8
95
102
88.9
89.6
97.9
108.6
100.8
95.1
101
100.9
102.5
105.4
98.4
105.3
96.5
88.1
107.9
107.1
92.5
95.7
85.2
85.5
94.7
86.2
88.8
93.4
83.4
82.9
96.7
96.2
92.8
92.8
90.2
95.9
107.5
98
95
108.5
91.8
91.7
108.3
105.1
104.8
103.2
98.6
102.4
121.2
102.6
108.9
105.5
90.8
99.6
111.6
104.7
103.1
101.7
98.8
101.4
114.2
96.9
98.3
104.8
94.4
94.5
102.4
105.5
101.2
99.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232329&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]5 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=232329&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232329&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.226688600692505
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.226688600692505 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232329&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]0.226688600692505[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232329&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232329&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
alpha0.226688600692505
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
398.886.712.1
484.489.5429320683793-5.1429320683793
591.488.47708799434182.92291200565822
695.789.23967882685186.46032117314823
778.590.8041599936169-12.3041599936169
881.788.1149471819672-6.41494718196718
994.386.76075178177077.53924821822929
1098.588.56981341063469.93018658936543
1195.490.92087351319334.47912648680671
1291.792.0362404288122-0.336240428812246
1392.892.06001855650860.739981443491445
1490.692.327763914472-1.72776391447205
15102.292.036099530373410.1639004696266
1691.894.4401399054109-2.64013990541092
179593.94165028462091.05834971537914
1810294.28156610064357.71843389935654
1988.996.1312470808262-7.23124708082618
2089.694.5920057988119-4.99200579881193
2197.993.56037498963044.33962501036963
22108.694.644118510761313.9558814892387
23100.897.90775775698722.89224224301277
2495.198.6633961039195-3.56339610391954
2510197.95561482740893.04438517259112
26100.998.74574224215262.15425775784743
27102.599.334087918813.16591208119003
28105.4100.151764098415.24823590158958
2998.4101.441479351046-3.04147935104592
30105.3100.8520106529224.44798934707782
3196.5101.960319133906-5.46031913390641
3288.1100.822527030107-12.7225270301066
33107.998.03847518037929.86152481962083
34107.1100.3739704424336.72602955756656
3592.5101.998684671055-9.49868467105462
3695.799.9454411345539-4.24544113455389
3785.299.0830480244395-13.8830480244395
3885.596.0359192944324-10.5359192944324
3994.793.74754649256840.952453507431628
4086.294.0634568453927-7.8634568453927
4188.892.3809008165047-3.58090081650472
4293.491.66915142119261.7308485788074
4383.492.1615150635331-8.76151506353305
4482.990.2753794738344-7.37537947383443
4596.788.70346502133477.99653497866532
4696.290.6161883460375.58381165396301
4792.891.98197479640440.818025203595639
4892.892.26741178513860.532588214861349
4990.292.4881434623109-2.28814346231088
5095.992.06944742265593.83055257734408
51107.593.037790026293114.4622099737069
529896.41620816815391.58379183184607
539596.8752357223033-1.87523572230333
54108.596.550141160445811.9498588395542
5591.899.3590379392573-7.55903793925728
5691.797.7454902062255-6.04549020622548
57108.396.47504649087611.824953509124
58105.199.25562865511325.84437134488677
59104.8100.6804810172134.11951898278701
60103.2101.7143290109471.48567098905282
6198.6102.151113688545-3.55111368854502
62102.4101.4461166955890.953883304411278
63121.2101.7623511670919.4376488329103
64102.6106.268644581774-3.66864458177442
65108.9105.5370046750943.36299532490618
66105.5106.399357379432-0.899357379432246
6790.8106.295483313566-15.4954833135663
6899.6102.88283388416-3.28283388415986
69111.6102.2386528646549.36134713534629
70104.7104.4607635473620.239236452637869
71103.1104.614995724045-1.51499572404525
72101.7104.371563463306-2.67156346330628
7398.8103.865950480148-5.06595048014816
74101.4102.817557254626-1.41755725462583
75114.2102.59621318417311.6037868158268
7696.9105.326659380187-8.4266593801871
7798.3103.51643175678-5.21643175678011
78104.8102.4339261412282.36607385877232
7994.4103.070288113408-8.67028811340788
8094.5101.204832633379-6.70483263337859
81102.499.78492350584052.61507649415947
82105.5100.4777315370055.02226846299459
83101.2101.716222547184-0.516222547183744
8499.5101.699200780317-2.19920078031674

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 98.8 & 86.7 & 12.1 \tabularnewline
4 & 84.4 & 89.5429320683793 & -5.1429320683793 \tabularnewline
5 & 91.4 & 88.4770879943418 & 2.92291200565822 \tabularnewline
6 & 95.7 & 89.2396788268518 & 6.46032117314823 \tabularnewline
7 & 78.5 & 90.8041599936169 & -12.3041599936169 \tabularnewline
8 & 81.7 & 88.1149471819672 & -6.41494718196718 \tabularnewline
9 & 94.3 & 86.7607517817707 & 7.53924821822929 \tabularnewline
10 & 98.5 & 88.5698134106346 & 9.93018658936543 \tabularnewline
11 & 95.4 & 90.9208735131933 & 4.47912648680671 \tabularnewline
12 & 91.7 & 92.0362404288122 & -0.336240428812246 \tabularnewline
13 & 92.8 & 92.0600185565086 & 0.739981443491445 \tabularnewline
14 & 90.6 & 92.327763914472 & -1.72776391447205 \tabularnewline
15 & 102.2 & 92.0360995303734 & 10.1639004696266 \tabularnewline
16 & 91.8 & 94.4401399054109 & -2.64013990541092 \tabularnewline
17 & 95 & 93.9416502846209 & 1.05834971537914 \tabularnewline
18 & 102 & 94.2815661006435 & 7.71843389935654 \tabularnewline
19 & 88.9 & 96.1312470808262 & -7.23124708082618 \tabularnewline
20 & 89.6 & 94.5920057988119 & -4.99200579881193 \tabularnewline
21 & 97.9 & 93.5603749896304 & 4.33962501036963 \tabularnewline
22 & 108.6 & 94.6441185107613 & 13.9558814892387 \tabularnewline
23 & 100.8 & 97.9077577569872 & 2.89224224301277 \tabularnewline
24 & 95.1 & 98.6633961039195 & -3.56339610391954 \tabularnewline
25 & 101 & 97.9556148274089 & 3.04438517259112 \tabularnewline
26 & 100.9 & 98.7457422421526 & 2.15425775784743 \tabularnewline
27 & 102.5 & 99.33408791881 & 3.16591208119003 \tabularnewline
28 & 105.4 & 100.15176409841 & 5.24823590158958 \tabularnewline
29 & 98.4 & 101.441479351046 & -3.04147935104592 \tabularnewline
30 & 105.3 & 100.852010652922 & 4.44798934707782 \tabularnewline
31 & 96.5 & 101.960319133906 & -5.46031913390641 \tabularnewline
32 & 88.1 & 100.822527030107 & -12.7225270301066 \tabularnewline
33 & 107.9 & 98.0384751803792 & 9.86152481962083 \tabularnewline
34 & 107.1 & 100.373970442433 & 6.72602955756656 \tabularnewline
35 & 92.5 & 101.998684671055 & -9.49868467105462 \tabularnewline
36 & 95.7 & 99.9454411345539 & -4.24544113455389 \tabularnewline
37 & 85.2 & 99.0830480244395 & -13.8830480244395 \tabularnewline
38 & 85.5 & 96.0359192944324 & -10.5359192944324 \tabularnewline
39 & 94.7 & 93.7475464925684 & 0.952453507431628 \tabularnewline
40 & 86.2 & 94.0634568453927 & -7.8634568453927 \tabularnewline
41 & 88.8 & 92.3809008165047 & -3.58090081650472 \tabularnewline
42 & 93.4 & 91.6691514211926 & 1.7308485788074 \tabularnewline
43 & 83.4 & 92.1615150635331 & -8.76151506353305 \tabularnewline
44 & 82.9 & 90.2753794738344 & -7.37537947383443 \tabularnewline
45 & 96.7 & 88.7034650213347 & 7.99653497866532 \tabularnewline
46 & 96.2 & 90.616188346037 & 5.58381165396301 \tabularnewline
47 & 92.8 & 91.9819747964044 & 0.818025203595639 \tabularnewline
48 & 92.8 & 92.2674117851386 & 0.532588214861349 \tabularnewline
49 & 90.2 & 92.4881434623109 & -2.28814346231088 \tabularnewline
50 & 95.9 & 92.0694474226559 & 3.83055257734408 \tabularnewline
51 & 107.5 & 93.0377900262931 & 14.4622099737069 \tabularnewline
52 & 98 & 96.4162081681539 & 1.58379183184607 \tabularnewline
53 & 95 & 96.8752357223033 & -1.87523572230333 \tabularnewline
54 & 108.5 & 96.5501411604458 & 11.9498588395542 \tabularnewline
55 & 91.8 & 99.3590379392573 & -7.55903793925728 \tabularnewline
56 & 91.7 & 97.7454902062255 & -6.04549020622548 \tabularnewline
57 & 108.3 & 96.475046490876 & 11.824953509124 \tabularnewline
58 & 105.1 & 99.2556286551132 & 5.84437134488677 \tabularnewline
59 & 104.8 & 100.680481017213 & 4.11951898278701 \tabularnewline
60 & 103.2 & 101.714329010947 & 1.48567098905282 \tabularnewline
61 & 98.6 & 102.151113688545 & -3.55111368854502 \tabularnewline
62 & 102.4 & 101.446116695589 & 0.953883304411278 \tabularnewline
63 & 121.2 & 101.76235116709 & 19.4376488329103 \tabularnewline
64 & 102.6 & 106.268644581774 & -3.66864458177442 \tabularnewline
65 & 108.9 & 105.537004675094 & 3.36299532490618 \tabularnewline
66 & 105.5 & 106.399357379432 & -0.899357379432246 \tabularnewline
67 & 90.8 & 106.295483313566 & -15.4954833135663 \tabularnewline
68 & 99.6 & 102.88283388416 & -3.28283388415986 \tabularnewline
69 & 111.6 & 102.238652864654 & 9.36134713534629 \tabularnewline
70 & 104.7 & 104.460763547362 & 0.239236452637869 \tabularnewline
71 & 103.1 & 104.614995724045 & -1.51499572404525 \tabularnewline
72 & 101.7 & 104.371563463306 & -2.67156346330628 \tabularnewline
73 & 98.8 & 103.865950480148 & -5.06595048014816 \tabularnewline
74 & 101.4 & 102.817557254626 & -1.41755725462583 \tabularnewline
75 & 114.2 & 102.596213184173 & 11.6037868158268 \tabularnewline
76 & 96.9 & 105.326659380187 & -8.4266593801871 \tabularnewline
77 & 98.3 & 103.51643175678 & -5.21643175678011 \tabularnewline
78 & 104.8 & 102.433926141228 & 2.36607385877232 \tabularnewline
79 & 94.4 & 103.070288113408 & -8.67028811340788 \tabularnewline
80 & 94.5 & 101.204832633379 & -6.70483263337859 \tabularnewline
81 & 102.4 & 99.7849235058405 & 2.61507649415947 \tabularnewline
82 & 105.5 & 100.477731537005 & 5.02226846299459 \tabularnewline
83 & 101.2 & 101.716222547184 & -0.516222547183744 \tabularnewline
84 & 99.5 & 101.699200780317 & -2.19920078031674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232329&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]98.8[/C][C]86.7[/C][C]12.1[/C][/ROW]
[ROW][C]4[/C][C]84.4[/C][C]89.5429320683793[/C][C]-5.1429320683793[/C][/ROW]
[ROW][C]5[/C][C]91.4[/C][C]88.4770879943418[/C][C]2.92291200565822[/C][/ROW]
[ROW][C]6[/C][C]95.7[/C][C]89.2396788268518[/C][C]6.46032117314823[/C][/ROW]
[ROW][C]7[/C][C]78.5[/C][C]90.8041599936169[/C][C]-12.3041599936169[/C][/ROW]
[ROW][C]8[/C][C]81.7[/C][C]88.1149471819672[/C][C]-6.41494718196718[/C][/ROW]
[ROW][C]9[/C][C]94.3[/C][C]86.7607517817707[/C][C]7.53924821822929[/C][/ROW]
[ROW][C]10[/C][C]98.5[/C][C]88.5698134106346[/C][C]9.93018658936543[/C][/ROW]
[ROW][C]11[/C][C]95.4[/C][C]90.9208735131933[/C][C]4.47912648680671[/C][/ROW]
[ROW][C]12[/C][C]91.7[/C][C]92.0362404288122[/C][C]-0.336240428812246[/C][/ROW]
[ROW][C]13[/C][C]92.8[/C][C]92.0600185565086[/C][C]0.739981443491445[/C][/ROW]
[ROW][C]14[/C][C]90.6[/C][C]92.327763914472[/C][C]-1.72776391447205[/C][/ROW]
[ROW][C]15[/C][C]102.2[/C][C]92.0360995303734[/C][C]10.1639004696266[/C][/ROW]
[ROW][C]16[/C][C]91.8[/C][C]94.4401399054109[/C][C]-2.64013990541092[/C][/ROW]
[ROW][C]17[/C][C]95[/C][C]93.9416502846209[/C][C]1.05834971537914[/C][/ROW]
[ROW][C]18[/C][C]102[/C][C]94.2815661006435[/C][C]7.71843389935654[/C][/ROW]
[ROW][C]19[/C][C]88.9[/C][C]96.1312470808262[/C][C]-7.23124708082618[/C][/ROW]
[ROW][C]20[/C][C]89.6[/C][C]94.5920057988119[/C][C]-4.99200579881193[/C][/ROW]
[ROW][C]21[/C][C]97.9[/C][C]93.5603749896304[/C][C]4.33962501036963[/C][/ROW]
[ROW][C]22[/C][C]108.6[/C][C]94.6441185107613[/C][C]13.9558814892387[/C][/ROW]
[ROW][C]23[/C][C]100.8[/C][C]97.9077577569872[/C][C]2.89224224301277[/C][/ROW]
[ROW][C]24[/C][C]95.1[/C][C]98.6633961039195[/C][C]-3.56339610391954[/C][/ROW]
[ROW][C]25[/C][C]101[/C][C]97.9556148274089[/C][C]3.04438517259112[/C][/ROW]
[ROW][C]26[/C][C]100.9[/C][C]98.7457422421526[/C][C]2.15425775784743[/C][/ROW]
[ROW][C]27[/C][C]102.5[/C][C]99.33408791881[/C][C]3.16591208119003[/C][/ROW]
[ROW][C]28[/C][C]105.4[/C][C]100.15176409841[/C][C]5.24823590158958[/C][/ROW]
[ROW][C]29[/C][C]98.4[/C][C]101.441479351046[/C][C]-3.04147935104592[/C][/ROW]
[ROW][C]30[/C][C]105.3[/C][C]100.852010652922[/C][C]4.44798934707782[/C][/ROW]
[ROW][C]31[/C][C]96.5[/C][C]101.960319133906[/C][C]-5.46031913390641[/C][/ROW]
[ROW][C]32[/C][C]88.1[/C][C]100.822527030107[/C][C]-12.7225270301066[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]98.0384751803792[/C][C]9.86152481962083[/C][/ROW]
[ROW][C]34[/C][C]107.1[/C][C]100.373970442433[/C][C]6.72602955756656[/C][/ROW]
[ROW][C]35[/C][C]92.5[/C][C]101.998684671055[/C][C]-9.49868467105462[/C][/ROW]
[ROW][C]36[/C][C]95.7[/C][C]99.9454411345539[/C][C]-4.24544113455389[/C][/ROW]
[ROW][C]37[/C][C]85.2[/C][C]99.0830480244395[/C][C]-13.8830480244395[/C][/ROW]
[ROW][C]38[/C][C]85.5[/C][C]96.0359192944324[/C][C]-10.5359192944324[/C][/ROW]
[ROW][C]39[/C][C]94.7[/C][C]93.7475464925684[/C][C]0.952453507431628[/C][/ROW]
[ROW][C]40[/C][C]86.2[/C][C]94.0634568453927[/C][C]-7.8634568453927[/C][/ROW]
[ROW][C]41[/C][C]88.8[/C][C]92.3809008165047[/C][C]-3.58090081650472[/C][/ROW]
[ROW][C]42[/C][C]93.4[/C][C]91.6691514211926[/C][C]1.7308485788074[/C][/ROW]
[ROW][C]43[/C][C]83.4[/C][C]92.1615150635331[/C][C]-8.76151506353305[/C][/ROW]
[ROW][C]44[/C][C]82.9[/C][C]90.2753794738344[/C][C]-7.37537947383443[/C][/ROW]
[ROW][C]45[/C][C]96.7[/C][C]88.7034650213347[/C][C]7.99653497866532[/C][/ROW]
[ROW][C]46[/C][C]96.2[/C][C]90.616188346037[/C][C]5.58381165396301[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]91.9819747964044[/C][C]0.818025203595639[/C][/ROW]
[ROW][C]48[/C][C]92.8[/C][C]92.2674117851386[/C][C]0.532588214861349[/C][/ROW]
[ROW][C]49[/C][C]90.2[/C][C]92.4881434623109[/C][C]-2.28814346231088[/C][/ROW]
[ROW][C]50[/C][C]95.9[/C][C]92.0694474226559[/C][C]3.83055257734408[/C][/ROW]
[ROW][C]51[/C][C]107.5[/C][C]93.0377900262931[/C][C]14.4622099737069[/C][/ROW]
[ROW][C]52[/C][C]98[/C][C]96.4162081681539[/C][C]1.58379183184607[/C][/ROW]
[ROW][C]53[/C][C]95[/C][C]96.8752357223033[/C][C]-1.87523572230333[/C][/ROW]
[ROW][C]54[/C][C]108.5[/C][C]96.5501411604458[/C][C]11.9498588395542[/C][/ROW]
[ROW][C]55[/C][C]91.8[/C][C]99.3590379392573[/C][C]-7.55903793925728[/C][/ROW]
[ROW][C]56[/C][C]91.7[/C][C]97.7454902062255[/C][C]-6.04549020622548[/C][/ROW]
[ROW][C]57[/C][C]108.3[/C][C]96.475046490876[/C][C]11.824953509124[/C][/ROW]
[ROW][C]58[/C][C]105.1[/C][C]99.2556286551132[/C][C]5.84437134488677[/C][/ROW]
[ROW][C]59[/C][C]104.8[/C][C]100.680481017213[/C][C]4.11951898278701[/C][/ROW]
[ROW][C]60[/C][C]103.2[/C][C]101.714329010947[/C][C]1.48567098905282[/C][/ROW]
[ROW][C]61[/C][C]98.6[/C][C]102.151113688545[/C][C]-3.55111368854502[/C][/ROW]
[ROW][C]62[/C][C]102.4[/C][C]101.446116695589[/C][C]0.953883304411278[/C][/ROW]
[ROW][C]63[/C][C]121.2[/C][C]101.76235116709[/C][C]19.4376488329103[/C][/ROW]
[ROW][C]64[/C][C]102.6[/C][C]106.268644581774[/C][C]-3.66864458177442[/C][/ROW]
[ROW][C]65[/C][C]108.9[/C][C]105.537004675094[/C][C]3.36299532490618[/C][/ROW]
[ROW][C]66[/C][C]105.5[/C][C]106.399357379432[/C][C]-0.899357379432246[/C][/ROW]
[ROW][C]67[/C][C]90.8[/C][C]106.295483313566[/C][C]-15.4954833135663[/C][/ROW]
[ROW][C]68[/C][C]99.6[/C][C]102.88283388416[/C][C]-3.28283388415986[/C][/ROW]
[ROW][C]69[/C][C]111.6[/C][C]102.238652864654[/C][C]9.36134713534629[/C][/ROW]
[ROW][C]70[/C][C]104.7[/C][C]104.460763547362[/C][C]0.239236452637869[/C][/ROW]
[ROW][C]71[/C][C]103.1[/C][C]104.614995724045[/C][C]-1.51499572404525[/C][/ROW]
[ROW][C]72[/C][C]101.7[/C][C]104.371563463306[/C][C]-2.67156346330628[/C][/ROW]
[ROW][C]73[/C][C]98.8[/C][C]103.865950480148[/C][C]-5.06595048014816[/C][/ROW]
[ROW][C]74[/C][C]101.4[/C][C]102.817557254626[/C][C]-1.41755725462583[/C][/ROW]
[ROW][C]75[/C][C]114.2[/C][C]102.596213184173[/C][C]11.6037868158268[/C][/ROW]
[ROW][C]76[/C][C]96.9[/C][C]105.326659380187[/C][C]-8.4266593801871[/C][/ROW]
[ROW][C]77[/C][C]98.3[/C][C]103.51643175678[/C][C]-5.21643175678011[/C][/ROW]
[ROW][C]78[/C][C]104.8[/C][C]102.433926141228[/C][C]2.36607385877232[/C][/ROW]
[ROW][C]79[/C][C]94.4[/C][C]103.070288113408[/C][C]-8.67028811340788[/C][/ROW]
[ROW][C]80[/C][C]94.5[/C][C]101.204832633379[/C][C]-6.70483263337859[/C][/ROW]
[ROW][C]81[/C][C]102.4[/C][C]99.7849235058405[/C][C]2.61507649415947[/C][/ROW]
[ROW][C]82[/C][C]105.5[/C][C]100.477731537005[/C][C]5.02226846299459[/C][/ROW]
[ROW][C]83[/C][C]101.2[/C][C]101.716222547184[/C][C]-0.516222547183744[/C][/ROW]
[ROW][C]84[/C][C]99.5[/C][C]101.699200780317[/C][C]-2.19920078031674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232329&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232329&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
398.886.712.1
484.489.5429320683793-5.1429320683793
591.488.47708799434182.92291200565822
695.789.23967882685186.46032117314823
778.590.8041599936169-12.3041599936169
881.788.1149471819672-6.41494718196718
994.386.76075178177077.53924821822929
1098.588.56981341063469.93018658936543
1195.490.92087351319334.47912648680671
1291.792.0362404288122-0.336240428812246
1392.892.06001855650860.739981443491445
1490.692.327763914472-1.72776391447205
15102.292.036099530373410.1639004696266
1691.894.4401399054109-2.64013990541092
179593.94165028462091.05834971537914
1810294.28156610064357.71843389935654
1988.996.1312470808262-7.23124708082618
2089.694.5920057988119-4.99200579881193
2197.993.56037498963044.33962501036963
22108.694.644118510761313.9558814892387
23100.897.90775775698722.89224224301277
2495.198.6633961039195-3.56339610391954
2510197.95561482740893.04438517259112
26100.998.74574224215262.15425775784743
27102.599.334087918813.16591208119003
28105.4100.151764098415.24823590158958
2998.4101.441479351046-3.04147935104592
30105.3100.8520106529224.44798934707782
3196.5101.960319133906-5.46031913390641
3288.1100.822527030107-12.7225270301066
33107.998.03847518037929.86152481962083
34107.1100.3739704424336.72602955756656
3592.5101.998684671055-9.49868467105462
3695.799.9454411345539-4.24544113455389
3785.299.0830480244395-13.8830480244395
3885.596.0359192944324-10.5359192944324
3994.793.74754649256840.952453507431628
4086.294.0634568453927-7.8634568453927
4188.892.3809008165047-3.58090081650472
4293.491.66915142119261.7308485788074
4383.492.1615150635331-8.76151506353305
4482.990.2753794738344-7.37537947383443
4596.788.70346502133477.99653497866532
4696.290.6161883460375.58381165396301
4792.891.98197479640440.818025203595639
4892.892.26741178513860.532588214861349
4990.292.4881434623109-2.28814346231088
5095.992.06944742265593.83055257734408
51107.593.037790026293114.4622099737069
529896.41620816815391.58379183184607
539596.8752357223033-1.87523572230333
54108.596.550141160445811.9498588395542
5591.899.3590379392573-7.55903793925728
5691.797.7454902062255-6.04549020622548
57108.396.47504649087611.824953509124
58105.199.25562865511325.84437134488677
59104.8100.6804810172134.11951898278701
60103.2101.7143290109471.48567098905282
6198.6102.151113688545-3.55111368854502
62102.4101.4461166955890.953883304411278
63121.2101.7623511670919.4376488329103
64102.6106.268644581774-3.66864458177442
65108.9105.5370046750943.36299532490618
66105.5106.399357379432-0.899357379432246
6790.8106.295483313566-15.4954833135663
6899.6102.88283388416-3.28283388415986
69111.6102.2386528646549.36134713534629
70104.7104.4607635473620.239236452637869
71103.1104.614995724045-1.51499572404525
72101.7104.371563463306-2.67156346330628
7398.8103.865950480148-5.06595048014816
74101.4102.817557254626-1.41755725462583
75114.2102.59621318417311.6037868158268
7696.9105.326659380187-8.4266593801871
7798.3103.51643175678-5.21643175678011
78104.8102.4339261412282.36607385877232
7994.4103.070288113408-8.67028811340788
8094.5101.204832633379-6.70483263337859
81102.499.78492350584052.61507649415947
82105.5100.4777315370055.02226846299459
83101.2101.716222547184-0.516222547183744
8499.5101.699200780317-2.19920078031674







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85101.30066703278587.4355877018725115.165746363697
86101.40066703278587.1838030219978115.617531043572
87101.50066703278586.9405152564491116.060818809121
88101.60066703278586.7051369247742116.496197140796
89101.70066703278586.4771452770487116.924188788521
90101.80066703278586.256072728137117.345261337433
91101.90066703278586.0414990361713117.759835029398
92102.00066703278585.8330448516003118.168289213969
93102.10066703278585.6303663542225118.570967711347
94102.20066703278585.4331507620019118.968183303568
95102.30066703278585.2411125444727119.360221521097
96102.40066703278585.0539902101652119.747343855404

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 101.300667032785 & 87.4355877018725 & 115.165746363697 \tabularnewline
86 & 101.400667032785 & 87.1838030219978 & 115.617531043572 \tabularnewline
87 & 101.500667032785 & 86.9405152564491 & 116.060818809121 \tabularnewline
88 & 101.600667032785 & 86.7051369247742 & 116.496197140796 \tabularnewline
89 & 101.700667032785 & 86.4771452770487 & 116.924188788521 \tabularnewline
90 & 101.800667032785 & 86.256072728137 & 117.345261337433 \tabularnewline
91 & 101.900667032785 & 86.0414990361713 & 117.759835029398 \tabularnewline
92 & 102.000667032785 & 85.8330448516003 & 118.168289213969 \tabularnewline
93 & 102.100667032785 & 85.6303663542225 & 118.570967711347 \tabularnewline
94 & 102.200667032785 & 85.4331507620019 & 118.968183303568 \tabularnewline
95 & 102.300667032785 & 85.2411125444727 & 119.360221521097 \tabularnewline
96 & 102.400667032785 & 85.0539902101652 & 119.747343855404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232329&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]101.300667032785[/C][C]87.4355877018725[/C][C]115.165746363697[/C][/ROW]
[ROW][C]86[/C][C]101.400667032785[/C][C]87.1838030219978[/C][C]115.617531043572[/C][/ROW]
[ROW][C]87[/C][C]101.500667032785[/C][C]86.9405152564491[/C][C]116.060818809121[/C][/ROW]
[ROW][C]88[/C][C]101.600667032785[/C][C]86.7051369247742[/C][C]116.496197140796[/C][/ROW]
[ROW][C]89[/C][C]101.700667032785[/C][C]86.4771452770487[/C][C]116.924188788521[/C][/ROW]
[ROW][C]90[/C][C]101.800667032785[/C][C]86.256072728137[/C][C]117.345261337433[/C][/ROW]
[ROW][C]91[/C][C]101.900667032785[/C][C]86.0414990361713[/C][C]117.759835029398[/C][/ROW]
[ROW][C]92[/C][C]102.000667032785[/C][C]85.8330448516003[/C][C]118.168289213969[/C][/ROW]
[ROW][C]93[/C][C]102.100667032785[/C][C]85.6303663542225[/C][C]118.570967711347[/C][/ROW]
[ROW][C]94[/C][C]102.200667032785[/C][C]85.4331507620019[/C][C]118.968183303568[/C][/ROW]
[ROW][C]95[/C][C]102.300667032785[/C][C]85.2411125444727[/C][C]119.360221521097[/C][/ROW]
[ROW][C]96[/C][C]102.400667032785[/C][C]85.0539902101652[/C][C]119.747343855404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232329&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232329&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
85101.30066703278587.4355877018725115.165746363697
86101.40066703278587.1838030219978115.617531043572
87101.50066703278586.9405152564491116.060818809121
88101.60066703278586.7051369247742116.496197140796
89101.70066703278586.4771452770487116.924188788521
90101.80066703278586.256072728137117.345261337433
91101.90066703278586.0414990361713117.759835029398
92102.00066703278585.8330448516003118.168289213969
93102.10066703278585.6303663542225118.570967711347
94102.20066703278585.4331507620019118.968183303568
95102.30066703278585.2411125444727119.360221521097
96102.40066703278585.0539902101652119.747343855404



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):
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
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')