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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 14:16:00 -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/26/t1369592259ue26kxsktf018rg.htm/, Retrieved Mon, 29 Apr 2024 10:02:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210649, Retrieved Mon, 29 Apr 2024 10:02:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Inschrijvingen ni...] [2013-05-06 21:00:33] [a12eb5ef392ea8ae41cc1fa625e5276e]
- RMPD    [Exponential Smoothing] [Interesse in de l...] [2013-05-26 18:16:00] [c6583091fa4b3042e72e3a6292788221] [Current]
- R P       [Exponential Smoothing] [Interesse in de l...] [2013-05-26 23:58:20] [a12eb5ef392ea8ae41cc1fa625e5276e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
38
35
33
35
33
32
33
38
45
42
40
44
50
37
37
35
33
40
38
39
52
48
49
50
48
45
42
39
38
44
47
45
51
51
47
49
44
40
40
38
36
45
39
43
50
49
47
49
58
43
39
44
45
57
54
52
61
59
60
58
52
49
60
51
52
56
56
57
58
100
70
70

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210649&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210649&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210649&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.203563261518397
beta0
gamma0.348668455960461

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.203563261518397 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.348668455960461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210649&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]0.203563261518397[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.348668455960461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210649&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210649&T=1

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


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.203563261518397
beta0
gamma0.348668455960461






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135048.20619658119661.79380341880342
143735.67274765704971.32725234295035
153735.96099274090381.03900725909617
163533.98222838203871.01777161796133
173331.91580789347031.08419210652966
184038.86290817618661.13709182381339
193836.69577689788661.30422310211343
203941.7293340743657-2.72933407436568
215248.27514052981313.72485947018689
224846.2181170069941.78188299300602
234944.93224152209314.06775847790695
245049.77835297299020.221647027009837
254856.1313296183187-8.13132961831869
264541.44793056914223.55206943085781
274242.1090232158284-0.109023215828429
283939.890665053695-0.890665053694995
293837.4542014345890.545798565410955
304444.3063944198473-0.30639441984728
314741.89183345424815.1081665457519
324546.5796457214438-1.57964572144379
335155.1517667758622-4.15176677586217
345150.95180178595910.0481982140409443
354749.9477819490803-2.94778194908033
364952.2977513134289-3.29775131342895
374455.6147498905364-11.6147498905364
384043.4666451963206-3.46664519632059
394041.6823279157577-1.68232791575772
403838.9266467447559-0.926646744755907
413636.8817535590207-0.881753559020723
424543.2067018898781.79329811012203
433942.7231434394144-3.72314343941442
444343.7560710181582-0.756071018158153
455051.7815832392148-1.7815832392148
464949.2303987634737-0.230398763473701
474747.3377059915946-0.337705991594561
484950.1218071091895-1.12180710918951
495851.5721809568916.42781904310902
504345.3595469272215-2.3595469272215
513944.2960854718204-5.2960854718204
524441.01462292010492.98537707989507
534539.77854055830175.2214594416983
545748.08872026552328.9112797344768
555447.52224765379796.47775234620212
565251.45563621539090.544363784609111
576159.46109226933931.53890773066071
585958.01658985535040.983410144649646
596056.34118558540173.65881441459827
605859.7210925356065-1.72109253560652
615263.1459474501407-11.1459474501407
624950.9157557322436-1.91575573224357
636049.127179518114810.8728204818852
645151.4368111429869-0.436811142986897
655250.12503999082011.87496000917987
665658.7786302930294-2.77863029302938
675655.15674948650580.843250513494183
685756.29550375880090.704496241199088
695864.6097341612241-6.6097341612241
7010061.352210186768538.6477898132315
717068.08682923197271.91317076802727
727069.61742816807470.382571831925318

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50 & 48.2061965811966 & 1.79380341880342 \tabularnewline
14 & 37 & 35.6727476570497 & 1.32725234295035 \tabularnewline
15 & 37 & 35.9609927409038 & 1.03900725909617 \tabularnewline
16 & 35 & 33.9822283820387 & 1.01777161796133 \tabularnewline
17 & 33 & 31.9158078934703 & 1.08419210652966 \tabularnewline
18 & 40 & 38.8629081761866 & 1.13709182381339 \tabularnewline
19 & 38 & 36.6957768978866 & 1.30422310211343 \tabularnewline
20 & 39 & 41.7293340743657 & -2.72933407436568 \tabularnewline
21 & 52 & 48.2751405298131 & 3.72485947018689 \tabularnewline
22 & 48 & 46.218117006994 & 1.78188299300602 \tabularnewline
23 & 49 & 44.9322415220931 & 4.06775847790695 \tabularnewline
24 & 50 & 49.7783529729902 & 0.221647027009837 \tabularnewline
25 & 48 & 56.1313296183187 & -8.13132961831869 \tabularnewline
26 & 45 & 41.4479305691422 & 3.55206943085781 \tabularnewline
27 & 42 & 42.1090232158284 & -0.109023215828429 \tabularnewline
28 & 39 & 39.890665053695 & -0.890665053694995 \tabularnewline
29 & 38 & 37.454201434589 & 0.545798565410955 \tabularnewline
30 & 44 & 44.3063944198473 & -0.30639441984728 \tabularnewline
31 & 47 & 41.8918334542481 & 5.1081665457519 \tabularnewline
32 & 45 & 46.5796457214438 & -1.57964572144379 \tabularnewline
33 & 51 & 55.1517667758622 & -4.15176677586217 \tabularnewline
34 & 51 & 50.9518017859591 & 0.0481982140409443 \tabularnewline
35 & 47 & 49.9477819490803 & -2.94778194908033 \tabularnewline
36 & 49 & 52.2977513134289 & -3.29775131342895 \tabularnewline
37 & 44 & 55.6147498905364 & -11.6147498905364 \tabularnewline
38 & 40 & 43.4666451963206 & -3.46664519632059 \tabularnewline
39 & 40 & 41.6823279157577 & -1.68232791575772 \tabularnewline
40 & 38 & 38.9266467447559 & -0.926646744755907 \tabularnewline
41 & 36 & 36.8817535590207 & -0.881753559020723 \tabularnewline
42 & 45 & 43.206701889878 & 1.79329811012203 \tabularnewline
43 & 39 & 42.7231434394144 & -3.72314343941442 \tabularnewline
44 & 43 & 43.7560710181582 & -0.756071018158153 \tabularnewline
45 & 50 & 51.7815832392148 & -1.7815832392148 \tabularnewline
46 & 49 & 49.2303987634737 & -0.230398763473701 \tabularnewline
47 & 47 & 47.3377059915946 & -0.337705991594561 \tabularnewline
48 & 49 & 50.1218071091895 & -1.12180710918951 \tabularnewline
49 & 58 & 51.572180956891 & 6.42781904310902 \tabularnewline
50 & 43 & 45.3595469272215 & -2.3595469272215 \tabularnewline
51 & 39 & 44.2960854718204 & -5.2960854718204 \tabularnewline
52 & 44 & 41.0146229201049 & 2.98537707989507 \tabularnewline
53 & 45 & 39.7785405583017 & 5.2214594416983 \tabularnewline
54 & 57 & 48.0887202655232 & 8.9112797344768 \tabularnewline
55 & 54 & 47.5222476537979 & 6.47775234620212 \tabularnewline
56 & 52 & 51.4556362153909 & 0.544363784609111 \tabularnewline
57 & 61 & 59.4610922693393 & 1.53890773066071 \tabularnewline
58 & 59 & 58.0165898553504 & 0.983410144649646 \tabularnewline
59 & 60 & 56.3411855854017 & 3.65881441459827 \tabularnewline
60 & 58 & 59.7210925356065 & -1.72109253560652 \tabularnewline
61 & 52 & 63.1459474501407 & -11.1459474501407 \tabularnewline
62 & 49 & 50.9157557322436 & -1.91575573224357 \tabularnewline
63 & 60 & 49.1271795181148 & 10.8728204818852 \tabularnewline
64 & 51 & 51.4368111429869 & -0.436811142986897 \tabularnewline
65 & 52 & 50.1250399908201 & 1.87496000917987 \tabularnewline
66 & 56 & 58.7786302930294 & -2.77863029302938 \tabularnewline
67 & 56 & 55.1567494865058 & 0.843250513494183 \tabularnewline
68 & 57 & 56.2955037588009 & 0.704496241199088 \tabularnewline
69 & 58 & 64.6097341612241 & -6.6097341612241 \tabularnewline
70 & 100 & 61.3522101867685 & 38.6477898132315 \tabularnewline
71 & 70 & 68.0868292319727 & 1.91317076802727 \tabularnewline
72 & 70 & 69.6174281680747 & 0.382571831925318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210649&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]50[/C][C]48.2061965811966[/C][C]1.79380341880342[/C][/ROW]
[ROW][C]14[/C][C]37[/C][C]35.6727476570497[/C][C]1.32725234295035[/C][/ROW]
[ROW][C]15[/C][C]37[/C][C]35.9609927409038[/C][C]1.03900725909617[/C][/ROW]
[ROW][C]16[/C][C]35[/C][C]33.9822283820387[/C][C]1.01777161796133[/C][/ROW]
[ROW][C]17[/C][C]33[/C][C]31.9158078934703[/C][C]1.08419210652966[/C][/ROW]
[ROW][C]18[/C][C]40[/C][C]38.8629081761866[/C][C]1.13709182381339[/C][/ROW]
[ROW][C]19[/C][C]38[/C][C]36.6957768978866[/C][C]1.30422310211343[/C][/ROW]
[ROW][C]20[/C][C]39[/C][C]41.7293340743657[/C][C]-2.72933407436568[/C][/ROW]
[ROW][C]21[/C][C]52[/C][C]48.2751405298131[/C][C]3.72485947018689[/C][/ROW]
[ROW][C]22[/C][C]48[/C][C]46.218117006994[/C][C]1.78188299300602[/C][/ROW]
[ROW][C]23[/C][C]49[/C][C]44.9322415220931[/C][C]4.06775847790695[/C][/ROW]
[ROW][C]24[/C][C]50[/C][C]49.7783529729902[/C][C]0.221647027009837[/C][/ROW]
[ROW][C]25[/C][C]48[/C][C]56.1313296183187[/C][C]-8.13132961831869[/C][/ROW]
[ROW][C]26[/C][C]45[/C][C]41.4479305691422[/C][C]3.55206943085781[/C][/ROW]
[ROW][C]27[/C][C]42[/C][C]42.1090232158284[/C][C]-0.109023215828429[/C][/ROW]
[ROW][C]28[/C][C]39[/C][C]39.890665053695[/C][C]-0.890665053694995[/C][/ROW]
[ROW][C]29[/C][C]38[/C][C]37.454201434589[/C][C]0.545798565410955[/C][/ROW]
[ROW][C]30[/C][C]44[/C][C]44.3063944198473[/C][C]-0.30639441984728[/C][/ROW]
[ROW][C]31[/C][C]47[/C][C]41.8918334542481[/C][C]5.1081665457519[/C][/ROW]
[ROW][C]32[/C][C]45[/C][C]46.5796457214438[/C][C]-1.57964572144379[/C][/ROW]
[ROW][C]33[/C][C]51[/C][C]55.1517667758622[/C][C]-4.15176677586217[/C][/ROW]
[ROW][C]34[/C][C]51[/C][C]50.9518017859591[/C][C]0.0481982140409443[/C][/ROW]
[ROW][C]35[/C][C]47[/C][C]49.9477819490803[/C][C]-2.94778194908033[/C][/ROW]
[ROW][C]36[/C][C]49[/C][C]52.2977513134289[/C][C]-3.29775131342895[/C][/ROW]
[ROW][C]37[/C][C]44[/C][C]55.6147498905364[/C][C]-11.6147498905364[/C][/ROW]
[ROW][C]38[/C][C]40[/C][C]43.4666451963206[/C][C]-3.46664519632059[/C][/ROW]
[ROW][C]39[/C][C]40[/C][C]41.6823279157577[/C][C]-1.68232791575772[/C][/ROW]
[ROW][C]40[/C][C]38[/C][C]38.9266467447559[/C][C]-0.926646744755907[/C][/ROW]
[ROW][C]41[/C][C]36[/C][C]36.8817535590207[/C][C]-0.881753559020723[/C][/ROW]
[ROW][C]42[/C][C]45[/C][C]43.206701889878[/C][C]1.79329811012203[/C][/ROW]
[ROW][C]43[/C][C]39[/C][C]42.7231434394144[/C][C]-3.72314343941442[/C][/ROW]
[ROW][C]44[/C][C]43[/C][C]43.7560710181582[/C][C]-0.756071018158153[/C][/ROW]
[ROW][C]45[/C][C]50[/C][C]51.7815832392148[/C][C]-1.7815832392148[/C][/ROW]
[ROW][C]46[/C][C]49[/C][C]49.2303987634737[/C][C]-0.230398763473701[/C][/ROW]
[ROW][C]47[/C][C]47[/C][C]47.3377059915946[/C][C]-0.337705991594561[/C][/ROW]
[ROW][C]48[/C][C]49[/C][C]50.1218071091895[/C][C]-1.12180710918951[/C][/ROW]
[ROW][C]49[/C][C]58[/C][C]51.572180956891[/C][C]6.42781904310902[/C][/ROW]
[ROW][C]50[/C][C]43[/C][C]45.3595469272215[/C][C]-2.3595469272215[/C][/ROW]
[ROW][C]51[/C][C]39[/C][C]44.2960854718204[/C][C]-5.2960854718204[/C][/ROW]
[ROW][C]52[/C][C]44[/C][C]41.0146229201049[/C][C]2.98537707989507[/C][/ROW]
[ROW][C]53[/C][C]45[/C][C]39.7785405583017[/C][C]5.2214594416983[/C][/ROW]
[ROW][C]54[/C][C]57[/C][C]48.0887202655232[/C][C]8.9112797344768[/C][/ROW]
[ROW][C]55[/C][C]54[/C][C]47.5222476537979[/C][C]6.47775234620212[/C][/ROW]
[ROW][C]56[/C][C]52[/C][C]51.4556362153909[/C][C]0.544363784609111[/C][/ROW]
[ROW][C]57[/C][C]61[/C][C]59.4610922693393[/C][C]1.53890773066071[/C][/ROW]
[ROW][C]58[/C][C]59[/C][C]58.0165898553504[/C][C]0.983410144649646[/C][/ROW]
[ROW][C]59[/C][C]60[/C][C]56.3411855854017[/C][C]3.65881441459827[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]59.7210925356065[/C][C]-1.72109253560652[/C][/ROW]
[ROW][C]61[/C][C]52[/C][C]63.1459474501407[/C][C]-11.1459474501407[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]50.9157557322436[/C][C]-1.91575573224357[/C][/ROW]
[ROW][C]63[/C][C]60[/C][C]49.1271795181148[/C][C]10.8728204818852[/C][/ROW]
[ROW][C]64[/C][C]51[/C][C]51.4368111429869[/C][C]-0.436811142986897[/C][/ROW]
[ROW][C]65[/C][C]52[/C][C]50.1250399908201[/C][C]1.87496000917987[/C][/ROW]
[ROW][C]66[/C][C]56[/C][C]58.7786302930294[/C][C]-2.77863029302938[/C][/ROW]
[ROW][C]67[/C][C]56[/C][C]55.1567494865058[/C][C]0.843250513494183[/C][/ROW]
[ROW][C]68[/C][C]57[/C][C]56.2955037588009[/C][C]0.704496241199088[/C][/ROW]
[ROW][C]69[/C][C]58[/C][C]64.6097341612241[/C][C]-6.6097341612241[/C][/ROW]
[ROW][C]70[/C][C]100[/C][C]61.3522101867685[/C][C]38.6477898132315[/C][/ROW]
[ROW][C]71[/C][C]70[/C][C]68.0868292319727[/C][C]1.91317076802727[/C][/ROW]
[ROW][C]72[/C][C]70[/C][C]69.6174281680747[/C][C]0.382571831925318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210649&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210649&T=2

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


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135048.20619658119661.79380341880342
143735.67274765704971.32725234295035
153735.96099274090381.03900725909617
163533.98222838203871.01777161796133
173331.91580789347031.08419210652966
184038.86290817618661.13709182381339
193836.69577689788661.30422310211343
203941.7293340743657-2.72933407436568
215248.27514052981313.72485947018689
224846.2181170069941.78188299300602
234944.93224152209314.06775847790695
245049.77835297299020.221647027009837
254856.1313296183187-8.13132961831869
264541.44793056914223.55206943085781
274242.1090232158284-0.109023215828429
283939.890665053695-0.890665053694995
293837.4542014345890.545798565410955
304444.3063944198473-0.30639441984728
314741.89183345424815.1081665457519
324546.5796457214438-1.57964572144379
335155.1517667758622-4.15176677586217
345150.95180178595910.0481982140409443
354749.9477819490803-2.94778194908033
364952.2977513134289-3.29775131342895
374455.6147498905364-11.6147498905364
384043.4666451963206-3.46664519632059
394041.6823279157577-1.68232791575772
403838.9266467447559-0.926646744755907
413636.8817535590207-0.881753559020723
424543.2067018898781.79329811012203
433942.7231434394144-3.72314343941442
444343.7560710181582-0.756071018158153
455051.7815832392148-1.7815832392148
464949.2303987634737-0.230398763473701
474747.3377059915946-0.337705991594561
484950.1218071091895-1.12180710918951
495851.5721809568916.42781904310902
504345.3595469272215-2.3595469272215
513944.2960854718204-5.2960854718204
524441.01462292010492.98537707989507
534539.77854055830175.2214594416983
545748.08872026552328.9112797344768
555447.52224765379796.47775234620212
565251.45563621539090.544363784609111
576159.46109226933931.53890773066071
585958.01658985535040.983410144649646
596056.34118558540173.65881441459827
605859.7210925356065-1.72109253560652
615263.1459474501407-11.1459474501407
624950.9157557322436-1.91575573224357
636049.127179518114810.8728204818852
645151.4368111429869-0.436811142986897
655250.12503999082011.87496000917987
665658.7786302930294-2.77863029302938
675655.15674948650580.843250513494183
685756.29550375880090.704496241199088
695864.6097341612241-6.6097341612241
7010061.352210186768538.6477898132315
717068.08682923197271.91317076802727
727069.61742816807470.382571831925318






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7370.853301584293658.355803018883583.3508001497038
7463.455169076157350.7013630945976.2089750577246
7565.60786035782852.60279735765478.6129233580019
7662.56358679778149.312029898249375.8151436973127
7761.982695551782248.489146838246675.4762442653178
7868.962346369158355.231069898720882.6936228395958
7966.911861264967952.946903329813780.876819200122
8067.840429710032453.645636764953782.0352226551111
8173.98014460022659.559179189523188.4011100109288
8284.635788666095869.992143628069299.2794337041224
8373.302214220734758.439225402103688.1652030393659
8474.018326232619958.939183908011889.097468557228

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 70.8533015842936 & 58.3558030188835 & 83.3508001497038 \tabularnewline
74 & 63.4551690761573 & 50.70136309459 & 76.2089750577246 \tabularnewline
75 & 65.607860357828 & 52.602797357654 & 78.6129233580019 \tabularnewline
76 & 62.563586797781 & 49.3120298982493 & 75.8151436973127 \tabularnewline
77 & 61.9826955517822 & 48.4891468382466 & 75.4762442653178 \tabularnewline
78 & 68.9623463691583 & 55.2310698987208 & 82.6936228395958 \tabularnewline
79 & 66.9118612649679 & 52.9469033298137 & 80.876819200122 \tabularnewline
80 & 67.8404297100324 & 53.6456367649537 & 82.0352226551111 \tabularnewline
81 & 73.980144600226 & 59.5591791895231 & 88.4011100109288 \tabularnewline
82 & 84.6357886660958 & 69.9921436280692 & 99.2794337041224 \tabularnewline
83 & 73.3022142207347 & 58.4392254021036 & 88.1652030393659 \tabularnewline
84 & 74.0183262326199 & 58.9391839080118 & 89.097468557228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210649&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]70.8533015842936[/C][C]58.3558030188835[/C][C]83.3508001497038[/C][/ROW]
[ROW][C]74[/C][C]63.4551690761573[/C][C]50.70136309459[/C][C]76.2089750577246[/C][/ROW]
[ROW][C]75[/C][C]65.607860357828[/C][C]52.602797357654[/C][C]78.6129233580019[/C][/ROW]
[ROW][C]76[/C][C]62.563586797781[/C][C]49.3120298982493[/C][C]75.8151436973127[/C][/ROW]
[ROW][C]77[/C][C]61.9826955517822[/C][C]48.4891468382466[/C][C]75.4762442653178[/C][/ROW]
[ROW][C]78[/C][C]68.9623463691583[/C][C]55.2310698987208[/C][C]82.6936228395958[/C][/ROW]
[ROW][C]79[/C][C]66.9118612649679[/C][C]52.9469033298137[/C][C]80.876819200122[/C][/ROW]
[ROW][C]80[/C][C]67.8404297100324[/C][C]53.6456367649537[/C][C]82.0352226551111[/C][/ROW]
[ROW][C]81[/C][C]73.980144600226[/C][C]59.5591791895231[/C][C]88.4011100109288[/C][/ROW]
[ROW][C]82[/C][C]84.6357886660958[/C][C]69.9921436280692[/C][C]99.2794337041224[/C][/ROW]
[ROW][C]83[/C][C]73.3022142207347[/C][C]58.4392254021036[/C][C]88.1652030393659[/C][/ROW]
[ROW][C]84[/C][C]74.0183262326199[/C][C]58.9391839080118[/C][C]89.097468557228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210649&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210649&T=3

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


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7370.853301584293658.355803018883583.3508001497038
7463.455169076157350.7013630945976.2089750577246
7565.60786035782852.60279735765478.6129233580019
7662.56358679778149.312029898249375.8151436973127
7761.982695551782248.489146838246675.4762442653178
7868.962346369158355.231069898720882.6936228395958
7966.911861264967952.946903329813780.876819200122
8067.840429710032453.645636764953782.0352226551111
8173.98014460022659.559179189523188.4011100109288
8284.635788666095869.992143628069299.2794337041224
8373.302214220734758.439225402103688.1652030393659
8474.018326232619958.939183908011889.097468557228


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')