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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 19 Nov 2013 15:00:59 -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/Nov/19/t13848913663wiaco4mr3d3num.htm/, Retrieved Fri, 03 May 2024 19:05:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226555, Retrieved Fri, 03 May 2024 19:05:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-11-19 20:00:59] [0e9124696d12fe9c83a0561864c9b933] [Current]
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Dataseries X:
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226555&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226555&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00520780154966176
beta0.748150946544559
gamma0.255285361715941

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00520780154966176 \tabularnewline
beta & 0.748150946544559 \tabularnewline
gamma & 0.255285361715941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226555&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]0.00520780154966176[/C][/ROW]
[ROW][C]beta[/C][C]0.748150946544559[/C][/ROW]
[ROW][C]gamma[/C][C]0.255285361715941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226555&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
alpha0.00520780154966176
beta0.748150946544559
gamma0.255285361715941







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134446.6829275162342-2.68292751623423
143637.4190430644542-1.41904306445421
157273.8530991175493-1.85309911754929
164546.4992868688017-1.4992868688017
175658.5280218487218-2.52802184872185
185456.6166500127844-2.61665001278436
195339.825039805755413.1749601942446
203526.74601746281428.25398253718579
216158.31243667088922.68756332911078
225270.6780753111068-18.6780753111068
234749.8765178807991-2.87651788079913
245160.2589543162225-9.25895431622246
255243.882072719088.11792728091996
266335.418266243930527.5817337560695
277470.70268774509053.29731225490951
284544.63472079341310.365279206586855
295156.2770561018972-5.27705610189717
306454.60763547971859.39236452028148
313642.3875265591061-6.38752655910609
323028.33724819333871.66275180666127
335558.0193961703378-3.01939617033784
346464.9214476297714-0.921447629771379
353948.5935132216705-9.59351322167048
364057.3421270513253-17.3421270513253
376345.535706492815417.4642935071846
384542.16704545574192.83295454425814
395970.8717659976263-11.8717659976263
405544.209867065326610.7901329346734
414054.35506464303-14.35506464303
426456.28766262056097.71233737943909
432740.2125612610768-13.2125612610768
442828.295078421395-0.295078421395029
454556.1952612610127-11.1952612610127
465763.2805438277329-6.2805438277329
474544.99887790693160.00112209306844591
486951.54672530186617.453274698134
496048.834228795537311.1657712044627
505641.873031578928414.1269684210716
515866.3961330279602-8.39613302796016
525045.99095018217284.00904981782725
535149.648274652871.35172534713003
545357.2022581613458-4.20225816134575
553736.17564932632340.82435067367657
562227.8097452362781-5.80974523627812
575552.58509862808442.4149013719156
587061.01439609669378.98560390330627
596244.709966828173817.2900331718262
605855.98672915223552.0132708477645
613951.7821660588517-12.7821660588517
624945.52007181638973.47992818361026
635864.3110080260309-6.31100802603088
644747.0876941001533-0.0876941001533496
654250.0740054721741-8.07400547217405
666256.15509613258535.84490386741474
673936.44605171344282.55394828655722
684026.398537237651613.6014627623484
697253.714171540765418.2858284592346
707064.29639572811645.70360427188363
715450.06746924684743.93253075315257
726557.70447279540937.29552720459067

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 44 & 46.6829275162342 & -2.68292751623423 \tabularnewline
14 & 36 & 37.4190430644542 & -1.41904306445421 \tabularnewline
15 & 72 & 73.8530991175493 & -1.85309911754929 \tabularnewline
16 & 45 & 46.4992868688017 & -1.4992868688017 \tabularnewline
17 & 56 & 58.5280218487218 & -2.52802184872185 \tabularnewline
18 & 54 & 56.6166500127844 & -2.61665001278436 \tabularnewline
19 & 53 & 39.8250398057554 & 13.1749601942446 \tabularnewline
20 & 35 & 26.7460174628142 & 8.25398253718579 \tabularnewline
21 & 61 & 58.3124366708892 & 2.68756332911078 \tabularnewline
22 & 52 & 70.6780753111068 & -18.6780753111068 \tabularnewline
23 & 47 & 49.8765178807991 & -2.87651788079913 \tabularnewline
24 & 51 & 60.2589543162225 & -9.25895431622246 \tabularnewline
25 & 52 & 43.88207271908 & 8.11792728091996 \tabularnewline
26 & 63 & 35.4182662439305 & 27.5817337560695 \tabularnewline
27 & 74 & 70.7026877450905 & 3.29731225490951 \tabularnewline
28 & 45 & 44.6347207934131 & 0.365279206586855 \tabularnewline
29 & 51 & 56.2770561018972 & -5.27705610189717 \tabularnewline
30 & 64 & 54.6076354797185 & 9.39236452028148 \tabularnewline
31 & 36 & 42.3875265591061 & -6.38752655910609 \tabularnewline
32 & 30 & 28.3372481933387 & 1.66275180666127 \tabularnewline
33 & 55 & 58.0193961703378 & -3.01939617033784 \tabularnewline
34 & 64 & 64.9214476297714 & -0.921447629771379 \tabularnewline
35 & 39 & 48.5935132216705 & -9.59351322167048 \tabularnewline
36 & 40 & 57.3421270513253 & -17.3421270513253 \tabularnewline
37 & 63 & 45.5357064928154 & 17.4642935071846 \tabularnewline
38 & 45 & 42.1670454557419 & 2.83295454425814 \tabularnewline
39 & 59 & 70.8717659976263 & -11.8717659976263 \tabularnewline
40 & 55 & 44.2098670653266 & 10.7901329346734 \tabularnewline
41 & 40 & 54.35506464303 & -14.35506464303 \tabularnewline
42 & 64 & 56.2876626205609 & 7.71233737943909 \tabularnewline
43 & 27 & 40.2125612610768 & -13.2125612610768 \tabularnewline
44 & 28 & 28.295078421395 & -0.295078421395029 \tabularnewline
45 & 45 & 56.1952612610127 & -11.1952612610127 \tabularnewline
46 & 57 & 63.2805438277329 & -6.2805438277329 \tabularnewline
47 & 45 & 44.9988779069316 & 0.00112209306844591 \tabularnewline
48 & 69 & 51.546725301866 & 17.453274698134 \tabularnewline
49 & 60 & 48.8342287955373 & 11.1657712044627 \tabularnewline
50 & 56 & 41.8730315789284 & 14.1269684210716 \tabularnewline
51 & 58 & 66.3961330279602 & -8.39613302796016 \tabularnewline
52 & 50 & 45.9909501821728 & 4.00904981782725 \tabularnewline
53 & 51 & 49.64827465287 & 1.35172534713003 \tabularnewline
54 & 53 & 57.2022581613458 & -4.20225816134575 \tabularnewline
55 & 37 & 36.1756493263234 & 0.82435067367657 \tabularnewline
56 & 22 & 27.8097452362781 & -5.80974523627812 \tabularnewline
57 & 55 & 52.5850986280844 & 2.4149013719156 \tabularnewline
58 & 70 & 61.0143960966937 & 8.98560390330627 \tabularnewline
59 & 62 & 44.7099668281738 & 17.2900331718262 \tabularnewline
60 & 58 & 55.9867291522355 & 2.0132708477645 \tabularnewline
61 & 39 & 51.7821660588517 & -12.7821660588517 \tabularnewline
62 & 49 & 45.5200718163897 & 3.47992818361026 \tabularnewline
63 & 58 & 64.3110080260309 & -6.31100802603088 \tabularnewline
64 & 47 & 47.0876941001533 & -0.0876941001533496 \tabularnewline
65 & 42 & 50.0740054721741 & -8.07400547217405 \tabularnewline
66 & 62 & 56.1550961325853 & 5.84490386741474 \tabularnewline
67 & 39 & 36.4460517134428 & 2.55394828655722 \tabularnewline
68 & 40 & 26.3985372376516 & 13.6014627623484 \tabularnewline
69 & 72 & 53.7141715407654 & 18.2858284592346 \tabularnewline
70 & 70 & 64.2963957281164 & 5.70360427188363 \tabularnewline
71 & 54 & 50.0674692468474 & 3.93253075315257 \tabularnewline
72 & 65 & 57.7044727954093 & 7.29552720459067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226555&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]44[/C][C]46.6829275162342[/C][C]-2.68292751623423[/C][/ROW]
[ROW][C]14[/C][C]36[/C][C]37.4190430644542[/C][C]-1.41904306445421[/C][/ROW]
[ROW][C]15[/C][C]72[/C][C]73.8530991175493[/C][C]-1.85309911754929[/C][/ROW]
[ROW][C]16[/C][C]45[/C][C]46.4992868688017[/C][C]-1.4992868688017[/C][/ROW]
[ROW][C]17[/C][C]56[/C][C]58.5280218487218[/C][C]-2.52802184872185[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]56.6166500127844[/C][C]-2.61665001278436[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]39.8250398057554[/C][C]13.1749601942446[/C][/ROW]
[ROW][C]20[/C][C]35[/C][C]26.7460174628142[/C][C]8.25398253718579[/C][/ROW]
[ROW][C]21[/C][C]61[/C][C]58.3124366708892[/C][C]2.68756332911078[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]70.6780753111068[/C][C]-18.6780753111068[/C][/ROW]
[ROW][C]23[/C][C]47[/C][C]49.8765178807991[/C][C]-2.87651788079913[/C][/ROW]
[ROW][C]24[/C][C]51[/C][C]60.2589543162225[/C][C]-9.25895431622246[/C][/ROW]
[ROW][C]25[/C][C]52[/C][C]43.88207271908[/C][C]8.11792728091996[/C][/ROW]
[ROW][C]26[/C][C]63[/C][C]35.4182662439305[/C][C]27.5817337560695[/C][/ROW]
[ROW][C]27[/C][C]74[/C][C]70.7026877450905[/C][C]3.29731225490951[/C][/ROW]
[ROW][C]28[/C][C]45[/C][C]44.6347207934131[/C][C]0.365279206586855[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]56.2770561018972[/C][C]-5.27705610189717[/C][/ROW]
[ROW][C]30[/C][C]64[/C][C]54.6076354797185[/C][C]9.39236452028148[/C][/ROW]
[ROW][C]31[/C][C]36[/C][C]42.3875265591061[/C][C]-6.38752655910609[/C][/ROW]
[ROW][C]32[/C][C]30[/C][C]28.3372481933387[/C][C]1.66275180666127[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]58.0193961703378[/C][C]-3.01939617033784[/C][/ROW]
[ROW][C]34[/C][C]64[/C][C]64.9214476297714[/C][C]-0.921447629771379[/C][/ROW]
[ROW][C]35[/C][C]39[/C][C]48.5935132216705[/C][C]-9.59351322167048[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]57.3421270513253[/C][C]-17.3421270513253[/C][/ROW]
[ROW][C]37[/C][C]63[/C][C]45.5357064928154[/C][C]17.4642935071846[/C][/ROW]
[ROW][C]38[/C][C]45[/C][C]42.1670454557419[/C][C]2.83295454425814[/C][/ROW]
[ROW][C]39[/C][C]59[/C][C]70.8717659976263[/C][C]-11.8717659976263[/C][/ROW]
[ROW][C]40[/C][C]55[/C][C]44.2098670653266[/C][C]10.7901329346734[/C][/ROW]
[ROW][C]41[/C][C]40[/C][C]54.35506464303[/C][C]-14.35506464303[/C][/ROW]
[ROW][C]42[/C][C]64[/C][C]56.2876626205609[/C][C]7.71233737943909[/C][/ROW]
[ROW][C]43[/C][C]27[/C][C]40.2125612610768[/C][C]-13.2125612610768[/C][/ROW]
[ROW][C]44[/C][C]28[/C][C]28.295078421395[/C][C]-0.295078421395029[/C][/ROW]
[ROW][C]45[/C][C]45[/C][C]56.1952612610127[/C][C]-11.1952612610127[/C][/ROW]
[ROW][C]46[/C][C]57[/C][C]63.2805438277329[/C][C]-6.2805438277329[/C][/ROW]
[ROW][C]47[/C][C]45[/C][C]44.9988779069316[/C][C]0.00112209306844591[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]51.546725301866[/C][C]17.453274698134[/C][/ROW]
[ROW][C]49[/C][C]60[/C][C]48.8342287955373[/C][C]11.1657712044627[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]41.8730315789284[/C][C]14.1269684210716[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]66.3961330279602[/C][C]-8.39613302796016[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]45.9909501821728[/C][C]4.00904981782725[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]49.64827465287[/C][C]1.35172534713003[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]57.2022581613458[/C][C]-4.20225816134575[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]36.1756493263234[/C][C]0.82435067367657[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]27.8097452362781[/C][C]-5.80974523627812[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]52.5850986280844[/C][C]2.4149013719156[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]61.0143960966937[/C][C]8.98560390330627[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]44.7099668281738[/C][C]17.2900331718262[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]55.9867291522355[/C][C]2.0132708477645[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]51.7821660588517[/C][C]-12.7821660588517[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]45.5200718163897[/C][C]3.47992818361026[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]64.3110080260309[/C][C]-6.31100802603088[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]47.0876941001533[/C][C]-0.0876941001533496[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]50.0740054721741[/C][C]-8.07400547217405[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]56.1550961325853[/C][C]5.84490386741474[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]36.4460517134428[/C][C]2.55394828655722[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]26.3985372376516[/C][C]13.6014627623484[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]53.7141715407654[/C][C]18.2858284592346[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]64.2963957281164[/C][C]5.70360427188363[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]50.0674692468474[/C][C]3.93253075315257[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]57.7044727954093[/C][C]7.29552720459067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226555&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
134446.6829275162342-2.68292751623423
143637.4190430644542-1.41904306445421
157273.8530991175493-1.85309911754929
164546.4992868688017-1.4992868688017
175658.5280218487218-2.52802184872185
185456.6166500127844-2.61665001278436
195339.825039805755413.1749601942446
203526.74601746281428.25398253718579
216158.31243667088922.68756332911078
225270.6780753111068-18.6780753111068
234749.8765178807991-2.87651788079913
245160.2589543162225-9.25895431622246
255243.882072719088.11792728091996
266335.418266243930527.5817337560695
277470.70268774509053.29731225490951
284544.63472079341310.365279206586855
295156.2770561018972-5.27705610189717
306454.60763547971859.39236452028148
313642.3875265591061-6.38752655910609
323028.33724819333871.66275180666127
335558.0193961703378-3.01939617033784
346464.9214476297714-0.921447629771379
353948.5935132216705-9.59351322167048
364057.3421270513253-17.3421270513253
376345.535706492815417.4642935071846
384542.16704545574192.83295454425814
395970.8717659976263-11.8717659976263
405544.209867065326610.7901329346734
414054.35506464303-14.35506464303
426456.28766262056097.71233737943909
432740.2125612610768-13.2125612610768
442828.295078421395-0.295078421395029
454556.1952612610127-11.1952612610127
465763.2805438277329-6.2805438277329
474544.99887790693160.00112209306844591
486951.54672530186617.453274698134
496048.834228795537311.1657712044627
505641.873031578928414.1269684210716
515866.3961330279602-8.39613302796016
525045.99095018217284.00904981782725
535149.648274652871.35172534713003
545357.2022581613458-4.20225816134575
553736.17564932632340.82435067367657
562227.8097452362781-5.80974523627812
575552.58509862808442.4149013719156
587061.01439609669378.98560390330627
596244.709966828173817.2900331718262
605855.98672915223552.0132708477645
613951.7821660588517-12.7821660588517
624945.52007181638973.47992818361026
635864.3110080260309-6.31100802603088
644747.0876941001533-0.0876941001533496
654250.0740054721741-8.07400547217405
666256.15509613258535.84490386741474
673936.44605171344282.55394828655722
684026.398537237651613.6014627623484
697253.714171540765418.2858284592346
707064.29639572811645.70360427188363
715450.06746924684743.93253075315257
726557.70447279540937.29552720459067







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7349.760097918435844.933993073522854.5862027633488
7447.845822213582943.016990789823352.6746536373425
7564.890662189884960.049021465991469.7323029137784
7648.942461022756144.098824892297553.7860971532147
7750.155622281104345.29680400060155.0144405616076
7860.550248972823255.647712921394865.4527850242516
7939.124302007804934.250606089980743.9979979256292
8031.598956331219326.727908196049736.4700044663889
8161.754062661525956.688978964590866.819146358461
8269.518974379392164.290732528811774.7472162299724
8354.00225558617648.856273588658159.1482375836939
8462.969937371506438.867976014510587.0718987285023

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 49.7600979184358 & 44.9339930735228 & 54.5862027633488 \tabularnewline
74 & 47.8458222135829 & 43.0169907898233 & 52.6746536373425 \tabularnewline
75 & 64.8906621898849 & 60.0490214659914 & 69.7323029137784 \tabularnewline
76 & 48.9424610227561 & 44.0988248922975 & 53.7860971532147 \tabularnewline
77 & 50.1556222811043 & 45.296804000601 & 55.0144405616076 \tabularnewline
78 & 60.5502489728232 & 55.6477129213948 & 65.4527850242516 \tabularnewline
79 & 39.1243020078049 & 34.2506060899807 & 43.9979979256292 \tabularnewline
80 & 31.5989563312193 & 26.7279081960497 & 36.4700044663889 \tabularnewline
81 & 61.7540626615259 & 56.6889789645908 & 66.819146358461 \tabularnewline
82 & 69.5189743793921 & 64.2907325288117 & 74.7472162299724 \tabularnewline
83 & 54.002255586176 & 48.8562735886581 & 59.1482375836939 \tabularnewline
84 & 62.9699373715064 & 38.8679760145105 & 87.0718987285023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226555&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]49.7600979184358[/C][C]44.9339930735228[/C][C]54.5862027633488[/C][/ROW]
[ROW][C]74[/C][C]47.8458222135829[/C][C]43.0169907898233[/C][C]52.6746536373425[/C][/ROW]
[ROW][C]75[/C][C]64.8906621898849[/C][C]60.0490214659914[/C][C]69.7323029137784[/C][/ROW]
[ROW][C]76[/C][C]48.9424610227561[/C][C]44.0988248922975[/C][C]53.7860971532147[/C][/ROW]
[ROW][C]77[/C][C]50.1556222811043[/C][C]45.296804000601[/C][C]55.0144405616076[/C][/ROW]
[ROW][C]78[/C][C]60.5502489728232[/C][C]55.6477129213948[/C][C]65.4527850242516[/C][/ROW]
[ROW][C]79[/C][C]39.1243020078049[/C][C]34.2506060899807[/C][C]43.9979979256292[/C][/ROW]
[ROW][C]80[/C][C]31.5989563312193[/C][C]26.7279081960497[/C][C]36.4700044663889[/C][/ROW]
[ROW][C]81[/C][C]61.7540626615259[/C][C]56.6889789645908[/C][C]66.819146358461[/C][/ROW]
[ROW][C]82[/C][C]69.5189743793921[/C][C]64.2907325288117[/C][C]74.7472162299724[/C][/ROW]
[ROW][C]83[/C][C]54.002255586176[/C][C]48.8562735886581[/C][C]59.1482375836939[/C][/ROW]
[ROW][C]84[/C][C]62.9699373715064[/C][C]38.8679760145105[/C][C]87.0718987285023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226555&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226555&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
7349.760097918435844.933993073522854.5862027633488
7447.845822213582943.016990789823352.6746536373425
7564.890662189884960.049021465991469.7323029137784
7648.942461022756144.098824892297553.7860971532147
7750.155622281104345.29680400060155.0144405616076
7860.550248972823255.647712921394865.4527850242516
7939.124302007804934.250606089980743.9979979256292
8031.598956331219326.727908196049736.4700044663889
8161.754062661525956.688978964590866.819146358461
8269.518974379392164.290732528811774.7472162299724
8354.00225558617648.856273588658159.1482375836939
8462.969937371506438.867976014510587.0718987285023



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')