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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 28 Dec 2012 05:33:53 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/28/t1356690918wnopwfnzslhpk6o.htm/, Retrieved Mon, 29 Apr 2024 12:02:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204812, Retrieved Mon, 29 Apr 2024 12:02:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

106

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [opdracht 10 oef 2] [2012-12-28 10:33:53] [e4a421093dfcf6fc9affa795b0900948] [Current]

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Dataseries X:

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2,08
2,09
2,36
2,99
2,75
1,58
1,69
1,3
1,97
1,84
1,96
1,86
2,75
2,62
2,41
3,61
2,03
1,45
1,4
1,3
1,58
2,1
2,27
2,54
2,55
2,05
2,32
2,6
2,1
1,61
1,55
1,12
1,39
2,18
1,94
2,27
2,41
2,2
2,58
2,9
2,12
1,34
1,07
0,86
1
1,54
1,29
1,44
2,6
2,77
3,31
3,2
2,07
1,42
1,43
1,28
1,59
1,68
2,01
2,52
2,74
3,06
2,69
2,32
1,67
1,04
0,98
0,86
0,97
1,3
1,82
1,99

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204812&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204812&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0
beta	0
gamma	0.415602455144669

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.415602455144669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204812&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.415602455144669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204812&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
Parameter	Value
alpha	0
beta	0
gamma	0.415602455144669

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.75	2.75165328104311	-0.00165328104310625
14	2.62	2.63502698167349	-0.0150269816734876
15	2.41	2.44121110626251	-0.0312111062625107
16	3.61	3.66400937849564	-0.0540093784956399
17	2.03	2.03582850158271	-0.00582850158270665
18	1.45	1.42529151970651	0.0247084802934936
19	1.4	1.72140993385817	-0.321409933858171
20	1.3	1.29208470435897	0.00791529564102844
21	1.58	1.93470283994451	-0.354702839944509
22	2.1	1.78266601236554	0.317333987634458
23	2.27	1.90139676362203	0.368603236377972
24	2.54	1.83325218903836	0.706747810961637
25	2.55	2.73052558588536	-0.180525585885356
26	2.05	2.60923691243219	-0.559236912432187
27	2.32	2.41017469925616	-0.0901746992561616
28	2.6	3.61445457639449	-1.01445457639449
29	2.1	2.01825976822409	0.0817402317759095
30	1.61	1.42486061024585	0.185139389754151
31	1.55	1.57598907065368	-0.0259890706536832
32	1.12	1.28570736143349	-0.165707361433488
33	1.39	1.77394122110925	-0.383941221109254
34	2.18	1.9002453310508	0.279754668949201
35	1.94	2.03922778045081	-0.0992277804508124
36	2.27	2.11106578044613	0.158934219553865
37	2.41	2.63561976938618	-0.22561976938618
38	2.2	2.35901283298067	-0.159012832980674
39	2.58	2.35491377848402	0.225086221515977
40	2.9	3.16889846123187	-0.268898461231869
41	2.12	2.03682987064807	0.0831701293519349
42	1.34	1.4905273762956	-0.150527376295602
43	1.07	1.55342700397326	-0.483427003973261
44	0.86	1.20768982265591	-0.347689822655905
45	1	1.60222856103959	-0.602228561039589
46	1.54	2.00133131107922	-0.461331311079222
47	1.29	1.98293773159055	-0.692937731590554
48	1.44	2.1607088086553	-0.720708808655296
49	2.6	2.52267993772289	0.0773200622771086
50	2.77	2.27562162606085	0.494378373939155
51	3.31	2.42996961660697	0.880030383393028
52	3.2	3.03404179196992	0.165958208030081
53	2.07	2.05573287595314	0.0142671240468606
54	1.42	1.4171635479175	0.00283645208249839
55	1.43	1.34227371829472	0.0877262817052766
56	1.28	1.05513462727583	0.224865372724168
57	1.59	1.34169246041505	0.248307539584952
58	1.68	1.79587447580932	-0.115874475809325
59	2.01	1.68208622304797	0.327913776952033
60	2.52	1.8470449303641	0.672955069635903
61	2.74	2.53539843084435	0.204601569155652
62	3.06	2.46221894063615	0.597781059363847
63	2.69	2.77443878264664	-0.0844387826466386
64	2.32	3.07938745045137	-0.759387450451366
65	1.67	2.04595444637463	-0.375954446374628
66	1.04	1.4075291158391	-0.367529115839095
67	0.98	1.36821500278533	-0.388215002785334
68	0.86	1.13982138390605	-0.279821383906054
69	0.97	1.43385298600706	-0.463852986007064
70	1.3	1.73435843336319	-0.434358433363195
71	1.82	1.80446080126687	0.015539198733131
72	1.99	2.1104507627814	-0.120450762781404

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.75 & 2.75165328104311 & -0.00165328104310625 \tabularnewline
14 & 2.62 & 2.63502698167349 & -0.0150269816734876 \tabularnewline
15 & 2.41 & 2.44121110626251 & -0.0312111062625107 \tabularnewline
16 & 3.61 & 3.66400937849564 & -0.0540093784956399 \tabularnewline
17 & 2.03 & 2.03582850158271 & -0.00582850158270665 \tabularnewline
18 & 1.45 & 1.42529151970651 & 0.0247084802934936 \tabularnewline
19 & 1.4 & 1.72140993385817 & -0.321409933858171 \tabularnewline
20 & 1.3 & 1.29208470435897 & 0.00791529564102844 \tabularnewline
21 & 1.58 & 1.93470283994451 & -0.354702839944509 \tabularnewline
22 & 2.1 & 1.78266601236554 & 0.317333987634458 \tabularnewline
23 & 2.27 & 1.90139676362203 & 0.368603236377972 \tabularnewline
24 & 2.54 & 1.83325218903836 & 0.706747810961637 \tabularnewline
25 & 2.55 & 2.73052558588536 & -0.180525585885356 \tabularnewline
26 & 2.05 & 2.60923691243219 & -0.559236912432187 \tabularnewline
27 & 2.32 & 2.41017469925616 & -0.0901746992561616 \tabularnewline
28 & 2.6 & 3.61445457639449 & -1.01445457639449 \tabularnewline
29 & 2.1 & 2.01825976822409 & 0.0817402317759095 \tabularnewline
30 & 1.61 & 1.42486061024585 & 0.185139389754151 \tabularnewline
31 & 1.55 & 1.57598907065368 & -0.0259890706536832 \tabularnewline
32 & 1.12 & 1.28570736143349 & -0.165707361433488 \tabularnewline
33 & 1.39 & 1.77394122110925 & -0.383941221109254 \tabularnewline
34 & 2.18 & 1.9002453310508 & 0.279754668949201 \tabularnewline
35 & 1.94 & 2.03922778045081 & -0.0992277804508124 \tabularnewline
36 & 2.27 & 2.11106578044613 & 0.158934219553865 \tabularnewline
37 & 2.41 & 2.63561976938618 & -0.22561976938618 \tabularnewline
38 & 2.2 & 2.35901283298067 & -0.159012832980674 \tabularnewline
39 & 2.58 & 2.35491377848402 & 0.225086221515977 \tabularnewline
40 & 2.9 & 3.16889846123187 & -0.268898461231869 \tabularnewline
41 & 2.12 & 2.03682987064807 & 0.0831701293519349 \tabularnewline
42 & 1.34 & 1.4905273762956 & -0.150527376295602 \tabularnewline
43 & 1.07 & 1.55342700397326 & -0.483427003973261 \tabularnewline
44 & 0.86 & 1.20768982265591 & -0.347689822655905 \tabularnewline
45 & 1 & 1.60222856103959 & -0.602228561039589 \tabularnewline
46 & 1.54 & 2.00133131107922 & -0.461331311079222 \tabularnewline
47 & 1.29 & 1.98293773159055 & -0.692937731590554 \tabularnewline
48 & 1.44 & 2.1607088086553 & -0.720708808655296 \tabularnewline
49 & 2.6 & 2.52267993772289 & 0.0773200622771086 \tabularnewline
50 & 2.77 & 2.27562162606085 & 0.494378373939155 \tabularnewline
51 & 3.31 & 2.42996961660697 & 0.880030383393028 \tabularnewline
52 & 3.2 & 3.03404179196992 & 0.165958208030081 \tabularnewline
53 & 2.07 & 2.05573287595314 & 0.0142671240468606 \tabularnewline
54 & 1.42 & 1.4171635479175 & 0.00283645208249839 \tabularnewline
55 & 1.43 & 1.34227371829472 & 0.0877262817052766 \tabularnewline
56 & 1.28 & 1.05513462727583 & 0.224865372724168 \tabularnewline
57 & 1.59 & 1.34169246041505 & 0.248307539584952 \tabularnewline
58 & 1.68 & 1.79587447580932 & -0.115874475809325 \tabularnewline
59 & 2.01 & 1.68208622304797 & 0.327913776952033 \tabularnewline
60 & 2.52 & 1.8470449303641 & 0.672955069635903 \tabularnewline
61 & 2.74 & 2.53539843084435 & 0.204601569155652 \tabularnewline
62 & 3.06 & 2.46221894063615 & 0.597781059363847 \tabularnewline
63 & 2.69 & 2.77443878264664 & -0.0844387826466386 \tabularnewline
64 & 2.32 & 3.07938745045137 & -0.759387450451366 \tabularnewline
65 & 1.67 & 2.04595444637463 & -0.375954446374628 \tabularnewline
66 & 1.04 & 1.4075291158391 & -0.367529115839095 \tabularnewline
67 & 0.98 & 1.36821500278533 & -0.388215002785334 \tabularnewline
68 & 0.86 & 1.13982138390605 & -0.279821383906054 \tabularnewline
69 & 0.97 & 1.43385298600706 & -0.463852986007064 \tabularnewline
70 & 1.3 & 1.73435843336319 & -0.434358433363195 \tabularnewline
71 & 1.82 & 1.80446080126687 & 0.015539198733131 \tabularnewline
72 & 1.99 & 2.1104507627814 & -0.120450762781404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204812&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]2.75[/C][C]2.75165328104311[/C][C]-0.00165328104310625[/C][/ROW]
[ROW][C]14[/C][C]2.62[/C][C]2.63502698167349[/C][C]-0.0150269816734876[/C][/ROW]
[ROW][C]15[/C][C]2.41[/C][C]2.44121110626251[/C][C]-0.0312111062625107[/C][/ROW]
[ROW][C]16[/C][C]3.61[/C][C]3.66400937849564[/C][C]-0.0540093784956399[/C][/ROW]
[ROW][C]17[/C][C]2.03[/C][C]2.03582850158271[/C][C]-0.00582850158270665[/C][/ROW]
[ROW][C]18[/C][C]1.45[/C][C]1.42529151970651[/C][C]0.0247084802934936[/C][/ROW]
[ROW][C]19[/C][C]1.4[/C][C]1.72140993385817[/C][C]-0.321409933858171[/C][/ROW]
[ROW][C]20[/C][C]1.3[/C][C]1.29208470435897[/C][C]0.00791529564102844[/C][/ROW]
[ROW][C]21[/C][C]1.58[/C][C]1.93470283994451[/C][C]-0.354702839944509[/C][/ROW]
[ROW][C]22[/C][C]2.1[/C][C]1.78266601236554[/C][C]0.317333987634458[/C][/ROW]
[ROW][C]23[/C][C]2.27[/C][C]1.90139676362203[/C][C]0.368603236377972[/C][/ROW]
[ROW][C]24[/C][C]2.54[/C][C]1.83325218903836[/C][C]0.706747810961637[/C][/ROW]
[ROW][C]25[/C][C]2.55[/C][C]2.73052558588536[/C][C]-0.180525585885356[/C][/ROW]
[ROW][C]26[/C][C]2.05[/C][C]2.60923691243219[/C][C]-0.559236912432187[/C][/ROW]
[ROW][C]27[/C][C]2.32[/C][C]2.41017469925616[/C][C]-0.0901746992561616[/C][/ROW]
[ROW][C]28[/C][C]2.6[/C][C]3.61445457639449[/C][C]-1.01445457639449[/C][/ROW]
[ROW][C]29[/C][C]2.1[/C][C]2.01825976822409[/C][C]0.0817402317759095[/C][/ROW]
[ROW][C]30[/C][C]1.61[/C][C]1.42486061024585[/C][C]0.185139389754151[/C][/ROW]
[ROW][C]31[/C][C]1.55[/C][C]1.57598907065368[/C][C]-0.0259890706536832[/C][/ROW]
[ROW][C]32[/C][C]1.12[/C][C]1.28570736143349[/C][C]-0.165707361433488[/C][/ROW]
[ROW][C]33[/C][C]1.39[/C][C]1.77394122110925[/C][C]-0.383941221109254[/C][/ROW]
[ROW][C]34[/C][C]2.18[/C][C]1.9002453310508[/C][C]0.279754668949201[/C][/ROW]
[ROW][C]35[/C][C]1.94[/C][C]2.03922778045081[/C][C]-0.0992277804508124[/C][/ROW]
[ROW][C]36[/C][C]2.27[/C][C]2.11106578044613[/C][C]0.158934219553865[/C][/ROW]
[ROW][C]37[/C][C]2.41[/C][C]2.63561976938618[/C][C]-0.22561976938618[/C][/ROW]
[ROW][C]38[/C][C]2.2[/C][C]2.35901283298067[/C][C]-0.159012832980674[/C][/ROW]
[ROW][C]39[/C][C]2.58[/C][C]2.35491377848402[/C][C]0.225086221515977[/C][/ROW]
[ROW][C]40[/C][C]2.9[/C][C]3.16889846123187[/C][C]-0.268898461231869[/C][/ROW]
[ROW][C]41[/C][C]2.12[/C][C]2.03682987064807[/C][C]0.0831701293519349[/C][/ROW]
[ROW][C]42[/C][C]1.34[/C][C]1.4905273762956[/C][C]-0.150527376295602[/C][/ROW]
[ROW][C]43[/C][C]1.07[/C][C]1.55342700397326[/C][C]-0.483427003973261[/C][/ROW]
[ROW][C]44[/C][C]0.86[/C][C]1.20768982265591[/C][C]-0.347689822655905[/C][/ROW]
[ROW][C]45[/C][C]1[/C][C]1.60222856103959[/C][C]-0.602228561039589[/C][/ROW]
[ROW][C]46[/C][C]1.54[/C][C]2.00133131107922[/C][C]-0.461331311079222[/C][/ROW]
[ROW][C]47[/C][C]1.29[/C][C]1.98293773159055[/C][C]-0.692937731590554[/C][/ROW]
[ROW][C]48[/C][C]1.44[/C][C]2.1607088086553[/C][C]-0.720708808655296[/C][/ROW]
[ROW][C]49[/C][C]2.6[/C][C]2.52267993772289[/C][C]0.0773200622771086[/C][/ROW]
[ROW][C]50[/C][C]2.77[/C][C]2.27562162606085[/C][C]0.494378373939155[/C][/ROW]
[ROW][C]51[/C][C]3.31[/C][C]2.42996961660697[/C][C]0.880030383393028[/C][/ROW]
[ROW][C]52[/C][C]3.2[/C][C]3.03404179196992[/C][C]0.165958208030081[/C][/ROW]
[ROW][C]53[/C][C]2.07[/C][C]2.05573287595314[/C][C]0.0142671240468606[/C][/ROW]
[ROW][C]54[/C][C]1.42[/C][C]1.4171635479175[/C][C]0.00283645208249839[/C][/ROW]
[ROW][C]55[/C][C]1.43[/C][C]1.34227371829472[/C][C]0.0877262817052766[/C][/ROW]
[ROW][C]56[/C][C]1.28[/C][C]1.05513462727583[/C][C]0.224865372724168[/C][/ROW]
[ROW][C]57[/C][C]1.59[/C][C]1.34169246041505[/C][C]0.248307539584952[/C][/ROW]
[ROW][C]58[/C][C]1.68[/C][C]1.79587447580932[/C][C]-0.115874475809325[/C][/ROW]
[ROW][C]59[/C][C]2.01[/C][C]1.68208622304797[/C][C]0.327913776952033[/C][/ROW]
[ROW][C]60[/C][C]2.52[/C][C]1.8470449303641[/C][C]0.672955069635903[/C][/ROW]
[ROW][C]61[/C][C]2.74[/C][C]2.53539843084435[/C][C]0.204601569155652[/C][/ROW]
[ROW][C]62[/C][C]3.06[/C][C]2.46221894063615[/C][C]0.597781059363847[/C][/ROW]
[ROW][C]63[/C][C]2.69[/C][C]2.77443878264664[/C][C]-0.0844387826466386[/C][/ROW]
[ROW][C]64[/C][C]2.32[/C][C]3.07938745045137[/C][C]-0.759387450451366[/C][/ROW]
[ROW][C]65[/C][C]1.67[/C][C]2.04595444637463[/C][C]-0.375954446374628[/C][/ROW]
[ROW][C]66[/C][C]1.04[/C][C]1.4075291158391[/C][C]-0.367529115839095[/C][/ROW]
[ROW][C]67[/C][C]0.98[/C][C]1.36821500278533[/C][C]-0.388215002785334[/C][/ROW]
[ROW][C]68[/C][C]0.86[/C][C]1.13982138390605[/C][C]-0.279821383906054[/C][/ROW]
[ROW][C]69[/C][C]0.97[/C][C]1.43385298600706[/C][C]-0.463852986007064[/C][/ROW]
[ROW][C]70[/C][C]1.3[/C][C]1.73435843336319[/C][C]-0.434358433363195[/C][/ROW]
[ROW][C]71[/C][C]1.82[/C][C]1.80446080126687[/C][C]0.015539198733131[/C][/ROW]
[ROW][C]72[/C][C]1.99[/C][C]2.1104507627814[/C][C]-0.120450762781404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204812&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204812&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
t	Observed	Fitted	Residuals
13	2.75	2.75165328104311	-0.00165328104310625
14	2.62	2.63502698167349	-0.0150269816734876
15	2.41	2.44121110626251	-0.0312111062625107
16	3.61	3.66400937849564	-0.0540093784956399
17	2.03	2.03582850158271	-0.00582850158270665
18	1.45	1.42529151970651	0.0247084802934936
19	1.4	1.72140993385817	-0.321409933858171
20	1.3	1.29208470435897	0.00791529564102844
21	1.58	1.93470283994451	-0.354702839944509
22	2.1	1.78266601236554	0.317333987634458
23	2.27	1.90139676362203	0.368603236377972
24	2.54	1.83325218903836	0.706747810961637
25	2.55	2.73052558588536	-0.180525585885356
26	2.05	2.60923691243219	-0.559236912432187
27	2.32	2.41017469925616	-0.0901746992561616
28	2.6	3.61445457639449	-1.01445457639449
29	2.1	2.01825976822409	0.0817402317759095
30	1.61	1.42486061024585	0.185139389754151
31	1.55	1.57598907065368	-0.0259890706536832
32	1.12	1.28570736143349	-0.165707361433488
33	1.39	1.77394122110925	-0.383941221109254
34	2.18	1.9002453310508	0.279754668949201
35	1.94	2.03922778045081	-0.0992277804508124
36	2.27	2.11106578044613	0.158934219553865
37	2.41	2.63561976938618	-0.22561976938618
38	2.2	2.35901283298067	-0.159012832980674
39	2.58	2.35491377848402	0.225086221515977
40	2.9	3.16889846123187	-0.268898461231869
41	2.12	2.03682987064807	0.0831701293519349
42	1.34	1.4905273762956	-0.150527376295602
43	1.07	1.55342700397326	-0.483427003973261
44	0.86	1.20768982265591	-0.347689822655905
45	1	1.60222856103959	-0.602228561039589
46	1.54	2.00133131107922	-0.461331311079222
47	1.29	1.98293773159055	-0.692937731590554
48	1.44	2.1607088086553	-0.720708808655296
49	2.6	2.52267993772289	0.0773200622771086
50	2.77	2.27562162606085	0.494378373939155
51	3.31	2.42996961660697	0.880030383393028
52	3.2	3.03404179196992	0.165958208030081
53	2.07	2.05573287595314	0.0142671240468606
54	1.42	1.4171635479175	0.00283645208249839
55	1.43	1.34227371829472	0.0877262817052766
56	1.28	1.05513462727583	0.224865372724168
57	1.59	1.34169246041505	0.248307539584952
58	1.68	1.79587447580932	-0.115874475809325
59	2.01	1.68208622304797	0.327913776952033
60	2.52	1.8470449303641	0.672955069635903
61	2.74	2.53539843084435	0.204601569155652
62	3.06	2.46221894063615	0.597781059363847
63	2.69	2.77443878264664	-0.0844387826466386
64	2.32	3.07938745045137	-0.759387450451366
65	1.67	2.04595444637463	-0.375954446374628
66	1.04	1.4075291158391	-0.367529115839095
67	0.98	1.36821500278533	-0.388215002785334
68	0.86	1.13982138390605	-0.279821383906054
69	0.97	1.43385298600706	-0.463852986007064
70	1.3	1.73435843336319	-0.434358433363195
71	1.82	1.80446080126687	0.015539198733131
72	1.99	2.1104507627814	-0.120450762781404

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	2.60036425424721	2.29708719241155	2.90364131608287
74	2.68988691859434	2.38660985675868	2.99316398043001
75	2.71834127842867	2.415064216593	3.02161834026433
76	2.7425786865911	2.43930162475544	3.04585574842676
77	1.8751985700058	1.57192150817014	2.17847563184147
78	1.24514330757837	0.941866245742705	1.54842036941403
79	1.19759422494226	0.894317163106596	1.50087128677792
80	1.01565365685593	0.712376595020263	1.31893071869159
81	1.23152170886706	0.928244647031395	1.53479877070272
82	1.54187007552508	1.23859301368942	1.84514713736075
83	1.79696196428899	1.49368490245333	2.10023902612465
84	2.04450124677612	-229.992943235671	234.081945729223

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.60036425424721 & 2.29708719241155 & 2.90364131608287 \tabularnewline
74 & 2.68988691859434 & 2.38660985675868 & 2.99316398043001 \tabularnewline
75 & 2.71834127842867 & 2.415064216593 & 3.02161834026433 \tabularnewline
76 & 2.7425786865911 & 2.43930162475544 & 3.04585574842676 \tabularnewline
77 & 1.8751985700058 & 1.57192150817014 & 2.17847563184147 \tabularnewline
78 & 1.24514330757837 & 0.941866245742705 & 1.54842036941403 \tabularnewline
79 & 1.19759422494226 & 0.894317163106596 & 1.50087128677792 \tabularnewline
80 & 1.01565365685593 & 0.712376595020263 & 1.31893071869159 \tabularnewline
81 & 1.23152170886706 & 0.928244647031395 & 1.53479877070272 \tabularnewline
82 & 1.54187007552508 & 1.23859301368942 & 1.84514713736075 \tabularnewline
83 & 1.79696196428899 & 1.49368490245333 & 2.10023902612465 \tabularnewline
84 & 2.04450124677612 & -229.992943235671 & 234.081945729223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204812&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]2.60036425424721[/C][C]2.29708719241155[/C][C]2.90364131608287[/C][/ROW]
[ROW][C]74[/C][C]2.68988691859434[/C][C]2.38660985675868[/C][C]2.99316398043001[/C][/ROW]
[ROW][C]75[/C][C]2.71834127842867[/C][C]2.415064216593[/C][C]3.02161834026433[/C][/ROW]
[ROW][C]76[/C][C]2.7425786865911[/C][C]2.43930162475544[/C][C]3.04585574842676[/C][/ROW]
[ROW][C]77[/C][C]1.8751985700058[/C][C]1.57192150817014[/C][C]2.17847563184147[/C][/ROW]
[ROW][C]78[/C][C]1.24514330757837[/C][C]0.941866245742705[/C][C]1.54842036941403[/C][/ROW]
[ROW][C]79[/C][C]1.19759422494226[/C][C]0.894317163106596[/C][C]1.50087128677792[/C][/ROW]
[ROW][C]80[/C][C]1.01565365685593[/C][C]0.712376595020263[/C][C]1.31893071869159[/C][/ROW]
[ROW][C]81[/C][C]1.23152170886706[/C][C]0.928244647031395[/C][C]1.53479877070272[/C][/ROW]
[ROW][C]82[/C][C]1.54187007552508[/C][C]1.23859301368942[/C][C]1.84514713736075[/C][/ROW]
[ROW][C]83[/C][C]1.79696196428899[/C][C]1.49368490245333[/C][C]2.10023902612465[/C][/ROW]
[ROW][C]84[/C][C]2.04450124677612[/C][C]-229.992943235671[/C][C]234.081945729223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204812&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204812&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	2.60036425424721	2.29708719241155	2.90364131608287
74	2.68988691859434	2.38660985675868	2.99316398043001
75	2.71834127842867	2.415064216593	3.02161834026433
76	2.7425786865911	2.43930162475544	3.04585574842676
77	1.8751985700058	1.57192150817014	2.17847563184147
78	1.24514330757837	0.941866245742705	1.54842036941403
79	1.19759422494226	0.894317163106596	1.50087128677792
80	1.01565365685593	0.712376595020263	1.31893071869159
81	1.23152170886706	0.928244647031395	1.53479877070272
82	1.54187007552508	1.23859301368942	1.84514713736075
83	1.79696196428899	1.49368490245333	2.10023902612465
84	2.04450124677612	-229.992943235671	234.081945729223

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code