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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 26 Dec 2013 07:41:08 -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/2013/Dec/26/t1388061795qx71yp0ugw7qwlm.htm/, Retrieved Thu, 18 Apr 2024 00:18:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232616, Retrieved Thu, 18 Apr 2024 00:18:07 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

155

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

-       [Exponential Smoothing] [] [2013-12-26 12:41:08] [1fa9a3525e57be7dc964ed2b4f1361ce] [Current]

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Dataseries X:

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1,49
1,55
1,57
1,6
1,61
1,68
1,72
1,72
1,73
1,74
1,74
1,75
1,75
1,75
1,75
1,76
1,76
1,77
1,78
1,78
1,78
1,78
1,78
1,79
1,79
1,79
1,79
1,79
1,79
1,8
1,8
1,8
1,8
1,8
1,81
1,81
1,82
1,82
1,82
1,82
1,83
1,83
1,84
1,84
1,84
1,85
1,85
1,85
1,86
1,86
1,86
1,86
1,87
1,87
1,87
1,87
1,88
1,9
1,9
1,91
1,91
1,91
1,92
1,92
1,92
1,92
1,92
1,92
1,92
1,92
1,93
1,93
1,93
1,94
1,95
1,95
1,95
1,95
1,98
1,98
2,01
2,02
2,11
2,14

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 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 & 7 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232616&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]7 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=232616&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232616&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	7 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.570074336371817
beta	0.146198857248525
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.570074336371817 \tabularnewline
beta & 0.146198857248525 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232616&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]0.570074336371817[/C][/ROW]
[ROW][C]beta[/C][C]0.146198857248525[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232616&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232616&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	0.570074336371817
beta	0.146198857248525
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.75	1.67788728632479	0.0721127136752133
14	1.75	1.72848463544242	0.0215153645575814
15	1.75	1.7524475822086	-0.00244758220859564
16	1.76	1.77337920951131	-0.0133792095113106
17	1.76	1.7773805835662	-0.0173805835661984
18	1.77	1.78765230584211	-0.017652305842111
19	1.78	1.83796457528831	-0.0579645752883147
20	1.78	1.79296484236876	-0.0129648423687649
21	1.78	1.78587109103399	-0.00587109103398498
22	1.78	1.78399865046806	-0.00399865046806269
23	1.78	1.77411037582474	0.00588962417526084
24	1.79	1.78326668556575	0.00673331443425318
25	1.79	1.81821825057023	-0.0282182505702322
26	1.79	1.7793867921841	0.010613207815902
27	1.79	1.77544418093097	0.0145558190690296
28	1.79	1.79139812650933	-0.00139812650933235
29	1.79	1.79153677178443	-0.00153677178442524
30	1.8	1.80307177092216	-0.00307177092215638
31	1.8	1.83792789995671	-0.0379278999567094
32	1.8	1.81893019248964	-0.0189301924896412
33	1.8	1.80622144748277	-0.00622144748276909
34	1.8	1.79966100135507	0.000338998644933364
35	1.81	1.79156496356164	0.0184350364383581
36	1.81	1.80434963389581	0.00565036610419334
37	1.82	1.81968082451847	0.000319175481526823
38	1.82	1.81221445173093	0.00778554826907052
39	1.82	1.80652121589212	0.0134787841078776
40	1.82	1.81307871799902	0.00692128200097808
41	1.83	1.8166703691415	0.0133296308584994
42	1.83	1.83602934780175	-0.00602934780175213
43	1.84	1.85397635724945	-0.0139763572494478
44	1.84	1.85855909764472	-0.0185590976447172
45	1.84	1.85331533458358	-0.0133153345835844
46	1.85	1.84672972983454	0.00327027016546433
47	1.85	1.84952737049838	0.00047262950162108
48	1.85	1.84652129774082	0.00347870225917624
49	1.86	1.85808708925019	0.00191291074981148
50	1.86	1.85463670430927	0.00536329569072569
51	1.86	1.8497058468878	0.0102941531122032
52	1.86	1.85105878782521	0.00894121217479382
53	1.87	1.85815556613115	0.0118444338688484
54	1.87	1.86781967095077	0.00218032904923238
55	1.87	1.88718913285081	-0.017189132850812
56	1.87	1.88786129803654	-0.0178612980365427
57	1.88	1.88521910191455	-0.00521910191455399
58	1.9	1.89100364390505	0.00899635609495064
59	1.9	1.89696415297693	0.00303584702307447
60	1.91	1.89802667321897	0.011973326781028
61	1.91	1.91578481668391	-0.00578481668390962
62	1.91	1.91081096133048	-0.000810961330477422
63	1.92	1.90534702938052	0.014652970619482
64	1.92	1.90983324731179	0.010166752688209
65	1.92	1.92020907706641	-0.000209077066405383
66	1.92	1.91917458027576	0.000825419724244103
67	1.92	1.92965893283891	-0.00965893283890873
68	1.92	1.93517720781478	-0.0151772078147849
69	1.92	1.94056636767796	-0.0205663676779591
70	1.92	1.9435003321767	-0.023500332176702
71	1.93	1.92545124104084	0.00454875895916063
72	1.93	1.92842328153822	0.00157671846178231
73	1.93	1.92895800269748	0.00104199730252463
74	1.94	1.92692140121996	0.0130785987800355
75	1.95	1.93408858110312	0.0159114188968772
76	1.95	1.93553304113016	0.0144669588698438
77	1.95	1.94242744314263	0.00757255685736724
78	1.95	1.94545033761441	0.00454966238558652
79	1.98	1.95303721194276	0.0269627880572449
80	1.98	1.97959926959504	0.000400730404964245
81	2.01	1.99538953264711	0.014610467352888
82	2.02	2.0238847656798	-0.003884765679802
83	2.11	2.03748111802159	0.0725188819784059
84	2.14	2.09199242976284	0.0480075702371647

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.75 & 1.67788728632479 & 0.0721127136752133 \tabularnewline
14 & 1.75 & 1.72848463544242 & 0.0215153645575814 \tabularnewline
15 & 1.75 & 1.7524475822086 & -0.00244758220859564 \tabularnewline
16 & 1.76 & 1.77337920951131 & -0.0133792095113106 \tabularnewline
17 & 1.76 & 1.7773805835662 & -0.0173805835661984 \tabularnewline
18 & 1.77 & 1.78765230584211 & -0.017652305842111 \tabularnewline
19 & 1.78 & 1.83796457528831 & -0.0579645752883147 \tabularnewline
20 & 1.78 & 1.79296484236876 & -0.0129648423687649 \tabularnewline
21 & 1.78 & 1.78587109103399 & -0.00587109103398498 \tabularnewline
22 & 1.78 & 1.78399865046806 & -0.00399865046806269 \tabularnewline
23 & 1.78 & 1.77411037582474 & 0.00588962417526084 \tabularnewline
24 & 1.79 & 1.78326668556575 & 0.00673331443425318 \tabularnewline
25 & 1.79 & 1.81821825057023 & -0.0282182505702322 \tabularnewline
26 & 1.79 & 1.7793867921841 & 0.010613207815902 \tabularnewline
27 & 1.79 & 1.77544418093097 & 0.0145558190690296 \tabularnewline
28 & 1.79 & 1.79139812650933 & -0.00139812650933235 \tabularnewline
29 & 1.79 & 1.79153677178443 & -0.00153677178442524 \tabularnewline
30 & 1.8 & 1.80307177092216 & -0.00307177092215638 \tabularnewline
31 & 1.8 & 1.83792789995671 & -0.0379278999567094 \tabularnewline
32 & 1.8 & 1.81893019248964 & -0.0189301924896412 \tabularnewline
33 & 1.8 & 1.80622144748277 & -0.00622144748276909 \tabularnewline
34 & 1.8 & 1.79966100135507 & 0.000338998644933364 \tabularnewline
35 & 1.81 & 1.79156496356164 & 0.0184350364383581 \tabularnewline
36 & 1.81 & 1.80434963389581 & 0.00565036610419334 \tabularnewline
37 & 1.82 & 1.81968082451847 & 0.000319175481526823 \tabularnewline
38 & 1.82 & 1.81221445173093 & 0.00778554826907052 \tabularnewline
39 & 1.82 & 1.80652121589212 & 0.0134787841078776 \tabularnewline
40 & 1.82 & 1.81307871799902 & 0.00692128200097808 \tabularnewline
41 & 1.83 & 1.8166703691415 & 0.0133296308584994 \tabularnewline
42 & 1.83 & 1.83602934780175 & -0.00602934780175213 \tabularnewline
43 & 1.84 & 1.85397635724945 & -0.0139763572494478 \tabularnewline
44 & 1.84 & 1.85855909764472 & -0.0185590976447172 \tabularnewline
45 & 1.84 & 1.85331533458358 & -0.0133153345835844 \tabularnewline
46 & 1.85 & 1.84672972983454 & 0.00327027016546433 \tabularnewline
47 & 1.85 & 1.84952737049838 & 0.00047262950162108 \tabularnewline
48 & 1.85 & 1.84652129774082 & 0.00347870225917624 \tabularnewline
49 & 1.86 & 1.85808708925019 & 0.00191291074981148 \tabularnewline
50 & 1.86 & 1.85463670430927 & 0.00536329569072569 \tabularnewline
51 & 1.86 & 1.8497058468878 & 0.0102941531122032 \tabularnewline
52 & 1.86 & 1.85105878782521 & 0.00894121217479382 \tabularnewline
53 & 1.87 & 1.85815556613115 & 0.0118444338688484 \tabularnewline
54 & 1.87 & 1.86781967095077 & 0.00218032904923238 \tabularnewline
55 & 1.87 & 1.88718913285081 & -0.017189132850812 \tabularnewline
56 & 1.87 & 1.88786129803654 & -0.0178612980365427 \tabularnewline
57 & 1.88 & 1.88521910191455 & -0.00521910191455399 \tabularnewline
58 & 1.9 & 1.89100364390505 & 0.00899635609495064 \tabularnewline
59 & 1.9 & 1.89696415297693 & 0.00303584702307447 \tabularnewline
60 & 1.91 & 1.89802667321897 & 0.011973326781028 \tabularnewline
61 & 1.91 & 1.91578481668391 & -0.00578481668390962 \tabularnewline
62 & 1.91 & 1.91081096133048 & -0.000810961330477422 \tabularnewline
63 & 1.92 & 1.90534702938052 & 0.014652970619482 \tabularnewline
64 & 1.92 & 1.90983324731179 & 0.010166752688209 \tabularnewline
65 & 1.92 & 1.92020907706641 & -0.000209077066405383 \tabularnewline
66 & 1.92 & 1.91917458027576 & 0.000825419724244103 \tabularnewline
67 & 1.92 & 1.92965893283891 & -0.00965893283890873 \tabularnewline
68 & 1.92 & 1.93517720781478 & -0.0151772078147849 \tabularnewline
69 & 1.92 & 1.94056636767796 & -0.0205663676779591 \tabularnewline
70 & 1.92 & 1.9435003321767 & -0.023500332176702 \tabularnewline
71 & 1.93 & 1.92545124104084 & 0.00454875895916063 \tabularnewline
72 & 1.93 & 1.92842328153822 & 0.00157671846178231 \tabularnewline
73 & 1.93 & 1.92895800269748 & 0.00104199730252463 \tabularnewline
74 & 1.94 & 1.92692140121996 & 0.0130785987800355 \tabularnewline
75 & 1.95 & 1.93408858110312 & 0.0159114188968772 \tabularnewline
76 & 1.95 & 1.93553304113016 & 0.0144669588698438 \tabularnewline
77 & 1.95 & 1.94242744314263 & 0.00757255685736724 \tabularnewline
78 & 1.95 & 1.94545033761441 & 0.00454966238558652 \tabularnewline
79 & 1.98 & 1.95303721194276 & 0.0269627880572449 \tabularnewline
80 & 1.98 & 1.97959926959504 & 0.000400730404964245 \tabularnewline
81 & 2.01 & 1.99538953264711 & 0.014610467352888 \tabularnewline
82 & 2.02 & 2.0238847656798 & -0.003884765679802 \tabularnewline
83 & 2.11 & 2.03748111802159 & 0.0725188819784059 \tabularnewline
84 & 2.14 & 2.09199242976284 & 0.0480075702371647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232616&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]1.75[/C][C]1.67788728632479[/C][C]0.0721127136752133[/C][/ROW]
[ROW][C]14[/C][C]1.75[/C][C]1.72848463544242[/C][C]0.0215153645575814[/C][/ROW]
[ROW][C]15[/C][C]1.75[/C][C]1.7524475822086[/C][C]-0.00244758220859564[/C][/ROW]
[ROW][C]16[/C][C]1.76[/C][C]1.77337920951131[/C][C]-0.0133792095113106[/C][/ROW]
[ROW][C]17[/C][C]1.76[/C][C]1.7773805835662[/C][C]-0.0173805835661984[/C][/ROW]
[ROW][C]18[/C][C]1.77[/C][C]1.78765230584211[/C][C]-0.017652305842111[/C][/ROW]
[ROW][C]19[/C][C]1.78[/C][C]1.83796457528831[/C][C]-0.0579645752883147[/C][/ROW]
[ROW][C]20[/C][C]1.78[/C][C]1.79296484236876[/C][C]-0.0129648423687649[/C][/ROW]
[ROW][C]21[/C][C]1.78[/C][C]1.78587109103399[/C][C]-0.00587109103398498[/C][/ROW]
[ROW][C]22[/C][C]1.78[/C][C]1.78399865046806[/C][C]-0.00399865046806269[/C][/ROW]
[ROW][C]23[/C][C]1.78[/C][C]1.77411037582474[/C][C]0.00588962417526084[/C][/ROW]
[ROW][C]24[/C][C]1.79[/C][C]1.78326668556575[/C][C]0.00673331443425318[/C][/ROW]
[ROW][C]25[/C][C]1.79[/C][C]1.81821825057023[/C][C]-0.0282182505702322[/C][/ROW]
[ROW][C]26[/C][C]1.79[/C][C]1.7793867921841[/C][C]0.010613207815902[/C][/ROW]
[ROW][C]27[/C][C]1.79[/C][C]1.77544418093097[/C][C]0.0145558190690296[/C][/ROW]
[ROW][C]28[/C][C]1.79[/C][C]1.79139812650933[/C][C]-0.00139812650933235[/C][/ROW]
[ROW][C]29[/C][C]1.79[/C][C]1.79153677178443[/C][C]-0.00153677178442524[/C][/ROW]
[ROW][C]30[/C][C]1.8[/C][C]1.80307177092216[/C][C]-0.00307177092215638[/C][/ROW]
[ROW][C]31[/C][C]1.8[/C][C]1.83792789995671[/C][C]-0.0379278999567094[/C][/ROW]
[ROW][C]32[/C][C]1.8[/C][C]1.81893019248964[/C][C]-0.0189301924896412[/C][/ROW]
[ROW][C]33[/C][C]1.8[/C][C]1.80622144748277[/C][C]-0.00622144748276909[/C][/ROW]
[ROW][C]34[/C][C]1.8[/C][C]1.79966100135507[/C][C]0.000338998644933364[/C][/ROW]
[ROW][C]35[/C][C]1.81[/C][C]1.79156496356164[/C][C]0.0184350364383581[/C][/ROW]
[ROW][C]36[/C][C]1.81[/C][C]1.80434963389581[/C][C]0.00565036610419334[/C][/ROW]
[ROW][C]37[/C][C]1.82[/C][C]1.81968082451847[/C][C]0.000319175481526823[/C][/ROW]
[ROW][C]38[/C][C]1.82[/C][C]1.81221445173093[/C][C]0.00778554826907052[/C][/ROW]
[ROW][C]39[/C][C]1.82[/C][C]1.80652121589212[/C][C]0.0134787841078776[/C][/ROW]
[ROW][C]40[/C][C]1.82[/C][C]1.81307871799902[/C][C]0.00692128200097808[/C][/ROW]
[ROW][C]41[/C][C]1.83[/C][C]1.8166703691415[/C][C]0.0133296308584994[/C][/ROW]
[ROW][C]42[/C][C]1.83[/C][C]1.83602934780175[/C][C]-0.00602934780175213[/C][/ROW]
[ROW][C]43[/C][C]1.84[/C][C]1.85397635724945[/C][C]-0.0139763572494478[/C][/ROW]
[ROW][C]44[/C][C]1.84[/C][C]1.85855909764472[/C][C]-0.0185590976447172[/C][/ROW]
[ROW][C]45[/C][C]1.84[/C][C]1.85331533458358[/C][C]-0.0133153345835844[/C][/ROW]
[ROW][C]46[/C][C]1.85[/C][C]1.84672972983454[/C][C]0.00327027016546433[/C][/ROW]
[ROW][C]47[/C][C]1.85[/C][C]1.84952737049838[/C][C]0.00047262950162108[/C][/ROW]
[ROW][C]48[/C][C]1.85[/C][C]1.84652129774082[/C][C]0.00347870225917624[/C][/ROW]
[ROW][C]49[/C][C]1.86[/C][C]1.85808708925019[/C][C]0.00191291074981148[/C][/ROW]
[ROW][C]50[/C][C]1.86[/C][C]1.85463670430927[/C][C]0.00536329569072569[/C][/ROW]
[ROW][C]51[/C][C]1.86[/C][C]1.8497058468878[/C][C]0.0102941531122032[/C][/ROW]
[ROW][C]52[/C][C]1.86[/C][C]1.85105878782521[/C][C]0.00894121217479382[/C][/ROW]
[ROW][C]53[/C][C]1.87[/C][C]1.85815556613115[/C][C]0.0118444338688484[/C][/ROW]
[ROW][C]54[/C][C]1.87[/C][C]1.86781967095077[/C][C]0.00218032904923238[/C][/ROW]
[ROW][C]55[/C][C]1.87[/C][C]1.88718913285081[/C][C]-0.017189132850812[/C][/ROW]
[ROW][C]56[/C][C]1.87[/C][C]1.88786129803654[/C][C]-0.0178612980365427[/C][/ROW]
[ROW][C]57[/C][C]1.88[/C][C]1.88521910191455[/C][C]-0.00521910191455399[/C][/ROW]
[ROW][C]58[/C][C]1.9[/C][C]1.89100364390505[/C][C]0.00899635609495064[/C][/ROW]
[ROW][C]59[/C][C]1.9[/C][C]1.89696415297693[/C][C]0.00303584702307447[/C][/ROW]
[ROW][C]60[/C][C]1.91[/C][C]1.89802667321897[/C][C]0.011973326781028[/C][/ROW]
[ROW][C]61[/C][C]1.91[/C][C]1.91578481668391[/C][C]-0.00578481668390962[/C][/ROW]
[ROW][C]62[/C][C]1.91[/C][C]1.91081096133048[/C][C]-0.000810961330477422[/C][/ROW]
[ROW][C]63[/C][C]1.92[/C][C]1.90534702938052[/C][C]0.014652970619482[/C][/ROW]
[ROW][C]64[/C][C]1.92[/C][C]1.90983324731179[/C][C]0.010166752688209[/C][/ROW]
[ROW][C]65[/C][C]1.92[/C][C]1.92020907706641[/C][C]-0.000209077066405383[/C][/ROW]
[ROW][C]66[/C][C]1.92[/C][C]1.91917458027576[/C][C]0.000825419724244103[/C][/ROW]
[ROW][C]67[/C][C]1.92[/C][C]1.92965893283891[/C][C]-0.00965893283890873[/C][/ROW]
[ROW][C]68[/C][C]1.92[/C][C]1.93517720781478[/C][C]-0.0151772078147849[/C][/ROW]
[ROW][C]69[/C][C]1.92[/C][C]1.94056636767796[/C][C]-0.0205663676779591[/C][/ROW]
[ROW][C]70[/C][C]1.92[/C][C]1.9435003321767[/C][C]-0.023500332176702[/C][/ROW]
[ROW][C]71[/C][C]1.93[/C][C]1.92545124104084[/C][C]0.00454875895916063[/C][/ROW]
[ROW][C]72[/C][C]1.93[/C][C]1.92842328153822[/C][C]0.00157671846178231[/C][/ROW]
[ROW][C]73[/C][C]1.93[/C][C]1.92895800269748[/C][C]0.00104199730252463[/C][/ROW]
[ROW][C]74[/C][C]1.94[/C][C]1.92692140121996[/C][C]0.0130785987800355[/C][/ROW]
[ROW][C]75[/C][C]1.95[/C][C]1.93408858110312[/C][C]0.0159114188968772[/C][/ROW]
[ROW][C]76[/C][C]1.95[/C][C]1.93553304113016[/C][C]0.0144669588698438[/C][/ROW]
[ROW][C]77[/C][C]1.95[/C][C]1.94242744314263[/C][C]0.00757255685736724[/C][/ROW]
[ROW][C]78[/C][C]1.95[/C][C]1.94545033761441[/C][C]0.00454966238558652[/C][/ROW]
[ROW][C]79[/C][C]1.98[/C][C]1.95303721194276[/C][C]0.0269627880572449[/C][/ROW]
[ROW][C]80[/C][C]1.98[/C][C]1.97959926959504[/C][C]0.000400730404964245[/C][/ROW]
[ROW][C]81[/C][C]2.01[/C][C]1.99538953264711[/C][C]0.014610467352888[/C][/ROW]
[ROW][C]82[/C][C]2.02[/C][C]2.0238847656798[/C][C]-0.003884765679802[/C][/ROW]
[ROW][C]83[/C][C]2.11[/C][C]2.03748111802159[/C][C]0.0725188819784059[/C][/ROW]
[ROW][C]84[/C][C]2.14[/C][C]2.09199242976284[/C][C]0.0480075702371647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232616&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232616&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	1.75	1.67788728632479	0.0721127136752133
14	1.75	1.72848463544242	0.0215153645575814
15	1.75	1.7524475822086	-0.00244758220859564
16	1.76	1.77337920951131	-0.0133792095113106
17	1.76	1.7773805835662	-0.0173805835661984
18	1.77	1.78765230584211	-0.017652305842111
19	1.78	1.83796457528831	-0.0579645752883147
20	1.78	1.79296484236876	-0.0129648423687649
21	1.78	1.78587109103399	-0.00587109103398498
22	1.78	1.78399865046806	-0.00399865046806269
23	1.78	1.77411037582474	0.00588962417526084
24	1.79	1.78326668556575	0.00673331443425318
25	1.79	1.81821825057023	-0.0282182505702322
26	1.79	1.7793867921841	0.010613207815902
27	1.79	1.77544418093097	0.0145558190690296
28	1.79	1.79139812650933	-0.00139812650933235
29	1.79	1.79153677178443	-0.00153677178442524
30	1.8	1.80307177092216	-0.00307177092215638
31	1.8	1.83792789995671	-0.0379278999567094
32	1.8	1.81893019248964	-0.0189301924896412
33	1.8	1.80622144748277	-0.00622144748276909
34	1.8	1.79966100135507	0.000338998644933364
35	1.81	1.79156496356164	0.0184350364383581
36	1.81	1.80434963389581	0.00565036610419334
37	1.82	1.81968082451847	0.000319175481526823
38	1.82	1.81221445173093	0.00778554826907052
39	1.82	1.80652121589212	0.0134787841078776
40	1.82	1.81307871799902	0.00692128200097808
41	1.83	1.8166703691415	0.0133296308584994
42	1.83	1.83602934780175	-0.00602934780175213
43	1.84	1.85397635724945	-0.0139763572494478
44	1.84	1.85855909764472	-0.0185590976447172
45	1.84	1.85331533458358	-0.0133153345835844
46	1.85	1.84672972983454	0.00327027016546433
47	1.85	1.84952737049838	0.00047262950162108
48	1.85	1.84652129774082	0.00347870225917624
49	1.86	1.85808708925019	0.00191291074981148
50	1.86	1.85463670430927	0.00536329569072569
51	1.86	1.8497058468878	0.0102941531122032
52	1.86	1.85105878782521	0.00894121217479382
53	1.87	1.85815556613115	0.0118444338688484
54	1.87	1.86781967095077	0.00218032904923238
55	1.87	1.88718913285081	-0.017189132850812
56	1.87	1.88786129803654	-0.0178612980365427
57	1.88	1.88521910191455	-0.00521910191455399
58	1.9	1.89100364390505	0.00899635609495064
59	1.9	1.89696415297693	0.00303584702307447
60	1.91	1.89802667321897	0.011973326781028
61	1.91	1.91578481668391	-0.00578481668390962
62	1.91	1.91081096133048	-0.000810961330477422
63	1.92	1.90534702938052	0.014652970619482
64	1.92	1.90983324731179	0.010166752688209
65	1.92	1.92020907706641	-0.000209077066405383
66	1.92	1.91917458027576	0.000825419724244103
67	1.92	1.92965893283891	-0.00965893283890873
68	1.92	1.93517720781478	-0.0151772078147849
69	1.92	1.94056636767796	-0.0205663676779591
70	1.92	1.9435003321767	-0.023500332176702
71	1.93	1.92545124104084	0.00454875895916063
72	1.93	1.92842328153822	0.00157671846178231
73	1.93	1.92895800269748	0.00104199730252463
74	1.94	1.92692140121996	0.0130785987800355
75	1.95	1.93408858110312	0.0159114188968772
76	1.95	1.93553304113016	0.0144669588698438
77	1.95	1.94242744314263	0.00757255685736724
78	1.95	1.94545033761441	0.00454966238558652
79	1.98	1.95303721194276	0.0269627880572449
80	1.98	1.97959926959504	0.000400730404964245
81	2.01	1.99538953264711	0.014610467352888
82	2.02	2.0238847656798	-0.003884765679802
83	2.11	2.03748111802159	0.0725188819784059
84	2.14	2.09199242976284	0.0480075702371647

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	2.13670504550337	2.09873009315876	2.17467999784798
86	2.15710117545186	2.11173809912467	2.20246425177905
87	2.17479236178363	2.12149501762812	2.22808970593914
88	2.18198087296497	2.12025141514274	2.24371033078721
89	2.19189396844576	2.12127102417258	2.26251691271895
90	2.20289920966812	2.12295007499271	2.28284834434352
91	2.2307481151002	2.14106337864753	2.32043285155287
92	2.24149217547514	2.14168186505338	2.3413024858969
93	2.27410223092783	2.16379295283205	2.38441150902362
94	2.2960382461231	2.17487099554722	2.41720549669898
95	2.35474227533519	2.2223707158605	2.48711383480987
96	2.36137554492007	2.21746462584893	2.5052864639912

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.13670504550337 & 2.09873009315876 & 2.17467999784798 \tabularnewline
86 & 2.15710117545186 & 2.11173809912467 & 2.20246425177905 \tabularnewline
87 & 2.17479236178363 & 2.12149501762812 & 2.22808970593914 \tabularnewline
88 & 2.18198087296497 & 2.12025141514274 & 2.24371033078721 \tabularnewline
89 & 2.19189396844576 & 2.12127102417258 & 2.26251691271895 \tabularnewline
90 & 2.20289920966812 & 2.12295007499271 & 2.28284834434352 \tabularnewline
91 & 2.2307481151002 & 2.14106337864753 & 2.32043285155287 \tabularnewline
92 & 2.24149217547514 & 2.14168186505338 & 2.3413024858969 \tabularnewline
93 & 2.27410223092783 & 2.16379295283205 & 2.38441150902362 \tabularnewline
94 & 2.2960382461231 & 2.17487099554722 & 2.41720549669898 \tabularnewline
95 & 2.35474227533519 & 2.2223707158605 & 2.48711383480987 \tabularnewline
96 & 2.36137554492007 & 2.21746462584893 & 2.5052864639912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232616&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]2.13670504550337[/C][C]2.09873009315876[/C][C]2.17467999784798[/C][/ROW]
[ROW][C]86[/C][C]2.15710117545186[/C][C]2.11173809912467[/C][C]2.20246425177905[/C][/ROW]
[ROW][C]87[/C][C]2.17479236178363[/C][C]2.12149501762812[/C][C]2.22808970593914[/C][/ROW]
[ROW][C]88[/C][C]2.18198087296497[/C][C]2.12025141514274[/C][C]2.24371033078721[/C][/ROW]
[ROW][C]89[/C][C]2.19189396844576[/C][C]2.12127102417258[/C][C]2.26251691271895[/C][/ROW]
[ROW][C]90[/C][C]2.20289920966812[/C][C]2.12295007499271[/C][C]2.28284834434352[/C][/ROW]
[ROW][C]91[/C][C]2.2307481151002[/C][C]2.14106337864753[/C][C]2.32043285155287[/C][/ROW]
[ROW][C]92[/C][C]2.24149217547514[/C][C]2.14168186505338[/C][C]2.3413024858969[/C][/ROW]
[ROW][C]93[/C][C]2.27410223092783[/C][C]2.16379295283205[/C][C]2.38441150902362[/C][/ROW]
[ROW][C]94[/C][C]2.2960382461231[/C][C]2.17487099554722[/C][C]2.41720549669898[/C][/ROW]
[ROW][C]95[/C][C]2.35474227533519[/C][C]2.2223707158605[/C][C]2.48711383480987[/C][/ROW]
[ROW][C]96[/C][C]2.36137554492007[/C][C]2.21746462584893[/C][C]2.5052864639912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232616&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232616&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
85	2.13670504550337	2.09873009315876	2.17467999784798
86	2.15710117545186	2.11173809912467	2.20246425177905
87	2.17479236178363	2.12149501762812	2.22808970593914
88	2.18198087296497	2.12025141514274	2.24371033078721
89	2.19189396844576	2.12127102417258	2.26251691271895
90	2.20289920966812	2.12295007499271	2.28284834434352
91	2.2307481151002	2.14106337864753	2.32043285155287
92	2.24149217547514	2.14168186505338	2.3413024858969
93	2.27410223092783	2.16379295283205	2.38441150902362
94	2.2960382461231	2.17487099554722	2.41720549669898
95	2.35474227533519	2.2223707158605	2.48711383480987
96	2.36137554492007	2.21746462584893	2.5052864639912

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 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code