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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 23 May 2008 08:30:52 -0600

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/2008/May/23/t1211553173oq5b925wnti9vn6.htm/, Retrieved Sun, 19 May 2024 21:16:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13048, Retrieved Sun, 19 May 2024 21:16:47 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

237

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

-       [Exponential Smoothing] [Prijzen van sigar...] [2008-05-23 14:30:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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3.42
3.42
3.43
3.47
3.51
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.58
3.6
3.61
3.61
3.61
3.63
3.68
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.78
3.79
3.79
3.8
3.8
3.8
3.8
3.81
3.95
3.99
4
4.06
4.16
4.19
4.2
4.2
4.2
4.2
4.2
4.23
4.38
4.43
4.44
4.44
4.44
4.44
4.44
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.46
4.46
4.46
4.48
4.58
4.67
4.68
4.68

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13048&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13048&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13048&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0663859853102358
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0663859853102358 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13048&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0663859853102358[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13048&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13048&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	1
beta	0.0663859853102358
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	3.43	3.42	0.0100000000000002
4	3.47	3.4306638598531	0.0393361401468977
5	3.51	3.47327522827506	0.0367247717249439
6	3.52	3.51571323843131	0.00428676156869079
7	3.52	3.52599781932184	-0.0059978193218373
8	3.52	3.52559964817644	-0.00559964817644421
9	3.52	3.52522791001486	-0.00522791001486045
10	3.52	3.52488085005741	-0.00488085005741068
11	3.52	3.5245568300172	-0.00455683001719764
12	3.52	3.52425432036662	-0.00425432036661499
13	3.52	3.52397189311725	-0.00397189311725166
14	3.52	3.52370821507912	-0.00370821507911590
15	3.58	3.52346204156735	0.0565379584326533
16	3.6	3.58721536964533	0.0127846303546724
17	3.61	3.60806408992825	0.00193591007174998
18	3.61	3.61819260722583	-0.0081926072258347
19	3.61	3.61764873292289	-0.00764873292288781
20	3.63	3.61714096425143	0.0128590357485727
21	3.68	3.63799462400974	0.0420053759902643
22	3.69	3.69078319228318	-0.000783192283176692
23	3.69	3.70073119929177	-0.0107311992917705
24	3.69	3.70001879805323	-0.0100187980532258
25	3.69	3.69935369027284	-0.00935369027283794
26	3.69	3.69873273632779	-0.0087327363277887
27	3.69	3.69815300502221	-0.00815300502221428
28	3.69	3.69761175975058	-0.00761175975057515
29	3.69	3.69710644557959	-0.00710644557958862
30	3.78	3.69663467718773	0.083365322812266
31	3.79	3.79216896628333	-0.00216896628333174
32	3.79	3.80202497731951	-0.0120249773195082
33	3.8	3.80122668735182	-0.00122668735181986
34	3.8	3.8111452525033	-0.0111452525033013
35	3.8	3.81040536393434	-0.0104053639343382
36	3.8	3.80971459359705	-0.00971459359704552
37	3.81	3.80906968072922	0.00093031927078302
38	3.95	3.81913144089066	0.130868559109339
39	3.99	3.96781927913327	0.0221807208667344
40	4	4.00929176814290	-0.00929176814289523
41	4.06	4.01867492495945	0.0413250750405449
42	4.16	4.08141833078404	0.0785816692159598
43	4.19	4.18663505232227	0.00336494767773488
44	4.2	4.21685843768937	-0.0168584376893692
45	4.2	4.22573927369257	-0.0257392736925688
46	4.2	4.22403054664732	-0.0240305466473183
47	4.2	4.22243525513059	-0.0224352551305920
48	4.2	4.22094586861306	-0.0209458686130617
49	4.23	4.21955535648700	0.0104446435129955
50	4.38	4.25024873443783	0.129751265562170
51	4.43	4.40886240004742	0.0211375999525760
52	4.44	4.46026564044737	-0.0202656404473682
53	4.44	4.46892028593833	-0.0289202859383275
54	4.44	4.46700038426086	-0.0270003842608579
55	4.44	4.46520793714795	-0.0252079371479459
56	4.44	4.46353448340274	-0.0235344834027407
57	4.45	4.46197212353328	-0.0119721235332833
58	4.45	4.47117734231627	-0.0211773423162702
59	4.45	4.46977146358035	-0.0197714635803523
60	4.45	4.46845891548955	-0.0184589154895454
61	4.45	4.46723350219701	-0.0172335021970129
62	4.45	4.46608943917332	-0.0160894391733182
63	4.45	4.46502132590071	-0.0150213259007081
64	4.45	4.46402412038012	-0.0140241203801237
65	4.46	4.46309311533058	-0.00309311533058043
66	4.46	4.47288777582168	-0.0128877758216808
67	4.46	4.4720322081253	-0.0120322081253015
68	4.48	4.47123343813345	0.00876656186655467
69	4.58	4.49181541498074	0.0881845850192597
70	4.67	4.59766963554642	0.072330364453582
71	4.68	4.69247135805852	-0.0124713580585176
72	4.68	4.70164343466565	-0.0216434346656458

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.43 & 3.42 & 0.0100000000000002 \tabularnewline
4 & 3.47 & 3.4306638598531 & 0.0393361401468977 \tabularnewline
5 & 3.51 & 3.47327522827506 & 0.0367247717249439 \tabularnewline
6 & 3.52 & 3.51571323843131 & 0.00428676156869079 \tabularnewline
7 & 3.52 & 3.52599781932184 & -0.0059978193218373 \tabularnewline
8 & 3.52 & 3.52559964817644 & -0.00559964817644421 \tabularnewline
9 & 3.52 & 3.52522791001486 & -0.00522791001486045 \tabularnewline
10 & 3.52 & 3.52488085005741 & -0.00488085005741068 \tabularnewline
11 & 3.52 & 3.5245568300172 & -0.00455683001719764 \tabularnewline
12 & 3.52 & 3.52425432036662 & -0.00425432036661499 \tabularnewline
13 & 3.52 & 3.52397189311725 & -0.00397189311725166 \tabularnewline
14 & 3.52 & 3.52370821507912 & -0.00370821507911590 \tabularnewline
15 & 3.58 & 3.52346204156735 & 0.0565379584326533 \tabularnewline
16 & 3.6 & 3.58721536964533 & 0.0127846303546724 \tabularnewline
17 & 3.61 & 3.60806408992825 & 0.00193591007174998 \tabularnewline
18 & 3.61 & 3.61819260722583 & -0.0081926072258347 \tabularnewline
19 & 3.61 & 3.61764873292289 & -0.00764873292288781 \tabularnewline
20 & 3.63 & 3.61714096425143 & 0.0128590357485727 \tabularnewline
21 & 3.68 & 3.63799462400974 & 0.0420053759902643 \tabularnewline
22 & 3.69 & 3.69078319228318 & -0.000783192283176692 \tabularnewline
23 & 3.69 & 3.70073119929177 & -0.0107311992917705 \tabularnewline
24 & 3.69 & 3.70001879805323 & -0.0100187980532258 \tabularnewline
25 & 3.69 & 3.69935369027284 & -0.00935369027283794 \tabularnewline
26 & 3.69 & 3.69873273632779 & -0.0087327363277887 \tabularnewline
27 & 3.69 & 3.69815300502221 & -0.00815300502221428 \tabularnewline
28 & 3.69 & 3.69761175975058 & -0.00761175975057515 \tabularnewline
29 & 3.69 & 3.69710644557959 & -0.00710644557958862 \tabularnewline
30 & 3.78 & 3.69663467718773 & 0.083365322812266 \tabularnewline
31 & 3.79 & 3.79216896628333 & -0.00216896628333174 \tabularnewline
32 & 3.79 & 3.80202497731951 & -0.0120249773195082 \tabularnewline
33 & 3.8 & 3.80122668735182 & -0.00122668735181986 \tabularnewline
34 & 3.8 & 3.8111452525033 & -0.0111452525033013 \tabularnewline
35 & 3.8 & 3.81040536393434 & -0.0104053639343382 \tabularnewline
36 & 3.8 & 3.80971459359705 & -0.00971459359704552 \tabularnewline
37 & 3.81 & 3.80906968072922 & 0.00093031927078302 \tabularnewline
38 & 3.95 & 3.81913144089066 & 0.130868559109339 \tabularnewline
39 & 3.99 & 3.96781927913327 & 0.0221807208667344 \tabularnewline
40 & 4 & 4.00929176814290 & -0.00929176814289523 \tabularnewline
41 & 4.06 & 4.01867492495945 & 0.0413250750405449 \tabularnewline
42 & 4.16 & 4.08141833078404 & 0.0785816692159598 \tabularnewline
43 & 4.19 & 4.18663505232227 & 0.00336494767773488 \tabularnewline
44 & 4.2 & 4.21685843768937 & -0.0168584376893692 \tabularnewline
45 & 4.2 & 4.22573927369257 & -0.0257392736925688 \tabularnewline
46 & 4.2 & 4.22403054664732 & -0.0240305466473183 \tabularnewline
47 & 4.2 & 4.22243525513059 & -0.0224352551305920 \tabularnewline
48 & 4.2 & 4.22094586861306 & -0.0209458686130617 \tabularnewline
49 & 4.23 & 4.21955535648700 & 0.0104446435129955 \tabularnewline
50 & 4.38 & 4.25024873443783 & 0.129751265562170 \tabularnewline
51 & 4.43 & 4.40886240004742 & 0.0211375999525760 \tabularnewline
52 & 4.44 & 4.46026564044737 & -0.0202656404473682 \tabularnewline
53 & 4.44 & 4.46892028593833 & -0.0289202859383275 \tabularnewline
54 & 4.44 & 4.46700038426086 & -0.0270003842608579 \tabularnewline
55 & 4.44 & 4.46520793714795 & -0.0252079371479459 \tabularnewline
56 & 4.44 & 4.46353448340274 & -0.0235344834027407 \tabularnewline
57 & 4.45 & 4.46197212353328 & -0.0119721235332833 \tabularnewline
58 & 4.45 & 4.47117734231627 & -0.0211773423162702 \tabularnewline
59 & 4.45 & 4.46977146358035 & -0.0197714635803523 \tabularnewline
60 & 4.45 & 4.46845891548955 & -0.0184589154895454 \tabularnewline
61 & 4.45 & 4.46723350219701 & -0.0172335021970129 \tabularnewline
62 & 4.45 & 4.46608943917332 & -0.0160894391733182 \tabularnewline
63 & 4.45 & 4.46502132590071 & -0.0150213259007081 \tabularnewline
64 & 4.45 & 4.46402412038012 & -0.0140241203801237 \tabularnewline
65 & 4.46 & 4.46309311533058 & -0.00309311533058043 \tabularnewline
66 & 4.46 & 4.47288777582168 & -0.0128877758216808 \tabularnewline
67 & 4.46 & 4.4720322081253 & -0.0120322081253015 \tabularnewline
68 & 4.48 & 4.47123343813345 & 0.00876656186655467 \tabularnewline
69 & 4.58 & 4.49181541498074 & 0.0881845850192597 \tabularnewline
70 & 4.67 & 4.59766963554642 & 0.072330364453582 \tabularnewline
71 & 4.68 & 4.69247135805852 & -0.0124713580585176 \tabularnewline
72 & 4.68 & 4.70164343466565 & -0.0216434346656458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13048&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]3.43[/C][C]3.42[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]4[/C][C]3.47[/C][C]3.4306638598531[/C][C]0.0393361401468977[/C][/ROW]
[ROW][C]5[/C][C]3.51[/C][C]3.47327522827506[/C][C]0.0367247717249439[/C][/ROW]
[ROW][C]6[/C][C]3.52[/C][C]3.51571323843131[/C][C]0.00428676156869079[/C][/ROW]
[ROW][C]7[/C][C]3.52[/C][C]3.52599781932184[/C][C]-0.0059978193218373[/C][/ROW]
[ROW][C]8[/C][C]3.52[/C][C]3.52559964817644[/C][C]-0.00559964817644421[/C][/ROW]
[ROW][C]9[/C][C]3.52[/C][C]3.52522791001486[/C][C]-0.00522791001486045[/C][/ROW]
[ROW][C]10[/C][C]3.52[/C][C]3.52488085005741[/C][C]-0.00488085005741068[/C][/ROW]
[ROW][C]11[/C][C]3.52[/C][C]3.5245568300172[/C][C]-0.00455683001719764[/C][/ROW]
[ROW][C]12[/C][C]3.52[/C][C]3.52425432036662[/C][C]-0.00425432036661499[/C][/ROW]
[ROW][C]13[/C][C]3.52[/C][C]3.52397189311725[/C][C]-0.00397189311725166[/C][/ROW]
[ROW][C]14[/C][C]3.52[/C][C]3.52370821507912[/C][C]-0.00370821507911590[/C][/ROW]
[ROW][C]15[/C][C]3.58[/C][C]3.52346204156735[/C][C]0.0565379584326533[/C][/ROW]
[ROW][C]16[/C][C]3.6[/C][C]3.58721536964533[/C][C]0.0127846303546724[/C][/ROW]
[ROW][C]17[/C][C]3.61[/C][C]3.60806408992825[/C][C]0.00193591007174998[/C][/ROW]
[ROW][C]18[/C][C]3.61[/C][C]3.61819260722583[/C][C]-0.0081926072258347[/C][/ROW]
[ROW][C]19[/C][C]3.61[/C][C]3.61764873292289[/C][C]-0.00764873292288781[/C][/ROW]
[ROW][C]20[/C][C]3.63[/C][C]3.61714096425143[/C][C]0.0128590357485727[/C][/ROW]
[ROW][C]21[/C][C]3.68[/C][C]3.63799462400974[/C][C]0.0420053759902643[/C][/ROW]
[ROW][C]22[/C][C]3.69[/C][C]3.69078319228318[/C][C]-0.000783192283176692[/C][/ROW]
[ROW][C]23[/C][C]3.69[/C][C]3.70073119929177[/C][C]-0.0107311992917705[/C][/ROW]
[ROW][C]24[/C][C]3.69[/C][C]3.70001879805323[/C][C]-0.0100187980532258[/C][/ROW]
[ROW][C]25[/C][C]3.69[/C][C]3.69935369027284[/C][C]-0.00935369027283794[/C][/ROW]
[ROW][C]26[/C][C]3.69[/C][C]3.69873273632779[/C][C]-0.0087327363277887[/C][/ROW]
[ROW][C]27[/C][C]3.69[/C][C]3.69815300502221[/C][C]-0.00815300502221428[/C][/ROW]
[ROW][C]28[/C][C]3.69[/C][C]3.69761175975058[/C][C]-0.00761175975057515[/C][/ROW]
[ROW][C]29[/C][C]3.69[/C][C]3.69710644557959[/C][C]-0.00710644557958862[/C][/ROW]
[ROW][C]30[/C][C]3.78[/C][C]3.69663467718773[/C][C]0.083365322812266[/C][/ROW]
[ROW][C]31[/C][C]3.79[/C][C]3.79216896628333[/C][C]-0.00216896628333174[/C][/ROW]
[ROW][C]32[/C][C]3.79[/C][C]3.80202497731951[/C][C]-0.0120249773195082[/C][/ROW]
[ROW][C]33[/C][C]3.8[/C][C]3.80122668735182[/C][C]-0.00122668735181986[/C][/ROW]
[ROW][C]34[/C][C]3.8[/C][C]3.8111452525033[/C][C]-0.0111452525033013[/C][/ROW]
[ROW][C]35[/C][C]3.8[/C][C]3.81040536393434[/C][C]-0.0104053639343382[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.80971459359705[/C][C]-0.00971459359704552[/C][/ROW]
[ROW][C]37[/C][C]3.81[/C][C]3.80906968072922[/C][C]0.00093031927078302[/C][/ROW]
[ROW][C]38[/C][C]3.95[/C][C]3.81913144089066[/C][C]0.130868559109339[/C][/ROW]
[ROW][C]39[/C][C]3.99[/C][C]3.96781927913327[/C][C]0.0221807208667344[/C][/ROW]
[ROW][C]40[/C][C]4[/C][C]4.00929176814290[/C][C]-0.00929176814289523[/C][/ROW]
[ROW][C]41[/C][C]4.06[/C][C]4.01867492495945[/C][C]0.0413250750405449[/C][/ROW]
[ROW][C]42[/C][C]4.16[/C][C]4.08141833078404[/C][C]0.0785816692159598[/C][/ROW]
[ROW][C]43[/C][C]4.19[/C][C]4.18663505232227[/C][C]0.00336494767773488[/C][/ROW]
[ROW][C]44[/C][C]4.2[/C][C]4.21685843768937[/C][C]-0.0168584376893692[/C][/ROW]
[ROW][C]45[/C][C]4.2[/C][C]4.22573927369257[/C][C]-0.0257392736925688[/C][/ROW]
[ROW][C]46[/C][C]4.2[/C][C]4.22403054664732[/C][C]-0.0240305466473183[/C][/ROW]
[ROW][C]47[/C][C]4.2[/C][C]4.22243525513059[/C][C]-0.0224352551305920[/C][/ROW]
[ROW][C]48[/C][C]4.2[/C][C]4.22094586861306[/C][C]-0.0209458686130617[/C][/ROW]
[ROW][C]49[/C][C]4.23[/C][C]4.21955535648700[/C][C]0.0104446435129955[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.25024873443783[/C][C]0.129751265562170[/C][/ROW]
[ROW][C]51[/C][C]4.43[/C][C]4.40886240004742[/C][C]0.0211375999525760[/C][/ROW]
[ROW][C]52[/C][C]4.44[/C][C]4.46026564044737[/C][C]-0.0202656404473682[/C][/ROW]
[ROW][C]53[/C][C]4.44[/C][C]4.46892028593833[/C][C]-0.0289202859383275[/C][/ROW]
[ROW][C]54[/C][C]4.44[/C][C]4.46700038426086[/C][C]-0.0270003842608579[/C][/ROW]
[ROW][C]55[/C][C]4.44[/C][C]4.46520793714795[/C][C]-0.0252079371479459[/C][/ROW]
[ROW][C]56[/C][C]4.44[/C][C]4.46353448340274[/C][C]-0.0235344834027407[/C][/ROW]
[ROW][C]57[/C][C]4.45[/C][C]4.46197212353328[/C][C]-0.0119721235332833[/C][/ROW]
[ROW][C]58[/C][C]4.45[/C][C]4.47117734231627[/C][C]-0.0211773423162702[/C][/ROW]
[ROW][C]59[/C][C]4.45[/C][C]4.46977146358035[/C][C]-0.0197714635803523[/C][/ROW]
[ROW][C]60[/C][C]4.45[/C][C]4.46845891548955[/C][C]-0.0184589154895454[/C][/ROW]
[ROW][C]61[/C][C]4.45[/C][C]4.46723350219701[/C][C]-0.0172335021970129[/C][/ROW]
[ROW][C]62[/C][C]4.45[/C][C]4.46608943917332[/C][C]-0.0160894391733182[/C][/ROW]
[ROW][C]63[/C][C]4.45[/C][C]4.46502132590071[/C][C]-0.0150213259007081[/C][/ROW]
[ROW][C]64[/C][C]4.45[/C][C]4.46402412038012[/C][C]-0.0140241203801237[/C][/ROW]
[ROW][C]65[/C][C]4.46[/C][C]4.46309311533058[/C][C]-0.00309311533058043[/C][/ROW]
[ROW][C]66[/C][C]4.46[/C][C]4.47288777582168[/C][C]-0.0128877758216808[/C][/ROW]
[ROW][C]67[/C][C]4.46[/C][C]4.4720322081253[/C][C]-0.0120322081253015[/C][/ROW]
[ROW][C]68[/C][C]4.48[/C][C]4.47123343813345[/C][C]0.00876656186655467[/C][/ROW]
[ROW][C]69[/C][C]4.58[/C][C]4.49181541498074[/C][C]0.0881845850192597[/C][/ROW]
[ROW][C]70[/C][C]4.67[/C][C]4.59766963554642[/C][C]0.072330364453582[/C][/ROW]
[ROW][C]71[/C][C]4.68[/C][C]4.69247135805852[/C][C]-0.0124713580585176[/C][/ROW]
[ROW][C]72[/C][C]4.68[/C][C]4.70164343466565[/C][C]-0.0216434346656458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13048&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13048&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
3	3.43	3.42	0.0100000000000002
4	3.47	3.4306638598531	0.0393361401468977
5	3.51	3.47327522827506	0.0367247717249439
6	3.52	3.51571323843131	0.00428676156869079
7	3.52	3.52599781932184	-0.0059978193218373
8	3.52	3.52559964817644	-0.00559964817644421
9	3.52	3.52522791001486	-0.00522791001486045
10	3.52	3.52488085005741	-0.00488085005741068
11	3.52	3.5245568300172	-0.00455683001719764
12	3.52	3.52425432036662	-0.00425432036661499
13	3.52	3.52397189311725	-0.00397189311725166
14	3.52	3.52370821507912	-0.00370821507911590
15	3.58	3.52346204156735	0.0565379584326533
16	3.6	3.58721536964533	0.0127846303546724
17	3.61	3.60806408992825	0.00193591007174998
18	3.61	3.61819260722583	-0.0081926072258347
19	3.61	3.61764873292289	-0.00764873292288781
20	3.63	3.61714096425143	0.0128590357485727
21	3.68	3.63799462400974	0.0420053759902643
22	3.69	3.69078319228318	-0.000783192283176692
23	3.69	3.70073119929177	-0.0107311992917705
24	3.69	3.70001879805323	-0.0100187980532258
25	3.69	3.69935369027284	-0.00935369027283794
26	3.69	3.69873273632779	-0.0087327363277887
27	3.69	3.69815300502221	-0.00815300502221428
28	3.69	3.69761175975058	-0.00761175975057515
29	3.69	3.69710644557959	-0.00710644557958862
30	3.78	3.69663467718773	0.083365322812266
31	3.79	3.79216896628333	-0.00216896628333174
32	3.79	3.80202497731951	-0.0120249773195082
33	3.8	3.80122668735182	-0.00122668735181986
34	3.8	3.8111452525033	-0.0111452525033013
35	3.8	3.81040536393434	-0.0104053639343382
36	3.8	3.80971459359705	-0.00971459359704552
37	3.81	3.80906968072922	0.00093031927078302
38	3.95	3.81913144089066	0.130868559109339
39	3.99	3.96781927913327	0.0221807208667344
40	4	4.00929176814290	-0.00929176814289523
41	4.06	4.01867492495945	0.0413250750405449
42	4.16	4.08141833078404	0.0785816692159598
43	4.19	4.18663505232227	0.00336494767773488
44	4.2	4.21685843768937	-0.0168584376893692
45	4.2	4.22573927369257	-0.0257392736925688
46	4.2	4.22403054664732	-0.0240305466473183
47	4.2	4.22243525513059	-0.0224352551305920
48	4.2	4.22094586861306	-0.0209458686130617
49	4.23	4.21955535648700	0.0104446435129955
50	4.38	4.25024873443783	0.129751265562170
51	4.43	4.40886240004742	0.0211375999525760
52	4.44	4.46026564044737	-0.0202656404473682
53	4.44	4.46892028593833	-0.0289202859383275
54	4.44	4.46700038426086	-0.0270003842608579
55	4.44	4.46520793714795	-0.0252079371479459
56	4.44	4.46353448340274	-0.0235344834027407
57	4.45	4.46197212353328	-0.0119721235332833
58	4.45	4.47117734231627	-0.0211773423162702
59	4.45	4.46977146358035	-0.0197714635803523
60	4.45	4.46845891548955	-0.0184589154895454
61	4.45	4.46723350219701	-0.0172335021970129
62	4.45	4.46608943917332	-0.0160894391733182
63	4.45	4.46502132590071	-0.0150213259007081
64	4.45	4.46402412038012	-0.0140241203801237
65	4.46	4.46309311533058	-0.00309311533058043
66	4.46	4.47288777582168	-0.0128877758216808
67	4.46	4.4720322081253	-0.0120322081253015
68	4.48	4.47123343813345	0.00876656186655467
69	4.58	4.49181541498074	0.0881845850192597
70	4.67	4.59766963554642	0.072330364453582
71	4.68	4.69247135805852	-0.0124713580585176
72	4.68	4.70164343466565	-0.0216434346656458

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	4.70020661392987	4.63337214938476	4.76704107847498
74	4.72041322785974	4.62270729644914	4.81811915927034
75	4.74061984178961	4.61701489930042	4.8642247842788
76	4.76082645571948	4.61351245218189	4.90814045925706
77	4.78103306964935	4.61116393711853	4.95090220218016
78	4.80123968357921	4.60945888914018	4.99302047801824
79	4.82144629750908	4.60810656823353	5.03478602678464
80	4.84165291143895	4.60692584703375	5.07637997584415
81	4.86185952536882	4.60579682053107	5.11792223020658
82	4.88206613929869	4.60463659169532	5.15949568690206
83	4.90227275322856	4.60338598261058	5.20115952384655
84	4.92247936715843	4.60200171774689	5.24295701656997

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.70020661392987 & 4.63337214938476 & 4.76704107847498 \tabularnewline
74 & 4.72041322785974 & 4.62270729644914 & 4.81811915927034 \tabularnewline
75 & 4.74061984178961 & 4.61701489930042 & 4.8642247842788 \tabularnewline
76 & 4.76082645571948 & 4.61351245218189 & 4.90814045925706 \tabularnewline
77 & 4.78103306964935 & 4.61116393711853 & 4.95090220218016 \tabularnewline
78 & 4.80123968357921 & 4.60945888914018 & 4.99302047801824 \tabularnewline
79 & 4.82144629750908 & 4.60810656823353 & 5.03478602678464 \tabularnewline
80 & 4.84165291143895 & 4.60692584703375 & 5.07637997584415 \tabularnewline
81 & 4.86185952536882 & 4.60579682053107 & 5.11792223020658 \tabularnewline
82 & 4.88206613929869 & 4.60463659169532 & 5.15949568690206 \tabularnewline
83 & 4.90227275322856 & 4.60338598261058 & 5.20115952384655 \tabularnewline
84 & 4.92247936715843 & 4.60200171774689 & 5.24295701656997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13048&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]4.70020661392987[/C][C]4.63337214938476[/C][C]4.76704107847498[/C][/ROW]
[ROW][C]74[/C][C]4.72041322785974[/C][C]4.62270729644914[/C][C]4.81811915927034[/C][/ROW]
[ROW][C]75[/C][C]4.74061984178961[/C][C]4.61701489930042[/C][C]4.8642247842788[/C][/ROW]
[ROW][C]76[/C][C]4.76082645571948[/C][C]4.61351245218189[/C][C]4.90814045925706[/C][/ROW]
[ROW][C]77[/C][C]4.78103306964935[/C][C]4.61116393711853[/C][C]4.95090220218016[/C][/ROW]
[ROW][C]78[/C][C]4.80123968357921[/C][C]4.60945888914018[/C][C]4.99302047801824[/C][/ROW]
[ROW][C]79[/C][C]4.82144629750908[/C][C]4.60810656823353[/C][C]5.03478602678464[/C][/ROW]
[ROW][C]80[/C][C]4.84165291143895[/C][C]4.60692584703375[/C][C]5.07637997584415[/C][/ROW]
[ROW][C]81[/C][C]4.86185952536882[/C][C]4.60579682053107[/C][C]5.11792223020658[/C][/ROW]
[ROW][C]82[/C][C]4.88206613929869[/C][C]4.60463659169532[/C][C]5.15949568690206[/C][/ROW]
[ROW][C]83[/C][C]4.90227275322856[/C][C]4.60338598261058[/C][C]5.20115952384655[/C][/ROW]
[ROW][C]84[/C][C]4.92247936715843[/C][C]4.60200171774689[/C][C]5.24295701656997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13048&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13048&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	4.70020661392987	4.63337214938476	4.76704107847498
74	4.72041322785974	4.62270729644914	4.81811915927034
75	4.74061984178961	4.61701489930042	4.8642247842788
76	4.76082645571948	4.61351245218189	4.90814045925706
77	4.78103306964935	4.61116393711853	4.95090220218016
78	4.80123968357921	4.60945888914018	4.99302047801824
79	4.82144629750908	4.60810656823353	5.03478602678464
80	4.84165291143895	4.60692584703375	5.07637997584415
81	4.86185952536882	4.60579682053107	5.11792223020658
82	4.88206613929869	4.60463659169532	5.15949568690206
83	4.90227275322856	4.60338598261058	5.20115952384655
84	4.92247936715843	4.60200171774689	5.24295701656997

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 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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