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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 13 Nov 2013 08:22:10 -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/Nov/13/t1384349153kuz5qargcva6ch4.htm/, Retrieved Mon, 29 Apr 2024 06:54:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224714, Retrieved Mon, 29 Apr 2024 06:54:28 +0000

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Original text written by user:

Howard Van den Branden

IsPrivate?

No (this computation is public)

User-defined keywords

Howard Van den Branden

Estimated Impact

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

-       [Exponential Smoothing] [WS8: single expon...] [2013-11-13 13:22:10] [c48df00dfd28bb130a7db97d228aa375] [Current]

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Dataseries X:

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Histogram

Boxplots

6.02
5.62
4.87
4.24
4.02
3.74
3.45
3.34
3.21
3.12
3.04
2.97
2.93
2.95
2.92
2.9
2.95
2.91
2.89
2.84
2.82
2.78
2.86
2.87
2.94
3.04
3.12
3.19
3.27
3.34
3.4
3.55
3.64
3.76
3.78
3.77
3.81
3.81
3.82
3.96
3.86
3.84
3.68
3.56
3.48
3.4
3.42
3.2
3.11
3.1
2.99
3.1
3
3.05
3.1
3.2
3.1
3.3
3.13
3.14

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224714&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224714&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224714&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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999921208544223
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999921208544223 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224714&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]0.999921208544223[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224714&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224714&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	0.999921208544223
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	5.62	6.02	-0.399999999999999
3	4.87	5.62003151658231	-0.750031516582311
4	4.24	4.87005909607507	-0.63005909607507
5	4.02	4.24004964327341	-0.220049643273406
6	3.74	4.02001733803174	-0.280017338031736
7	3.45	3.74002206297371	-0.290022062973706
8	3.34	3.45002285126055	-0.110022851260549
9	3.21	3.34000866886062	-0.130008668860619
10	3.12	3.21001024357228	-0.0900102435722832
11	3.04	3.12000709203813	-0.0800070920381262
12	2.97	3.04000630387525	-0.0700063038752541
13	2.93	2.9700055158986	-0.0400055158985961
14	2.95	2.93000315209284	0.0199968479071631
15	2.92	2.94999842441924	-0.0299984244192428
16	2.9	2.92000236361953	-0.0200023636195312
17	2.95	2.90000157601535	0.0499984239846518
18	2.91	2.94999606055139	-0.0399960605513878
19	2.89	2.91000315134784	-0.020003151347836
20	2.84	2.89000157607741	-0.0500015760774151
21	2.82	2.84000393969697	-0.0200039396969705
22	2.78	2.82000157613953	-0.04000157613953
23	2.86	2.78000315178242	0.0799968482175828
24	2.87	2.85999369693187	0.010006303068129
25	2.94	2.86999921158881	0.0700007884111855
26	3.04	2.93999448453598	0.100005515464025
27	3.12	3.03999212041985	0.0800078795801493
28	3.19	3.11999369606269	0.0700063039373058
29	3.27	3.1899944841014	0.0800055158986011
30	3.34	3.26999369624893	0.0700063037510676
31	3.4	3.33999448410141	0.0600055158985864
32	3.55	3.39999527207805	0.150004727921952
33	3.64	3.54998818090911	0.0900118190908867
34	3.76	3.63999290783774	0.120007092162263
35	3.78	3.7599905444665	0.0200094555334949
36	3.77	3.77999842342587	-0.00999842342586899
37	3.81	3.77000078779034	0.0399992122096626
38	3.81	3.80999684840384	3.15159616004479e-06
39	3.82	3.80999999975168	0.0100000002483185
40	3.96	3.81999921208542	0.140000787914577
41	3.86	3.95998896913411	-0.0999889691341105
42	3.84	3.86000787827644	-0.0200078782764397
43	3.68	3.84000157644986	-0.160001576449856
44	3.56	3.68001260675714	-0.120012606757135
45	3.48	3.560009455968	-0.080009455967998
46	3.4	3.48000630406151	-0.0800063040615115
47	3.42	3.40000630381317	0.0199936961868317
48	3.2	3.41999842466757	-0.219998424667571
49	3.11	3.20001733399615	-0.0900173339961485
50	3.1	3.11000709259679	-0.0100070925967906
51	2.99	3.10000078847339	-0.110000788473394
52	3.1	2.99000866712226	0.10999133287774
53	3	3.09999133362276	-0.0999913336227598
54	3.05	3.00000787846274	0.0499921215372585
55	3.1	3.04999606104797	0.0500039389520337
56	3.2	3.09999606011686	0.100003939883145
57	3.1	3.19999212054399	-0.0999921205439933
58	3.3	3.10000787852474	0.199992121475256
59	3.13	3.29998424232961	-0.169984242329605
60	3.14	3.13001339330591	0.00998660669408791

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5.62 & 6.02 & -0.399999999999999 \tabularnewline
3 & 4.87 & 5.62003151658231 & -0.750031516582311 \tabularnewline
4 & 4.24 & 4.87005909607507 & -0.63005909607507 \tabularnewline
5 & 4.02 & 4.24004964327341 & -0.220049643273406 \tabularnewline
6 & 3.74 & 4.02001733803174 & -0.280017338031736 \tabularnewline
7 & 3.45 & 3.74002206297371 & -0.290022062973706 \tabularnewline
8 & 3.34 & 3.45002285126055 & -0.110022851260549 \tabularnewline
9 & 3.21 & 3.34000866886062 & -0.130008668860619 \tabularnewline
10 & 3.12 & 3.21001024357228 & -0.0900102435722832 \tabularnewline
11 & 3.04 & 3.12000709203813 & -0.0800070920381262 \tabularnewline
12 & 2.97 & 3.04000630387525 & -0.0700063038752541 \tabularnewline
13 & 2.93 & 2.9700055158986 & -0.0400055158985961 \tabularnewline
14 & 2.95 & 2.93000315209284 & 0.0199968479071631 \tabularnewline
15 & 2.92 & 2.94999842441924 & -0.0299984244192428 \tabularnewline
16 & 2.9 & 2.92000236361953 & -0.0200023636195312 \tabularnewline
17 & 2.95 & 2.90000157601535 & 0.0499984239846518 \tabularnewline
18 & 2.91 & 2.94999606055139 & -0.0399960605513878 \tabularnewline
19 & 2.89 & 2.91000315134784 & -0.020003151347836 \tabularnewline
20 & 2.84 & 2.89000157607741 & -0.0500015760774151 \tabularnewline
21 & 2.82 & 2.84000393969697 & -0.0200039396969705 \tabularnewline
22 & 2.78 & 2.82000157613953 & -0.04000157613953 \tabularnewline
23 & 2.86 & 2.78000315178242 & 0.0799968482175828 \tabularnewline
24 & 2.87 & 2.85999369693187 & 0.010006303068129 \tabularnewline
25 & 2.94 & 2.86999921158881 & 0.0700007884111855 \tabularnewline
26 & 3.04 & 2.93999448453598 & 0.100005515464025 \tabularnewline
27 & 3.12 & 3.03999212041985 & 0.0800078795801493 \tabularnewline
28 & 3.19 & 3.11999369606269 & 0.0700063039373058 \tabularnewline
29 & 3.27 & 3.1899944841014 & 0.0800055158986011 \tabularnewline
30 & 3.34 & 3.26999369624893 & 0.0700063037510676 \tabularnewline
31 & 3.4 & 3.33999448410141 & 0.0600055158985864 \tabularnewline
32 & 3.55 & 3.39999527207805 & 0.150004727921952 \tabularnewline
33 & 3.64 & 3.54998818090911 & 0.0900118190908867 \tabularnewline
34 & 3.76 & 3.63999290783774 & 0.120007092162263 \tabularnewline
35 & 3.78 & 3.7599905444665 & 0.0200094555334949 \tabularnewline
36 & 3.77 & 3.77999842342587 & -0.00999842342586899 \tabularnewline
37 & 3.81 & 3.77000078779034 & 0.0399992122096626 \tabularnewline
38 & 3.81 & 3.80999684840384 & 3.15159616004479e-06 \tabularnewline
39 & 3.82 & 3.80999999975168 & 0.0100000002483185 \tabularnewline
40 & 3.96 & 3.81999921208542 & 0.140000787914577 \tabularnewline
41 & 3.86 & 3.95998896913411 & -0.0999889691341105 \tabularnewline
42 & 3.84 & 3.86000787827644 & -0.0200078782764397 \tabularnewline
43 & 3.68 & 3.84000157644986 & -0.160001576449856 \tabularnewline
44 & 3.56 & 3.68001260675714 & -0.120012606757135 \tabularnewline
45 & 3.48 & 3.560009455968 & -0.080009455967998 \tabularnewline
46 & 3.4 & 3.48000630406151 & -0.0800063040615115 \tabularnewline
47 & 3.42 & 3.40000630381317 & 0.0199936961868317 \tabularnewline
48 & 3.2 & 3.41999842466757 & -0.219998424667571 \tabularnewline
49 & 3.11 & 3.20001733399615 & -0.0900173339961485 \tabularnewline
50 & 3.1 & 3.11000709259679 & -0.0100070925967906 \tabularnewline
51 & 2.99 & 3.10000078847339 & -0.110000788473394 \tabularnewline
52 & 3.1 & 2.99000866712226 & 0.10999133287774 \tabularnewline
53 & 3 & 3.09999133362276 & -0.0999913336227598 \tabularnewline
54 & 3.05 & 3.00000787846274 & 0.0499921215372585 \tabularnewline
55 & 3.1 & 3.04999606104797 & 0.0500039389520337 \tabularnewline
56 & 3.2 & 3.09999606011686 & 0.100003939883145 \tabularnewline
57 & 3.1 & 3.19999212054399 & -0.0999921205439933 \tabularnewline
58 & 3.3 & 3.10000787852474 & 0.199992121475256 \tabularnewline
59 & 3.13 & 3.29998424232961 & -0.169984242329605 \tabularnewline
60 & 3.14 & 3.13001339330591 & 0.00998660669408791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224714&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]2[/C][C]5.62[/C][C]6.02[/C][C]-0.399999999999999[/C][/ROW]
[ROW][C]3[/C][C]4.87[/C][C]5.62003151658231[/C][C]-0.750031516582311[/C][/ROW]
[ROW][C]4[/C][C]4.24[/C][C]4.87005909607507[/C][C]-0.63005909607507[/C][/ROW]
[ROW][C]5[/C][C]4.02[/C][C]4.24004964327341[/C][C]-0.220049643273406[/C][/ROW]
[ROW][C]6[/C][C]3.74[/C][C]4.02001733803174[/C][C]-0.280017338031736[/C][/ROW]
[ROW][C]7[/C][C]3.45[/C][C]3.74002206297371[/C][C]-0.290022062973706[/C][/ROW]
[ROW][C]8[/C][C]3.34[/C][C]3.45002285126055[/C][C]-0.110022851260549[/C][/ROW]
[ROW][C]9[/C][C]3.21[/C][C]3.34000866886062[/C][C]-0.130008668860619[/C][/ROW]
[ROW][C]10[/C][C]3.12[/C][C]3.21001024357228[/C][C]-0.0900102435722832[/C][/ROW]
[ROW][C]11[/C][C]3.04[/C][C]3.12000709203813[/C][C]-0.0800070920381262[/C][/ROW]
[ROW][C]12[/C][C]2.97[/C][C]3.04000630387525[/C][C]-0.0700063038752541[/C][/ROW]
[ROW][C]13[/C][C]2.93[/C][C]2.9700055158986[/C][C]-0.0400055158985961[/C][/ROW]
[ROW][C]14[/C][C]2.95[/C][C]2.93000315209284[/C][C]0.0199968479071631[/C][/ROW]
[ROW][C]15[/C][C]2.92[/C][C]2.94999842441924[/C][C]-0.0299984244192428[/C][/ROW]
[ROW][C]16[/C][C]2.9[/C][C]2.92000236361953[/C][C]-0.0200023636195312[/C][/ROW]
[ROW][C]17[/C][C]2.95[/C][C]2.90000157601535[/C][C]0.0499984239846518[/C][/ROW]
[ROW][C]18[/C][C]2.91[/C][C]2.94999606055139[/C][C]-0.0399960605513878[/C][/ROW]
[ROW][C]19[/C][C]2.89[/C][C]2.91000315134784[/C][C]-0.020003151347836[/C][/ROW]
[ROW][C]20[/C][C]2.84[/C][C]2.89000157607741[/C][C]-0.0500015760774151[/C][/ROW]
[ROW][C]21[/C][C]2.82[/C][C]2.84000393969697[/C][C]-0.0200039396969705[/C][/ROW]
[ROW][C]22[/C][C]2.78[/C][C]2.82000157613953[/C][C]-0.04000157613953[/C][/ROW]
[ROW][C]23[/C][C]2.86[/C][C]2.78000315178242[/C][C]0.0799968482175828[/C][/ROW]
[ROW][C]24[/C][C]2.87[/C][C]2.85999369693187[/C][C]0.010006303068129[/C][/ROW]
[ROW][C]25[/C][C]2.94[/C][C]2.86999921158881[/C][C]0.0700007884111855[/C][/ROW]
[ROW][C]26[/C][C]3.04[/C][C]2.93999448453598[/C][C]0.100005515464025[/C][/ROW]
[ROW][C]27[/C][C]3.12[/C][C]3.03999212041985[/C][C]0.0800078795801493[/C][/ROW]
[ROW][C]28[/C][C]3.19[/C][C]3.11999369606269[/C][C]0.0700063039373058[/C][/ROW]
[ROW][C]29[/C][C]3.27[/C][C]3.1899944841014[/C][C]0.0800055158986011[/C][/ROW]
[ROW][C]30[/C][C]3.34[/C][C]3.26999369624893[/C][C]0.0700063037510676[/C][/ROW]
[ROW][C]31[/C][C]3.4[/C][C]3.33999448410141[/C][C]0.0600055158985864[/C][/ROW]
[ROW][C]32[/C][C]3.55[/C][C]3.39999527207805[/C][C]0.150004727921952[/C][/ROW]
[ROW][C]33[/C][C]3.64[/C][C]3.54998818090911[/C][C]0.0900118190908867[/C][/ROW]
[ROW][C]34[/C][C]3.76[/C][C]3.63999290783774[/C][C]0.120007092162263[/C][/ROW]
[ROW][C]35[/C][C]3.78[/C][C]3.7599905444665[/C][C]0.0200094555334949[/C][/ROW]
[ROW][C]36[/C][C]3.77[/C][C]3.77999842342587[/C][C]-0.00999842342586899[/C][/ROW]
[ROW][C]37[/C][C]3.81[/C][C]3.77000078779034[/C][C]0.0399992122096626[/C][/ROW]
[ROW][C]38[/C][C]3.81[/C][C]3.80999684840384[/C][C]3.15159616004479e-06[/C][/ROW]
[ROW][C]39[/C][C]3.82[/C][C]3.80999999975168[/C][C]0.0100000002483185[/C][/ROW]
[ROW][C]40[/C][C]3.96[/C][C]3.81999921208542[/C][C]0.140000787914577[/C][/ROW]
[ROW][C]41[/C][C]3.86[/C][C]3.95998896913411[/C][C]-0.0999889691341105[/C][/ROW]
[ROW][C]42[/C][C]3.84[/C][C]3.86000787827644[/C][C]-0.0200078782764397[/C][/ROW]
[ROW][C]43[/C][C]3.68[/C][C]3.84000157644986[/C][C]-0.160001576449856[/C][/ROW]
[ROW][C]44[/C][C]3.56[/C][C]3.68001260675714[/C][C]-0.120012606757135[/C][/ROW]
[ROW][C]45[/C][C]3.48[/C][C]3.560009455968[/C][C]-0.080009455967998[/C][/ROW]
[ROW][C]46[/C][C]3.4[/C][C]3.48000630406151[/C][C]-0.0800063040615115[/C][/ROW]
[ROW][C]47[/C][C]3.42[/C][C]3.40000630381317[/C][C]0.0199936961868317[/C][/ROW]
[ROW][C]48[/C][C]3.2[/C][C]3.41999842466757[/C][C]-0.219998424667571[/C][/ROW]
[ROW][C]49[/C][C]3.11[/C][C]3.20001733399615[/C][C]-0.0900173339961485[/C][/ROW]
[ROW][C]50[/C][C]3.1[/C][C]3.11000709259679[/C][C]-0.0100070925967906[/C][/ROW]
[ROW][C]51[/C][C]2.99[/C][C]3.10000078847339[/C][C]-0.110000788473394[/C][/ROW]
[ROW][C]52[/C][C]3.1[/C][C]2.99000866712226[/C][C]0.10999133287774[/C][/ROW]
[ROW][C]53[/C][C]3[/C][C]3.09999133362276[/C][C]-0.0999913336227598[/C][/ROW]
[ROW][C]54[/C][C]3.05[/C][C]3.00000787846274[/C][C]0.0499921215372585[/C][/ROW]
[ROW][C]55[/C][C]3.1[/C][C]3.04999606104797[/C][C]0.0500039389520337[/C][/ROW]
[ROW][C]56[/C][C]3.2[/C][C]3.09999606011686[/C][C]0.100003939883145[/C][/ROW]
[ROW][C]57[/C][C]3.1[/C][C]3.19999212054399[/C][C]-0.0999921205439933[/C][/ROW]
[ROW][C]58[/C][C]3.3[/C][C]3.10000787852474[/C][C]0.199992121475256[/C][/ROW]
[ROW][C]59[/C][C]3.13[/C][C]3.29998424232961[/C][C]-0.169984242329605[/C][/ROW]
[ROW][C]60[/C][C]3.14[/C][C]3.13001339330591[/C][C]0.00998660669408791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224714&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224714&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
2	5.62	6.02	-0.399999999999999
3	4.87	5.62003151658231	-0.750031516582311
4	4.24	4.87005909607507	-0.63005909607507
5	4.02	4.24004964327341	-0.220049643273406
6	3.74	4.02001733803174	-0.280017338031736
7	3.45	3.74002206297371	-0.290022062973706
8	3.34	3.45002285126055	-0.110022851260549
9	3.21	3.34000866886062	-0.130008668860619
10	3.12	3.21001024357228	-0.0900102435722832
11	3.04	3.12000709203813	-0.0800070920381262
12	2.97	3.04000630387525	-0.0700063038752541
13	2.93	2.9700055158986	-0.0400055158985961
14	2.95	2.93000315209284	0.0199968479071631
15	2.92	2.94999842441924	-0.0299984244192428
16	2.9	2.92000236361953	-0.0200023636195312
17	2.95	2.90000157601535	0.0499984239846518
18	2.91	2.94999606055139	-0.0399960605513878
19	2.89	2.91000315134784	-0.020003151347836
20	2.84	2.89000157607741	-0.0500015760774151
21	2.82	2.84000393969697	-0.0200039396969705
22	2.78	2.82000157613953	-0.04000157613953
23	2.86	2.78000315178242	0.0799968482175828
24	2.87	2.85999369693187	0.010006303068129
25	2.94	2.86999921158881	0.0700007884111855
26	3.04	2.93999448453598	0.100005515464025
27	3.12	3.03999212041985	0.0800078795801493
28	3.19	3.11999369606269	0.0700063039373058
29	3.27	3.1899944841014	0.0800055158986011
30	3.34	3.26999369624893	0.0700063037510676
31	3.4	3.33999448410141	0.0600055158985864
32	3.55	3.39999527207805	0.150004727921952
33	3.64	3.54998818090911	0.0900118190908867
34	3.76	3.63999290783774	0.120007092162263
35	3.78	3.7599905444665	0.0200094555334949
36	3.77	3.77999842342587	-0.00999842342586899
37	3.81	3.77000078779034	0.0399992122096626
38	3.81	3.80999684840384	3.15159616004479e-06
39	3.82	3.80999999975168	0.0100000002483185
40	3.96	3.81999921208542	0.140000787914577
41	3.86	3.95998896913411	-0.0999889691341105
42	3.84	3.86000787827644	-0.0200078782764397
43	3.68	3.84000157644986	-0.160001576449856
44	3.56	3.68001260675714	-0.120012606757135
45	3.48	3.560009455968	-0.080009455967998
46	3.4	3.48000630406151	-0.0800063040615115
47	3.42	3.40000630381317	0.0199936961868317
48	3.2	3.41999842466757	-0.219998424667571
49	3.11	3.20001733399615	-0.0900173339961485
50	3.1	3.11000709259679	-0.0100070925967906
51	2.99	3.10000078847339	-0.110000788473394
52	3.1	2.99000866712226	0.10999133287774
53	3	3.09999133362276	-0.0999913336227598
54	3.05	3.00000787846274	0.0499921215372585
55	3.1	3.04999606104797	0.0500039389520337
56	3.2	3.09999606011686	0.100003939883145
57	3.1	3.19999212054399	-0.0999921205439933
58	3.3	3.10000787852474	0.199992121475256
59	3.13	3.29998424232961	-0.169984242329605
60	3.14	3.13001339330591	0.00998660669408791

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	3.13999921314072	2.81310896291688	3.46688946336456
62	3.13999921314072	2.67772479986234	3.6022736264191
63	3.13999921314072	2.57383843151386	3.70615999476758
64	3.13999921314072	2.48625734655055	3.79374107973089
65	3.13999921314072	2.40909646611259	3.87090196016885
66	3.13999921314072	2.33933747239515	3.9406609538863
67	3.13999921314072	2.27518731418569	4.00481111209575
68	3.13999921314072	2.21547770551926	4.06452072076219
69	3.13999921314072	2.15939714525838	4.12060128102307
70	3.13999921314072	2.10635478055493	4.17364364572651
71	3.13999921314072	2.05590456298509	4.22409386329635
72	3.13999921314072	2.00769995588735	4.27229847039409

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.13999921314072 & 2.81310896291688 & 3.46688946336456 \tabularnewline
62 & 3.13999921314072 & 2.67772479986234 & 3.6022736264191 \tabularnewline
63 & 3.13999921314072 & 2.57383843151386 & 3.70615999476758 \tabularnewline
64 & 3.13999921314072 & 2.48625734655055 & 3.79374107973089 \tabularnewline
65 & 3.13999921314072 & 2.40909646611259 & 3.87090196016885 \tabularnewline
66 & 3.13999921314072 & 2.33933747239515 & 3.9406609538863 \tabularnewline
67 & 3.13999921314072 & 2.27518731418569 & 4.00481111209575 \tabularnewline
68 & 3.13999921314072 & 2.21547770551926 & 4.06452072076219 \tabularnewline
69 & 3.13999921314072 & 2.15939714525838 & 4.12060128102307 \tabularnewline
70 & 3.13999921314072 & 2.10635478055493 & 4.17364364572651 \tabularnewline
71 & 3.13999921314072 & 2.05590456298509 & 4.22409386329635 \tabularnewline
72 & 3.13999921314072 & 2.00769995588735 & 4.27229847039409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224714&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]61[/C][C]3.13999921314072[/C][C]2.81310896291688[/C][C]3.46688946336456[/C][/ROW]
[ROW][C]62[/C][C]3.13999921314072[/C][C]2.67772479986234[/C][C]3.6022736264191[/C][/ROW]
[ROW][C]63[/C][C]3.13999921314072[/C][C]2.57383843151386[/C][C]3.70615999476758[/C][/ROW]
[ROW][C]64[/C][C]3.13999921314072[/C][C]2.48625734655055[/C][C]3.79374107973089[/C][/ROW]
[ROW][C]65[/C][C]3.13999921314072[/C][C]2.40909646611259[/C][C]3.87090196016885[/C][/ROW]
[ROW][C]66[/C][C]3.13999921314072[/C][C]2.33933747239515[/C][C]3.9406609538863[/C][/ROW]
[ROW][C]67[/C][C]3.13999921314072[/C][C]2.27518731418569[/C][C]4.00481111209575[/C][/ROW]
[ROW][C]68[/C][C]3.13999921314072[/C][C]2.21547770551926[/C][C]4.06452072076219[/C][/ROW]
[ROW][C]69[/C][C]3.13999921314072[/C][C]2.15939714525838[/C][C]4.12060128102307[/C][/ROW]
[ROW][C]70[/C][C]3.13999921314072[/C][C]2.10635478055493[/C][C]4.17364364572651[/C][/ROW]
[ROW][C]71[/C][C]3.13999921314072[/C][C]2.05590456298509[/C][C]4.22409386329635[/C][/ROW]
[ROW][C]72[/C][C]3.13999921314072[/C][C]2.00769995588735[/C][C]4.27229847039409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224714&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224714&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
61	3.13999921314072	2.81310896291688	3.46688946336456
62	3.13999921314072	2.67772479986234	3.6022736264191
63	3.13999921314072	2.57383843151386	3.70615999476758
64	3.13999921314072	2.48625734655055	3.79374107973089
65	3.13999921314072	2.40909646611259	3.87090196016885
66	3.13999921314072	2.33933747239515	3.9406609538863
67	3.13999921314072	2.27518731418569	4.00481111209575
68	3.13999921314072	2.21547770551926	4.06452072076219
69	3.13999921314072	2.15939714525838	4.12060128102307
70	3.13999921314072	2.10635478055493	4.17364364572651
71	3.13999921314072	2.05590456298509	4.22409386329635
72	3.13999921314072	2.00769995588735	4.27229847039409

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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