Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 28 Nov 2016 09:58:33 +0000

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/2016/Nov/28/t1480327208mb18kr71niblyvo.htm/, Retrieved Sat, 04 May 2024 09:08:32 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 09:08:32 +0200

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.284499870646122
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.284499870646122 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.284499870646122[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.284499870646122
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	99	98.37	0.629999999999995
4	98.88	98.5792349185071	0.300765081492941
5	98.9	98.5448025452867	0.355197454713334
6	98.92	98.6658561752065	0.254143824793545
7	98.8	98.7581600604857	0.0418399395142757
8	98.83	98.6500635178654	0.179936482134622
9	98.88	98.7312554237572	0.148744576242805
10	98.88	98.8235732364576	0.0564267635424187
11	98.89	98.8396266433864	0.0503733566136191
12	98.89	98.863957856827	0.0260421431730293
13	99.05	98.871366843191	0.178633156808957
14	99.2	99.0821879531963	0.117812046803706
15	99.13	99.2657054652725	-0.135705465272522
16	98.92	99.1570972779565	-0.237097277956494
17	98.98	98.8796431330473	0.100356866952666
18	98.99	98.9681946487138	0.0218053512861758
19	99.08	98.9843982683341	0.0956017316658802
20	99.1	99.1015969486266	-0.00159694862661297
21	99.1	99.1211426169489	-0.0211426169489073
22	99.06	99.1151275451618	-0.0551275451618238
23	99.05	99.0594437656943	-0.00944376569425742
24	99.11	99.0467570155758	0.0632429844241784
25	99.75	99.1247496364638	0.625250363536225
26	99.8	99.9426332840113	-0.142633284011282
27	99.95	99.9520541331602	-0.00205413316022884
28	99.69	100.101469732542	-0.41146973254186
29	99.55	99.7244066468589	-0.174406646858898
30	99.14	99.5347879783877	-0.394787978387726
31	99.05	99.0124708496038	0.0375291503962245
32	99	98.933147888037	0.0668521119630441
33	99.03	98.9021673052429	0.127832694757132
34	99.16	98.9685356903656	0.191464309634384
35	99.01	99.1530072616899	-0.143007261689931
36	99	98.9623217142377	0.037678285762297
37	99.9	98.9630411816632	0.936958818336763
38	100.18	100.129605844281	0.0503941557192036
39	100.2	100.423942975064	-0.223942975064233
40	100.13	100.380231227626	-0.250231227626358
41	99.85	100.239040475735	-0.38904047573503
42	99.88	99.8483585107123	0.0316414892876935
43	99.88	99.8873605103217	-0.00736051032170337
44	99.89	99.8852664460873	0.00473355391271468
45	99.96	99.8966131415632	0.0633868584368429
46	100.05	99.9846466945891	0.065353305410909
47	100.04	100.093239701525	-0.0532397015247881
48	100.06	100.068093013328	-0.00809301332776613
49	99.72	100.085790552083	-0.365790552082871
50	99.7	99.6417231873317	0.0582768126682822
51	99.63	99.6383029329975	-0.00830293299752327
52	99.73	99.5659407496337	0.164059250366279
53	99.77	99.7126155851413	0.0573844148587455
54	99.76	99.7689414437457	-0.00894144374565542
55	99.61	99.7563976041566	-0.146397604156633
56	99.61	99.5647475047112	0.0452524952888353
57	99.59	99.5776218337673	0.0123781662327502
58	99.42	99.5611434204593	-0.141143420459315
59	99.52	99.3509881355961	0.169011864403913
60	99.46	99.4990719891566	-0.0390719891566533
61	100.55	99.4279560132957	1.1220439867043
62	100.4	100.837177382372	-0.437177382372326
63	100.15	100.562800473638	-0.412800473638001
64	100.2	100.195358792285	0.0046412077146698
65	100.16	100.24667921528	-0.0866792152798013
66	100.19	100.182018989745	0.00798101025502262
67	100.23	100.21428958613	0.0157104138698401
68	100.08	100.258759196844	-0.178759196843941
69	100.15	100.057902228465	0.0920977715349807
70	100.13	100.154104032554	-0.024104032553538
71	100.26	100.12724643841	0.132753561590022
72	100.24	100.29501480951	-0.055014809510169

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99 & 98.37 & 0.629999999999995 \tabularnewline
4 & 98.88 & 98.5792349185071 & 0.300765081492941 \tabularnewline
5 & 98.9 & 98.5448025452867 & 0.355197454713334 \tabularnewline
6 & 98.92 & 98.6658561752065 & 0.254143824793545 \tabularnewline
7 & 98.8 & 98.7581600604857 & 0.0418399395142757 \tabularnewline
8 & 98.83 & 98.6500635178654 & 0.179936482134622 \tabularnewline
9 & 98.88 & 98.7312554237572 & 0.148744576242805 \tabularnewline
10 & 98.88 & 98.8235732364576 & 0.0564267635424187 \tabularnewline
11 & 98.89 & 98.8396266433864 & 0.0503733566136191 \tabularnewline
12 & 98.89 & 98.863957856827 & 0.0260421431730293 \tabularnewline
13 & 99.05 & 98.871366843191 & 0.178633156808957 \tabularnewline
14 & 99.2 & 99.0821879531963 & 0.117812046803706 \tabularnewline
15 & 99.13 & 99.2657054652725 & -0.135705465272522 \tabularnewline
16 & 98.92 & 99.1570972779565 & -0.237097277956494 \tabularnewline
17 & 98.98 & 98.8796431330473 & 0.100356866952666 \tabularnewline
18 & 98.99 & 98.9681946487138 & 0.0218053512861758 \tabularnewline
19 & 99.08 & 98.9843982683341 & 0.0956017316658802 \tabularnewline
20 & 99.1 & 99.1015969486266 & -0.00159694862661297 \tabularnewline
21 & 99.1 & 99.1211426169489 & -0.0211426169489073 \tabularnewline
22 & 99.06 & 99.1151275451618 & -0.0551275451618238 \tabularnewline
23 & 99.05 & 99.0594437656943 & -0.00944376569425742 \tabularnewline
24 & 99.11 & 99.0467570155758 & 0.0632429844241784 \tabularnewline
25 & 99.75 & 99.1247496364638 & 0.625250363536225 \tabularnewline
26 & 99.8 & 99.9426332840113 & -0.142633284011282 \tabularnewline
27 & 99.95 & 99.9520541331602 & -0.00205413316022884 \tabularnewline
28 & 99.69 & 100.101469732542 & -0.41146973254186 \tabularnewline
29 & 99.55 & 99.7244066468589 & -0.174406646858898 \tabularnewline
30 & 99.14 & 99.5347879783877 & -0.394787978387726 \tabularnewline
31 & 99.05 & 99.0124708496038 & 0.0375291503962245 \tabularnewline
32 & 99 & 98.933147888037 & 0.0668521119630441 \tabularnewline
33 & 99.03 & 98.9021673052429 & 0.127832694757132 \tabularnewline
34 & 99.16 & 98.9685356903656 & 0.191464309634384 \tabularnewline
35 & 99.01 & 99.1530072616899 & -0.143007261689931 \tabularnewline
36 & 99 & 98.9623217142377 & 0.037678285762297 \tabularnewline
37 & 99.9 & 98.9630411816632 & 0.936958818336763 \tabularnewline
38 & 100.18 & 100.129605844281 & 0.0503941557192036 \tabularnewline
39 & 100.2 & 100.423942975064 & -0.223942975064233 \tabularnewline
40 & 100.13 & 100.380231227626 & -0.250231227626358 \tabularnewline
41 & 99.85 & 100.239040475735 & -0.38904047573503 \tabularnewline
42 & 99.88 & 99.8483585107123 & 0.0316414892876935 \tabularnewline
43 & 99.88 & 99.8873605103217 & -0.00736051032170337 \tabularnewline
44 & 99.89 & 99.8852664460873 & 0.00473355391271468 \tabularnewline
45 & 99.96 & 99.8966131415632 & 0.0633868584368429 \tabularnewline
46 & 100.05 & 99.9846466945891 & 0.065353305410909 \tabularnewline
47 & 100.04 & 100.093239701525 & -0.0532397015247881 \tabularnewline
48 & 100.06 & 100.068093013328 & -0.00809301332776613 \tabularnewline
49 & 99.72 & 100.085790552083 & -0.365790552082871 \tabularnewline
50 & 99.7 & 99.6417231873317 & 0.0582768126682822 \tabularnewline
51 & 99.63 & 99.6383029329975 & -0.00830293299752327 \tabularnewline
52 & 99.73 & 99.5659407496337 & 0.164059250366279 \tabularnewline
53 & 99.77 & 99.7126155851413 & 0.0573844148587455 \tabularnewline
54 & 99.76 & 99.7689414437457 & -0.00894144374565542 \tabularnewline
55 & 99.61 & 99.7563976041566 & -0.146397604156633 \tabularnewline
56 & 99.61 & 99.5647475047112 & 0.0452524952888353 \tabularnewline
57 & 99.59 & 99.5776218337673 & 0.0123781662327502 \tabularnewline
58 & 99.42 & 99.5611434204593 & -0.141143420459315 \tabularnewline
59 & 99.52 & 99.3509881355961 & 0.169011864403913 \tabularnewline
60 & 99.46 & 99.4990719891566 & -0.0390719891566533 \tabularnewline
61 & 100.55 & 99.4279560132957 & 1.1220439867043 \tabularnewline
62 & 100.4 & 100.837177382372 & -0.437177382372326 \tabularnewline
63 & 100.15 & 100.562800473638 & -0.412800473638001 \tabularnewline
64 & 100.2 & 100.195358792285 & 0.0046412077146698 \tabularnewline
65 & 100.16 & 100.24667921528 & -0.0866792152798013 \tabularnewline
66 & 100.19 & 100.182018989745 & 0.00798101025502262 \tabularnewline
67 & 100.23 & 100.21428958613 & 0.0157104138698401 \tabularnewline
68 & 100.08 & 100.258759196844 & -0.178759196843941 \tabularnewline
69 & 100.15 & 100.057902228465 & 0.0920977715349807 \tabularnewline
70 & 100.13 & 100.154104032554 & -0.024104032553538 \tabularnewline
71 & 100.26 & 100.12724643841 & 0.132753561590022 \tabularnewline
72 & 100.24 & 100.29501480951 & -0.055014809510169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]99[/C][C]98.37[/C][C]0.629999999999995[/C][/ROW]
[ROW][C]4[/C][C]98.88[/C][C]98.5792349185071[/C][C]0.300765081492941[/C][/ROW]
[ROW][C]5[/C][C]98.9[/C][C]98.5448025452867[/C][C]0.355197454713334[/C][/ROW]
[ROW][C]6[/C][C]98.92[/C][C]98.6658561752065[/C][C]0.254143824793545[/C][/ROW]
[ROW][C]7[/C][C]98.8[/C][C]98.7581600604857[/C][C]0.0418399395142757[/C][/ROW]
[ROW][C]8[/C][C]98.83[/C][C]98.6500635178654[/C][C]0.179936482134622[/C][/ROW]
[ROW][C]9[/C][C]98.88[/C][C]98.7312554237572[/C][C]0.148744576242805[/C][/ROW]
[ROW][C]10[/C][C]98.88[/C][C]98.8235732364576[/C][C]0.0564267635424187[/C][/ROW]
[ROW][C]11[/C][C]98.89[/C][C]98.8396266433864[/C][C]0.0503733566136191[/C][/ROW]
[ROW][C]12[/C][C]98.89[/C][C]98.863957856827[/C][C]0.0260421431730293[/C][/ROW]
[ROW][C]13[/C][C]99.05[/C][C]98.871366843191[/C][C]0.178633156808957[/C][/ROW]
[ROW][C]14[/C][C]99.2[/C][C]99.0821879531963[/C][C]0.117812046803706[/C][/ROW]
[ROW][C]15[/C][C]99.13[/C][C]99.2657054652725[/C][C]-0.135705465272522[/C][/ROW]
[ROW][C]16[/C][C]98.92[/C][C]99.1570972779565[/C][C]-0.237097277956494[/C][/ROW]
[ROW][C]17[/C][C]98.98[/C][C]98.8796431330473[/C][C]0.100356866952666[/C][/ROW]
[ROW][C]18[/C][C]98.99[/C][C]98.9681946487138[/C][C]0.0218053512861758[/C][/ROW]
[ROW][C]19[/C][C]99.08[/C][C]98.9843982683341[/C][C]0.0956017316658802[/C][/ROW]
[ROW][C]20[/C][C]99.1[/C][C]99.1015969486266[/C][C]-0.00159694862661297[/C][/ROW]
[ROW][C]21[/C][C]99.1[/C][C]99.1211426169489[/C][C]-0.0211426169489073[/C][/ROW]
[ROW][C]22[/C][C]99.06[/C][C]99.1151275451618[/C][C]-0.0551275451618238[/C][/ROW]
[ROW][C]23[/C][C]99.05[/C][C]99.0594437656943[/C][C]-0.00944376569425742[/C][/ROW]
[ROW][C]24[/C][C]99.11[/C][C]99.0467570155758[/C][C]0.0632429844241784[/C][/ROW]
[ROW][C]25[/C][C]99.75[/C][C]99.1247496364638[/C][C]0.625250363536225[/C][/ROW]
[ROW][C]26[/C][C]99.8[/C][C]99.9426332840113[/C][C]-0.142633284011282[/C][/ROW]
[ROW][C]27[/C][C]99.95[/C][C]99.9520541331602[/C][C]-0.00205413316022884[/C][/ROW]
[ROW][C]28[/C][C]99.69[/C][C]100.101469732542[/C][C]-0.41146973254186[/C][/ROW]
[ROW][C]29[/C][C]99.55[/C][C]99.7244066468589[/C][C]-0.174406646858898[/C][/ROW]
[ROW][C]30[/C][C]99.14[/C][C]99.5347879783877[/C][C]-0.394787978387726[/C][/ROW]
[ROW][C]31[/C][C]99.05[/C][C]99.0124708496038[/C][C]0.0375291503962245[/C][/ROW]
[ROW][C]32[/C][C]99[/C][C]98.933147888037[/C][C]0.0668521119630441[/C][/ROW]
[ROW][C]33[/C][C]99.03[/C][C]98.9021673052429[/C][C]0.127832694757132[/C][/ROW]
[ROW][C]34[/C][C]99.16[/C][C]98.9685356903656[/C][C]0.191464309634384[/C][/ROW]
[ROW][C]35[/C][C]99.01[/C][C]99.1530072616899[/C][C]-0.143007261689931[/C][/ROW]
[ROW][C]36[/C][C]99[/C][C]98.9623217142377[/C][C]0.037678285762297[/C][/ROW]
[ROW][C]37[/C][C]99.9[/C][C]98.9630411816632[/C][C]0.936958818336763[/C][/ROW]
[ROW][C]38[/C][C]100.18[/C][C]100.129605844281[/C][C]0.0503941557192036[/C][/ROW]
[ROW][C]39[/C][C]100.2[/C][C]100.423942975064[/C][C]-0.223942975064233[/C][/ROW]
[ROW][C]40[/C][C]100.13[/C][C]100.380231227626[/C][C]-0.250231227626358[/C][/ROW]
[ROW][C]41[/C][C]99.85[/C][C]100.239040475735[/C][C]-0.38904047573503[/C][/ROW]
[ROW][C]42[/C][C]99.88[/C][C]99.8483585107123[/C][C]0.0316414892876935[/C][/ROW]
[ROW][C]43[/C][C]99.88[/C][C]99.8873605103217[/C][C]-0.00736051032170337[/C][/ROW]
[ROW][C]44[/C][C]99.89[/C][C]99.8852664460873[/C][C]0.00473355391271468[/C][/ROW]
[ROW][C]45[/C][C]99.96[/C][C]99.8966131415632[/C][C]0.0633868584368429[/C][/ROW]
[ROW][C]46[/C][C]100.05[/C][C]99.9846466945891[/C][C]0.065353305410909[/C][/ROW]
[ROW][C]47[/C][C]100.04[/C][C]100.093239701525[/C][C]-0.0532397015247881[/C][/ROW]
[ROW][C]48[/C][C]100.06[/C][C]100.068093013328[/C][C]-0.00809301332776613[/C][/ROW]
[ROW][C]49[/C][C]99.72[/C][C]100.085790552083[/C][C]-0.365790552082871[/C][/ROW]
[ROW][C]50[/C][C]99.7[/C][C]99.6417231873317[/C][C]0.0582768126682822[/C][/ROW]
[ROW][C]51[/C][C]99.63[/C][C]99.6383029329975[/C][C]-0.00830293299752327[/C][/ROW]
[ROW][C]52[/C][C]99.73[/C][C]99.5659407496337[/C][C]0.164059250366279[/C][/ROW]
[ROW][C]53[/C][C]99.77[/C][C]99.7126155851413[/C][C]0.0573844148587455[/C][/ROW]
[ROW][C]54[/C][C]99.76[/C][C]99.7689414437457[/C][C]-0.00894144374565542[/C][/ROW]
[ROW][C]55[/C][C]99.61[/C][C]99.7563976041566[/C][C]-0.146397604156633[/C][/ROW]
[ROW][C]56[/C][C]99.61[/C][C]99.5647475047112[/C][C]0.0452524952888353[/C][/ROW]
[ROW][C]57[/C][C]99.59[/C][C]99.5776218337673[/C][C]0.0123781662327502[/C][/ROW]
[ROW][C]58[/C][C]99.42[/C][C]99.5611434204593[/C][C]-0.141143420459315[/C][/ROW]
[ROW][C]59[/C][C]99.52[/C][C]99.3509881355961[/C][C]0.169011864403913[/C][/ROW]
[ROW][C]60[/C][C]99.46[/C][C]99.4990719891566[/C][C]-0.0390719891566533[/C][/ROW]
[ROW][C]61[/C][C]100.55[/C][C]99.4279560132957[/C][C]1.1220439867043[/C][/ROW]
[ROW][C]62[/C][C]100.4[/C][C]100.837177382372[/C][C]-0.437177382372326[/C][/ROW]
[ROW][C]63[/C][C]100.15[/C][C]100.562800473638[/C][C]-0.412800473638001[/C][/ROW]
[ROW][C]64[/C][C]100.2[/C][C]100.195358792285[/C][C]0.0046412077146698[/C][/ROW]
[ROW][C]65[/C][C]100.16[/C][C]100.24667921528[/C][C]-0.0866792152798013[/C][/ROW]
[ROW][C]66[/C][C]100.19[/C][C]100.182018989745[/C][C]0.00798101025502262[/C][/ROW]
[ROW][C]67[/C][C]100.23[/C][C]100.21428958613[/C][C]0.0157104138698401[/C][/ROW]
[ROW][C]68[/C][C]100.08[/C][C]100.258759196844[/C][C]-0.178759196843941[/C][/ROW]
[ROW][C]69[/C][C]100.15[/C][C]100.057902228465[/C][C]0.0920977715349807[/C][/ROW]
[ROW][C]70[/C][C]100.13[/C][C]100.154104032554[/C][C]-0.024104032553538[/C][/ROW]
[ROW][C]71[/C][C]100.26[/C][C]100.12724643841[/C][C]0.132753561590022[/C][/ROW]
[ROW][C]72[/C][C]100.24[/C][C]100.29501480951[/C][C]-0.055014809510169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	99	98.37	0.629999999999995
4	98.88	98.5792349185071	0.300765081492941
5	98.9	98.5448025452867	0.355197454713334
6	98.92	98.6658561752065	0.254143824793545
7	98.8	98.7581600604857	0.0418399395142757
8	98.83	98.6500635178654	0.179936482134622
9	98.88	98.7312554237572	0.148744576242805
10	98.88	98.8235732364576	0.0564267635424187
11	98.89	98.8396266433864	0.0503733566136191
12	98.89	98.863957856827	0.0260421431730293
13	99.05	98.871366843191	0.178633156808957
14	99.2	99.0821879531963	0.117812046803706
15	99.13	99.2657054652725	-0.135705465272522
16	98.92	99.1570972779565	-0.237097277956494
17	98.98	98.8796431330473	0.100356866952666
18	98.99	98.9681946487138	0.0218053512861758
19	99.08	98.9843982683341	0.0956017316658802
20	99.1	99.1015969486266	-0.00159694862661297
21	99.1	99.1211426169489	-0.0211426169489073
22	99.06	99.1151275451618	-0.0551275451618238
23	99.05	99.0594437656943	-0.00944376569425742
24	99.11	99.0467570155758	0.0632429844241784
25	99.75	99.1247496364638	0.625250363536225
26	99.8	99.9426332840113	-0.142633284011282
27	99.95	99.9520541331602	-0.00205413316022884
28	99.69	100.101469732542	-0.41146973254186
29	99.55	99.7244066468589	-0.174406646858898
30	99.14	99.5347879783877	-0.394787978387726
31	99.05	99.0124708496038	0.0375291503962245
32	99	98.933147888037	0.0668521119630441
33	99.03	98.9021673052429	0.127832694757132
34	99.16	98.9685356903656	0.191464309634384
35	99.01	99.1530072616899	-0.143007261689931
36	99	98.9623217142377	0.037678285762297
37	99.9	98.9630411816632	0.936958818336763
38	100.18	100.129605844281	0.0503941557192036
39	100.2	100.423942975064	-0.223942975064233
40	100.13	100.380231227626	-0.250231227626358
41	99.85	100.239040475735	-0.38904047573503
42	99.88	99.8483585107123	0.0316414892876935
43	99.88	99.8873605103217	-0.00736051032170337
44	99.89	99.8852664460873	0.00473355391271468
45	99.96	99.8966131415632	0.0633868584368429
46	100.05	99.9846466945891	0.065353305410909
47	100.04	100.093239701525	-0.0532397015247881
48	100.06	100.068093013328	-0.00809301332776613
49	99.72	100.085790552083	-0.365790552082871
50	99.7	99.6417231873317	0.0582768126682822
51	99.63	99.6383029329975	-0.00830293299752327
52	99.73	99.5659407496337	0.164059250366279
53	99.77	99.7126155851413	0.0573844148587455
54	99.76	99.7689414437457	-0.00894144374565542
55	99.61	99.7563976041566	-0.146397604156633
56	99.61	99.5647475047112	0.0452524952888353
57	99.59	99.5776218337673	0.0123781662327502
58	99.42	99.5611434204593	-0.141143420459315
59	99.52	99.3509881355961	0.169011864403913
60	99.46	99.4990719891566	-0.0390719891566533
61	100.55	99.4279560132957	1.1220439867043
62	100.4	100.837177382372	-0.437177382372326
63	100.15	100.562800473638	-0.412800473638001
64	100.2	100.195358792285	0.0046412077146698
65	100.16	100.24667921528	-0.0866792152798013
66	100.19	100.182018989745	0.00798101025502262
67	100.23	100.21428958613	0.0157104138698401
68	100.08	100.258759196844	-0.178759196843941
69	100.15	100.057902228465	0.0920977715349807
70	100.13	100.154104032554	-0.024104032553538
71	100.26	100.12724643841	0.132753561590022
72	100.24	100.29501480951	-0.055014809510169

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	100.259363103321	99.7447711563962	100.773955050246
74	100.278726206642	99.4410407046264	101.116411708657
75	100.298089309963	99.1346448156199	101.461533804305
76	100.317452413284	98.8130156910169	101.82188913555
77	100.336815516604	98.4730118826276	102.200619150581
78	100.356178619925	98.1139091888232	102.598448051028
79	100.375541723246	97.7358028717177	103.015280574775
80	100.394904826567	97.3390943448876	103.450715308247
81	100.414267929888	96.9242953806048	103.904240479171
82	100.433631033209	96.4919461149578	104.37531595146
83	100.45299413653	96.0425792800711	104.863408992989
84	100.472357239851	95.5767048078723	105.368009671829

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 100.259363103321 & 99.7447711563962 & 100.773955050246 \tabularnewline
74 & 100.278726206642 & 99.4410407046264 & 101.116411708657 \tabularnewline
75 & 100.298089309963 & 99.1346448156199 & 101.461533804305 \tabularnewline
76 & 100.317452413284 & 98.8130156910169 & 101.82188913555 \tabularnewline
77 & 100.336815516604 & 98.4730118826276 & 102.200619150581 \tabularnewline
78 & 100.356178619925 & 98.1139091888232 & 102.598448051028 \tabularnewline
79 & 100.375541723246 & 97.7358028717177 & 103.015280574775 \tabularnewline
80 & 100.394904826567 & 97.3390943448876 & 103.450715308247 \tabularnewline
81 & 100.414267929888 & 96.9242953806048 & 103.904240479171 \tabularnewline
82 & 100.433631033209 & 96.4919461149578 & 104.37531595146 \tabularnewline
83 & 100.45299413653 & 96.0425792800711 & 104.863408992989 \tabularnewline
84 & 100.472357239851 & 95.5767048078723 & 105.368009671829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.259363103321[/C][C]99.7447711563962[/C][C]100.773955050246[/C][/ROW]
[ROW][C]74[/C][C]100.278726206642[/C][C]99.4410407046264[/C][C]101.116411708657[/C][/ROW]
[ROW][C]75[/C][C]100.298089309963[/C][C]99.1346448156199[/C][C]101.461533804305[/C][/ROW]
[ROW][C]76[/C][C]100.317452413284[/C][C]98.8130156910169[/C][C]101.82188913555[/C][/ROW]
[ROW][C]77[/C][C]100.336815516604[/C][C]98.4730118826276[/C][C]102.200619150581[/C][/ROW]
[ROW][C]78[/C][C]100.356178619925[/C][C]98.1139091888232[/C][C]102.598448051028[/C][/ROW]
[ROW][C]79[/C][C]100.375541723246[/C][C]97.7358028717177[/C][C]103.015280574775[/C][/ROW]
[ROW][C]80[/C][C]100.394904826567[/C][C]97.3390943448876[/C][C]103.450715308247[/C][/ROW]
[ROW][C]81[/C][C]100.414267929888[/C][C]96.9242953806048[/C][C]103.904240479171[/C][/ROW]
[ROW][C]82[/C][C]100.433631033209[/C][C]96.4919461149578[/C][C]104.37531595146[/C][/ROW]
[ROW][C]83[/C][C]100.45299413653[/C][C]96.0425792800711[/C][C]104.863408992989[/C][/ROW]
[ROW][C]84[/C][C]100.472357239851[/C][C]95.5767048078723[/C][C]105.368009671829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	100.259363103321	99.7447711563962	100.773955050246
74	100.278726206642	99.4410407046264	101.116411708657
75	100.298089309963	99.1346448156199	101.461533804305
76	100.317452413284	98.8130156910169	101.82188913555
77	100.336815516604	98.4730118826276	102.200619150581
78	100.356178619925	98.1139091888232	102.598448051028
79	100.375541723246	97.7358028717177	103.015280574775
80	100.394904826567	97.3390943448876	103.450715308247
81	100.414267929888	96.9242953806048	103.904240479171
82	100.433631033209	96.4919461149578	104.37531595146
83	100.45299413653	96.0425792800711	104.863408992989
84	100.472357239851	95.5767048078723	105.368009671829

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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