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

Sun, 10 Jan 2016 15:28:10 +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/Jan/10/t1452439731v8h1yr0pqnufhw2.htm/, Retrieved Sat, 04 May 2024 22:22:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287903, Retrieved Sat, 04 May 2024 22:22:48 +0000

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

101

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

-       [Exponential Smoothing] [Juiste exponentia...] [2016-01-10 15:28:10] [442c3b7d1457f8bc4e82a9331e05e70d] [Current]

Feedback Forum

Post a new message

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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287903&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287903&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287903&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.783130982224961
beta	0.234826889608407
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.783130982224961 \tabularnewline
beta & 0.234826889608407 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287903&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]0.783130982224961[/C][/ROW]
[ROW][C]beta[/C][C]0.234826889608407[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287903&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287903&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	0.783130982224961
beta	0.234826889608407
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	86.87	86.1685924145299	0.701407585470108
14	87.32	87.3172702435646	0.00272975643538587
15	87.13	87.282627154211	-0.152627154211018
16	87.42	87.5578344220358	-0.137834422035809
17	87.22	87.294695223874	-0.0746952238740164
18	87.17	87.1868491537599	-0.0168491537598925
19	87.52	87.850788903725	-0.330788903724994
20	87.49	87.6680405591827	-0.178040559182691
21	87.53	87.4455058123634	0.0844941876366505
22	87.93	87.4399419921014	0.490058007898568
23	88.54	88.1033595366499	0.436640463350145
24	88.96	88.7069090878234	0.253090912176575
25	89.3	89.4632890120717	-0.163289012071672
26	90.01	89.8224248845663	0.18757511543366
27	90.52	89.9719912367303	0.548008763269664
28	90.64	91.0010867929312	-0.361086792931161
29	91.25	90.7377390324986	0.512260967501362
30	91.59	91.3709772802577	0.219022719742256
31	92.09	92.4638044034828	-0.373804403482779
32	91.81	92.584837718757	-0.774837718756984
33	92.03	92.1464592011992	-0.116459201199234
34	92.15	92.2291123349036	-0.0791123349035701
35	91.98	92.4881753437127	-0.508175343712708
36	92.11	92.1912173294018	-0.0812173294018379
37	92.28	92.4132240265248	-0.133224026524772
38	92.53	92.695259056284	-0.165259056284029
39	91.97	92.4050534258347	-0.435053425834653
40	92.05	92.044719015939	0.00528098406100241
41	91.87	91.9026535476405	-0.0326535476404928
42	91.49	91.5903144340195	-0.100314434019523
43	91.48	91.7905231007876	-0.310523100787549
44	91.63	91.3718099069993	0.258190093000707
45	91.46	91.5728510544554	-0.112851054455433
46	91.61	91.3547344345269	0.25526556547311
47	91.7	91.5324060472668	0.167593952733185
48	91.87	91.7313293720529	0.138670627947064
49	92.21	92.0287674430195	0.181232556980461
50	92.65	92.5224533361916	0.12754666380836
51	92.83	92.4292275069455	0.400772493054532
52	93.02	92.9988423350708	0.0211576649291487
53	93.33	93.0437964620397	0.286203537960318
54	93.35	93.207941446165	0.142058553835042
55	93.45	93.8383953909897	-0.388395390989714
56	93.51	93.7537367641905	-0.24373676419053
57	93.8	93.6606341523338	0.139365847666156
58	93.94	93.9456502770051	-0.0056502770051452
59	94.02	94.0777756587908	-0.0577756587907743
60	94.26	94.2302852713907	0.0297147286093065
61	94.71	94.5679427386567	0.142057261343268
62	95.26	95.1284178649791	0.131582135020878
63	95.54	95.2074601073233	0.332539892676692
64	95.69	95.7386187392999	-0.0486187392998687
65	96.03	95.8708827069715	0.159117293028473
66	96.4	95.9653444132091	0.43465558679091
67	96.55	96.8248122695166	-0.274812269516602
68	96.45	96.9962751743638	-0.546275174363799
69	96.65	96.8294906651997	-0.179490665199722
70	96.84	96.8548753085739	-0.014875308573906
71	97.21	96.9882998540406	0.221700145959375
72	97.31	97.4498731945078	-0.139873194507814
73	97.91	97.7191210765684	0.190878923431612
74	98.51	98.3645728996327	0.145427100367343
75	98.54	98.5495998377901	-0.00959983779013385
76	98.52	98.7187979422303	-0.198797942230314
77	98.66	98.7395266389006	-0.0795266389005604
78	98.53	98.6239911440198	-0.0939911440197676
79	98.71	98.7355160599592	-0.0255160599592017
80	98.92	98.9091025730134	0.0108974269866025
81	98.96	99.2264294628447	-0.266429462844712
82	99.25	99.1716696237415	0.0783303762584922
83	99.32	99.3987728732546	-0.0787728732545929
84	99.41	99.4607459337846	-0.0507459337845688
85	99.36	99.802036050161	-0.442036050160993
86	99.58	99.7560962859327	-0.176096285932687
87	99.77	99.4107003696953	0.359299630304676
88	99.77	99.6505971712374	0.11940282876256
89	100.03	99.827735491498	0.202264508501969
90	100.2	99.8629144144508	0.33708558554919
91	100.24	100.339326042321	-0.0993260423207829
92	100.1	100.461880002148	-0.361880002147899
93	100.03	100.357449252648	-0.327449252647511
94	100.18	100.248768626069	-0.0687686260691294
95	100.29	100.21864969695	0.0713503030501812
96	100.41	100.32392116184	0.0860788381604749
97	100.6	100.632320516735	-0.0323205167346288
98	100.75	100.985078773512	-0.235078773511603
99	100.79	100.71891873573	0.0710812642696368
100	100.44	100.637389308058	-0.197389308057794
101	100.29	100.48246256739	-0.192462567390095
102	100.34	100.063221154268	0.276778845731641
103	100.46	100.212134274413	0.247865725586905
104	100.12	100.427867414796	-0.307867414796164
105	100.06	100.261357854724	-0.201357854724222
106	100.28	100.218866652772	0.0611333472279085
107	100.28	100.256097969562	0.0239020304383644
108	100.4	100.25391216907	0.146087830929559

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 86.87 & 86.1685924145299 & 0.701407585470108 \tabularnewline
14 & 87.32 & 87.3172702435646 & 0.00272975643538587 \tabularnewline
15 & 87.13 & 87.282627154211 & -0.152627154211018 \tabularnewline
16 & 87.42 & 87.5578344220358 & -0.137834422035809 \tabularnewline
17 & 87.22 & 87.294695223874 & -0.0746952238740164 \tabularnewline
18 & 87.17 & 87.1868491537599 & -0.0168491537598925 \tabularnewline
19 & 87.52 & 87.850788903725 & -0.330788903724994 \tabularnewline
20 & 87.49 & 87.6680405591827 & -0.178040559182691 \tabularnewline
21 & 87.53 & 87.4455058123634 & 0.0844941876366505 \tabularnewline
22 & 87.93 & 87.4399419921014 & 0.490058007898568 \tabularnewline
23 & 88.54 & 88.1033595366499 & 0.436640463350145 \tabularnewline
24 & 88.96 & 88.7069090878234 & 0.253090912176575 \tabularnewline
25 & 89.3 & 89.4632890120717 & -0.163289012071672 \tabularnewline
26 & 90.01 & 89.8224248845663 & 0.18757511543366 \tabularnewline
27 & 90.52 & 89.9719912367303 & 0.548008763269664 \tabularnewline
28 & 90.64 & 91.0010867929312 & -0.361086792931161 \tabularnewline
29 & 91.25 & 90.7377390324986 & 0.512260967501362 \tabularnewline
30 & 91.59 & 91.3709772802577 & 0.219022719742256 \tabularnewline
31 & 92.09 & 92.4638044034828 & -0.373804403482779 \tabularnewline
32 & 91.81 & 92.584837718757 & -0.774837718756984 \tabularnewline
33 & 92.03 & 92.1464592011992 & -0.116459201199234 \tabularnewline
34 & 92.15 & 92.2291123349036 & -0.0791123349035701 \tabularnewline
35 & 91.98 & 92.4881753437127 & -0.508175343712708 \tabularnewline
36 & 92.11 & 92.1912173294018 & -0.0812173294018379 \tabularnewline
37 & 92.28 & 92.4132240265248 & -0.133224026524772 \tabularnewline
38 & 92.53 & 92.695259056284 & -0.165259056284029 \tabularnewline
39 & 91.97 & 92.4050534258347 & -0.435053425834653 \tabularnewline
40 & 92.05 & 92.044719015939 & 0.00528098406100241 \tabularnewline
41 & 91.87 & 91.9026535476405 & -0.0326535476404928 \tabularnewline
42 & 91.49 & 91.5903144340195 & -0.100314434019523 \tabularnewline
43 & 91.48 & 91.7905231007876 & -0.310523100787549 \tabularnewline
44 & 91.63 & 91.3718099069993 & 0.258190093000707 \tabularnewline
45 & 91.46 & 91.5728510544554 & -0.112851054455433 \tabularnewline
46 & 91.61 & 91.3547344345269 & 0.25526556547311 \tabularnewline
47 & 91.7 & 91.5324060472668 & 0.167593952733185 \tabularnewline
48 & 91.87 & 91.7313293720529 & 0.138670627947064 \tabularnewline
49 & 92.21 & 92.0287674430195 & 0.181232556980461 \tabularnewline
50 & 92.65 & 92.5224533361916 & 0.12754666380836 \tabularnewline
51 & 92.83 & 92.4292275069455 & 0.400772493054532 \tabularnewline
52 & 93.02 & 92.9988423350708 & 0.0211576649291487 \tabularnewline
53 & 93.33 & 93.0437964620397 & 0.286203537960318 \tabularnewline
54 & 93.35 & 93.207941446165 & 0.142058553835042 \tabularnewline
55 & 93.45 & 93.8383953909897 & -0.388395390989714 \tabularnewline
56 & 93.51 & 93.7537367641905 & -0.24373676419053 \tabularnewline
57 & 93.8 & 93.6606341523338 & 0.139365847666156 \tabularnewline
58 & 93.94 & 93.9456502770051 & -0.0056502770051452 \tabularnewline
59 & 94.02 & 94.0777756587908 & -0.0577756587907743 \tabularnewline
60 & 94.26 & 94.2302852713907 & 0.0297147286093065 \tabularnewline
61 & 94.71 & 94.5679427386567 & 0.142057261343268 \tabularnewline
62 & 95.26 & 95.1284178649791 & 0.131582135020878 \tabularnewline
63 & 95.54 & 95.2074601073233 & 0.332539892676692 \tabularnewline
64 & 95.69 & 95.7386187392999 & -0.0486187392998687 \tabularnewline
65 & 96.03 & 95.8708827069715 & 0.159117293028473 \tabularnewline
66 & 96.4 & 95.9653444132091 & 0.43465558679091 \tabularnewline
67 & 96.55 & 96.8248122695166 & -0.274812269516602 \tabularnewline
68 & 96.45 & 96.9962751743638 & -0.546275174363799 \tabularnewline
69 & 96.65 & 96.8294906651997 & -0.179490665199722 \tabularnewline
70 & 96.84 & 96.8548753085739 & -0.014875308573906 \tabularnewline
71 & 97.21 & 96.9882998540406 & 0.221700145959375 \tabularnewline
72 & 97.31 & 97.4498731945078 & -0.139873194507814 \tabularnewline
73 & 97.91 & 97.7191210765684 & 0.190878923431612 \tabularnewline
74 & 98.51 & 98.3645728996327 & 0.145427100367343 \tabularnewline
75 & 98.54 & 98.5495998377901 & -0.00959983779013385 \tabularnewline
76 & 98.52 & 98.7187979422303 & -0.198797942230314 \tabularnewline
77 & 98.66 & 98.7395266389006 & -0.0795266389005604 \tabularnewline
78 & 98.53 & 98.6239911440198 & -0.0939911440197676 \tabularnewline
79 & 98.71 & 98.7355160599592 & -0.0255160599592017 \tabularnewline
80 & 98.92 & 98.9091025730134 & 0.0108974269866025 \tabularnewline
81 & 98.96 & 99.2264294628447 & -0.266429462844712 \tabularnewline
82 & 99.25 & 99.1716696237415 & 0.0783303762584922 \tabularnewline
83 & 99.32 & 99.3987728732546 & -0.0787728732545929 \tabularnewline
84 & 99.41 & 99.4607459337846 & -0.0507459337845688 \tabularnewline
85 & 99.36 & 99.802036050161 & -0.442036050160993 \tabularnewline
86 & 99.58 & 99.7560962859327 & -0.176096285932687 \tabularnewline
87 & 99.77 & 99.4107003696953 & 0.359299630304676 \tabularnewline
88 & 99.77 & 99.6505971712374 & 0.11940282876256 \tabularnewline
89 & 100.03 & 99.827735491498 & 0.202264508501969 \tabularnewline
90 & 100.2 & 99.8629144144508 & 0.33708558554919 \tabularnewline
91 & 100.24 & 100.339326042321 & -0.0993260423207829 \tabularnewline
92 & 100.1 & 100.461880002148 & -0.361880002147899 \tabularnewline
93 & 100.03 & 100.357449252648 & -0.327449252647511 \tabularnewline
94 & 100.18 & 100.248768626069 & -0.0687686260691294 \tabularnewline
95 & 100.29 & 100.21864969695 & 0.0713503030501812 \tabularnewline
96 & 100.41 & 100.32392116184 & 0.0860788381604749 \tabularnewline
97 & 100.6 & 100.632320516735 & -0.0323205167346288 \tabularnewline
98 & 100.75 & 100.985078773512 & -0.235078773511603 \tabularnewline
99 & 100.79 & 100.71891873573 & 0.0710812642696368 \tabularnewline
100 & 100.44 & 100.637389308058 & -0.197389308057794 \tabularnewline
101 & 100.29 & 100.48246256739 & -0.192462567390095 \tabularnewline
102 & 100.34 & 100.063221154268 & 0.276778845731641 \tabularnewline
103 & 100.46 & 100.212134274413 & 0.247865725586905 \tabularnewline
104 & 100.12 & 100.427867414796 & -0.307867414796164 \tabularnewline
105 & 100.06 & 100.261357854724 & -0.201357854724222 \tabularnewline
106 & 100.28 & 100.218866652772 & 0.0611333472279085 \tabularnewline
107 & 100.28 & 100.256097969562 & 0.0239020304383644 \tabularnewline
108 & 100.4 & 100.25391216907 & 0.146087830929559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287903&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]86.87[/C][C]86.1685924145299[/C][C]0.701407585470108[/C][/ROW]
[ROW][C]14[/C][C]87.32[/C][C]87.3172702435646[/C][C]0.00272975643538587[/C][/ROW]
[ROW][C]15[/C][C]87.13[/C][C]87.282627154211[/C][C]-0.152627154211018[/C][/ROW]
[ROW][C]16[/C][C]87.42[/C][C]87.5578344220358[/C][C]-0.137834422035809[/C][/ROW]
[ROW][C]17[/C][C]87.22[/C][C]87.294695223874[/C][C]-0.0746952238740164[/C][/ROW]
[ROW][C]18[/C][C]87.17[/C][C]87.1868491537599[/C][C]-0.0168491537598925[/C][/ROW]
[ROW][C]19[/C][C]87.52[/C][C]87.850788903725[/C][C]-0.330788903724994[/C][/ROW]
[ROW][C]20[/C][C]87.49[/C][C]87.6680405591827[/C][C]-0.178040559182691[/C][/ROW]
[ROW][C]21[/C][C]87.53[/C][C]87.4455058123634[/C][C]0.0844941876366505[/C][/ROW]
[ROW][C]22[/C][C]87.93[/C][C]87.4399419921014[/C][C]0.490058007898568[/C][/ROW]
[ROW][C]23[/C][C]88.54[/C][C]88.1033595366499[/C][C]0.436640463350145[/C][/ROW]
[ROW][C]24[/C][C]88.96[/C][C]88.7069090878234[/C][C]0.253090912176575[/C][/ROW]
[ROW][C]25[/C][C]89.3[/C][C]89.4632890120717[/C][C]-0.163289012071672[/C][/ROW]
[ROW][C]26[/C][C]90.01[/C][C]89.8224248845663[/C][C]0.18757511543366[/C][/ROW]
[ROW][C]27[/C][C]90.52[/C][C]89.9719912367303[/C][C]0.548008763269664[/C][/ROW]
[ROW][C]28[/C][C]90.64[/C][C]91.0010867929312[/C][C]-0.361086792931161[/C][/ROW]
[ROW][C]29[/C][C]91.25[/C][C]90.7377390324986[/C][C]0.512260967501362[/C][/ROW]
[ROW][C]30[/C][C]91.59[/C][C]91.3709772802577[/C][C]0.219022719742256[/C][/ROW]
[ROW][C]31[/C][C]92.09[/C][C]92.4638044034828[/C][C]-0.373804403482779[/C][/ROW]
[ROW][C]32[/C][C]91.81[/C][C]92.584837718757[/C][C]-0.774837718756984[/C][/ROW]
[ROW][C]33[/C][C]92.03[/C][C]92.1464592011992[/C][C]-0.116459201199234[/C][/ROW]
[ROW][C]34[/C][C]92.15[/C][C]92.2291123349036[/C][C]-0.0791123349035701[/C][/ROW]
[ROW][C]35[/C][C]91.98[/C][C]92.4881753437127[/C][C]-0.508175343712708[/C][/ROW]
[ROW][C]36[/C][C]92.11[/C][C]92.1912173294018[/C][C]-0.0812173294018379[/C][/ROW]
[ROW][C]37[/C][C]92.28[/C][C]92.4132240265248[/C][C]-0.133224026524772[/C][/ROW]
[ROW][C]38[/C][C]92.53[/C][C]92.695259056284[/C][C]-0.165259056284029[/C][/ROW]
[ROW][C]39[/C][C]91.97[/C][C]92.4050534258347[/C][C]-0.435053425834653[/C][/ROW]
[ROW][C]40[/C][C]92.05[/C][C]92.044719015939[/C][C]0.00528098406100241[/C][/ROW]
[ROW][C]41[/C][C]91.87[/C][C]91.9026535476405[/C][C]-0.0326535476404928[/C][/ROW]
[ROW][C]42[/C][C]91.49[/C][C]91.5903144340195[/C][C]-0.100314434019523[/C][/ROW]
[ROW][C]43[/C][C]91.48[/C][C]91.7905231007876[/C][C]-0.310523100787549[/C][/ROW]
[ROW][C]44[/C][C]91.63[/C][C]91.3718099069993[/C][C]0.258190093000707[/C][/ROW]
[ROW][C]45[/C][C]91.46[/C][C]91.5728510544554[/C][C]-0.112851054455433[/C][/ROW]
[ROW][C]46[/C][C]91.61[/C][C]91.3547344345269[/C][C]0.25526556547311[/C][/ROW]
[ROW][C]47[/C][C]91.7[/C][C]91.5324060472668[/C][C]0.167593952733185[/C][/ROW]
[ROW][C]48[/C][C]91.87[/C][C]91.7313293720529[/C][C]0.138670627947064[/C][/ROW]
[ROW][C]49[/C][C]92.21[/C][C]92.0287674430195[/C][C]0.181232556980461[/C][/ROW]
[ROW][C]50[/C][C]92.65[/C][C]92.5224533361916[/C][C]0.12754666380836[/C][/ROW]
[ROW][C]51[/C][C]92.83[/C][C]92.4292275069455[/C][C]0.400772493054532[/C][/ROW]
[ROW][C]52[/C][C]93.02[/C][C]92.9988423350708[/C][C]0.0211576649291487[/C][/ROW]
[ROW][C]53[/C][C]93.33[/C][C]93.0437964620397[/C][C]0.286203537960318[/C][/ROW]
[ROW][C]54[/C][C]93.35[/C][C]93.207941446165[/C][C]0.142058553835042[/C][/ROW]
[ROW][C]55[/C][C]93.45[/C][C]93.8383953909897[/C][C]-0.388395390989714[/C][/ROW]
[ROW][C]56[/C][C]93.51[/C][C]93.7537367641905[/C][C]-0.24373676419053[/C][/ROW]
[ROW][C]57[/C][C]93.8[/C][C]93.6606341523338[/C][C]0.139365847666156[/C][/ROW]
[ROW][C]58[/C][C]93.94[/C][C]93.9456502770051[/C][C]-0.0056502770051452[/C][/ROW]
[ROW][C]59[/C][C]94.02[/C][C]94.0777756587908[/C][C]-0.0577756587907743[/C][/ROW]
[ROW][C]60[/C][C]94.26[/C][C]94.2302852713907[/C][C]0.0297147286093065[/C][/ROW]
[ROW][C]61[/C][C]94.71[/C][C]94.5679427386567[/C][C]0.142057261343268[/C][/ROW]
[ROW][C]62[/C][C]95.26[/C][C]95.1284178649791[/C][C]0.131582135020878[/C][/ROW]
[ROW][C]63[/C][C]95.54[/C][C]95.2074601073233[/C][C]0.332539892676692[/C][/ROW]
[ROW][C]64[/C][C]95.69[/C][C]95.7386187392999[/C][C]-0.0486187392998687[/C][/ROW]
[ROW][C]65[/C][C]96.03[/C][C]95.8708827069715[/C][C]0.159117293028473[/C][/ROW]
[ROW][C]66[/C][C]96.4[/C][C]95.9653444132091[/C][C]0.43465558679091[/C][/ROW]
[ROW][C]67[/C][C]96.55[/C][C]96.8248122695166[/C][C]-0.274812269516602[/C][/ROW]
[ROW][C]68[/C][C]96.45[/C][C]96.9962751743638[/C][C]-0.546275174363799[/C][/ROW]
[ROW][C]69[/C][C]96.65[/C][C]96.8294906651997[/C][C]-0.179490665199722[/C][/ROW]
[ROW][C]70[/C][C]96.84[/C][C]96.8548753085739[/C][C]-0.014875308573906[/C][/ROW]
[ROW][C]71[/C][C]97.21[/C][C]96.9882998540406[/C][C]0.221700145959375[/C][/ROW]
[ROW][C]72[/C][C]97.31[/C][C]97.4498731945078[/C][C]-0.139873194507814[/C][/ROW]
[ROW][C]73[/C][C]97.91[/C][C]97.7191210765684[/C][C]0.190878923431612[/C][/ROW]
[ROW][C]74[/C][C]98.51[/C][C]98.3645728996327[/C][C]0.145427100367343[/C][/ROW]
[ROW][C]75[/C][C]98.54[/C][C]98.5495998377901[/C][C]-0.00959983779013385[/C][/ROW]
[ROW][C]76[/C][C]98.52[/C][C]98.7187979422303[/C][C]-0.198797942230314[/C][/ROW]
[ROW][C]77[/C][C]98.66[/C][C]98.7395266389006[/C][C]-0.0795266389005604[/C][/ROW]
[ROW][C]78[/C][C]98.53[/C][C]98.6239911440198[/C][C]-0.0939911440197676[/C][/ROW]
[ROW][C]79[/C][C]98.71[/C][C]98.7355160599592[/C][C]-0.0255160599592017[/C][/ROW]
[ROW][C]80[/C][C]98.92[/C][C]98.9091025730134[/C][C]0.0108974269866025[/C][/ROW]
[ROW][C]81[/C][C]98.96[/C][C]99.2264294628447[/C][C]-0.266429462844712[/C][/ROW]
[ROW][C]82[/C][C]99.25[/C][C]99.1716696237415[/C][C]0.0783303762584922[/C][/ROW]
[ROW][C]83[/C][C]99.32[/C][C]99.3987728732546[/C][C]-0.0787728732545929[/C][/ROW]
[ROW][C]84[/C][C]99.41[/C][C]99.4607459337846[/C][C]-0.0507459337845688[/C][/ROW]
[ROW][C]85[/C][C]99.36[/C][C]99.802036050161[/C][C]-0.442036050160993[/C][/ROW]
[ROW][C]86[/C][C]99.58[/C][C]99.7560962859327[/C][C]-0.176096285932687[/C][/ROW]
[ROW][C]87[/C][C]99.77[/C][C]99.4107003696953[/C][C]0.359299630304676[/C][/ROW]
[ROW][C]88[/C][C]99.77[/C][C]99.6505971712374[/C][C]0.11940282876256[/C][/ROW]
[ROW][C]89[/C][C]100.03[/C][C]99.827735491498[/C][C]0.202264508501969[/C][/ROW]
[ROW][C]90[/C][C]100.2[/C][C]99.8629144144508[/C][C]0.33708558554919[/C][/ROW]
[ROW][C]91[/C][C]100.24[/C][C]100.339326042321[/C][C]-0.0993260423207829[/C][/ROW]
[ROW][C]92[/C][C]100.1[/C][C]100.461880002148[/C][C]-0.361880002147899[/C][/ROW]
[ROW][C]93[/C][C]100.03[/C][C]100.357449252648[/C][C]-0.327449252647511[/C][/ROW]
[ROW][C]94[/C][C]100.18[/C][C]100.248768626069[/C][C]-0.0687686260691294[/C][/ROW]
[ROW][C]95[/C][C]100.29[/C][C]100.21864969695[/C][C]0.0713503030501812[/C][/ROW]
[ROW][C]96[/C][C]100.41[/C][C]100.32392116184[/C][C]0.0860788381604749[/C][/ROW]
[ROW][C]97[/C][C]100.6[/C][C]100.632320516735[/C][C]-0.0323205167346288[/C][/ROW]
[ROW][C]98[/C][C]100.75[/C][C]100.985078773512[/C][C]-0.235078773511603[/C][/ROW]
[ROW][C]99[/C][C]100.79[/C][C]100.71891873573[/C][C]0.0710812642696368[/C][/ROW]
[ROW][C]100[/C][C]100.44[/C][C]100.637389308058[/C][C]-0.197389308057794[/C][/ROW]
[ROW][C]101[/C][C]100.29[/C][C]100.48246256739[/C][C]-0.192462567390095[/C][/ROW]
[ROW][C]102[/C][C]100.34[/C][C]100.063221154268[/C][C]0.276778845731641[/C][/ROW]
[ROW][C]103[/C][C]100.46[/C][C]100.212134274413[/C][C]0.247865725586905[/C][/ROW]
[ROW][C]104[/C][C]100.12[/C][C]100.427867414796[/C][C]-0.307867414796164[/C][/ROW]
[ROW][C]105[/C][C]100.06[/C][C]100.261357854724[/C][C]-0.201357854724222[/C][/ROW]
[ROW][C]106[/C][C]100.28[/C][C]100.218866652772[/C][C]0.0611333472279085[/C][/ROW]
[ROW][C]107[/C][C]100.28[/C][C]100.256097969562[/C][C]0.0239020304383644[/C][/ROW]
[ROW][C]108[/C][C]100.4[/C][C]100.25391216907[/C][C]0.146087830929559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287903&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287903&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	86.87	86.1685924145299	0.701407585470108
14	87.32	87.3172702435646	0.00272975643538587
15	87.13	87.282627154211	-0.152627154211018
16	87.42	87.5578344220358	-0.137834422035809
17	87.22	87.294695223874	-0.0746952238740164
18	87.17	87.1868491537599	-0.0168491537598925
19	87.52	87.850788903725	-0.330788903724994
20	87.49	87.6680405591827	-0.178040559182691
21	87.53	87.4455058123634	0.0844941876366505
22	87.93	87.4399419921014	0.490058007898568
23	88.54	88.1033595366499	0.436640463350145
24	88.96	88.7069090878234	0.253090912176575
25	89.3	89.4632890120717	-0.163289012071672
26	90.01	89.8224248845663	0.18757511543366
27	90.52	89.9719912367303	0.548008763269664
28	90.64	91.0010867929312	-0.361086792931161
29	91.25	90.7377390324986	0.512260967501362
30	91.59	91.3709772802577	0.219022719742256
31	92.09	92.4638044034828	-0.373804403482779
32	91.81	92.584837718757	-0.774837718756984
33	92.03	92.1464592011992	-0.116459201199234
34	92.15	92.2291123349036	-0.0791123349035701
35	91.98	92.4881753437127	-0.508175343712708
36	92.11	92.1912173294018	-0.0812173294018379
37	92.28	92.4132240265248	-0.133224026524772
38	92.53	92.695259056284	-0.165259056284029
39	91.97	92.4050534258347	-0.435053425834653
40	92.05	92.044719015939	0.00528098406100241
41	91.87	91.9026535476405	-0.0326535476404928
42	91.49	91.5903144340195	-0.100314434019523
43	91.48	91.7905231007876	-0.310523100787549
44	91.63	91.3718099069993	0.258190093000707
45	91.46	91.5728510544554	-0.112851054455433
46	91.61	91.3547344345269	0.25526556547311
47	91.7	91.5324060472668	0.167593952733185
48	91.87	91.7313293720529	0.138670627947064
49	92.21	92.0287674430195	0.181232556980461
50	92.65	92.5224533361916	0.12754666380836
51	92.83	92.4292275069455	0.400772493054532
52	93.02	92.9988423350708	0.0211576649291487
53	93.33	93.0437964620397	0.286203537960318
54	93.35	93.207941446165	0.142058553835042
55	93.45	93.8383953909897	-0.388395390989714
56	93.51	93.7537367641905	-0.24373676419053
57	93.8	93.6606341523338	0.139365847666156
58	93.94	93.9456502770051	-0.0056502770051452
59	94.02	94.0777756587908	-0.0577756587907743
60	94.26	94.2302852713907	0.0297147286093065
61	94.71	94.5679427386567	0.142057261343268
62	95.26	95.1284178649791	0.131582135020878
63	95.54	95.2074601073233	0.332539892676692
64	95.69	95.7386187392999	-0.0486187392998687
65	96.03	95.8708827069715	0.159117293028473
66	96.4	95.9653444132091	0.43465558679091
67	96.55	96.8248122695166	-0.274812269516602
68	96.45	96.9962751743638	-0.546275174363799
69	96.65	96.8294906651997	-0.179490665199722
70	96.84	96.8548753085739	-0.014875308573906
71	97.21	96.9882998540406	0.221700145959375
72	97.31	97.4498731945078	-0.139873194507814
73	97.91	97.7191210765684	0.190878923431612
74	98.51	98.3645728996327	0.145427100367343
75	98.54	98.5495998377901	-0.00959983779013385
76	98.52	98.7187979422303	-0.198797942230314
77	98.66	98.7395266389006	-0.0795266389005604
78	98.53	98.6239911440198	-0.0939911440197676
79	98.71	98.7355160599592	-0.0255160599592017
80	98.92	98.9091025730134	0.0108974269866025
81	98.96	99.2264294628447	-0.266429462844712
82	99.25	99.1716696237415	0.0783303762584922
83	99.32	99.3987728732546	-0.0787728732545929
84	99.41	99.4607459337846	-0.0507459337845688
85	99.36	99.802036050161	-0.442036050160993
86	99.58	99.7560962859327	-0.176096285932687
87	99.77	99.4107003696953	0.359299630304676
88	99.77	99.6505971712374	0.11940282876256
89	100.03	99.827735491498	0.202264508501969
90	100.2	99.8629144144508	0.33708558554919
91	100.24	100.339326042321	-0.0993260423207829
92	100.1	100.461880002148	-0.361880002147899
93	100.03	100.357449252648	-0.327449252647511
94	100.18	100.248768626069	-0.0687686260691294
95	100.29	100.21864969695	0.0713503030501812
96	100.41	100.32392116184	0.0860788381604749
97	100.6	100.632320516735	-0.0323205167346288
98	100.75	100.985078773512	-0.235078773511603
99	100.79	100.71891873573	0.0710812642696368
100	100.44	100.637389308058	-0.197389308057794
101	100.29	100.48246256739	-0.192462567390095
102	100.34	100.063221154268	0.276778845731641
103	100.46	100.212134274413	0.247865725586905
104	100.12	100.427867414796	-0.307867414796164
105	100.06	100.261357854724	-0.201357854724222
106	100.28	100.218866652772	0.0611333472279085
107	100.28	100.256097969562	0.0239020304383644
108	100.4	100.25391216907	0.146087830929559

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	100.521171724161	100.014341860153	101.028001588168
110	100.79875539541	100.093706171058	101.503804619762
111	100.769806692007	99.854730679871	101.684882704143
112	100.54803375199	99.4100265594522	101.686040944527
113	100.558702464453	99.1848182054498	101.932586723457
114	100.43728759524	98.8148722260655	102.059702964415
115	100.357615797601	98.4744121042124	102.240819490991
116	100.207573280386	98.0517425169328	102.36340404384
117	100.310736709844	97.8708480277015	102.750625391986
118	100.525364898806	97.7903726841716	103.26035711344
119	100.537907649896	97.4971251945432	103.578690105248
120	100.570367326551	97.2134404398297	103.927294213273

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 100.521171724161 & 100.014341860153 & 101.028001588168 \tabularnewline
110 & 100.79875539541 & 100.093706171058 & 101.503804619762 \tabularnewline
111 & 100.769806692007 & 99.854730679871 & 101.684882704143 \tabularnewline
112 & 100.54803375199 & 99.4100265594522 & 101.686040944527 \tabularnewline
113 & 100.558702464453 & 99.1848182054498 & 101.932586723457 \tabularnewline
114 & 100.43728759524 & 98.8148722260655 & 102.059702964415 \tabularnewline
115 & 100.357615797601 & 98.4744121042124 & 102.240819490991 \tabularnewline
116 & 100.207573280386 & 98.0517425169328 & 102.36340404384 \tabularnewline
117 & 100.310736709844 & 97.8708480277015 & 102.750625391986 \tabularnewline
118 & 100.525364898806 & 97.7903726841716 & 103.26035711344 \tabularnewline
119 & 100.537907649896 & 97.4971251945432 & 103.578690105248 \tabularnewline
120 & 100.570367326551 & 97.2134404398297 & 103.927294213273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287903&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]109[/C][C]100.521171724161[/C][C]100.014341860153[/C][C]101.028001588168[/C][/ROW]
[ROW][C]110[/C][C]100.79875539541[/C][C]100.093706171058[/C][C]101.503804619762[/C][/ROW]
[ROW][C]111[/C][C]100.769806692007[/C][C]99.854730679871[/C][C]101.684882704143[/C][/ROW]
[ROW][C]112[/C][C]100.54803375199[/C][C]99.4100265594522[/C][C]101.686040944527[/C][/ROW]
[ROW][C]113[/C][C]100.558702464453[/C][C]99.1848182054498[/C][C]101.932586723457[/C][/ROW]
[ROW][C]114[/C][C]100.43728759524[/C][C]98.8148722260655[/C][C]102.059702964415[/C][/ROW]
[ROW][C]115[/C][C]100.357615797601[/C][C]98.4744121042124[/C][C]102.240819490991[/C][/ROW]
[ROW][C]116[/C][C]100.207573280386[/C][C]98.0517425169328[/C][C]102.36340404384[/C][/ROW]
[ROW][C]117[/C][C]100.310736709844[/C][C]97.8708480277015[/C][C]102.750625391986[/C][/ROW]
[ROW][C]118[/C][C]100.525364898806[/C][C]97.7903726841716[/C][C]103.26035711344[/C][/ROW]
[ROW][C]119[/C][C]100.537907649896[/C][C]97.4971251945432[/C][C]103.578690105248[/C][/ROW]
[ROW][C]120[/C][C]100.570367326551[/C][C]97.2134404398297[/C][C]103.927294213273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287903&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287903&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
109	100.521171724161	100.014341860153	101.028001588168
110	100.79875539541	100.093706171058	101.503804619762
111	100.769806692007	99.854730679871	101.684882704143
112	100.54803375199	99.4100265594522	101.686040944527
113	100.558702464453	99.1848182054498	101.932586723457
114	100.43728759524	98.8148722260655	102.059702964415
115	100.357615797601	98.4744121042124	102.240819490991
116	100.207573280386	98.0517425169328	102.36340404384
117	100.310736709844	97.8708480277015	102.750625391986
118	100.525364898806	97.7903726841716	103.26035711344
119	100.537907649896	97.4971251945432	103.578690105248
120	100.570367326551	97.2134404398297	103.927294213273

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 = grey ; par2 = no ;

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