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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 27 Nov 2012 10:27:42 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/27/t1354030127yg2rdmpx23dzgia.htm/, Retrieved Sat, 04 May 2024 06:32:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=193932, Retrieved Sat, 04 May 2024 06:32:10 +0000

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Estimated Impact

121

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Classical Decomposition] [Interest rate of ...] [2012-11-27 14:55:13] [820ccc95823c30a4d29a22de4f981486]
- RMPD      [Exponential Smoothing] [Interest rate EUR...] [2012-11-27 15:27:42] [28bea00984b2b9577d411997e7bfd037] [Current]

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Dataseries X:

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4.69
4.88
4.84
4.81
5.22
5.16
5.27
5.35
5.33
5.29
5.28
4.94
4.70
4.73
4.57
4.61
4.69
4.53
4.55
4.31
4.03
3.72
3.64
3.81
3.95
4.26
4.55
4.54
4.55
4.39
4.21
4.00
3.67
3.60
3.53
3.35
3.10
2.89
2.97
3.03
2.71
2.44
2.60
2.93
2.86
2.88
3.00
2.90
2.64
2.75
2.70
2.87
3.03
3.14
3.02
2.86
3.07
2.93
2.83
2.72
2.73
2.72
2.77
2.61
2.47
2.30
2.38
2.43
2.39
2.60
2.84
2.87
2.92
3.08
3.33
3.48
3.57
3.66
3.77
3.75
3.75
3.81
3.82
3.89
4.05
4.10
4.07
4.26
4.40
4.61
4.63
4.48
4.46
4.45
4.32
4.52
4.21
3.97
4.12
4.50
4.73
5.26
5.20
4.94
4.95
4.52
3.85
3.41
2.95
2.68
2.53
2.44
2.16
2.20
2.10
2.29
2.03
2.05
1.94
1.87
1.89
1.94
1.79
1.71
1.66
1.74
1.83
1.64
1.69
1.78
1.89
1.95
2.05
2.24
2.38
2.53
2.36
2.22
2.12
1.75
1.76
1.81
1.71
1.74
1.48
1.24
1.16
1.11
0.98
0.94
0.65
0.42
0.41
0.40

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193932&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]3 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=193932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193932&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.904344694666365
beta	0.465568295859685
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.904344694666365 \tabularnewline
beta & 0.465568295859685 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193932&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]0.904344694666365[/C][/ROW]
[ROW][C]beta[/C][C]0.465568295859685[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=193932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193932&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	0.904344694666365
beta	0.465568295859685
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	4.7	4.90931356837607	-0.209313568376067
14	4.73	4.67056656418675	0.0594334358132533
15	4.57	4.5340496643026	0.035950335697402
16	4.61	4.61351560223803	-0.00351560223802849
17	4.69	4.70997720640782	-0.0199772064078152
18	4.53	4.52480742536258	0.00519257463741774
19	4.55	4.43166938720862	0.118330612791376
20	4.31	4.55400170402283	-0.244001704022828
21	4.03	4.15759431235348	-0.127594312353484
22	3.72	3.79482108952395	-0.0748210895239509
23	3.64	3.48910414516911	0.150895854830892
24	3.81	3.13896210689787	0.671037893102132
25	3.95	3.62963238959929	0.320367610400714
26	4.26	4.27087395236728	-0.0108739523672803
27	4.55	4.41419396596922	0.135806034030784
28	4.54	4.96789672457306	-0.427896724573057
29	4.55	4.88802587432993	-0.338025874329933
30	4.39	4.49275772045436	-0.102757720454365
31	4.21	4.34248652067432	-0.132486520674322
32	4	4.12740095081224	-0.127400950812239
33	3.67	3.82073498898702	-0.150734988987023
34	3.6	3.40549881274811	0.194501187251888
35	3.53	3.44174311406491	0.0882568859350923
36	3.35	3.13514510305551	0.21485489694449
37	3.1	3.03809349017706	0.0619065098229372
38	2.89	3.16345939733002	-0.273459397330024
39	2.97	2.72233220049034	0.247667799509655
40	3.03	3.00936284946455	0.0206371505354483
41	2.71	3.21865341840654	-0.508653418406536
42	2.44	2.49467932795565	-0.0546793279556463
43	2.6	2.20838202888369	0.391617971116307
44	2.93	2.51175814139021	0.418241858609791
45	2.86	2.97004773270316	-0.110047732703156
46	2.88	2.91549965762313	-0.035499657623133
47	3	2.92761198302832	0.0723880169716775
48	2.9	2.8061223781212	0.0938776218787987
49	2.64	2.72144927340619	-0.0814492734061854
50	2.75	2.76114890987356	-0.0111489098735649
51	2.7	2.79358738248179	-0.0935873824817892
52	2.87	2.79310691386389	0.0768930861361143
53	3.03	3.0691463444185	-0.0391463444184956
54	3.14	3.07737561527735	0.0626243847226551
55	3.02	3.25342298742656	-0.233422987426561
56	2.86	3.04450068637003	-0.184500686370026
57	3.07	2.70380166157492	0.366198338425084
58	2.93	3.08422311432215	-0.154223114322146
59	2.83	2.94644990335422	-0.116449903354222
60	2.72	2.52389545895523	0.196104541044773
61	2.73	2.42559494673312	0.304405053266877
62	2.72	2.89411754220865	-0.174117542208651
63	2.77	2.77582819179425	-0.0058281917942451
64	2.61	2.91250693751264	-0.302506937512643
65	2.47	2.71608508450967	-0.246085084509671
66	2.3	2.34152392527821	-0.0415239252782134
67	2.38	2.14583543321028	0.234164566789723
68	2.43	2.31209210332012	0.117907896679879
69	2.39	2.37251529055661	0.017484709443393
70	2.6	2.31594131076508	0.284058689234917
71	2.84	2.69081372897927	0.149186271020734
72	2.87	2.76289995678558	0.107100043214416
73	2.92	2.781510794924	0.138489205075996
74	3.08	3.17140137610073	-0.0914013761007335
75	3.33	3.29602638496385	0.0339736150361536
76	3.48	3.60909137424452	-0.129091374244525
77	3.57	3.81667848828993	-0.246678488289928
78	3.66	3.70268267720468	-0.0426826772046751
79	3.77	3.77336409621469	-0.0033640962146877
80	3.75	3.85473147321074	-0.10473147321074
81	3.75	3.75150618412767	-0.0015061841276709
82	3.81	3.74256155719096	0.0674384428090424
83	3.82	3.85673325758296	-0.0367332575829571
84	3.89	3.62647980682169	0.263520193178308
85	4.05	3.72523058488877	0.324769415111225
86	4.1	4.27570244193343	-0.175702441933433
87	4.07	4.31469938879119	-0.244699388791188
88	4.26	4.22143540040574	0.0385645995942632
89	4.4	4.50126788175432	-0.101267881754323
90	4.61	4.53138391202895	0.0786160879710467
91	4.63	4.75969043664461	-0.129690436644611
92	4.48	4.70809939845644	-0.22809939845644
93	4.46	4.44221937723124	0.0177806227687629
94	4.45	4.40447034679594	0.0455296532040625
95	4.32	4.42679877929415	-0.106798779294147
96	4.52	4.07033720459649	0.449662795403507
97	4.21	4.33009069888729	-0.120090698887294
98	3.97	4.22988838171736	-0.259888381717364
99	4.12	3.9502126332381	0.169787366761899
100	4.5	4.19745669038361	0.302543309616387
101	4.73	4.75235871262396	-0.0223587126239559
102	5.26	4.95398366143489	0.30601633856511
103	5.2	5.54669703281501	-0.346697032815014
104	4.94	5.3767609495731	-0.436760949573101
105	4.95	4.94516209523332	0.00483790476667689
106	4.52	4.89237680637264	-0.372376806372637
107	3.85	4.34026388496181	-0.490263884961809
108	3.41	3.34685540556038	0.0631445944396218
109	2.95	2.69643510969163	0.253564890308374
110	2.68	2.57196747987753	0.108032520122472
111	2.53	2.47222072894606	0.0577792710539433
112	2.44	2.38981134519681	0.0501886548031889
113	2.16	2.33811090317119	-0.178110903171188
114	2.2	2.01740772988735	0.182592270112646
115	2.1	1.97121667606911	0.12878332393089
116	2.29	1.95800611289755	0.331993887102453
117	2.03	2.32288245511187	-0.292882455111869
118	2.05	1.89843685617811	0.151563143821891
119	1.94	1.96313047820039	-0.0231304782003925
120	1.87	1.79604797641295	0.0739520235870541
121	1.89	1.52910623321984	0.360893766780161
122	1.94	1.88845928965493	0.0515407103450678
123	1.79	2.10971182493531	-0.31971182493531
124	1.71	1.90315196454926	-0.193151964549263
125	1.66	1.7250526090442	-0.0650526090442045
126	1.74	1.70420063546927	0.0357993645307328
127	1.83	1.62141060788522	0.208589392114776
128	1.64	1.83471101587233	-0.19471101587233
129	1.69	1.57663165731026	0.113368342689738
130	1.78	1.64627569984924	0.133724300150756
131	1.89	1.75480103118923	0.135198968810766
132	1.95	1.88352604083847	0.0664739591615251
133	2.05	1.77745718847524	0.272542811524765
134	2.24	2.13030862946077	0.109691370539229
135	2.38	2.4961099121968	-0.116109912196803
136	2.53	2.6989786367314	-0.168978636731399
137	2.36	2.77836763636126	-0.418367636361264
138	2.22	2.52226035365533	-0.302260353655335
139	2.12	2.0825576221324	0.0374423778675981
140	1.75	1.96272708857666	-0.212727088576665
141	1.76	1.57046180873363	0.189538191266367
142	1.81	1.59564431108889	0.214355688911113
143	1.71	1.69588535073744	0.0141146492625623
144	1.74	1.57620992455523	0.163790075444774
145	1.48	1.48650881754583	-0.00650881754583255
146	1.24	1.36258236229749	-0.122582362297495
147	1.16	1.1900924152013	-0.0300924152012998
148	1.11	1.19527312123142	-0.0852731212314246
149	0.98	1.0913279535301	-0.111327953530101
150	0.94	1.01809344420984	-0.0780934442098431
151	0.65	0.80208796355857	-0.15208796355857
152	0.42	0.395606602487347	0.024393397512653
153	0.41	0.264774590852937	0.145225409147063
154	0.4	0.242115597972844	0.157884402027156

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.7 & 4.90931356837607 & -0.209313568376067 \tabularnewline
14 & 4.73 & 4.67056656418675 & 0.0594334358132533 \tabularnewline
15 & 4.57 & 4.5340496643026 & 0.035950335697402 \tabularnewline
16 & 4.61 & 4.61351560223803 & -0.00351560223802849 \tabularnewline
17 & 4.69 & 4.70997720640782 & -0.0199772064078152 \tabularnewline
18 & 4.53 & 4.52480742536258 & 0.00519257463741774 \tabularnewline
19 & 4.55 & 4.43166938720862 & 0.118330612791376 \tabularnewline
20 & 4.31 & 4.55400170402283 & -0.244001704022828 \tabularnewline
21 & 4.03 & 4.15759431235348 & -0.127594312353484 \tabularnewline
22 & 3.72 & 3.79482108952395 & -0.0748210895239509 \tabularnewline
23 & 3.64 & 3.48910414516911 & 0.150895854830892 \tabularnewline
24 & 3.81 & 3.13896210689787 & 0.671037893102132 \tabularnewline
25 & 3.95 & 3.62963238959929 & 0.320367610400714 \tabularnewline
26 & 4.26 & 4.27087395236728 & -0.0108739523672803 \tabularnewline
27 & 4.55 & 4.41419396596922 & 0.135806034030784 \tabularnewline
28 & 4.54 & 4.96789672457306 & -0.427896724573057 \tabularnewline
29 & 4.55 & 4.88802587432993 & -0.338025874329933 \tabularnewline
30 & 4.39 & 4.49275772045436 & -0.102757720454365 \tabularnewline
31 & 4.21 & 4.34248652067432 & -0.132486520674322 \tabularnewline
32 & 4 & 4.12740095081224 & -0.127400950812239 \tabularnewline
33 & 3.67 & 3.82073498898702 & -0.150734988987023 \tabularnewline
34 & 3.6 & 3.40549881274811 & 0.194501187251888 \tabularnewline
35 & 3.53 & 3.44174311406491 & 0.0882568859350923 \tabularnewline
36 & 3.35 & 3.13514510305551 & 0.21485489694449 \tabularnewline
37 & 3.1 & 3.03809349017706 & 0.0619065098229372 \tabularnewline
38 & 2.89 & 3.16345939733002 & -0.273459397330024 \tabularnewline
39 & 2.97 & 2.72233220049034 & 0.247667799509655 \tabularnewline
40 & 3.03 & 3.00936284946455 & 0.0206371505354483 \tabularnewline
41 & 2.71 & 3.21865341840654 & -0.508653418406536 \tabularnewline
42 & 2.44 & 2.49467932795565 & -0.0546793279556463 \tabularnewline
43 & 2.6 & 2.20838202888369 & 0.391617971116307 \tabularnewline
44 & 2.93 & 2.51175814139021 & 0.418241858609791 \tabularnewline
45 & 2.86 & 2.97004773270316 & -0.110047732703156 \tabularnewline
46 & 2.88 & 2.91549965762313 & -0.035499657623133 \tabularnewline
47 & 3 & 2.92761198302832 & 0.0723880169716775 \tabularnewline
48 & 2.9 & 2.8061223781212 & 0.0938776218787987 \tabularnewline
49 & 2.64 & 2.72144927340619 & -0.0814492734061854 \tabularnewline
50 & 2.75 & 2.76114890987356 & -0.0111489098735649 \tabularnewline
51 & 2.7 & 2.79358738248179 & -0.0935873824817892 \tabularnewline
52 & 2.87 & 2.79310691386389 & 0.0768930861361143 \tabularnewline
53 & 3.03 & 3.0691463444185 & -0.0391463444184956 \tabularnewline
54 & 3.14 & 3.07737561527735 & 0.0626243847226551 \tabularnewline
55 & 3.02 & 3.25342298742656 & -0.233422987426561 \tabularnewline
56 & 2.86 & 3.04450068637003 & -0.184500686370026 \tabularnewline
57 & 3.07 & 2.70380166157492 & 0.366198338425084 \tabularnewline
58 & 2.93 & 3.08422311432215 & -0.154223114322146 \tabularnewline
59 & 2.83 & 2.94644990335422 & -0.116449903354222 \tabularnewline
60 & 2.72 & 2.52389545895523 & 0.196104541044773 \tabularnewline
61 & 2.73 & 2.42559494673312 & 0.304405053266877 \tabularnewline
62 & 2.72 & 2.89411754220865 & -0.174117542208651 \tabularnewline
63 & 2.77 & 2.77582819179425 & -0.0058281917942451 \tabularnewline
64 & 2.61 & 2.91250693751264 & -0.302506937512643 \tabularnewline
65 & 2.47 & 2.71608508450967 & -0.246085084509671 \tabularnewline
66 & 2.3 & 2.34152392527821 & -0.0415239252782134 \tabularnewline
67 & 2.38 & 2.14583543321028 & 0.234164566789723 \tabularnewline
68 & 2.43 & 2.31209210332012 & 0.117907896679879 \tabularnewline
69 & 2.39 & 2.37251529055661 & 0.017484709443393 \tabularnewline
70 & 2.6 & 2.31594131076508 & 0.284058689234917 \tabularnewline
71 & 2.84 & 2.69081372897927 & 0.149186271020734 \tabularnewline
72 & 2.87 & 2.76289995678558 & 0.107100043214416 \tabularnewline
73 & 2.92 & 2.781510794924 & 0.138489205075996 \tabularnewline
74 & 3.08 & 3.17140137610073 & -0.0914013761007335 \tabularnewline
75 & 3.33 & 3.29602638496385 & 0.0339736150361536 \tabularnewline
76 & 3.48 & 3.60909137424452 & -0.129091374244525 \tabularnewline
77 & 3.57 & 3.81667848828993 & -0.246678488289928 \tabularnewline
78 & 3.66 & 3.70268267720468 & -0.0426826772046751 \tabularnewline
79 & 3.77 & 3.77336409621469 & -0.0033640962146877 \tabularnewline
80 & 3.75 & 3.85473147321074 & -0.10473147321074 \tabularnewline
81 & 3.75 & 3.75150618412767 & -0.0015061841276709 \tabularnewline
82 & 3.81 & 3.74256155719096 & 0.0674384428090424 \tabularnewline
83 & 3.82 & 3.85673325758296 & -0.0367332575829571 \tabularnewline
84 & 3.89 & 3.62647980682169 & 0.263520193178308 \tabularnewline
85 & 4.05 & 3.72523058488877 & 0.324769415111225 \tabularnewline
86 & 4.1 & 4.27570244193343 & -0.175702441933433 \tabularnewline
87 & 4.07 & 4.31469938879119 & -0.244699388791188 \tabularnewline
88 & 4.26 & 4.22143540040574 & 0.0385645995942632 \tabularnewline
89 & 4.4 & 4.50126788175432 & -0.101267881754323 \tabularnewline
90 & 4.61 & 4.53138391202895 & 0.0786160879710467 \tabularnewline
91 & 4.63 & 4.75969043664461 & -0.129690436644611 \tabularnewline
92 & 4.48 & 4.70809939845644 & -0.22809939845644 \tabularnewline
93 & 4.46 & 4.44221937723124 & 0.0177806227687629 \tabularnewline
94 & 4.45 & 4.40447034679594 & 0.0455296532040625 \tabularnewline
95 & 4.32 & 4.42679877929415 & -0.106798779294147 \tabularnewline
96 & 4.52 & 4.07033720459649 & 0.449662795403507 \tabularnewline
97 & 4.21 & 4.33009069888729 & -0.120090698887294 \tabularnewline
98 & 3.97 & 4.22988838171736 & -0.259888381717364 \tabularnewline
99 & 4.12 & 3.9502126332381 & 0.169787366761899 \tabularnewline
100 & 4.5 & 4.19745669038361 & 0.302543309616387 \tabularnewline
101 & 4.73 & 4.75235871262396 & -0.0223587126239559 \tabularnewline
102 & 5.26 & 4.95398366143489 & 0.30601633856511 \tabularnewline
103 & 5.2 & 5.54669703281501 & -0.346697032815014 \tabularnewline
104 & 4.94 & 5.3767609495731 & -0.436760949573101 \tabularnewline
105 & 4.95 & 4.94516209523332 & 0.00483790476667689 \tabularnewline
106 & 4.52 & 4.89237680637264 & -0.372376806372637 \tabularnewline
107 & 3.85 & 4.34026388496181 & -0.490263884961809 \tabularnewline
108 & 3.41 & 3.34685540556038 & 0.0631445944396218 \tabularnewline
109 & 2.95 & 2.69643510969163 & 0.253564890308374 \tabularnewline
110 & 2.68 & 2.57196747987753 & 0.108032520122472 \tabularnewline
111 & 2.53 & 2.47222072894606 & 0.0577792710539433 \tabularnewline
112 & 2.44 & 2.38981134519681 & 0.0501886548031889 \tabularnewline
113 & 2.16 & 2.33811090317119 & -0.178110903171188 \tabularnewline
114 & 2.2 & 2.01740772988735 & 0.182592270112646 \tabularnewline
115 & 2.1 & 1.97121667606911 & 0.12878332393089 \tabularnewline
116 & 2.29 & 1.95800611289755 & 0.331993887102453 \tabularnewline
117 & 2.03 & 2.32288245511187 & -0.292882455111869 \tabularnewline
118 & 2.05 & 1.89843685617811 & 0.151563143821891 \tabularnewline
119 & 1.94 & 1.96313047820039 & -0.0231304782003925 \tabularnewline
120 & 1.87 & 1.79604797641295 & 0.0739520235870541 \tabularnewline
121 & 1.89 & 1.52910623321984 & 0.360893766780161 \tabularnewline
122 & 1.94 & 1.88845928965493 & 0.0515407103450678 \tabularnewline
123 & 1.79 & 2.10971182493531 & -0.31971182493531 \tabularnewline
124 & 1.71 & 1.90315196454926 & -0.193151964549263 \tabularnewline
125 & 1.66 & 1.7250526090442 & -0.0650526090442045 \tabularnewline
126 & 1.74 & 1.70420063546927 & 0.0357993645307328 \tabularnewline
127 & 1.83 & 1.62141060788522 & 0.208589392114776 \tabularnewline
128 & 1.64 & 1.83471101587233 & -0.19471101587233 \tabularnewline
129 & 1.69 & 1.57663165731026 & 0.113368342689738 \tabularnewline
130 & 1.78 & 1.64627569984924 & 0.133724300150756 \tabularnewline
131 & 1.89 & 1.75480103118923 & 0.135198968810766 \tabularnewline
132 & 1.95 & 1.88352604083847 & 0.0664739591615251 \tabularnewline
133 & 2.05 & 1.77745718847524 & 0.272542811524765 \tabularnewline
134 & 2.24 & 2.13030862946077 & 0.109691370539229 \tabularnewline
135 & 2.38 & 2.4961099121968 & -0.116109912196803 \tabularnewline
136 & 2.53 & 2.6989786367314 & -0.168978636731399 \tabularnewline
137 & 2.36 & 2.77836763636126 & -0.418367636361264 \tabularnewline
138 & 2.22 & 2.52226035365533 & -0.302260353655335 \tabularnewline
139 & 2.12 & 2.0825576221324 & 0.0374423778675981 \tabularnewline
140 & 1.75 & 1.96272708857666 & -0.212727088576665 \tabularnewline
141 & 1.76 & 1.57046180873363 & 0.189538191266367 \tabularnewline
142 & 1.81 & 1.59564431108889 & 0.214355688911113 \tabularnewline
143 & 1.71 & 1.69588535073744 & 0.0141146492625623 \tabularnewline
144 & 1.74 & 1.57620992455523 & 0.163790075444774 \tabularnewline
145 & 1.48 & 1.48650881754583 & -0.00650881754583255 \tabularnewline
146 & 1.24 & 1.36258236229749 & -0.122582362297495 \tabularnewline
147 & 1.16 & 1.1900924152013 & -0.0300924152012998 \tabularnewline
148 & 1.11 & 1.19527312123142 & -0.0852731212314246 \tabularnewline
149 & 0.98 & 1.0913279535301 & -0.111327953530101 \tabularnewline
150 & 0.94 & 1.01809344420984 & -0.0780934442098431 \tabularnewline
151 & 0.65 & 0.80208796355857 & -0.15208796355857 \tabularnewline
152 & 0.42 & 0.395606602487347 & 0.024393397512653 \tabularnewline
153 & 0.41 & 0.264774590852937 & 0.145225409147063 \tabularnewline
154 & 0.4 & 0.242115597972844 & 0.157884402027156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193932&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]4.7[/C][C]4.90931356837607[/C][C]-0.209313568376067[/C][/ROW]
[ROW][C]14[/C][C]4.73[/C][C]4.67056656418675[/C][C]0.0594334358132533[/C][/ROW]
[ROW][C]15[/C][C]4.57[/C][C]4.5340496643026[/C][C]0.035950335697402[/C][/ROW]
[ROW][C]16[/C][C]4.61[/C][C]4.61351560223803[/C][C]-0.00351560223802849[/C][/ROW]
[ROW][C]17[/C][C]4.69[/C][C]4.70997720640782[/C][C]-0.0199772064078152[/C][/ROW]
[ROW][C]18[/C][C]4.53[/C][C]4.52480742536258[/C][C]0.00519257463741774[/C][/ROW]
[ROW][C]19[/C][C]4.55[/C][C]4.43166938720862[/C][C]0.118330612791376[/C][/ROW]
[ROW][C]20[/C][C]4.31[/C][C]4.55400170402283[/C][C]-0.244001704022828[/C][/ROW]
[ROW][C]21[/C][C]4.03[/C][C]4.15759431235348[/C][C]-0.127594312353484[/C][/ROW]
[ROW][C]22[/C][C]3.72[/C][C]3.79482108952395[/C][C]-0.0748210895239509[/C][/ROW]
[ROW][C]23[/C][C]3.64[/C][C]3.48910414516911[/C][C]0.150895854830892[/C][/ROW]
[ROW][C]24[/C][C]3.81[/C][C]3.13896210689787[/C][C]0.671037893102132[/C][/ROW]
[ROW][C]25[/C][C]3.95[/C][C]3.62963238959929[/C][C]0.320367610400714[/C][/ROW]
[ROW][C]26[/C][C]4.26[/C][C]4.27087395236728[/C][C]-0.0108739523672803[/C][/ROW]
[ROW][C]27[/C][C]4.55[/C][C]4.41419396596922[/C][C]0.135806034030784[/C][/ROW]
[ROW][C]28[/C][C]4.54[/C][C]4.96789672457306[/C][C]-0.427896724573057[/C][/ROW]
[ROW][C]29[/C][C]4.55[/C][C]4.88802587432993[/C][C]-0.338025874329933[/C][/ROW]
[ROW][C]30[/C][C]4.39[/C][C]4.49275772045436[/C][C]-0.102757720454365[/C][/ROW]
[ROW][C]31[/C][C]4.21[/C][C]4.34248652067432[/C][C]-0.132486520674322[/C][/ROW]
[ROW][C]32[/C][C]4[/C][C]4.12740095081224[/C][C]-0.127400950812239[/C][/ROW]
[ROW][C]33[/C][C]3.67[/C][C]3.82073498898702[/C][C]-0.150734988987023[/C][/ROW]
[ROW][C]34[/C][C]3.6[/C][C]3.40549881274811[/C][C]0.194501187251888[/C][/ROW]
[ROW][C]35[/C][C]3.53[/C][C]3.44174311406491[/C][C]0.0882568859350923[/C][/ROW]
[ROW][C]36[/C][C]3.35[/C][C]3.13514510305551[/C][C]0.21485489694449[/C][/ROW]
[ROW][C]37[/C][C]3.1[/C][C]3.03809349017706[/C][C]0.0619065098229372[/C][/ROW]
[ROW][C]38[/C][C]2.89[/C][C]3.16345939733002[/C][C]-0.273459397330024[/C][/ROW]
[ROW][C]39[/C][C]2.97[/C][C]2.72233220049034[/C][C]0.247667799509655[/C][/ROW]
[ROW][C]40[/C][C]3.03[/C][C]3.00936284946455[/C][C]0.0206371505354483[/C][/ROW]
[ROW][C]41[/C][C]2.71[/C][C]3.21865341840654[/C][C]-0.508653418406536[/C][/ROW]
[ROW][C]42[/C][C]2.44[/C][C]2.49467932795565[/C][C]-0.0546793279556463[/C][/ROW]
[ROW][C]43[/C][C]2.6[/C][C]2.20838202888369[/C][C]0.391617971116307[/C][/ROW]
[ROW][C]44[/C][C]2.93[/C][C]2.51175814139021[/C][C]0.418241858609791[/C][/ROW]
[ROW][C]45[/C][C]2.86[/C][C]2.97004773270316[/C][C]-0.110047732703156[/C][/ROW]
[ROW][C]46[/C][C]2.88[/C][C]2.91549965762313[/C][C]-0.035499657623133[/C][/ROW]
[ROW][C]47[/C][C]3[/C][C]2.92761198302832[/C][C]0.0723880169716775[/C][/ROW]
[ROW][C]48[/C][C]2.9[/C][C]2.8061223781212[/C][C]0.0938776218787987[/C][/ROW]
[ROW][C]49[/C][C]2.64[/C][C]2.72144927340619[/C][C]-0.0814492734061854[/C][/ROW]
[ROW][C]50[/C][C]2.75[/C][C]2.76114890987356[/C][C]-0.0111489098735649[/C][/ROW]
[ROW][C]51[/C][C]2.7[/C][C]2.79358738248179[/C][C]-0.0935873824817892[/C][/ROW]
[ROW][C]52[/C][C]2.87[/C][C]2.79310691386389[/C][C]0.0768930861361143[/C][/ROW]
[ROW][C]53[/C][C]3.03[/C][C]3.0691463444185[/C][C]-0.0391463444184956[/C][/ROW]
[ROW][C]54[/C][C]3.14[/C][C]3.07737561527735[/C][C]0.0626243847226551[/C][/ROW]
[ROW][C]55[/C][C]3.02[/C][C]3.25342298742656[/C][C]-0.233422987426561[/C][/ROW]
[ROW][C]56[/C][C]2.86[/C][C]3.04450068637003[/C][C]-0.184500686370026[/C][/ROW]
[ROW][C]57[/C][C]3.07[/C][C]2.70380166157492[/C][C]0.366198338425084[/C][/ROW]
[ROW][C]58[/C][C]2.93[/C][C]3.08422311432215[/C][C]-0.154223114322146[/C][/ROW]
[ROW][C]59[/C][C]2.83[/C][C]2.94644990335422[/C][C]-0.116449903354222[/C][/ROW]
[ROW][C]60[/C][C]2.72[/C][C]2.52389545895523[/C][C]0.196104541044773[/C][/ROW]
[ROW][C]61[/C][C]2.73[/C][C]2.42559494673312[/C][C]0.304405053266877[/C][/ROW]
[ROW][C]62[/C][C]2.72[/C][C]2.89411754220865[/C][C]-0.174117542208651[/C][/ROW]
[ROW][C]63[/C][C]2.77[/C][C]2.77582819179425[/C][C]-0.0058281917942451[/C][/ROW]
[ROW][C]64[/C][C]2.61[/C][C]2.91250693751264[/C][C]-0.302506937512643[/C][/ROW]
[ROW][C]65[/C][C]2.47[/C][C]2.71608508450967[/C][C]-0.246085084509671[/C][/ROW]
[ROW][C]66[/C][C]2.3[/C][C]2.34152392527821[/C][C]-0.0415239252782134[/C][/ROW]
[ROW][C]67[/C][C]2.38[/C][C]2.14583543321028[/C][C]0.234164566789723[/C][/ROW]
[ROW][C]68[/C][C]2.43[/C][C]2.31209210332012[/C][C]0.117907896679879[/C][/ROW]
[ROW][C]69[/C][C]2.39[/C][C]2.37251529055661[/C][C]0.017484709443393[/C][/ROW]
[ROW][C]70[/C][C]2.6[/C][C]2.31594131076508[/C][C]0.284058689234917[/C][/ROW]
[ROW][C]71[/C][C]2.84[/C][C]2.69081372897927[/C][C]0.149186271020734[/C][/ROW]
[ROW][C]72[/C][C]2.87[/C][C]2.76289995678558[/C][C]0.107100043214416[/C][/ROW]
[ROW][C]73[/C][C]2.92[/C][C]2.781510794924[/C][C]0.138489205075996[/C][/ROW]
[ROW][C]74[/C][C]3.08[/C][C]3.17140137610073[/C][C]-0.0914013761007335[/C][/ROW]
[ROW][C]75[/C][C]3.33[/C][C]3.29602638496385[/C][C]0.0339736150361536[/C][/ROW]
[ROW][C]76[/C][C]3.48[/C][C]3.60909137424452[/C][C]-0.129091374244525[/C][/ROW]
[ROW][C]77[/C][C]3.57[/C][C]3.81667848828993[/C][C]-0.246678488289928[/C][/ROW]
[ROW][C]78[/C][C]3.66[/C][C]3.70268267720468[/C][C]-0.0426826772046751[/C][/ROW]
[ROW][C]79[/C][C]3.77[/C][C]3.77336409621469[/C][C]-0.0033640962146877[/C][/ROW]
[ROW][C]80[/C][C]3.75[/C][C]3.85473147321074[/C][C]-0.10473147321074[/C][/ROW]
[ROW][C]81[/C][C]3.75[/C][C]3.75150618412767[/C][C]-0.0015061841276709[/C][/ROW]
[ROW][C]82[/C][C]3.81[/C][C]3.74256155719096[/C][C]0.0674384428090424[/C][/ROW]
[ROW][C]83[/C][C]3.82[/C][C]3.85673325758296[/C][C]-0.0367332575829571[/C][/ROW]
[ROW][C]84[/C][C]3.89[/C][C]3.62647980682169[/C][C]0.263520193178308[/C][/ROW]
[ROW][C]85[/C][C]4.05[/C][C]3.72523058488877[/C][C]0.324769415111225[/C][/ROW]
[ROW][C]86[/C][C]4.1[/C][C]4.27570244193343[/C][C]-0.175702441933433[/C][/ROW]
[ROW][C]87[/C][C]4.07[/C][C]4.31469938879119[/C][C]-0.244699388791188[/C][/ROW]
[ROW][C]88[/C][C]4.26[/C][C]4.22143540040574[/C][C]0.0385645995942632[/C][/ROW]
[ROW][C]89[/C][C]4.4[/C][C]4.50126788175432[/C][C]-0.101267881754323[/C][/ROW]
[ROW][C]90[/C][C]4.61[/C][C]4.53138391202895[/C][C]0.0786160879710467[/C][/ROW]
[ROW][C]91[/C][C]4.63[/C][C]4.75969043664461[/C][C]-0.129690436644611[/C][/ROW]
[ROW][C]92[/C][C]4.48[/C][C]4.70809939845644[/C][C]-0.22809939845644[/C][/ROW]
[ROW][C]93[/C][C]4.46[/C][C]4.44221937723124[/C][C]0.0177806227687629[/C][/ROW]
[ROW][C]94[/C][C]4.45[/C][C]4.40447034679594[/C][C]0.0455296532040625[/C][/ROW]
[ROW][C]95[/C][C]4.32[/C][C]4.42679877929415[/C][C]-0.106798779294147[/C][/ROW]
[ROW][C]96[/C][C]4.52[/C][C]4.07033720459649[/C][C]0.449662795403507[/C][/ROW]
[ROW][C]97[/C][C]4.21[/C][C]4.33009069888729[/C][C]-0.120090698887294[/C][/ROW]
[ROW][C]98[/C][C]3.97[/C][C]4.22988838171736[/C][C]-0.259888381717364[/C][/ROW]
[ROW][C]99[/C][C]4.12[/C][C]3.9502126332381[/C][C]0.169787366761899[/C][/ROW]
[ROW][C]100[/C][C]4.5[/C][C]4.19745669038361[/C][C]0.302543309616387[/C][/ROW]
[ROW][C]101[/C][C]4.73[/C][C]4.75235871262396[/C][C]-0.0223587126239559[/C][/ROW]
[ROW][C]102[/C][C]5.26[/C][C]4.95398366143489[/C][C]0.30601633856511[/C][/ROW]
[ROW][C]103[/C][C]5.2[/C][C]5.54669703281501[/C][C]-0.346697032815014[/C][/ROW]
[ROW][C]104[/C][C]4.94[/C][C]5.3767609495731[/C][C]-0.436760949573101[/C][/ROW]
[ROW][C]105[/C][C]4.95[/C][C]4.94516209523332[/C][C]0.00483790476667689[/C][/ROW]
[ROW][C]106[/C][C]4.52[/C][C]4.89237680637264[/C][C]-0.372376806372637[/C][/ROW]
[ROW][C]107[/C][C]3.85[/C][C]4.34026388496181[/C][C]-0.490263884961809[/C][/ROW]
[ROW][C]108[/C][C]3.41[/C][C]3.34685540556038[/C][C]0.0631445944396218[/C][/ROW]
[ROW][C]109[/C][C]2.95[/C][C]2.69643510969163[/C][C]0.253564890308374[/C][/ROW]
[ROW][C]110[/C][C]2.68[/C][C]2.57196747987753[/C][C]0.108032520122472[/C][/ROW]
[ROW][C]111[/C][C]2.53[/C][C]2.47222072894606[/C][C]0.0577792710539433[/C][/ROW]
[ROW][C]112[/C][C]2.44[/C][C]2.38981134519681[/C][C]0.0501886548031889[/C][/ROW]
[ROW][C]113[/C][C]2.16[/C][C]2.33811090317119[/C][C]-0.178110903171188[/C][/ROW]
[ROW][C]114[/C][C]2.2[/C][C]2.01740772988735[/C][C]0.182592270112646[/C][/ROW]
[ROW][C]115[/C][C]2.1[/C][C]1.97121667606911[/C][C]0.12878332393089[/C][/ROW]
[ROW][C]116[/C][C]2.29[/C][C]1.95800611289755[/C][C]0.331993887102453[/C][/ROW]
[ROW][C]117[/C][C]2.03[/C][C]2.32288245511187[/C][C]-0.292882455111869[/C][/ROW]
[ROW][C]118[/C][C]2.05[/C][C]1.89843685617811[/C][C]0.151563143821891[/C][/ROW]
[ROW][C]119[/C][C]1.94[/C][C]1.96313047820039[/C][C]-0.0231304782003925[/C][/ROW]
[ROW][C]120[/C][C]1.87[/C][C]1.79604797641295[/C][C]0.0739520235870541[/C][/ROW]
[ROW][C]121[/C][C]1.89[/C][C]1.52910623321984[/C][C]0.360893766780161[/C][/ROW]
[ROW][C]122[/C][C]1.94[/C][C]1.88845928965493[/C][C]0.0515407103450678[/C][/ROW]
[ROW][C]123[/C][C]1.79[/C][C]2.10971182493531[/C][C]-0.31971182493531[/C][/ROW]
[ROW][C]124[/C][C]1.71[/C][C]1.90315196454926[/C][C]-0.193151964549263[/C][/ROW]
[ROW][C]125[/C][C]1.66[/C][C]1.7250526090442[/C][C]-0.0650526090442045[/C][/ROW]
[ROW][C]126[/C][C]1.74[/C][C]1.70420063546927[/C][C]0.0357993645307328[/C][/ROW]
[ROW][C]127[/C][C]1.83[/C][C]1.62141060788522[/C][C]0.208589392114776[/C][/ROW]
[ROW][C]128[/C][C]1.64[/C][C]1.83471101587233[/C][C]-0.19471101587233[/C][/ROW]
[ROW][C]129[/C][C]1.69[/C][C]1.57663165731026[/C][C]0.113368342689738[/C][/ROW]
[ROW][C]130[/C][C]1.78[/C][C]1.64627569984924[/C][C]0.133724300150756[/C][/ROW]
[ROW][C]131[/C][C]1.89[/C][C]1.75480103118923[/C][C]0.135198968810766[/C][/ROW]
[ROW][C]132[/C][C]1.95[/C][C]1.88352604083847[/C][C]0.0664739591615251[/C][/ROW]
[ROW][C]133[/C][C]2.05[/C][C]1.77745718847524[/C][C]0.272542811524765[/C][/ROW]
[ROW][C]134[/C][C]2.24[/C][C]2.13030862946077[/C][C]0.109691370539229[/C][/ROW]
[ROW][C]135[/C][C]2.38[/C][C]2.4961099121968[/C][C]-0.116109912196803[/C][/ROW]
[ROW][C]136[/C][C]2.53[/C][C]2.6989786367314[/C][C]-0.168978636731399[/C][/ROW]
[ROW][C]137[/C][C]2.36[/C][C]2.77836763636126[/C][C]-0.418367636361264[/C][/ROW]
[ROW][C]138[/C][C]2.22[/C][C]2.52226035365533[/C][C]-0.302260353655335[/C][/ROW]
[ROW][C]139[/C][C]2.12[/C][C]2.0825576221324[/C][C]0.0374423778675981[/C][/ROW]
[ROW][C]140[/C][C]1.75[/C][C]1.96272708857666[/C][C]-0.212727088576665[/C][/ROW]
[ROW][C]141[/C][C]1.76[/C][C]1.57046180873363[/C][C]0.189538191266367[/C][/ROW]
[ROW][C]142[/C][C]1.81[/C][C]1.59564431108889[/C][C]0.214355688911113[/C][/ROW]
[ROW][C]143[/C][C]1.71[/C][C]1.69588535073744[/C][C]0.0141146492625623[/C][/ROW]
[ROW][C]144[/C][C]1.74[/C][C]1.57620992455523[/C][C]0.163790075444774[/C][/ROW]
[ROW][C]145[/C][C]1.48[/C][C]1.48650881754583[/C][C]-0.00650881754583255[/C][/ROW]
[ROW][C]146[/C][C]1.24[/C][C]1.36258236229749[/C][C]-0.122582362297495[/C][/ROW]
[ROW][C]147[/C][C]1.16[/C][C]1.1900924152013[/C][C]-0.0300924152012998[/C][/ROW]
[ROW][C]148[/C][C]1.11[/C][C]1.19527312123142[/C][C]-0.0852731212314246[/C][/ROW]
[ROW][C]149[/C][C]0.98[/C][C]1.0913279535301[/C][C]-0.111327953530101[/C][/ROW]
[ROW][C]150[/C][C]0.94[/C][C]1.01809344420984[/C][C]-0.0780934442098431[/C][/ROW]
[ROW][C]151[/C][C]0.65[/C][C]0.80208796355857[/C][C]-0.15208796355857[/C][/ROW]
[ROW][C]152[/C][C]0.42[/C][C]0.395606602487347[/C][C]0.024393397512653[/C][/ROW]
[ROW][C]153[/C][C]0.41[/C][C]0.264774590852937[/C][C]0.145225409147063[/C][/ROW]
[ROW][C]154[/C][C]0.4[/C][C]0.242115597972844[/C][C]0.157884402027156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=193932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193932&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	4.7	4.90931356837607	-0.209313568376067
14	4.73	4.67056656418675	0.0594334358132533
15	4.57	4.5340496643026	0.035950335697402
16	4.61	4.61351560223803	-0.00351560223802849
17	4.69	4.70997720640782	-0.0199772064078152
18	4.53	4.52480742536258	0.00519257463741774
19	4.55	4.43166938720862	0.118330612791376
20	4.31	4.55400170402283	-0.244001704022828
21	4.03	4.15759431235348	-0.127594312353484
22	3.72	3.79482108952395	-0.0748210895239509
23	3.64	3.48910414516911	0.150895854830892
24	3.81	3.13896210689787	0.671037893102132
25	3.95	3.62963238959929	0.320367610400714
26	4.26	4.27087395236728	-0.0108739523672803
27	4.55	4.41419396596922	0.135806034030784
28	4.54	4.96789672457306	-0.427896724573057
29	4.55	4.88802587432993	-0.338025874329933
30	4.39	4.49275772045436	-0.102757720454365
31	4.21	4.34248652067432	-0.132486520674322
32	4	4.12740095081224	-0.127400950812239
33	3.67	3.82073498898702	-0.150734988987023
34	3.6	3.40549881274811	0.194501187251888
35	3.53	3.44174311406491	0.0882568859350923
36	3.35	3.13514510305551	0.21485489694449
37	3.1	3.03809349017706	0.0619065098229372
38	2.89	3.16345939733002	-0.273459397330024
39	2.97	2.72233220049034	0.247667799509655
40	3.03	3.00936284946455	0.0206371505354483
41	2.71	3.21865341840654	-0.508653418406536
42	2.44	2.49467932795565	-0.0546793279556463
43	2.6	2.20838202888369	0.391617971116307
44	2.93	2.51175814139021	0.418241858609791
45	2.86	2.97004773270316	-0.110047732703156
46	2.88	2.91549965762313	-0.035499657623133
47	3	2.92761198302832	0.0723880169716775
48	2.9	2.8061223781212	0.0938776218787987
49	2.64	2.72144927340619	-0.0814492734061854
50	2.75	2.76114890987356	-0.0111489098735649
51	2.7	2.79358738248179	-0.0935873824817892
52	2.87	2.79310691386389	0.0768930861361143
53	3.03	3.0691463444185	-0.0391463444184956
54	3.14	3.07737561527735	0.0626243847226551
55	3.02	3.25342298742656	-0.233422987426561
56	2.86	3.04450068637003	-0.184500686370026
57	3.07	2.70380166157492	0.366198338425084
58	2.93	3.08422311432215	-0.154223114322146
59	2.83	2.94644990335422	-0.116449903354222
60	2.72	2.52389545895523	0.196104541044773
61	2.73	2.42559494673312	0.304405053266877
62	2.72	2.89411754220865	-0.174117542208651
63	2.77	2.77582819179425	-0.0058281917942451
64	2.61	2.91250693751264	-0.302506937512643
65	2.47	2.71608508450967	-0.246085084509671
66	2.3	2.34152392527821	-0.0415239252782134
67	2.38	2.14583543321028	0.234164566789723
68	2.43	2.31209210332012	0.117907896679879
69	2.39	2.37251529055661	0.017484709443393
70	2.6	2.31594131076508	0.284058689234917
71	2.84	2.69081372897927	0.149186271020734
72	2.87	2.76289995678558	0.107100043214416
73	2.92	2.781510794924	0.138489205075996
74	3.08	3.17140137610073	-0.0914013761007335
75	3.33	3.29602638496385	0.0339736150361536
76	3.48	3.60909137424452	-0.129091374244525
77	3.57	3.81667848828993	-0.246678488289928
78	3.66	3.70268267720468	-0.0426826772046751
79	3.77	3.77336409621469	-0.0033640962146877
80	3.75	3.85473147321074	-0.10473147321074
81	3.75	3.75150618412767	-0.0015061841276709
82	3.81	3.74256155719096	0.0674384428090424
83	3.82	3.85673325758296	-0.0367332575829571
84	3.89	3.62647980682169	0.263520193178308
85	4.05	3.72523058488877	0.324769415111225
86	4.1	4.27570244193343	-0.175702441933433
87	4.07	4.31469938879119	-0.244699388791188
88	4.26	4.22143540040574	0.0385645995942632
89	4.4	4.50126788175432	-0.101267881754323
90	4.61	4.53138391202895	0.0786160879710467
91	4.63	4.75969043664461	-0.129690436644611
92	4.48	4.70809939845644	-0.22809939845644
93	4.46	4.44221937723124	0.0177806227687629
94	4.45	4.40447034679594	0.0455296532040625
95	4.32	4.42679877929415	-0.106798779294147
96	4.52	4.07033720459649	0.449662795403507
97	4.21	4.33009069888729	-0.120090698887294
98	3.97	4.22988838171736	-0.259888381717364
99	4.12	3.9502126332381	0.169787366761899
100	4.5	4.19745669038361	0.302543309616387
101	4.73	4.75235871262396	-0.0223587126239559
102	5.26	4.95398366143489	0.30601633856511
103	5.2	5.54669703281501	-0.346697032815014
104	4.94	5.3767609495731	-0.436760949573101
105	4.95	4.94516209523332	0.00483790476667689
106	4.52	4.89237680637264	-0.372376806372637
107	3.85	4.34026388496181	-0.490263884961809
108	3.41	3.34685540556038	0.0631445944396218
109	2.95	2.69643510969163	0.253564890308374
110	2.68	2.57196747987753	0.108032520122472
111	2.53	2.47222072894606	0.0577792710539433
112	2.44	2.38981134519681	0.0501886548031889
113	2.16	2.33811090317119	-0.178110903171188
114	2.2	2.01740772988735	0.182592270112646
115	2.1	1.97121667606911	0.12878332393089
116	2.29	1.95800611289755	0.331993887102453
117	2.03	2.32288245511187	-0.292882455111869
118	2.05	1.89843685617811	0.151563143821891
119	1.94	1.96313047820039	-0.0231304782003925
120	1.87	1.79604797641295	0.0739520235870541
121	1.89	1.52910623321984	0.360893766780161
122	1.94	1.88845928965493	0.0515407103450678
123	1.79	2.10971182493531	-0.31971182493531
124	1.71	1.90315196454926	-0.193151964549263
125	1.66	1.7250526090442	-0.0650526090442045
126	1.74	1.70420063546927	0.0357993645307328
127	1.83	1.62141060788522	0.208589392114776
128	1.64	1.83471101587233	-0.19471101587233
129	1.69	1.57663165731026	0.113368342689738
130	1.78	1.64627569984924	0.133724300150756
131	1.89	1.75480103118923	0.135198968810766
132	1.95	1.88352604083847	0.0664739591615251
133	2.05	1.77745718847524	0.272542811524765
134	2.24	2.13030862946077	0.109691370539229
135	2.38	2.4961099121968	-0.116109912196803
136	2.53	2.6989786367314	-0.168978636731399
137	2.36	2.77836763636126	-0.418367636361264
138	2.22	2.52226035365533	-0.302260353655335
139	2.12	2.0825576221324	0.0374423778675981
140	1.75	1.96272708857666	-0.212727088576665
141	1.76	1.57046180873363	0.189538191266367
142	1.81	1.59564431108889	0.214355688911113
143	1.71	1.69588535073744	0.0141146492625623
144	1.74	1.57620992455523	0.163790075444774
145	1.48	1.48650881754583	-0.00650881754583255
146	1.24	1.36258236229749	-0.122582362297495
147	1.16	1.1900924152013	-0.0300924152012998
148	1.11	1.19527312123142	-0.0852731212314246
149	0.98	1.0913279535301	-0.111327953530101
150	0.94	1.01809344420984	-0.0780934442098431
151	0.65	0.80208796355857	-0.15208796355857
152	0.42	0.395606602487347	0.024393397512653
153	0.41	0.264774590852937	0.145225409147063
154	0.4	0.242115597972844	0.157884402027156

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
155	0.238215275871042	-0.162203771955309	0.638634323697392
156	0.0802321045158322	-0.584587640802581	0.745051849834245
157	-0.282703392846695	-1.24758768866519	0.682180902971802
158	-0.517927960914044	-1.81570679538249	0.779850873554407
159	-0.625183952852479	-2.28606177739979	1.03569387169483
160	-0.639867629531615	-2.69186731194623	1.412132052883
161	-0.675085854905756	-3.14442540355854	1.79425369374703
162	-0.603486654566728	-3.51487218992313	2.30789888078967
163	-0.682090890977925	-4.05894323319416	2.69476145123831
164	-0.796260873121688	-4.66089294890375	3.06837120266037
165	-0.809975098987915	-5.18373309563744	3.56378289766161
166	-0.896282284532126	-5.79965977306837	4.00709520400412

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
155 & 0.238215275871042 & -0.162203771955309 & 0.638634323697392 \tabularnewline
156 & 0.0802321045158322 & -0.584587640802581 & 0.745051849834245 \tabularnewline
157 & -0.282703392846695 & -1.24758768866519 & 0.682180902971802 \tabularnewline
158 & -0.517927960914044 & -1.81570679538249 & 0.779850873554407 \tabularnewline
159 & -0.625183952852479 & -2.28606177739979 & 1.03569387169483 \tabularnewline
160 & -0.639867629531615 & -2.69186731194623 & 1.412132052883 \tabularnewline
161 & -0.675085854905756 & -3.14442540355854 & 1.79425369374703 \tabularnewline
162 & -0.603486654566728 & -3.51487218992313 & 2.30789888078967 \tabularnewline
163 & -0.682090890977925 & -4.05894323319416 & 2.69476145123831 \tabularnewline
164 & -0.796260873121688 & -4.66089294890375 & 3.06837120266037 \tabularnewline
165 & -0.809975098987915 & -5.18373309563744 & 3.56378289766161 \tabularnewline
166 & -0.896282284532126 & -5.79965977306837 & 4.00709520400412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193932&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]155[/C][C]0.238215275871042[/C][C]-0.162203771955309[/C][C]0.638634323697392[/C][/ROW]
[ROW][C]156[/C][C]0.0802321045158322[/C][C]-0.584587640802581[/C][C]0.745051849834245[/C][/ROW]
[ROW][C]157[/C][C]-0.282703392846695[/C][C]-1.24758768866519[/C][C]0.682180902971802[/C][/ROW]
[ROW][C]158[/C][C]-0.517927960914044[/C][C]-1.81570679538249[/C][C]0.779850873554407[/C][/ROW]
[ROW][C]159[/C][C]-0.625183952852479[/C][C]-2.28606177739979[/C][C]1.03569387169483[/C][/ROW]
[ROW][C]160[/C][C]-0.639867629531615[/C][C]-2.69186731194623[/C][C]1.412132052883[/C][/ROW]
[ROW][C]161[/C][C]-0.675085854905756[/C][C]-3.14442540355854[/C][C]1.79425369374703[/C][/ROW]
[ROW][C]162[/C][C]-0.603486654566728[/C][C]-3.51487218992313[/C][C]2.30789888078967[/C][/ROW]
[ROW][C]163[/C][C]-0.682090890977925[/C][C]-4.05894323319416[/C][C]2.69476145123831[/C][/ROW]
[ROW][C]164[/C][C]-0.796260873121688[/C][C]-4.66089294890375[/C][C]3.06837120266037[/C][/ROW]
[ROW][C]165[/C][C]-0.809975098987915[/C][C]-5.18373309563744[/C][C]3.56378289766161[/C][/ROW]
[ROW][C]166[/C][C]-0.896282284532126[/C][C]-5.79965977306837[/C][C]4.00709520400412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=193932&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193932&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
155	0.238215275871042	-0.162203771955309	0.638634323697392
156	0.0802321045158322	-0.584587640802581	0.745051849834245
157	-0.282703392846695	-1.24758768866519	0.682180902971802
158	-0.517927960914044	-1.81570679538249	0.779850873554407
159	-0.625183952852479	-2.28606177739979	1.03569387169483
160	-0.639867629531615	-2.69186731194623	1.412132052883
161	-0.675085854905756	-3.14442540355854	1.79425369374703
162	-0.603486654566728	-3.51487218992313	2.30789888078967
163	-0.682090890977925	-4.05894323319416	2.69476145123831
164	-0.796260873121688	-4.66089294890375	3.06837120266037
165	-0.809975098987915	-5.18373309563744	3.56378289766161
166	-0.896282284532126	-5.79965977306837	4.00709520400412

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code