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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 23 Nov 2015 19:05:27 +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/2015/Nov/23/t1448305555406eq8polv4sns5.htm/, Retrieved Tue, 14 May 2024 22:03:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283962, Retrieved Tue, 14 May 2024 22:03:33 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

146

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

-       [Exponential Smoothing] [] [2015-11-23 19:05:27] [2c14a834423fb5dcfbeb4b507321e1ef] [Current]
- R PD    [Exponential Smoothing] [] [2016-01-11 20:52:51] [bd4e4aa6178eab1df445b78d9e683708] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283962&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283962&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.236011063337066
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.236011063337066 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283962&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]0.236011063337066[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283962&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	0.236011063337066
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	94.44	95.45	-1.00999999999999
4	94.91	95.8816288260296	-0.971628826029558
5	94.78	96.1223136736294	-1.34231367362938
6	94.51	95.6755127961842	-1.16551279618422
7	94.36	95.1304388818238	-0.770438881823836
8	96.6	94.7986067820884	1.80139321791162
9	96.72	97.4637555109359	-0.74375551093587
10	96.71	97.4082209819371	-0.698220981937098
11	97.44	97.2334331055459	0.206566894454141
12	97.83	98.0121851779562	-0.182185177956228
13	98.92	98.3591874603825	0.560812539617487
14	97.98	99.5815454241904	-1.60154542419041
15	98.76	98.2635629856446	0.496437014355379
16	99.76	99.1607276132825	0.599272386717487
17	99.87	100.3021625265	-0.43216252650025
18	100.09	100.310167389086	-0.220167389086484
19	100.07	100.478205449476	-0.408205449476057
20	99.46	100.361864447285	-0.901864447285206
21	100.4	99.5390144600955	0.860985539904476
22	101.25	100.682216572886	0.567783427113767
23	102.29	101.666219743265	0.6237802567355
24	102.1	102.853438784945	-0.753438784945331
25	105.91	102.485618896151	3.42438110384902
26	108.95	107.103810721742	1.84618927825825
27	110.07	110.579531816425	-0.509531816424982
28	109.92	111.579276670626	-1.65927667062644
29	109.87	111.037669019222	-1.16766901922151
30	110.54	110.712086212369	-0.172086212369294
31	110.79	111.341471962402	-0.551471962402374
32	110.32	111.461318478155	-1.14131847815523
33	110.76	110.72195469052	0.0380453094804523
34	110.24	111.170933804465	-0.930933804465027
35	110.27	110.431223127377	-0.161223127376815
36	110.11	110.42317268565	-0.313172685650073
37	110.39	110.189260467102	0.200739532898325
38	111.05	110.516637217715	0.533362782285195
39	110.85	111.302516735106	-0.452516735106343
40	110.24	110.995717779276	-0.755717779276083
41	108.7	110.207360022606	-1.50736002260639
42	109.93	108.311606380839	1.61839361916071
43	109.53	109.923565179795	-0.393565179795331
44	109.83	109.430679443219	0.399320556780609
45	107.86	109.824923512438	-1.96492351243752
46	104.61	107.391179824891	-2.78117982489114
47	103.61	103.484790617087	0.125209382913013
48	103.11	102.514341416688	0.595658583311931
49	102.59	102.154923432321	0.435076567678635
50	102.91	101.737606315692	1.17239368430775
51	101.94	102.334304195775	-0.394304195775376
52	101.8	101.271244043252	0.52875595674783
53	102.25	101.25603629885	0.99396370114998
54	102.6	101.940622728877	0.65937727112312
55	102.49	102.446243059775	0.0437569402250659
56	102.13	102.346570181766	-0.216570181765832
57	100.76	101.93545722288	-1.17545722288017
58	100.86	100.288036313801	0.571963686198998
59	101.12	100.523026071571	0.596973928428994
60	100.74	100.923918523204	-0.183918523204056
61	99.99	100.500511716975	-0.510511716975273
62	99.39	99.6300253038059	-0.240025303805893
63	99.52	98.9733766766269	0.546623323373126
64	99.21	99.232385828421	-0.0223858284210081
65	99.38	98.9171025252517	0.462897474748317
66	99.37	99.1963514504831	0.17364854951694
67	99.38	99.2273344293015	0.152665570698488
68	99.26	99.273365192977	-0.0133651929770053
69	99.36	99.1502108595708	0.209789140429194
70	99.2	99.2997234176801	-0.0997234176800674
71	98.53	99.1161875878338	-0.586187587833791
72	98.65	98.3078408319141	0.342159168085857
73	99.15	98.5085941810046	0.641405818995381
74	100.17	99.1599730503763	1.01002694962369
75	99.98	100.418350584756	-0.43835058475608
76	100.07	100.124894997133	-0.0548949971333883
77	99.94	100.201939170488	-0.261939170488034
78	100.05	100.010118628332	0.0398813716684714
79	99.13	100.129531073266	-0.99953107326634
80	98.74	98.9736306818263	-0.233630681826313
81	98.64	98.5284912561803	0.111508743819684
82	98.44	98.4548085533806	-0.0148085533805897
83	98.81	98.2513135709507	0.55868642904926
84	98.88	98.7531697491427	0.126830250857338
85	99.63	98.8531030915108	0.776896908489206
86	100.08	99.7864593569866	0.293540643013387
87	100.07	100.305738196277	-0.235738196276856
88	100.55	100.240101373904	0.309898626095617
89	99.98	100.793240878176	-0.813240878175904
90	99.89	100.031307033768	-0.141307033768456
91	99.86	99.9079570104717	-0.0479570104717482
92	99.61	99.8666386254358	-0.256638625435841
93	100.12	99.5560690705534	0.563930929446641
94	100.24	100.199163008861	0.0408369911392583
95	100.1	100.328800990563	-0.228800990562988
96	99.86	100.134801425488	-0.274801425487638
97	97.99	99.8299452488518	-1.83994524885178
98	97.57	97.5256978141883	0.0443021858117163
99	98.28	97.1161536201699	1.16384637983015
100	97.97	98.1008342418346	-0.130834241834563
101	97.99	97.7599559132983	0.23004408670171
102	97.84	97.8342488628152	0.00575113718484488
103	97.33	97.6856061948176	-0.355606194817568
104	96.7	97.0916791986494	-0.391679198649413
105	96.79	96.3692385744892	0.420761425510847
106	96.76	96.5585429259352	0.201457074064805
107	96.23	96.576089024202	-0.346089024202001
108	96.29	95.9644081855908	0.325591814409208

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 94.44 & 95.45 & -1.00999999999999 \tabularnewline
4 & 94.91 & 95.8816288260296 & -0.971628826029558 \tabularnewline
5 & 94.78 & 96.1223136736294 & -1.34231367362938 \tabularnewline
6 & 94.51 & 95.6755127961842 & -1.16551279618422 \tabularnewline
7 & 94.36 & 95.1304388818238 & -0.770438881823836 \tabularnewline
8 & 96.6 & 94.7986067820884 & 1.80139321791162 \tabularnewline
9 & 96.72 & 97.4637555109359 & -0.74375551093587 \tabularnewline
10 & 96.71 & 97.4082209819371 & -0.698220981937098 \tabularnewline
11 & 97.44 & 97.2334331055459 & 0.206566894454141 \tabularnewline
12 & 97.83 & 98.0121851779562 & -0.182185177956228 \tabularnewline
13 & 98.92 & 98.3591874603825 & 0.560812539617487 \tabularnewline
14 & 97.98 & 99.5815454241904 & -1.60154542419041 \tabularnewline
15 & 98.76 & 98.2635629856446 & 0.496437014355379 \tabularnewline
16 & 99.76 & 99.1607276132825 & 0.599272386717487 \tabularnewline
17 & 99.87 & 100.3021625265 & -0.43216252650025 \tabularnewline
18 & 100.09 & 100.310167389086 & -0.220167389086484 \tabularnewline
19 & 100.07 & 100.478205449476 & -0.408205449476057 \tabularnewline
20 & 99.46 & 100.361864447285 & -0.901864447285206 \tabularnewline
21 & 100.4 & 99.5390144600955 & 0.860985539904476 \tabularnewline
22 & 101.25 & 100.682216572886 & 0.567783427113767 \tabularnewline
23 & 102.29 & 101.666219743265 & 0.6237802567355 \tabularnewline
24 & 102.1 & 102.853438784945 & -0.753438784945331 \tabularnewline
25 & 105.91 & 102.485618896151 & 3.42438110384902 \tabularnewline
26 & 108.95 & 107.103810721742 & 1.84618927825825 \tabularnewline
27 & 110.07 & 110.579531816425 & -0.509531816424982 \tabularnewline
28 & 109.92 & 111.579276670626 & -1.65927667062644 \tabularnewline
29 & 109.87 & 111.037669019222 & -1.16766901922151 \tabularnewline
30 & 110.54 & 110.712086212369 & -0.172086212369294 \tabularnewline
31 & 110.79 & 111.341471962402 & -0.551471962402374 \tabularnewline
32 & 110.32 & 111.461318478155 & -1.14131847815523 \tabularnewline
33 & 110.76 & 110.72195469052 & 0.0380453094804523 \tabularnewline
34 & 110.24 & 111.170933804465 & -0.930933804465027 \tabularnewline
35 & 110.27 & 110.431223127377 & -0.161223127376815 \tabularnewline
36 & 110.11 & 110.42317268565 & -0.313172685650073 \tabularnewline
37 & 110.39 & 110.189260467102 & 0.200739532898325 \tabularnewline
38 & 111.05 & 110.516637217715 & 0.533362782285195 \tabularnewline
39 & 110.85 & 111.302516735106 & -0.452516735106343 \tabularnewline
40 & 110.24 & 110.995717779276 & -0.755717779276083 \tabularnewline
41 & 108.7 & 110.207360022606 & -1.50736002260639 \tabularnewline
42 & 109.93 & 108.311606380839 & 1.61839361916071 \tabularnewline
43 & 109.53 & 109.923565179795 & -0.393565179795331 \tabularnewline
44 & 109.83 & 109.430679443219 & 0.399320556780609 \tabularnewline
45 & 107.86 & 109.824923512438 & -1.96492351243752 \tabularnewline
46 & 104.61 & 107.391179824891 & -2.78117982489114 \tabularnewline
47 & 103.61 & 103.484790617087 & 0.125209382913013 \tabularnewline
48 & 103.11 & 102.514341416688 & 0.595658583311931 \tabularnewline
49 & 102.59 & 102.154923432321 & 0.435076567678635 \tabularnewline
50 & 102.91 & 101.737606315692 & 1.17239368430775 \tabularnewline
51 & 101.94 & 102.334304195775 & -0.394304195775376 \tabularnewline
52 & 101.8 & 101.271244043252 & 0.52875595674783 \tabularnewline
53 & 102.25 & 101.25603629885 & 0.99396370114998 \tabularnewline
54 & 102.6 & 101.940622728877 & 0.65937727112312 \tabularnewline
55 & 102.49 & 102.446243059775 & 0.0437569402250659 \tabularnewline
56 & 102.13 & 102.346570181766 & -0.216570181765832 \tabularnewline
57 & 100.76 & 101.93545722288 & -1.17545722288017 \tabularnewline
58 & 100.86 & 100.288036313801 & 0.571963686198998 \tabularnewline
59 & 101.12 & 100.523026071571 & 0.596973928428994 \tabularnewline
60 & 100.74 & 100.923918523204 & -0.183918523204056 \tabularnewline
61 & 99.99 & 100.500511716975 & -0.510511716975273 \tabularnewline
62 & 99.39 & 99.6300253038059 & -0.240025303805893 \tabularnewline
63 & 99.52 & 98.9733766766269 & 0.546623323373126 \tabularnewline
64 & 99.21 & 99.232385828421 & -0.0223858284210081 \tabularnewline
65 & 99.38 & 98.9171025252517 & 0.462897474748317 \tabularnewline
66 & 99.37 & 99.1963514504831 & 0.17364854951694 \tabularnewline
67 & 99.38 & 99.2273344293015 & 0.152665570698488 \tabularnewline
68 & 99.26 & 99.273365192977 & -0.0133651929770053 \tabularnewline
69 & 99.36 & 99.1502108595708 & 0.209789140429194 \tabularnewline
70 & 99.2 & 99.2997234176801 & -0.0997234176800674 \tabularnewline
71 & 98.53 & 99.1161875878338 & -0.586187587833791 \tabularnewline
72 & 98.65 & 98.3078408319141 & 0.342159168085857 \tabularnewline
73 & 99.15 & 98.5085941810046 & 0.641405818995381 \tabularnewline
74 & 100.17 & 99.1599730503763 & 1.01002694962369 \tabularnewline
75 & 99.98 & 100.418350584756 & -0.43835058475608 \tabularnewline
76 & 100.07 & 100.124894997133 & -0.0548949971333883 \tabularnewline
77 & 99.94 & 100.201939170488 & -0.261939170488034 \tabularnewline
78 & 100.05 & 100.010118628332 & 0.0398813716684714 \tabularnewline
79 & 99.13 & 100.129531073266 & -0.99953107326634 \tabularnewline
80 & 98.74 & 98.9736306818263 & -0.233630681826313 \tabularnewline
81 & 98.64 & 98.5284912561803 & 0.111508743819684 \tabularnewline
82 & 98.44 & 98.4548085533806 & -0.0148085533805897 \tabularnewline
83 & 98.81 & 98.2513135709507 & 0.55868642904926 \tabularnewline
84 & 98.88 & 98.7531697491427 & 0.126830250857338 \tabularnewline
85 & 99.63 & 98.8531030915108 & 0.776896908489206 \tabularnewline
86 & 100.08 & 99.7864593569866 & 0.293540643013387 \tabularnewline
87 & 100.07 & 100.305738196277 & -0.235738196276856 \tabularnewline
88 & 100.55 & 100.240101373904 & 0.309898626095617 \tabularnewline
89 & 99.98 & 100.793240878176 & -0.813240878175904 \tabularnewline
90 & 99.89 & 100.031307033768 & -0.141307033768456 \tabularnewline
91 & 99.86 & 99.9079570104717 & -0.0479570104717482 \tabularnewline
92 & 99.61 & 99.8666386254358 & -0.256638625435841 \tabularnewline
93 & 100.12 & 99.5560690705534 & 0.563930929446641 \tabularnewline
94 & 100.24 & 100.199163008861 & 0.0408369911392583 \tabularnewline
95 & 100.1 & 100.328800990563 & -0.228800990562988 \tabularnewline
96 & 99.86 & 100.134801425488 & -0.274801425487638 \tabularnewline
97 & 97.99 & 99.8299452488518 & -1.83994524885178 \tabularnewline
98 & 97.57 & 97.5256978141883 & 0.0443021858117163 \tabularnewline
99 & 98.28 & 97.1161536201699 & 1.16384637983015 \tabularnewline
100 & 97.97 & 98.1008342418346 & -0.130834241834563 \tabularnewline
101 & 97.99 & 97.7599559132983 & 0.23004408670171 \tabularnewline
102 & 97.84 & 97.8342488628152 & 0.00575113718484488 \tabularnewline
103 & 97.33 & 97.6856061948176 & -0.355606194817568 \tabularnewline
104 & 96.7 & 97.0916791986494 & -0.391679198649413 \tabularnewline
105 & 96.79 & 96.3692385744892 & 0.420761425510847 \tabularnewline
106 & 96.76 & 96.5585429259352 & 0.201457074064805 \tabularnewline
107 & 96.23 & 96.576089024202 & -0.346089024202001 \tabularnewline
108 & 96.29 & 95.9644081855908 & 0.325591814409208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283962&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]94.44[/C][C]95.45[/C][C]-1.00999999999999[/C][/ROW]
[ROW][C]4[/C][C]94.91[/C][C]95.8816288260296[/C][C]-0.971628826029558[/C][/ROW]
[ROW][C]5[/C][C]94.78[/C][C]96.1223136736294[/C][C]-1.34231367362938[/C][/ROW]
[ROW][C]6[/C][C]94.51[/C][C]95.6755127961842[/C][C]-1.16551279618422[/C][/ROW]
[ROW][C]7[/C][C]94.36[/C][C]95.1304388818238[/C][C]-0.770438881823836[/C][/ROW]
[ROW][C]8[/C][C]96.6[/C][C]94.7986067820884[/C][C]1.80139321791162[/C][/ROW]
[ROW][C]9[/C][C]96.72[/C][C]97.4637555109359[/C][C]-0.74375551093587[/C][/ROW]
[ROW][C]10[/C][C]96.71[/C][C]97.4082209819371[/C][C]-0.698220981937098[/C][/ROW]
[ROW][C]11[/C][C]97.44[/C][C]97.2334331055459[/C][C]0.206566894454141[/C][/ROW]
[ROW][C]12[/C][C]97.83[/C][C]98.0121851779562[/C][C]-0.182185177956228[/C][/ROW]
[ROW][C]13[/C][C]98.92[/C][C]98.3591874603825[/C][C]0.560812539617487[/C][/ROW]
[ROW][C]14[/C][C]97.98[/C][C]99.5815454241904[/C][C]-1.60154542419041[/C][/ROW]
[ROW][C]15[/C][C]98.76[/C][C]98.2635629856446[/C][C]0.496437014355379[/C][/ROW]
[ROW][C]16[/C][C]99.76[/C][C]99.1607276132825[/C][C]0.599272386717487[/C][/ROW]
[ROW][C]17[/C][C]99.87[/C][C]100.3021625265[/C][C]-0.43216252650025[/C][/ROW]
[ROW][C]18[/C][C]100.09[/C][C]100.310167389086[/C][C]-0.220167389086484[/C][/ROW]
[ROW][C]19[/C][C]100.07[/C][C]100.478205449476[/C][C]-0.408205449476057[/C][/ROW]
[ROW][C]20[/C][C]99.46[/C][C]100.361864447285[/C][C]-0.901864447285206[/C][/ROW]
[ROW][C]21[/C][C]100.4[/C][C]99.5390144600955[/C][C]0.860985539904476[/C][/ROW]
[ROW][C]22[/C][C]101.25[/C][C]100.682216572886[/C][C]0.567783427113767[/C][/ROW]
[ROW][C]23[/C][C]102.29[/C][C]101.666219743265[/C][C]0.6237802567355[/C][/ROW]
[ROW][C]24[/C][C]102.1[/C][C]102.853438784945[/C][C]-0.753438784945331[/C][/ROW]
[ROW][C]25[/C][C]105.91[/C][C]102.485618896151[/C][C]3.42438110384902[/C][/ROW]
[ROW][C]26[/C][C]108.95[/C][C]107.103810721742[/C][C]1.84618927825825[/C][/ROW]
[ROW][C]27[/C][C]110.07[/C][C]110.579531816425[/C][C]-0.509531816424982[/C][/ROW]
[ROW][C]28[/C][C]109.92[/C][C]111.579276670626[/C][C]-1.65927667062644[/C][/ROW]
[ROW][C]29[/C][C]109.87[/C][C]111.037669019222[/C][C]-1.16766901922151[/C][/ROW]
[ROW][C]30[/C][C]110.54[/C][C]110.712086212369[/C][C]-0.172086212369294[/C][/ROW]
[ROW][C]31[/C][C]110.79[/C][C]111.341471962402[/C][C]-0.551471962402374[/C][/ROW]
[ROW][C]32[/C][C]110.32[/C][C]111.461318478155[/C][C]-1.14131847815523[/C][/ROW]
[ROW][C]33[/C][C]110.76[/C][C]110.72195469052[/C][C]0.0380453094804523[/C][/ROW]
[ROW][C]34[/C][C]110.24[/C][C]111.170933804465[/C][C]-0.930933804465027[/C][/ROW]
[ROW][C]35[/C][C]110.27[/C][C]110.431223127377[/C][C]-0.161223127376815[/C][/ROW]
[ROW][C]36[/C][C]110.11[/C][C]110.42317268565[/C][C]-0.313172685650073[/C][/ROW]
[ROW][C]37[/C][C]110.39[/C][C]110.189260467102[/C][C]0.200739532898325[/C][/ROW]
[ROW][C]38[/C][C]111.05[/C][C]110.516637217715[/C][C]0.533362782285195[/C][/ROW]
[ROW][C]39[/C][C]110.85[/C][C]111.302516735106[/C][C]-0.452516735106343[/C][/ROW]
[ROW][C]40[/C][C]110.24[/C][C]110.995717779276[/C][C]-0.755717779276083[/C][/ROW]
[ROW][C]41[/C][C]108.7[/C][C]110.207360022606[/C][C]-1.50736002260639[/C][/ROW]
[ROW][C]42[/C][C]109.93[/C][C]108.311606380839[/C][C]1.61839361916071[/C][/ROW]
[ROW][C]43[/C][C]109.53[/C][C]109.923565179795[/C][C]-0.393565179795331[/C][/ROW]
[ROW][C]44[/C][C]109.83[/C][C]109.430679443219[/C][C]0.399320556780609[/C][/ROW]
[ROW][C]45[/C][C]107.86[/C][C]109.824923512438[/C][C]-1.96492351243752[/C][/ROW]
[ROW][C]46[/C][C]104.61[/C][C]107.391179824891[/C][C]-2.78117982489114[/C][/ROW]
[ROW][C]47[/C][C]103.61[/C][C]103.484790617087[/C][C]0.125209382913013[/C][/ROW]
[ROW][C]48[/C][C]103.11[/C][C]102.514341416688[/C][C]0.595658583311931[/C][/ROW]
[ROW][C]49[/C][C]102.59[/C][C]102.154923432321[/C][C]0.435076567678635[/C][/ROW]
[ROW][C]50[/C][C]102.91[/C][C]101.737606315692[/C][C]1.17239368430775[/C][/ROW]
[ROW][C]51[/C][C]101.94[/C][C]102.334304195775[/C][C]-0.394304195775376[/C][/ROW]
[ROW][C]52[/C][C]101.8[/C][C]101.271244043252[/C][C]0.52875595674783[/C][/ROW]
[ROW][C]53[/C][C]102.25[/C][C]101.25603629885[/C][C]0.99396370114998[/C][/ROW]
[ROW][C]54[/C][C]102.6[/C][C]101.940622728877[/C][C]0.65937727112312[/C][/ROW]
[ROW][C]55[/C][C]102.49[/C][C]102.446243059775[/C][C]0.0437569402250659[/C][/ROW]
[ROW][C]56[/C][C]102.13[/C][C]102.346570181766[/C][C]-0.216570181765832[/C][/ROW]
[ROW][C]57[/C][C]100.76[/C][C]101.93545722288[/C][C]-1.17545722288017[/C][/ROW]
[ROW][C]58[/C][C]100.86[/C][C]100.288036313801[/C][C]0.571963686198998[/C][/ROW]
[ROW][C]59[/C][C]101.12[/C][C]100.523026071571[/C][C]0.596973928428994[/C][/ROW]
[ROW][C]60[/C][C]100.74[/C][C]100.923918523204[/C][C]-0.183918523204056[/C][/ROW]
[ROW][C]61[/C][C]99.99[/C][C]100.500511716975[/C][C]-0.510511716975273[/C][/ROW]
[ROW][C]62[/C][C]99.39[/C][C]99.6300253038059[/C][C]-0.240025303805893[/C][/ROW]
[ROW][C]63[/C][C]99.52[/C][C]98.9733766766269[/C][C]0.546623323373126[/C][/ROW]
[ROW][C]64[/C][C]99.21[/C][C]99.232385828421[/C][C]-0.0223858284210081[/C][/ROW]
[ROW][C]65[/C][C]99.38[/C][C]98.9171025252517[/C][C]0.462897474748317[/C][/ROW]
[ROW][C]66[/C][C]99.37[/C][C]99.1963514504831[/C][C]0.17364854951694[/C][/ROW]
[ROW][C]67[/C][C]99.38[/C][C]99.2273344293015[/C][C]0.152665570698488[/C][/ROW]
[ROW][C]68[/C][C]99.26[/C][C]99.273365192977[/C][C]-0.0133651929770053[/C][/ROW]
[ROW][C]69[/C][C]99.36[/C][C]99.1502108595708[/C][C]0.209789140429194[/C][/ROW]
[ROW][C]70[/C][C]99.2[/C][C]99.2997234176801[/C][C]-0.0997234176800674[/C][/ROW]
[ROW][C]71[/C][C]98.53[/C][C]99.1161875878338[/C][C]-0.586187587833791[/C][/ROW]
[ROW][C]72[/C][C]98.65[/C][C]98.3078408319141[/C][C]0.342159168085857[/C][/ROW]
[ROW][C]73[/C][C]99.15[/C][C]98.5085941810046[/C][C]0.641405818995381[/C][/ROW]
[ROW][C]74[/C][C]100.17[/C][C]99.1599730503763[/C][C]1.01002694962369[/C][/ROW]
[ROW][C]75[/C][C]99.98[/C][C]100.418350584756[/C][C]-0.43835058475608[/C][/ROW]
[ROW][C]76[/C][C]100.07[/C][C]100.124894997133[/C][C]-0.0548949971333883[/C][/ROW]
[ROW][C]77[/C][C]99.94[/C][C]100.201939170488[/C][C]-0.261939170488034[/C][/ROW]
[ROW][C]78[/C][C]100.05[/C][C]100.010118628332[/C][C]0.0398813716684714[/C][/ROW]
[ROW][C]79[/C][C]99.13[/C][C]100.129531073266[/C][C]-0.99953107326634[/C][/ROW]
[ROW][C]80[/C][C]98.74[/C][C]98.9736306818263[/C][C]-0.233630681826313[/C][/ROW]
[ROW][C]81[/C][C]98.64[/C][C]98.5284912561803[/C][C]0.111508743819684[/C][/ROW]
[ROW][C]82[/C][C]98.44[/C][C]98.4548085533806[/C][C]-0.0148085533805897[/C][/ROW]
[ROW][C]83[/C][C]98.81[/C][C]98.2513135709507[/C][C]0.55868642904926[/C][/ROW]
[ROW][C]84[/C][C]98.88[/C][C]98.7531697491427[/C][C]0.126830250857338[/C][/ROW]
[ROW][C]85[/C][C]99.63[/C][C]98.8531030915108[/C][C]0.776896908489206[/C][/ROW]
[ROW][C]86[/C][C]100.08[/C][C]99.7864593569866[/C][C]0.293540643013387[/C][/ROW]
[ROW][C]87[/C][C]100.07[/C][C]100.305738196277[/C][C]-0.235738196276856[/C][/ROW]
[ROW][C]88[/C][C]100.55[/C][C]100.240101373904[/C][C]0.309898626095617[/C][/ROW]
[ROW][C]89[/C][C]99.98[/C][C]100.793240878176[/C][C]-0.813240878175904[/C][/ROW]
[ROW][C]90[/C][C]99.89[/C][C]100.031307033768[/C][C]-0.141307033768456[/C][/ROW]
[ROW][C]91[/C][C]99.86[/C][C]99.9079570104717[/C][C]-0.0479570104717482[/C][/ROW]
[ROW][C]92[/C][C]99.61[/C][C]99.8666386254358[/C][C]-0.256638625435841[/C][/ROW]
[ROW][C]93[/C][C]100.12[/C][C]99.5560690705534[/C][C]0.563930929446641[/C][/ROW]
[ROW][C]94[/C][C]100.24[/C][C]100.199163008861[/C][C]0.0408369911392583[/C][/ROW]
[ROW][C]95[/C][C]100.1[/C][C]100.328800990563[/C][C]-0.228800990562988[/C][/ROW]
[ROW][C]96[/C][C]99.86[/C][C]100.134801425488[/C][C]-0.274801425487638[/C][/ROW]
[ROW][C]97[/C][C]97.99[/C][C]99.8299452488518[/C][C]-1.83994524885178[/C][/ROW]
[ROW][C]98[/C][C]97.57[/C][C]97.5256978141883[/C][C]0.0443021858117163[/C][/ROW]
[ROW][C]99[/C][C]98.28[/C][C]97.1161536201699[/C][C]1.16384637983015[/C][/ROW]
[ROW][C]100[/C][C]97.97[/C][C]98.1008342418346[/C][C]-0.130834241834563[/C][/ROW]
[ROW][C]101[/C][C]97.99[/C][C]97.7599559132983[/C][C]0.23004408670171[/C][/ROW]
[ROW][C]102[/C][C]97.84[/C][C]97.8342488628152[/C][C]0.00575113718484488[/C][/ROW]
[ROW][C]103[/C][C]97.33[/C][C]97.6856061948176[/C][C]-0.355606194817568[/C][/ROW]
[ROW][C]104[/C][C]96.7[/C][C]97.0916791986494[/C][C]-0.391679198649413[/C][/ROW]
[ROW][C]105[/C][C]96.79[/C][C]96.3692385744892[/C][C]0.420761425510847[/C][/ROW]
[ROW][C]106[/C][C]96.76[/C][C]96.5585429259352[/C][C]0.201457074064805[/C][/ROW]
[ROW][C]107[/C][C]96.23[/C][C]96.576089024202[/C][C]-0.346089024202001[/C][/ROW]
[ROW][C]108[/C][C]96.29[/C][C]95.9644081855908[/C][C]0.325591814409208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283962&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283962&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	94.44	95.45	-1.00999999999999
4	94.91	95.8816288260296	-0.971628826029558
5	94.78	96.1223136736294	-1.34231367362938
6	94.51	95.6755127961842	-1.16551279618422
7	94.36	95.1304388818238	-0.770438881823836
8	96.6	94.7986067820884	1.80139321791162
9	96.72	97.4637555109359	-0.74375551093587
10	96.71	97.4082209819371	-0.698220981937098
11	97.44	97.2334331055459	0.206566894454141
12	97.83	98.0121851779562	-0.182185177956228
13	98.92	98.3591874603825	0.560812539617487
14	97.98	99.5815454241904	-1.60154542419041
15	98.76	98.2635629856446	0.496437014355379
16	99.76	99.1607276132825	0.599272386717487
17	99.87	100.3021625265	-0.43216252650025
18	100.09	100.310167389086	-0.220167389086484
19	100.07	100.478205449476	-0.408205449476057
20	99.46	100.361864447285	-0.901864447285206
21	100.4	99.5390144600955	0.860985539904476
22	101.25	100.682216572886	0.567783427113767
23	102.29	101.666219743265	0.6237802567355
24	102.1	102.853438784945	-0.753438784945331
25	105.91	102.485618896151	3.42438110384902
26	108.95	107.103810721742	1.84618927825825
27	110.07	110.579531816425	-0.509531816424982
28	109.92	111.579276670626	-1.65927667062644
29	109.87	111.037669019222	-1.16766901922151
30	110.54	110.712086212369	-0.172086212369294
31	110.79	111.341471962402	-0.551471962402374
32	110.32	111.461318478155	-1.14131847815523
33	110.76	110.72195469052	0.0380453094804523
34	110.24	111.170933804465	-0.930933804465027
35	110.27	110.431223127377	-0.161223127376815
36	110.11	110.42317268565	-0.313172685650073
37	110.39	110.189260467102	0.200739532898325
38	111.05	110.516637217715	0.533362782285195
39	110.85	111.302516735106	-0.452516735106343
40	110.24	110.995717779276	-0.755717779276083
41	108.7	110.207360022606	-1.50736002260639
42	109.93	108.311606380839	1.61839361916071
43	109.53	109.923565179795	-0.393565179795331
44	109.83	109.430679443219	0.399320556780609
45	107.86	109.824923512438	-1.96492351243752
46	104.61	107.391179824891	-2.78117982489114
47	103.61	103.484790617087	0.125209382913013
48	103.11	102.514341416688	0.595658583311931
49	102.59	102.154923432321	0.435076567678635
50	102.91	101.737606315692	1.17239368430775
51	101.94	102.334304195775	-0.394304195775376
52	101.8	101.271244043252	0.52875595674783
53	102.25	101.25603629885	0.99396370114998
54	102.6	101.940622728877	0.65937727112312
55	102.49	102.446243059775	0.0437569402250659
56	102.13	102.346570181766	-0.216570181765832
57	100.76	101.93545722288	-1.17545722288017
58	100.86	100.288036313801	0.571963686198998
59	101.12	100.523026071571	0.596973928428994
60	100.74	100.923918523204	-0.183918523204056
61	99.99	100.500511716975	-0.510511716975273
62	99.39	99.6300253038059	-0.240025303805893
63	99.52	98.9733766766269	0.546623323373126
64	99.21	99.232385828421	-0.0223858284210081
65	99.38	98.9171025252517	0.462897474748317
66	99.37	99.1963514504831	0.17364854951694
67	99.38	99.2273344293015	0.152665570698488
68	99.26	99.273365192977	-0.0133651929770053
69	99.36	99.1502108595708	0.209789140429194
70	99.2	99.2997234176801	-0.0997234176800674
71	98.53	99.1161875878338	-0.586187587833791
72	98.65	98.3078408319141	0.342159168085857
73	99.15	98.5085941810046	0.641405818995381
74	100.17	99.1599730503763	1.01002694962369
75	99.98	100.418350584756	-0.43835058475608
76	100.07	100.124894997133	-0.0548949971333883
77	99.94	100.201939170488	-0.261939170488034
78	100.05	100.010118628332	0.0398813716684714
79	99.13	100.129531073266	-0.99953107326634
80	98.74	98.9736306818263	-0.233630681826313
81	98.64	98.5284912561803	0.111508743819684
82	98.44	98.4548085533806	-0.0148085533805897
83	98.81	98.2513135709507	0.55868642904926
84	98.88	98.7531697491427	0.126830250857338
85	99.63	98.8531030915108	0.776896908489206
86	100.08	99.7864593569866	0.293540643013387
87	100.07	100.305738196277	-0.235738196276856
88	100.55	100.240101373904	0.309898626095617
89	99.98	100.793240878176	-0.813240878175904
90	99.89	100.031307033768	-0.141307033768456
91	99.86	99.9079570104717	-0.0479570104717482
92	99.61	99.8666386254358	-0.256638625435841
93	100.12	99.5560690705534	0.563930929446641
94	100.24	100.199163008861	0.0408369911392583
95	100.1	100.328800990563	-0.228800990562988
96	99.86	100.134801425488	-0.274801425487638
97	97.99	99.8299452488518	-1.83994524885178
98	97.57	97.5256978141883	0.0443021858117163
99	98.28	97.1161536201699	1.16384637983015
100	97.97	98.1008342418346	-0.130834241834563
101	97.99	97.7599559132983	0.23004408670171
102	97.84	97.8342488628152	0.00575113718484488
103	97.33	97.6856061948176	-0.355606194817568
104	96.7	97.0916791986494	-0.391679198649413
105	96.79	96.3692385744892	0.420761425510847
106	96.76	96.5585429259352	0.201457074064805
107	96.23	96.576089024202	-0.346089024202001
108	96.29	95.9644081855908	0.325591814409208

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	96.1012514559234	94.4530196576474	97.7494832541994
110	95.9125029118467	93.2920095827099	98.5329962409836
111	95.7237543677701	92.1525367682366	99.2949719673036
112	95.5350058236935	90.9875734615841	100.082438185803
113	95.3462572796168	89.7833204128272	100.909194146406
114	95.1575087355402	88.5350005179077	101.780016953173
115	94.9687601914635	87.2411583593465	102.696362023581
116	94.7800116473869	85.9017485855666	103.658274709207
117	94.5912631033102	84.5173644879949	104.665161718626
118	94.4025145592336	83.0888896543828	105.716139464084
119	94.213766015157	81.6173290592351	106.810202971079
120	94.0250174710803	80.1037235921399	107.946311350021

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 96.1012514559234 & 94.4530196576474 & 97.7494832541994 \tabularnewline
110 & 95.9125029118467 & 93.2920095827099 & 98.5329962409836 \tabularnewline
111 & 95.7237543677701 & 92.1525367682366 & 99.2949719673036 \tabularnewline
112 & 95.5350058236935 & 90.9875734615841 & 100.082438185803 \tabularnewline
113 & 95.3462572796168 & 89.7833204128272 & 100.909194146406 \tabularnewline
114 & 95.1575087355402 & 88.5350005179077 & 101.780016953173 \tabularnewline
115 & 94.9687601914635 & 87.2411583593465 & 102.696362023581 \tabularnewline
116 & 94.7800116473869 & 85.9017485855666 & 103.658274709207 \tabularnewline
117 & 94.5912631033102 & 84.5173644879949 & 104.665161718626 \tabularnewline
118 & 94.4025145592336 & 83.0888896543828 & 105.716139464084 \tabularnewline
119 & 94.213766015157 & 81.6173290592351 & 106.810202971079 \tabularnewline
120 & 94.0250174710803 & 80.1037235921399 & 107.946311350021 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283962&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]96.1012514559234[/C][C]94.4530196576474[/C][C]97.7494832541994[/C][/ROW]
[ROW][C]110[/C][C]95.9125029118467[/C][C]93.2920095827099[/C][C]98.5329962409836[/C][/ROW]
[ROW][C]111[/C][C]95.7237543677701[/C][C]92.1525367682366[/C][C]99.2949719673036[/C][/ROW]
[ROW][C]112[/C][C]95.5350058236935[/C][C]90.9875734615841[/C][C]100.082438185803[/C][/ROW]
[ROW][C]113[/C][C]95.3462572796168[/C][C]89.7833204128272[/C][C]100.909194146406[/C][/ROW]
[ROW][C]114[/C][C]95.1575087355402[/C][C]88.5350005179077[/C][C]101.780016953173[/C][/ROW]
[ROW][C]115[/C][C]94.9687601914635[/C][C]87.2411583593465[/C][C]102.696362023581[/C][/ROW]
[ROW][C]116[/C][C]94.7800116473869[/C][C]85.9017485855666[/C][C]103.658274709207[/C][/ROW]
[ROW][C]117[/C][C]94.5912631033102[/C][C]84.5173644879949[/C][C]104.665161718626[/C][/ROW]
[ROW][C]118[/C][C]94.4025145592336[/C][C]83.0888896543828[/C][C]105.716139464084[/C][/ROW]
[ROW][C]119[/C][C]94.213766015157[/C][C]81.6173290592351[/C][C]106.810202971079[/C][/ROW]
[ROW][C]120[/C][C]94.0250174710803[/C][C]80.1037235921399[/C][C]107.946311350021[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283962&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283962&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	96.1012514559234	94.4530196576474	97.7494832541994
110	95.9125029118467	93.2920095827099	98.5329962409836
111	95.7237543677701	92.1525367682366	99.2949719673036
112	95.5350058236935	90.9875734615841	100.082438185803
113	95.3462572796168	89.7833204128272	100.909194146406
114	95.1575087355402	88.5350005179077	101.780016953173
115	94.9687601914635	87.2411583593465	102.696362023581
116	94.7800116473869	85.9017485855666	103.658274709207
117	94.5912631033102	84.5173644879949	104.665161718626
118	94.4025145592336	83.0888896543828	105.716139464084
119	94.213766015157	81.6173290592351	106.810202971079
120	94.0250174710803	80.1037235921399	107.946311350021

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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