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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 29 Nov 2015 15:14:08 +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/29/t14488100667hn3bsgh0w4p707.htm/, Retrieved Sun, 12 May 2024 15:13:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284479, Retrieved Sun, 12 May 2024 15:13:10 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [Saghar Najafi Zadeh] [2015-11-29 15:14:08] [c23f68ac64e5ceef3ca8a84a34b0ff7e] [Current]
- R PD    [Exponential Smoothing] [Saghar Najafi Zadeh] [2016-01-07 23:00:03] [a726dea3093235710caf789b0c5edf8a] 

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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	1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284479&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284479&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.950473356747252
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.950473356747252 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284479&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]0.950473356747252[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284479&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	0.950473356747252
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	89.01	88.83	0.180000000000007
3	88.21	89.0010852042145	-0.791085204214525
4	87.78	88.2491797946916	-0.469179794691641
5	87.93	87.8032369003131	0.126763099686912
6	88.11	87.9237218491842	0.186278150815795
7	88.2	88.1007742684788	0.0992257315212299
8	88.12	88.1950856825935	-0.0750856825934534
9	88.38	88.1237187418152	0.256281258184799
10	87.65	88.3673072495535	-0.7173072495535
11	88.24	87.6855258202513	0.554474179748738
12	87.83	88.2125387551067	-0.382538755106722
13	87.75	87.8489458604545	-0.0989458604545206
14	87.88	87.7549004563321	0.125099543667929
15	87.61	87.8738042395297	-0.263804239529676
16	88.05	87.6230653384598	0.426934661540244
17	87.77	88.0288553593257	-0.258855359325665
18	87.79	87.7828202370354	0.00717976296462552
19	88.34	87.789644410441	0.55035558955899
20	88.48	88.3127427350538	0.167257264946244
21	88.75	88.4717163091076	0.278283690892422
22	87.95	88.7362175429181	-0.786217542918109
23	89.09	87.9889387157671	1.10106128423286
24	88.73	89.0354681305764	-0.305468130576386
25	89.24	88.7451288111281	0.494871188871855
26	89.77	89.2154906911727	0.554509308827321
27	89.84	89.7425370152814	0.0974629847186321
28	90.97	89.8351729855255	1.1348270144745
29	91.53	90.9137958273005	0.616204172699454
30	92.2	91.4994814757679	0.700518524232152
31	92.27	92.1653056689584	0.104694331041571
32	92.42	92.2648148412159	0.155185158784093
33	92.07	92.4123142000028	-0.342314200002789
34	91.73	92.0869536732639	-0.356953673263874
35	92.1	91.7476787172335	0.352321282766496
36	91.68	92.0825507095181	-0.402550709518067
37	92.63	91.6999369853815	0.93006301461854
38	93.02	92.5839371008724	0.436062899127592
39	92.66	92.9984032683591	-0.338403268359144
40	93.23	92.6767599779476	0.553240022052421
41	93.79	93.2025998787947	0.587400121205334
42	93.92	93.7609080437504	0.159091956249554
43	94.04	93.9121207094384	0.127879290561566
44	94.23	94.033666567997	0.196333432003044
45	94.37	94.2202762641546	0.149723735845399
46	94.29	94.3625846859483	-0.0725846859483141
47	94.38	94.2935948758466	0.0864051241534156
48	94	94.3757206442408	-0.375720644240843
49	94.11	94.01860818231	0.0913918176899813
50	93.98	94.105473670049	-0.125473670049033
51	93.42	93.9862142896941	-0.56621428969413
52	93.3	93.4480426931303	-0.148042693130293
53	93.32	93.3073320576488	0.0126679423511433
54	93.75	93.3193725993384	0.430627400661578
55	93.82	93.7286724703526	0.0913275296474154
56	94.06	93.81547685402	0.244523145980011
57	94.09	94.047889589382	0.0421104106179939
58	93.64	94.0879144127161	-0.447914412716102
59	93.9	93.6621836973264	0.23781630267365
60	93.18	93.8882217568178	-0.708221756817792
61	93.54	93.2150758462938	0.324924153706249
62	93.55	93.5239075973552	0.0260924026448066
63	93.8	93.5487077308826	0.2512922691174
64	93.39	93.7875543374352	-0.397554337435238
65	93.27	93.4096895318437	-0.139689531843743
66	93.58	93.2769183536098	0.30308164639024
67	93.47	93.5649893834228	-0.0949893834227709
68	93.75	93.4747045053056	0.275295494694433
69	93.3	93.7363655382452	-0.436365538245184
70	92.65	93.3216117203405	-0.671611720340465
71	92.96	92.6832626740777	0.276737325922312
72	92.84	92.9462941291843	-0.10629412918432
73	93.29	92.845264391416	0.444735608584025
74	93.57	93.2679737381719	0.302026261828118
75	93.54	93.5550416530775	-0.0150416530774606
76	94.38	93.5407449625859	0.839255037414091
77	93.98	94.3384345151639	-0.358434515163907
78	94.48	93.997752058362	0.482247941638008
79	94.63	94.4561158782351	0.173884121764871
80	95.45	94.621388103134	0.828611896865979
81	95.59	95.4089616341889	0.181038365811062
82	94.76	95.5810337774414	-0.8210337774414
83	95.66	94.8006630469938	0.859336953006192
84	95.03	95.6174399252945	-0.587439925294547
85	96.45	95.0590939276125	1.39090607238752
86	97.15	96.3811130911548	0.768886908845218
87	97.5	97.1119196123639	0.38808038763608
88	98.54	97.4807796810882	1.05922031891185
89	99.54	98.4875403731392	1.05245962686081
90	100.33	99.4878752075225	0.842124792477449
91	100.28	100.288292385829	-0.00829238582866765
92	101.81	100.280410694035	1.52958930596535
93	101.91	101.73424457612	0.175755423879764
94	101.92	101.901295423822	0.0187045761782372
95	102.68	101.919073625128	0.760926374871573
96	101.9	102.64231387089	-0.742313870890129
97	102.14	101.936764314265	0.203235685734853
98	102.3	102.129934418696	0.170065581303618
99	102.06	102.291577222625	-0.231577222625191
100	102.4	102.07146924249	0.328530757509583
101	102.99	102.383728974375	0.606271025624721
102	102.99	102.959973431199	0.0300265688005936
103	102.83	102.988512884839	-0.158512884838913
104	103.01	102.837850611098	0.17214938890163
105	102.6	103.00147401863	-0.401474018629699
106	102.18	102.619883660496	-0.439883660495909
107	102.6	102.201785961126	0.398214038873888
108	101.44	102.580277795358	-1.14027779535846

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 89.01 & 88.83 & 0.180000000000007 \tabularnewline
3 & 88.21 & 89.0010852042145 & -0.791085204214525 \tabularnewline
4 & 87.78 & 88.2491797946916 & -0.469179794691641 \tabularnewline
5 & 87.93 & 87.8032369003131 & 0.126763099686912 \tabularnewline
6 & 88.11 & 87.9237218491842 & 0.186278150815795 \tabularnewline
7 & 88.2 & 88.1007742684788 & 0.0992257315212299 \tabularnewline
8 & 88.12 & 88.1950856825935 & -0.0750856825934534 \tabularnewline
9 & 88.38 & 88.1237187418152 & 0.256281258184799 \tabularnewline
10 & 87.65 & 88.3673072495535 & -0.7173072495535 \tabularnewline
11 & 88.24 & 87.6855258202513 & 0.554474179748738 \tabularnewline
12 & 87.83 & 88.2125387551067 & -0.382538755106722 \tabularnewline
13 & 87.75 & 87.8489458604545 & -0.0989458604545206 \tabularnewline
14 & 87.88 & 87.7549004563321 & 0.125099543667929 \tabularnewline
15 & 87.61 & 87.8738042395297 & -0.263804239529676 \tabularnewline
16 & 88.05 & 87.6230653384598 & 0.426934661540244 \tabularnewline
17 & 87.77 & 88.0288553593257 & -0.258855359325665 \tabularnewline
18 & 87.79 & 87.7828202370354 & 0.00717976296462552 \tabularnewline
19 & 88.34 & 87.789644410441 & 0.55035558955899 \tabularnewline
20 & 88.48 & 88.3127427350538 & 0.167257264946244 \tabularnewline
21 & 88.75 & 88.4717163091076 & 0.278283690892422 \tabularnewline
22 & 87.95 & 88.7362175429181 & -0.786217542918109 \tabularnewline
23 & 89.09 & 87.9889387157671 & 1.10106128423286 \tabularnewline
24 & 88.73 & 89.0354681305764 & -0.305468130576386 \tabularnewline
25 & 89.24 & 88.7451288111281 & 0.494871188871855 \tabularnewline
26 & 89.77 & 89.2154906911727 & 0.554509308827321 \tabularnewline
27 & 89.84 & 89.7425370152814 & 0.0974629847186321 \tabularnewline
28 & 90.97 & 89.8351729855255 & 1.1348270144745 \tabularnewline
29 & 91.53 & 90.9137958273005 & 0.616204172699454 \tabularnewline
30 & 92.2 & 91.4994814757679 & 0.700518524232152 \tabularnewline
31 & 92.27 & 92.1653056689584 & 0.104694331041571 \tabularnewline
32 & 92.42 & 92.2648148412159 & 0.155185158784093 \tabularnewline
33 & 92.07 & 92.4123142000028 & -0.342314200002789 \tabularnewline
34 & 91.73 & 92.0869536732639 & -0.356953673263874 \tabularnewline
35 & 92.1 & 91.7476787172335 & 0.352321282766496 \tabularnewline
36 & 91.68 & 92.0825507095181 & -0.402550709518067 \tabularnewline
37 & 92.63 & 91.6999369853815 & 0.93006301461854 \tabularnewline
38 & 93.02 & 92.5839371008724 & 0.436062899127592 \tabularnewline
39 & 92.66 & 92.9984032683591 & -0.338403268359144 \tabularnewline
40 & 93.23 & 92.6767599779476 & 0.553240022052421 \tabularnewline
41 & 93.79 & 93.2025998787947 & 0.587400121205334 \tabularnewline
42 & 93.92 & 93.7609080437504 & 0.159091956249554 \tabularnewline
43 & 94.04 & 93.9121207094384 & 0.127879290561566 \tabularnewline
44 & 94.23 & 94.033666567997 & 0.196333432003044 \tabularnewline
45 & 94.37 & 94.2202762641546 & 0.149723735845399 \tabularnewline
46 & 94.29 & 94.3625846859483 & -0.0725846859483141 \tabularnewline
47 & 94.38 & 94.2935948758466 & 0.0864051241534156 \tabularnewline
48 & 94 & 94.3757206442408 & -0.375720644240843 \tabularnewline
49 & 94.11 & 94.01860818231 & 0.0913918176899813 \tabularnewline
50 & 93.98 & 94.105473670049 & -0.125473670049033 \tabularnewline
51 & 93.42 & 93.9862142896941 & -0.56621428969413 \tabularnewline
52 & 93.3 & 93.4480426931303 & -0.148042693130293 \tabularnewline
53 & 93.32 & 93.3073320576488 & 0.0126679423511433 \tabularnewline
54 & 93.75 & 93.3193725993384 & 0.430627400661578 \tabularnewline
55 & 93.82 & 93.7286724703526 & 0.0913275296474154 \tabularnewline
56 & 94.06 & 93.81547685402 & 0.244523145980011 \tabularnewline
57 & 94.09 & 94.047889589382 & 0.0421104106179939 \tabularnewline
58 & 93.64 & 94.0879144127161 & -0.447914412716102 \tabularnewline
59 & 93.9 & 93.6621836973264 & 0.23781630267365 \tabularnewline
60 & 93.18 & 93.8882217568178 & -0.708221756817792 \tabularnewline
61 & 93.54 & 93.2150758462938 & 0.324924153706249 \tabularnewline
62 & 93.55 & 93.5239075973552 & 0.0260924026448066 \tabularnewline
63 & 93.8 & 93.5487077308826 & 0.2512922691174 \tabularnewline
64 & 93.39 & 93.7875543374352 & -0.397554337435238 \tabularnewline
65 & 93.27 & 93.4096895318437 & -0.139689531843743 \tabularnewline
66 & 93.58 & 93.2769183536098 & 0.30308164639024 \tabularnewline
67 & 93.47 & 93.5649893834228 & -0.0949893834227709 \tabularnewline
68 & 93.75 & 93.4747045053056 & 0.275295494694433 \tabularnewline
69 & 93.3 & 93.7363655382452 & -0.436365538245184 \tabularnewline
70 & 92.65 & 93.3216117203405 & -0.671611720340465 \tabularnewline
71 & 92.96 & 92.6832626740777 & 0.276737325922312 \tabularnewline
72 & 92.84 & 92.9462941291843 & -0.10629412918432 \tabularnewline
73 & 93.29 & 92.845264391416 & 0.444735608584025 \tabularnewline
74 & 93.57 & 93.2679737381719 & 0.302026261828118 \tabularnewline
75 & 93.54 & 93.5550416530775 & -0.0150416530774606 \tabularnewline
76 & 94.38 & 93.5407449625859 & 0.839255037414091 \tabularnewline
77 & 93.98 & 94.3384345151639 & -0.358434515163907 \tabularnewline
78 & 94.48 & 93.997752058362 & 0.482247941638008 \tabularnewline
79 & 94.63 & 94.4561158782351 & 0.173884121764871 \tabularnewline
80 & 95.45 & 94.621388103134 & 0.828611896865979 \tabularnewline
81 & 95.59 & 95.4089616341889 & 0.181038365811062 \tabularnewline
82 & 94.76 & 95.5810337774414 & -0.8210337774414 \tabularnewline
83 & 95.66 & 94.8006630469938 & 0.859336953006192 \tabularnewline
84 & 95.03 & 95.6174399252945 & -0.587439925294547 \tabularnewline
85 & 96.45 & 95.0590939276125 & 1.39090607238752 \tabularnewline
86 & 97.15 & 96.3811130911548 & 0.768886908845218 \tabularnewline
87 & 97.5 & 97.1119196123639 & 0.38808038763608 \tabularnewline
88 & 98.54 & 97.4807796810882 & 1.05922031891185 \tabularnewline
89 & 99.54 & 98.4875403731392 & 1.05245962686081 \tabularnewline
90 & 100.33 & 99.4878752075225 & 0.842124792477449 \tabularnewline
91 & 100.28 & 100.288292385829 & -0.00829238582866765 \tabularnewline
92 & 101.81 & 100.280410694035 & 1.52958930596535 \tabularnewline
93 & 101.91 & 101.73424457612 & 0.175755423879764 \tabularnewline
94 & 101.92 & 101.901295423822 & 0.0187045761782372 \tabularnewline
95 & 102.68 & 101.919073625128 & 0.760926374871573 \tabularnewline
96 & 101.9 & 102.64231387089 & -0.742313870890129 \tabularnewline
97 & 102.14 & 101.936764314265 & 0.203235685734853 \tabularnewline
98 & 102.3 & 102.129934418696 & 0.170065581303618 \tabularnewline
99 & 102.06 & 102.291577222625 & -0.231577222625191 \tabularnewline
100 & 102.4 & 102.07146924249 & 0.328530757509583 \tabularnewline
101 & 102.99 & 102.383728974375 & 0.606271025624721 \tabularnewline
102 & 102.99 & 102.959973431199 & 0.0300265688005936 \tabularnewline
103 & 102.83 & 102.988512884839 & -0.158512884838913 \tabularnewline
104 & 103.01 & 102.837850611098 & 0.17214938890163 \tabularnewline
105 & 102.6 & 103.00147401863 & -0.401474018629699 \tabularnewline
106 & 102.18 & 102.619883660496 & -0.439883660495909 \tabularnewline
107 & 102.6 & 102.201785961126 & 0.398214038873888 \tabularnewline
108 & 101.44 & 102.580277795358 & -1.14027779535846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284479&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]89.01[/C][C]88.83[/C][C]0.180000000000007[/C][/ROW]
[ROW][C]3[/C][C]88.21[/C][C]89.0010852042145[/C][C]-0.791085204214525[/C][/ROW]
[ROW][C]4[/C][C]87.78[/C][C]88.2491797946916[/C][C]-0.469179794691641[/C][/ROW]
[ROW][C]5[/C][C]87.93[/C][C]87.8032369003131[/C][C]0.126763099686912[/C][/ROW]
[ROW][C]6[/C][C]88.11[/C][C]87.9237218491842[/C][C]0.186278150815795[/C][/ROW]
[ROW][C]7[/C][C]88.2[/C][C]88.1007742684788[/C][C]0.0992257315212299[/C][/ROW]
[ROW][C]8[/C][C]88.12[/C][C]88.1950856825935[/C][C]-0.0750856825934534[/C][/ROW]
[ROW][C]9[/C][C]88.38[/C][C]88.1237187418152[/C][C]0.256281258184799[/C][/ROW]
[ROW][C]10[/C][C]87.65[/C][C]88.3673072495535[/C][C]-0.7173072495535[/C][/ROW]
[ROW][C]11[/C][C]88.24[/C][C]87.6855258202513[/C][C]0.554474179748738[/C][/ROW]
[ROW][C]12[/C][C]87.83[/C][C]88.2125387551067[/C][C]-0.382538755106722[/C][/ROW]
[ROW][C]13[/C][C]87.75[/C][C]87.8489458604545[/C][C]-0.0989458604545206[/C][/ROW]
[ROW][C]14[/C][C]87.88[/C][C]87.7549004563321[/C][C]0.125099543667929[/C][/ROW]
[ROW][C]15[/C][C]87.61[/C][C]87.8738042395297[/C][C]-0.263804239529676[/C][/ROW]
[ROW][C]16[/C][C]88.05[/C][C]87.6230653384598[/C][C]0.426934661540244[/C][/ROW]
[ROW][C]17[/C][C]87.77[/C][C]88.0288553593257[/C][C]-0.258855359325665[/C][/ROW]
[ROW][C]18[/C][C]87.79[/C][C]87.7828202370354[/C][C]0.00717976296462552[/C][/ROW]
[ROW][C]19[/C][C]88.34[/C][C]87.789644410441[/C][C]0.55035558955899[/C][/ROW]
[ROW][C]20[/C][C]88.48[/C][C]88.3127427350538[/C][C]0.167257264946244[/C][/ROW]
[ROW][C]21[/C][C]88.75[/C][C]88.4717163091076[/C][C]0.278283690892422[/C][/ROW]
[ROW][C]22[/C][C]87.95[/C][C]88.7362175429181[/C][C]-0.786217542918109[/C][/ROW]
[ROW][C]23[/C][C]89.09[/C][C]87.9889387157671[/C][C]1.10106128423286[/C][/ROW]
[ROW][C]24[/C][C]88.73[/C][C]89.0354681305764[/C][C]-0.305468130576386[/C][/ROW]
[ROW][C]25[/C][C]89.24[/C][C]88.7451288111281[/C][C]0.494871188871855[/C][/ROW]
[ROW][C]26[/C][C]89.77[/C][C]89.2154906911727[/C][C]0.554509308827321[/C][/ROW]
[ROW][C]27[/C][C]89.84[/C][C]89.7425370152814[/C][C]0.0974629847186321[/C][/ROW]
[ROW][C]28[/C][C]90.97[/C][C]89.8351729855255[/C][C]1.1348270144745[/C][/ROW]
[ROW][C]29[/C][C]91.53[/C][C]90.9137958273005[/C][C]0.616204172699454[/C][/ROW]
[ROW][C]30[/C][C]92.2[/C][C]91.4994814757679[/C][C]0.700518524232152[/C][/ROW]
[ROW][C]31[/C][C]92.27[/C][C]92.1653056689584[/C][C]0.104694331041571[/C][/ROW]
[ROW][C]32[/C][C]92.42[/C][C]92.2648148412159[/C][C]0.155185158784093[/C][/ROW]
[ROW][C]33[/C][C]92.07[/C][C]92.4123142000028[/C][C]-0.342314200002789[/C][/ROW]
[ROW][C]34[/C][C]91.73[/C][C]92.0869536732639[/C][C]-0.356953673263874[/C][/ROW]
[ROW][C]35[/C][C]92.1[/C][C]91.7476787172335[/C][C]0.352321282766496[/C][/ROW]
[ROW][C]36[/C][C]91.68[/C][C]92.0825507095181[/C][C]-0.402550709518067[/C][/ROW]
[ROW][C]37[/C][C]92.63[/C][C]91.6999369853815[/C][C]0.93006301461854[/C][/ROW]
[ROW][C]38[/C][C]93.02[/C][C]92.5839371008724[/C][C]0.436062899127592[/C][/ROW]
[ROW][C]39[/C][C]92.66[/C][C]92.9984032683591[/C][C]-0.338403268359144[/C][/ROW]
[ROW][C]40[/C][C]93.23[/C][C]92.6767599779476[/C][C]0.553240022052421[/C][/ROW]
[ROW][C]41[/C][C]93.79[/C][C]93.2025998787947[/C][C]0.587400121205334[/C][/ROW]
[ROW][C]42[/C][C]93.92[/C][C]93.7609080437504[/C][C]0.159091956249554[/C][/ROW]
[ROW][C]43[/C][C]94.04[/C][C]93.9121207094384[/C][C]0.127879290561566[/C][/ROW]
[ROW][C]44[/C][C]94.23[/C][C]94.033666567997[/C][C]0.196333432003044[/C][/ROW]
[ROW][C]45[/C][C]94.37[/C][C]94.2202762641546[/C][C]0.149723735845399[/C][/ROW]
[ROW][C]46[/C][C]94.29[/C][C]94.3625846859483[/C][C]-0.0725846859483141[/C][/ROW]
[ROW][C]47[/C][C]94.38[/C][C]94.2935948758466[/C][C]0.0864051241534156[/C][/ROW]
[ROW][C]48[/C][C]94[/C][C]94.3757206442408[/C][C]-0.375720644240843[/C][/ROW]
[ROW][C]49[/C][C]94.11[/C][C]94.01860818231[/C][C]0.0913918176899813[/C][/ROW]
[ROW][C]50[/C][C]93.98[/C][C]94.105473670049[/C][C]-0.125473670049033[/C][/ROW]
[ROW][C]51[/C][C]93.42[/C][C]93.9862142896941[/C][C]-0.56621428969413[/C][/ROW]
[ROW][C]52[/C][C]93.3[/C][C]93.4480426931303[/C][C]-0.148042693130293[/C][/ROW]
[ROW][C]53[/C][C]93.32[/C][C]93.3073320576488[/C][C]0.0126679423511433[/C][/ROW]
[ROW][C]54[/C][C]93.75[/C][C]93.3193725993384[/C][C]0.430627400661578[/C][/ROW]
[ROW][C]55[/C][C]93.82[/C][C]93.7286724703526[/C][C]0.0913275296474154[/C][/ROW]
[ROW][C]56[/C][C]94.06[/C][C]93.81547685402[/C][C]0.244523145980011[/C][/ROW]
[ROW][C]57[/C][C]94.09[/C][C]94.047889589382[/C][C]0.0421104106179939[/C][/ROW]
[ROW][C]58[/C][C]93.64[/C][C]94.0879144127161[/C][C]-0.447914412716102[/C][/ROW]
[ROW][C]59[/C][C]93.9[/C][C]93.6621836973264[/C][C]0.23781630267365[/C][/ROW]
[ROW][C]60[/C][C]93.18[/C][C]93.8882217568178[/C][C]-0.708221756817792[/C][/ROW]
[ROW][C]61[/C][C]93.54[/C][C]93.2150758462938[/C][C]0.324924153706249[/C][/ROW]
[ROW][C]62[/C][C]93.55[/C][C]93.5239075973552[/C][C]0.0260924026448066[/C][/ROW]
[ROW][C]63[/C][C]93.8[/C][C]93.5487077308826[/C][C]0.2512922691174[/C][/ROW]
[ROW][C]64[/C][C]93.39[/C][C]93.7875543374352[/C][C]-0.397554337435238[/C][/ROW]
[ROW][C]65[/C][C]93.27[/C][C]93.4096895318437[/C][C]-0.139689531843743[/C][/ROW]
[ROW][C]66[/C][C]93.58[/C][C]93.2769183536098[/C][C]0.30308164639024[/C][/ROW]
[ROW][C]67[/C][C]93.47[/C][C]93.5649893834228[/C][C]-0.0949893834227709[/C][/ROW]
[ROW][C]68[/C][C]93.75[/C][C]93.4747045053056[/C][C]0.275295494694433[/C][/ROW]
[ROW][C]69[/C][C]93.3[/C][C]93.7363655382452[/C][C]-0.436365538245184[/C][/ROW]
[ROW][C]70[/C][C]92.65[/C][C]93.3216117203405[/C][C]-0.671611720340465[/C][/ROW]
[ROW][C]71[/C][C]92.96[/C][C]92.6832626740777[/C][C]0.276737325922312[/C][/ROW]
[ROW][C]72[/C][C]92.84[/C][C]92.9462941291843[/C][C]-0.10629412918432[/C][/ROW]
[ROW][C]73[/C][C]93.29[/C][C]92.845264391416[/C][C]0.444735608584025[/C][/ROW]
[ROW][C]74[/C][C]93.57[/C][C]93.2679737381719[/C][C]0.302026261828118[/C][/ROW]
[ROW][C]75[/C][C]93.54[/C][C]93.5550416530775[/C][C]-0.0150416530774606[/C][/ROW]
[ROW][C]76[/C][C]94.38[/C][C]93.5407449625859[/C][C]0.839255037414091[/C][/ROW]
[ROW][C]77[/C][C]93.98[/C][C]94.3384345151639[/C][C]-0.358434515163907[/C][/ROW]
[ROW][C]78[/C][C]94.48[/C][C]93.997752058362[/C][C]0.482247941638008[/C][/ROW]
[ROW][C]79[/C][C]94.63[/C][C]94.4561158782351[/C][C]0.173884121764871[/C][/ROW]
[ROW][C]80[/C][C]95.45[/C][C]94.621388103134[/C][C]0.828611896865979[/C][/ROW]
[ROW][C]81[/C][C]95.59[/C][C]95.4089616341889[/C][C]0.181038365811062[/C][/ROW]
[ROW][C]82[/C][C]94.76[/C][C]95.5810337774414[/C][C]-0.8210337774414[/C][/ROW]
[ROW][C]83[/C][C]95.66[/C][C]94.8006630469938[/C][C]0.859336953006192[/C][/ROW]
[ROW][C]84[/C][C]95.03[/C][C]95.6174399252945[/C][C]-0.587439925294547[/C][/ROW]
[ROW][C]85[/C][C]96.45[/C][C]95.0590939276125[/C][C]1.39090607238752[/C][/ROW]
[ROW][C]86[/C][C]97.15[/C][C]96.3811130911548[/C][C]0.768886908845218[/C][/ROW]
[ROW][C]87[/C][C]97.5[/C][C]97.1119196123639[/C][C]0.38808038763608[/C][/ROW]
[ROW][C]88[/C][C]98.54[/C][C]97.4807796810882[/C][C]1.05922031891185[/C][/ROW]
[ROW][C]89[/C][C]99.54[/C][C]98.4875403731392[/C][C]1.05245962686081[/C][/ROW]
[ROW][C]90[/C][C]100.33[/C][C]99.4878752075225[/C][C]0.842124792477449[/C][/ROW]
[ROW][C]91[/C][C]100.28[/C][C]100.288292385829[/C][C]-0.00829238582866765[/C][/ROW]
[ROW][C]92[/C][C]101.81[/C][C]100.280410694035[/C][C]1.52958930596535[/C][/ROW]
[ROW][C]93[/C][C]101.91[/C][C]101.73424457612[/C][C]0.175755423879764[/C][/ROW]
[ROW][C]94[/C][C]101.92[/C][C]101.901295423822[/C][C]0.0187045761782372[/C][/ROW]
[ROW][C]95[/C][C]102.68[/C][C]101.919073625128[/C][C]0.760926374871573[/C][/ROW]
[ROW][C]96[/C][C]101.9[/C][C]102.64231387089[/C][C]-0.742313870890129[/C][/ROW]
[ROW][C]97[/C][C]102.14[/C][C]101.936764314265[/C][C]0.203235685734853[/C][/ROW]
[ROW][C]98[/C][C]102.3[/C][C]102.129934418696[/C][C]0.170065581303618[/C][/ROW]
[ROW][C]99[/C][C]102.06[/C][C]102.291577222625[/C][C]-0.231577222625191[/C][/ROW]
[ROW][C]100[/C][C]102.4[/C][C]102.07146924249[/C][C]0.328530757509583[/C][/ROW]
[ROW][C]101[/C][C]102.99[/C][C]102.383728974375[/C][C]0.606271025624721[/C][/ROW]
[ROW][C]102[/C][C]102.99[/C][C]102.959973431199[/C][C]0.0300265688005936[/C][/ROW]
[ROW][C]103[/C][C]102.83[/C][C]102.988512884839[/C][C]-0.158512884838913[/C][/ROW]
[ROW][C]104[/C][C]103.01[/C][C]102.837850611098[/C][C]0.17214938890163[/C][/ROW]
[ROW][C]105[/C][C]102.6[/C][C]103.00147401863[/C][C]-0.401474018629699[/C][/ROW]
[ROW][C]106[/C][C]102.18[/C][C]102.619883660496[/C][C]-0.439883660495909[/C][/ROW]
[ROW][C]107[/C][C]102.6[/C][C]102.201785961126[/C][C]0.398214038873888[/C][/ROW]
[ROW][C]108[/C][C]101.44[/C][C]102.580277795358[/C][C]-1.14027779535846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284479&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	89.01	88.83	0.180000000000007
3	88.21	89.0010852042145	-0.791085204214525
4	87.78	88.2491797946916	-0.469179794691641
5	87.93	87.8032369003131	0.126763099686912
6	88.11	87.9237218491842	0.186278150815795
7	88.2	88.1007742684788	0.0992257315212299
8	88.12	88.1950856825935	-0.0750856825934534
9	88.38	88.1237187418152	0.256281258184799
10	87.65	88.3673072495535	-0.7173072495535
11	88.24	87.6855258202513	0.554474179748738
12	87.83	88.2125387551067	-0.382538755106722
13	87.75	87.8489458604545	-0.0989458604545206
14	87.88	87.7549004563321	0.125099543667929
15	87.61	87.8738042395297	-0.263804239529676
16	88.05	87.6230653384598	0.426934661540244
17	87.77	88.0288553593257	-0.258855359325665
18	87.79	87.7828202370354	0.00717976296462552
19	88.34	87.789644410441	0.55035558955899
20	88.48	88.3127427350538	0.167257264946244
21	88.75	88.4717163091076	0.278283690892422
22	87.95	88.7362175429181	-0.786217542918109
23	89.09	87.9889387157671	1.10106128423286
24	88.73	89.0354681305764	-0.305468130576386
25	89.24	88.7451288111281	0.494871188871855
26	89.77	89.2154906911727	0.554509308827321
27	89.84	89.7425370152814	0.0974629847186321
28	90.97	89.8351729855255	1.1348270144745
29	91.53	90.9137958273005	0.616204172699454
30	92.2	91.4994814757679	0.700518524232152
31	92.27	92.1653056689584	0.104694331041571
32	92.42	92.2648148412159	0.155185158784093
33	92.07	92.4123142000028	-0.342314200002789
34	91.73	92.0869536732639	-0.356953673263874
35	92.1	91.7476787172335	0.352321282766496
36	91.68	92.0825507095181	-0.402550709518067
37	92.63	91.6999369853815	0.93006301461854
38	93.02	92.5839371008724	0.436062899127592
39	92.66	92.9984032683591	-0.338403268359144
40	93.23	92.6767599779476	0.553240022052421
41	93.79	93.2025998787947	0.587400121205334
42	93.92	93.7609080437504	0.159091956249554
43	94.04	93.9121207094384	0.127879290561566
44	94.23	94.033666567997	0.196333432003044
45	94.37	94.2202762641546	0.149723735845399
46	94.29	94.3625846859483	-0.0725846859483141
47	94.38	94.2935948758466	0.0864051241534156
48	94	94.3757206442408	-0.375720644240843
49	94.11	94.01860818231	0.0913918176899813
50	93.98	94.105473670049	-0.125473670049033
51	93.42	93.9862142896941	-0.56621428969413
52	93.3	93.4480426931303	-0.148042693130293
53	93.32	93.3073320576488	0.0126679423511433
54	93.75	93.3193725993384	0.430627400661578
55	93.82	93.7286724703526	0.0913275296474154
56	94.06	93.81547685402	0.244523145980011
57	94.09	94.047889589382	0.0421104106179939
58	93.64	94.0879144127161	-0.447914412716102
59	93.9	93.6621836973264	0.23781630267365
60	93.18	93.8882217568178	-0.708221756817792
61	93.54	93.2150758462938	0.324924153706249
62	93.55	93.5239075973552	0.0260924026448066
63	93.8	93.5487077308826	0.2512922691174
64	93.39	93.7875543374352	-0.397554337435238
65	93.27	93.4096895318437	-0.139689531843743
66	93.58	93.2769183536098	0.30308164639024
67	93.47	93.5649893834228	-0.0949893834227709
68	93.75	93.4747045053056	0.275295494694433
69	93.3	93.7363655382452	-0.436365538245184
70	92.65	93.3216117203405	-0.671611720340465
71	92.96	92.6832626740777	0.276737325922312
72	92.84	92.9462941291843	-0.10629412918432
73	93.29	92.845264391416	0.444735608584025
74	93.57	93.2679737381719	0.302026261828118
75	93.54	93.5550416530775	-0.0150416530774606
76	94.38	93.5407449625859	0.839255037414091
77	93.98	94.3384345151639	-0.358434515163907
78	94.48	93.997752058362	0.482247941638008
79	94.63	94.4561158782351	0.173884121764871
80	95.45	94.621388103134	0.828611896865979
81	95.59	95.4089616341889	0.181038365811062
82	94.76	95.5810337774414	-0.8210337774414
83	95.66	94.8006630469938	0.859336953006192
84	95.03	95.6174399252945	-0.587439925294547
85	96.45	95.0590939276125	1.39090607238752
86	97.15	96.3811130911548	0.768886908845218
87	97.5	97.1119196123639	0.38808038763608
88	98.54	97.4807796810882	1.05922031891185
89	99.54	98.4875403731392	1.05245962686081
90	100.33	99.4878752075225	0.842124792477449
91	100.28	100.288292385829	-0.00829238582866765
92	101.81	100.280410694035	1.52958930596535
93	101.91	101.73424457612	0.175755423879764
94	101.92	101.901295423822	0.0187045761782372
95	102.68	101.919073625128	0.760926374871573
96	101.9	102.64231387089	-0.742313870890129
97	102.14	101.936764314265	0.203235685734853
98	102.3	102.129934418696	0.170065581303618
99	102.06	102.291577222625	-0.231577222625191
100	102.4	102.07146924249	0.328530757509583
101	102.99	102.383728974375	0.606271025624721
102	102.99	102.959973431199	0.0300265688005936
103	102.83	102.988512884839	-0.158512884838913
104	103.01	102.837850611098	0.17214938890163
105	102.6	103.00147401863	-0.401474018629699
106	102.18	102.619883660496	-0.439883660495909
107	102.6	102.201785961126	0.398214038873888
108	101.44	102.580277795358	-1.14027779535846

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	101.49647413158	100.517620613589	102.475327649571
110	101.49647413158	100.146011121624	102.846937141535
111	101.49647413158	99.8565514282698	103.13639683489
112	101.49647413158	99.6110185886392	103.38192967452
113	101.49647413158	99.3939664060341	103.598981857125
114	101.49647413158	99.1973145313012	103.795633731858
115	101.49647413158	99.0162057994982	103.976742463661
116	101.49647413158	98.8474503244575	104.145497938702
117	101.49647413158	98.6888197258036	104.304128537356
118	101.49647413158	98.5386845187357	104.454263744424
119	101.49647413158	98.3958104082098	104.59713785495
120	101.49647413158	98.259235855364	104.733712407795

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 101.49647413158 & 100.517620613589 & 102.475327649571 \tabularnewline
110 & 101.49647413158 & 100.146011121624 & 102.846937141535 \tabularnewline
111 & 101.49647413158 & 99.8565514282698 & 103.13639683489 \tabularnewline
112 & 101.49647413158 & 99.6110185886392 & 103.38192967452 \tabularnewline
113 & 101.49647413158 & 99.3939664060341 & 103.598981857125 \tabularnewline
114 & 101.49647413158 & 99.1973145313012 & 103.795633731858 \tabularnewline
115 & 101.49647413158 & 99.0162057994982 & 103.976742463661 \tabularnewline
116 & 101.49647413158 & 98.8474503244575 & 104.145497938702 \tabularnewline
117 & 101.49647413158 & 98.6888197258036 & 104.304128537356 \tabularnewline
118 & 101.49647413158 & 98.5386845187357 & 104.454263744424 \tabularnewline
119 & 101.49647413158 & 98.3958104082098 & 104.59713785495 \tabularnewline
120 & 101.49647413158 & 98.259235855364 & 104.733712407795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284479&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]101.49647413158[/C][C]100.517620613589[/C][C]102.475327649571[/C][/ROW]
[ROW][C]110[/C][C]101.49647413158[/C][C]100.146011121624[/C][C]102.846937141535[/C][/ROW]
[ROW][C]111[/C][C]101.49647413158[/C][C]99.8565514282698[/C][C]103.13639683489[/C][/ROW]
[ROW][C]112[/C][C]101.49647413158[/C][C]99.6110185886392[/C][C]103.38192967452[/C][/ROW]
[ROW][C]113[/C][C]101.49647413158[/C][C]99.3939664060341[/C][C]103.598981857125[/C][/ROW]
[ROW][C]114[/C][C]101.49647413158[/C][C]99.1973145313012[/C][C]103.795633731858[/C][/ROW]
[ROW][C]115[/C][C]101.49647413158[/C][C]99.0162057994982[/C][C]103.976742463661[/C][/ROW]
[ROW][C]116[/C][C]101.49647413158[/C][C]98.8474503244575[/C][C]104.145497938702[/C][/ROW]
[ROW][C]117[/C][C]101.49647413158[/C][C]98.6888197258036[/C][C]104.304128537356[/C][/ROW]
[ROW][C]118[/C][C]101.49647413158[/C][C]98.5386845187357[/C][C]104.454263744424[/C][/ROW]
[ROW][C]119[/C][C]101.49647413158[/C][C]98.3958104082098[/C][C]104.59713785495[/C][/ROW]
[ROW][C]120[/C][C]101.49647413158[/C][C]98.259235855364[/C][C]104.733712407795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284479&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284479&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	101.49647413158	100.517620613589	102.475327649571
110	101.49647413158	100.146011121624	102.846937141535
111	101.49647413158	99.8565514282698	103.13639683489
112	101.49647413158	99.6110185886392	103.38192967452
113	101.49647413158	99.3939664060341	103.598981857125
114	101.49647413158	99.1973145313012	103.795633731858
115	101.49647413158	99.0162057994982	103.976742463661
116	101.49647413158	98.8474503244575	104.145497938702
117	101.49647413158	98.6888197258036	104.304128537356
118	101.49647413158	98.5386845187357	104.454263744424
119	101.49647413158	98.3958104082098	104.59713785495
120	101.49647413158	98.259235855364	104.733712407795

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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