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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 29 Nov 2014 12:32:58 +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/2014/Nov/29/t1417264401ferxj4lq4zj8x64.htm/, Retrieved Sun, 19 May 2024 13:04:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261096, Retrieved Sun, 19 May 2024 13:04:01 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

128

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

-       [Exponential Smoothing] [Addititief2] [2014-11-29 12:32:58] [d0f5aeb11a4aa291a6c63b9267d14d48] [Current]

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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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261096&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261096&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261096&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.235159112418892
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.235159112418892 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261096&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]0.235159112418892[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261096&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261096&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	0.235159112418892
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	39.99	40.44	-0.449999999999996
4	40.06	40.2741783994115	-0.214178399411502
5	40.08	40.2938123971066	-0.213812397106594
6	40.1	40.2635324635788	-0.163532463578846
7	40.1	40.245076314592	-0.145076314591975
8	40.12	40.2109602972195	-0.0909602972195245
9	40.07	40.20957015446	-0.139570154460017
10	40.24	40.126748960817	0.11325103918297
11	40.58	40.3233809746718	0.256619025328177
12	40.72	40.7237272768978	-0.0037272768977914
13	40.72	40.8628507737708	-0.142850773770768
14	40.89	40.8292581126025	0.0607418873975192
15	40.9	41.0135421209295	-0.11354212092953
16	41.04	40.9968416565496	0.0431583434504148
17	41.27	41.1469907342889	0.123009265711147
18	41.29	41.4059174840328	-0.115917484032792
19	41.29	41.3986584313738	-0.108658431373804
20	41.33	41.3731064110951	-0.0431064110951098
21	41.34	41.4029695457224	-0.0629695457224173
22	41.37	41.3981616832409	-0.0281616832409242
23	41.33	41.4215392068058	-0.0915392068057557
24	41.37	41.3600129281818	0.0099870718182089
25	41.37	41.4023614791262	-0.032361479126223
26	41.42	41.3947513824183	0.0252486175816671
27	41.61	41.4506888249187	0.159311175081349
28	41.58	41.6781522994492	-0.0981522994491897
29	41.75	41.6250708918288	0.124929108171159
30	41.75	41.8244491100217	-0.0744491100216536
31	41.75	41.8069417233886	-0.05694172338859
32	41.85	41.7935513582569	0.0564486417430743
33	41.84	41.9068257707465	-0.0668257707464761
34	41.97	41.881111081811	0.0888889181889638
35	42.01	42.0320141209162	-0.022014120916225
36	42.04	42.0668372997809	-0.0268372997808797
37	42.04	42.0905262641847	-0.0505262641846898
38	42.06	42.0786445527452	-0.0186445527451724
39	41.93	42.0942601162702	-0.164260116270178
40	41.93	41.9256328531223	0.00436714687774753
41	41.99	41.9266598275058	0.063340172494172
42	42.03	42.00155484625	0.0284451537499848
43	42.03	42.0482439833585	-0.0182439833584809
44	42.12	42.0439537444249	0.0760462555750792
45	42.22	42.1518367143887	0.0681632856112699
46	42.21	42.2678659321326	-0.0578659321326285
47	42.23	42.244258230893	-0.0142582308930344
48	42.22	42.2609052779716	-0.0409052779715608
49	42.22	42.2412860291105	-0.0212860291105201
50	42.25	42.236280425398	0.0137195746020353
51	42.27	42.2695067083841	0.000493291615853764
52	42.16	42.2896227104027	-0.1296227104027
53	42.24	42.1491407488751	0.0908592511249395
54	42.26	42.2505071297247	0.00949287027534496
55	42.26	42.2727394646729	-0.0127394646729115
56	42.26	42.2697436634677	-0.00974366346773792
57	42.36	42.267452352215	0.0925476477850466
58	42.33	42.3892157749245	-0.0592157749245459
59	42.23	42.3452906458521	-0.115290645852092
60	42.23	42.2181789999033	0.0118210000966883
61	40.9	42.2209588157939	-1.32095881579395
62	40.9	40.5803233131299	0.319676686870061
63	40.87	40.6554981990753	0.214501800924687
64	40.69	40.675940252193	0.0140597478069822
65	40.92	40.4992465300081	0.420753469991865
66	41.05	40.8281905425586	0.221809457441402
67	41.36	41.0103510576966	0.349648942303368
68	41.79	41.4025741926269	0.387425807373106
69	41.82	41.9236809016169	-0.103680901616926
70	41.8	41.9292993928179	-0.129299392817906
71	41.87	41.8788934623665	-0.00889346236654376
72	41.87	41.9468020836501	-0.0768020836500938

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 39.99 & 40.44 & -0.449999999999996 \tabularnewline
4 & 40.06 & 40.2741783994115 & -0.214178399411502 \tabularnewline
5 & 40.08 & 40.2938123971066 & -0.213812397106594 \tabularnewline
6 & 40.1 & 40.2635324635788 & -0.163532463578846 \tabularnewline
7 & 40.1 & 40.245076314592 & -0.145076314591975 \tabularnewline
8 & 40.12 & 40.2109602972195 & -0.0909602972195245 \tabularnewline
9 & 40.07 & 40.20957015446 & -0.139570154460017 \tabularnewline
10 & 40.24 & 40.126748960817 & 0.11325103918297 \tabularnewline
11 & 40.58 & 40.3233809746718 & 0.256619025328177 \tabularnewline
12 & 40.72 & 40.7237272768978 & -0.0037272768977914 \tabularnewline
13 & 40.72 & 40.8628507737708 & -0.142850773770768 \tabularnewline
14 & 40.89 & 40.8292581126025 & 0.0607418873975192 \tabularnewline
15 & 40.9 & 41.0135421209295 & -0.11354212092953 \tabularnewline
16 & 41.04 & 40.9968416565496 & 0.0431583434504148 \tabularnewline
17 & 41.27 & 41.1469907342889 & 0.123009265711147 \tabularnewline
18 & 41.29 & 41.4059174840328 & -0.115917484032792 \tabularnewline
19 & 41.29 & 41.3986584313738 & -0.108658431373804 \tabularnewline
20 & 41.33 & 41.3731064110951 & -0.0431064110951098 \tabularnewline
21 & 41.34 & 41.4029695457224 & -0.0629695457224173 \tabularnewline
22 & 41.37 & 41.3981616832409 & -0.0281616832409242 \tabularnewline
23 & 41.33 & 41.4215392068058 & -0.0915392068057557 \tabularnewline
24 & 41.37 & 41.3600129281818 & 0.0099870718182089 \tabularnewline
25 & 41.37 & 41.4023614791262 & -0.032361479126223 \tabularnewline
26 & 41.42 & 41.3947513824183 & 0.0252486175816671 \tabularnewline
27 & 41.61 & 41.4506888249187 & 0.159311175081349 \tabularnewline
28 & 41.58 & 41.6781522994492 & -0.0981522994491897 \tabularnewline
29 & 41.75 & 41.6250708918288 & 0.124929108171159 \tabularnewline
30 & 41.75 & 41.8244491100217 & -0.0744491100216536 \tabularnewline
31 & 41.75 & 41.8069417233886 & -0.05694172338859 \tabularnewline
32 & 41.85 & 41.7935513582569 & 0.0564486417430743 \tabularnewline
33 & 41.84 & 41.9068257707465 & -0.0668257707464761 \tabularnewline
34 & 41.97 & 41.881111081811 & 0.0888889181889638 \tabularnewline
35 & 42.01 & 42.0320141209162 & -0.022014120916225 \tabularnewline
36 & 42.04 & 42.0668372997809 & -0.0268372997808797 \tabularnewline
37 & 42.04 & 42.0905262641847 & -0.0505262641846898 \tabularnewline
38 & 42.06 & 42.0786445527452 & -0.0186445527451724 \tabularnewline
39 & 41.93 & 42.0942601162702 & -0.164260116270178 \tabularnewline
40 & 41.93 & 41.9256328531223 & 0.00436714687774753 \tabularnewline
41 & 41.99 & 41.9266598275058 & 0.063340172494172 \tabularnewline
42 & 42.03 & 42.00155484625 & 0.0284451537499848 \tabularnewline
43 & 42.03 & 42.0482439833585 & -0.0182439833584809 \tabularnewline
44 & 42.12 & 42.0439537444249 & 0.0760462555750792 \tabularnewline
45 & 42.22 & 42.1518367143887 & 0.0681632856112699 \tabularnewline
46 & 42.21 & 42.2678659321326 & -0.0578659321326285 \tabularnewline
47 & 42.23 & 42.244258230893 & -0.0142582308930344 \tabularnewline
48 & 42.22 & 42.2609052779716 & -0.0409052779715608 \tabularnewline
49 & 42.22 & 42.2412860291105 & -0.0212860291105201 \tabularnewline
50 & 42.25 & 42.236280425398 & 0.0137195746020353 \tabularnewline
51 & 42.27 & 42.2695067083841 & 0.000493291615853764 \tabularnewline
52 & 42.16 & 42.2896227104027 & -0.1296227104027 \tabularnewline
53 & 42.24 & 42.1491407488751 & 0.0908592511249395 \tabularnewline
54 & 42.26 & 42.2505071297247 & 0.00949287027534496 \tabularnewline
55 & 42.26 & 42.2727394646729 & -0.0127394646729115 \tabularnewline
56 & 42.26 & 42.2697436634677 & -0.00974366346773792 \tabularnewline
57 & 42.36 & 42.267452352215 & 0.0925476477850466 \tabularnewline
58 & 42.33 & 42.3892157749245 & -0.0592157749245459 \tabularnewline
59 & 42.23 & 42.3452906458521 & -0.115290645852092 \tabularnewline
60 & 42.23 & 42.2181789999033 & 0.0118210000966883 \tabularnewline
61 & 40.9 & 42.2209588157939 & -1.32095881579395 \tabularnewline
62 & 40.9 & 40.5803233131299 & 0.319676686870061 \tabularnewline
63 & 40.87 & 40.6554981990753 & 0.214501800924687 \tabularnewline
64 & 40.69 & 40.675940252193 & 0.0140597478069822 \tabularnewline
65 & 40.92 & 40.4992465300081 & 0.420753469991865 \tabularnewline
66 & 41.05 & 40.8281905425586 & 0.221809457441402 \tabularnewline
67 & 41.36 & 41.0103510576966 & 0.349648942303368 \tabularnewline
68 & 41.79 & 41.4025741926269 & 0.387425807373106 \tabularnewline
69 & 41.82 & 41.9236809016169 & -0.103680901616926 \tabularnewline
70 & 41.8 & 41.9292993928179 & -0.129299392817906 \tabularnewline
71 & 41.87 & 41.8788934623665 & -0.00889346236654376 \tabularnewline
72 & 41.87 & 41.9468020836501 & -0.0768020836500938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261096&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]39.99[/C][C]40.44[/C][C]-0.449999999999996[/C][/ROW]
[ROW][C]4[/C][C]40.06[/C][C]40.2741783994115[/C][C]-0.214178399411502[/C][/ROW]
[ROW][C]5[/C][C]40.08[/C][C]40.2938123971066[/C][C]-0.213812397106594[/C][/ROW]
[ROW][C]6[/C][C]40.1[/C][C]40.2635324635788[/C][C]-0.163532463578846[/C][/ROW]
[ROW][C]7[/C][C]40.1[/C][C]40.245076314592[/C][C]-0.145076314591975[/C][/ROW]
[ROW][C]8[/C][C]40.12[/C][C]40.2109602972195[/C][C]-0.0909602972195245[/C][/ROW]
[ROW][C]9[/C][C]40.07[/C][C]40.20957015446[/C][C]-0.139570154460017[/C][/ROW]
[ROW][C]10[/C][C]40.24[/C][C]40.126748960817[/C][C]0.11325103918297[/C][/ROW]
[ROW][C]11[/C][C]40.58[/C][C]40.3233809746718[/C][C]0.256619025328177[/C][/ROW]
[ROW][C]12[/C][C]40.72[/C][C]40.7237272768978[/C][C]-0.0037272768977914[/C][/ROW]
[ROW][C]13[/C][C]40.72[/C][C]40.8628507737708[/C][C]-0.142850773770768[/C][/ROW]
[ROW][C]14[/C][C]40.89[/C][C]40.8292581126025[/C][C]0.0607418873975192[/C][/ROW]
[ROW][C]15[/C][C]40.9[/C][C]41.0135421209295[/C][C]-0.11354212092953[/C][/ROW]
[ROW][C]16[/C][C]41.04[/C][C]40.9968416565496[/C][C]0.0431583434504148[/C][/ROW]
[ROW][C]17[/C][C]41.27[/C][C]41.1469907342889[/C][C]0.123009265711147[/C][/ROW]
[ROW][C]18[/C][C]41.29[/C][C]41.4059174840328[/C][C]-0.115917484032792[/C][/ROW]
[ROW][C]19[/C][C]41.29[/C][C]41.3986584313738[/C][C]-0.108658431373804[/C][/ROW]
[ROW][C]20[/C][C]41.33[/C][C]41.3731064110951[/C][C]-0.0431064110951098[/C][/ROW]
[ROW][C]21[/C][C]41.34[/C][C]41.4029695457224[/C][C]-0.0629695457224173[/C][/ROW]
[ROW][C]22[/C][C]41.37[/C][C]41.3981616832409[/C][C]-0.0281616832409242[/C][/ROW]
[ROW][C]23[/C][C]41.33[/C][C]41.4215392068058[/C][C]-0.0915392068057557[/C][/ROW]
[ROW][C]24[/C][C]41.37[/C][C]41.3600129281818[/C][C]0.0099870718182089[/C][/ROW]
[ROW][C]25[/C][C]41.37[/C][C]41.4023614791262[/C][C]-0.032361479126223[/C][/ROW]
[ROW][C]26[/C][C]41.42[/C][C]41.3947513824183[/C][C]0.0252486175816671[/C][/ROW]
[ROW][C]27[/C][C]41.61[/C][C]41.4506888249187[/C][C]0.159311175081349[/C][/ROW]
[ROW][C]28[/C][C]41.58[/C][C]41.6781522994492[/C][C]-0.0981522994491897[/C][/ROW]
[ROW][C]29[/C][C]41.75[/C][C]41.6250708918288[/C][C]0.124929108171159[/C][/ROW]
[ROW][C]30[/C][C]41.75[/C][C]41.8244491100217[/C][C]-0.0744491100216536[/C][/ROW]
[ROW][C]31[/C][C]41.75[/C][C]41.8069417233886[/C][C]-0.05694172338859[/C][/ROW]
[ROW][C]32[/C][C]41.85[/C][C]41.7935513582569[/C][C]0.0564486417430743[/C][/ROW]
[ROW][C]33[/C][C]41.84[/C][C]41.9068257707465[/C][C]-0.0668257707464761[/C][/ROW]
[ROW][C]34[/C][C]41.97[/C][C]41.881111081811[/C][C]0.0888889181889638[/C][/ROW]
[ROW][C]35[/C][C]42.01[/C][C]42.0320141209162[/C][C]-0.022014120916225[/C][/ROW]
[ROW][C]36[/C][C]42.04[/C][C]42.0668372997809[/C][C]-0.0268372997808797[/C][/ROW]
[ROW][C]37[/C][C]42.04[/C][C]42.0905262641847[/C][C]-0.0505262641846898[/C][/ROW]
[ROW][C]38[/C][C]42.06[/C][C]42.0786445527452[/C][C]-0.0186445527451724[/C][/ROW]
[ROW][C]39[/C][C]41.93[/C][C]42.0942601162702[/C][C]-0.164260116270178[/C][/ROW]
[ROW][C]40[/C][C]41.93[/C][C]41.9256328531223[/C][C]0.00436714687774753[/C][/ROW]
[ROW][C]41[/C][C]41.99[/C][C]41.9266598275058[/C][C]0.063340172494172[/C][/ROW]
[ROW][C]42[/C][C]42.03[/C][C]42.00155484625[/C][C]0.0284451537499848[/C][/ROW]
[ROW][C]43[/C][C]42.03[/C][C]42.0482439833585[/C][C]-0.0182439833584809[/C][/ROW]
[ROW][C]44[/C][C]42.12[/C][C]42.0439537444249[/C][C]0.0760462555750792[/C][/ROW]
[ROW][C]45[/C][C]42.22[/C][C]42.1518367143887[/C][C]0.0681632856112699[/C][/ROW]
[ROW][C]46[/C][C]42.21[/C][C]42.2678659321326[/C][C]-0.0578659321326285[/C][/ROW]
[ROW][C]47[/C][C]42.23[/C][C]42.244258230893[/C][C]-0.0142582308930344[/C][/ROW]
[ROW][C]48[/C][C]42.22[/C][C]42.2609052779716[/C][C]-0.0409052779715608[/C][/ROW]
[ROW][C]49[/C][C]42.22[/C][C]42.2412860291105[/C][C]-0.0212860291105201[/C][/ROW]
[ROW][C]50[/C][C]42.25[/C][C]42.236280425398[/C][C]0.0137195746020353[/C][/ROW]
[ROW][C]51[/C][C]42.27[/C][C]42.2695067083841[/C][C]0.000493291615853764[/C][/ROW]
[ROW][C]52[/C][C]42.16[/C][C]42.2896227104027[/C][C]-0.1296227104027[/C][/ROW]
[ROW][C]53[/C][C]42.24[/C][C]42.1491407488751[/C][C]0.0908592511249395[/C][/ROW]
[ROW][C]54[/C][C]42.26[/C][C]42.2505071297247[/C][C]0.00949287027534496[/C][/ROW]
[ROW][C]55[/C][C]42.26[/C][C]42.2727394646729[/C][C]-0.0127394646729115[/C][/ROW]
[ROW][C]56[/C][C]42.26[/C][C]42.2697436634677[/C][C]-0.00974366346773792[/C][/ROW]
[ROW][C]57[/C][C]42.36[/C][C]42.267452352215[/C][C]0.0925476477850466[/C][/ROW]
[ROW][C]58[/C][C]42.33[/C][C]42.3892157749245[/C][C]-0.0592157749245459[/C][/ROW]
[ROW][C]59[/C][C]42.23[/C][C]42.3452906458521[/C][C]-0.115290645852092[/C][/ROW]
[ROW][C]60[/C][C]42.23[/C][C]42.2181789999033[/C][C]0.0118210000966883[/C][/ROW]
[ROW][C]61[/C][C]40.9[/C][C]42.2209588157939[/C][C]-1.32095881579395[/C][/ROW]
[ROW][C]62[/C][C]40.9[/C][C]40.5803233131299[/C][C]0.319676686870061[/C][/ROW]
[ROW][C]63[/C][C]40.87[/C][C]40.6554981990753[/C][C]0.214501800924687[/C][/ROW]
[ROW][C]64[/C][C]40.69[/C][C]40.675940252193[/C][C]0.0140597478069822[/C][/ROW]
[ROW][C]65[/C][C]40.92[/C][C]40.4992465300081[/C][C]0.420753469991865[/C][/ROW]
[ROW][C]66[/C][C]41.05[/C][C]40.8281905425586[/C][C]0.221809457441402[/C][/ROW]
[ROW][C]67[/C][C]41.36[/C][C]41.0103510576966[/C][C]0.349648942303368[/C][/ROW]
[ROW][C]68[/C][C]41.79[/C][C]41.4025741926269[/C][C]0.387425807373106[/C][/ROW]
[ROW][C]69[/C][C]41.82[/C][C]41.9236809016169[/C][C]-0.103680901616926[/C][/ROW]
[ROW][C]70[/C][C]41.8[/C][C]41.9292993928179[/C][C]-0.129299392817906[/C][/ROW]
[ROW][C]71[/C][C]41.87[/C][C]41.8788934623665[/C][C]-0.00889346236654376[/C][/ROW]
[ROW][C]72[/C][C]41.87[/C][C]41.9468020836501[/C][C]-0.0768020836500938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261096&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261096&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	39.99	40.44	-0.449999999999996
4	40.06	40.2741783994115	-0.214178399411502
5	40.08	40.2938123971066	-0.213812397106594
6	40.1	40.2635324635788	-0.163532463578846
7	40.1	40.245076314592	-0.145076314591975
8	40.12	40.2109602972195	-0.0909602972195245
9	40.07	40.20957015446	-0.139570154460017
10	40.24	40.126748960817	0.11325103918297
11	40.58	40.3233809746718	0.256619025328177
12	40.72	40.7237272768978	-0.0037272768977914
13	40.72	40.8628507737708	-0.142850773770768
14	40.89	40.8292581126025	0.0607418873975192
15	40.9	41.0135421209295	-0.11354212092953
16	41.04	40.9968416565496	0.0431583434504148
17	41.27	41.1469907342889	0.123009265711147
18	41.29	41.4059174840328	-0.115917484032792
19	41.29	41.3986584313738	-0.108658431373804
20	41.33	41.3731064110951	-0.0431064110951098
21	41.34	41.4029695457224	-0.0629695457224173
22	41.37	41.3981616832409	-0.0281616832409242
23	41.33	41.4215392068058	-0.0915392068057557
24	41.37	41.3600129281818	0.0099870718182089
25	41.37	41.4023614791262	-0.032361479126223
26	41.42	41.3947513824183	0.0252486175816671
27	41.61	41.4506888249187	0.159311175081349
28	41.58	41.6781522994492	-0.0981522994491897
29	41.75	41.6250708918288	0.124929108171159
30	41.75	41.8244491100217	-0.0744491100216536
31	41.75	41.8069417233886	-0.05694172338859
32	41.85	41.7935513582569	0.0564486417430743
33	41.84	41.9068257707465	-0.0668257707464761
34	41.97	41.881111081811	0.0888889181889638
35	42.01	42.0320141209162	-0.022014120916225
36	42.04	42.0668372997809	-0.0268372997808797
37	42.04	42.0905262641847	-0.0505262641846898
38	42.06	42.0786445527452	-0.0186445527451724
39	41.93	42.0942601162702	-0.164260116270178
40	41.93	41.9256328531223	0.00436714687774753
41	41.99	41.9266598275058	0.063340172494172
42	42.03	42.00155484625	0.0284451537499848
43	42.03	42.0482439833585	-0.0182439833584809
44	42.12	42.0439537444249	0.0760462555750792
45	42.22	42.1518367143887	0.0681632856112699
46	42.21	42.2678659321326	-0.0578659321326285
47	42.23	42.244258230893	-0.0142582308930344
48	42.22	42.2609052779716	-0.0409052779715608
49	42.22	42.2412860291105	-0.0212860291105201
50	42.25	42.236280425398	0.0137195746020353
51	42.27	42.2695067083841	0.000493291615853764
52	42.16	42.2896227104027	-0.1296227104027
53	42.24	42.1491407488751	0.0908592511249395
54	42.26	42.2505071297247	0.00949287027534496
55	42.26	42.2727394646729	-0.0127394646729115
56	42.26	42.2697436634677	-0.00974366346773792
57	42.36	42.267452352215	0.0925476477850466
58	42.33	42.3892157749245	-0.0592157749245459
59	42.23	42.3452906458521	-0.115290645852092
60	42.23	42.2181789999033	0.0118210000966883
61	40.9	42.2209588157939	-1.32095881579395
62	40.9	40.5803233131299	0.319676686870061
63	40.87	40.6554981990753	0.214501800924687
64	40.69	40.675940252193	0.0140597478069822
65	40.92	40.4992465300081	0.420753469991865
66	41.05	40.8281905425586	0.221809457441402
67	41.36	41.0103510576966	0.349648942303368
68	41.79	41.4025741926269	0.387425807373106
69	41.82	41.9236809016169	-0.103680901616926
70	41.8	41.9292993928179	-0.129299392817906
71	41.87	41.8788934623665	-0.00889346236654376
72	41.87	41.9468020836501	-0.0768020836500938

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	41.928741373827	41.5119823858589	42.3455003617952
74	41.987482747654	41.3251613140363	42.6498041812718
75	42.046224121481	41.1439188991382	42.9485293438239
76	42.1049654953081	40.9563345777804	43.2535964128358
77	42.1637068691351	40.7589028526029	43.5685108856673
78	42.2224482429621	40.5504050117938	43.8944914741304
79	42.2811896167891	40.3304652531415	44.2319139804367
80	42.3399309906161	40.0990661832041	44.5807957980282
81	42.3986723644432	39.856353142642	44.9409915862443
82	42.4574137382702	39.6025457559653	45.312281720575
83	42.5161551120972	39.3378949858989	45.6944152382955
84	42.5748964859242	39.0626613631209	46.0871316087275

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 41.928741373827 & 41.5119823858589 & 42.3455003617952 \tabularnewline
74 & 41.987482747654 & 41.3251613140363 & 42.6498041812718 \tabularnewline
75 & 42.046224121481 & 41.1439188991382 & 42.9485293438239 \tabularnewline
76 & 42.1049654953081 & 40.9563345777804 & 43.2535964128358 \tabularnewline
77 & 42.1637068691351 & 40.7589028526029 & 43.5685108856673 \tabularnewline
78 & 42.2224482429621 & 40.5504050117938 & 43.8944914741304 \tabularnewline
79 & 42.2811896167891 & 40.3304652531415 & 44.2319139804367 \tabularnewline
80 & 42.3399309906161 & 40.0990661832041 & 44.5807957980282 \tabularnewline
81 & 42.3986723644432 & 39.856353142642 & 44.9409915862443 \tabularnewline
82 & 42.4574137382702 & 39.6025457559653 & 45.312281720575 \tabularnewline
83 & 42.5161551120972 & 39.3378949858989 & 45.6944152382955 \tabularnewline
84 & 42.5748964859242 & 39.0626613631209 & 46.0871316087275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261096&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]41.928741373827[/C][C]41.5119823858589[/C][C]42.3455003617952[/C][/ROW]
[ROW][C]74[/C][C]41.987482747654[/C][C]41.3251613140363[/C][C]42.6498041812718[/C][/ROW]
[ROW][C]75[/C][C]42.046224121481[/C][C]41.1439188991382[/C][C]42.9485293438239[/C][/ROW]
[ROW][C]76[/C][C]42.1049654953081[/C][C]40.9563345777804[/C][C]43.2535964128358[/C][/ROW]
[ROW][C]77[/C][C]42.1637068691351[/C][C]40.7589028526029[/C][C]43.5685108856673[/C][/ROW]
[ROW][C]78[/C][C]42.2224482429621[/C][C]40.5504050117938[/C][C]43.8944914741304[/C][/ROW]
[ROW][C]79[/C][C]42.2811896167891[/C][C]40.3304652531415[/C][C]44.2319139804367[/C][/ROW]
[ROW][C]80[/C][C]42.3399309906161[/C][C]40.0990661832041[/C][C]44.5807957980282[/C][/ROW]
[ROW][C]81[/C][C]42.3986723644432[/C][C]39.856353142642[/C][C]44.9409915862443[/C][/ROW]
[ROW][C]82[/C][C]42.4574137382702[/C][C]39.6025457559653[/C][C]45.312281720575[/C][/ROW]
[ROW][C]83[/C][C]42.5161551120972[/C][C]39.3378949858989[/C][C]45.6944152382955[/C][/ROW]
[ROW][C]84[/C][C]42.5748964859242[/C][C]39.0626613631209[/C][C]46.0871316087275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261096&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261096&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	41.928741373827	41.5119823858589	42.3455003617952
74	41.987482747654	41.3251613140363	42.6498041812718
75	42.046224121481	41.1439188991382	42.9485293438239
76	42.1049654953081	40.9563345777804	43.2535964128358
77	42.1637068691351	40.7589028526029	43.5685108856673
78	42.2224482429621	40.5504050117938	43.8944914741304
79	42.2811896167891	40.3304652531415	44.2319139804367
80	42.3399309906161	40.0990661832041	44.5807957980282
81	42.3986723644432	39.856353142642	44.9409915862443
82	42.4574137382702	39.6025457559653	45.312281720575
83	42.5161551120972	39.3378949858989	45.6944152382955
84	42.5748964859242	39.0626613631209	46.0871316087275

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code