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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

Wed, 20 Jan 2010 09:42:27 -0700

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/2010/Jan/20/t1264005810hhmytqxdqhg3xbo.htm/, Retrieved Mon, 06 May 2024 06:04:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72316, Retrieved Mon, 06 May 2024 06:04:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

175

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

-       [Exponential Smoothing] [] [2010-01-20 16:42:27] [58d9ccda37eeb031a0ffa1e9ea016ece] [Current]

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Dataseries X:

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Boxplots

4,26
4,26
4,07
4,26
4,4
4,46
4,34
4,18
4,11
3,98
3,85
3,66
3,59
3,57
3,76
3,6
3,43
3,26
3,3
3,31
3,14
3,3
3,49
3,39
3,37
3,54
3,7
3,96
4,03
4,02
4,04
3,92
3,79
3,83
3,76
3,82
4,06
4,11
4,01
4,22
4,34
4,64
4,62
4,44
4,39
4,42
4,28
4,41
4,25
4,23
4,23
4,37
4,51
4,84
4,85
4,58
4,56
4,46
4,26
3,87
4,13
4,24
4,03
3,93
4,03
4,12
3,92
3,77

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72316&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72316&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.770019236878996
beta	0.0459442665820473
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.770019236878996 \tabularnewline
beta & 0.0459442665820473 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72316&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]0.770019236878996[/C][/ROW]
[ROW][C]beta[/C][C]0.0459442665820473[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72316&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	0.770019236878996
beta	0.0459442665820473
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.59	4.00846955128205	-0.418469551282054
14	3.57	3.66284997093498	-0.0928499709349788
15	3.76	3.77176222129098	-0.0117622212909771
16	3.6	3.58478080858013	0.0152191914198729
17	3.43	3.3836973601118	0.0463026398881983
18	3.26	3.19110352494215	0.0688964750578451
19	3.3	3.55709479485318	-0.257094794853185
20	3.31	3.16463769083862	0.145362309161376
21	3.14	3.16222292221461	-0.0222229222146098
22	3.3	2.96872809975901	0.331271900240985
23	3.49	3.08665081777928	0.403349182220716
24	3.39	3.23684410436798	0.153155895632024
25	3.37	3.22647881180731	0.143521188192688
26	3.54	3.42114828365876	0.118851716341236
27	3.7	3.75187223626913	-0.0518722362691264
28	3.96	3.57894024347777	0.381059756522229
29	4.03	3.71838205633193	0.311617943668066
30	4.02	3.79634096634602	0.223659033653977
31	4.04	4.27306455749515	-0.233064557495147
32	3.92	4.0590526264077	-0.139052626407704
33	3.79	3.85641351993006	-0.0664135199300588
34	3.83	3.76594673576181	0.0640532642381868
35	3.76	3.74098733886507	0.0190126611349264
36	3.82	3.57040240918538	0.249597590814619
37	4.06	3.66820313247483	0.391796867525171
38	4.11	4.09327949150078	0.0167205084992190
39	4.01	4.34738737176980	-0.337387371769804
40	4.22	4.08535846395236	0.134641536047645
41	4.34	4.04155465107101	0.298445348928992
42	4.64	4.11114695829864	0.528853041701364
43	4.62	4.75064071659109	-0.130640716591087
44	4.44	4.67354414644109	-0.233544146441088
45	4.39	4.44793352835303	-0.05793352835303
46	4.42	4.42738453568961	-0.00738453568961361
47	4.28	4.36791404633415	-0.087914046334145
48	4.41	4.19509660330618	0.214903396693819
49	4.25	4.32473082800756	-0.0747308280075609
50	4.23	4.31365233738552	-0.0836523373855202
51	4.23	4.41482300521861	-0.184823005218613
52	4.37	4.39001639067437	-0.0200163906743729
53	4.51	4.27051046934986	0.239489530650142
54	4.84	4.3513250066527	0.488674993347297
55	4.85	4.8104186065169	0.0395813934831004
56	4.58	4.84896122840081	-0.268961228400814
57	4.56	4.6434435574781	-0.0834435574781
58	4.46	4.62095187216924	-0.160951872169243
59	4.26	4.42535366537929	-0.165353665379286
60	3.87	4.26045108029768	-0.39045108029768
61	4.13	3.83382686825878	0.296173131741222
62	4.24	4.09590807066401	0.144091929335993
63	4.03	4.34684431171796	-0.316844311717957
64	3.93	4.25127587092082	-0.321275870920824
65	4.03	3.94181254420326	0.0881874557967421
66	4.12	3.94041349589949	0.179586504100506
67	3.92	4.02426926105732	-0.104269261057318
68	3.77	3.84204523678205	-0.0720452367820461

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.59 & 4.00846955128205 & -0.418469551282054 \tabularnewline
14 & 3.57 & 3.66284997093498 & -0.0928499709349788 \tabularnewline
15 & 3.76 & 3.77176222129098 & -0.0117622212909771 \tabularnewline
16 & 3.6 & 3.58478080858013 & 0.0152191914198729 \tabularnewline
17 & 3.43 & 3.3836973601118 & 0.0463026398881983 \tabularnewline
18 & 3.26 & 3.19110352494215 & 0.0688964750578451 \tabularnewline
19 & 3.3 & 3.55709479485318 & -0.257094794853185 \tabularnewline
20 & 3.31 & 3.16463769083862 & 0.145362309161376 \tabularnewline
21 & 3.14 & 3.16222292221461 & -0.0222229222146098 \tabularnewline
22 & 3.3 & 2.96872809975901 & 0.331271900240985 \tabularnewline
23 & 3.49 & 3.08665081777928 & 0.403349182220716 \tabularnewline
24 & 3.39 & 3.23684410436798 & 0.153155895632024 \tabularnewline
25 & 3.37 & 3.22647881180731 & 0.143521188192688 \tabularnewline
26 & 3.54 & 3.42114828365876 & 0.118851716341236 \tabularnewline
27 & 3.7 & 3.75187223626913 & -0.0518722362691264 \tabularnewline
28 & 3.96 & 3.57894024347777 & 0.381059756522229 \tabularnewline
29 & 4.03 & 3.71838205633193 & 0.311617943668066 \tabularnewline
30 & 4.02 & 3.79634096634602 & 0.223659033653977 \tabularnewline
31 & 4.04 & 4.27306455749515 & -0.233064557495147 \tabularnewline
32 & 3.92 & 4.0590526264077 & -0.139052626407704 \tabularnewline
33 & 3.79 & 3.85641351993006 & -0.0664135199300588 \tabularnewline
34 & 3.83 & 3.76594673576181 & 0.0640532642381868 \tabularnewline
35 & 3.76 & 3.74098733886507 & 0.0190126611349264 \tabularnewline
36 & 3.82 & 3.57040240918538 & 0.249597590814619 \tabularnewline
37 & 4.06 & 3.66820313247483 & 0.391796867525171 \tabularnewline
38 & 4.11 & 4.09327949150078 & 0.0167205084992190 \tabularnewline
39 & 4.01 & 4.34738737176980 & -0.337387371769804 \tabularnewline
40 & 4.22 & 4.08535846395236 & 0.134641536047645 \tabularnewline
41 & 4.34 & 4.04155465107101 & 0.298445348928992 \tabularnewline
42 & 4.64 & 4.11114695829864 & 0.528853041701364 \tabularnewline
43 & 4.62 & 4.75064071659109 & -0.130640716591087 \tabularnewline
44 & 4.44 & 4.67354414644109 & -0.233544146441088 \tabularnewline
45 & 4.39 & 4.44793352835303 & -0.05793352835303 \tabularnewline
46 & 4.42 & 4.42738453568961 & -0.00738453568961361 \tabularnewline
47 & 4.28 & 4.36791404633415 & -0.087914046334145 \tabularnewline
48 & 4.41 & 4.19509660330618 & 0.214903396693819 \tabularnewline
49 & 4.25 & 4.32473082800756 & -0.0747308280075609 \tabularnewline
50 & 4.23 & 4.31365233738552 & -0.0836523373855202 \tabularnewline
51 & 4.23 & 4.41482300521861 & -0.184823005218613 \tabularnewline
52 & 4.37 & 4.39001639067437 & -0.0200163906743729 \tabularnewline
53 & 4.51 & 4.27051046934986 & 0.239489530650142 \tabularnewline
54 & 4.84 & 4.3513250066527 & 0.488674993347297 \tabularnewline
55 & 4.85 & 4.8104186065169 & 0.0395813934831004 \tabularnewline
56 & 4.58 & 4.84896122840081 & -0.268961228400814 \tabularnewline
57 & 4.56 & 4.6434435574781 & -0.0834435574781 \tabularnewline
58 & 4.46 & 4.62095187216924 & -0.160951872169243 \tabularnewline
59 & 4.26 & 4.42535366537929 & -0.165353665379286 \tabularnewline
60 & 3.87 & 4.26045108029768 & -0.39045108029768 \tabularnewline
61 & 4.13 & 3.83382686825878 & 0.296173131741222 \tabularnewline
62 & 4.24 & 4.09590807066401 & 0.144091929335993 \tabularnewline
63 & 4.03 & 4.34684431171796 & -0.316844311717957 \tabularnewline
64 & 3.93 & 4.25127587092082 & -0.321275870920824 \tabularnewline
65 & 4.03 & 3.94181254420326 & 0.0881874557967421 \tabularnewline
66 & 4.12 & 3.94041349589949 & 0.179586504100506 \tabularnewline
67 & 3.92 & 4.02426926105732 & -0.104269261057318 \tabularnewline
68 & 3.77 & 3.84204523678205 & -0.0720452367820461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72316&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]3.59[/C][C]4.00846955128205[/C][C]-0.418469551282054[/C][/ROW]
[ROW][C]14[/C][C]3.57[/C][C]3.66284997093498[/C][C]-0.0928499709349788[/C][/ROW]
[ROW][C]15[/C][C]3.76[/C][C]3.77176222129098[/C][C]-0.0117622212909771[/C][/ROW]
[ROW][C]16[/C][C]3.6[/C][C]3.58478080858013[/C][C]0.0152191914198729[/C][/ROW]
[ROW][C]17[/C][C]3.43[/C][C]3.3836973601118[/C][C]0.0463026398881983[/C][/ROW]
[ROW][C]18[/C][C]3.26[/C][C]3.19110352494215[/C][C]0.0688964750578451[/C][/ROW]
[ROW][C]19[/C][C]3.3[/C][C]3.55709479485318[/C][C]-0.257094794853185[/C][/ROW]
[ROW][C]20[/C][C]3.31[/C][C]3.16463769083862[/C][C]0.145362309161376[/C][/ROW]
[ROW][C]21[/C][C]3.14[/C][C]3.16222292221461[/C][C]-0.0222229222146098[/C][/ROW]
[ROW][C]22[/C][C]3.3[/C][C]2.96872809975901[/C][C]0.331271900240985[/C][/ROW]
[ROW][C]23[/C][C]3.49[/C][C]3.08665081777928[/C][C]0.403349182220716[/C][/ROW]
[ROW][C]24[/C][C]3.39[/C][C]3.23684410436798[/C][C]0.153155895632024[/C][/ROW]
[ROW][C]25[/C][C]3.37[/C][C]3.22647881180731[/C][C]0.143521188192688[/C][/ROW]
[ROW][C]26[/C][C]3.54[/C][C]3.42114828365876[/C][C]0.118851716341236[/C][/ROW]
[ROW][C]27[/C][C]3.7[/C][C]3.75187223626913[/C][C]-0.0518722362691264[/C][/ROW]
[ROW][C]28[/C][C]3.96[/C][C]3.57894024347777[/C][C]0.381059756522229[/C][/ROW]
[ROW][C]29[/C][C]4.03[/C][C]3.71838205633193[/C][C]0.311617943668066[/C][/ROW]
[ROW][C]30[/C][C]4.02[/C][C]3.79634096634602[/C][C]0.223659033653977[/C][/ROW]
[ROW][C]31[/C][C]4.04[/C][C]4.27306455749515[/C][C]-0.233064557495147[/C][/ROW]
[ROW][C]32[/C][C]3.92[/C][C]4.0590526264077[/C][C]-0.139052626407704[/C][/ROW]
[ROW][C]33[/C][C]3.79[/C][C]3.85641351993006[/C][C]-0.0664135199300588[/C][/ROW]
[ROW][C]34[/C][C]3.83[/C][C]3.76594673576181[/C][C]0.0640532642381868[/C][/ROW]
[ROW][C]35[/C][C]3.76[/C][C]3.74098733886507[/C][C]0.0190126611349264[/C][/ROW]
[ROW][C]36[/C][C]3.82[/C][C]3.57040240918538[/C][C]0.249597590814619[/C][/ROW]
[ROW][C]37[/C][C]4.06[/C][C]3.66820313247483[/C][C]0.391796867525171[/C][/ROW]
[ROW][C]38[/C][C]4.11[/C][C]4.09327949150078[/C][C]0.0167205084992190[/C][/ROW]
[ROW][C]39[/C][C]4.01[/C][C]4.34738737176980[/C][C]-0.337387371769804[/C][/ROW]
[ROW][C]40[/C][C]4.22[/C][C]4.08535846395236[/C][C]0.134641536047645[/C][/ROW]
[ROW][C]41[/C][C]4.34[/C][C]4.04155465107101[/C][C]0.298445348928992[/C][/ROW]
[ROW][C]42[/C][C]4.64[/C][C]4.11114695829864[/C][C]0.528853041701364[/C][/ROW]
[ROW][C]43[/C][C]4.62[/C][C]4.75064071659109[/C][C]-0.130640716591087[/C][/ROW]
[ROW][C]44[/C][C]4.44[/C][C]4.67354414644109[/C][C]-0.233544146441088[/C][/ROW]
[ROW][C]45[/C][C]4.39[/C][C]4.44793352835303[/C][C]-0.05793352835303[/C][/ROW]
[ROW][C]46[/C][C]4.42[/C][C]4.42738453568961[/C][C]-0.00738453568961361[/C][/ROW]
[ROW][C]47[/C][C]4.28[/C][C]4.36791404633415[/C][C]-0.087914046334145[/C][/ROW]
[ROW][C]48[/C][C]4.41[/C][C]4.19509660330618[/C][C]0.214903396693819[/C][/ROW]
[ROW][C]49[/C][C]4.25[/C][C]4.32473082800756[/C][C]-0.0747308280075609[/C][/ROW]
[ROW][C]50[/C][C]4.23[/C][C]4.31365233738552[/C][C]-0.0836523373855202[/C][/ROW]
[ROW][C]51[/C][C]4.23[/C][C]4.41482300521861[/C][C]-0.184823005218613[/C][/ROW]
[ROW][C]52[/C][C]4.37[/C][C]4.39001639067437[/C][C]-0.0200163906743729[/C][/ROW]
[ROW][C]53[/C][C]4.51[/C][C]4.27051046934986[/C][C]0.239489530650142[/C][/ROW]
[ROW][C]54[/C][C]4.84[/C][C]4.3513250066527[/C][C]0.488674993347297[/C][/ROW]
[ROW][C]55[/C][C]4.85[/C][C]4.8104186065169[/C][C]0.0395813934831004[/C][/ROW]
[ROW][C]56[/C][C]4.58[/C][C]4.84896122840081[/C][C]-0.268961228400814[/C][/ROW]
[ROW][C]57[/C][C]4.56[/C][C]4.6434435574781[/C][C]-0.0834435574781[/C][/ROW]
[ROW][C]58[/C][C]4.46[/C][C]4.62095187216924[/C][C]-0.160951872169243[/C][/ROW]
[ROW][C]59[/C][C]4.26[/C][C]4.42535366537929[/C][C]-0.165353665379286[/C][/ROW]
[ROW][C]60[/C][C]3.87[/C][C]4.26045108029768[/C][C]-0.39045108029768[/C][/ROW]
[ROW][C]61[/C][C]4.13[/C][C]3.83382686825878[/C][C]0.296173131741222[/C][/ROW]
[ROW][C]62[/C][C]4.24[/C][C]4.09590807066401[/C][C]0.144091929335993[/C][/ROW]
[ROW][C]63[/C][C]4.03[/C][C]4.34684431171796[/C][C]-0.316844311717957[/C][/ROW]
[ROW][C]64[/C][C]3.93[/C][C]4.25127587092082[/C][C]-0.321275870920824[/C][/ROW]
[ROW][C]65[/C][C]4.03[/C][C]3.94181254420326[/C][C]0.0881874557967421[/C][/ROW]
[ROW][C]66[/C][C]4.12[/C][C]3.94041349589949[/C][C]0.179586504100506[/C][/ROW]
[ROW][C]67[/C][C]3.92[/C][C]4.02426926105732[/C][C]-0.104269261057318[/C][/ROW]
[ROW][C]68[/C][C]3.77[/C][C]3.84204523678205[/C][C]-0.0720452367820461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72316&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.59	4.00846955128205	-0.418469551282054
14	3.57	3.66284997093498	-0.0928499709349788
15	3.76	3.77176222129098	-0.0117622212909771
16	3.6	3.58478080858013	0.0152191914198729
17	3.43	3.3836973601118	0.0463026398881983
18	3.26	3.19110352494215	0.0688964750578451
19	3.3	3.55709479485318	-0.257094794853185
20	3.31	3.16463769083862	0.145362309161376
21	3.14	3.16222292221461	-0.0222229222146098
22	3.3	2.96872809975901	0.331271900240985
23	3.49	3.08665081777928	0.403349182220716
24	3.39	3.23684410436798	0.153155895632024
25	3.37	3.22647881180731	0.143521188192688
26	3.54	3.42114828365876	0.118851716341236
27	3.7	3.75187223626913	-0.0518722362691264
28	3.96	3.57894024347777	0.381059756522229
29	4.03	3.71838205633193	0.311617943668066
30	4.02	3.79634096634602	0.223659033653977
31	4.04	4.27306455749515	-0.233064557495147
32	3.92	4.0590526264077	-0.139052626407704
33	3.79	3.85641351993006	-0.0664135199300588
34	3.83	3.76594673576181	0.0640532642381868
35	3.76	3.74098733886507	0.0190126611349264
36	3.82	3.57040240918538	0.249597590814619
37	4.06	3.66820313247483	0.391796867525171
38	4.11	4.09327949150078	0.0167205084992190
39	4.01	4.34738737176980	-0.337387371769804
40	4.22	4.08535846395236	0.134641536047645
41	4.34	4.04155465107101	0.298445348928992
42	4.64	4.11114695829864	0.528853041701364
43	4.62	4.75064071659109	-0.130640716591087
44	4.44	4.67354414644109	-0.233544146441088
45	4.39	4.44793352835303	-0.05793352835303
46	4.42	4.42738453568961	-0.00738453568961361
47	4.28	4.36791404633415	-0.087914046334145
48	4.41	4.19509660330618	0.214903396693819
49	4.25	4.32473082800756	-0.0747308280075609
50	4.23	4.31365233738552	-0.0836523373855202
51	4.23	4.41482300521861	-0.184823005218613
52	4.37	4.39001639067437	-0.0200163906743729
53	4.51	4.27051046934986	0.239489530650142
54	4.84	4.3513250066527	0.488674993347297
55	4.85	4.8104186065169	0.0395813934831004
56	4.58	4.84896122840081	-0.268961228400814
57	4.56	4.6434435574781	-0.0834435574781
58	4.46	4.62095187216924	-0.160951872169243
59	4.26	4.42535366537929	-0.165353665379286
60	3.87	4.26045108029768	-0.39045108029768
61	4.13	3.83382686825878	0.296173131741222
62	4.24	4.09590807066401	0.144091929335993
63	4.03	4.34684431171796	-0.316844311717957
64	3.93	4.25127587092082	-0.321275870920824
65	4.03	3.94181254420326	0.0881874557967421
66	4.12	3.94041349589949	0.179586504100506
67	3.92	4.02426926105732	-0.104269261057318
68	3.77	3.84204523678205	-0.0720452367820461

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
69	3.79874864356221	3.35663752519815	4.24085976192627
70	3.79356322551774	3.22589105872594	4.36123539230953
71	3.69746142328074	3.01891554202909	4.37600730453238
72	3.59053883756575	2.80921304484179	4.3718646302897
73	3.61871576632481	2.73958129734942	4.49785023530021
74	3.60352014260283	2.62979736130801	4.57724292389766
75	3.61815661164457	2.55197876693690	4.68433445635223
76	3.75741477478896	2.60019218552895	4.91463736404897
77	3.79274438739595	2.54538232696154	5.04010644783036
78	3.74457508149109	2.40761268708644	5.08153747589573
79	3.61862676946526	2.19233002433441	5.04492351459612
80	3.52155417355281	2.00598059417063	5.03712775293499

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
69 & 3.79874864356221 & 3.35663752519815 & 4.24085976192627 \tabularnewline
70 & 3.79356322551774 & 3.22589105872594 & 4.36123539230953 \tabularnewline
71 & 3.69746142328074 & 3.01891554202909 & 4.37600730453238 \tabularnewline
72 & 3.59053883756575 & 2.80921304484179 & 4.3718646302897 \tabularnewline
73 & 3.61871576632481 & 2.73958129734942 & 4.49785023530021 \tabularnewline
74 & 3.60352014260283 & 2.62979736130801 & 4.57724292389766 \tabularnewline
75 & 3.61815661164457 & 2.55197876693690 & 4.68433445635223 \tabularnewline
76 & 3.75741477478896 & 2.60019218552895 & 4.91463736404897 \tabularnewline
77 & 3.79274438739595 & 2.54538232696154 & 5.04010644783036 \tabularnewline
78 & 3.74457508149109 & 2.40761268708644 & 5.08153747589573 \tabularnewline
79 & 3.61862676946526 & 2.19233002433441 & 5.04492351459612 \tabularnewline
80 & 3.52155417355281 & 2.00598059417063 & 5.03712775293499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72316&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]69[/C][C]3.79874864356221[/C][C]3.35663752519815[/C][C]4.24085976192627[/C][/ROW]
[ROW][C]70[/C][C]3.79356322551774[/C][C]3.22589105872594[/C][C]4.36123539230953[/C][/ROW]
[ROW][C]71[/C][C]3.69746142328074[/C][C]3.01891554202909[/C][C]4.37600730453238[/C][/ROW]
[ROW][C]72[/C][C]3.59053883756575[/C][C]2.80921304484179[/C][C]4.3718646302897[/C][/ROW]
[ROW][C]73[/C][C]3.61871576632481[/C][C]2.73958129734942[/C][C]4.49785023530021[/C][/ROW]
[ROW][C]74[/C][C]3.60352014260283[/C][C]2.62979736130801[/C][C]4.57724292389766[/C][/ROW]
[ROW][C]75[/C][C]3.61815661164457[/C][C]2.55197876693690[/C][C]4.68433445635223[/C][/ROW]
[ROW][C]76[/C][C]3.75741477478896[/C][C]2.60019218552895[/C][C]4.91463736404897[/C][/ROW]
[ROW][C]77[/C][C]3.79274438739595[/C][C]2.54538232696154[/C][C]5.04010644783036[/C][/ROW]
[ROW][C]78[/C][C]3.74457508149109[/C][C]2.40761268708644[/C][C]5.08153747589573[/C][/ROW]
[ROW][C]79[/C][C]3.61862676946526[/C][C]2.19233002433441[/C][C]5.04492351459612[/C][/ROW]
[ROW][C]80[/C][C]3.52155417355281[/C][C]2.00598059417063[/C][C]5.03712775293499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72316&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72316&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
69	3.79874864356221	3.35663752519815	4.24085976192627
70	3.79356322551774	3.22589105872594	4.36123539230953
71	3.69746142328074	3.01891554202909	4.37600730453238
72	3.59053883756575	2.80921304484179	4.3718646302897
73	3.61871576632481	2.73958129734942	4.49785023530021
74	3.60352014260283	2.62979736130801	4.57724292389766
75	3.61815661164457	2.55197876693690	4.68433445635223
76	3.75741477478896	2.60019218552895	4.91463736404897
77	3.79274438739595	2.54538232696154	5.04010644783036
78	3.74457508149109	2.40761268708644	5.08153747589573
79	3.61862676946526	2.19233002433441	5.04492351459612
80	3.52155417355281	2.00598059417063	5.03712775293499

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code