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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 14 May 2012 06:12:58 -0400

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/2012/May/14/t1336990415xto16tbq4if4qd2.htm/, Retrieved Sun, 05 May 2024 10:24:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166442, Retrieved Sun, 05 May 2024 10:24:31 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-       [Exponential Smoothing] [] [2012-05-14 10:12:58] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Histogram

Boxplots

1,45
1,45
1,45
1,44
1,44
1,44
1,44
1,45
1,44
1,45
1,46
1,46
1,47
1,46
1,46
1,45
1,45
1,45
1,44
1,45
1,44
1,45
1,47
1,48
1,5
1,5
1,52
1,54
1,55
1,54
1,55
1,54
1,57
1,61
1,62
1,64
1,63
1,63
1,67
1,7
1,69
1,68
1,67
1,68
1,66
1,65
1,65
1,66
1,67
1,67
1,65
1,65
1,65
1,65
1,66
1,66
1,67
1,67
1,67
1,66

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	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166442&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166442&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.112463488654287
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.112463488654287 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166442&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]0.112463488654287[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166442&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	0.112463488654287
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.45	1.45	0
4	1.44	1.45	-0.01
5	1.44	1.43887536511346	0.0011246348865428
6	1.44	1.43900184547626	0.000998154523739858
7	1.44	1.43911410141622	0.000885898583784073
8	1.45	1.43921373266154	0.0107862673384578
9	1.44	1.45042679391598	-0.010426793915983
10	1.45	1.43925416029671	0.0107458397032878
11	1.46	1.45046267491826	0.00953732508173633
12	1.46	1.46153527576939	-0.00153527576938584
13	1.47	1.46136261330031	0.00863738669968583
14	1.46	1.47233400394142	-0.012334003941417
15	1.46	1.46094687882909	-0.000946878829089615
16	1.45	1.46084038953264	-0.0108403895326372
17	1.45	1.44962124150743	0.000378758492574516
18	1.45	1.44966383800886	0.00033616199114217
19	1.44	1.44970164395913	-0.00970164395913464
20	1.45	1.43861056323381	0.0113894367661915
21	1.44	1.44989145902634	-0.00989145902634192
22	1.45	1.43877903103636	0.0112209689636416
23	1.47	1.45004098035209	0.0199590196479089
24	1.48	1.47228564133181	0.00771435866818559
25	1.5	1.48315322502037	0.0168467749796311
26	1.5	1.50504787210715	-0.00504787210715207
27	1.52	1.5044801707997	0.0155198292002989
28	1.54	1.52622558493489	0.0137744150651147
29	1.55	1.54777470370728	0.00222529629271961
30	1.54	1.55802496829165	-0.0180249682916491
31	1.55	1.54599781747469	0.0040021825253127
32	1.54	1.55644791688372	-0.0164479168837153
33	1.57	1.54459812676988	0.0254018732301231
34	1.61	1.57745491005169	0.0325450899483095
35	1.62	1.62111504440585	-0.00111504440584498
36	1.64	1.63098964262196	0.00901035737804068
37	1.63	1.65200297884672	-0.0220029788467155
38	1.63	1.63952844708483	-0.00952844708482736
39	1.67	1.63845684468421	0.0315431553157901
40	1.7	1.68200429797419	0.0179957020258124
41	1.69	1.71402815740479	-0.0240281574047936
42	1.68	1.70132586699712	-0.0213258669971161
43	1.67	1.68892748559604	-0.0189274855960431
44	1.68	1.67679883453446	0.00320116546554172
45	1.66	1.68715884877047	-0.0271588487704728
46	1.65	1.66410446988991	-0.0141044698899113
47	1.65	1.65251823200047	-0.00251823200047241
48	1.66	1.65223502284446	0.00776497715554147
49	1.67	1.66310829926469	0.00689170073530843
50	1.67	1.67388336397215	-0.00388336397214561
51	1.65	1.67344662731212	-0.0234466273121237
52	1.65	1.65080973780743	-0.000809737807425437
53	1.65	1.65071867186871	-0.00071867186870711
54	1.65	1.65063784752315	-0.000637847523154544
55	1.66	1.65056611296547	0.00943388703452896
56	1.66	1.66162708081294	-0.0016270808129446
57	1.67	1.6614440936284	0.00855590637160164
58	1.67	1.67240632070755	-0.0024063207075482
59	1.67	1.67213569748596	-0.00213569748595632
60	1.66	1.67189550949598	-0.0118955094959754

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.45 & 1.45 & 0 \tabularnewline
4 & 1.44 & 1.45 & -0.01 \tabularnewline
5 & 1.44 & 1.43887536511346 & 0.0011246348865428 \tabularnewline
6 & 1.44 & 1.43900184547626 & 0.000998154523739858 \tabularnewline
7 & 1.44 & 1.43911410141622 & 0.000885898583784073 \tabularnewline
8 & 1.45 & 1.43921373266154 & 0.0107862673384578 \tabularnewline
9 & 1.44 & 1.45042679391598 & -0.010426793915983 \tabularnewline
10 & 1.45 & 1.43925416029671 & 0.0107458397032878 \tabularnewline
11 & 1.46 & 1.45046267491826 & 0.00953732508173633 \tabularnewline
12 & 1.46 & 1.46153527576939 & -0.00153527576938584 \tabularnewline
13 & 1.47 & 1.46136261330031 & 0.00863738669968583 \tabularnewline
14 & 1.46 & 1.47233400394142 & -0.012334003941417 \tabularnewline
15 & 1.46 & 1.46094687882909 & -0.000946878829089615 \tabularnewline
16 & 1.45 & 1.46084038953264 & -0.0108403895326372 \tabularnewline
17 & 1.45 & 1.44962124150743 & 0.000378758492574516 \tabularnewline
18 & 1.45 & 1.44966383800886 & 0.00033616199114217 \tabularnewline
19 & 1.44 & 1.44970164395913 & -0.00970164395913464 \tabularnewline
20 & 1.45 & 1.43861056323381 & 0.0113894367661915 \tabularnewline
21 & 1.44 & 1.44989145902634 & -0.00989145902634192 \tabularnewline
22 & 1.45 & 1.43877903103636 & 0.0112209689636416 \tabularnewline
23 & 1.47 & 1.45004098035209 & 0.0199590196479089 \tabularnewline
24 & 1.48 & 1.47228564133181 & 0.00771435866818559 \tabularnewline
25 & 1.5 & 1.48315322502037 & 0.0168467749796311 \tabularnewline
26 & 1.5 & 1.50504787210715 & -0.00504787210715207 \tabularnewline
27 & 1.52 & 1.5044801707997 & 0.0155198292002989 \tabularnewline
28 & 1.54 & 1.52622558493489 & 0.0137744150651147 \tabularnewline
29 & 1.55 & 1.54777470370728 & 0.00222529629271961 \tabularnewline
30 & 1.54 & 1.55802496829165 & -0.0180249682916491 \tabularnewline
31 & 1.55 & 1.54599781747469 & 0.0040021825253127 \tabularnewline
32 & 1.54 & 1.55644791688372 & -0.0164479168837153 \tabularnewline
33 & 1.57 & 1.54459812676988 & 0.0254018732301231 \tabularnewline
34 & 1.61 & 1.57745491005169 & 0.0325450899483095 \tabularnewline
35 & 1.62 & 1.62111504440585 & -0.00111504440584498 \tabularnewline
36 & 1.64 & 1.63098964262196 & 0.00901035737804068 \tabularnewline
37 & 1.63 & 1.65200297884672 & -0.0220029788467155 \tabularnewline
38 & 1.63 & 1.63952844708483 & -0.00952844708482736 \tabularnewline
39 & 1.67 & 1.63845684468421 & 0.0315431553157901 \tabularnewline
40 & 1.7 & 1.68200429797419 & 0.0179957020258124 \tabularnewline
41 & 1.69 & 1.71402815740479 & -0.0240281574047936 \tabularnewline
42 & 1.68 & 1.70132586699712 & -0.0213258669971161 \tabularnewline
43 & 1.67 & 1.68892748559604 & -0.0189274855960431 \tabularnewline
44 & 1.68 & 1.67679883453446 & 0.00320116546554172 \tabularnewline
45 & 1.66 & 1.68715884877047 & -0.0271588487704728 \tabularnewline
46 & 1.65 & 1.66410446988991 & -0.0141044698899113 \tabularnewline
47 & 1.65 & 1.65251823200047 & -0.00251823200047241 \tabularnewline
48 & 1.66 & 1.65223502284446 & 0.00776497715554147 \tabularnewline
49 & 1.67 & 1.66310829926469 & 0.00689170073530843 \tabularnewline
50 & 1.67 & 1.67388336397215 & -0.00388336397214561 \tabularnewline
51 & 1.65 & 1.67344662731212 & -0.0234466273121237 \tabularnewline
52 & 1.65 & 1.65080973780743 & -0.000809737807425437 \tabularnewline
53 & 1.65 & 1.65071867186871 & -0.00071867186870711 \tabularnewline
54 & 1.65 & 1.65063784752315 & -0.000637847523154544 \tabularnewline
55 & 1.66 & 1.65056611296547 & 0.00943388703452896 \tabularnewline
56 & 1.66 & 1.66162708081294 & -0.0016270808129446 \tabularnewline
57 & 1.67 & 1.6614440936284 & 0.00855590637160164 \tabularnewline
58 & 1.67 & 1.67240632070755 & -0.0024063207075482 \tabularnewline
59 & 1.67 & 1.67213569748596 & -0.00213569748595632 \tabularnewline
60 & 1.66 & 1.67189550949598 & -0.0118955094959754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166442&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]1.45[/C][C]1.45[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]1.44[/C][C]1.45[/C][C]-0.01[/C][/ROW]
[ROW][C]5[/C][C]1.44[/C][C]1.43887536511346[/C][C]0.0011246348865428[/C][/ROW]
[ROW][C]6[/C][C]1.44[/C][C]1.43900184547626[/C][C]0.000998154523739858[/C][/ROW]
[ROW][C]7[/C][C]1.44[/C][C]1.43911410141622[/C][C]0.000885898583784073[/C][/ROW]
[ROW][C]8[/C][C]1.45[/C][C]1.43921373266154[/C][C]0.0107862673384578[/C][/ROW]
[ROW][C]9[/C][C]1.44[/C][C]1.45042679391598[/C][C]-0.010426793915983[/C][/ROW]
[ROW][C]10[/C][C]1.45[/C][C]1.43925416029671[/C][C]0.0107458397032878[/C][/ROW]
[ROW][C]11[/C][C]1.46[/C][C]1.45046267491826[/C][C]0.00953732508173633[/C][/ROW]
[ROW][C]12[/C][C]1.46[/C][C]1.46153527576939[/C][C]-0.00153527576938584[/C][/ROW]
[ROW][C]13[/C][C]1.47[/C][C]1.46136261330031[/C][C]0.00863738669968583[/C][/ROW]
[ROW][C]14[/C][C]1.46[/C][C]1.47233400394142[/C][C]-0.012334003941417[/C][/ROW]
[ROW][C]15[/C][C]1.46[/C][C]1.46094687882909[/C][C]-0.000946878829089615[/C][/ROW]
[ROW][C]16[/C][C]1.45[/C][C]1.46084038953264[/C][C]-0.0108403895326372[/C][/ROW]
[ROW][C]17[/C][C]1.45[/C][C]1.44962124150743[/C][C]0.000378758492574516[/C][/ROW]
[ROW][C]18[/C][C]1.45[/C][C]1.44966383800886[/C][C]0.00033616199114217[/C][/ROW]
[ROW][C]19[/C][C]1.44[/C][C]1.44970164395913[/C][C]-0.00970164395913464[/C][/ROW]
[ROW][C]20[/C][C]1.45[/C][C]1.43861056323381[/C][C]0.0113894367661915[/C][/ROW]
[ROW][C]21[/C][C]1.44[/C][C]1.44989145902634[/C][C]-0.00989145902634192[/C][/ROW]
[ROW][C]22[/C][C]1.45[/C][C]1.43877903103636[/C][C]0.0112209689636416[/C][/ROW]
[ROW][C]23[/C][C]1.47[/C][C]1.45004098035209[/C][C]0.0199590196479089[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.47228564133181[/C][C]0.00771435866818559[/C][/ROW]
[ROW][C]25[/C][C]1.5[/C][C]1.48315322502037[/C][C]0.0168467749796311[/C][/ROW]
[ROW][C]26[/C][C]1.5[/C][C]1.50504787210715[/C][C]-0.00504787210715207[/C][/ROW]
[ROW][C]27[/C][C]1.52[/C][C]1.5044801707997[/C][C]0.0155198292002989[/C][/ROW]
[ROW][C]28[/C][C]1.54[/C][C]1.52622558493489[/C][C]0.0137744150651147[/C][/ROW]
[ROW][C]29[/C][C]1.55[/C][C]1.54777470370728[/C][C]0.00222529629271961[/C][/ROW]
[ROW][C]30[/C][C]1.54[/C][C]1.55802496829165[/C][C]-0.0180249682916491[/C][/ROW]
[ROW][C]31[/C][C]1.55[/C][C]1.54599781747469[/C][C]0.0040021825253127[/C][/ROW]
[ROW][C]32[/C][C]1.54[/C][C]1.55644791688372[/C][C]-0.0164479168837153[/C][/ROW]
[ROW][C]33[/C][C]1.57[/C][C]1.54459812676988[/C][C]0.0254018732301231[/C][/ROW]
[ROW][C]34[/C][C]1.61[/C][C]1.57745491005169[/C][C]0.0325450899483095[/C][/ROW]
[ROW][C]35[/C][C]1.62[/C][C]1.62111504440585[/C][C]-0.00111504440584498[/C][/ROW]
[ROW][C]36[/C][C]1.64[/C][C]1.63098964262196[/C][C]0.00901035737804068[/C][/ROW]
[ROW][C]37[/C][C]1.63[/C][C]1.65200297884672[/C][C]-0.0220029788467155[/C][/ROW]
[ROW][C]38[/C][C]1.63[/C][C]1.63952844708483[/C][C]-0.00952844708482736[/C][/ROW]
[ROW][C]39[/C][C]1.67[/C][C]1.63845684468421[/C][C]0.0315431553157901[/C][/ROW]
[ROW][C]40[/C][C]1.7[/C][C]1.68200429797419[/C][C]0.0179957020258124[/C][/ROW]
[ROW][C]41[/C][C]1.69[/C][C]1.71402815740479[/C][C]-0.0240281574047936[/C][/ROW]
[ROW][C]42[/C][C]1.68[/C][C]1.70132586699712[/C][C]-0.0213258669971161[/C][/ROW]
[ROW][C]43[/C][C]1.67[/C][C]1.68892748559604[/C][C]-0.0189274855960431[/C][/ROW]
[ROW][C]44[/C][C]1.68[/C][C]1.67679883453446[/C][C]0.00320116546554172[/C][/ROW]
[ROW][C]45[/C][C]1.66[/C][C]1.68715884877047[/C][C]-0.0271588487704728[/C][/ROW]
[ROW][C]46[/C][C]1.65[/C][C]1.66410446988991[/C][C]-0.0141044698899113[/C][/ROW]
[ROW][C]47[/C][C]1.65[/C][C]1.65251823200047[/C][C]-0.00251823200047241[/C][/ROW]
[ROW][C]48[/C][C]1.66[/C][C]1.65223502284446[/C][C]0.00776497715554147[/C][/ROW]
[ROW][C]49[/C][C]1.67[/C][C]1.66310829926469[/C][C]0.00689170073530843[/C][/ROW]
[ROW][C]50[/C][C]1.67[/C][C]1.67388336397215[/C][C]-0.00388336397214561[/C][/ROW]
[ROW][C]51[/C][C]1.65[/C][C]1.67344662731212[/C][C]-0.0234466273121237[/C][/ROW]
[ROW][C]52[/C][C]1.65[/C][C]1.65080973780743[/C][C]-0.000809737807425437[/C][/ROW]
[ROW][C]53[/C][C]1.65[/C][C]1.65071867186871[/C][C]-0.00071867186870711[/C][/ROW]
[ROW][C]54[/C][C]1.65[/C][C]1.65063784752315[/C][C]-0.000637847523154544[/C][/ROW]
[ROW][C]55[/C][C]1.66[/C][C]1.65056611296547[/C][C]0.00943388703452896[/C][/ROW]
[ROW][C]56[/C][C]1.66[/C][C]1.66162708081294[/C][C]-0.0016270808129446[/C][/ROW]
[ROW][C]57[/C][C]1.67[/C][C]1.6614440936284[/C][C]0.00855590637160164[/C][/ROW]
[ROW][C]58[/C][C]1.67[/C][C]1.67240632070755[/C][C]-0.0024063207075482[/C][/ROW]
[ROW][C]59[/C][C]1.67[/C][C]1.67213569748596[/C][C]-0.00213569748595632[/C][/ROW]
[ROW][C]60[/C][C]1.66[/C][C]1.67189550949598[/C][C]-0.0118955094959754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166442&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166442&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	1.45	1.45	0
4	1.44	1.45	-0.01
5	1.44	1.43887536511346	0.0011246348865428
6	1.44	1.43900184547626	0.000998154523739858
7	1.44	1.43911410141622	0.000885898583784073
8	1.45	1.43921373266154	0.0107862673384578
9	1.44	1.45042679391598	-0.010426793915983
10	1.45	1.43925416029671	0.0107458397032878
11	1.46	1.45046267491826	0.00953732508173633
12	1.46	1.46153527576939	-0.00153527576938584
13	1.47	1.46136261330031	0.00863738669968583
14	1.46	1.47233400394142	-0.012334003941417
15	1.46	1.46094687882909	-0.000946878829089615
16	1.45	1.46084038953264	-0.0108403895326372
17	1.45	1.44962124150743	0.000378758492574516
18	1.45	1.44966383800886	0.00033616199114217
19	1.44	1.44970164395913	-0.00970164395913464
20	1.45	1.43861056323381	0.0113894367661915
21	1.44	1.44989145902634	-0.00989145902634192
22	1.45	1.43877903103636	0.0112209689636416
23	1.47	1.45004098035209	0.0199590196479089
24	1.48	1.47228564133181	0.00771435866818559
25	1.5	1.48315322502037	0.0168467749796311
26	1.5	1.50504787210715	-0.00504787210715207
27	1.52	1.5044801707997	0.0155198292002989
28	1.54	1.52622558493489	0.0137744150651147
29	1.55	1.54777470370728	0.00222529629271961
30	1.54	1.55802496829165	-0.0180249682916491
31	1.55	1.54599781747469	0.0040021825253127
32	1.54	1.55644791688372	-0.0164479168837153
33	1.57	1.54459812676988	0.0254018732301231
34	1.61	1.57745491005169	0.0325450899483095
35	1.62	1.62111504440585	-0.00111504440584498
36	1.64	1.63098964262196	0.00901035737804068
37	1.63	1.65200297884672	-0.0220029788467155
38	1.63	1.63952844708483	-0.00952844708482736
39	1.67	1.63845684468421	0.0315431553157901
40	1.7	1.68200429797419	0.0179957020258124
41	1.69	1.71402815740479	-0.0240281574047936
42	1.68	1.70132586699712	-0.0213258669971161
43	1.67	1.68892748559604	-0.0189274855960431
44	1.68	1.67679883453446	0.00320116546554172
45	1.66	1.68715884877047	-0.0271588487704728
46	1.65	1.66410446988991	-0.0141044698899113
47	1.65	1.65251823200047	-0.00251823200047241
48	1.66	1.65223502284446	0.00776497715554147
49	1.67	1.66310829926469	0.00689170073530843
50	1.67	1.67388336397215	-0.00388336397214561
51	1.65	1.67344662731212	-0.0234466273121237
52	1.65	1.65080973780743	-0.000809737807425437
53	1.65	1.65071867186871	-0.00071867186870711
54	1.65	1.65063784752315	-0.000637847523154544
55	1.66	1.65056611296547	0.00943388703452896
56	1.66	1.66162708081294	-0.0016270808129446
57	1.67	1.6614440936284	0.00855590637160164
58	1.67	1.67240632070755	-0.0024063207075482
59	1.67	1.67213569748596	-0.00213569748595632
60	1.66	1.67189550949598	-0.0118955094959754

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.66055769899874	1.63439220369056	1.68672319430691
62	1.66111539799748	1.62197567369971	1.70025512229524
63	1.66167309699621	1.61108482612385	1.71226136786857
64	1.66223079599495	1.60071886975557	1.72374272223433
65	1.66278849499369	1.59051908025079	1.73505790973659
66	1.66334619399243	1.5803164078168	1.74637598016805
67	1.66390389299116	1.57001956599964	1.75778821998269
68	1.6644615919899	1.5595752190722	1.7693479649076
69	1.66501929098864	1.54895070337935	1.78108787859793
70	1.66557698998738	1.53812549803177	1.79302848194299
71	1.66613468898612	1.52708661431472	1.80518276365751
72	1.66669238798485	1.51582592927498	1.81755884669473

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.66055769899874 & 1.63439220369056 & 1.68672319430691 \tabularnewline
62 & 1.66111539799748 & 1.62197567369971 & 1.70025512229524 \tabularnewline
63 & 1.66167309699621 & 1.61108482612385 & 1.71226136786857 \tabularnewline
64 & 1.66223079599495 & 1.60071886975557 & 1.72374272223433 \tabularnewline
65 & 1.66278849499369 & 1.59051908025079 & 1.73505790973659 \tabularnewline
66 & 1.66334619399243 & 1.5803164078168 & 1.74637598016805 \tabularnewline
67 & 1.66390389299116 & 1.57001956599964 & 1.75778821998269 \tabularnewline
68 & 1.6644615919899 & 1.5595752190722 & 1.7693479649076 \tabularnewline
69 & 1.66501929098864 & 1.54895070337935 & 1.78108787859793 \tabularnewline
70 & 1.66557698998738 & 1.53812549803177 & 1.79302848194299 \tabularnewline
71 & 1.66613468898612 & 1.52708661431472 & 1.80518276365751 \tabularnewline
72 & 1.66669238798485 & 1.51582592927498 & 1.81755884669473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166442&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]61[/C][C]1.66055769899874[/C][C]1.63439220369056[/C][C]1.68672319430691[/C][/ROW]
[ROW][C]62[/C][C]1.66111539799748[/C][C]1.62197567369971[/C][C]1.70025512229524[/C][/ROW]
[ROW][C]63[/C][C]1.66167309699621[/C][C]1.61108482612385[/C][C]1.71226136786857[/C][/ROW]
[ROW][C]64[/C][C]1.66223079599495[/C][C]1.60071886975557[/C][C]1.72374272223433[/C][/ROW]
[ROW][C]65[/C][C]1.66278849499369[/C][C]1.59051908025079[/C][C]1.73505790973659[/C][/ROW]
[ROW][C]66[/C][C]1.66334619399243[/C][C]1.5803164078168[/C][C]1.74637598016805[/C][/ROW]
[ROW][C]67[/C][C]1.66390389299116[/C][C]1.57001956599964[/C][C]1.75778821998269[/C][/ROW]
[ROW][C]68[/C][C]1.6644615919899[/C][C]1.5595752190722[/C][C]1.7693479649076[/C][/ROW]
[ROW][C]69[/C][C]1.66501929098864[/C][C]1.54895070337935[/C][C]1.78108787859793[/C][/ROW]
[ROW][C]70[/C][C]1.66557698998738[/C][C]1.53812549803177[/C][C]1.79302848194299[/C][/ROW]
[ROW][C]71[/C][C]1.66613468898612[/C][C]1.52708661431472[/C][C]1.80518276365751[/C][/ROW]
[ROW][C]72[/C][C]1.66669238798485[/C][C]1.51582592927498[/C][C]1.81755884669473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166442&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166442&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
61	1.66055769899874	1.63439220369056	1.68672319430691
62	1.66111539799748	1.62197567369971	1.70025512229524
63	1.66167309699621	1.61108482612385	1.71226136786857
64	1.66223079599495	1.60071886975557	1.72374272223433
65	1.66278849499369	1.59051908025079	1.73505790973659
66	1.66334619399243	1.5803164078168	1.74637598016805
67	1.66390389299116	1.57001956599964	1.75778821998269
68	1.6644615919899	1.5595752190722	1.7693479649076
69	1.66501929098864	1.54895070337935	1.78108787859793
70	1.66557698998738	1.53812549803177	1.79302848194299
71	1.66613468898612	1.52708661431472	1.80518276365751
72	1.66669238798485	1.51582592927498	1.81755884669473

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