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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 29 Nov 2014 20:01:08 +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/2014/Nov/29/t14172912831i8vbt9v8cmlot6.htm/, Retrieved Sun, 19 May 2024 12:56:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261271, Retrieved Sun, 19 May 2024 12:56:46 +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] [] [2014-11-29 20:01:08] [0d07a52a2a76253e93d9e0b2a80fc19c] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261271&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261271&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261271&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.888150490215508
beta	0.0016750039719437
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.888150490215508 \tabularnewline
beta & 0.0016750039719437 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261271&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]0.888150490215508[/C][/ROW]
[ROW][C]beta[/C][C]0.0016750039719437[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261271&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261271&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	0.888150490215508
beta	0.0016750039719437
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	103.86	103.87	-0.00999999999999091
4	103.9	103.911103618542	-0.0111036185418385
5	103.63	103.951210539374	-0.321210539374476
6	103.65	103.715417995793	-0.0654179957930694
7	103.7	103.706710405739	-0.00671040573925552
8	103.77	103.750134007798	0.0198659922015452
9	103.94	103.817191004471	0.122808995528558
10	104.03	103.975859577503	0.05414042249663
11	104.03	104.073620666037	-0.0436206660372278
12	104.29	104.084490303338	0.205509696662304
13	104.35	104.316930922048	0.0330690779518221
14	104.67	104.396267516117	0.27373248388318
15	104.73	104.689756651803	0.0402433481974498
16	104.86	104.775932165411	0.0840678345887227
17	104.05	104.901155482077	-0.851155482076663
18	104.15	104.194493525366	-0.0444935253663488
19	104.27	104.204202589904	0.0657974100956125
20	104.33	104.311964486725	0.0180355132751941
21	104.41	104.377333462103	0.0326665378971569
22	104.4	104.455745585729	-0.0557455857292268
23	104.41	104.455551508183	-0.0455515081831379
24	104.6	104.464343540651	0.135656459349278
25	104.61	104.634277328404	-0.0242773284044091
26	104.65	104.662129727859	-0.0121297278591186
27	104.55	104.700752979836	-0.150752979835516
28	104.51	104.616033654099	-0.106033654099321
29	104.74	104.570874077879	0.169125922121339
30	104.89	104.770349215291	0.119650784709194
31	104.91	104.926060984317	-0.0160609843166526
32	104.93	104.961216385941	-0.0312163859409367
33	104.95	104.982865070952	-0.0328650709518854
34	104.97	105.003000583655	-0.0330005836553511
35	105.16	105.022966647182	0.13703335281825
36	105.29	105.194152293175	0.0958477068250119
37	105.35	105.328901475867	0.0210985241327961
38	105.36	105.397293522646	-0.0372935226456548
39	105.45	105.413769164535	0.0362308354646217
40	105.3	105.495599400129	-0.195599400128756
41	105.73	105.37123851379	0.35876148620963
42	105.86	105.739767233943	0.120232766056688
43	105.85	105.89662541931	-0.0466254193095494
44	105.95	105.90521906298	0.0447809370198087
45	105.97	105.995061925445	-0.0250619254452431
46	106.15	106.02283653186	0.127163468139813
47	105.37	106.185999371656	-0.815999371656304
48	105.39	105.510277746901	-0.120277746900584
49	105.39	105.452282692362	-0.062282692361606
50	105.38	105.445703318746	-0.0657033187455056
51	105.23	105.43598817022	-0.205988170219683
52	105.34	105.301372522633	0.0386274773674273
53	104.98	105.384069846747	-0.404069846747305
54	105.16	105.072984208663	0.0870157913373646
55	105.27	105.19818597031	0.0718140296901737
56	105.27	105.309993114441	-0.0399931144412591
57	105.33	105.322439192722	0.00756080727785502
58	105.33	105.377131557767	-0.0471315577668179
59	105.46	105.38317875646	0.0768212435397828
60	105.54	105.499428979951	0.0405710200492848
61	105.59	105.583543905383	0.00645609461714969
62	105.57	105.637369247514	-0.0673692475140655
63	105.62	105.625526353603	-0.00552635360284626
64	105.57	105.668601034924	-0.0986010349243713
65	105.33	105.628864708022	-0.298864708021867
66	105.34	105.410819493929	-0.0708194939292781
67	105.5	105.395207393508	0.10479260649231
68	105.47	105.535721161471	-0.0657211614710747
69	105.59	105.524695272375	0.0653047276245502
70	105.65	105.630137241855	0.0198627581452797
71	105.8	105.695249452808	0.104750547192012
72	105.87	105.835910627954	0.0340893720455995

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 103.86 & 103.87 & -0.00999999999999091 \tabularnewline
4 & 103.9 & 103.911103618542 & -0.0111036185418385 \tabularnewline
5 & 103.63 & 103.951210539374 & -0.321210539374476 \tabularnewline
6 & 103.65 & 103.715417995793 & -0.0654179957930694 \tabularnewline
7 & 103.7 & 103.706710405739 & -0.00671040573925552 \tabularnewline
8 & 103.77 & 103.750134007798 & 0.0198659922015452 \tabularnewline
9 & 103.94 & 103.817191004471 & 0.122808995528558 \tabularnewline
10 & 104.03 & 103.975859577503 & 0.05414042249663 \tabularnewline
11 & 104.03 & 104.073620666037 & -0.0436206660372278 \tabularnewline
12 & 104.29 & 104.084490303338 & 0.205509696662304 \tabularnewline
13 & 104.35 & 104.316930922048 & 0.0330690779518221 \tabularnewline
14 & 104.67 & 104.396267516117 & 0.27373248388318 \tabularnewline
15 & 104.73 & 104.689756651803 & 0.0402433481974498 \tabularnewline
16 & 104.86 & 104.775932165411 & 0.0840678345887227 \tabularnewline
17 & 104.05 & 104.901155482077 & -0.851155482076663 \tabularnewline
18 & 104.15 & 104.194493525366 & -0.0444935253663488 \tabularnewline
19 & 104.27 & 104.204202589904 & 0.0657974100956125 \tabularnewline
20 & 104.33 & 104.311964486725 & 0.0180355132751941 \tabularnewline
21 & 104.41 & 104.377333462103 & 0.0326665378971569 \tabularnewline
22 & 104.4 & 104.455745585729 & -0.0557455857292268 \tabularnewline
23 & 104.41 & 104.455551508183 & -0.0455515081831379 \tabularnewline
24 & 104.6 & 104.464343540651 & 0.135656459349278 \tabularnewline
25 & 104.61 & 104.634277328404 & -0.0242773284044091 \tabularnewline
26 & 104.65 & 104.662129727859 & -0.0121297278591186 \tabularnewline
27 & 104.55 & 104.700752979836 & -0.150752979835516 \tabularnewline
28 & 104.51 & 104.616033654099 & -0.106033654099321 \tabularnewline
29 & 104.74 & 104.570874077879 & 0.169125922121339 \tabularnewline
30 & 104.89 & 104.770349215291 & 0.119650784709194 \tabularnewline
31 & 104.91 & 104.926060984317 & -0.0160609843166526 \tabularnewline
32 & 104.93 & 104.961216385941 & -0.0312163859409367 \tabularnewline
33 & 104.95 & 104.982865070952 & -0.0328650709518854 \tabularnewline
34 & 104.97 & 105.003000583655 & -0.0330005836553511 \tabularnewline
35 & 105.16 & 105.022966647182 & 0.13703335281825 \tabularnewline
36 & 105.29 & 105.194152293175 & 0.0958477068250119 \tabularnewline
37 & 105.35 & 105.328901475867 & 0.0210985241327961 \tabularnewline
38 & 105.36 & 105.397293522646 & -0.0372935226456548 \tabularnewline
39 & 105.45 & 105.413769164535 & 0.0362308354646217 \tabularnewline
40 & 105.3 & 105.495599400129 & -0.195599400128756 \tabularnewline
41 & 105.73 & 105.37123851379 & 0.35876148620963 \tabularnewline
42 & 105.86 & 105.739767233943 & 0.120232766056688 \tabularnewline
43 & 105.85 & 105.89662541931 & -0.0466254193095494 \tabularnewline
44 & 105.95 & 105.90521906298 & 0.0447809370198087 \tabularnewline
45 & 105.97 & 105.995061925445 & -0.0250619254452431 \tabularnewline
46 & 106.15 & 106.02283653186 & 0.127163468139813 \tabularnewline
47 & 105.37 & 106.185999371656 & -0.815999371656304 \tabularnewline
48 & 105.39 & 105.510277746901 & -0.120277746900584 \tabularnewline
49 & 105.39 & 105.452282692362 & -0.062282692361606 \tabularnewline
50 & 105.38 & 105.445703318746 & -0.0657033187455056 \tabularnewline
51 & 105.23 & 105.43598817022 & -0.205988170219683 \tabularnewline
52 & 105.34 & 105.301372522633 & 0.0386274773674273 \tabularnewline
53 & 104.98 & 105.384069846747 & -0.404069846747305 \tabularnewline
54 & 105.16 & 105.072984208663 & 0.0870157913373646 \tabularnewline
55 & 105.27 & 105.19818597031 & 0.0718140296901737 \tabularnewline
56 & 105.27 & 105.309993114441 & -0.0399931144412591 \tabularnewline
57 & 105.33 & 105.322439192722 & 0.00756080727785502 \tabularnewline
58 & 105.33 & 105.377131557767 & -0.0471315577668179 \tabularnewline
59 & 105.46 & 105.38317875646 & 0.0768212435397828 \tabularnewline
60 & 105.54 & 105.499428979951 & 0.0405710200492848 \tabularnewline
61 & 105.59 & 105.583543905383 & 0.00645609461714969 \tabularnewline
62 & 105.57 & 105.637369247514 & -0.0673692475140655 \tabularnewline
63 & 105.62 & 105.625526353603 & -0.00552635360284626 \tabularnewline
64 & 105.57 & 105.668601034924 & -0.0986010349243713 \tabularnewline
65 & 105.33 & 105.628864708022 & -0.298864708021867 \tabularnewline
66 & 105.34 & 105.410819493929 & -0.0708194939292781 \tabularnewline
67 & 105.5 & 105.395207393508 & 0.10479260649231 \tabularnewline
68 & 105.47 & 105.535721161471 & -0.0657211614710747 \tabularnewline
69 & 105.59 & 105.524695272375 & 0.0653047276245502 \tabularnewline
70 & 105.65 & 105.630137241855 & 0.0198627581452797 \tabularnewline
71 & 105.8 & 105.695249452808 & 0.104750547192012 \tabularnewline
72 & 105.87 & 105.835910627954 & 0.0340893720455995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261271&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]103.86[/C][C]103.87[/C][C]-0.00999999999999091[/C][/ROW]
[ROW][C]4[/C][C]103.9[/C][C]103.911103618542[/C][C]-0.0111036185418385[/C][/ROW]
[ROW][C]5[/C][C]103.63[/C][C]103.951210539374[/C][C]-0.321210539374476[/C][/ROW]
[ROW][C]6[/C][C]103.65[/C][C]103.715417995793[/C][C]-0.0654179957930694[/C][/ROW]
[ROW][C]7[/C][C]103.7[/C][C]103.706710405739[/C][C]-0.00671040573925552[/C][/ROW]
[ROW][C]8[/C][C]103.77[/C][C]103.750134007798[/C][C]0.0198659922015452[/C][/ROW]
[ROW][C]9[/C][C]103.94[/C][C]103.817191004471[/C][C]0.122808995528558[/C][/ROW]
[ROW][C]10[/C][C]104.03[/C][C]103.975859577503[/C][C]0.05414042249663[/C][/ROW]
[ROW][C]11[/C][C]104.03[/C][C]104.073620666037[/C][C]-0.0436206660372278[/C][/ROW]
[ROW][C]12[/C][C]104.29[/C][C]104.084490303338[/C][C]0.205509696662304[/C][/ROW]
[ROW][C]13[/C][C]104.35[/C][C]104.316930922048[/C][C]0.0330690779518221[/C][/ROW]
[ROW][C]14[/C][C]104.67[/C][C]104.396267516117[/C][C]0.27373248388318[/C][/ROW]
[ROW][C]15[/C][C]104.73[/C][C]104.689756651803[/C][C]0.0402433481974498[/C][/ROW]
[ROW][C]16[/C][C]104.86[/C][C]104.775932165411[/C][C]0.0840678345887227[/C][/ROW]
[ROW][C]17[/C][C]104.05[/C][C]104.901155482077[/C][C]-0.851155482076663[/C][/ROW]
[ROW][C]18[/C][C]104.15[/C][C]104.194493525366[/C][C]-0.0444935253663488[/C][/ROW]
[ROW][C]19[/C][C]104.27[/C][C]104.204202589904[/C][C]0.0657974100956125[/C][/ROW]
[ROW][C]20[/C][C]104.33[/C][C]104.311964486725[/C][C]0.0180355132751941[/C][/ROW]
[ROW][C]21[/C][C]104.41[/C][C]104.377333462103[/C][C]0.0326665378971569[/C][/ROW]
[ROW][C]22[/C][C]104.4[/C][C]104.455745585729[/C][C]-0.0557455857292268[/C][/ROW]
[ROW][C]23[/C][C]104.41[/C][C]104.455551508183[/C][C]-0.0455515081831379[/C][/ROW]
[ROW][C]24[/C][C]104.6[/C][C]104.464343540651[/C][C]0.135656459349278[/C][/ROW]
[ROW][C]25[/C][C]104.61[/C][C]104.634277328404[/C][C]-0.0242773284044091[/C][/ROW]
[ROW][C]26[/C][C]104.65[/C][C]104.662129727859[/C][C]-0.0121297278591186[/C][/ROW]
[ROW][C]27[/C][C]104.55[/C][C]104.700752979836[/C][C]-0.150752979835516[/C][/ROW]
[ROW][C]28[/C][C]104.51[/C][C]104.616033654099[/C][C]-0.106033654099321[/C][/ROW]
[ROW][C]29[/C][C]104.74[/C][C]104.570874077879[/C][C]0.169125922121339[/C][/ROW]
[ROW][C]30[/C][C]104.89[/C][C]104.770349215291[/C][C]0.119650784709194[/C][/ROW]
[ROW][C]31[/C][C]104.91[/C][C]104.926060984317[/C][C]-0.0160609843166526[/C][/ROW]
[ROW][C]32[/C][C]104.93[/C][C]104.961216385941[/C][C]-0.0312163859409367[/C][/ROW]
[ROW][C]33[/C][C]104.95[/C][C]104.982865070952[/C][C]-0.0328650709518854[/C][/ROW]
[ROW][C]34[/C][C]104.97[/C][C]105.003000583655[/C][C]-0.0330005836553511[/C][/ROW]
[ROW][C]35[/C][C]105.16[/C][C]105.022966647182[/C][C]0.13703335281825[/C][/ROW]
[ROW][C]36[/C][C]105.29[/C][C]105.194152293175[/C][C]0.0958477068250119[/C][/ROW]
[ROW][C]37[/C][C]105.35[/C][C]105.328901475867[/C][C]0.0210985241327961[/C][/ROW]
[ROW][C]38[/C][C]105.36[/C][C]105.397293522646[/C][C]-0.0372935226456548[/C][/ROW]
[ROW][C]39[/C][C]105.45[/C][C]105.413769164535[/C][C]0.0362308354646217[/C][/ROW]
[ROW][C]40[/C][C]105.3[/C][C]105.495599400129[/C][C]-0.195599400128756[/C][/ROW]
[ROW][C]41[/C][C]105.73[/C][C]105.37123851379[/C][C]0.35876148620963[/C][/ROW]
[ROW][C]42[/C][C]105.86[/C][C]105.739767233943[/C][C]0.120232766056688[/C][/ROW]
[ROW][C]43[/C][C]105.85[/C][C]105.89662541931[/C][C]-0.0466254193095494[/C][/ROW]
[ROW][C]44[/C][C]105.95[/C][C]105.90521906298[/C][C]0.0447809370198087[/C][/ROW]
[ROW][C]45[/C][C]105.97[/C][C]105.995061925445[/C][C]-0.0250619254452431[/C][/ROW]
[ROW][C]46[/C][C]106.15[/C][C]106.02283653186[/C][C]0.127163468139813[/C][/ROW]
[ROW][C]47[/C][C]105.37[/C][C]106.185999371656[/C][C]-0.815999371656304[/C][/ROW]
[ROW][C]48[/C][C]105.39[/C][C]105.510277746901[/C][C]-0.120277746900584[/C][/ROW]
[ROW][C]49[/C][C]105.39[/C][C]105.452282692362[/C][C]-0.062282692361606[/C][/ROW]
[ROW][C]50[/C][C]105.38[/C][C]105.445703318746[/C][C]-0.0657033187455056[/C][/ROW]
[ROW][C]51[/C][C]105.23[/C][C]105.43598817022[/C][C]-0.205988170219683[/C][/ROW]
[ROW][C]52[/C][C]105.34[/C][C]105.301372522633[/C][C]0.0386274773674273[/C][/ROW]
[ROW][C]53[/C][C]104.98[/C][C]105.384069846747[/C][C]-0.404069846747305[/C][/ROW]
[ROW][C]54[/C][C]105.16[/C][C]105.072984208663[/C][C]0.0870157913373646[/C][/ROW]
[ROW][C]55[/C][C]105.27[/C][C]105.19818597031[/C][C]0.0718140296901737[/C][/ROW]
[ROW][C]56[/C][C]105.27[/C][C]105.309993114441[/C][C]-0.0399931144412591[/C][/ROW]
[ROW][C]57[/C][C]105.33[/C][C]105.322439192722[/C][C]0.00756080727785502[/C][/ROW]
[ROW][C]58[/C][C]105.33[/C][C]105.377131557767[/C][C]-0.0471315577668179[/C][/ROW]
[ROW][C]59[/C][C]105.46[/C][C]105.38317875646[/C][C]0.0768212435397828[/C][/ROW]
[ROW][C]60[/C][C]105.54[/C][C]105.499428979951[/C][C]0.0405710200492848[/C][/ROW]
[ROW][C]61[/C][C]105.59[/C][C]105.583543905383[/C][C]0.00645609461714969[/C][/ROW]
[ROW][C]62[/C][C]105.57[/C][C]105.637369247514[/C][C]-0.0673692475140655[/C][/ROW]
[ROW][C]63[/C][C]105.62[/C][C]105.625526353603[/C][C]-0.00552635360284626[/C][/ROW]
[ROW][C]64[/C][C]105.57[/C][C]105.668601034924[/C][C]-0.0986010349243713[/C][/ROW]
[ROW][C]65[/C][C]105.33[/C][C]105.628864708022[/C][C]-0.298864708021867[/C][/ROW]
[ROW][C]66[/C][C]105.34[/C][C]105.410819493929[/C][C]-0.0708194939292781[/C][/ROW]
[ROW][C]67[/C][C]105.5[/C][C]105.395207393508[/C][C]0.10479260649231[/C][/ROW]
[ROW][C]68[/C][C]105.47[/C][C]105.535721161471[/C][C]-0.0657211614710747[/C][/ROW]
[ROW][C]69[/C][C]105.59[/C][C]105.524695272375[/C][C]0.0653047276245502[/C][/ROW]
[ROW][C]70[/C][C]105.65[/C][C]105.630137241855[/C][C]0.0198627581452797[/C][/ROW]
[ROW][C]71[/C][C]105.8[/C][C]105.695249452808[/C][C]0.104750547192012[/C][/ROW]
[ROW][C]72[/C][C]105.87[/C][C]105.835910627954[/C][C]0.0340893720455995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261271&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261271&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	103.86	103.87	-0.00999999999999091
4	103.9	103.911103618542	-0.0111036185418385
5	103.63	103.951210539374	-0.321210539374476
6	103.65	103.715417995793	-0.0654179957930694
7	103.7	103.706710405739	-0.00671040573925552
8	103.77	103.750134007798	0.0198659922015452
9	103.94	103.817191004471	0.122808995528558
10	104.03	103.975859577503	0.05414042249663
11	104.03	104.073620666037	-0.0436206660372278
12	104.29	104.084490303338	0.205509696662304
13	104.35	104.316930922048	0.0330690779518221
14	104.67	104.396267516117	0.27373248388318
15	104.73	104.689756651803	0.0402433481974498
16	104.86	104.775932165411	0.0840678345887227
17	104.05	104.901155482077	-0.851155482076663
18	104.15	104.194493525366	-0.0444935253663488
19	104.27	104.204202589904	0.0657974100956125
20	104.33	104.311964486725	0.0180355132751941
21	104.41	104.377333462103	0.0326665378971569
22	104.4	104.455745585729	-0.0557455857292268
23	104.41	104.455551508183	-0.0455515081831379
24	104.6	104.464343540651	0.135656459349278
25	104.61	104.634277328404	-0.0242773284044091
26	104.65	104.662129727859	-0.0121297278591186
27	104.55	104.700752979836	-0.150752979835516
28	104.51	104.616033654099	-0.106033654099321
29	104.74	104.570874077879	0.169125922121339
30	104.89	104.770349215291	0.119650784709194
31	104.91	104.926060984317	-0.0160609843166526
32	104.93	104.961216385941	-0.0312163859409367
33	104.95	104.982865070952	-0.0328650709518854
34	104.97	105.003000583655	-0.0330005836553511
35	105.16	105.022966647182	0.13703335281825
36	105.29	105.194152293175	0.0958477068250119
37	105.35	105.328901475867	0.0210985241327961
38	105.36	105.397293522646	-0.0372935226456548
39	105.45	105.413769164535	0.0362308354646217
40	105.3	105.495599400129	-0.195599400128756
41	105.73	105.37123851379	0.35876148620963
42	105.86	105.739767233943	0.120232766056688
43	105.85	105.89662541931	-0.0466254193095494
44	105.95	105.90521906298	0.0447809370198087
45	105.97	105.995061925445	-0.0250619254452431
46	106.15	106.02283653186	0.127163468139813
47	105.37	106.185999371656	-0.815999371656304
48	105.39	105.510277746901	-0.120277746900584
49	105.39	105.452282692362	-0.062282692361606
50	105.38	105.445703318746	-0.0657033187455056
51	105.23	105.43598817022	-0.205988170219683
52	105.34	105.301372522633	0.0386274773674273
53	104.98	105.384069846747	-0.404069846747305
54	105.16	105.072984208663	0.0870157913373646
55	105.27	105.19818597031	0.0718140296901737
56	105.27	105.309993114441	-0.0399931144412591
57	105.33	105.322439192722	0.00756080727785502
58	105.33	105.377131557767	-0.0471315577668179
59	105.46	105.38317875646	0.0768212435397828
60	105.54	105.499428979951	0.0405710200492848
61	105.59	105.583543905383	0.00645609461714969
62	105.57	105.637369247514	-0.0673692475140655
63	105.62	105.625526353603	-0.00552635360284626
64	105.57	105.668601034924	-0.0986010349243713
65	105.33	105.628864708022	-0.298864708021867
66	105.34	105.410819493929	-0.0708194939292781
67	105.5	105.395207393508	0.10479260649231
68	105.47	105.535721161471	-0.0657211614710747
69	105.59	105.524695272375	0.0653047276245502
70	105.65	105.630137241855	0.0198627581452797
71	105.8	105.695249452808	0.104750547192012
72	105.87	105.835910627954	0.0340893720455995

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	105.913864759001	105.552073263879	106.275656254122
74	105.961542397553	105.477301539963	106.445783255144
75	106.009220036106	105.427470874046	106.590969198166
76	106.056897674659	105.391523867314	106.722271482003
77	106.104575313211	105.364737198926	106.844413427497
78	106.152252951764	105.344572902195	106.959933001333
79	106.199930590317	105.329480842066	107.070380338567
80	106.247608228869	105.318432185277	107.176784272462
81	106.295285867422	105.310702854615	107.279868880229
82	106.342963505975	105.305760482957	107.380166528993
83	106.390641144527	105.30320015537	107.478082133684
84	106.43831878308	105.30270543766	107.5739321285

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 105.913864759001 & 105.552073263879 & 106.275656254122 \tabularnewline
74 & 105.961542397553 & 105.477301539963 & 106.445783255144 \tabularnewline
75 & 106.009220036106 & 105.427470874046 & 106.590969198166 \tabularnewline
76 & 106.056897674659 & 105.391523867314 & 106.722271482003 \tabularnewline
77 & 106.104575313211 & 105.364737198926 & 106.844413427497 \tabularnewline
78 & 106.152252951764 & 105.344572902195 & 106.959933001333 \tabularnewline
79 & 106.199930590317 & 105.329480842066 & 107.070380338567 \tabularnewline
80 & 106.247608228869 & 105.318432185277 & 107.176784272462 \tabularnewline
81 & 106.295285867422 & 105.310702854615 & 107.279868880229 \tabularnewline
82 & 106.342963505975 & 105.305760482957 & 107.380166528993 \tabularnewline
83 & 106.390641144527 & 105.30320015537 & 107.478082133684 \tabularnewline
84 & 106.43831878308 & 105.30270543766 & 107.5739321285 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261271&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]105.913864759001[/C][C]105.552073263879[/C][C]106.275656254122[/C][/ROW]
[ROW][C]74[/C][C]105.961542397553[/C][C]105.477301539963[/C][C]106.445783255144[/C][/ROW]
[ROW][C]75[/C][C]106.009220036106[/C][C]105.427470874046[/C][C]106.590969198166[/C][/ROW]
[ROW][C]76[/C][C]106.056897674659[/C][C]105.391523867314[/C][C]106.722271482003[/C][/ROW]
[ROW][C]77[/C][C]106.104575313211[/C][C]105.364737198926[/C][C]106.844413427497[/C][/ROW]
[ROW][C]78[/C][C]106.152252951764[/C][C]105.344572902195[/C][C]106.959933001333[/C][/ROW]
[ROW][C]79[/C][C]106.199930590317[/C][C]105.329480842066[/C][C]107.070380338567[/C][/ROW]
[ROW][C]80[/C][C]106.247608228869[/C][C]105.318432185277[/C][C]107.176784272462[/C][/ROW]
[ROW][C]81[/C][C]106.295285867422[/C][C]105.310702854615[/C][C]107.279868880229[/C][/ROW]
[ROW][C]82[/C][C]106.342963505975[/C][C]105.305760482957[/C][C]107.380166528993[/C][/ROW]
[ROW][C]83[/C][C]106.390641144527[/C][C]105.30320015537[/C][C]107.478082133684[/C][/ROW]
[ROW][C]84[/C][C]106.43831878308[/C][C]105.30270543766[/C][C]107.5739321285[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261271&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261271&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	105.913864759001	105.552073263879	106.275656254122
74	105.961542397553	105.477301539963	106.445783255144
75	106.009220036106	105.427470874046	106.590969198166
76	106.056897674659	105.391523867314	106.722271482003
77	106.104575313211	105.364737198926	106.844413427497
78	106.152252951764	105.344572902195	106.959933001333
79	106.199930590317	105.329480842066	107.070380338567
80	106.247608228869	105.318432185277	107.176784272462
81	106.295285867422	105.310702854615	107.279868880229
82	106.342963505975	105.305760482957	107.380166528993
83	106.390641144527	105.30320015537	107.478082133684
84	106.43831878308	105.30270543766	107.5739321285

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