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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 30 Nov 2014 14:05:36 +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/30/t1417357440nbuy9g82lk4r7pq.htm/, Retrieved Sun, 19 May 2024 12:55:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261459, Retrieved Sun, 19 May 2024 12:55:54 +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] [] [2014-11-30 14:05:36] [af43fcfc4e3257f4a3dbe682dec77e63] [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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261459&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261459&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261459&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	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.140599853910577
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.140599853910577 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261459&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]0.140599853910577[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261459&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261459&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	0.140599853910577
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	111.01	111.83	-0.820000000000007
4	111.01	112.294708119793	-1.28470811979334
5	110.76	112.114078345833	-1.35407834583266
6	111.13	111.673695128225	-0.543695128225124
7	111.07	111.967251672625	-0.897251672624762
8	111.09	111.781098218533	-0.691098218532687
9	110.96	111.703929909969	-0.743929909969154
10	110.64	111.469333473308	-0.82933347330777
11	110.62	111.032729308118	-0.412729308117548
12	110.59	110.954699627692	-0.364699627691607
13	111.33	110.873422913317	0.456577086683069
14	113.94	111.677617585003	2.26238241499651
15	114.61	114.605708222042	0.00429177795814439
16	114.64	115.276311645396	-0.636311645395779
17	114.62	115.216846321012	-0.59684632101154
18	114.71	115.11292981547	-0.402929815470259
19	114.72	115.146277942279	-0.426277942278915
20	114.66	115.096343325869	-0.436343325869203
21	114.76	114.974993517997	-0.214993517997129
22	114.68	115.044765460775	-0.364765460775018
23	114.75	114.913479490278	-0.163479490278434
24	114.74	114.960494297828	-0.220494297827912
25	116.36	114.919492831765	1.44050716823482
26	117.53	116.742027929176	0.787972070823869
27	118.82	118.02281668722	0.797183312780405
28	119.83	119.424900544536	0.405099455463542
29	119.97	120.491857468794	-0.521857468793897
30	121.29	120.558484384919	0.731515615080681
31	120.94	121.981335373533	-1.04133537353299
32	121.02	121.484923772142	-0.464923772142328
33	120.98	121.4995555577	-0.519555557699547
34	121.02	121.386506122189	-0.366506122188582
35	120.89	121.374975414952	-0.484975414951521
36	120.76	121.176787942459	-0.416787942459109
37	123.28	120.988187618638	2.29181238136232
38	123.98	123.830416104648	0.149583895352336
39	125.91	124.551447578482	1.35855242151841
40	125.84	126.672459850477	-0.832459850476923
41	125.98	126.485416117113	-0.505416117113455
42	127.24	126.554354684883	0.68564531511673
43	127.23	127.910756316023	-0.680756316023135
44	127.82	127.805042077442	0.0149579225584091
45	127.59	128.397145159168	-0.807145159168101
46	127.74	128.053660667704	-0.31366066770444
47	127.44	128.159560023648	-0.719560023647688
48	127.35	127.758389989443	-0.408389989442952
49	128.54	127.610970416589	0.929029583411278
50	129.3	128.931591840295	0.368408159705069
51	130.67	129.743389973729	0.926610026271021
52	130.76	131.243671208055	-0.483671208054716
53	131.34	131.265667106861	0.0743328931385179
54	130.69	131.856118300778	-1.16611830077753
55	130.96	131.042162238046	-0.0821622380457256
56	130.68	131.30061023938	-0.620610239379545
57	130.61	130.933352530387	-0.323352530387353
58	130.59	130.817889211853	-0.227889211853295
59	130.44	130.765848021959	-0.325848021958933
60	129.04	130.570033837674	-1.53003383767447
61	131.46	128.954911303619	2.50508869638082
62	132.77	131.727126408363	1.04287359163663
63	134.48	133.183754282995	1.29624571700532
64	134.52	135.076006241438	-0.556006241437814
65	136.11	135.037831845118	1.07216815488169
66	136.12	136.778578531062	-0.658578531062261
67	136.03	136.695982485806	-0.665982485806239
68	135.84	136.512345445595	-0.672345445594885
69	137.75	136.227813774167	1.5221862258332
70	137.45	138.351832935144	-0.901832935143659
71	136.84	137.925035356211	-1.08503535621068
72	136.79	137.16247954364	-0.372479543639685
73	140.12	137.060108974219	3.05989102578076
74	140.68	140.820329205426	-0.140329205426298
75	140.35	141.360598939644	-1.01059893964398
76	140.42	140.888508876368	-0.468508876367849
77	140.19	140.892636596795	-0.702636596794719
78	140.14	140.563845993933	-0.423845993933185
79	140.13	140.454253309106	-0.324253309105558
80	139.45	140.398663341215	-0.948663341215308
81	139.59	139.58528141403	0.00471858596989705
82	139.44	139.725944846528	-0.285944846528167
83	139.53	139.53574104288	-0.00574104287980504
84	139.28	139.62493385309	-0.3449338530896

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 111.01 & 111.83 & -0.820000000000007 \tabularnewline
4 & 111.01 & 112.294708119793 & -1.28470811979334 \tabularnewline
5 & 110.76 & 112.114078345833 & -1.35407834583266 \tabularnewline
6 & 111.13 & 111.673695128225 & -0.543695128225124 \tabularnewline
7 & 111.07 & 111.967251672625 & -0.897251672624762 \tabularnewline
8 & 111.09 & 111.781098218533 & -0.691098218532687 \tabularnewline
9 & 110.96 & 111.703929909969 & -0.743929909969154 \tabularnewline
10 & 110.64 & 111.469333473308 & -0.82933347330777 \tabularnewline
11 & 110.62 & 111.032729308118 & -0.412729308117548 \tabularnewline
12 & 110.59 & 110.954699627692 & -0.364699627691607 \tabularnewline
13 & 111.33 & 110.873422913317 & 0.456577086683069 \tabularnewline
14 & 113.94 & 111.677617585003 & 2.26238241499651 \tabularnewline
15 & 114.61 & 114.605708222042 & 0.00429177795814439 \tabularnewline
16 & 114.64 & 115.276311645396 & -0.636311645395779 \tabularnewline
17 & 114.62 & 115.216846321012 & -0.59684632101154 \tabularnewline
18 & 114.71 & 115.11292981547 & -0.402929815470259 \tabularnewline
19 & 114.72 & 115.146277942279 & -0.426277942278915 \tabularnewline
20 & 114.66 & 115.096343325869 & -0.436343325869203 \tabularnewline
21 & 114.76 & 114.974993517997 & -0.214993517997129 \tabularnewline
22 & 114.68 & 115.044765460775 & -0.364765460775018 \tabularnewline
23 & 114.75 & 114.913479490278 & -0.163479490278434 \tabularnewline
24 & 114.74 & 114.960494297828 & -0.220494297827912 \tabularnewline
25 & 116.36 & 114.919492831765 & 1.44050716823482 \tabularnewline
26 & 117.53 & 116.742027929176 & 0.787972070823869 \tabularnewline
27 & 118.82 & 118.02281668722 & 0.797183312780405 \tabularnewline
28 & 119.83 & 119.424900544536 & 0.405099455463542 \tabularnewline
29 & 119.97 & 120.491857468794 & -0.521857468793897 \tabularnewline
30 & 121.29 & 120.558484384919 & 0.731515615080681 \tabularnewline
31 & 120.94 & 121.981335373533 & -1.04133537353299 \tabularnewline
32 & 121.02 & 121.484923772142 & -0.464923772142328 \tabularnewline
33 & 120.98 & 121.4995555577 & -0.519555557699547 \tabularnewline
34 & 121.02 & 121.386506122189 & -0.366506122188582 \tabularnewline
35 & 120.89 & 121.374975414952 & -0.484975414951521 \tabularnewline
36 & 120.76 & 121.176787942459 & -0.416787942459109 \tabularnewline
37 & 123.28 & 120.988187618638 & 2.29181238136232 \tabularnewline
38 & 123.98 & 123.830416104648 & 0.149583895352336 \tabularnewline
39 & 125.91 & 124.551447578482 & 1.35855242151841 \tabularnewline
40 & 125.84 & 126.672459850477 & -0.832459850476923 \tabularnewline
41 & 125.98 & 126.485416117113 & -0.505416117113455 \tabularnewline
42 & 127.24 & 126.554354684883 & 0.68564531511673 \tabularnewline
43 & 127.23 & 127.910756316023 & -0.680756316023135 \tabularnewline
44 & 127.82 & 127.805042077442 & 0.0149579225584091 \tabularnewline
45 & 127.59 & 128.397145159168 & -0.807145159168101 \tabularnewline
46 & 127.74 & 128.053660667704 & -0.31366066770444 \tabularnewline
47 & 127.44 & 128.159560023648 & -0.719560023647688 \tabularnewline
48 & 127.35 & 127.758389989443 & -0.408389989442952 \tabularnewline
49 & 128.54 & 127.610970416589 & 0.929029583411278 \tabularnewline
50 & 129.3 & 128.931591840295 & 0.368408159705069 \tabularnewline
51 & 130.67 & 129.743389973729 & 0.926610026271021 \tabularnewline
52 & 130.76 & 131.243671208055 & -0.483671208054716 \tabularnewline
53 & 131.34 & 131.265667106861 & 0.0743328931385179 \tabularnewline
54 & 130.69 & 131.856118300778 & -1.16611830077753 \tabularnewline
55 & 130.96 & 131.042162238046 & -0.0821622380457256 \tabularnewline
56 & 130.68 & 131.30061023938 & -0.620610239379545 \tabularnewline
57 & 130.61 & 130.933352530387 & -0.323352530387353 \tabularnewline
58 & 130.59 & 130.817889211853 & -0.227889211853295 \tabularnewline
59 & 130.44 & 130.765848021959 & -0.325848021958933 \tabularnewline
60 & 129.04 & 130.570033837674 & -1.53003383767447 \tabularnewline
61 & 131.46 & 128.954911303619 & 2.50508869638082 \tabularnewline
62 & 132.77 & 131.727126408363 & 1.04287359163663 \tabularnewline
63 & 134.48 & 133.183754282995 & 1.29624571700532 \tabularnewline
64 & 134.52 & 135.076006241438 & -0.556006241437814 \tabularnewline
65 & 136.11 & 135.037831845118 & 1.07216815488169 \tabularnewline
66 & 136.12 & 136.778578531062 & -0.658578531062261 \tabularnewline
67 & 136.03 & 136.695982485806 & -0.665982485806239 \tabularnewline
68 & 135.84 & 136.512345445595 & -0.672345445594885 \tabularnewline
69 & 137.75 & 136.227813774167 & 1.5221862258332 \tabularnewline
70 & 137.45 & 138.351832935144 & -0.901832935143659 \tabularnewline
71 & 136.84 & 137.925035356211 & -1.08503535621068 \tabularnewline
72 & 136.79 & 137.16247954364 & -0.372479543639685 \tabularnewline
73 & 140.12 & 137.060108974219 & 3.05989102578076 \tabularnewline
74 & 140.68 & 140.820329205426 & -0.140329205426298 \tabularnewline
75 & 140.35 & 141.360598939644 & -1.01059893964398 \tabularnewline
76 & 140.42 & 140.888508876368 & -0.468508876367849 \tabularnewline
77 & 140.19 & 140.892636596795 & -0.702636596794719 \tabularnewline
78 & 140.14 & 140.563845993933 & -0.423845993933185 \tabularnewline
79 & 140.13 & 140.454253309106 & -0.324253309105558 \tabularnewline
80 & 139.45 & 140.398663341215 & -0.948663341215308 \tabularnewline
81 & 139.59 & 139.58528141403 & 0.00471858596989705 \tabularnewline
82 & 139.44 & 139.725944846528 & -0.285944846528167 \tabularnewline
83 & 139.53 & 139.53574104288 & -0.00574104287980504 \tabularnewline
84 & 139.28 & 139.62493385309 & -0.3449338530896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261459&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]111.01[/C][C]111.83[/C][C]-0.820000000000007[/C][/ROW]
[ROW][C]4[/C][C]111.01[/C][C]112.294708119793[/C][C]-1.28470811979334[/C][/ROW]
[ROW][C]5[/C][C]110.76[/C][C]112.114078345833[/C][C]-1.35407834583266[/C][/ROW]
[ROW][C]6[/C][C]111.13[/C][C]111.673695128225[/C][C]-0.543695128225124[/C][/ROW]
[ROW][C]7[/C][C]111.07[/C][C]111.967251672625[/C][C]-0.897251672624762[/C][/ROW]
[ROW][C]8[/C][C]111.09[/C][C]111.781098218533[/C][C]-0.691098218532687[/C][/ROW]
[ROW][C]9[/C][C]110.96[/C][C]111.703929909969[/C][C]-0.743929909969154[/C][/ROW]
[ROW][C]10[/C][C]110.64[/C][C]111.469333473308[/C][C]-0.82933347330777[/C][/ROW]
[ROW][C]11[/C][C]110.62[/C][C]111.032729308118[/C][C]-0.412729308117548[/C][/ROW]
[ROW][C]12[/C][C]110.59[/C][C]110.954699627692[/C][C]-0.364699627691607[/C][/ROW]
[ROW][C]13[/C][C]111.33[/C][C]110.873422913317[/C][C]0.456577086683069[/C][/ROW]
[ROW][C]14[/C][C]113.94[/C][C]111.677617585003[/C][C]2.26238241499651[/C][/ROW]
[ROW][C]15[/C][C]114.61[/C][C]114.605708222042[/C][C]0.00429177795814439[/C][/ROW]
[ROW][C]16[/C][C]114.64[/C][C]115.276311645396[/C][C]-0.636311645395779[/C][/ROW]
[ROW][C]17[/C][C]114.62[/C][C]115.216846321012[/C][C]-0.59684632101154[/C][/ROW]
[ROW][C]18[/C][C]114.71[/C][C]115.11292981547[/C][C]-0.402929815470259[/C][/ROW]
[ROW][C]19[/C][C]114.72[/C][C]115.146277942279[/C][C]-0.426277942278915[/C][/ROW]
[ROW][C]20[/C][C]114.66[/C][C]115.096343325869[/C][C]-0.436343325869203[/C][/ROW]
[ROW][C]21[/C][C]114.76[/C][C]114.974993517997[/C][C]-0.214993517997129[/C][/ROW]
[ROW][C]22[/C][C]114.68[/C][C]115.044765460775[/C][C]-0.364765460775018[/C][/ROW]
[ROW][C]23[/C][C]114.75[/C][C]114.913479490278[/C][C]-0.163479490278434[/C][/ROW]
[ROW][C]24[/C][C]114.74[/C][C]114.960494297828[/C][C]-0.220494297827912[/C][/ROW]
[ROW][C]25[/C][C]116.36[/C][C]114.919492831765[/C][C]1.44050716823482[/C][/ROW]
[ROW][C]26[/C][C]117.53[/C][C]116.742027929176[/C][C]0.787972070823869[/C][/ROW]
[ROW][C]27[/C][C]118.82[/C][C]118.02281668722[/C][C]0.797183312780405[/C][/ROW]
[ROW][C]28[/C][C]119.83[/C][C]119.424900544536[/C][C]0.405099455463542[/C][/ROW]
[ROW][C]29[/C][C]119.97[/C][C]120.491857468794[/C][C]-0.521857468793897[/C][/ROW]
[ROW][C]30[/C][C]121.29[/C][C]120.558484384919[/C][C]0.731515615080681[/C][/ROW]
[ROW][C]31[/C][C]120.94[/C][C]121.981335373533[/C][C]-1.04133537353299[/C][/ROW]
[ROW][C]32[/C][C]121.02[/C][C]121.484923772142[/C][C]-0.464923772142328[/C][/ROW]
[ROW][C]33[/C][C]120.98[/C][C]121.4995555577[/C][C]-0.519555557699547[/C][/ROW]
[ROW][C]34[/C][C]121.02[/C][C]121.386506122189[/C][C]-0.366506122188582[/C][/ROW]
[ROW][C]35[/C][C]120.89[/C][C]121.374975414952[/C][C]-0.484975414951521[/C][/ROW]
[ROW][C]36[/C][C]120.76[/C][C]121.176787942459[/C][C]-0.416787942459109[/C][/ROW]
[ROW][C]37[/C][C]123.28[/C][C]120.988187618638[/C][C]2.29181238136232[/C][/ROW]
[ROW][C]38[/C][C]123.98[/C][C]123.830416104648[/C][C]0.149583895352336[/C][/ROW]
[ROW][C]39[/C][C]125.91[/C][C]124.551447578482[/C][C]1.35855242151841[/C][/ROW]
[ROW][C]40[/C][C]125.84[/C][C]126.672459850477[/C][C]-0.832459850476923[/C][/ROW]
[ROW][C]41[/C][C]125.98[/C][C]126.485416117113[/C][C]-0.505416117113455[/C][/ROW]
[ROW][C]42[/C][C]127.24[/C][C]126.554354684883[/C][C]0.68564531511673[/C][/ROW]
[ROW][C]43[/C][C]127.23[/C][C]127.910756316023[/C][C]-0.680756316023135[/C][/ROW]
[ROW][C]44[/C][C]127.82[/C][C]127.805042077442[/C][C]0.0149579225584091[/C][/ROW]
[ROW][C]45[/C][C]127.59[/C][C]128.397145159168[/C][C]-0.807145159168101[/C][/ROW]
[ROW][C]46[/C][C]127.74[/C][C]128.053660667704[/C][C]-0.31366066770444[/C][/ROW]
[ROW][C]47[/C][C]127.44[/C][C]128.159560023648[/C][C]-0.719560023647688[/C][/ROW]
[ROW][C]48[/C][C]127.35[/C][C]127.758389989443[/C][C]-0.408389989442952[/C][/ROW]
[ROW][C]49[/C][C]128.54[/C][C]127.610970416589[/C][C]0.929029583411278[/C][/ROW]
[ROW][C]50[/C][C]129.3[/C][C]128.931591840295[/C][C]0.368408159705069[/C][/ROW]
[ROW][C]51[/C][C]130.67[/C][C]129.743389973729[/C][C]0.926610026271021[/C][/ROW]
[ROW][C]52[/C][C]130.76[/C][C]131.243671208055[/C][C]-0.483671208054716[/C][/ROW]
[ROW][C]53[/C][C]131.34[/C][C]131.265667106861[/C][C]0.0743328931385179[/C][/ROW]
[ROW][C]54[/C][C]130.69[/C][C]131.856118300778[/C][C]-1.16611830077753[/C][/ROW]
[ROW][C]55[/C][C]130.96[/C][C]131.042162238046[/C][C]-0.0821622380457256[/C][/ROW]
[ROW][C]56[/C][C]130.68[/C][C]131.30061023938[/C][C]-0.620610239379545[/C][/ROW]
[ROW][C]57[/C][C]130.61[/C][C]130.933352530387[/C][C]-0.323352530387353[/C][/ROW]
[ROW][C]58[/C][C]130.59[/C][C]130.817889211853[/C][C]-0.227889211853295[/C][/ROW]
[ROW][C]59[/C][C]130.44[/C][C]130.765848021959[/C][C]-0.325848021958933[/C][/ROW]
[ROW][C]60[/C][C]129.04[/C][C]130.570033837674[/C][C]-1.53003383767447[/C][/ROW]
[ROW][C]61[/C][C]131.46[/C][C]128.954911303619[/C][C]2.50508869638082[/C][/ROW]
[ROW][C]62[/C][C]132.77[/C][C]131.727126408363[/C][C]1.04287359163663[/C][/ROW]
[ROW][C]63[/C][C]134.48[/C][C]133.183754282995[/C][C]1.29624571700532[/C][/ROW]
[ROW][C]64[/C][C]134.52[/C][C]135.076006241438[/C][C]-0.556006241437814[/C][/ROW]
[ROW][C]65[/C][C]136.11[/C][C]135.037831845118[/C][C]1.07216815488169[/C][/ROW]
[ROW][C]66[/C][C]136.12[/C][C]136.778578531062[/C][C]-0.658578531062261[/C][/ROW]
[ROW][C]67[/C][C]136.03[/C][C]136.695982485806[/C][C]-0.665982485806239[/C][/ROW]
[ROW][C]68[/C][C]135.84[/C][C]136.512345445595[/C][C]-0.672345445594885[/C][/ROW]
[ROW][C]69[/C][C]137.75[/C][C]136.227813774167[/C][C]1.5221862258332[/C][/ROW]
[ROW][C]70[/C][C]137.45[/C][C]138.351832935144[/C][C]-0.901832935143659[/C][/ROW]
[ROW][C]71[/C][C]136.84[/C][C]137.925035356211[/C][C]-1.08503535621068[/C][/ROW]
[ROW][C]72[/C][C]136.79[/C][C]137.16247954364[/C][C]-0.372479543639685[/C][/ROW]
[ROW][C]73[/C][C]140.12[/C][C]137.060108974219[/C][C]3.05989102578076[/C][/ROW]
[ROW][C]74[/C][C]140.68[/C][C]140.820329205426[/C][C]-0.140329205426298[/C][/ROW]
[ROW][C]75[/C][C]140.35[/C][C]141.360598939644[/C][C]-1.01059893964398[/C][/ROW]
[ROW][C]76[/C][C]140.42[/C][C]140.888508876368[/C][C]-0.468508876367849[/C][/ROW]
[ROW][C]77[/C][C]140.19[/C][C]140.892636596795[/C][C]-0.702636596794719[/C][/ROW]
[ROW][C]78[/C][C]140.14[/C][C]140.563845993933[/C][C]-0.423845993933185[/C][/ROW]
[ROW][C]79[/C][C]140.13[/C][C]140.454253309106[/C][C]-0.324253309105558[/C][/ROW]
[ROW][C]80[/C][C]139.45[/C][C]140.398663341215[/C][C]-0.948663341215308[/C][/ROW]
[ROW][C]81[/C][C]139.59[/C][C]139.58528141403[/C][C]0.00471858596989705[/C][/ROW]
[ROW][C]82[/C][C]139.44[/C][C]139.725944846528[/C][C]-0.285944846528167[/C][/ROW]
[ROW][C]83[/C][C]139.53[/C][C]139.53574104288[/C][C]-0.00574104287980504[/C][/ROW]
[ROW][C]84[/C][C]139.28[/C][C]139.62493385309[/C][C]-0.3449338530896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261459&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261459&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	111.01	111.83	-0.820000000000007
4	111.01	112.294708119793	-1.28470811979334
5	110.76	112.114078345833	-1.35407834583266
6	111.13	111.673695128225	-0.543695128225124
7	111.07	111.967251672625	-0.897251672624762
8	111.09	111.781098218533	-0.691098218532687
9	110.96	111.703929909969	-0.743929909969154
10	110.64	111.469333473308	-0.82933347330777
11	110.62	111.032729308118	-0.412729308117548
12	110.59	110.954699627692	-0.364699627691607
13	111.33	110.873422913317	0.456577086683069
14	113.94	111.677617585003	2.26238241499651
15	114.61	114.605708222042	0.00429177795814439
16	114.64	115.276311645396	-0.636311645395779
17	114.62	115.216846321012	-0.59684632101154
18	114.71	115.11292981547	-0.402929815470259
19	114.72	115.146277942279	-0.426277942278915
20	114.66	115.096343325869	-0.436343325869203
21	114.76	114.974993517997	-0.214993517997129
22	114.68	115.044765460775	-0.364765460775018
23	114.75	114.913479490278	-0.163479490278434
24	114.74	114.960494297828	-0.220494297827912
25	116.36	114.919492831765	1.44050716823482
26	117.53	116.742027929176	0.787972070823869
27	118.82	118.02281668722	0.797183312780405
28	119.83	119.424900544536	0.405099455463542
29	119.97	120.491857468794	-0.521857468793897
30	121.29	120.558484384919	0.731515615080681
31	120.94	121.981335373533	-1.04133537353299
32	121.02	121.484923772142	-0.464923772142328
33	120.98	121.4995555577	-0.519555557699547
34	121.02	121.386506122189	-0.366506122188582
35	120.89	121.374975414952	-0.484975414951521
36	120.76	121.176787942459	-0.416787942459109
37	123.28	120.988187618638	2.29181238136232
38	123.98	123.830416104648	0.149583895352336
39	125.91	124.551447578482	1.35855242151841
40	125.84	126.672459850477	-0.832459850476923
41	125.98	126.485416117113	-0.505416117113455
42	127.24	126.554354684883	0.68564531511673
43	127.23	127.910756316023	-0.680756316023135
44	127.82	127.805042077442	0.0149579225584091
45	127.59	128.397145159168	-0.807145159168101
46	127.74	128.053660667704	-0.31366066770444
47	127.44	128.159560023648	-0.719560023647688
48	127.35	127.758389989443	-0.408389989442952
49	128.54	127.610970416589	0.929029583411278
50	129.3	128.931591840295	0.368408159705069
51	130.67	129.743389973729	0.926610026271021
52	130.76	131.243671208055	-0.483671208054716
53	131.34	131.265667106861	0.0743328931385179
54	130.69	131.856118300778	-1.16611830077753
55	130.96	131.042162238046	-0.0821622380457256
56	130.68	131.30061023938	-0.620610239379545
57	130.61	130.933352530387	-0.323352530387353
58	130.59	130.817889211853	-0.227889211853295
59	130.44	130.765848021959	-0.325848021958933
60	129.04	130.570033837674	-1.53003383767447
61	131.46	128.954911303619	2.50508869638082
62	132.77	131.727126408363	1.04287359163663
63	134.48	133.183754282995	1.29624571700532
64	134.52	135.076006241438	-0.556006241437814
65	136.11	135.037831845118	1.07216815488169
66	136.12	136.778578531062	-0.658578531062261
67	136.03	136.695982485806	-0.665982485806239
68	135.84	136.512345445595	-0.672345445594885
69	137.75	136.227813774167	1.5221862258332
70	137.45	138.351832935144	-0.901832935143659
71	136.84	137.925035356211	-1.08503535621068
72	136.79	137.16247954364	-0.372479543639685
73	140.12	137.060108974219	3.05989102578076
74	140.68	140.820329205426	-0.140329205426298
75	140.35	141.360598939644	-1.01059893964398
76	140.42	140.888508876368	-0.468508876367849
77	140.19	140.892636596795	-0.702636596794719
78	140.14	140.563845993933	-0.423845993933185
79	140.13	140.454253309106	-0.324253309105558
80	139.45	140.398663341215	-0.948663341215308
81	139.59	139.58528141403	0.00471858596989705
82	139.44	139.725944846528	-0.285944846528167
83	139.53	139.53574104288	-0.00574104287980504
84	139.28	139.62493385309	-0.3449338530896

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	139.326436203736	137.569168707324	141.083703700148
86	139.372872407473	136.707283526933	142.038461288012
87	139.419308611209	135.930152010653	142.908465211766
88	139.465744814946	135.174285055344	143.757204574547
89	139.512181018682	134.417606253293	144.606755784071
90	139.558617222418	133.650106580668	145.467127864169
91	139.605053426155	132.866646087341	146.343460764968
92	139.651489629891	132.064415943331	147.238563316452
93	139.697925833628	131.241848274077	148.154003393178
94	139.744362037364	130.398084496431	149.090639578297
95	139.7907982411	129.532691965222	150.048904516979
96	139.837234444837	128.645502769924	151.02896611975

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 139.326436203736 & 137.569168707324 & 141.083703700148 \tabularnewline
86 & 139.372872407473 & 136.707283526933 & 142.038461288012 \tabularnewline
87 & 139.419308611209 & 135.930152010653 & 142.908465211766 \tabularnewline
88 & 139.465744814946 & 135.174285055344 & 143.757204574547 \tabularnewline
89 & 139.512181018682 & 134.417606253293 & 144.606755784071 \tabularnewline
90 & 139.558617222418 & 133.650106580668 & 145.467127864169 \tabularnewline
91 & 139.605053426155 & 132.866646087341 & 146.343460764968 \tabularnewline
92 & 139.651489629891 & 132.064415943331 & 147.238563316452 \tabularnewline
93 & 139.697925833628 & 131.241848274077 & 148.154003393178 \tabularnewline
94 & 139.744362037364 & 130.398084496431 & 149.090639578297 \tabularnewline
95 & 139.7907982411 & 129.532691965222 & 150.048904516979 \tabularnewline
96 & 139.837234444837 & 128.645502769924 & 151.02896611975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261459&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]85[/C][C]139.326436203736[/C][C]137.569168707324[/C][C]141.083703700148[/C][/ROW]
[ROW][C]86[/C][C]139.372872407473[/C][C]136.707283526933[/C][C]142.038461288012[/C][/ROW]
[ROW][C]87[/C][C]139.419308611209[/C][C]135.930152010653[/C][C]142.908465211766[/C][/ROW]
[ROW][C]88[/C][C]139.465744814946[/C][C]135.174285055344[/C][C]143.757204574547[/C][/ROW]
[ROW][C]89[/C][C]139.512181018682[/C][C]134.417606253293[/C][C]144.606755784071[/C][/ROW]
[ROW][C]90[/C][C]139.558617222418[/C][C]133.650106580668[/C][C]145.467127864169[/C][/ROW]
[ROW][C]91[/C][C]139.605053426155[/C][C]132.866646087341[/C][C]146.343460764968[/C][/ROW]
[ROW][C]92[/C][C]139.651489629891[/C][C]132.064415943331[/C][C]147.238563316452[/C][/ROW]
[ROW][C]93[/C][C]139.697925833628[/C][C]131.241848274077[/C][C]148.154003393178[/C][/ROW]
[ROW][C]94[/C][C]139.744362037364[/C][C]130.398084496431[/C][C]149.090639578297[/C][/ROW]
[ROW][C]95[/C][C]139.7907982411[/C][C]129.532691965222[/C][C]150.048904516979[/C][/ROW]
[ROW][C]96[/C][C]139.837234444837[/C][C]128.645502769924[/C][C]151.02896611975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261459&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261459&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
85	139.326436203736	137.569168707324	141.083703700148
86	139.372872407473	136.707283526933	142.038461288012
87	139.419308611209	135.930152010653	142.908465211766
88	139.465744814946	135.174285055344	143.757204574547
89	139.512181018682	134.417606253293	144.606755784071
90	139.558617222418	133.650106580668	145.467127864169
91	139.605053426155	132.866646087341	146.343460764968
92	139.651489629891	132.064415943331	147.238563316452
93	139.697925833628	131.241848274077	148.154003393178
94	139.744362037364	130.398084496431	149.090639578297
95	139.7907982411	129.532691965222	150.048904516979
96	139.837234444837	128.645502769924	151.02896611975

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