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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 19 Aug 2009 03:43:33 -0600

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/2009/Aug/19/t1250675074yjmqar8uey12t36.htm/, Retrieved Tue, 07 May 2024 08:47:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42911, Retrieved Tue, 07 May 2024 08:47:53 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

162

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

-     [Exponential Smoothing] [exonential smooth...] [2009-06-07 14:38:56] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [exponential smoot...] [2009-08-19 09:43:33] [f3c9ae0d0dd86c9c5120b223ccb0da06] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42911&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42911&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42911&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.846107257208812
beta	0.0470191847945091
gamma	0.383076569353457

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.846107257208812 \tabularnewline
beta & 0.0470191847945091 \tabularnewline
gamma & 0.383076569353457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42911&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]0.846107257208812[/C][/ROW]
[ROW][C]beta[/C][C]0.0470191847945091[/C][/ROW]
[ROW][C]gamma[/C][C]0.383076569353457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42911&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42911&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	0.846107257208812
beta	0.0470191847945091
gamma	0.383076569353457

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	103.6	102.869284019506	0.730715980494367
14	103.7	103.620358668199	0.0796413318009428
15	103.8	103.819530923376	-0.0195309233760952
16	104	104.034039230561	-0.0340392305605519
17	104	104.03487490211	-0.0348749021100048
18	104.1	104.133615423051	-0.0336154230506907
19	104.2	104.269707049563	-0.0697070495629362
20	104.3	104.343029328404	-0.0430293284039323
21	104.4	104.335813744886	0.0641862551144357
22	104.5	104.616246080153	-0.116246080152990
23	104.7	104.633729749252	0.0662702507485022
24	104.7	104.808257117621	-0.108257117620596
25	104.9	105.081542298681	-0.181542298680569
26	105	105.004477949696	-0.00447794969601034
27	105.2	105.105809878778	0.0941901212221126
28	105.3	105.400754181454	-0.100754181454008
29	105.4	105.324963794677	0.0750362053225473
30	105.5	105.502270990402	-0.00227099040216672
31	105.7	105.649967803123	0.0500321968774102
32	105.8	105.817798259421	-0.0177982594209283
33	105.9	105.829497006814	0.0705029931860253
34	106	106.098669181665	-0.0986691816651302
35	106.1	106.135313429479	-0.0353134294793875
36	106.2	106.202818306406	-0.00281830640589931
37	106.6	106.558006518396	0.0419934816037824
38	106.8	106.682564441141	0.117435558859199
39	107	106.900122973572	0.099877026428345
40	107.1	107.197390404024	-0.0973904040235993
41	107.3	107.140864687014	0.159135312986479
42	107.4	107.395636415119	0.00436358488083499
43	107.6	107.563939713598	0.0360602864022752
44	107.7	107.726706048313	-0.0267060483128603
45	107.9	107.744867751482	0.155132248518456
46	108.2	108.090845601655	0.109154398344955
47	108.3	108.329145797695	-0.0291457976945964
48	108.5	108.425621244396	0.074378755604215
49	108.92	108.879320476131	0.0406795238688886
50	109.23	109.031907870880	0.198092129119829
51	109.41	109.344968499889	0.0650315001114166
52	109.65	109.629846022794	0.0201539772058084
53	109.91	109.717627909634	0.19237209036622
54	110.01	110.023941713478	-0.0139417134775499
55	110.2	110.211787012894	-0.0117870128943025
56	110.49	110.360667396763	0.129332603237160
57	110.57	110.556058135053	0.0139418649465171
58	110.72	110.812667543877	-0.092667543876857
59	110.94	110.894900823338	0.0450991766624469
60	111.09	111.085850380536	0.00414961946357550
61	111.28	111.507141263227	-0.227141263227026
62	111.41	111.454498797205	-0.0444987972049233
63	111.62	111.557024101364	0.062975898636239
64	111.76	111.841759096411	-0.08175909641065
65	111.89	111.850743885063	0.0392561149365918
66	112.04	112.007441613573	0.0325583864265582
67	112.12	112.229960908603	-0.109960908603099
68	112.3	112.294804361104	0.00519563889550057
69	112.47	112.362629746186	0.107370253813556
70	112.59	112.682630414063	-0.0926304140631515
71	112.78	112.762523123765	0.0174768762346247
72	112.73	112.915768525520	-0.185768525519819
73	112.99	113.147052434465	-0.157052434464575
74	113.1	113.147926783101	-0.0479267831010048
75	113.33	113.237175053830	0.092824946170424
76	113.38	113.524224418429	-0.144224418428891
77	113.68	113.468619829236	0.211380170763562
78	113.65	113.759015207191	-0.109015207191050
79	113.81	113.837127504860	-0.0271275048595072
80	113.88	113.965671097104	-0.0856710971041537
81	114.02	113.944508997233	0.075491002767464
82	114.25	114.208362893174	0.041637106826002
83	114.28	114.395636229815	-0.115636229814953
84	114.38	114.405734508492	-0.0257345084923486
85	114.73	114.765810354900	-0.0358103548997093
86	114.97	114.868678191532	0.101321808467731
87	115.05	115.091395109796	-0.0413951097961984
88	115.29	115.245273664701	0.0447263352987477
89	115.37	115.370738575217	-0.0007385752172695
90	115.54	115.454643826653	0.0853561733471082
91	115.76	115.702984395919	0.0570156040805614
92	115.92	115.903123998771	0.0168760012288089
93	116.02	115.984657942668	0.0353420573318886
94	116.21	116.219760167804	-0.00976016780424516
95	116.26	116.358445224737	-0.0984452247368353
96	116.51	116.392813158478	0.117186841522269

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 103.6 & 102.869284019506 & 0.730715980494367 \tabularnewline
14 & 103.7 & 103.620358668199 & 0.0796413318009428 \tabularnewline
15 & 103.8 & 103.819530923376 & -0.0195309233760952 \tabularnewline
16 & 104 & 104.034039230561 & -0.0340392305605519 \tabularnewline
17 & 104 & 104.03487490211 & -0.0348749021100048 \tabularnewline
18 & 104.1 & 104.133615423051 & -0.0336154230506907 \tabularnewline
19 & 104.2 & 104.269707049563 & -0.0697070495629362 \tabularnewline
20 & 104.3 & 104.343029328404 & -0.0430293284039323 \tabularnewline
21 & 104.4 & 104.335813744886 & 0.0641862551144357 \tabularnewline
22 & 104.5 & 104.616246080153 & -0.116246080152990 \tabularnewline
23 & 104.7 & 104.633729749252 & 0.0662702507485022 \tabularnewline
24 & 104.7 & 104.808257117621 & -0.108257117620596 \tabularnewline
25 & 104.9 & 105.081542298681 & -0.181542298680569 \tabularnewline
26 & 105 & 105.004477949696 & -0.00447794969601034 \tabularnewline
27 & 105.2 & 105.105809878778 & 0.0941901212221126 \tabularnewline
28 & 105.3 & 105.400754181454 & -0.100754181454008 \tabularnewline
29 & 105.4 & 105.324963794677 & 0.0750362053225473 \tabularnewline
30 & 105.5 & 105.502270990402 & -0.00227099040216672 \tabularnewline
31 & 105.7 & 105.649967803123 & 0.0500321968774102 \tabularnewline
32 & 105.8 & 105.817798259421 & -0.0177982594209283 \tabularnewline
33 & 105.9 & 105.829497006814 & 0.0705029931860253 \tabularnewline
34 & 106 & 106.098669181665 & -0.0986691816651302 \tabularnewline
35 & 106.1 & 106.135313429479 & -0.0353134294793875 \tabularnewline
36 & 106.2 & 106.202818306406 & -0.00281830640589931 \tabularnewline
37 & 106.6 & 106.558006518396 & 0.0419934816037824 \tabularnewline
38 & 106.8 & 106.682564441141 & 0.117435558859199 \tabularnewline
39 & 107 & 106.900122973572 & 0.099877026428345 \tabularnewline
40 & 107.1 & 107.197390404024 & -0.0973904040235993 \tabularnewline
41 & 107.3 & 107.140864687014 & 0.159135312986479 \tabularnewline
42 & 107.4 & 107.395636415119 & 0.00436358488083499 \tabularnewline
43 & 107.6 & 107.563939713598 & 0.0360602864022752 \tabularnewline
44 & 107.7 & 107.726706048313 & -0.0267060483128603 \tabularnewline
45 & 107.9 & 107.744867751482 & 0.155132248518456 \tabularnewline
46 & 108.2 & 108.090845601655 & 0.109154398344955 \tabularnewline
47 & 108.3 & 108.329145797695 & -0.0291457976945964 \tabularnewline
48 & 108.5 & 108.425621244396 & 0.074378755604215 \tabularnewline
49 & 108.92 & 108.879320476131 & 0.0406795238688886 \tabularnewline
50 & 109.23 & 109.031907870880 & 0.198092129119829 \tabularnewline
51 & 109.41 & 109.344968499889 & 0.0650315001114166 \tabularnewline
52 & 109.65 & 109.629846022794 & 0.0201539772058084 \tabularnewline
53 & 109.91 & 109.717627909634 & 0.19237209036622 \tabularnewline
54 & 110.01 & 110.023941713478 & -0.0139417134775499 \tabularnewline
55 & 110.2 & 110.211787012894 & -0.0117870128943025 \tabularnewline
56 & 110.49 & 110.360667396763 & 0.129332603237160 \tabularnewline
57 & 110.57 & 110.556058135053 & 0.0139418649465171 \tabularnewline
58 & 110.72 & 110.812667543877 & -0.092667543876857 \tabularnewline
59 & 110.94 & 110.894900823338 & 0.0450991766624469 \tabularnewline
60 & 111.09 & 111.085850380536 & 0.00414961946357550 \tabularnewline
61 & 111.28 & 111.507141263227 & -0.227141263227026 \tabularnewline
62 & 111.41 & 111.454498797205 & -0.0444987972049233 \tabularnewline
63 & 111.62 & 111.557024101364 & 0.062975898636239 \tabularnewline
64 & 111.76 & 111.841759096411 & -0.08175909641065 \tabularnewline
65 & 111.89 & 111.850743885063 & 0.0392561149365918 \tabularnewline
66 & 112.04 & 112.007441613573 & 0.0325583864265582 \tabularnewline
67 & 112.12 & 112.229960908603 & -0.109960908603099 \tabularnewline
68 & 112.3 & 112.294804361104 & 0.00519563889550057 \tabularnewline
69 & 112.47 & 112.362629746186 & 0.107370253813556 \tabularnewline
70 & 112.59 & 112.682630414063 & -0.0926304140631515 \tabularnewline
71 & 112.78 & 112.762523123765 & 0.0174768762346247 \tabularnewline
72 & 112.73 & 112.915768525520 & -0.185768525519819 \tabularnewline
73 & 112.99 & 113.147052434465 & -0.157052434464575 \tabularnewline
74 & 113.1 & 113.147926783101 & -0.0479267831010048 \tabularnewline
75 & 113.33 & 113.237175053830 & 0.092824946170424 \tabularnewline
76 & 113.38 & 113.524224418429 & -0.144224418428891 \tabularnewline
77 & 113.68 & 113.468619829236 & 0.211380170763562 \tabularnewline
78 & 113.65 & 113.759015207191 & -0.109015207191050 \tabularnewline
79 & 113.81 & 113.837127504860 & -0.0271275048595072 \tabularnewline
80 & 113.88 & 113.965671097104 & -0.0856710971041537 \tabularnewline
81 & 114.02 & 113.944508997233 & 0.075491002767464 \tabularnewline
82 & 114.25 & 114.208362893174 & 0.041637106826002 \tabularnewline
83 & 114.28 & 114.395636229815 & -0.115636229814953 \tabularnewline
84 & 114.38 & 114.405734508492 & -0.0257345084923486 \tabularnewline
85 & 114.73 & 114.765810354900 & -0.0358103548997093 \tabularnewline
86 & 114.97 & 114.868678191532 & 0.101321808467731 \tabularnewline
87 & 115.05 & 115.091395109796 & -0.0413951097961984 \tabularnewline
88 & 115.29 & 115.245273664701 & 0.0447263352987477 \tabularnewline
89 & 115.37 & 115.370738575217 & -0.0007385752172695 \tabularnewline
90 & 115.54 & 115.454643826653 & 0.0853561733471082 \tabularnewline
91 & 115.76 & 115.702984395919 & 0.0570156040805614 \tabularnewline
92 & 115.92 & 115.903123998771 & 0.0168760012288089 \tabularnewline
93 & 116.02 & 115.984657942668 & 0.0353420573318886 \tabularnewline
94 & 116.21 & 116.219760167804 & -0.00976016780424516 \tabularnewline
95 & 116.26 & 116.358445224737 & -0.0984452247368353 \tabularnewline
96 & 116.51 & 116.392813158478 & 0.117186841522269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42911&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]103.6[/C][C]102.869284019506[/C][C]0.730715980494367[/C][/ROW]
[ROW][C]14[/C][C]103.7[/C][C]103.620358668199[/C][C]0.0796413318009428[/C][/ROW]
[ROW][C]15[/C][C]103.8[/C][C]103.819530923376[/C][C]-0.0195309233760952[/C][/ROW]
[ROW][C]16[/C][C]104[/C][C]104.034039230561[/C][C]-0.0340392305605519[/C][/ROW]
[ROW][C]17[/C][C]104[/C][C]104.03487490211[/C][C]-0.0348749021100048[/C][/ROW]
[ROW][C]18[/C][C]104.1[/C][C]104.133615423051[/C][C]-0.0336154230506907[/C][/ROW]
[ROW][C]19[/C][C]104.2[/C][C]104.269707049563[/C][C]-0.0697070495629362[/C][/ROW]
[ROW][C]20[/C][C]104.3[/C][C]104.343029328404[/C][C]-0.0430293284039323[/C][/ROW]
[ROW][C]21[/C][C]104.4[/C][C]104.335813744886[/C][C]0.0641862551144357[/C][/ROW]
[ROW][C]22[/C][C]104.5[/C][C]104.616246080153[/C][C]-0.116246080152990[/C][/ROW]
[ROW][C]23[/C][C]104.7[/C][C]104.633729749252[/C][C]0.0662702507485022[/C][/ROW]
[ROW][C]24[/C][C]104.7[/C][C]104.808257117621[/C][C]-0.108257117620596[/C][/ROW]
[ROW][C]25[/C][C]104.9[/C][C]105.081542298681[/C][C]-0.181542298680569[/C][/ROW]
[ROW][C]26[/C][C]105[/C][C]105.004477949696[/C][C]-0.00447794969601034[/C][/ROW]
[ROW][C]27[/C][C]105.2[/C][C]105.105809878778[/C][C]0.0941901212221126[/C][/ROW]
[ROW][C]28[/C][C]105.3[/C][C]105.400754181454[/C][C]-0.100754181454008[/C][/ROW]
[ROW][C]29[/C][C]105.4[/C][C]105.324963794677[/C][C]0.0750362053225473[/C][/ROW]
[ROW][C]30[/C][C]105.5[/C][C]105.502270990402[/C][C]-0.00227099040216672[/C][/ROW]
[ROW][C]31[/C][C]105.7[/C][C]105.649967803123[/C][C]0.0500321968774102[/C][/ROW]
[ROW][C]32[/C][C]105.8[/C][C]105.817798259421[/C][C]-0.0177982594209283[/C][/ROW]
[ROW][C]33[/C][C]105.9[/C][C]105.829497006814[/C][C]0.0705029931860253[/C][/ROW]
[ROW][C]34[/C][C]106[/C][C]106.098669181665[/C][C]-0.0986691816651302[/C][/ROW]
[ROW][C]35[/C][C]106.1[/C][C]106.135313429479[/C][C]-0.0353134294793875[/C][/ROW]
[ROW][C]36[/C][C]106.2[/C][C]106.202818306406[/C][C]-0.00281830640589931[/C][/ROW]
[ROW][C]37[/C][C]106.6[/C][C]106.558006518396[/C][C]0.0419934816037824[/C][/ROW]
[ROW][C]38[/C][C]106.8[/C][C]106.682564441141[/C][C]0.117435558859199[/C][/ROW]
[ROW][C]39[/C][C]107[/C][C]106.900122973572[/C][C]0.099877026428345[/C][/ROW]
[ROW][C]40[/C][C]107.1[/C][C]107.197390404024[/C][C]-0.0973904040235993[/C][/ROW]
[ROW][C]41[/C][C]107.3[/C][C]107.140864687014[/C][C]0.159135312986479[/C][/ROW]
[ROW][C]42[/C][C]107.4[/C][C]107.395636415119[/C][C]0.00436358488083499[/C][/ROW]
[ROW][C]43[/C][C]107.6[/C][C]107.563939713598[/C][C]0.0360602864022752[/C][/ROW]
[ROW][C]44[/C][C]107.7[/C][C]107.726706048313[/C][C]-0.0267060483128603[/C][/ROW]
[ROW][C]45[/C][C]107.9[/C][C]107.744867751482[/C][C]0.155132248518456[/C][/ROW]
[ROW][C]46[/C][C]108.2[/C][C]108.090845601655[/C][C]0.109154398344955[/C][/ROW]
[ROW][C]47[/C][C]108.3[/C][C]108.329145797695[/C][C]-0.0291457976945964[/C][/ROW]
[ROW][C]48[/C][C]108.5[/C][C]108.425621244396[/C][C]0.074378755604215[/C][/ROW]
[ROW][C]49[/C][C]108.92[/C][C]108.879320476131[/C][C]0.0406795238688886[/C][/ROW]
[ROW][C]50[/C][C]109.23[/C][C]109.031907870880[/C][C]0.198092129119829[/C][/ROW]
[ROW][C]51[/C][C]109.41[/C][C]109.344968499889[/C][C]0.0650315001114166[/C][/ROW]
[ROW][C]52[/C][C]109.65[/C][C]109.629846022794[/C][C]0.0201539772058084[/C][/ROW]
[ROW][C]53[/C][C]109.91[/C][C]109.717627909634[/C][C]0.19237209036622[/C][/ROW]
[ROW][C]54[/C][C]110.01[/C][C]110.023941713478[/C][C]-0.0139417134775499[/C][/ROW]
[ROW][C]55[/C][C]110.2[/C][C]110.211787012894[/C][C]-0.0117870128943025[/C][/ROW]
[ROW][C]56[/C][C]110.49[/C][C]110.360667396763[/C][C]0.129332603237160[/C][/ROW]
[ROW][C]57[/C][C]110.57[/C][C]110.556058135053[/C][C]0.0139418649465171[/C][/ROW]
[ROW][C]58[/C][C]110.72[/C][C]110.812667543877[/C][C]-0.092667543876857[/C][/ROW]
[ROW][C]59[/C][C]110.94[/C][C]110.894900823338[/C][C]0.0450991766624469[/C][/ROW]
[ROW][C]60[/C][C]111.09[/C][C]111.085850380536[/C][C]0.00414961946357550[/C][/ROW]
[ROW][C]61[/C][C]111.28[/C][C]111.507141263227[/C][C]-0.227141263227026[/C][/ROW]
[ROW][C]62[/C][C]111.41[/C][C]111.454498797205[/C][C]-0.0444987972049233[/C][/ROW]
[ROW][C]63[/C][C]111.62[/C][C]111.557024101364[/C][C]0.062975898636239[/C][/ROW]
[ROW][C]64[/C][C]111.76[/C][C]111.841759096411[/C][C]-0.08175909641065[/C][/ROW]
[ROW][C]65[/C][C]111.89[/C][C]111.850743885063[/C][C]0.0392561149365918[/C][/ROW]
[ROW][C]66[/C][C]112.04[/C][C]112.007441613573[/C][C]0.0325583864265582[/C][/ROW]
[ROW][C]67[/C][C]112.12[/C][C]112.229960908603[/C][C]-0.109960908603099[/C][/ROW]
[ROW][C]68[/C][C]112.3[/C][C]112.294804361104[/C][C]0.00519563889550057[/C][/ROW]
[ROW][C]69[/C][C]112.47[/C][C]112.362629746186[/C][C]0.107370253813556[/C][/ROW]
[ROW][C]70[/C][C]112.59[/C][C]112.682630414063[/C][C]-0.0926304140631515[/C][/ROW]
[ROW][C]71[/C][C]112.78[/C][C]112.762523123765[/C][C]0.0174768762346247[/C][/ROW]
[ROW][C]72[/C][C]112.73[/C][C]112.915768525520[/C][C]-0.185768525519819[/C][/ROW]
[ROW][C]73[/C][C]112.99[/C][C]113.147052434465[/C][C]-0.157052434464575[/C][/ROW]
[ROW][C]74[/C][C]113.1[/C][C]113.147926783101[/C][C]-0.0479267831010048[/C][/ROW]
[ROW][C]75[/C][C]113.33[/C][C]113.237175053830[/C][C]0.092824946170424[/C][/ROW]
[ROW][C]76[/C][C]113.38[/C][C]113.524224418429[/C][C]-0.144224418428891[/C][/ROW]
[ROW][C]77[/C][C]113.68[/C][C]113.468619829236[/C][C]0.211380170763562[/C][/ROW]
[ROW][C]78[/C][C]113.65[/C][C]113.759015207191[/C][C]-0.109015207191050[/C][/ROW]
[ROW][C]79[/C][C]113.81[/C][C]113.837127504860[/C][C]-0.0271275048595072[/C][/ROW]
[ROW][C]80[/C][C]113.88[/C][C]113.965671097104[/C][C]-0.0856710971041537[/C][/ROW]
[ROW][C]81[/C][C]114.02[/C][C]113.944508997233[/C][C]0.075491002767464[/C][/ROW]
[ROW][C]82[/C][C]114.25[/C][C]114.208362893174[/C][C]0.041637106826002[/C][/ROW]
[ROW][C]83[/C][C]114.28[/C][C]114.395636229815[/C][C]-0.115636229814953[/C][/ROW]
[ROW][C]84[/C][C]114.38[/C][C]114.405734508492[/C][C]-0.0257345084923486[/C][/ROW]
[ROW][C]85[/C][C]114.73[/C][C]114.765810354900[/C][C]-0.0358103548997093[/C][/ROW]
[ROW][C]86[/C][C]114.97[/C][C]114.868678191532[/C][C]0.101321808467731[/C][/ROW]
[ROW][C]87[/C][C]115.05[/C][C]115.091395109796[/C][C]-0.0413951097961984[/C][/ROW]
[ROW][C]88[/C][C]115.29[/C][C]115.245273664701[/C][C]0.0447263352987477[/C][/ROW]
[ROW][C]89[/C][C]115.37[/C][C]115.370738575217[/C][C]-0.0007385752172695[/C][/ROW]
[ROW][C]90[/C][C]115.54[/C][C]115.454643826653[/C][C]0.0853561733471082[/C][/ROW]
[ROW][C]91[/C][C]115.76[/C][C]115.702984395919[/C][C]0.0570156040805614[/C][/ROW]
[ROW][C]92[/C][C]115.92[/C][C]115.903123998771[/C][C]0.0168760012288089[/C][/ROW]
[ROW][C]93[/C][C]116.02[/C][C]115.984657942668[/C][C]0.0353420573318886[/C][/ROW]
[ROW][C]94[/C][C]116.21[/C][C]116.219760167804[/C][C]-0.00976016780424516[/C][/ROW]
[ROW][C]95[/C][C]116.26[/C][C]116.358445224737[/C][C]-0.0984452247368353[/C][/ROW]
[ROW][C]96[/C][C]116.51[/C][C]116.392813158478[/C][C]0.117186841522269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42911&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42911&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	103.6	102.869284019506	0.730715980494367
14	103.7	103.620358668199	0.0796413318009428
15	103.8	103.819530923376	-0.0195309233760952
16	104	104.034039230561	-0.0340392305605519
17	104	104.03487490211	-0.0348749021100048
18	104.1	104.133615423051	-0.0336154230506907
19	104.2	104.269707049563	-0.0697070495629362
20	104.3	104.343029328404	-0.0430293284039323
21	104.4	104.335813744886	0.0641862551144357
22	104.5	104.616246080153	-0.116246080152990
23	104.7	104.633729749252	0.0662702507485022
24	104.7	104.808257117621	-0.108257117620596
25	104.9	105.081542298681	-0.181542298680569
26	105	105.004477949696	-0.00447794969601034
27	105.2	105.105809878778	0.0941901212221126
28	105.3	105.400754181454	-0.100754181454008
29	105.4	105.324963794677	0.0750362053225473
30	105.5	105.502270990402	-0.00227099040216672
31	105.7	105.649967803123	0.0500321968774102
32	105.8	105.817798259421	-0.0177982594209283
33	105.9	105.829497006814	0.0705029931860253
34	106	106.098669181665	-0.0986691816651302
35	106.1	106.135313429479	-0.0353134294793875
36	106.2	106.202818306406	-0.00281830640589931
37	106.6	106.558006518396	0.0419934816037824
38	106.8	106.682564441141	0.117435558859199
39	107	106.900122973572	0.099877026428345
40	107.1	107.197390404024	-0.0973904040235993
41	107.3	107.140864687014	0.159135312986479
42	107.4	107.395636415119	0.00436358488083499
43	107.6	107.563939713598	0.0360602864022752
44	107.7	107.726706048313	-0.0267060483128603
45	107.9	107.744867751482	0.155132248518456
46	108.2	108.090845601655	0.109154398344955
47	108.3	108.329145797695	-0.0291457976945964
48	108.5	108.425621244396	0.074378755604215
49	108.92	108.879320476131	0.0406795238688886
50	109.23	109.031907870880	0.198092129119829
51	109.41	109.344968499889	0.0650315001114166
52	109.65	109.629846022794	0.0201539772058084
53	109.91	109.717627909634	0.19237209036622
54	110.01	110.023941713478	-0.0139417134775499
55	110.2	110.211787012894	-0.0117870128943025
56	110.49	110.360667396763	0.129332603237160
57	110.57	110.556058135053	0.0139418649465171
58	110.72	110.812667543877	-0.092667543876857
59	110.94	110.894900823338	0.0450991766624469
60	111.09	111.085850380536	0.00414961946357550
61	111.28	111.507141263227	-0.227141263227026
62	111.41	111.454498797205	-0.0444987972049233
63	111.62	111.557024101364	0.062975898636239
64	111.76	111.841759096411	-0.08175909641065
65	111.89	111.850743885063	0.0392561149365918
66	112.04	112.007441613573	0.0325583864265582
67	112.12	112.229960908603	-0.109960908603099
68	112.3	112.294804361104	0.00519563889550057
69	112.47	112.362629746186	0.107370253813556
70	112.59	112.682630414063	-0.0926304140631515
71	112.78	112.762523123765	0.0174768762346247
72	112.73	112.915768525520	-0.185768525519819
73	112.99	113.147052434465	-0.157052434464575
74	113.1	113.147926783101	-0.0479267831010048
75	113.33	113.237175053830	0.092824946170424
76	113.38	113.524224418429	-0.144224418428891
77	113.68	113.468619829236	0.211380170763562
78	113.65	113.759015207191	-0.109015207191050
79	113.81	113.837127504860	-0.0271275048595072
80	113.88	113.965671097104	-0.0856710971041537
81	114.02	113.944508997233	0.075491002767464
82	114.25	114.208362893174	0.041637106826002
83	114.28	114.395636229815	-0.115636229814953
84	114.38	114.405734508492	-0.0257345084923486
85	114.73	114.765810354900	-0.0358103548997093
86	114.97	114.868678191532	0.101321808467731
87	115.05	115.091395109796	-0.0413951097961984
88	115.29	115.245273664701	0.0447263352987477
89	115.37	115.370738575217	-0.0007385752172695
90	115.54	115.454643826653	0.0853561733471082
91	115.76	115.702984395919	0.0570156040805614
92	115.92	115.903123998771	0.0168760012288089
93	116.02	115.984657942668	0.0353420573318886
94	116.21	116.219760167804	-0.00976016780424516
95	116.26	116.358445224737	-0.0984452247368353
96	116.51	116.392813158478	0.117186841522269

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	116.888266642542	116.675873826554	117.10065945853
98	117.041579647035	116.744386770874	117.338772523197
99	117.177890715279	116.809827050053	117.545954380504
100	117.382485556277	116.950166844580	117.814804267973
101	117.474233041144	116.981978573018	117.966487509271
102	117.570750089386	117.021068314577	118.120431864195
103	117.750192749921	117.144380703015	118.356004796827
104	117.901975676058	117.241257461976	118.56269389014
105	117.970499911358	117.256058984311	118.684940838404
106	118.174075675467	117.405600602066	118.942550748868
107	118.316191837995	117.494319792615	119.138063883375
108	118.450737262555	116.895360912129	120.00611361298

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 116.888266642542 & 116.675873826554 & 117.10065945853 \tabularnewline
98 & 117.041579647035 & 116.744386770874 & 117.338772523197 \tabularnewline
99 & 117.177890715279 & 116.809827050053 & 117.545954380504 \tabularnewline
100 & 117.382485556277 & 116.950166844580 & 117.814804267973 \tabularnewline
101 & 117.474233041144 & 116.981978573018 & 117.966487509271 \tabularnewline
102 & 117.570750089386 & 117.021068314577 & 118.120431864195 \tabularnewline
103 & 117.750192749921 & 117.144380703015 & 118.356004796827 \tabularnewline
104 & 117.901975676058 & 117.241257461976 & 118.56269389014 \tabularnewline
105 & 117.970499911358 & 117.256058984311 & 118.684940838404 \tabularnewline
106 & 118.174075675467 & 117.405600602066 & 118.942550748868 \tabularnewline
107 & 118.316191837995 & 117.494319792615 & 119.138063883375 \tabularnewline
108 & 118.450737262555 & 116.895360912129 & 120.00611361298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42911&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]97[/C][C]116.888266642542[/C][C]116.675873826554[/C][C]117.10065945853[/C][/ROW]
[ROW][C]98[/C][C]117.041579647035[/C][C]116.744386770874[/C][C]117.338772523197[/C][/ROW]
[ROW][C]99[/C][C]117.177890715279[/C][C]116.809827050053[/C][C]117.545954380504[/C][/ROW]
[ROW][C]100[/C][C]117.382485556277[/C][C]116.950166844580[/C][C]117.814804267973[/C][/ROW]
[ROW][C]101[/C][C]117.474233041144[/C][C]116.981978573018[/C][C]117.966487509271[/C][/ROW]
[ROW][C]102[/C][C]117.570750089386[/C][C]117.021068314577[/C][C]118.120431864195[/C][/ROW]
[ROW][C]103[/C][C]117.750192749921[/C][C]117.144380703015[/C][C]118.356004796827[/C][/ROW]
[ROW][C]104[/C][C]117.901975676058[/C][C]117.241257461976[/C][C]118.56269389014[/C][/ROW]
[ROW][C]105[/C][C]117.970499911358[/C][C]117.256058984311[/C][C]118.684940838404[/C][/ROW]
[ROW][C]106[/C][C]118.174075675467[/C][C]117.405600602066[/C][C]118.942550748868[/C][/ROW]
[ROW][C]107[/C][C]118.316191837995[/C][C]117.494319792615[/C][C]119.138063883375[/C][/ROW]
[ROW][C]108[/C][C]118.450737262555[/C][C]116.895360912129[/C][C]120.00611361298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42911&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42911&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
97	116.888266642542	116.675873826554	117.10065945853
98	117.041579647035	116.744386770874	117.338772523197
99	117.177890715279	116.809827050053	117.545954380504
100	117.382485556277	116.950166844580	117.814804267973
101	117.474233041144	116.981978573018	117.966487509271
102	117.570750089386	117.021068314577	118.120431864195
103	117.750192749921	117.144380703015	118.356004796827
104	117.901975676058	117.241257461976	118.56269389014
105	117.970499911358	117.256058984311	118.684940838404
106	118.174075675467	117.405600602066	118.942550748868
107	118.316191837995	117.494319792615	119.138063883375
108	118.450737262555	116.895360912129	120.00611361298

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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