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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 12 Jan 2014 13:47:58 -0500

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/Jan/12/t1389552542j17aelu44kt95d2.htm/, Retrieved Sat, 15 Aug 2026 16:35:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233035, Retrieved Sat, 15 Aug 2026 16:35:29 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

381

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

-       [Exponential Smoothing] [] [2014-01-12 18:47:58] [50ab323715771b694b8972a989c47bb3] [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	5 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233035&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233035&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233035&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	5 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0587108329381535
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0587108329381535 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233035&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]0.0587108329381535[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233035&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233035&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	0.0587108329381535
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	96.5	96.68	-0.179999999999993
4	96.01	96.3994320500711	-0.389432050071122
5	96.07	95.8865681700386	0.18343182996135
6	95.93	95.957337605563	-0.0273376055630337
7	95.93	95.8157325919699	0.114267408030102
8	95.83	95.822441326673	0.00755867332695459
9	96.24	95.72288510268	0.517114897320027
10	96.25	96.1632453490263	0.0867546509736599
11	96.59	96.1783387868463	0.411661213153735
12	96.62	96.5425077595589	0.0774922404411456
13	96.62	96.5770573935414	0.0429426064585954
14	96.81	96.5795785897351	0.230421410264881
15	96.71	96.7831068226586	-0.0731068226585592
16	96.45	96.6788146602068	-0.228814660206808
17	96.63	96.4053807609176	0.224619239082386
18	96.56	96.5985683435381	-0.0385683435380599
19	96.56	96.5263039639639	0.0336960360360905
20	96.65	96.5282822863063	0.121717713693698
21	97.04	96.6254284346606	0.414571565339415
22	97.14	97.0397682765741	0.100231723425864
23	97.2	97.1456529645433	0.0543470354567148
24	97.26	97.2088437242627	0.051156275737327
25	97.26	97.2718471518212	-0.0118471518212289
26	97.24	97.2711515956699	-0.0311515956698685
27	97.35	97.2493226595407	0.100677340459271
28	97.36	97.3652335100571	-0.0052335100570815
29	97.28	97.3749262463224	-0.0949262463224443
30	97.31	97.2893530473332	0.0206469526668371
31	97.31	97.3205652471219	-0.0105652471218747
32	97.31	97.3199449526631	-0.00994495266314743
33	97.23	97.3193610762088	-0.0893610762087604
34	97.78	97.2341146129923	0.545885387007701
35	97.64	97.8161639987523	-0.176163998752287
36	97.68	97.6658212636518	0.0141787363481853
37	97.68	97.7066537090728	-0.026653709072832
38	97.81	97.7050888476123	0.104911152387714
39	97.75	97.8412482687535	-0.0912482687534606
40	97.63	97.7758910068908	-0.145891006890793
41	97.6	97.647325624358	-0.047325624358038
42	97.65	97.6145470975327	0.0354529024673553
43	97.65	97.6666285669666	-0.0166285669665882
44	97.65	97.6656522899494	-0.0156522899494149
45	97.86	97.6647333309691	0.1952666690309
46	98.41	97.886197599753	0.523802400247035
47	98.79	98.4669504749665	0.323049525033539
48	98.75	98.8659169816615	-0.115916981661471
49	98.74	98.8191113991164	-0.0791113991164423
50	98.55	98.8044667029794	-0.254466702979414
51	98.65	98.5995267508925	0.0504732491075401
52	98.86	98.7024900773887	0.157509922611325
53	98.94	98.9217376161412	0.0182623838587972
54	99.05	99.002809815909	0.0471901840910078
55	99.05	99.1155803909235	-0.065580390923472
56	99.05	99.1117301115479	-0.0617301115479449
57	99.17	99.1081058852816	0.0618941147183989
58	98.99	99.2317397403107	-0.241739740310692
59	98.91	99.0375469988028	-0.127546998802799
60	98.89	98.9500586082643	-0.0600586082643133
61	98.89	98.926532517348	-0.0365325173480215
62	98.72	98.9243876628252	-0.204387662825184
63	98.89	98.7423878928984	0.147612107101565
64	98.97	98.9210543226581	0.0489456773418766
65	99.16	99.0039279641436	0.156072035856411
66	99.54	99.2030910833671	0.336908916632936
67	99.54	99.6028712864869	-0.0628712864868817
68	99.55	99.5991800608894	-0.0491800608893556
69	100.01	99.6062926585506	0.403707341449419
70	99.52	100.08999465283	-0.569994652830331
71	99.44	99.5665297919924	-0.126529791992368
72	99.39	99.479101122513	-0.0891011225130001
73	99.39	99.4238699213945	-0.0338699213945404
74	99.4	99.4218813900979	-0.0218813900979029
75	100.43	99.4305967154594	0.999403284540577
76	100.62	100.519272514736	0.100727485264073
77	101.05	100.715186309296	0.334813690704451
78	100.95	101.164843499956	-0.21484349995589
79	100.95	101.052229859122	-0.102229859122147
80	100.91	101.046227858942	-0.136227858941936
81	101.13	100.998229807874	0.131770192125927
82	100.81	101.22596614561	-0.415966145610199
83	100.47	100.881544426727	-0.41154442672736
84	100.56	100.517382310643	0.0426176893568737

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 96.5 & 96.68 & -0.179999999999993 \tabularnewline
4 & 96.01 & 96.3994320500711 & -0.389432050071122 \tabularnewline
5 & 96.07 & 95.8865681700386 & 0.18343182996135 \tabularnewline
6 & 95.93 & 95.957337605563 & -0.0273376055630337 \tabularnewline
7 & 95.93 & 95.8157325919699 & 0.114267408030102 \tabularnewline
8 & 95.83 & 95.822441326673 & 0.00755867332695459 \tabularnewline
9 & 96.24 & 95.72288510268 & 0.517114897320027 \tabularnewline
10 & 96.25 & 96.1632453490263 & 0.0867546509736599 \tabularnewline
11 & 96.59 & 96.1783387868463 & 0.411661213153735 \tabularnewline
12 & 96.62 & 96.5425077595589 & 0.0774922404411456 \tabularnewline
13 & 96.62 & 96.5770573935414 & 0.0429426064585954 \tabularnewline
14 & 96.81 & 96.5795785897351 & 0.230421410264881 \tabularnewline
15 & 96.71 & 96.7831068226586 & -0.0731068226585592 \tabularnewline
16 & 96.45 & 96.6788146602068 & -0.228814660206808 \tabularnewline
17 & 96.63 & 96.4053807609176 & 0.224619239082386 \tabularnewline
18 & 96.56 & 96.5985683435381 & -0.0385683435380599 \tabularnewline
19 & 96.56 & 96.5263039639639 & 0.0336960360360905 \tabularnewline
20 & 96.65 & 96.5282822863063 & 0.121717713693698 \tabularnewline
21 & 97.04 & 96.6254284346606 & 0.414571565339415 \tabularnewline
22 & 97.14 & 97.0397682765741 & 0.100231723425864 \tabularnewline
23 & 97.2 & 97.1456529645433 & 0.0543470354567148 \tabularnewline
24 & 97.26 & 97.2088437242627 & 0.051156275737327 \tabularnewline
25 & 97.26 & 97.2718471518212 & -0.0118471518212289 \tabularnewline
26 & 97.24 & 97.2711515956699 & -0.0311515956698685 \tabularnewline
27 & 97.35 & 97.2493226595407 & 0.100677340459271 \tabularnewline
28 & 97.36 & 97.3652335100571 & -0.0052335100570815 \tabularnewline
29 & 97.28 & 97.3749262463224 & -0.0949262463224443 \tabularnewline
30 & 97.31 & 97.2893530473332 & 0.0206469526668371 \tabularnewline
31 & 97.31 & 97.3205652471219 & -0.0105652471218747 \tabularnewline
32 & 97.31 & 97.3199449526631 & -0.00994495266314743 \tabularnewline
33 & 97.23 & 97.3193610762088 & -0.0893610762087604 \tabularnewline
34 & 97.78 & 97.2341146129923 & 0.545885387007701 \tabularnewline
35 & 97.64 & 97.8161639987523 & -0.176163998752287 \tabularnewline
36 & 97.68 & 97.6658212636518 & 0.0141787363481853 \tabularnewline
37 & 97.68 & 97.7066537090728 & -0.026653709072832 \tabularnewline
38 & 97.81 & 97.7050888476123 & 0.104911152387714 \tabularnewline
39 & 97.75 & 97.8412482687535 & -0.0912482687534606 \tabularnewline
40 & 97.63 & 97.7758910068908 & -0.145891006890793 \tabularnewline
41 & 97.6 & 97.647325624358 & -0.047325624358038 \tabularnewline
42 & 97.65 & 97.6145470975327 & 0.0354529024673553 \tabularnewline
43 & 97.65 & 97.6666285669666 & -0.0166285669665882 \tabularnewline
44 & 97.65 & 97.6656522899494 & -0.0156522899494149 \tabularnewline
45 & 97.86 & 97.6647333309691 & 0.1952666690309 \tabularnewline
46 & 98.41 & 97.886197599753 & 0.523802400247035 \tabularnewline
47 & 98.79 & 98.4669504749665 & 0.323049525033539 \tabularnewline
48 & 98.75 & 98.8659169816615 & -0.115916981661471 \tabularnewline
49 & 98.74 & 98.8191113991164 & -0.0791113991164423 \tabularnewline
50 & 98.55 & 98.8044667029794 & -0.254466702979414 \tabularnewline
51 & 98.65 & 98.5995267508925 & 0.0504732491075401 \tabularnewline
52 & 98.86 & 98.7024900773887 & 0.157509922611325 \tabularnewline
53 & 98.94 & 98.9217376161412 & 0.0182623838587972 \tabularnewline
54 & 99.05 & 99.002809815909 & 0.0471901840910078 \tabularnewline
55 & 99.05 & 99.1155803909235 & -0.065580390923472 \tabularnewline
56 & 99.05 & 99.1117301115479 & -0.0617301115479449 \tabularnewline
57 & 99.17 & 99.1081058852816 & 0.0618941147183989 \tabularnewline
58 & 98.99 & 99.2317397403107 & -0.241739740310692 \tabularnewline
59 & 98.91 & 99.0375469988028 & -0.127546998802799 \tabularnewline
60 & 98.89 & 98.9500586082643 & -0.0600586082643133 \tabularnewline
61 & 98.89 & 98.926532517348 & -0.0365325173480215 \tabularnewline
62 & 98.72 & 98.9243876628252 & -0.204387662825184 \tabularnewline
63 & 98.89 & 98.7423878928984 & 0.147612107101565 \tabularnewline
64 & 98.97 & 98.9210543226581 & 0.0489456773418766 \tabularnewline
65 & 99.16 & 99.0039279641436 & 0.156072035856411 \tabularnewline
66 & 99.54 & 99.2030910833671 & 0.336908916632936 \tabularnewline
67 & 99.54 & 99.6028712864869 & -0.0628712864868817 \tabularnewline
68 & 99.55 & 99.5991800608894 & -0.0491800608893556 \tabularnewline
69 & 100.01 & 99.6062926585506 & 0.403707341449419 \tabularnewline
70 & 99.52 & 100.08999465283 & -0.569994652830331 \tabularnewline
71 & 99.44 & 99.5665297919924 & -0.126529791992368 \tabularnewline
72 & 99.39 & 99.479101122513 & -0.0891011225130001 \tabularnewline
73 & 99.39 & 99.4238699213945 & -0.0338699213945404 \tabularnewline
74 & 99.4 & 99.4218813900979 & -0.0218813900979029 \tabularnewline
75 & 100.43 & 99.4305967154594 & 0.999403284540577 \tabularnewline
76 & 100.62 & 100.519272514736 & 0.100727485264073 \tabularnewline
77 & 101.05 & 100.715186309296 & 0.334813690704451 \tabularnewline
78 & 100.95 & 101.164843499956 & -0.21484349995589 \tabularnewline
79 & 100.95 & 101.052229859122 & -0.102229859122147 \tabularnewline
80 & 100.91 & 101.046227858942 & -0.136227858941936 \tabularnewline
81 & 101.13 & 100.998229807874 & 0.131770192125927 \tabularnewline
82 & 100.81 & 101.22596614561 & -0.415966145610199 \tabularnewline
83 & 100.47 & 100.881544426727 & -0.41154442672736 \tabularnewline
84 & 100.56 & 100.517382310643 & 0.0426176893568737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233035&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]96.5[/C][C]96.68[/C][C]-0.179999999999993[/C][/ROW]
[ROW][C]4[/C][C]96.01[/C][C]96.3994320500711[/C][C]-0.389432050071122[/C][/ROW]
[ROW][C]5[/C][C]96.07[/C][C]95.8865681700386[/C][C]0.18343182996135[/C][/ROW]
[ROW][C]6[/C][C]95.93[/C][C]95.957337605563[/C][C]-0.0273376055630337[/C][/ROW]
[ROW][C]7[/C][C]95.93[/C][C]95.8157325919699[/C][C]0.114267408030102[/C][/ROW]
[ROW][C]8[/C][C]95.83[/C][C]95.822441326673[/C][C]0.00755867332695459[/C][/ROW]
[ROW][C]9[/C][C]96.24[/C][C]95.72288510268[/C][C]0.517114897320027[/C][/ROW]
[ROW][C]10[/C][C]96.25[/C][C]96.1632453490263[/C][C]0.0867546509736599[/C][/ROW]
[ROW][C]11[/C][C]96.59[/C][C]96.1783387868463[/C][C]0.411661213153735[/C][/ROW]
[ROW][C]12[/C][C]96.62[/C][C]96.5425077595589[/C][C]0.0774922404411456[/C][/ROW]
[ROW][C]13[/C][C]96.62[/C][C]96.5770573935414[/C][C]0.0429426064585954[/C][/ROW]
[ROW][C]14[/C][C]96.81[/C][C]96.5795785897351[/C][C]0.230421410264881[/C][/ROW]
[ROW][C]15[/C][C]96.71[/C][C]96.7831068226586[/C][C]-0.0731068226585592[/C][/ROW]
[ROW][C]16[/C][C]96.45[/C][C]96.6788146602068[/C][C]-0.228814660206808[/C][/ROW]
[ROW][C]17[/C][C]96.63[/C][C]96.4053807609176[/C][C]0.224619239082386[/C][/ROW]
[ROW][C]18[/C][C]96.56[/C][C]96.5985683435381[/C][C]-0.0385683435380599[/C][/ROW]
[ROW][C]19[/C][C]96.56[/C][C]96.5263039639639[/C][C]0.0336960360360905[/C][/ROW]
[ROW][C]20[/C][C]96.65[/C][C]96.5282822863063[/C][C]0.121717713693698[/C][/ROW]
[ROW][C]21[/C][C]97.04[/C][C]96.6254284346606[/C][C]0.414571565339415[/C][/ROW]
[ROW][C]22[/C][C]97.14[/C][C]97.0397682765741[/C][C]0.100231723425864[/C][/ROW]
[ROW][C]23[/C][C]97.2[/C][C]97.1456529645433[/C][C]0.0543470354567148[/C][/ROW]
[ROW][C]24[/C][C]97.26[/C][C]97.2088437242627[/C][C]0.051156275737327[/C][/ROW]
[ROW][C]25[/C][C]97.26[/C][C]97.2718471518212[/C][C]-0.0118471518212289[/C][/ROW]
[ROW][C]26[/C][C]97.24[/C][C]97.2711515956699[/C][C]-0.0311515956698685[/C][/ROW]
[ROW][C]27[/C][C]97.35[/C][C]97.2493226595407[/C][C]0.100677340459271[/C][/ROW]
[ROW][C]28[/C][C]97.36[/C][C]97.3652335100571[/C][C]-0.0052335100570815[/C][/ROW]
[ROW][C]29[/C][C]97.28[/C][C]97.3749262463224[/C][C]-0.0949262463224443[/C][/ROW]
[ROW][C]30[/C][C]97.31[/C][C]97.2893530473332[/C][C]0.0206469526668371[/C][/ROW]
[ROW][C]31[/C][C]97.31[/C][C]97.3205652471219[/C][C]-0.0105652471218747[/C][/ROW]
[ROW][C]32[/C][C]97.31[/C][C]97.3199449526631[/C][C]-0.00994495266314743[/C][/ROW]
[ROW][C]33[/C][C]97.23[/C][C]97.3193610762088[/C][C]-0.0893610762087604[/C][/ROW]
[ROW][C]34[/C][C]97.78[/C][C]97.2341146129923[/C][C]0.545885387007701[/C][/ROW]
[ROW][C]35[/C][C]97.64[/C][C]97.8161639987523[/C][C]-0.176163998752287[/C][/ROW]
[ROW][C]36[/C][C]97.68[/C][C]97.6658212636518[/C][C]0.0141787363481853[/C][/ROW]
[ROW][C]37[/C][C]97.68[/C][C]97.7066537090728[/C][C]-0.026653709072832[/C][/ROW]
[ROW][C]38[/C][C]97.81[/C][C]97.7050888476123[/C][C]0.104911152387714[/C][/ROW]
[ROW][C]39[/C][C]97.75[/C][C]97.8412482687535[/C][C]-0.0912482687534606[/C][/ROW]
[ROW][C]40[/C][C]97.63[/C][C]97.7758910068908[/C][C]-0.145891006890793[/C][/ROW]
[ROW][C]41[/C][C]97.6[/C][C]97.647325624358[/C][C]-0.047325624358038[/C][/ROW]
[ROW][C]42[/C][C]97.65[/C][C]97.6145470975327[/C][C]0.0354529024673553[/C][/ROW]
[ROW][C]43[/C][C]97.65[/C][C]97.6666285669666[/C][C]-0.0166285669665882[/C][/ROW]
[ROW][C]44[/C][C]97.65[/C][C]97.6656522899494[/C][C]-0.0156522899494149[/C][/ROW]
[ROW][C]45[/C][C]97.86[/C][C]97.6647333309691[/C][C]0.1952666690309[/C][/ROW]
[ROW][C]46[/C][C]98.41[/C][C]97.886197599753[/C][C]0.523802400247035[/C][/ROW]
[ROW][C]47[/C][C]98.79[/C][C]98.4669504749665[/C][C]0.323049525033539[/C][/ROW]
[ROW][C]48[/C][C]98.75[/C][C]98.8659169816615[/C][C]-0.115916981661471[/C][/ROW]
[ROW][C]49[/C][C]98.74[/C][C]98.8191113991164[/C][C]-0.0791113991164423[/C][/ROW]
[ROW][C]50[/C][C]98.55[/C][C]98.8044667029794[/C][C]-0.254466702979414[/C][/ROW]
[ROW][C]51[/C][C]98.65[/C][C]98.5995267508925[/C][C]0.0504732491075401[/C][/ROW]
[ROW][C]52[/C][C]98.86[/C][C]98.7024900773887[/C][C]0.157509922611325[/C][/ROW]
[ROW][C]53[/C][C]98.94[/C][C]98.9217376161412[/C][C]0.0182623838587972[/C][/ROW]
[ROW][C]54[/C][C]99.05[/C][C]99.002809815909[/C][C]0.0471901840910078[/C][/ROW]
[ROW][C]55[/C][C]99.05[/C][C]99.1155803909235[/C][C]-0.065580390923472[/C][/ROW]
[ROW][C]56[/C][C]99.05[/C][C]99.1117301115479[/C][C]-0.0617301115479449[/C][/ROW]
[ROW][C]57[/C][C]99.17[/C][C]99.1081058852816[/C][C]0.0618941147183989[/C][/ROW]
[ROW][C]58[/C][C]98.99[/C][C]99.2317397403107[/C][C]-0.241739740310692[/C][/ROW]
[ROW][C]59[/C][C]98.91[/C][C]99.0375469988028[/C][C]-0.127546998802799[/C][/ROW]
[ROW][C]60[/C][C]98.89[/C][C]98.9500586082643[/C][C]-0.0600586082643133[/C][/ROW]
[ROW][C]61[/C][C]98.89[/C][C]98.926532517348[/C][C]-0.0365325173480215[/C][/ROW]
[ROW][C]62[/C][C]98.72[/C][C]98.9243876628252[/C][C]-0.204387662825184[/C][/ROW]
[ROW][C]63[/C][C]98.89[/C][C]98.7423878928984[/C][C]0.147612107101565[/C][/ROW]
[ROW][C]64[/C][C]98.97[/C][C]98.9210543226581[/C][C]0.0489456773418766[/C][/ROW]
[ROW][C]65[/C][C]99.16[/C][C]99.0039279641436[/C][C]0.156072035856411[/C][/ROW]
[ROW][C]66[/C][C]99.54[/C][C]99.2030910833671[/C][C]0.336908916632936[/C][/ROW]
[ROW][C]67[/C][C]99.54[/C][C]99.6028712864869[/C][C]-0.0628712864868817[/C][/ROW]
[ROW][C]68[/C][C]99.55[/C][C]99.5991800608894[/C][C]-0.0491800608893556[/C][/ROW]
[ROW][C]69[/C][C]100.01[/C][C]99.6062926585506[/C][C]0.403707341449419[/C][/ROW]
[ROW][C]70[/C][C]99.52[/C][C]100.08999465283[/C][C]-0.569994652830331[/C][/ROW]
[ROW][C]71[/C][C]99.44[/C][C]99.5665297919924[/C][C]-0.126529791992368[/C][/ROW]
[ROW][C]72[/C][C]99.39[/C][C]99.479101122513[/C][C]-0.0891011225130001[/C][/ROW]
[ROW][C]73[/C][C]99.39[/C][C]99.4238699213945[/C][C]-0.0338699213945404[/C][/ROW]
[ROW][C]74[/C][C]99.4[/C][C]99.4218813900979[/C][C]-0.0218813900979029[/C][/ROW]
[ROW][C]75[/C][C]100.43[/C][C]99.4305967154594[/C][C]0.999403284540577[/C][/ROW]
[ROW][C]76[/C][C]100.62[/C][C]100.519272514736[/C][C]0.100727485264073[/C][/ROW]
[ROW][C]77[/C][C]101.05[/C][C]100.715186309296[/C][C]0.334813690704451[/C][/ROW]
[ROW][C]78[/C][C]100.95[/C][C]101.164843499956[/C][C]-0.21484349995589[/C][/ROW]
[ROW][C]79[/C][C]100.95[/C][C]101.052229859122[/C][C]-0.102229859122147[/C][/ROW]
[ROW][C]80[/C][C]100.91[/C][C]101.046227858942[/C][C]-0.136227858941936[/C][/ROW]
[ROW][C]81[/C][C]101.13[/C][C]100.998229807874[/C][C]0.131770192125927[/C][/ROW]
[ROW][C]82[/C][C]100.81[/C][C]101.22596614561[/C][C]-0.415966145610199[/C][/ROW]
[ROW][C]83[/C][C]100.47[/C][C]100.881544426727[/C][C]-0.41154442672736[/C][/ROW]
[ROW][C]84[/C][C]100.56[/C][C]100.517382310643[/C][C]0.0426176893568737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233035&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233035&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	96.5	96.68	-0.179999999999993
4	96.01	96.3994320500711	-0.389432050071122
5	96.07	95.8865681700386	0.18343182996135
6	95.93	95.957337605563	-0.0273376055630337
7	95.93	95.8157325919699	0.114267408030102
8	95.83	95.822441326673	0.00755867332695459
9	96.24	95.72288510268	0.517114897320027
10	96.25	96.1632453490263	0.0867546509736599
11	96.59	96.1783387868463	0.411661213153735
12	96.62	96.5425077595589	0.0774922404411456
13	96.62	96.5770573935414	0.0429426064585954
14	96.81	96.5795785897351	0.230421410264881
15	96.71	96.7831068226586	-0.0731068226585592
16	96.45	96.6788146602068	-0.228814660206808
17	96.63	96.4053807609176	0.224619239082386
18	96.56	96.5985683435381	-0.0385683435380599
19	96.56	96.5263039639639	0.0336960360360905
20	96.65	96.5282822863063	0.121717713693698
21	97.04	96.6254284346606	0.414571565339415
22	97.14	97.0397682765741	0.100231723425864
23	97.2	97.1456529645433	0.0543470354567148
24	97.26	97.2088437242627	0.051156275737327
25	97.26	97.2718471518212	-0.0118471518212289
26	97.24	97.2711515956699	-0.0311515956698685
27	97.35	97.2493226595407	0.100677340459271
28	97.36	97.3652335100571	-0.0052335100570815
29	97.28	97.3749262463224	-0.0949262463224443
30	97.31	97.2893530473332	0.0206469526668371
31	97.31	97.3205652471219	-0.0105652471218747
32	97.31	97.3199449526631	-0.00994495266314743
33	97.23	97.3193610762088	-0.0893610762087604
34	97.78	97.2341146129923	0.545885387007701
35	97.64	97.8161639987523	-0.176163998752287
36	97.68	97.6658212636518	0.0141787363481853
37	97.68	97.7066537090728	-0.026653709072832
38	97.81	97.7050888476123	0.104911152387714
39	97.75	97.8412482687535	-0.0912482687534606
40	97.63	97.7758910068908	-0.145891006890793
41	97.6	97.647325624358	-0.047325624358038
42	97.65	97.6145470975327	0.0354529024673553
43	97.65	97.6666285669666	-0.0166285669665882
44	97.65	97.6656522899494	-0.0156522899494149
45	97.86	97.6647333309691	0.1952666690309
46	98.41	97.886197599753	0.523802400247035
47	98.79	98.4669504749665	0.323049525033539
48	98.75	98.8659169816615	-0.115916981661471
49	98.74	98.8191113991164	-0.0791113991164423
50	98.55	98.8044667029794	-0.254466702979414
51	98.65	98.5995267508925	0.0504732491075401
52	98.86	98.7024900773887	0.157509922611325
53	98.94	98.9217376161412	0.0182623838587972
54	99.05	99.002809815909	0.0471901840910078
55	99.05	99.1155803909235	-0.065580390923472
56	99.05	99.1117301115479	-0.0617301115479449
57	99.17	99.1081058852816	0.0618941147183989
58	98.99	99.2317397403107	-0.241739740310692
59	98.91	99.0375469988028	-0.127546998802799
60	98.89	98.9500586082643	-0.0600586082643133
61	98.89	98.926532517348	-0.0365325173480215
62	98.72	98.9243876628252	-0.204387662825184
63	98.89	98.7423878928984	0.147612107101565
64	98.97	98.9210543226581	0.0489456773418766
65	99.16	99.0039279641436	0.156072035856411
66	99.54	99.2030910833671	0.336908916632936
67	99.54	99.6028712864869	-0.0628712864868817
68	99.55	99.5991800608894	-0.0491800608893556
69	100.01	99.6062926585506	0.403707341449419
70	99.52	100.08999465283	-0.569994652830331
71	99.44	99.5665297919924	-0.126529791992368
72	99.39	99.479101122513	-0.0891011225130001
73	99.39	99.4238699213945	-0.0338699213945404
74	99.4	99.4218813900979	-0.0218813900979029
75	100.43	99.4305967154594	0.999403284540577
76	100.62	100.519272514736	0.100727485264073
77	101.05	100.715186309296	0.334813690704451
78	100.95	101.164843499956	-0.21484349995589
79	100.95	101.052229859122	-0.102229859122147
80	100.91	101.046227858942	-0.136227858941936
81	101.13	100.998229807874	0.131770192125927
82	100.81	101.22596614561	-0.415966145610199
83	100.47	100.881544426727	-0.41154442672736
84	100.56	100.517382310643	0.0426176893568737

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	100.609884430683	100.15890372713	101.060865134236
86	100.659768861366	100.002996537047	101.316541185686
87	100.70965329205	99.881824213041	101.537482371058
88	100.759537722733	99.7763597123165	101.742715733149
89	100.809422153416	99.6794814269436	101.939362879888
90	100.859306584099	99.5876603162305	102.130952851968
91	100.909191014782	99.4988734381691	102.319508591395
92	100.959075445465	99.4118513294086	102.506299561522
93	101.008959876149	99.3257466582812	102.692173094016
94	101.058844306832	99.2399681174229	102.877720496241
95	101.108728737515	99.1540890921837	103.063368382846
96	101.158613168198	99.0677938312114	103.249432505185

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 100.609884430683 & 100.15890372713 & 101.060865134236 \tabularnewline
86 & 100.659768861366 & 100.002996537047 & 101.316541185686 \tabularnewline
87 & 100.70965329205 & 99.881824213041 & 101.537482371058 \tabularnewline
88 & 100.759537722733 & 99.7763597123165 & 101.742715733149 \tabularnewline
89 & 100.809422153416 & 99.6794814269436 & 101.939362879888 \tabularnewline
90 & 100.859306584099 & 99.5876603162305 & 102.130952851968 \tabularnewline
91 & 100.909191014782 & 99.4988734381691 & 102.319508591395 \tabularnewline
92 & 100.959075445465 & 99.4118513294086 & 102.506299561522 \tabularnewline
93 & 101.008959876149 & 99.3257466582812 & 102.692173094016 \tabularnewline
94 & 101.058844306832 & 99.2399681174229 & 102.877720496241 \tabularnewline
95 & 101.108728737515 & 99.1540890921837 & 103.063368382846 \tabularnewline
96 & 101.158613168198 & 99.0677938312114 & 103.249432505185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233035&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]100.609884430683[/C][C]100.15890372713[/C][C]101.060865134236[/C][/ROW]
[ROW][C]86[/C][C]100.659768861366[/C][C]100.002996537047[/C][C]101.316541185686[/C][/ROW]
[ROW][C]87[/C][C]100.70965329205[/C][C]99.881824213041[/C][C]101.537482371058[/C][/ROW]
[ROW][C]88[/C][C]100.759537722733[/C][C]99.7763597123165[/C][C]101.742715733149[/C][/ROW]
[ROW][C]89[/C][C]100.809422153416[/C][C]99.6794814269436[/C][C]101.939362879888[/C][/ROW]
[ROW][C]90[/C][C]100.859306584099[/C][C]99.5876603162305[/C][C]102.130952851968[/C][/ROW]
[ROW][C]91[/C][C]100.909191014782[/C][C]99.4988734381691[/C][C]102.319508591395[/C][/ROW]
[ROW][C]92[/C][C]100.959075445465[/C][C]99.4118513294086[/C][C]102.506299561522[/C][/ROW]
[ROW][C]93[/C][C]101.008959876149[/C][C]99.3257466582812[/C][C]102.692173094016[/C][/ROW]
[ROW][C]94[/C][C]101.058844306832[/C][C]99.2399681174229[/C][C]102.877720496241[/C][/ROW]
[ROW][C]95[/C][C]101.108728737515[/C][C]99.1540890921837[/C][C]103.063368382846[/C][/ROW]
[ROW][C]96[/C][C]101.158613168198[/C][C]99.0677938312114[/C][C]103.249432505185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233035&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233035&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	100.609884430683	100.15890372713	101.060865134236
86	100.659768861366	100.002996537047	101.316541185686
87	100.70965329205	99.881824213041	101.537482371058
88	100.759537722733	99.7763597123165	101.742715733149
89	100.809422153416	99.6794814269436	101.939362879888
90	100.859306584099	99.5876603162305	102.130952851968
91	100.909191014782	99.4988734381691	102.319508591395
92	100.959075445465	99.4118513294086	102.506299561522
93	101.008959876149	99.3257466582812	102.692173094016
94	101.058844306832	99.2399681174229	102.877720496241
95	101.108728737515	99.1540890921837	103.063368382846
96	101.158613168198	99.0677938312114	103.249432505185

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