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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 30 Dec 2013 10:19:29 -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/2013/Dec/30/t13884168382pw1uhhq7mfstu8.htm/, Retrieved Fri, 19 Apr 2024 01:01:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232686, Retrieved Fri, 19 Apr 2024 01:01:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

112

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

-     [Exponential Smoothing] [T10D1] [2011-12-27 13:49:01] [2f0f353a58a70fd7baf0f5141860d820]
- R PD    [Exponential Smoothing] [] [2013-12-30 15:19:29] [b8fb8add5dd4685cce14e083083037bd] [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	6 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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232686&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]6 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=232686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232686&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	6 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.108679430970285
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.108679430970285 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232686&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]0.108679430970285[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232686&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	0.108679430970285
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	19.7	19.63	0.0700000000000003
4	19.76	19.8676075601679	-0.107607560167917
5	19.9	19.9159128317608	-0.0159128317607724
6	19.97	20.0541834342599	-0.0841834342598844
7	20.1	20.1150344265274	-0.015034426527393
8	20.26	20.2434004936074	0.0165995063925664
9	20.44	20.4052045185166	0.0347954814834353
10	20.43	20.5889860716445	-0.158986071644524
11	20.57	20.561707555846	0.0082924441540051
12	20.6	20.702608773958	-0.102608773958003
13	20.69	20.7214573107917	-0.0314573107916907
14	20.93	20.808038548155	0.121961451845003
15	20.98	21.0612932493418	-0.0812932493418188
16	21.11	21.1024583452616	0.00754165473837531
17	21.14	21.2332779680072	-0.0932779680071647
18	21.16	21.2531405715221	-0.0931405715220812
19	21.32	21.2630181072088	0.0569818927911854
20	21.32	21.429210866893	-0.109210866892973
21	21.48	21.4173418920233	0.0626581079767305
22	21.58	21.5841515395439	-0.00415153954385872
23	21.74	21.6837003525886	0.0562996474114215
24	21.75	21.8498189662331	-0.0998189662330802
25	21.81	21.8489706977828	-0.0389706977828297
26	21.89	21.9047353845233	-0.0147353845232736
27	22.21	21.9831339513182	0.226866048681842
28	22.37	22.3277896243954	0.0422103756046219
29	22.47	22.4923770239971	-0.0223770239971302
30	22.51	22.5899451017623	-0.0799451017623092
31	22.55	22.6212567135939	-0.0712567135939253
32	22.61	22.6535125745077	-0.0435125745077229
33	22.58	22.7087836526702	-0.128783652670172
34	22.85	22.6647875185797	0.185212481420301
35	22.93	22.9549163056691	-0.0249163056690556
36	22.98	23.0322084157471	-0.0522084157470601
37	23.01	23.0765344348318	-0.0665344348318087
38	23.11	23.0993035103144	0.010696489685639
39	23.18	23.2004659987268	-0.0204659987267739
40	23.18	23.2682417656309	-0.088241765630908
41	23.21	23.2586517007543	-0.048651700754327
42	23.22	23.2833642616006	-0.0633642616006149
43	23.12	23.286477869706	-0.166477869706004
44	23.15	23.1683851495572	-0.0183851495572149
45	23.16	23.196387061965	-0.0363870619650299
46	23.21	23.202432536776	0.00756746322401014
47	23.21	23.2532549643731	-0.0432549643730624
48	23.22	23.2485540394584	-0.0285540394583599
49	23.25	23.2554508026981	-0.00545080269812104
50	23.39	23.2848584125626	0.105141587437441
51	23.41	23.4362851404566	-0.0262851404565723
52	23.45	23.4534284863488	-0.00342848634877768
53	23.46	23.4930558804033	-0.0330558804033032
54	23.44	23.4994633861309	-0.0594633861308509
55	23.54	23.4730009391626	0.0669990608374142
56	23.62	23.5802823589699	0.0397176410300659
57	23.86	23.6645988495966	0.195401150403431
58	24.07	23.9258349354334	0.14416506456665
59	24.13	24.1515027126162	-0.0215027126162504
60	24.12	24.2091658100448	-0.0891658100447934
61	24.17	24.1894753205471	-0.019475320547123
62	24.23	24.2373587537921	-0.00735875379210071
63	24.28	24.2965590086173	-0.0165590086173211
64	24.12	24.3447593849834	-0.224759384983361
65	24.14	24.1603326629181	-0.0203326629181397
66	24.17	24.1781229206821	-0.00812292068208365
67	24.2	24.2072401262845	-0.00724012628453963
68	24.36	24.2364532734798	0.123546726520217
69	24.34	24.4098802614162	-0.069880261416241
70	24.38	24.3822857143695	-0.00228571436947078
71	24.46	24.4220373042324	0.0379626957675683
72	24.6	24.5061630684066	0.0938369315934509
73	24.63	24.6563612127361	-0.026361212736127
74	24.75	24.6834962911363	0.0665037088637241
75	24.64	24.810723876373	-0.170723876373
76	24.69	24.6821697026357	0.00783029736426144
77	24.7	24.7330206948976	-0.0330206948976191
78	24.74	24.7394320245659	0.000567975434098145
79	24.87	24.7794937518129	0.0905062481871184
80	24.92	24.9193299193651	0.000670080634886716
81	24.94	24.9694027433472	-0.0294027433472195
82	24.98	24.9862072699313	-0.00620726993127718
83	25.13	25.0255326673673	0.104467332632733
84	25.15	25.1868861176328	-0.0368861176327755

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 19.7 & 19.63 & 0.0700000000000003 \tabularnewline
4 & 19.76 & 19.8676075601679 & -0.107607560167917 \tabularnewline
5 & 19.9 & 19.9159128317608 & -0.0159128317607724 \tabularnewline
6 & 19.97 & 20.0541834342599 & -0.0841834342598844 \tabularnewline
7 & 20.1 & 20.1150344265274 & -0.015034426527393 \tabularnewline
8 & 20.26 & 20.2434004936074 & 0.0165995063925664 \tabularnewline
9 & 20.44 & 20.4052045185166 & 0.0347954814834353 \tabularnewline
10 & 20.43 & 20.5889860716445 & -0.158986071644524 \tabularnewline
11 & 20.57 & 20.561707555846 & 0.0082924441540051 \tabularnewline
12 & 20.6 & 20.702608773958 & -0.102608773958003 \tabularnewline
13 & 20.69 & 20.7214573107917 & -0.0314573107916907 \tabularnewline
14 & 20.93 & 20.808038548155 & 0.121961451845003 \tabularnewline
15 & 20.98 & 21.0612932493418 & -0.0812932493418188 \tabularnewline
16 & 21.11 & 21.1024583452616 & 0.00754165473837531 \tabularnewline
17 & 21.14 & 21.2332779680072 & -0.0932779680071647 \tabularnewline
18 & 21.16 & 21.2531405715221 & -0.0931405715220812 \tabularnewline
19 & 21.32 & 21.2630181072088 & 0.0569818927911854 \tabularnewline
20 & 21.32 & 21.429210866893 & -0.109210866892973 \tabularnewline
21 & 21.48 & 21.4173418920233 & 0.0626581079767305 \tabularnewline
22 & 21.58 & 21.5841515395439 & -0.00415153954385872 \tabularnewline
23 & 21.74 & 21.6837003525886 & 0.0562996474114215 \tabularnewline
24 & 21.75 & 21.8498189662331 & -0.0998189662330802 \tabularnewline
25 & 21.81 & 21.8489706977828 & -0.0389706977828297 \tabularnewline
26 & 21.89 & 21.9047353845233 & -0.0147353845232736 \tabularnewline
27 & 22.21 & 21.9831339513182 & 0.226866048681842 \tabularnewline
28 & 22.37 & 22.3277896243954 & 0.0422103756046219 \tabularnewline
29 & 22.47 & 22.4923770239971 & -0.0223770239971302 \tabularnewline
30 & 22.51 & 22.5899451017623 & -0.0799451017623092 \tabularnewline
31 & 22.55 & 22.6212567135939 & -0.0712567135939253 \tabularnewline
32 & 22.61 & 22.6535125745077 & -0.0435125745077229 \tabularnewline
33 & 22.58 & 22.7087836526702 & -0.128783652670172 \tabularnewline
34 & 22.85 & 22.6647875185797 & 0.185212481420301 \tabularnewline
35 & 22.93 & 22.9549163056691 & -0.0249163056690556 \tabularnewline
36 & 22.98 & 23.0322084157471 & -0.0522084157470601 \tabularnewline
37 & 23.01 & 23.0765344348318 & -0.0665344348318087 \tabularnewline
38 & 23.11 & 23.0993035103144 & 0.010696489685639 \tabularnewline
39 & 23.18 & 23.2004659987268 & -0.0204659987267739 \tabularnewline
40 & 23.18 & 23.2682417656309 & -0.088241765630908 \tabularnewline
41 & 23.21 & 23.2586517007543 & -0.048651700754327 \tabularnewline
42 & 23.22 & 23.2833642616006 & -0.0633642616006149 \tabularnewline
43 & 23.12 & 23.286477869706 & -0.166477869706004 \tabularnewline
44 & 23.15 & 23.1683851495572 & -0.0183851495572149 \tabularnewline
45 & 23.16 & 23.196387061965 & -0.0363870619650299 \tabularnewline
46 & 23.21 & 23.202432536776 & 0.00756746322401014 \tabularnewline
47 & 23.21 & 23.2532549643731 & -0.0432549643730624 \tabularnewline
48 & 23.22 & 23.2485540394584 & -0.0285540394583599 \tabularnewline
49 & 23.25 & 23.2554508026981 & -0.00545080269812104 \tabularnewline
50 & 23.39 & 23.2848584125626 & 0.105141587437441 \tabularnewline
51 & 23.41 & 23.4362851404566 & -0.0262851404565723 \tabularnewline
52 & 23.45 & 23.4534284863488 & -0.00342848634877768 \tabularnewline
53 & 23.46 & 23.4930558804033 & -0.0330558804033032 \tabularnewline
54 & 23.44 & 23.4994633861309 & -0.0594633861308509 \tabularnewline
55 & 23.54 & 23.4730009391626 & 0.0669990608374142 \tabularnewline
56 & 23.62 & 23.5802823589699 & 0.0397176410300659 \tabularnewline
57 & 23.86 & 23.6645988495966 & 0.195401150403431 \tabularnewline
58 & 24.07 & 23.9258349354334 & 0.14416506456665 \tabularnewline
59 & 24.13 & 24.1515027126162 & -0.0215027126162504 \tabularnewline
60 & 24.12 & 24.2091658100448 & -0.0891658100447934 \tabularnewline
61 & 24.17 & 24.1894753205471 & -0.019475320547123 \tabularnewline
62 & 24.23 & 24.2373587537921 & -0.00735875379210071 \tabularnewline
63 & 24.28 & 24.2965590086173 & -0.0165590086173211 \tabularnewline
64 & 24.12 & 24.3447593849834 & -0.224759384983361 \tabularnewline
65 & 24.14 & 24.1603326629181 & -0.0203326629181397 \tabularnewline
66 & 24.17 & 24.1781229206821 & -0.00812292068208365 \tabularnewline
67 & 24.2 & 24.2072401262845 & -0.00724012628453963 \tabularnewline
68 & 24.36 & 24.2364532734798 & 0.123546726520217 \tabularnewline
69 & 24.34 & 24.4098802614162 & -0.069880261416241 \tabularnewline
70 & 24.38 & 24.3822857143695 & -0.00228571436947078 \tabularnewline
71 & 24.46 & 24.4220373042324 & 0.0379626957675683 \tabularnewline
72 & 24.6 & 24.5061630684066 & 0.0938369315934509 \tabularnewline
73 & 24.63 & 24.6563612127361 & -0.026361212736127 \tabularnewline
74 & 24.75 & 24.6834962911363 & 0.0665037088637241 \tabularnewline
75 & 24.64 & 24.810723876373 & -0.170723876373 \tabularnewline
76 & 24.69 & 24.6821697026357 & 0.00783029736426144 \tabularnewline
77 & 24.7 & 24.7330206948976 & -0.0330206948976191 \tabularnewline
78 & 24.74 & 24.7394320245659 & 0.000567975434098145 \tabularnewline
79 & 24.87 & 24.7794937518129 & 0.0905062481871184 \tabularnewline
80 & 24.92 & 24.9193299193651 & 0.000670080634886716 \tabularnewline
81 & 24.94 & 24.9694027433472 & -0.0294027433472195 \tabularnewline
82 & 24.98 & 24.9862072699313 & -0.00620726993127718 \tabularnewline
83 & 25.13 & 25.0255326673673 & 0.104467332632733 \tabularnewline
84 & 25.15 & 25.1868861176328 & -0.0368861176327755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232686&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]19.7[/C][C]19.63[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]4[/C][C]19.76[/C][C]19.8676075601679[/C][C]-0.107607560167917[/C][/ROW]
[ROW][C]5[/C][C]19.9[/C][C]19.9159128317608[/C][C]-0.0159128317607724[/C][/ROW]
[ROW][C]6[/C][C]19.97[/C][C]20.0541834342599[/C][C]-0.0841834342598844[/C][/ROW]
[ROW][C]7[/C][C]20.1[/C][C]20.1150344265274[/C][C]-0.015034426527393[/C][/ROW]
[ROW][C]8[/C][C]20.26[/C][C]20.2434004936074[/C][C]0.0165995063925664[/C][/ROW]
[ROW][C]9[/C][C]20.44[/C][C]20.4052045185166[/C][C]0.0347954814834353[/C][/ROW]
[ROW][C]10[/C][C]20.43[/C][C]20.5889860716445[/C][C]-0.158986071644524[/C][/ROW]
[ROW][C]11[/C][C]20.57[/C][C]20.561707555846[/C][C]0.0082924441540051[/C][/ROW]
[ROW][C]12[/C][C]20.6[/C][C]20.702608773958[/C][C]-0.102608773958003[/C][/ROW]
[ROW][C]13[/C][C]20.69[/C][C]20.7214573107917[/C][C]-0.0314573107916907[/C][/ROW]
[ROW][C]14[/C][C]20.93[/C][C]20.808038548155[/C][C]0.121961451845003[/C][/ROW]
[ROW][C]15[/C][C]20.98[/C][C]21.0612932493418[/C][C]-0.0812932493418188[/C][/ROW]
[ROW][C]16[/C][C]21.11[/C][C]21.1024583452616[/C][C]0.00754165473837531[/C][/ROW]
[ROW][C]17[/C][C]21.14[/C][C]21.2332779680072[/C][C]-0.0932779680071647[/C][/ROW]
[ROW][C]18[/C][C]21.16[/C][C]21.2531405715221[/C][C]-0.0931405715220812[/C][/ROW]
[ROW][C]19[/C][C]21.32[/C][C]21.2630181072088[/C][C]0.0569818927911854[/C][/ROW]
[ROW][C]20[/C][C]21.32[/C][C]21.429210866893[/C][C]-0.109210866892973[/C][/ROW]
[ROW][C]21[/C][C]21.48[/C][C]21.4173418920233[/C][C]0.0626581079767305[/C][/ROW]
[ROW][C]22[/C][C]21.58[/C][C]21.5841515395439[/C][C]-0.00415153954385872[/C][/ROW]
[ROW][C]23[/C][C]21.74[/C][C]21.6837003525886[/C][C]0.0562996474114215[/C][/ROW]
[ROW][C]24[/C][C]21.75[/C][C]21.8498189662331[/C][C]-0.0998189662330802[/C][/ROW]
[ROW][C]25[/C][C]21.81[/C][C]21.8489706977828[/C][C]-0.0389706977828297[/C][/ROW]
[ROW][C]26[/C][C]21.89[/C][C]21.9047353845233[/C][C]-0.0147353845232736[/C][/ROW]
[ROW][C]27[/C][C]22.21[/C][C]21.9831339513182[/C][C]0.226866048681842[/C][/ROW]
[ROW][C]28[/C][C]22.37[/C][C]22.3277896243954[/C][C]0.0422103756046219[/C][/ROW]
[ROW][C]29[/C][C]22.47[/C][C]22.4923770239971[/C][C]-0.0223770239971302[/C][/ROW]
[ROW][C]30[/C][C]22.51[/C][C]22.5899451017623[/C][C]-0.0799451017623092[/C][/ROW]
[ROW][C]31[/C][C]22.55[/C][C]22.6212567135939[/C][C]-0.0712567135939253[/C][/ROW]
[ROW][C]32[/C][C]22.61[/C][C]22.6535125745077[/C][C]-0.0435125745077229[/C][/ROW]
[ROW][C]33[/C][C]22.58[/C][C]22.7087836526702[/C][C]-0.128783652670172[/C][/ROW]
[ROW][C]34[/C][C]22.85[/C][C]22.6647875185797[/C][C]0.185212481420301[/C][/ROW]
[ROW][C]35[/C][C]22.93[/C][C]22.9549163056691[/C][C]-0.0249163056690556[/C][/ROW]
[ROW][C]36[/C][C]22.98[/C][C]23.0322084157471[/C][C]-0.0522084157470601[/C][/ROW]
[ROW][C]37[/C][C]23.01[/C][C]23.0765344348318[/C][C]-0.0665344348318087[/C][/ROW]
[ROW][C]38[/C][C]23.11[/C][C]23.0993035103144[/C][C]0.010696489685639[/C][/ROW]
[ROW][C]39[/C][C]23.18[/C][C]23.2004659987268[/C][C]-0.0204659987267739[/C][/ROW]
[ROW][C]40[/C][C]23.18[/C][C]23.2682417656309[/C][C]-0.088241765630908[/C][/ROW]
[ROW][C]41[/C][C]23.21[/C][C]23.2586517007543[/C][C]-0.048651700754327[/C][/ROW]
[ROW][C]42[/C][C]23.22[/C][C]23.2833642616006[/C][C]-0.0633642616006149[/C][/ROW]
[ROW][C]43[/C][C]23.12[/C][C]23.286477869706[/C][C]-0.166477869706004[/C][/ROW]
[ROW][C]44[/C][C]23.15[/C][C]23.1683851495572[/C][C]-0.0183851495572149[/C][/ROW]
[ROW][C]45[/C][C]23.16[/C][C]23.196387061965[/C][C]-0.0363870619650299[/C][/ROW]
[ROW][C]46[/C][C]23.21[/C][C]23.202432536776[/C][C]0.00756746322401014[/C][/ROW]
[ROW][C]47[/C][C]23.21[/C][C]23.2532549643731[/C][C]-0.0432549643730624[/C][/ROW]
[ROW][C]48[/C][C]23.22[/C][C]23.2485540394584[/C][C]-0.0285540394583599[/C][/ROW]
[ROW][C]49[/C][C]23.25[/C][C]23.2554508026981[/C][C]-0.00545080269812104[/C][/ROW]
[ROW][C]50[/C][C]23.39[/C][C]23.2848584125626[/C][C]0.105141587437441[/C][/ROW]
[ROW][C]51[/C][C]23.41[/C][C]23.4362851404566[/C][C]-0.0262851404565723[/C][/ROW]
[ROW][C]52[/C][C]23.45[/C][C]23.4534284863488[/C][C]-0.00342848634877768[/C][/ROW]
[ROW][C]53[/C][C]23.46[/C][C]23.4930558804033[/C][C]-0.0330558804033032[/C][/ROW]
[ROW][C]54[/C][C]23.44[/C][C]23.4994633861309[/C][C]-0.0594633861308509[/C][/ROW]
[ROW][C]55[/C][C]23.54[/C][C]23.4730009391626[/C][C]0.0669990608374142[/C][/ROW]
[ROW][C]56[/C][C]23.62[/C][C]23.5802823589699[/C][C]0.0397176410300659[/C][/ROW]
[ROW][C]57[/C][C]23.86[/C][C]23.6645988495966[/C][C]0.195401150403431[/C][/ROW]
[ROW][C]58[/C][C]24.07[/C][C]23.9258349354334[/C][C]0.14416506456665[/C][/ROW]
[ROW][C]59[/C][C]24.13[/C][C]24.1515027126162[/C][C]-0.0215027126162504[/C][/ROW]
[ROW][C]60[/C][C]24.12[/C][C]24.2091658100448[/C][C]-0.0891658100447934[/C][/ROW]
[ROW][C]61[/C][C]24.17[/C][C]24.1894753205471[/C][C]-0.019475320547123[/C][/ROW]
[ROW][C]62[/C][C]24.23[/C][C]24.2373587537921[/C][C]-0.00735875379210071[/C][/ROW]
[ROW][C]63[/C][C]24.28[/C][C]24.2965590086173[/C][C]-0.0165590086173211[/C][/ROW]
[ROW][C]64[/C][C]24.12[/C][C]24.3447593849834[/C][C]-0.224759384983361[/C][/ROW]
[ROW][C]65[/C][C]24.14[/C][C]24.1603326629181[/C][C]-0.0203326629181397[/C][/ROW]
[ROW][C]66[/C][C]24.17[/C][C]24.1781229206821[/C][C]-0.00812292068208365[/C][/ROW]
[ROW][C]67[/C][C]24.2[/C][C]24.2072401262845[/C][C]-0.00724012628453963[/C][/ROW]
[ROW][C]68[/C][C]24.36[/C][C]24.2364532734798[/C][C]0.123546726520217[/C][/ROW]
[ROW][C]69[/C][C]24.34[/C][C]24.4098802614162[/C][C]-0.069880261416241[/C][/ROW]
[ROW][C]70[/C][C]24.38[/C][C]24.3822857143695[/C][C]-0.00228571436947078[/C][/ROW]
[ROW][C]71[/C][C]24.46[/C][C]24.4220373042324[/C][C]0.0379626957675683[/C][/ROW]
[ROW][C]72[/C][C]24.6[/C][C]24.5061630684066[/C][C]0.0938369315934509[/C][/ROW]
[ROW][C]73[/C][C]24.63[/C][C]24.6563612127361[/C][C]-0.026361212736127[/C][/ROW]
[ROW][C]74[/C][C]24.75[/C][C]24.6834962911363[/C][C]0.0665037088637241[/C][/ROW]
[ROW][C]75[/C][C]24.64[/C][C]24.810723876373[/C][C]-0.170723876373[/C][/ROW]
[ROW][C]76[/C][C]24.69[/C][C]24.6821697026357[/C][C]0.00783029736426144[/C][/ROW]
[ROW][C]77[/C][C]24.7[/C][C]24.7330206948976[/C][C]-0.0330206948976191[/C][/ROW]
[ROW][C]78[/C][C]24.74[/C][C]24.7394320245659[/C][C]0.000567975434098145[/C][/ROW]
[ROW][C]79[/C][C]24.87[/C][C]24.7794937518129[/C][C]0.0905062481871184[/C][/ROW]
[ROW][C]80[/C][C]24.92[/C][C]24.9193299193651[/C][C]0.000670080634886716[/C][/ROW]
[ROW][C]81[/C][C]24.94[/C][C]24.9694027433472[/C][C]-0.0294027433472195[/C][/ROW]
[ROW][C]82[/C][C]24.98[/C][C]24.9862072699313[/C][C]-0.00620726993127718[/C][/ROW]
[ROW][C]83[/C][C]25.13[/C][C]25.0255326673673[/C][C]0.104467332632733[/C][/ROW]
[ROW][C]84[/C][C]25.15[/C][C]25.1868861176328[/C][C]-0.0368861176327755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232686&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232686&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	19.7	19.63	0.0700000000000003
4	19.76	19.8676075601679	-0.107607560167917
5	19.9	19.9159128317608	-0.0159128317607724
6	19.97	20.0541834342599	-0.0841834342598844
7	20.1	20.1150344265274	-0.015034426527393
8	20.26	20.2434004936074	0.0165995063925664
9	20.44	20.4052045185166	0.0347954814834353
10	20.43	20.5889860716445	-0.158986071644524
11	20.57	20.561707555846	0.0082924441540051
12	20.6	20.702608773958	-0.102608773958003
13	20.69	20.7214573107917	-0.0314573107916907
14	20.93	20.808038548155	0.121961451845003
15	20.98	21.0612932493418	-0.0812932493418188
16	21.11	21.1024583452616	0.00754165473837531
17	21.14	21.2332779680072	-0.0932779680071647
18	21.16	21.2531405715221	-0.0931405715220812
19	21.32	21.2630181072088	0.0569818927911854
20	21.32	21.429210866893	-0.109210866892973
21	21.48	21.4173418920233	0.0626581079767305
22	21.58	21.5841515395439	-0.00415153954385872
23	21.74	21.6837003525886	0.0562996474114215
24	21.75	21.8498189662331	-0.0998189662330802
25	21.81	21.8489706977828	-0.0389706977828297
26	21.89	21.9047353845233	-0.0147353845232736
27	22.21	21.9831339513182	0.226866048681842
28	22.37	22.3277896243954	0.0422103756046219
29	22.47	22.4923770239971	-0.0223770239971302
30	22.51	22.5899451017623	-0.0799451017623092
31	22.55	22.6212567135939	-0.0712567135939253
32	22.61	22.6535125745077	-0.0435125745077229
33	22.58	22.7087836526702	-0.128783652670172
34	22.85	22.6647875185797	0.185212481420301
35	22.93	22.9549163056691	-0.0249163056690556
36	22.98	23.0322084157471	-0.0522084157470601
37	23.01	23.0765344348318	-0.0665344348318087
38	23.11	23.0993035103144	0.010696489685639
39	23.18	23.2004659987268	-0.0204659987267739
40	23.18	23.2682417656309	-0.088241765630908
41	23.21	23.2586517007543	-0.048651700754327
42	23.22	23.2833642616006	-0.0633642616006149
43	23.12	23.286477869706	-0.166477869706004
44	23.15	23.1683851495572	-0.0183851495572149
45	23.16	23.196387061965	-0.0363870619650299
46	23.21	23.202432536776	0.00756746322401014
47	23.21	23.2532549643731	-0.0432549643730624
48	23.22	23.2485540394584	-0.0285540394583599
49	23.25	23.2554508026981	-0.00545080269812104
50	23.39	23.2848584125626	0.105141587437441
51	23.41	23.4362851404566	-0.0262851404565723
52	23.45	23.4534284863488	-0.00342848634877768
53	23.46	23.4930558804033	-0.0330558804033032
54	23.44	23.4994633861309	-0.0594633861308509
55	23.54	23.4730009391626	0.0669990608374142
56	23.62	23.5802823589699	0.0397176410300659
57	23.86	23.6645988495966	0.195401150403431
58	24.07	23.9258349354334	0.14416506456665
59	24.13	24.1515027126162	-0.0215027126162504
60	24.12	24.2091658100448	-0.0891658100447934
61	24.17	24.1894753205471	-0.019475320547123
62	24.23	24.2373587537921	-0.00735875379210071
63	24.28	24.2965590086173	-0.0165590086173211
64	24.12	24.3447593849834	-0.224759384983361
65	24.14	24.1603326629181	-0.0203326629181397
66	24.17	24.1781229206821	-0.00812292068208365
67	24.2	24.2072401262845	-0.00724012628453963
68	24.36	24.2364532734798	0.123546726520217
69	24.34	24.4098802614162	-0.069880261416241
70	24.38	24.3822857143695	-0.00228571436947078
71	24.46	24.4220373042324	0.0379626957675683
72	24.6	24.5061630684066	0.0938369315934509
73	24.63	24.6563612127361	-0.026361212736127
74	24.75	24.6834962911363	0.0665037088637241
75	24.64	24.810723876373	-0.170723876373
76	24.69	24.6821697026357	0.00783029736426144
77	24.7	24.7330206948976	-0.0330206948976191
78	24.74	24.7394320245659	0.000567975434098145
79	24.87	24.7794937518129	0.0905062481871184
80	24.92	24.9193299193651	0.000670080634886716
81	24.94	24.9694027433472	-0.0294027433472195
82	24.98	24.9862072699313	-0.00620726993127718
83	25.13	25.0255326673673	0.104467332632733
84	25.15	25.1868861176328	-0.0368861176327755

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	25.2028773553577	25.0451082082489	25.3606465024666
86	25.2557547107155	25.0201989767167	25.4913104447143
87	25.3086320660732	25.0047008425006	25.6125632896458
88	25.361509421431	24.9925349685903	25.7304838742716
89	25.4143867767887	24.9815145474629	25.8472590061145
90	25.4672641321465	24.970604452465	25.9639238118279
91	25.5201414875042	24.9592426134725	26.0810403615359
92	25.5730188428619	24.9470983336362	26.1989393520877
93	25.6258961982197	24.933967273473	26.3178251229664
94	25.6787735535774	24.9197195406595	26.4378275664953
95	25.7316509089352	24.9042715852341	26.5590302326362
96	25.7845282642929	24.8875699164716	26.6814866121143

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 25.2028773553577 & 25.0451082082489 & 25.3606465024666 \tabularnewline
86 & 25.2557547107155 & 25.0201989767167 & 25.4913104447143 \tabularnewline
87 & 25.3086320660732 & 25.0047008425006 & 25.6125632896458 \tabularnewline
88 & 25.361509421431 & 24.9925349685903 & 25.7304838742716 \tabularnewline
89 & 25.4143867767887 & 24.9815145474629 & 25.8472590061145 \tabularnewline
90 & 25.4672641321465 & 24.970604452465 & 25.9639238118279 \tabularnewline
91 & 25.5201414875042 & 24.9592426134725 & 26.0810403615359 \tabularnewline
92 & 25.5730188428619 & 24.9470983336362 & 26.1989393520877 \tabularnewline
93 & 25.6258961982197 & 24.933967273473 & 26.3178251229664 \tabularnewline
94 & 25.6787735535774 & 24.9197195406595 & 26.4378275664953 \tabularnewline
95 & 25.7316509089352 & 24.9042715852341 & 26.5590302326362 \tabularnewline
96 & 25.7845282642929 & 24.8875699164716 & 26.6814866121143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232686&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]25.2028773553577[/C][C]25.0451082082489[/C][C]25.3606465024666[/C][/ROW]
[ROW][C]86[/C][C]25.2557547107155[/C][C]25.0201989767167[/C][C]25.4913104447143[/C][/ROW]
[ROW][C]87[/C][C]25.3086320660732[/C][C]25.0047008425006[/C][C]25.6125632896458[/C][/ROW]
[ROW][C]88[/C][C]25.361509421431[/C][C]24.9925349685903[/C][C]25.7304838742716[/C][/ROW]
[ROW][C]89[/C][C]25.4143867767887[/C][C]24.9815145474629[/C][C]25.8472590061145[/C][/ROW]
[ROW][C]90[/C][C]25.4672641321465[/C][C]24.970604452465[/C][C]25.9639238118279[/C][/ROW]
[ROW][C]91[/C][C]25.5201414875042[/C][C]24.9592426134725[/C][C]26.0810403615359[/C][/ROW]
[ROW][C]92[/C][C]25.5730188428619[/C][C]24.9470983336362[/C][C]26.1989393520877[/C][/ROW]
[ROW][C]93[/C][C]25.6258961982197[/C][C]24.933967273473[/C][C]26.3178251229664[/C][/ROW]
[ROW][C]94[/C][C]25.6787735535774[/C][C]24.9197195406595[/C][C]26.4378275664953[/C][/ROW]
[ROW][C]95[/C][C]25.7316509089352[/C][C]24.9042715852341[/C][C]26.5590302326362[/C][/ROW]
[ROW][C]96[/C][C]25.7845282642929[/C][C]24.8875699164716[/C][C]26.6814866121143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232686&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232686&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	25.2028773553577	25.0451082082489	25.3606465024666
86	25.2557547107155	25.0201989767167	25.4913104447143
87	25.3086320660732	25.0047008425006	25.6125632896458
88	25.361509421431	24.9925349685903	25.7304838742716
89	25.4143867767887	24.9815145474629	25.8472590061145
90	25.4672641321465	24.970604452465	25.9639238118279
91	25.5201414875042	24.9592426134725	26.0810403615359
92	25.5730188428619	24.9470983336362	26.1989393520877
93	25.6258961982197	24.933967273473	26.3178251229664
94	25.6787735535774	24.9197195406595	26.4378275664953
95	25.7316509089352	24.9042715852341	26.5590302326362
96	25.7845282642929	24.8875699164716	26.6814866121143

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