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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 12 Jan 2014 17:24:03 -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/t138956610839l9ej0qsp21fcm.htm/, Retrieved Mon, 27 May 2024 01:45:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233080, Retrieved Mon, 27 May 2024 01:45:08 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2014-01-12 22:24:03] [a1d0d08f2289aa3245b26ed4a32c5bef] [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	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233080&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233080&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233080&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999949933898369
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999949933898369 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233080&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]0.999949933898369[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233080&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233080&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	0.999949933898369
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	20.1	20.1	0
3	20.1	20.1	0
4	20.3	20.1	0.199999999999999
5	20.7	20.2999899867797	0.400010013220324
6	20.6	20.699979973058	-0.0999799730580229
7	20.3	20.6000050056075	-0.300005005607492
8	19.9	20.3000150200811	-0.400015020081103
9	19.7	19.9000200271926	-0.200020027192647
10	19.4	19.700010014223	-0.300010014223009
11	19.1	19.4000150203319	-0.300015020331859
12	18.8	19.1000150205825	-0.300015020582499
13	18.9	18.8000150205825	0.099984979417485
14	18.7	18.8999949941419	-0.199994994141857
15	18.8	18.7000100129697	0.0999899870302983
16	19.5	18.7999949938911	0.700005006108853
17	19.3	19.4999649534782	-0.199964953478222
18	19.1	19.3000100114657	-0.200010011465682
19	19.1	19.1000100137216	-1.00137215603979e-05
20	19	19.1000000005013	-0.10000000050135
21	18.8	19.0000050066102	-0.200005006610187
22	19.2	18.800010013471	0.399989986529011
23	18.9	19.1999799740607	-0.299979974060683
24	18.7	18.9000150188279	-0.200015018827866
25	18.5	18.7000100139723	-0.20001001397226
26	18.4	18.5000100137217	-0.10001001372169
27	18.3	18.4000050071115	-0.100005007111509
28	18.3	18.3000050068609	-5.00686084947688e-06
29	18.3	18.3000000002507	-2.50672371748806e-10
30	18.5	18.3	0.199999999999985
31	19.2	18.4999899867797	0.700010013220325
32	19.4	19.1999649532275	0.200035046772463
33	19.1	19.399989985025	-0.299989985025015
34	19.5	19.1000150193291	0.399984980670919
35	18.8	19.4999799743113	-0.699979974311308
36	19.3	18.8000350452685	0.499964954731468
37	20.4	19.2999749687038	1.10002503129623
38	20.9	20.399944926035	0.500055073965012
39	21.1	20.8999749641918	0.200025035808157
40	20.6	21.0999899855262	-0.499989985526227
41	20.4	20.6000250325494	-0.200025032549433
42	20.8	20.4000100144736	0.399989985526393
43	21.1	20.7999799740607	0.300020025939268
44	21.6	21.0999849791669	0.500015020833111
45	22	21.5999749661972	0.400025033802848
46	22.2	21.999979972306	0.200020027693995
47	22.4	22.199989985777	0.200010014223032
48	22.8	22.3999899862783	0.400010013721701
49	22.7	22.799979973058	-0.0999799730580015
50	22.8	22.7000050056075	0.0999949943925103
51	22.9	22.7999949936404	0.100005006359549
52	22.9	22.8999949931392	5.00686081039703e-06
53	22.6	22.8999999997493	-0.299999999749325
54	21.9	22.6000150198305	-0.700015019830481
55	20.8	21.9000350470231	-1.10003504702312
56	20.3	20.8000550744665	-0.500055074466463
57	20.4	20.3000250358082	0.0999749641918193
58	21.2	20.3999949946433	0.80000500535672
59	21.4	21.1999599468681	0.200040053131904
60	20.9	21.3999899847744	-0.49998998477437
61	20	20.9000250325494	-0.90002503254939
62	19.5	20.0000450607447	-0.50004506074475
63	19.2	19.5000250353068	-0.300025035306831
64	19.3	19.2000150210839	0.0999849789160905
65	19.4	19.2999949941419	0.100005005858115
66	19.5	19.3999949931392	0.100005006860787
67	20	19.4999949931392	0.500005006860839
68	20.1	19.9999749666985	0.100025033301492
69	19.5	20.0999949921365	-0.599994992136519
70	18.6	19.5000300394103	-0.900030039410254
71	18.4	18.6000450609954	-0.200045060995425
72	18.4	18.4000100154764	-1.0015476355818e-05
73	19.3	18.4000000005014	0.899999999498565
74	19.8	19.2999549405086	0.500045059491441
75	19.8	19.7999749646932	2.50353067698939e-05
76	19.8	19.7999999987466	1.25341870216289e-09
77	20.1	19.7999999999999	0.300000000000065
78	20.3	20.0999849801695	0.200015019830488
79	19.7	20.2999899860277	-0.59998998602769
80	20.2	19.7000300391596	0.499969960840382
81	20.6	20.1999749684531	0.400025031546875
82	21	20.5999799723061	0.400020027693884
83	21.4	20.9999799725566	0.400020027443361
84	21.9	21.3999799725567	0.500020027443348

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 20.1 & 20.1 & 0 \tabularnewline
3 & 20.1 & 20.1 & 0 \tabularnewline
4 & 20.3 & 20.1 & 0.199999999999999 \tabularnewline
5 & 20.7 & 20.2999899867797 & 0.400010013220324 \tabularnewline
6 & 20.6 & 20.699979973058 & -0.0999799730580229 \tabularnewline
7 & 20.3 & 20.6000050056075 & -0.300005005607492 \tabularnewline
8 & 19.9 & 20.3000150200811 & -0.400015020081103 \tabularnewline
9 & 19.7 & 19.9000200271926 & -0.200020027192647 \tabularnewline
10 & 19.4 & 19.700010014223 & -0.300010014223009 \tabularnewline
11 & 19.1 & 19.4000150203319 & -0.300015020331859 \tabularnewline
12 & 18.8 & 19.1000150205825 & -0.300015020582499 \tabularnewline
13 & 18.9 & 18.8000150205825 & 0.099984979417485 \tabularnewline
14 & 18.7 & 18.8999949941419 & -0.199994994141857 \tabularnewline
15 & 18.8 & 18.7000100129697 & 0.0999899870302983 \tabularnewline
16 & 19.5 & 18.7999949938911 & 0.700005006108853 \tabularnewline
17 & 19.3 & 19.4999649534782 & -0.199964953478222 \tabularnewline
18 & 19.1 & 19.3000100114657 & -0.200010011465682 \tabularnewline
19 & 19.1 & 19.1000100137216 & -1.00137215603979e-05 \tabularnewline
20 & 19 & 19.1000000005013 & -0.10000000050135 \tabularnewline
21 & 18.8 & 19.0000050066102 & -0.200005006610187 \tabularnewline
22 & 19.2 & 18.800010013471 & 0.399989986529011 \tabularnewline
23 & 18.9 & 19.1999799740607 & -0.299979974060683 \tabularnewline
24 & 18.7 & 18.9000150188279 & -0.200015018827866 \tabularnewline
25 & 18.5 & 18.7000100139723 & -0.20001001397226 \tabularnewline
26 & 18.4 & 18.5000100137217 & -0.10001001372169 \tabularnewline
27 & 18.3 & 18.4000050071115 & -0.100005007111509 \tabularnewline
28 & 18.3 & 18.3000050068609 & -5.00686084947688e-06 \tabularnewline
29 & 18.3 & 18.3000000002507 & -2.50672371748806e-10 \tabularnewline
30 & 18.5 & 18.3 & 0.199999999999985 \tabularnewline
31 & 19.2 & 18.4999899867797 & 0.700010013220325 \tabularnewline
32 & 19.4 & 19.1999649532275 & 0.200035046772463 \tabularnewline
33 & 19.1 & 19.399989985025 & -0.299989985025015 \tabularnewline
34 & 19.5 & 19.1000150193291 & 0.399984980670919 \tabularnewline
35 & 18.8 & 19.4999799743113 & -0.699979974311308 \tabularnewline
36 & 19.3 & 18.8000350452685 & 0.499964954731468 \tabularnewline
37 & 20.4 & 19.2999749687038 & 1.10002503129623 \tabularnewline
38 & 20.9 & 20.399944926035 & 0.500055073965012 \tabularnewline
39 & 21.1 & 20.8999749641918 & 0.200025035808157 \tabularnewline
40 & 20.6 & 21.0999899855262 & -0.499989985526227 \tabularnewline
41 & 20.4 & 20.6000250325494 & -0.200025032549433 \tabularnewline
42 & 20.8 & 20.4000100144736 & 0.399989985526393 \tabularnewline
43 & 21.1 & 20.7999799740607 & 0.300020025939268 \tabularnewline
44 & 21.6 & 21.0999849791669 & 0.500015020833111 \tabularnewline
45 & 22 & 21.5999749661972 & 0.400025033802848 \tabularnewline
46 & 22.2 & 21.999979972306 & 0.200020027693995 \tabularnewline
47 & 22.4 & 22.199989985777 & 0.200010014223032 \tabularnewline
48 & 22.8 & 22.3999899862783 & 0.400010013721701 \tabularnewline
49 & 22.7 & 22.799979973058 & -0.0999799730580015 \tabularnewline
50 & 22.8 & 22.7000050056075 & 0.0999949943925103 \tabularnewline
51 & 22.9 & 22.7999949936404 & 0.100005006359549 \tabularnewline
52 & 22.9 & 22.8999949931392 & 5.00686081039703e-06 \tabularnewline
53 & 22.6 & 22.8999999997493 & -0.299999999749325 \tabularnewline
54 & 21.9 & 22.6000150198305 & -0.700015019830481 \tabularnewline
55 & 20.8 & 21.9000350470231 & -1.10003504702312 \tabularnewline
56 & 20.3 & 20.8000550744665 & -0.500055074466463 \tabularnewline
57 & 20.4 & 20.3000250358082 & 0.0999749641918193 \tabularnewline
58 & 21.2 & 20.3999949946433 & 0.80000500535672 \tabularnewline
59 & 21.4 & 21.1999599468681 & 0.200040053131904 \tabularnewline
60 & 20.9 & 21.3999899847744 & -0.49998998477437 \tabularnewline
61 & 20 & 20.9000250325494 & -0.90002503254939 \tabularnewline
62 & 19.5 & 20.0000450607447 & -0.50004506074475 \tabularnewline
63 & 19.2 & 19.5000250353068 & -0.300025035306831 \tabularnewline
64 & 19.3 & 19.2000150210839 & 0.0999849789160905 \tabularnewline
65 & 19.4 & 19.2999949941419 & 0.100005005858115 \tabularnewline
66 & 19.5 & 19.3999949931392 & 0.100005006860787 \tabularnewline
67 & 20 & 19.4999949931392 & 0.500005006860839 \tabularnewline
68 & 20.1 & 19.9999749666985 & 0.100025033301492 \tabularnewline
69 & 19.5 & 20.0999949921365 & -0.599994992136519 \tabularnewline
70 & 18.6 & 19.5000300394103 & -0.900030039410254 \tabularnewline
71 & 18.4 & 18.6000450609954 & -0.200045060995425 \tabularnewline
72 & 18.4 & 18.4000100154764 & -1.0015476355818e-05 \tabularnewline
73 & 19.3 & 18.4000000005014 & 0.899999999498565 \tabularnewline
74 & 19.8 & 19.2999549405086 & 0.500045059491441 \tabularnewline
75 & 19.8 & 19.7999749646932 & 2.50353067698939e-05 \tabularnewline
76 & 19.8 & 19.7999999987466 & 1.25341870216289e-09 \tabularnewline
77 & 20.1 & 19.7999999999999 & 0.300000000000065 \tabularnewline
78 & 20.3 & 20.0999849801695 & 0.200015019830488 \tabularnewline
79 & 19.7 & 20.2999899860277 & -0.59998998602769 \tabularnewline
80 & 20.2 & 19.7000300391596 & 0.499969960840382 \tabularnewline
81 & 20.6 & 20.1999749684531 & 0.400025031546875 \tabularnewline
82 & 21 & 20.5999799723061 & 0.400020027693884 \tabularnewline
83 & 21.4 & 20.9999799725566 & 0.400020027443361 \tabularnewline
84 & 21.9 & 21.3999799725567 & 0.500020027443348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233080&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]2[/C][C]20.1[/C][C]20.1[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]20.1[/C][C]20.1[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]20.3[/C][C]20.1[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]5[/C][C]20.7[/C][C]20.2999899867797[/C][C]0.400010013220324[/C][/ROW]
[ROW][C]6[/C][C]20.6[/C][C]20.699979973058[/C][C]-0.0999799730580229[/C][/ROW]
[ROW][C]7[/C][C]20.3[/C][C]20.6000050056075[/C][C]-0.300005005607492[/C][/ROW]
[ROW][C]8[/C][C]19.9[/C][C]20.3000150200811[/C][C]-0.400015020081103[/C][/ROW]
[ROW][C]9[/C][C]19.7[/C][C]19.9000200271926[/C][C]-0.200020027192647[/C][/ROW]
[ROW][C]10[/C][C]19.4[/C][C]19.700010014223[/C][C]-0.300010014223009[/C][/ROW]
[ROW][C]11[/C][C]19.1[/C][C]19.4000150203319[/C][C]-0.300015020331859[/C][/ROW]
[ROW][C]12[/C][C]18.8[/C][C]19.1000150205825[/C][C]-0.300015020582499[/C][/ROW]
[ROW][C]13[/C][C]18.9[/C][C]18.8000150205825[/C][C]0.099984979417485[/C][/ROW]
[ROW][C]14[/C][C]18.7[/C][C]18.8999949941419[/C][C]-0.199994994141857[/C][/ROW]
[ROW][C]15[/C][C]18.8[/C][C]18.7000100129697[/C][C]0.0999899870302983[/C][/ROW]
[ROW][C]16[/C][C]19.5[/C][C]18.7999949938911[/C][C]0.700005006108853[/C][/ROW]
[ROW][C]17[/C][C]19.3[/C][C]19.4999649534782[/C][C]-0.199964953478222[/C][/ROW]
[ROW][C]18[/C][C]19.1[/C][C]19.3000100114657[/C][C]-0.200010011465682[/C][/ROW]
[ROW][C]19[/C][C]19.1[/C][C]19.1000100137216[/C][C]-1.00137215603979e-05[/C][/ROW]
[ROW][C]20[/C][C]19[/C][C]19.1000000005013[/C][C]-0.10000000050135[/C][/ROW]
[ROW][C]21[/C][C]18.8[/C][C]19.0000050066102[/C][C]-0.200005006610187[/C][/ROW]
[ROW][C]22[/C][C]19.2[/C][C]18.800010013471[/C][C]0.399989986529011[/C][/ROW]
[ROW][C]23[/C][C]18.9[/C][C]19.1999799740607[/C][C]-0.299979974060683[/C][/ROW]
[ROW][C]24[/C][C]18.7[/C][C]18.9000150188279[/C][C]-0.200015018827866[/C][/ROW]
[ROW][C]25[/C][C]18.5[/C][C]18.7000100139723[/C][C]-0.20001001397226[/C][/ROW]
[ROW][C]26[/C][C]18.4[/C][C]18.5000100137217[/C][C]-0.10001001372169[/C][/ROW]
[ROW][C]27[/C][C]18.3[/C][C]18.4000050071115[/C][C]-0.100005007111509[/C][/ROW]
[ROW][C]28[/C][C]18.3[/C][C]18.3000050068609[/C][C]-5.00686084947688e-06[/C][/ROW]
[ROW][C]29[/C][C]18.3[/C][C]18.3000000002507[/C][C]-2.50672371748806e-10[/C][/ROW]
[ROW][C]30[/C][C]18.5[/C][C]18.3[/C][C]0.199999999999985[/C][/ROW]
[ROW][C]31[/C][C]19.2[/C][C]18.4999899867797[/C][C]0.700010013220325[/C][/ROW]
[ROW][C]32[/C][C]19.4[/C][C]19.1999649532275[/C][C]0.200035046772463[/C][/ROW]
[ROW][C]33[/C][C]19.1[/C][C]19.399989985025[/C][C]-0.299989985025015[/C][/ROW]
[ROW][C]34[/C][C]19.5[/C][C]19.1000150193291[/C][C]0.399984980670919[/C][/ROW]
[ROW][C]35[/C][C]18.8[/C][C]19.4999799743113[/C][C]-0.699979974311308[/C][/ROW]
[ROW][C]36[/C][C]19.3[/C][C]18.8000350452685[/C][C]0.499964954731468[/C][/ROW]
[ROW][C]37[/C][C]20.4[/C][C]19.2999749687038[/C][C]1.10002503129623[/C][/ROW]
[ROW][C]38[/C][C]20.9[/C][C]20.399944926035[/C][C]0.500055073965012[/C][/ROW]
[ROW][C]39[/C][C]21.1[/C][C]20.8999749641918[/C][C]0.200025035808157[/C][/ROW]
[ROW][C]40[/C][C]20.6[/C][C]21.0999899855262[/C][C]-0.499989985526227[/C][/ROW]
[ROW][C]41[/C][C]20.4[/C][C]20.6000250325494[/C][C]-0.200025032549433[/C][/ROW]
[ROW][C]42[/C][C]20.8[/C][C]20.4000100144736[/C][C]0.399989985526393[/C][/ROW]
[ROW][C]43[/C][C]21.1[/C][C]20.7999799740607[/C][C]0.300020025939268[/C][/ROW]
[ROW][C]44[/C][C]21.6[/C][C]21.0999849791669[/C][C]0.500015020833111[/C][/ROW]
[ROW][C]45[/C][C]22[/C][C]21.5999749661972[/C][C]0.400025033802848[/C][/ROW]
[ROW][C]46[/C][C]22.2[/C][C]21.999979972306[/C][C]0.200020027693995[/C][/ROW]
[ROW][C]47[/C][C]22.4[/C][C]22.199989985777[/C][C]0.200010014223032[/C][/ROW]
[ROW][C]48[/C][C]22.8[/C][C]22.3999899862783[/C][C]0.400010013721701[/C][/ROW]
[ROW][C]49[/C][C]22.7[/C][C]22.799979973058[/C][C]-0.0999799730580015[/C][/ROW]
[ROW][C]50[/C][C]22.8[/C][C]22.7000050056075[/C][C]0.0999949943925103[/C][/ROW]
[ROW][C]51[/C][C]22.9[/C][C]22.7999949936404[/C][C]0.100005006359549[/C][/ROW]
[ROW][C]52[/C][C]22.9[/C][C]22.8999949931392[/C][C]5.00686081039703e-06[/C][/ROW]
[ROW][C]53[/C][C]22.6[/C][C]22.8999999997493[/C][C]-0.299999999749325[/C][/ROW]
[ROW][C]54[/C][C]21.9[/C][C]22.6000150198305[/C][C]-0.700015019830481[/C][/ROW]
[ROW][C]55[/C][C]20.8[/C][C]21.9000350470231[/C][C]-1.10003504702312[/C][/ROW]
[ROW][C]56[/C][C]20.3[/C][C]20.8000550744665[/C][C]-0.500055074466463[/C][/ROW]
[ROW][C]57[/C][C]20.4[/C][C]20.3000250358082[/C][C]0.0999749641918193[/C][/ROW]
[ROW][C]58[/C][C]21.2[/C][C]20.3999949946433[/C][C]0.80000500535672[/C][/ROW]
[ROW][C]59[/C][C]21.4[/C][C]21.1999599468681[/C][C]0.200040053131904[/C][/ROW]
[ROW][C]60[/C][C]20.9[/C][C]21.3999899847744[/C][C]-0.49998998477437[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]20.9000250325494[/C][C]-0.90002503254939[/C][/ROW]
[ROW][C]62[/C][C]19.5[/C][C]20.0000450607447[/C][C]-0.50004506074475[/C][/ROW]
[ROW][C]63[/C][C]19.2[/C][C]19.5000250353068[/C][C]-0.300025035306831[/C][/ROW]
[ROW][C]64[/C][C]19.3[/C][C]19.2000150210839[/C][C]0.0999849789160905[/C][/ROW]
[ROW][C]65[/C][C]19.4[/C][C]19.2999949941419[/C][C]0.100005005858115[/C][/ROW]
[ROW][C]66[/C][C]19.5[/C][C]19.3999949931392[/C][C]0.100005006860787[/C][/ROW]
[ROW][C]67[/C][C]20[/C][C]19.4999949931392[/C][C]0.500005006860839[/C][/ROW]
[ROW][C]68[/C][C]20.1[/C][C]19.9999749666985[/C][C]0.100025033301492[/C][/ROW]
[ROW][C]69[/C][C]19.5[/C][C]20.0999949921365[/C][C]-0.599994992136519[/C][/ROW]
[ROW][C]70[/C][C]18.6[/C][C]19.5000300394103[/C][C]-0.900030039410254[/C][/ROW]
[ROW][C]71[/C][C]18.4[/C][C]18.6000450609954[/C][C]-0.200045060995425[/C][/ROW]
[ROW][C]72[/C][C]18.4[/C][C]18.4000100154764[/C][C]-1.0015476355818e-05[/C][/ROW]
[ROW][C]73[/C][C]19.3[/C][C]18.4000000005014[/C][C]0.899999999498565[/C][/ROW]
[ROW][C]74[/C][C]19.8[/C][C]19.2999549405086[/C][C]0.500045059491441[/C][/ROW]
[ROW][C]75[/C][C]19.8[/C][C]19.7999749646932[/C][C]2.50353067698939e-05[/C][/ROW]
[ROW][C]76[/C][C]19.8[/C][C]19.7999999987466[/C][C]1.25341870216289e-09[/C][/ROW]
[ROW][C]77[/C][C]20.1[/C][C]19.7999999999999[/C][C]0.300000000000065[/C][/ROW]
[ROW][C]78[/C][C]20.3[/C][C]20.0999849801695[/C][C]0.200015019830488[/C][/ROW]
[ROW][C]79[/C][C]19.7[/C][C]20.2999899860277[/C][C]-0.59998998602769[/C][/ROW]
[ROW][C]80[/C][C]20.2[/C][C]19.7000300391596[/C][C]0.499969960840382[/C][/ROW]
[ROW][C]81[/C][C]20.6[/C][C]20.1999749684531[/C][C]0.400025031546875[/C][/ROW]
[ROW][C]82[/C][C]21[/C][C]20.5999799723061[/C][C]0.400020027693884[/C][/ROW]
[ROW][C]83[/C][C]21.4[/C][C]20.9999799725566[/C][C]0.400020027443361[/C][/ROW]
[ROW][C]84[/C][C]21.9[/C][C]21.3999799725567[/C][C]0.500020027443348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233080&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233080&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
2	20.1	20.1	0
3	20.1	20.1	0
4	20.3	20.1	0.199999999999999
5	20.7	20.2999899867797	0.400010013220324
6	20.6	20.699979973058	-0.0999799730580229
7	20.3	20.6000050056075	-0.300005005607492
8	19.9	20.3000150200811	-0.400015020081103
9	19.7	19.9000200271926	-0.200020027192647
10	19.4	19.700010014223	-0.300010014223009
11	19.1	19.4000150203319	-0.300015020331859
12	18.8	19.1000150205825	-0.300015020582499
13	18.9	18.8000150205825	0.099984979417485
14	18.7	18.8999949941419	-0.199994994141857
15	18.8	18.7000100129697	0.0999899870302983
16	19.5	18.7999949938911	0.700005006108853
17	19.3	19.4999649534782	-0.199964953478222
18	19.1	19.3000100114657	-0.200010011465682
19	19.1	19.1000100137216	-1.00137215603979e-05
20	19	19.1000000005013	-0.10000000050135
21	18.8	19.0000050066102	-0.200005006610187
22	19.2	18.800010013471	0.399989986529011
23	18.9	19.1999799740607	-0.299979974060683
24	18.7	18.9000150188279	-0.200015018827866
25	18.5	18.7000100139723	-0.20001001397226
26	18.4	18.5000100137217	-0.10001001372169
27	18.3	18.4000050071115	-0.100005007111509
28	18.3	18.3000050068609	-5.00686084947688e-06
29	18.3	18.3000000002507	-2.50672371748806e-10
30	18.5	18.3	0.199999999999985
31	19.2	18.4999899867797	0.700010013220325
32	19.4	19.1999649532275	0.200035046772463
33	19.1	19.399989985025	-0.299989985025015
34	19.5	19.1000150193291	0.399984980670919
35	18.8	19.4999799743113	-0.699979974311308
36	19.3	18.8000350452685	0.499964954731468
37	20.4	19.2999749687038	1.10002503129623
38	20.9	20.399944926035	0.500055073965012
39	21.1	20.8999749641918	0.200025035808157
40	20.6	21.0999899855262	-0.499989985526227
41	20.4	20.6000250325494	-0.200025032549433
42	20.8	20.4000100144736	0.399989985526393
43	21.1	20.7999799740607	0.300020025939268
44	21.6	21.0999849791669	0.500015020833111
45	22	21.5999749661972	0.400025033802848
46	22.2	21.999979972306	0.200020027693995
47	22.4	22.199989985777	0.200010014223032
48	22.8	22.3999899862783	0.400010013721701
49	22.7	22.799979973058	-0.0999799730580015
50	22.8	22.7000050056075	0.0999949943925103
51	22.9	22.7999949936404	0.100005006359549
52	22.9	22.8999949931392	5.00686081039703e-06
53	22.6	22.8999999997493	-0.299999999749325
54	21.9	22.6000150198305	-0.700015019830481
55	20.8	21.9000350470231	-1.10003504702312
56	20.3	20.8000550744665	-0.500055074466463
57	20.4	20.3000250358082	0.0999749641918193
58	21.2	20.3999949946433	0.80000500535672
59	21.4	21.1999599468681	0.200040053131904
60	20.9	21.3999899847744	-0.49998998477437
61	20	20.9000250325494	-0.90002503254939
62	19.5	20.0000450607447	-0.50004506074475
63	19.2	19.5000250353068	-0.300025035306831
64	19.3	19.2000150210839	0.0999849789160905
65	19.4	19.2999949941419	0.100005005858115
66	19.5	19.3999949931392	0.100005006860787
67	20	19.4999949931392	0.500005006860839
68	20.1	19.9999749666985	0.100025033301492
69	19.5	20.0999949921365	-0.599994992136519
70	18.6	19.5000300394103	-0.900030039410254
71	18.4	18.6000450609954	-0.200045060995425
72	18.4	18.4000100154764	-1.0015476355818e-05
73	19.3	18.4000000005014	0.899999999498565
74	19.8	19.2999549405086	0.500045059491441
75	19.8	19.7999749646932	2.50353067698939e-05
76	19.8	19.7999999987466	1.25341870216289e-09
77	20.1	19.7999999999999	0.300000000000065
78	20.3	20.0999849801695	0.200015019830488
79	19.7	20.2999899860277	-0.59998998602769
80	20.2	19.7000300391596	0.499969960840382
81	20.6	20.1999749684531	0.400025031546875
82	21	20.5999799723061	0.400020027693884
83	21.4	20.9999799725566	0.400020027443361
84	21.9	21.3999799725567	0.500020027443348

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	21.8999749659465	21.0843154094534	22.7156345224396
86	21.8999749659465	20.7464870345581	23.0534628973349
87	21.8999749659465	20.4872583264116	23.3126916054814
88	21.8999749659465	20.2687171079183	23.5312328239747
89	21.8999749659465	20.076177802022	23.7237721298709
90	21.8999749659465	19.9021086063271	23.8978413255659
91	21.8999749659465	19.7420352340126	24.0579146978804
92	21.8999749659465	19.5930424176436	24.2069075142493
93	21.8999749659465	19.4531051945489	24.3468447373441
94	21.8999749659465	19.3207491956931	24.4792007361999
95	21.8999749659465	19.1948613879799	24.6050885439131
96	21.8999749659465	19.074577053181	24.7253728787119

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 21.8999749659465 & 21.0843154094534 & 22.7156345224396 \tabularnewline
86 & 21.8999749659465 & 20.7464870345581 & 23.0534628973349 \tabularnewline
87 & 21.8999749659465 & 20.4872583264116 & 23.3126916054814 \tabularnewline
88 & 21.8999749659465 & 20.2687171079183 & 23.5312328239747 \tabularnewline
89 & 21.8999749659465 & 20.076177802022 & 23.7237721298709 \tabularnewline
90 & 21.8999749659465 & 19.9021086063271 & 23.8978413255659 \tabularnewline
91 & 21.8999749659465 & 19.7420352340126 & 24.0579146978804 \tabularnewline
92 & 21.8999749659465 & 19.5930424176436 & 24.2069075142493 \tabularnewline
93 & 21.8999749659465 & 19.4531051945489 & 24.3468447373441 \tabularnewline
94 & 21.8999749659465 & 19.3207491956931 & 24.4792007361999 \tabularnewline
95 & 21.8999749659465 & 19.1948613879799 & 24.6050885439131 \tabularnewline
96 & 21.8999749659465 & 19.074577053181 & 24.7253728787119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233080&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]21.8999749659465[/C][C]21.0843154094534[/C][C]22.7156345224396[/C][/ROW]
[ROW][C]86[/C][C]21.8999749659465[/C][C]20.7464870345581[/C][C]23.0534628973349[/C][/ROW]
[ROW][C]87[/C][C]21.8999749659465[/C][C]20.4872583264116[/C][C]23.3126916054814[/C][/ROW]
[ROW][C]88[/C][C]21.8999749659465[/C][C]20.2687171079183[/C][C]23.5312328239747[/C][/ROW]
[ROW][C]89[/C][C]21.8999749659465[/C][C]20.076177802022[/C][C]23.7237721298709[/C][/ROW]
[ROW][C]90[/C][C]21.8999749659465[/C][C]19.9021086063271[/C][C]23.8978413255659[/C][/ROW]
[ROW][C]91[/C][C]21.8999749659465[/C][C]19.7420352340126[/C][C]24.0579146978804[/C][/ROW]
[ROW][C]92[/C][C]21.8999749659465[/C][C]19.5930424176436[/C][C]24.2069075142493[/C][/ROW]
[ROW][C]93[/C][C]21.8999749659465[/C][C]19.4531051945489[/C][C]24.3468447373441[/C][/ROW]
[ROW][C]94[/C][C]21.8999749659465[/C][C]19.3207491956931[/C][C]24.4792007361999[/C][/ROW]
[ROW][C]95[/C][C]21.8999749659465[/C][C]19.1948613879799[/C][C]24.6050885439131[/C][/ROW]
[ROW][C]96[/C][C]21.8999749659465[/C][C]19.074577053181[/C][C]24.7253728787119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233080&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233080&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	21.8999749659465	21.0843154094534	22.7156345224396
86	21.8999749659465	20.7464870345581	23.0534628973349
87	21.8999749659465	20.4872583264116	23.3126916054814
88	21.8999749659465	20.2687171079183	23.5312328239747
89	21.8999749659465	20.076177802022	23.7237721298709
90	21.8999749659465	19.9021086063271	23.8978413255659
91	21.8999749659465	19.7420352340126	24.0579146978804
92	21.8999749659465	19.5930424176436	24.2069075142493
93	21.8999749659465	19.4531051945489	24.3468447373441
94	21.8999749659465	19.3207491956931	24.4792007361999
95	21.8999749659465	19.1948613879799	24.6050885439131
96	21.8999749659465	19.074577053181	24.7253728787119

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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