Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 04 Jun 2009 01:26:31 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/04/t1244100436u3j4bba85x0ktdu.htm/, Retrieved Tue, 14 May 2024 05:04:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41526, Retrieved Tue, 14 May 2024 05:04:55 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

149

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

-       [Exponential Smoothing] [double exponentia...] [2009-06-04 07:26:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41526&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41526&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.909175725154546
beta	0.0452112664258505
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.909175725154546 \tabularnewline
beta & 0.0452112664258505 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41526&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]0.909175725154546[/C][/ROW]
[ROW][C]beta[/C][C]0.0452112664258505[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41526&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	0.909175725154546
beta	0.0452112664258505
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	20.74	20.73	0.00999999999999801
4	20.74	20.7395028071109	0.000497192889074682
5	20.75	20.7403863297825	0.00961367021751869
6	20.75	20.7499535021191	4.64978809162631e-05
7	20.77	20.7508243449036	0.0191756550963795
8	20.78	20.7698751681042	0.0101248318957943
9	20.78	20.7811133836309	-0.00111338363085522
10	20.8	20.7820883207881	0.0179116792118705
11	20.84	20.8010966425737	0.0389033574263209
12	20.85	20.840789210582	0.00921078941799536
13	20.86	20.8538646259092	0.00613537409083165
14	20.86	20.8643961427418	-0.00439614274183242
15	20.86	20.8651719567356	-0.00517195673559456
16	20.86	20.8650298262701	-0.00502982627010695
17	20.9	20.8648101664355	0.0351898335644556
18	20.92	20.9026037226104	0.0173962773896434
19	20.95	20.9249348831843	0.0250651168156644
20	20.95	20.9552686676788	-0.00526866767879497
21	20.95	20.9578071431480	-0.00780714314797493
22	20.96	20.9577167858324	0.00228321416763677
23	21.1	20.9668941879325	0.133105812067502
24	21.18	21.1004836328781	0.0795163671218688
25	21.19	21.1886193745071	0.00138062549294204
26	21.19	21.2057727471715	-0.0157727471714928
27	21.19	21.2066823512542	-0.0166823512542074
28	21.19	21.2060792375717	-0.0160792375717023
29	21.19	21.2053635233746	-0.0153635233745639
30	21.21	21.2046670017393	0.00533299826065559
31	21.22	21.2230064679885	-0.00300646798851290
32	21.22	21.2336403131388	-0.0136403131388008
33	21.22	21.2340454395336	-0.0140454395336356
34	21.23	21.2335048972501	-0.00350489725014569
35	21.41	21.2424034913886	0.167596508611410
36	21.42	21.4137523824059	0.0062476175941164
37	21.43	21.438663586663	-0.00866358666300115
38	21.44	21.4496617693688	-0.00966176936876906
39	21.44	21.4593552816951	-0.0193552816951481
40	21.44	21.459440089341	-0.0194400893409963
41	21.48	21.4586487073349	0.0213512926650594
42	21.53	21.4958215042290	0.0341784957709557
43	21.54	21.5460613893967	-0.00606138939670231
44	21.54	21.559466994461	-0.0194669944610020
45	21.54	21.5598843582863	-0.0198843582862587
46	21.54	21.5591049187853	-0.0191049187852954
47	21.54	21.5582488193398	-0.0182488193398171
48	21.54	21.5574209472661	-0.0174209472661424
49	21.54	21.556629668593	-0.0166296685929872
50	21.54	21.5558742389876	-0.0158742389876316
51	21.54	21.5551531172712	-0.0151531172711650
52	21.54	21.5544647532418	-0.0144647532418496
53	21.57	21.5538076595995	0.0161923404005471
54	21.6	21.581688837225	0.0183111627750208
55	21.61	21.6122490768077	-0.00224907680766506
56	21.6	21.6240239973879	-0.0240239973878538
57	21.6	21.6150141826846	-0.015014182684574
58	21.71	21.6135787150295	0.0964212849704609
59	21.75	21.7174210650505	0.0325789349494734
60	21.84	21.7645586568586	0.0754413431414171
61	21.85	21.8537667250654	-0.00376672506537901
62	21.92	21.8708059092413	0.0491940907586716
63	21.92	21.9380179039577	-0.0180179039577446
64	21.93	21.9433817589500	-0.0133817589499685
65	22	21.9524106274281	0.0475893725719025
66	22	22.0188291291115	-0.0188291291114773
67	21.99	22.0240875702758	-0.0340875702758439
68	22.01	22.014072238033	-0.00407223803301804
69	22.01	22.0311787279607	-0.0211787279607378
70	22.06	22.0318618611886	0.0281381388114283
71	22.03	22.0785393103265	-0.0485393103264933
72	22.05	22.0535082763730	-0.00350827637304363
73	22.05	22.0692741577177	-0.0192741577176996
74	22.06	22.0699138184762	-0.00991381847617845
75	22.06	22.0786561650832	-0.018656165083204
76	22.13	22.0786833209708	0.0513166790291635
77	22.06	22.1444374595153	-0.0844374595153283
78	22.25	22.0832964301199	0.166703569880106
79	22.28	22.2573390761368	0.022660923863171
80	22.18	22.3013531219649	-0.121353121964873

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 20.74 & 20.73 & 0.00999999999999801 \tabularnewline
4 & 20.74 & 20.7395028071109 & 0.000497192889074682 \tabularnewline
5 & 20.75 & 20.7403863297825 & 0.00961367021751869 \tabularnewline
6 & 20.75 & 20.7499535021191 & 4.64978809162631e-05 \tabularnewline
7 & 20.77 & 20.7508243449036 & 0.0191756550963795 \tabularnewline
8 & 20.78 & 20.7698751681042 & 0.0101248318957943 \tabularnewline
9 & 20.78 & 20.7811133836309 & -0.00111338363085522 \tabularnewline
10 & 20.8 & 20.7820883207881 & 0.0179116792118705 \tabularnewline
11 & 20.84 & 20.8010966425737 & 0.0389033574263209 \tabularnewline
12 & 20.85 & 20.840789210582 & 0.00921078941799536 \tabularnewline
13 & 20.86 & 20.8538646259092 & 0.00613537409083165 \tabularnewline
14 & 20.86 & 20.8643961427418 & -0.00439614274183242 \tabularnewline
15 & 20.86 & 20.8651719567356 & -0.00517195673559456 \tabularnewline
16 & 20.86 & 20.8650298262701 & -0.00502982627010695 \tabularnewline
17 & 20.9 & 20.8648101664355 & 0.0351898335644556 \tabularnewline
18 & 20.92 & 20.9026037226104 & 0.0173962773896434 \tabularnewline
19 & 20.95 & 20.9249348831843 & 0.0250651168156644 \tabularnewline
20 & 20.95 & 20.9552686676788 & -0.00526866767879497 \tabularnewline
21 & 20.95 & 20.9578071431480 & -0.00780714314797493 \tabularnewline
22 & 20.96 & 20.9577167858324 & 0.00228321416763677 \tabularnewline
23 & 21.1 & 20.9668941879325 & 0.133105812067502 \tabularnewline
24 & 21.18 & 21.1004836328781 & 0.0795163671218688 \tabularnewline
25 & 21.19 & 21.1886193745071 & 0.00138062549294204 \tabularnewline
26 & 21.19 & 21.2057727471715 & -0.0157727471714928 \tabularnewline
27 & 21.19 & 21.2066823512542 & -0.0166823512542074 \tabularnewline
28 & 21.19 & 21.2060792375717 & -0.0160792375717023 \tabularnewline
29 & 21.19 & 21.2053635233746 & -0.0153635233745639 \tabularnewline
30 & 21.21 & 21.2046670017393 & 0.00533299826065559 \tabularnewline
31 & 21.22 & 21.2230064679885 & -0.00300646798851290 \tabularnewline
32 & 21.22 & 21.2336403131388 & -0.0136403131388008 \tabularnewline
33 & 21.22 & 21.2340454395336 & -0.0140454395336356 \tabularnewline
34 & 21.23 & 21.2335048972501 & -0.00350489725014569 \tabularnewline
35 & 21.41 & 21.2424034913886 & 0.167596508611410 \tabularnewline
36 & 21.42 & 21.4137523824059 & 0.0062476175941164 \tabularnewline
37 & 21.43 & 21.438663586663 & -0.00866358666300115 \tabularnewline
38 & 21.44 & 21.4496617693688 & -0.00966176936876906 \tabularnewline
39 & 21.44 & 21.4593552816951 & -0.0193552816951481 \tabularnewline
40 & 21.44 & 21.459440089341 & -0.0194400893409963 \tabularnewline
41 & 21.48 & 21.4586487073349 & 0.0213512926650594 \tabularnewline
42 & 21.53 & 21.4958215042290 & 0.0341784957709557 \tabularnewline
43 & 21.54 & 21.5460613893967 & -0.00606138939670231 \tabularnewline
44 & 21.54 & 21.559466994461 & -0.0194669944610020 \tabularnewline
45 & 21.54 & 21.5598843582863 & -0.0198843582862587 \tabularnewline
46 & 21.54 & 21.5591049187853 & -0.0191049187852954 \tabularnewline
47 & 21.54 & 21.5582488193398 & -0.0182488193398171 \tabularnewline
48 & 21.54 & 21.5574209472661 & -0.0174209472661424 \tabularnewline
49 & 21.54 & 21.556629668593 & -0.0166296685929872 \tabularnewline
50 & 21.54 & 21.5558742389876 & -0.0158742389876316 \tabularnewline
51 & 21.54 & 21.5551531172712 & -0.0151531172711650 \tabularnewline
52 & 21.54 & 21.5544647532418 & -0.0144647532418496 \tabularnewline
53 & 21.57 & 21.5538076595995 & 0.0161923404005471 \tabularnewline
54 & 21.6 & 21.581688837225 & 0.0183111627750208 \tabularnewline
55 & 21.61 & 21.6122490768077 & -0.00224907680766506 \tabularnewline
56 & 21.6 & 21.6240239973879 & -0.0240239973878538 \tabularnewline
57 & 21.6 & 21.6150141826846 & -0.015014182684574 \tabularnewline
58 & 21.71 & 21.6135787150295 & 0.0964212849704609 \tabularnewline
59 & 21.75 & 21.7174210650505 & 0.0325789349494734 \tabularnewline
60 & 21.84 & 21.7645586568586 & 0.0754413431414171 \tabularnewline
61 & 21.85 & 21.8537667250654 & -0.00376672506537901 \tabularnewline
62 & 21.92 & 21.8708059092413 & 0.0491940907586716 \tabularnewline
63 & 21.92 & 21.9380179039577 & -0.0180179039577446 \tabularnewline
64 & 21.93 & 21.9433817589500 & -0.0133817589499685 \tabularnewline
65 & 22 & 21.9524106274281 & 0.0475893725719025 \tabularnewline
66 & 22 & 22.0188291291115 & -0.0188291291114773 \tabularnewline
67 & 21.99 & 22.0240875702758 & -0.0340875702758439 \tabularnewline
68 & 22.01 & 22.014072238033 & -0.00407223803301804 \tabularnewline
69 & 22.01 & 22.0311787279607 & -0.0211787279607378 \tabularnewline
70 & 22.06 & 22.0318618611886 & 0.0281381388114283 \tabularnewline
71 & 22.03 & 22.0785393103265 & -0.0485393103264933 \tabularnewline
72 & 22.05 & 22.0535082763730 & -0.00350827637304363 \tabularnewline
73 & 22.05 & 22.0692741577177 & -0.0192741577176996 \tabularnewline
74 & 22.06 & 22.0699138184762 & -0.00991381847617845 \tabularnewline
75 & 22.06 & 22.0786561650832 & -0.018656165083204 \tabularnewline
76 & 22.13 & 22.0786833209708 & 0.0513166790291635 \tabularnewline
77 & 22.06 & 22.1444374595153 & -0.0844374595153283 \tabularnewline
78 & 22.25 & 22.0832964301199 & 0.166703569880106 \tabularnewline
79 & 22.28 & 22.2573390761368 & 0.022660923863171 \tabularnewline
80 & 22.18 & 22.3013531219649 & -0.121353121964873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41526&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]20.74[/C][C]20.73[/C][C]0.00999999999999801[/C][/ROW]
[ROW][C]4[/C][C]20.74[/C][C]20.7395028071109[/C][C]0.000497192889074682[/C][/ROW]
[ROW][C]5[/C][C]20.75[/C][C]20.7403863297825[/C][C]0.00961367021751869[/C][/ROW]
[ROW][C]6[/C][C]20.75[/C][C]20.7499535021191[/C][C]4.64978809162631e-05[/C][/ROW]
[ROW][C]7[/C][C]20.77[/C][C]20.7508243449036[/C][C]0.0191756550963795[/C][/ROW]
[ROW][C]8[/C][C]20.78[/C][C]20.7698751681042[/C][C]0.0101248318957943[/C][/ROW]
[ROW][C]9[/C][C]20.78[/C][C]20.7811133836309[/C][C]-0.00111338363085522[/C][/ROW]
[ROW][C]10[/C][C]20.8[/C][C]20.7820883207881[/C][C]0.0179116792118705[/C][/ROW]
[ROW][C]11[/C][C]20.84[/C][C]20.8010966425737[/C][C]0.0389033574263209[/C][/ROW]
[ROW][C]12[/C][C]20.85[/C][C]20.840789210582[/C][C]0.00921078941799536[/C][/ROW]
[ROW][C]13[/C][C]20.86[/C][C]20.8538646259092[/C][C]0.00613537409083165[/C][/ROW]
[ROW][C]14[/C][C]20.86[/C][C]20.8643961427418[/C][C]-0.00439614274183242[/C][/ROW]
[ROW][C]15[/C][C]20.86[/C][C]20.8651719567356[/C][C]-0.00517195673559456[/C][/ROW]
[ROW][C]16[/C][C]20.86[/C][C]20.8650298262701[/C][C]-0.00502982627010695[/C][/ROW]
[ROW][C]17[/C][C]20.9[/C][C]20.8648101664355[/C][C]0.0351898335644556[/C][/ROW]
[ROW][C]18[/C][C]20.92[/C][C]20.9026037226104[/C][C]0.0173962773896434[/C][/ROW]
[ROW][C]19[/C][C]20.95[/C][C]20.9249348831843[/C][C]0.0250651168156644[/C][/ROW]
[ROW][C]20[/C][C]20.95[/C][C]20.9552686676788[/C][C]-0.00526866767879497[/C][/ROW]
[ROW][C]21[/C][C]20.95[/C][C]20.9578071431480[/C][C]-0.00780714314797493[/C][/ROW]
[ROW][C]22[/C][C]20.96[/C][C]20.9577167858324[/C][C]0.00228321416763677[/C][/ROW]
[ROW][C]23[/C][C]21.1[/C][C]20.9668941879325[/C][C]0.133105812067502[/C][/ROW]
[ROW][C]24[/C][C]21.18[/C][C]21.1004836328781[/C][C]0.0795163671218688[/C][/ROW]
[ROW][C]25[/C][C]21.19[/C][C]21.1886193745071[/C][C]0.00138062549294204[/C][/ROW]
[ROW][C]26[/C][C]21.19[/C][C]21.2057727471715[/C][C]-0.0157727471714928[/C][/ROW]
[ROW][C]27[/C][C]21.19[/C][C]21.2066823512542[/C][C]-0.0166823512542074[/C][/ROW]
[ROW][C]28[/C][C]21.19[/C][C]21.2060792375717[/C][C]-0.0160792375717023[/C][/ROW]
[ROW][C]29[/C][C]21.19[/C][C]21.2053635233746[/C][C]-0.0153635233745639[/C][/ROW]
[ROW][C]30[/C][C]21.21[/C][C]21.2046670017393[/C][C]0.00533299826065559[/C][/ROW]
[ROW][C]31[/C][C]21.22[/C][C]21.2230064679885[/C][C]-0.00300646798851290[/C][/ROW]
[ROW][C]32[/C][C]21.22[/C][C]21.2336403131388[/C][C]-0.0136403131388008[/C][/ROW]
[ROW][C]33[/C][C]21.22[/C][C]21.2340454395336[/C][C]-0.0140454395336356[/C][/ROW]
[ROW][C]34[/C][C]21.23[/C][C]21.2335048972501[/C][C]-0.00350489725014569[/C][/ROW]
[ROW][C]35[/C][C]21.41[/C][C]21.2424034913886[/C][C]0.167596508611410[/C][/ROW]
[ROW][C]36[/C][C]21.42[/C][C]21.4137523824059[/C][C]0.0062476175941164[/C][/ROW]
[ROW][C]37[/C][C]21.43[/C][C]21.438663586663[/C][C]-0.00866358666300115[/C][/ROW]
[ROW][C]38[/C][C]21.44[/C][C]21.4496617693688[/C][C]-0.00966176936876906[/C][/ROW]
[ROW][C]39[/C][C]21.44[/C][C]21.4593552816951[/C][C]-0.0193552816951481[/C][/ROW]
[ROW][C]40[/C][C]21.44[/C][C]21.459440089341[/C][C]-0.0194400893409963[/C][/ROW]
[ROW][C]41[/C][C]21.48[/C][C]21.4586487073349[/C][C]0.0213512926650594[/C][/ROW]
[ROW][C]42[/C][C]21.53[/C][C]21.4958215042290[/C][C]0.0341784957709557[/C][/ROW]
[ROW][C]43[/C][C]21.54[/C][C]21.5460613893967[/C][C]-0.00606138939670231[/C][/ROW]
[ROW][C]44[/C][C]21.54[/C][C]21.559466994461[/C][C]-0.0194669944610020[/C][/ROW]
[ROW][C]45[/C][C]21.54[/C][C]21.5598843582863[/C][C]-0.0198843582862587[/C][/ROW]
[ROW][C]46[/C][C]21.54[/C][C]21.5591049187853[/C][C]-0.0191049187852954[/C][/ROW]
[ROW][C]47[/C][C]21.54[/C][C]21.5582488193398[/C][C]-0.0182488193398171[/C][/ROW]
[ROW][C]48[/C][C]21.54[/C][C]21.5574209472661[/C][C]-0.0174209472661424[/C][/ROW]
[ROW][C]49[/C][C]21.54[/C][C]21.556629668593[/C][C]-0.0166296685929872[/C][/ROW]
[ROW][C]50[/C][C]21.54[/C][C]21.5558742389876[/C][C]-0.0158742389876316[/C][/ROW]
[ROW][C]51[/C][C]21.54[/C][C]21.5551531172712[/C][C]-0.0151531172711650[/C][/ROW]
[ROW][C]52[/C][C]21.54[/C][C]21.5544647532418[/C][C]-0.0144647532418496[/C][/ROW]
[ROW][C]53[/C][C]21.57[/C][C]21.5538076595995[/C][C]0.0161923404005471[/C][/ROW]
[ROW][C]54[/C][C]21.6[/C][C]21.581688837225[/C][C]0.0183111627750208[/C][/ROW]
[ROW][C]55[/C][C]21.61[/C][C]21.6122490768077[/C][C]-0.00224907680766506[/C][/ROW]
[ROW][C]56[/C][C]21.6[/C][C]21.6240239973879[/C][C]-0.0240239973878538[/C][/ROW]
[ROW][C]57[/C][C]21.6[/C][C]21.6150141826846[/C][C]-0.015014182684574[/C][/ROW]
[ROW][C]58[/C][C]21.71[/C][C]21.6135787150295[/C][C]0.0964212849704609[/C][/ROW]
[ROW][C]59[/C][C]21.75[/C][C]21.7174210650505[/C][C]0.0325789349494734[/C][/ROW]
[ROW][C]60[/C][C]21.84[/C][C]21.7645586568586[/C][C]0.0754413431414171[/C][/ROW]
[ROW][C]61[/C][C]21.85[/C][C]21.8537667250654[/C][C]-0.00376672506537901[/C][/ROW]
[ROW][C]62[/C][C]21.92[/C][C]21.8708059092413[/C][C]0.0491940907586716[/C][/ROW]
[ROW][C]63[/C][C]21.92[/C][C]21.9380179039577[/C][C]-0.0180179039577446[/C][/ROW]
[ROW][C]64[/C][C]21.93[/C][C]21.9433817589500[/C][C]-0.0133817589499685[/C][/ROW]
[ROW][C]65[/C][C]22[/C][C]21.9524106274281[/C][C]0.0475893725719025[/C][/ROW]
[ROW][C]66[/C][C]22[/C][C]22.0188291291115[/C][C]-0.0188291291114773[/C][/ROW]
[ROW][C]67[/C][C]21.99[/C][C]22.0240875702758[/C][C]-0.0340875702758439[/C][/ROW]
[ROW][C]68[/C][C]22.01[/C][C]22.014072238033[/C][C]-0.00407223803301804[/C][/ROW]
[ROW][C]69[/C][C]22.01[/C][C]22.0311787279607[/C][C]-0.0211787279607378[/C][/ROW]
[ROW][C]70[/C][C]22.06[/C][C]22.0318618611886[/C][C]0.0281381388114283[/C][/ROW]
[ROW][C]71[/C][C]22.03[/C][C]22.0785393103265[/C][C]-0.0485393103264933[/C][/ROW]
[ROW][C]72[/C][C]22.05[/C][C]22.0535082763730[/C][C]-0.00350827637304363[/C][/ROW]
[ROW][C]73[/C][C]22.05[/C][C]22.0692741577177[/C][C]-0.0192741577176996[/C][/ROW]
[ROW][C]74[/C][C]22.06[/C][C]22.0699138184762[/C][C]-0.00991381847617845[/C][/ROW]
[ROW][C]75[/C][C]22.06[/C][C]22.0786561650832[/C][C]-0.018656165083204[/C][/ROW]
[ROW][C]76[/C][C]22.13[/C][C]22.0786833209708[/C][C]0.0513166790291635[/C][/ROW]
[ROW][C]77[/C][C]22.06[/C][C]22.1444374595153[/C][C]-0.0844374595153283[/C][/ROW]
[ROW][C]78[/C][C]22.25[/C][C]22.0832964301199[/C][C]0.166703569880106[/C][/ROW]
[ROW][C]79[/C][C]22.28[/C][C]22.2573390761368[/C][C]0.022660923863171[/C][/ROW]
[ROW][C]80[/C][C]22.18[/C][C]22.3013531219649[/C][C]-0.121353121964873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41526&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41526&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	20.74	20.73	0.00999999999999801
4	20.74	20.7395028071109	0.000497192889074682
5	20.75	20.7403863297825	0.00961367021751869
6	20.75	20.7499535021191	4.64978809162631e-05
7	20.77	20.7508243449036	0.0191756550963795
8	20.78	20.7698751681042	0.0101248318957943
9	20.78	20.7811133836309	-0.00111338363085522
10	20.8	20.7820883207881	0.0179116792118705
11	20.84	20.8010966425737	0.0389033574263209
12	20.85	20.840789210582	0.00921078941799536
13	20.86	20.8538646259092	0.00613537409083165
14	20.86	20.8643961427418	-0.00439614274183242
15	20.86	20.8651719567356	-0.00517195673559456
16	20.86	20.8650298262701	-0.00502982627010695
17	20.9	20.8648101664355	0.0351898335644556
18	20.92	20.9026037226104	0.0173962773896434
19	20.95	20.9249348831843	0.0250651168156644
20	20.95	20.9552686676788	-0.00526866767879497
21	20.95	20.9578071431480	-0.00780714314797493
22	20.96	20.9577167858324	0.00228321416763677
23	21.1	20.9668941879325	0.133105812067502
24	21.18	21.1004836328781	0.0795163671218688
25	21.19	21.1886193745071	0.00138062549294204
26	21.19	21.2057727471715	-0.0157727471714928
27	21.19	21.2066823512542	-0.0166823512542074
28	21.19	21.2060792375717	-0.0160792375717023
29	21.19	21.2053635233746	-0.0153635233745639
30	21.21	21.2046670017393	0.00533299826065559
31	21.22	21.2230064679885	-0.00300646798851290
32	21.22	21.2336403131388	-0.0136403131388008
33	21.22	21.2340454395336	-0.0140454395336356
34	21.23	21.2335048972501	-0.00350489725014569
35	21.41	21.2424034913886	0.167596508611410
36	21.42	21.4137523824059	0.0062476175941164
37	21.43	21.438663586663	-0.00866358666300115
38	21.44	21.4496617693688	-0.00966176936876906
39	21.44	21.4593552816951	-0.0193552816951481
40	21.44	21.459440089341	-0.0194400893409963
41	21.48	21.4586487073349	0.0213512926650594
42	21.53	21.4958215042290	0.0341784957709557
43	21.54	21.5460613893967	-0.00606138939670231
44	21.54	21.559466994461	-0.0194669944610020
45	21.54	21.5598843582863	-0.0198843582862587
46	21.54	21.5591049187853	-0.0191049187852954
47	21.54	21.5582488193398	-0.0182488193398171
48	21.54	21.5574209472661	-0.0174209472661424
49	21.54	21.556629668593	-0.0166296685929872
50	21.54	21.5558742389876	-0.0158742389876316
51	21.54	21.5551531172712	-0.0151531172711650
52	21.54	21.5544647532418	-0.0144647532418496
53	21.57	21.5538076595995	0.0161923404005471
54	21.6	21.581688837225	0.0183111627750208
55	21.61	21.6122490768077	-0.00224907680766506
56	21.6	21.6240239973879	-0.0240239973878538
57	21.6	21.6150141826846	-0.015014182684574
58	21.71	21.6135787150295	0.0964212849704609
59	21.75	21.7174210650505	0.0325789349494734
60	21.84	21.7645586568586	0.0754413431414171
61	21.85	21.8537667250654	-0.00376672506537901
62	21.92	21.8708059092413	0.0491940907586716
63	21.92	21.9380179039577	-0.0180179039577446
64	21.93	21.9433817589500	-0.0133817589499685
65	22	21.9524106274281	0.0475893725719025
66	22	22.0188291291115	-0.0188291291114773
67	21.99	22.0240875702758	-0.0340875702758439
68	22.01	22.014072238033	-0.00407223803301804
69	22.01	22.0311787279607	-0.0211787279607378
70	22.06	22.0318618611886	0.0281381388114283
71	22.03	22.0785393103265	-0.0485393103264933
72	22.05	22.0535082763730	-0.00350827637304363
73	22.05	22.0692741577177	-0.0192741577176996
74	22.06	22.0699138184762	-0.00991381847617845
75	22.06	22.0786561650832	-0.018656165083204
76	22.13	22.0786833209708	0.0513166790291635
77	22.06	22.1444374595153	-0.0844374595153283
78	22.25	22.0832964301199	0.166703569880106
79	22.28	22.2573390761368	0.022660923863171
80	22.18	22.3013531219649	-0.121353121964873

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	22.2094448748729	22.125057913068	22.2938318366778
82	22.2278679404431	22.1114557235134	22.3442801573727
83	22.2462910060133	22.1029354886460	22.3896465233805
84	22.2647140715834	22.0969576298155	22.4324705133514
85	22.2831371371536	22.0924800456513	22.4737942286559
86	22.3015602027238	22.0889606335319	22.5141597719157
87	22.319983268294	22.0860780766016	22.5538884599864
88	22.3384063338642	22.0836252979042	22.5931873698241
89	22.3568293994344	22.0814608215652	22.6321979773036
90	22.3752524650046	22.0794837462667	22.6710211837425
91	22.3936755305748	22.0776197059048	22.7097313552447
92	22.4120985961450	22.0758124594188	22.7483847328711

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 22.2094448748729 & 22.125057913068 & 22.2938318366778 \tabularnewline
82 & 22.2278679404431 & 22.1114557235134 & 22.3442801573727 \tabularnewline
83 & 22.2462910060133 & 22.1029354886460 & 22.3896465233805 \tabularnewline
84 & 22.2647140715834 & 22.0969576298155 & 22.4324705133514 \tabularnewline
85 & 22.2831371371536 & 22.0924800456513 & 22.4737942286559 \tabularnewline
86 & 22.3015602027238 & 22.0889606335319 & 22.5141597719157 \tabularnewline
87 & 22.319983268294 & 22.0860780766016 & 22.5538884599864 \tabularnewline
88 & 22.3384063338642 & 22.0836252979042 & 22.5931873698241 \tabularnewline
89 & 22.3568293994344 & 22.0814608215652 & 22.6321979773036 \tabularnewline
90 & 22.3752524650046 & 22.0794837462667 & 22.6710211837425 \tabularnewline
91 & 22.3936755305748 & 22.0776197059048 & 22.7097313552447 \tabularnewline
92 & 22.4120985961450 & 22.0758124594188 & 22.7483847328711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41526&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]81[/C][C]22.2094448748729[/C][C]22.125057913068[/C][C]22.2938318366778[/C][/ROW]
[ROW][C]82[/C][C]22.2278679404431[/C][C]22.1114557235134[/C][C]22.3442801573727[/C][/ROW]
[ROW][C]83[/C][C]22.2462910060133[/C][C]22.1029354886460[/C][C]22.3896465233805[/C][/ROW]
[ROW][C]84[/C][C]22.2647140715834[/C][C]22.0969576298155[/C][C]22.4324705133514[/C][/ROW]
[ROW][C]85[/C][C]22.2831371371536[/C][C]22.0924800456513[/C][C]22.4737942286559[/C][/ROW]
[ROW][C]86[/C][C]22.3015602027238[/C][C]22.0889606335319[/C][C]22.5141597719157[/C][/ROW]
[ROW][C]87[/C][C]22.319983268294[/C][C]22.0860780766016[/C][C]22.5538884599864[/C][/ROW]
[ROW][C]88[/C][C]22.3384063338642[/C][C]22.0836252979042[/C][C]22.5931873698241[/C][/ROW]
[ROW][C]89[/C][C]22.3568293994344[/C][C]22.0814608215652[/C][C]22.6321979773036[/C][/ROW]
[ROW][C]90[/C][C]22.3752524650046[/C][C]22.0794837462667[/C][C]22.6710211837425[/C][/ROW]
[ROW][C]91[/C][C]22.3936755305748[/C][C]22.0776197059048[/C][C]22.7097313552447[/C][/ROW]
[ROW][C]92[/C][C]22.4120985961450[/C][C]22.0758124594188[/C][C]22.7483847328711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41526&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41526&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
81	22.2094448748729	22.125057913068	22.2938318366778
82	22.2278679404431	22.1114557235134	22.3442801573727
83	22.2462910060133	22.1029354886460	22.3896465233805
84	22.2647140715834	22.0969576298155	22.4324705133514
85	22.2831371371536	22.0924800456513	22.4737942286559
86	22.3015602027238	22.0889606335319	22.5141597719157
87	22.319983268294	22.0860780766016	22.5538884599864
88	22.3384063338642	22.0836252979042	22.5931873698241
89	22.3568293994344	22.0814608215652	22.6321979773036
90	22.3752524650046	22.0794837462667	22.6710211837425
91	22.3936755305748	22.0776197059048	22.7097313552447
92	22.4120985961450	22.0758124594188	22.7483847328711

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code