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

Mon, 31 May 2010 20:33:21 +0000

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/2010/May/31/t1275338065olnvbx87ride6j9.htm/, Retrieved Mon, 29 Apr 2024 15:51:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76793, Retrieved Mon, 29 Apr 2024 15:51:29 +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

KDGP2W62

Estimated Impact

121

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

-       [Exponential Smoothing] [smoothing- zakje ...] [2010-05-31 20:33:21] [17264c076bcd9ffe53c701d21c08cfe9] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

2.06
2.06
2.05
2.04
2.04
2.03
2.03
2.03
2.02
2.02
2.02
2.02
2.01
2.01
2.01
2
2
1.99
1.99
1.99
1.98
1.97
1.97
1.96
1.96
1.96
1.96
1.95
1.94
1.94
1.93
1.93
1.93
1.92
1.92
1.9
1.9
1.9
1.9
1.89
1.88
1.88
1.87
1.86
1.86
1.85
1.83
1.82
1.8
1.8
1.79
1.78
1.78
1.78
1.77
1.77
1.76
1.75
1.75
1.75
1.75
1.75
1.74
1.74
1.74
1.74
1.73
1.73
1.73
1.73
1.73
1.72
1.71
1.71
1.71
1.7
1.7
1.7
1.7
1.7
1.69
1.68
1.67
1.65
1.61

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76793&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76793&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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.927762771241466
beta	0.198109645413317
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.927762771241466 \tabularnewline
beta & 0.198109645413317 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76793&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]0.927762771241466[/C][/ROW]
[ROW][C]beta[/C][C]0.198109645413317[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76793&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	0.927762771241466
beta	0.198109645413317
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.01	2.03072115384615	-0.0207211538461549
14	2.01	2.00748144002278	0.00251855997722172
15	2.01	2.00626557568381	0.0037344243161872
16	2	1.99728079421496	0.00271920578504181
17	2	1.99827058408908	0.0017294159109249
18	1.99	1.98907661492225	0.000923385077747696
19	1.99	1.98430455738235	0.00569544261764721
20	1.99	1.98958998575807	0.000410014241930323
21	1.98	1.97963048389671	0.000369516103292167
22	1.97	1.97928465930258	-0.00928465930257993
23	1.97	1.96827554137208	0.00172445862792125
24	1.96	1.96779722654822	-0.00779722654821624
25	1.96	1.94555508744653	0.0144449125534722
26	1.96	1.95977894513417	0.000221054865829018
27	1.96	1.95925612495126	0.000743875048742071
28	1.95	1.94961058059993	0.000389419400073532
29	1.94	1.95012626385646	-0.0101262638564608
30	1.94	1.92945463390813	0.0105453660918706
31	1.93	1.93530254343693	-0.00530254343692627
32	1.93	1.92932956005059	0.000670439949406409
33	1.93	1.91898352686913	0.0110164731308733
34	1.92	1.92914984006377	-0.00914984006376707
35	1.92	1.92041752849116	-0.000417528491158947
36	1.9	1.9182269009656	-0.0182269009656035
37	1.9	1.886961010909	0.0130389890910043
38	1.9	1.89764040830256	0.0023595916974426
39	1.9	1.89831986567758	0.00168013432242087
40	1.89	1.88886988183789	0.00113011816211439
41	1.88	1.88880181242994	-0.00880181242994271
42	1.88	1.87058433140664	0.0094156685933584
43	1.87	1.87376381453316	-0.00376381453316266
44	1.86	1.86945716870631	-0.0094571687063083
45	1.86	1.84840833457007	0.0115916654299335
46	1.85	1.85570309936632	-0.00570309936631874
47	1.83	1.84948441830759	-0.0194844183075893
48	1.82	1.82349834477349	-0.00349834477348709
49	1.8	1.80604331658941	-0.00604331658940715
50	1.8	1.79262780162109	0.0073721983789079
51	1.79	1.79321038811514	-0.00321038811513552
52	1.78	1.77358625742501	0.00641374257498684
53	1.78	1.77307663592639	0.0069233640736075
54	1.78	1.7690285894445	0.010971410555505
55	1.77	1.77124954700737	-0.0012495470073739
56	1.77	1.76787655639738	0.00212344360261807
57	1.76	1.76023307832219	-0.00023307832219488
58	1.75	1.75427537268716	-0.00427537268715872
59	1.75	1.74761558586639	0.00238441413360846
60	1.75	1.74632268158529	0.0036773184147143
61	1.75	1.73990929381816	0.0100907061818423
62	1.75	1.7499650063908	3.49936092007841e-05
63	1.74	1.74916096388099	-0.00916096388099419
64	1.74	1.72980263579681	0.0101973642031861
65	1.74	1.73862686090827	0.00137313909172843
66	1.74	1.73448854722002	0.00551145277997622
67	1.73	1.73452422292915	-0.00452422292915178
68	1.73	1.73151795586241	-0.00151795586240877
69	1.73	1.72281780008888	0.00718219991111613
70	1.73	1.72730253406541	0.00269746593458664
71	1.73	1.73272939559088	-0.0027293955908827
72	1.72	1.73098199671585	-0.0109819967158451
73	1.71	1.7129336754931	-0.00293367549309709
74	1.71	1.70928773771625	0.000712262283754761
75	1.71	1.7076805134186	0.00231948658139758
76	1.7	1.70171456836556	-0.00171456836556105
77	1.7	1.69800336649949	0.00199663350050594
78	1.7	1.69401050368088	0.0059894963191156
79	1.7	1.69312066044991	0.00687933955008502
80	1.7	1.70236323854667	-0.0023632385466672
81	1.69	1.69480385424044	-0.00480385424044405
82	1.68	1.68693790496287	-0.00693790496287483
83	1.67	1.68035593379931	-0.0103559337993102
84	1.65	1.66685755060263	-0.0168575506026325
85	1.61	1.63878035710017	-0.0287803571001695

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.01 & 2.03072115384615 & -0.0207211538461549 \tabularnewline
14 & 2.01 & 2.00748144002278 & 0.00251855997722172 \tabularnewline
15 & 2.01 & 2.00626557568381 & 0.0037344243161872 \tabularnewline
16 & 2 & 1.99728079421496 & 0.00271920578504181 \tabularnewline
17 & 2 & 1.99827058408908 & 0.0017294159109249 \tabularnewline
18 & 1.99 & 1.98907661492225 & 0.000923385077747696 \tabularnewline
19 & 1.99 & 1.98430455738235 & 0.00569544261764721 \tabularnewline
20 & 1.99 & 1.98958998575807 & 0.000410014241930323 \tabularnewline
21 & 1.98 & 1.97963048389671 & 0.000369516103292167 \tabularnewline
22 & 1.97 & 1.97928465930258 & -0.00928465930257993 \tabularnewline
23 & 1.97 & 1.96827554137208 & 0.00172445862792125 \tabularnewline
24 & 1.96 & 1.96779722654822 & -0.00779722654821624 \tabularnewline
25 & 1.96 & 1.94555508744653 & 0.0144449125534722 \tabularnewline
26 & 1.96 & 1.95977894513417 & 0.000221054865829018 \tabularnewline
27 & 1.96 & 1.95925612495126 & 0.000743875048742071 \tabularnewline
28 & 1.95 & 1.94961058059993 & 0.000389419400073532 \tabularnewline
29 & 1.94 & 1.95012626385646 & -0.0101262638564608 \tabularnewline
30 & 1.94 & 1.92945463390813 & 0.0105453660918706 \tabularnewline
31 & 1.93 & 1.93530254343693 & -0.00530254343692627 \tabularnewline
32 & 1.93 & 1.92932956005059 & 0.000670439949406409 \tabularnewline
33 & 1.93 & 1.91898352686913 & 0.0110164731308733 \tabularnewline
34 & 1.92 & 1.92914984006377 & -0.00914984006376707 \tabularnewline
35 & 1.92 & 1.92041752849116 & -0.000417528491158947 \tabularnewline
36 & 1.9 & 1.9182269009656 & -0.0182269009656035 \tabularnewline
37 & 1.9 & 1.886961010909 & 0.0130389890910043 \tabularnewline
38 & 1.9 & 1.89764040830256 & 0.0023595916974426 \tabularnewline
39 & 1.9 & 1.89831986567758 & 0.00168013432242087 \tabularnewline
40 & 1.89 & 1.88886988183789 & 0.00113011816211439 \tabularnewline
41 & 1.88 & 1.88880181242994 & -0.00880181242994271 \tabularnewline
42 & 1.88 & 1.87058433140664 & 0.0094156685933584 \tabularnewline
43 & 1.87 & 1.87376381453316 & -0.00376381453316266 \tabularnewline
44 & 1.86 & 1.86945716870631 & -0.0094571687063083 \tabularnewline
45 & 1.86 & 1.84840833457007 & 0.0115916654299335 \tabularnewline
46 & 1.85 & 1.85570309936632 & -0.00570309936631874 \tabularnewline
47 & 1.83 & 1.84948441830759 & -0.0194844183075893 \tabularnewline
48 & 1.82 & 1.82349834477349 & -0.00349834477348709 \tabularnewline
49 & 1.8 & 1.80604331658941 & -0.00604331658940715 \tabularnewline
50 & 1.8 & 1.79262780162109 & 0.0073721983789079 \tabularnewline
51 & 1.79 & 1.79321038811514 & -0.00321038811513552 \tabularnewline
52 & 1.78 & 1.77358625742501 & 0.00641374257498684 \tabularnewline
53 & 1.78 & 1.77307663592639 & 0.0069233640736075 \tabularnewline
54 & 1.78 & 1.7690285894445 & 0.010971410555505 \tabularnewline
55 & 1.77 & 1.77124954700737 & -0.0012495470073739 \tabularnewline
56 & 1.77 & 1.76787655639738 & 0.00212344360261807 \tabularnewline
57 & 1.76 & 1.76023307832219 & -0.00023307832219488 \tabularnewline
58 & 1.75 & 1.75427537268716 & -0.00427537268715872 \tabularnewline
59 & 1.75 & 1.74761558586639 & 0.00238441413360846 \tabularnewline
60 & 1.75 & 1.74632268158529 & 0.0036773184147143 \tabularnewline
61 & 1.75 & 1.73990929381816 & 0.0100907061818423 \tabularnewline
62 & 1.75 & 1.7499650063908 & 3.49936092007841e-05 \tabularnewline
63 & 1.74 & 1.74916096388099 & -0.00916096388099419 \tabularnewline
64 & 1.74 & 1.72980263579681 & 0.0101973642031861 \tabularnewline
65 & 1.74 & 1.73862686090827 & 0.00137313909172843 \tabularnewline
66 & 1.74 & 1.73448854722002 & 0.00551145277997622 \tabularnewline
67 & 1.73 & 1.73452422292915 & -0.00452422292915178 \tabularnewline
68 & 1.73 & 1.73151795586241 & -0.00151795586240877 \tabularnewline
69 & 1.73 & 1.72281780008888 & 0.00718219991111613 \tabularnewline
70 & 1.73 & 1.72730253406541 & 0.00269746593458664 \tabularnewline
71 & 1.73 & 1.73272939559088 & -0.0027293955908827 \tabularnewline
72 & 1.72 & 1.73098199671585 & -0.0109819967158451 \tabularnewline
73 & 1.71 & 1.7129336754931 & -0.00293367549309709 \tabularnewline
74 & 1.71 & 1.70928773771625 & 0.000712262283754761 \tabularnewline
75 & 1.71 & 1.7076805134186 & 0.00231948658139758 \tabularnewline
76 & 1.7 & 1.70171456836556 & -0.00171456836556105 \tabularnewline
77 & 1.7 & 1.69800336649949 & 0.00199663350050594 \tabularnewline
78 & 1.7 & 1.69401050368088 & 0.0059894963191156 \tabularnewline
79 & 1.7 & 1.69312066044991 & 0.00687933955008502 \tabularnewline
80 & 1.7 & 1.70236323854667 & -0.0023632385466672 \tabularnewline
81 & 1.69 & 1.69480385424044 & -0.00480385424044405 \tabularnewline
82 & 1.68 & 1.68693790496287 & -0.00693790496287483 \tabularnewline
83 & 1.67 & 1.68035593379931 & -0.0103559337993102 \tabularnewline
84 & 1.65 & 1.66685755060263 & -0.0168575506026325 \tabularnewline
85 & 1.61 & 1.63878035710017 & -0.0287803571001695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76793&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]2.01[/C][C]2.03072115384615[/C][C]-0.0207211538461549[/C][/ROW]
[ROW][C]14[/C][C]2.01[/C][C]2.00748144002278[/C][C]0.00251855997722172[/C][/ROW]
[ROW][C]15[/C][C]2.01[/C][C]2.00626557568381[/C][C]0.0037344243161872[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]1.99728079421496[/C][C]0.00271920578504181[/C][/ROW]
[ROW][C]17[/C][C]2[/C][C]1.99827058408908[/C][C]0.0017294159109249[/C][/ROW]
[ROW][C]18[/C][C]1.99[/C][C]1.98907661492225[/C][C]0.000923385077747696[/C][/ROW]
[ROW][C]19[/C][C]1.99[/C][C]1.98430455738235[/C][C]0.00569544261764721[/C][/ROW]
[ROW][C]20[/C][C]1.99[/C][C]1.98958998575807[/C][C]0.000410014241930323[/C][/ROW]
[ROW][C]21[/C][C]1.98[/C][C]1.97963048389671[/C][C]0.000369516103292167[/C][/ROW]
[ROW][C]22[/C][C]1.97[/C][C]1.97928465930258[/C][C]-0.00928465930257993[/C][/ROW]
[ROW][C]23[/C][C]1.97[/C][C]1.96827554137208[/C][C]0.00172445862792125[/C][/ROW]
[ROW][C]24[/C][C]1.96[/C][C]1.96779722654822[/C][C]-0.00779722654821624[/C][/ROW]
[ROW][C]25[/C][C]1.96[/C][C]1.94555508744653[/C][C]0.0144449125534722[/C][/ROW]
[ROW][C]26[/C][C]1.96[/C][C]1.95977894513417[/C][C]0.000221054865829018[/C][/ROW]
[ROW][C]27[/C][C]1.96[/C][C]1.95925612495126[/C][C]0.000743875048742071[/C][/ROW]
[ROW][C]28[/C][C]1.95[/C][C]1.94961058059993[/C][C]0.000389419400073532[/C][/ROW]
[ROW][C]29[/C][C]1.94[/C][C]1.95012626385646[/C][C]-0.0101262638564608[/C][/ROW]
[ROW][C]30[/C][C]1.94[/C][C]1.92945463390813[/C][C]0.0105453660918706[/C][/ROW]
[ROW][C]31[/C][C]1.93[/C][C]1.93530254343693[/C][C]-0.00530254343692627[/C][/ROW]
[ROW][C]32[/C][C]1.93[/C][C]1.92932956005059[/C][C]0.000670439949406409[/C][/ROW]
[ROW][C]33[/C][C]1.93[/C][C]1.91898352686913[/C][C]0.0110164731308733[/C][/ROW]
[ROW][C]34[/C][C]1.92[/C][C]1.92914984006377[/C][C]-0.00914984006376707[/C][/ROW]
[ROW][C]35[/C][C]1.92[/C][C]1.92041752849116[/C][C]-0.000417528491158947[/C][/ROW]
[ROW][C]36[/C][C]1.9[/C][C]1.9182269009656[/C][C]-0.0182269009656035[/C][/ROW]
[ROW][C]37[/C][C]1.9[/C][C]1.886961010909[/C][C]0.0130389890910043[/C][/ROW]
[ROW][C]38[/C][C]1.9[/C][C]1.89764040830256[/C][C]0.0023595916974426[/C][/ROW]
[ROW][C]39[/C][C]1.9[/C][C]1.89831986567758[/C][C]0.00168013432242087[/C][/ROW]
[ROW][C]40[/C][C]1.89[/C][C]1.88886988183789[/C][C]0.00113011816211439[/C][/ROW]
[ROW][C]41[/C][C]1.88[/C][C]1.88880181242994[/C][C]-0.00880181242994271[/C][/ROW]
[ROW][C]42[/C][C]1.88[/C][C]1.87058433140664[/C][C]0.0094156685933584[/C][/ROW]
[ROW][C]43[/C][C]1.87[/C][C]1.87376381453316[/C][C]-0.00376381453316266[/C][/ROW]
[ROW][C]44[/C][C]1.86[/C][C]1.86945716870631[/C][C]-0.0094571687063083[/C][/ROW]
[ROW][C]45[/C][C]1.86[/C][C]1.84840833457007[/C][C]0.0115916654299335[/C][/ROW]
[ROW][C]46[/C][C]1.85[/C][C]1.85570309936632[/C][C]-0.00570309936631874[/C][/ROW]
[ROW][C]47[/C][C]1.83[/C][C]1.84948441830759[/C][C]-0.0194844183075893[/C][/ROW]
[ROW][C]48[/C][C]1.82[/C][C]1.82349834477349[/C][C]-0.00349834477348709[/C][/ROW]
[ROW][C]49[/C][C]1.8[/C][C]1.80604331658941[/C][C]-0.00604331658940715[/C][/ROW]
[ROW][C]50[/C][C]1.8[/C][C]1.79262780162109[/C][C]0.0073721983789079[/C][/ROW]
[ROW][C]51[/C][C]1.79[/C][C]1.79321038811514[/C][C]-0.00321038811513552[/C][/ROW]
[ROW][C]52[/C][C]1.78[/C][C]1.77358625742501[/C][C]0.00641374257498684[/C][/ROW]
[ROW][C]53[/C][C]1.78[/C][C]1.77307663592639[/C][C]0.0069233640736075[/C][/ROW]
[ROW][C]54[/C][C]1.78[/C][C]1.7690285894445[/C][C]0.010971410555505[/C][/ROW]
[ROW][C]55[/C][C]1.77[/C][C]1.77124954700737[/C][C]-0.0012495470073739[/C][/ROW]
[ROW][C]56[/C][C]1.77[/C][C]1.76787655639738[/C][C]0.00212344360261807[/C][/ROW]
[ROW][C]57[/C][C]1.76[/C][C]1.76023307832219[/C][C]-0.00023307832219488[/C][/ROW]
[ROW][C]58[/C][C]1.75[/C][C]1.75427537268716[/C][C]-0.00427537268715872[/C][/ROW]
[ROW][C]59[/C][C]1.75[/C][C]1.74761558586639[/C][C]0.00238441413360846[/C][/ROW]
[ROW][C]60[/C][C]1.75[/C][C]1.74632268158529[/C][C]0.0036773184147143[/C][/ROW]
[ROW][C]61[/C][C]1.75[/C][C]1.73990929381816[/C][C]0.0100907061818423[/C][/ROW]
[ROW][C]62[/C][C]1.75[/C][C]1.7499650063908[/C][C]3.49936092007841e-05[/C][/ROW]
[ROW][C]63[/C][C]1.74[/C][C]1.74916096388099[/C][C]-0.00916096388099419[/C][/ROW]
[ROW][C]64[/C][C]1.74[/C][C]1.72980263579681[/C][C]0.0101973642031861[/C][/ROW]
[ROW][C]65[/C][C]1.74[/C][C]1.73862686090827[/C][C]0.00137313909172843[/C][/ROW]
[ROW][C]66[/C][C]1.74[/C][C]1.73448854722002[/C][C]0.00551145277997622[/C][/ROW]
[ROW][C]67[/C][C]1.73[/C][C]1.73452422292915[/C][C]-0.00452422292915178[/C][/ROW]
[ROW][C]68[/C][C]1.73[/C][C]1.73151795586241[/C][C]-0.00151795586240877[/C][/ROW]
[ROW][C]69[/C][C]1.73[/C][C]1.72281780008888[/C][C]0.00718219991111613[/C][/ROW]
[ROW][C]70[/C][C]1.73[/C][C]1.72730253406541[/C][C]0.00269746593458664[/C][/ROW]
[ROW][C]71[/C][C]1.73[/C][C]1.73272939559088[/C][C]-0.0027293955908827[/C][/ROW]
[ROW][C]72[/C][C]1.72[/C][C]1.73098199671585[/C][C]-0.0109819967158451[/C][/ROW]
[ROW][C]73[/C][C]1.71[/C][C]1.7129336754931[/C][C]-0.00293367549309709[/C][/ROW]
[ROW][C]74[/C][C]1.71[/C][C]1.70928773771625[/C][C]0.000712262283754761[/C][/ROW]
[ROW][C]75[/C][C]1.71[/C][C]1.7076805134186[/C][C]0.00231948658139758[/C][/ROW]
[ROW][C]76[/C][C]1.7[/C][C]1.70171456836556[/C][C]-0.00171456836556105[/C][/ROW]
[ROW][C]77[/C][C]1.7[/C][C]1.69800336649949[/C][C]0.00199663350050594[/C][/ROW]
[ROW][C]78[/C][C]1.7[/C][C]1.69401050368088[/C][C]0.0059894963191156[/C][/ROW]
[ROW][C]79[/C][C]1.7[/C][C]1.69312066044991[/C][C]0.00687933955008502[/C][/ROW]
[ROW][C]80[/C][C]1.7[/C][C]1.70236323854667[/C][C]-0.0023632385466672[/C][/ROW]
[ROW][C]81[/C][C]1.69[/C][C]1.69480385424044[/C][C]-0.00480385424044405[/C][/ROW]
[ROW][C]82[/C][C]1.68[/C][C]1.68693790496287[/C][C]-0.00693790496287483[/C][/ROW]
[ROW][C]83[/C][C]1.67[/C][C]1.68035593379931[/C][C]-0.0103559337993102[/C][/ROW]
[ROW][C]84[/C][C]1.65[/C][C]1.66685755060263[/C][C]-0.0168575506026325[/C][/ROW]
[ROW][C]85[/C][C]1.61[/C][C]1.63878035710017[/C][C]-0.0287803571001695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76793&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.01	2.03072115384615	-0.0207211538461549
14	2.01	2.00748144002278	0.00251855997722172
15	2.01	2.00626557568381	0.0037344243161872
16	2	1.99728079421496	0.00271920578504181
17	2	1.99827058408908	0.0017294159109249
18	1.99	1.98907661492225	0.000923385077747696
19	1.99	1.98430455738235	0.00569544261764721
20	1.99	1.98958998575807	0.000410014241930323
21	1.98	1.97963048389671	0.000369516103292167
22	1.97	1.97928465930258	-0.00928465930257993
23	1.97	1.96827554137208	0.00172445862792125
24	1.96	1.96779722654822	-0.00779722654821624
25	1.96	1.94555508744653	0.0144449125534722
26	1.96	1.95977894513417	0.000221054865829018
27	1.96	1.95925612495126	0.000743875048742071
28	1.95	1.94961058059993	0.000389419400073532
29	1.94	1.95012626385646	-0.0101262638564608
30	1.94	1.92945463390813	0.0105453660918706
31	1.93	1.93530254343693	-0.00530254343692627
32	1.93	1.92932956005059	0.000670439949406409
33	1.93	1.91898352686913	0.0110164731308733
34	1.92	1.92914984006377	-0.00914984006376707
35	1.92	1.92041752849116	-0.000417528491158947
36	1.9	1.9182269009656	-0.0182269009656035
37	1.9	1.886961010909	0.0130389890910043
38	1.9	1.89764040830256	0.0023595916974426
39	1.9	1.89831986567758	0.00168013432242087
40	1.89	1.88886988183789	0.00113011816211439
41	1.88	1.88880181242994	-0.00880181242994271
42	1.88	1.87058433140664	0.0094156685933584
43	1.87	1.87376381453316	-0.00376381453316266
44	1.86	1.86945716870631	-0.0094571687063083
45	1.86	1.84840833457007	0.0115916654299335
46	1.85	1.85570309936632	-0.00570309936631874
47	1.83	1.84948441830759	-0.0194844183075893
48	1.82	1.82349834477349	-0.00349834477348709
49	1.8	1.80604331658941	-0.00604331658940715
50	1.8	1.79262780162109	0.0073721983789079
51	1.79	1.79321038811514	-0.00321038811513552
52	1.78	1.77358625742501	0.00641374257498684
53	1.78	1.77307663592639	0.0069233640736075
54	1.78	1.7690285894445	0.010971410555505
55	1.77	1.77124954700737	-0.0012495470073739
56	1.77	1.76787655639738	0.00212344360261807
57	1.76	1.76023307832219	-0.00023307832219488
58	1.75	1.75427537268716	-0.00427537268715872
59	1.75	1.74761558586639	0.00238441413360846
60	1.75	1.74632268158529	0.0036773184147143
61	1.75	1.73990929381816	0.0100907061818423
62	1.75	1.7499650063908	3.49936092007841e-05
63	1.74	1.74916096388099	-0.00916096388099419
64	1.74	1.72980263579681	0.0101973642031861
65	1.74	1.73862686090827	0.00137313909172843
66	1.74	1.73448854722002	0.00551145277997622
67	1.73	1.73452422292915	-0.00452422292915178
68	1.73	1.73151795586241	-0.00151795586240877
69	1.73	1.72281780008888	0.00718219991111613
70	1.73	1.72730253406541	0.00269746593458664
71	1.73	1.73272939559088	-0.0027293955908827
72	1.72	1.73098199671585	-0.0109819967158451
73	1.71	1.7129336754931	-0.00293367549309709
74	1.71	1.70928773771625	0.000712262283754761
75	1.71	1.7076805134186	0.00231948658139758
76	1.7	1.70171456836556	-0.00171456836556105
77	1.7	1.69800336649949	0.00199663350050594
78	1.7	1.69401050368088	0.0059894963191156
79	1.7	1.69312066044991	0.00687933955008502
80	1.7	1.70236323854667	-0.0023632385466672
81	1.69	1.69480385424044	-0.00480385424044405
82	1.68	1.68693790496287	-0.00693790496287483
83	1.67	1.68035593379931	-0.0103559337993102
84	1.65	1.66685755060263	-0.0168575506026325
85	1.61	1.63878035710017	-0.0287803571001695

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	1.60150847439988	1.5853706468716	1.61764630192816
87	1.58931589977176	1.5651869115552	1.61344488798833
88	1.57043965239783	1.53851477396908	1.60236453082659
89	1.55843542562462	1.51857323180532	1.59829761944393
90	1.54235979062877	1.49430572087092	1.59041386038661
91	1.5243577302526	1.46781225401399	1.58090320649121
92	1.51366617570973	1.44831189557359	1.57902045584587
93	1.49567329384589	1.42118730579965	1.57015928189212
94	1.4805432472163	1.39660322112547	1.56448327330714
95	1.46985949877724	1.37614677672424	1.56357222083023
96	1.45711111608624	1.35331228687163	1.56090994530085
97	1.43852266618254	1.32433032124163	1.55271501112344

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 1.60150847439988 & 1.5853706468716 & 1.61764630192816 \tabularnewline
87 & 1.58931589977176 & 1.5651869115552 & 1.61344488798833 \tabularnewline
88 & 1.57043965239783 & 1.53851477396908 & 1.60236453082659 \tabularnewline
89 & 1.55843542562462 & 1.51857323180532 & 1.59829761944393 \tabularnewline
90 & 1.54235979062877 & 1.49430572087092 & 1.59041386038661 \tabularnewline
91 & 1.5243577302526 & 1.46781225401399 & 1.58090320649121 \tabularnewline
92 & 1.51366617570973 & 1.44831189557359 & 1.57902045584587 \tabularnewline
93 & 1.49567329384589 & 1.42118730579965 & 1.57015928189212 \tabularnewline
94 & 1.4805432472163 & 1.39660322112547 & 1.56448327330714 \tabularnewline
95 & 1.46985949877724 & 1.37614677672424 & 1.56357222083023 \tabularnewline
96 & 1.45711111608624 & 1.35331228687163 & 1.56090994530085 \tabularnewline
97 & 1.43852266618254 & 1.32433032124163 & 1.55271501112344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76793&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]86[/C][C]1.60150847439988[/C][C]1.5853706468716[/C][C]1.61764630192816[/C][/ROW]
[ROW][C]87[/C][C]1.58931589977176[/C][C]1.5651869115552[/C][C]1.61344488798833[/C][/ROW]
[ROW][C]88[/C][C]1.57043965239783[/C][C]1.53851477396908[/C][C]1.60236453082659[/C][/ROW]
[ROW][C]89[/C][C]1.55843542562462[/C][C]1.51857323180532[/C][C]1.59829761944393[/C][/ROW]
[ROW][C]90[/C][C]1.54235979062877[/C][C]1.49430572087092[/C][C]1.59041386038661[/C][/ROW]
[ROW][C]91[/C][C]1.5243577302526[/C][C]1.46781225401399[/C][C]1.58090320649121[/C][/ROW]
[ROW][C]92[/C][C]1.51366617570973[/C][C]1.44831189557359[/C][C]1.57902045584587[/C][/ROW]
[ROW][C]93[/C][C]1.49567329384589[/C][C]1.42118730579965[/C][C]1.57015928189212[/C][/ROW]
[ROW][C]94[/C][C]1.4805432472163[/C][C]1.39660322112547[/C][C]1.56448327330714[/C][/ROW]
[ROW][C]95[/C][C]1.46985949877724[/C][C]1.37614677672424[/C][C]1.56357222083023[/C][/ROW]
[ROW][C]96[/C][C]1.45711111608624[/C][C]1.35331228687163[/C][C]1.56090994530085[/C][/ROW]
[ROW][C]97[/C][C]1.43852266618254[/C][C]1.32433032124163[/C][C]1.55271501112344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76793&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76793&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
86	1.60150847439988	1.5853706468716	1.61764630192816
87	1.58931589977176	1.5651869115552	1.61344488798833
88	1.57043965239783	1.53851477396908	1.60236453082659
89	1.55843542562462	1.51857323180532	1.59829761944393
90	1.54235979062877	1.49430572087092	1.59041386038661
91	1.5243577302526	1.46781225401399	1.58090320649121
92	1.51366617570973	1.44831189557359	1.57902045584587
93	1.49567329384589	1.42118730579965	1.57015928189212
94	1.4805432472163	1.39660322112547	1.56448327330714
95	1.46985949877724	1.37614677672424	1.56357222083023
96	1.45711111608624	1.35331228687163	1.56090994530085
97	1.43852266618254	1.32433032124163	1.55271501112344

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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