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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 26 Jan 2010 16:39:27 -0700

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/Jan/27/t12645493903our76es8bx6w04.htm/, Retrieved Mon, 06 May 2024 02:44:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72675, Retrieved Mon, 06 May 2024 02:44:31 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

233

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

-     [Standard Deviation Plot] [Spreidingsgrafiek...] [2009-12-17 20:25:30] [f713c1ac4846c73da8c41c71cf7e0185]
- RMPD    [Exponential Smoothing] [Triple exponentia...] [2010-01-26 23:39:27] [5b65373266815c68befe61a173c7d8fa] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72675&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72675&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72675&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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72675&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[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72675&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72675&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
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	87.9	81.9	5.99999999999997
14	88.9	88.9	1.4210854715202e-14
15	89.9	89.9	2.8421709430404e-14
16	90.9	90.9	-1.4210854715202e-14
17	91.9	91.9	-1.4210854715202e-14
18	92.9	92.9	0
19	93.9	93.9	-1.4210854715202e-14
20	94.9	94.9	4.2632564145606e-14
21	95.9	95.9	0
22	96.9	96.9	-4.2632564145606e-14
23	97.9	97.9	4.2632564145606e-14
24	98.9	98.9	0
25	99.9	99.9	-4.2632564145606e-14
26	100.9	100.9	1.4210854715202e-14
27	101.9	101.9	2.8421709430404e-14
28	102.9	102.9	-1.4210854715202e-14
29	103.9	103.9	-1.4210854715202e-14
30	104.9	104.9	0
31	105.9	105.9	-1.4210854715202e-14
32	106.9	106.9	4.2632564145606e-14
33	107.9	107.9	0
34	108.9	108.9	-4.2632564145606e-14
35	109.9	109.9	4.2632564145606e-14
36	110.9	110.9	0
37	111.9	111.9	-4.2632564145606e-14
38	112.9	112.9	1.4210854715202e-14
39	113.9	113.9	2.8421709430404e-14
40	114.9	114.9	-1.4210854715202e-14
41	115.9	115.9	-1.4210854715202e-14
42	116.9	116.9	0
43	117.9	117.9	-1.4210854715202e-14
44	118.9	118.9	4.2632564145606e-14
45	119.9	119.9	0
46	120.9	120.9	-4.2632564145606e-14
47	121.9	121.9	4.2632564145606e-14
48	122.9	122.9	0
49	123.9	123.9	-4.2632564145606e-14
50	124.9	124.9	1.4210854715202e-14
51	125.9	125.9	2.8421709430404e-14
52	126.9	126.9	-1.4210854715202e-14
53	127.9	127.9	-1.4210854715202e-14
54	128.9	128.9	2.8421709430404e-14
55	129.9	129.9	-2.8421709430404e-14
56	130.9	130.9	5.6843418860808e-14
57	131.9	131.9	0
58	132.9	132.9	-5.6843418860808e-14
59	133.9	133.9	5.6843418860808e-14
60	134.9	134.9	0
61	135.9	135.9	-5.6843418860808e-14
62	136.9	136.9	2.8421709430404e-14
63	137.9	137.9	2.8421709430404e-14
64	138.9	138.9	-2.8421709430404e-14
65	139.9	139.9	0
66	140.9	140.9	0
67	141.9	141.9	-2.8421709430404e-14
68	142.9	142.9	5.6843418860808e-14
69	143.9	143.9	0
70	144.9	144.9	-5.6843418860808e-14
71	145.9	145.9	5.6843418860808e-14
72	146.9	146.9	0
73	147.9	147.9	-5.6843418860808e-14
74	148.9	148.9	2.8421709430404e-14
75	149.9	149.9	2.8421709430404e-14
76	150.9	150.9	-2.8421709430404e-14
77	151.9	151.9	0
78	152.9	152.9	0
79	153.9	153.9	-2.8421709430404e-14
80	154.9	154.9	5.6843418860808e-14
81	155.9	155.9	0
82	156.9	156.9	-5.6843418860808e-14
83	157.9	157.9	5.6843418860808e-14
84	158.9	158.9	0
85	159.9	159.9	-5.6843418860808e-14
86	160.9	160.9	2.8421709430404e-14
87	161.9	161.9	2.8421709430404e-14
88	162.9	162.9	-2.8421709430404e-14
89	163.9	163.9	0
90	164.9	164.9	0
91	165.9	165.9	-2.8421709430404e-14
92	166.9	166.9	5.6843418860808e-14
93	167.9	167.9	0
94	168.9	168.9	-5.6843418860808e-14
95	169.9	169.9	5.6843418860808e-14
96	170.9	170.9	0
97	171.9	171.9	-5.6843418860808e-14
98	172.9	172.9	2.8421709430404e-14
99	173.9	173.9	2.8421709430404e-14
100	174.9	174.9	-2.8421709430404e-14
101	175.9	175.9	0
102	176.9	176.9	0
103	177.9	177.9	-2.8421709430404e-14
104	178.9	178.9	5.6843418860808e-14
105	179.9	179.9	0
106	180.9	180.9	-5.6843418860808e-14
107	181.9	181.9	5.6843418860808e-14
108	182.9	182.9	0

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 87.9 & 81.9 & 5.99999999999997 \tabularnewline
14 & 88.9 & 88.9 & 1.4210854715202e-14 \tabularnewline
15 & 89.9 & 89.9 & 2.8421709430404e-14 \tabularnewline
16 & 90.9 & 90.9 & -1.4210854715202e-14 \tabularnewline
17 & 91.9 & 91.9 & -1.4210854715202e-14 \tabularnewline
18 & 92.9 & 92.9 & 0 \tabularnewline
19 & 93.9 & 93.9 & -1.4210854715202e-14 \tabularnewline
20 & 94.9 & 94.9 & 4.2632564145606e-14 \tabularnewline
21 & 95.9 & 95.9 & 0 \tabularnewline
22 & 96.9 & 96.9 & -4.2632564145606e-14 \tabularnewline
23 & 97.9 & 97.9 & 4.2632564145606e-14 \tabularnewline
24 & 98.9 & 98.9 & 0 \tabularnewline
25 & 99.9 & 99.9 & -4.2632564145606e-14 \tabularnewline
26 & 100.9 & 100.9 & 1.4210854715202e-14 \tabularnewline
27 & 101.9 & 101.9 & 2.8421709430404e-14 \tabularnewline
28 & 102.9 & 102.9 & -1.4210854715202e-14 \tabularnewline
29 & 103.9 & 103.9 & -1.4210854715202e-14 \tabularnewline
30 & 104.9 & 104.9 & 0 \tabularnewline
31 & 105.9 & 105.9 & -1.4210854715202e-14 \tabularnewline
32 & 106.9 & 106.9 & 4.2632564145606e-14 \tabularnewline
33 & 107.9 & 107.9 & 0 \tabularnewline
34 & 108.9 & 108.9 & -4.2632564145606e-14 \tabularnewline
35 & 109.9 & 109.9 & 4.2632564145606e-14 \tabularnewline
36 & 110.9 & 110.9 & 0 \tabularnewline
37 & 111.9 & 111.9 & -4.2632564145606e-14 \tabularnewline
38 & 112.9 & 112.9 & 1.4210854715202e-14 \tabularnewline
39 & 113.9 & 113.9 & 2.8421709430404e-14 \tabularnewline
40 & 114.9 & 114.9 & -1.4210854715202e-14 \tabularnewline
41 & 115.9 & 115.9 & -1.4210854715202e-14 \tabularnewline
42 & 116.9 & 116.9 & 0 \tabularnewline
43 & 117.9 & 117.9 & -1.4210854715202e-14 \tabularnewline
44 & 118.9 & 118.9 & 4.2632564145606e-14 \tabularnewline
45 & 119.9 & 119.9 & 0 \tabularnewline
46 & 120.9 & 120.9 & -4.2632564145606e-14 \tabularnewline
47 & 121.9 & 121.9 & 4.2632564145606e-14 \tabularnewline
48 & 122.9 & 122.9 & 0 \tabularnewline
49 & 123.9 & 123.9 & -4.2632564145606e-14 \tabularnewline
50 & 124.9 & 124.9 & 1.4210854715202e-14 \tabularnewline
51 & 125.9 & 125.9 & 2.8421709430404e-14 \tabularnewline
52 & 126.9 & 126.9 & -1.4210854715202e-14 \tabularnewline
53 & 127.9 & 127.9 & -1.4210854715202e-14 \tabularnewline
54 & 128.9 & 128.9 & 2.8421709430404e-14 \tabularnewline
55 & 129.9 & 129.9 & -2.8421709430404e-14 \tabularnewline
56 & 130.9 & 130.9 & 5.6843418860808e-14 \tabularnewline
57 & 131.9 & 131.9 & 0 \tabularnewline
58 & 132.9 & 132.9 & -5.6843418860808e-14 \tabularnewline
59 & 133.9 & 133.9 & 5.6843418860808e-14 \tabularnewline
60 & 134.9 & 134.9 & 0 \tabularnewline
61 & 135.9 & 135.9 & -5.6843418860808e-14 \tabularnewline
62 & 136.9 & 136.9 & 2.8421709430404e-14 \tabularnewline
63 & 137.9 & 137.9 & 2.8421709430404e-14 \tabularnewline
64 & 138.9 & 138.9 & -2.8421709430404e-14 \tabularnewline
65 & 139.9 & 139.9 & 0 \tabularnewline
66 & 140.9 & 140.9 & 0 \tabularnewline
67 & 141.9 & 141.9 & -2.8421709430404e-14 \tabularnewline
68 & 142.9 & 142.9 & 5.6843418860808e-14 \tabularnewline
69 & 143.9 & 143.9 & 0 \tabularnewline
70 & 144.9 & 144.9 & -5.6843418860808e-14 \tabularnewline
71 & 145.9 & 145.9 & 5.6843418860808e-14 \tabularnewline
72 & 146.9 & 146.9 & 0 \tabularnewline
73 & 147.9 & 147.9 & -5.6843418860808e-14 \tabularnewline
74 & 148.9 & 148.9 & 2.8421709430404e-14 \tabularnewline
75 & 149.9 & 149.9 & 2.8421709430404e-14 \tabularnewline
76 & 150.9 & 150.9 & -2.8421709430404e-14 \tabularnewline
77 & 151.9 & 151.9 & 0 \tabularnewline
78 & 152.9 & 152.9 & 0 \tabularnewline
79 & 153.9 & 153.9 & -2.8421709430404e-14 \tabularnewline
80 & 154.9 & 154.9 & 5.6843418860808e-14 \tabularnewline
81 & 155.9 & 155.9 & 0 \tabularnewline
82 & 156.9 & 156.9 & -5.6843418860808e-14 \tabularnewline
83 & 157.9 & 157.9 & 5.6843418860808e-14 \tabularnewline
84 & 158.9 & 158.9 & 0 \tabularnewline
85 & 159.9 & 159.9 & -5.6843418860808e-14 \tabularnewline
86 & 160.9 & 160.9 & 2.8421709430404e-14 \tabularnewline
87 & 161.9 & 161.9 & 2.8421709430404e-14 \tabularnewline
88 & 162.9 & 162.9 & -2.8421709430404e-14 \tabularnewline
89 & 163.9 & 163.9 & 0 \tabularnewline
90 & 164.9 & 164.9 & 0 \tabularnewline
91 & 165.9 & 165.9 & -2.8421709430404e-14 \tabularnewline
92 & 166.9 & 166.9 & 5.6843418860808e-14 \tabularnewline
93 & 167.9 & 167.9 & 0 \tabularnewline
94 & 168.9 & 168.9 & -5.6843418860808e-14 \tabularnewline
95 & 169.9 & 169.9 & 5.6843418860808e-14 \tabularnewline
96 & 170.9 & 170.9 & 0 \tabularnewline
97 & 171.9 & 171.9 & -5.6843418860808e-14 \tabularnewline
98 & 172.9 & 172.9 & 2.8421709430404e-14 \tabularnewline
99 & 173.9 & 173.9 & 2.8421709430404e-14 \tabularnewline
100 & 174.9 & 174.9 & -2.8421709430404e-14 \tabularnewline
101 & 175.9 & 175.9 & 0 \tabularnewline
102 & 176.9 & 176.9 & 0 \tabularnewline
103 & 177.9 & 177.9 & -2.8421709430404e-14 \tabularnewline
104 & 178.9 & 178.9 & 5.6843418860808e-14 \tabularnewline
105 & 179.9 & 179.9 & 0 \tabularnewline
106 & 180.9 & 180.9 & -5.6843418860808e-14 \tabularnewline
107 & 181.9 & 181.9 & 5.6843418860808e-14 \tabularnewline
108 & 182.9 & 182.9 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72675&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]87.9[/C][C]81.9[/C][C]5.99999999999997[/C][/ROW]
[ROW][C]14[/C][C]88.9[/C][C]88.9[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]15[/C][C]89.9[/C][C]89.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]16[/C][C]90.9[/C][C]90.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]17[/C][C]91.9[/C][C]91.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]18[/C][C]92.9[/C][C]92.9[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]93.9[/C][C]93.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]20[/C][C]94.9[/C][C]94.9[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]21[/C][C]95.9[/C][C]95.9[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]96.9[/C][C]96.9[/C][C]-4.2632564145606e-14[/C][/ROW]
[ROW][C]23[/C][C]97.9[/C][C]97.9[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]24[/C][C]98.9[/C][C]98.9[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]99.9[/C][C]99.9[/C][C]-4.2632564145606e-14[/C][/ROW]
[ROW][C]26[/C][C]100.9[/C][C]100.9[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]27[/C][C]101.9[/C][C]101.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]28[/C][C]102.9[/C][C]102.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]29[/C][C]103.9[/C][C]103.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]30[/C][C]104.9[/C][C]104.9[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]105.9[/C][C]105.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]32[/C][C]106.9[/C][C]106.9[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]107.9[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]108.9[/C][C]108.9[/C][C]-4.2632564145606e-14[/C][/ROW]
[ROW][C]35[/C][C]109.9[/C][C]109.9[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]36[/C][C]110.9[/C][C]110.9[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]111.9[/C][C]111.9[/C][C]-4.2632564145606e-14[/C][/ROW]
[ROW][C]38[/C][C]112.9[/C][C]112.9[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]39[/C][C]113.9[/C][C]113.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]40[/C][C]114.9[/C][C]114.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]41[/C][C]115.9[/C][C]115.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]42[/C][C]116.9[/C][C]116.9[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]117.9[/C][C]117.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]44[/C][C]118.9[/C][C]118.9[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]45[/C][C]119.9[/C][C]119.9[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]120.9[/C][C]120.9[/C][C]-4.2632564145606e-14[/C][/ROW]
[ROW][C]47[/C][C]121.9[/C][C]121.9[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]48[/C][C]122.9[/C][C]122.9[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]123.9[/C][C]123.9[/C][C]-4.2632564145606e-14[/C][/ROW]
[ROW][C]50[/C][C]124.9[/C][C]124.9[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]51[/C][C]125.9[/C][C]125.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]52[/C][C]126.9[/C][C]126.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]53[/C][C]127.9[/C][C]127.9[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]54[/C][C]128.9[/C][C]128.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]55[/C][C]129.9[/C][C]129.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]56[/C][C]130.9[/C][C]130.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]57[/C][C]131.9[/C][C]131.9[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]132.9[/C][C]132.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]59[/C][C]133.9[/C][C]133.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]60[/C][C]134.9[/C][C]134.9[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]135.9[/C][C]135.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]62[/C][C]136.9[/C][C]136.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]63[/C][C]137.9[/C][C]137.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]64[/C][C]138.9[/C][C]138.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]65[/C][C]139.9[/C][C]139.9[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]140.9[/C][C]140.9[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]141.9[/C][C]141.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]68[/C][C]142.9[/C][C]142.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]69[/C][C]143.9[/C][C]143.9[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]144.9[/C][C]144.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]71[/C][C]145.9[/C][C]145.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]72[/C][C]146.9[/C][C]146.9[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]147.9[/C][C]147.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]74[/C][C]148.9[/C][C]148.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]75[/C][C]149.9[/C][C]149.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]76[/C][C]150.9[/C][C]150.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]77[/C][C]151.9[/C][C]151.9[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]152.9[/C][C]152.9[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]153.9[/C][C]153.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]80[/C][C]154.9[/C][C]154.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]81[/C][C]155.9[/C][C]155.9[/C][C]0[/C][/ROW]
[ROW][C]82[/C][C]156.9[/C][C]156.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]83[/C][C]157.9[/C][C]157.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]84[/C][C]158.9[/C][C]158.9[/C][C]0[/C][/ROW]
[ROW][C]85[/C][C]159.9[/C][C]159.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]86[/C][C]160.9[/C][C]160.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]87[/C][C]161.9[/C][C]161.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]88[/C][C]162.9[/C][C]162.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]89[/C][C]163.9[/C][C]163.9[/C][C]0[/C][/ROW]
[ROW][C]90[/C][C]164.9[/C][C]164.9[/C][C]0[/C][/ROW]
[ROW][C]91[/C][C]165.9[/C][C]165.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]92[/C][C]166.9[/C][C]166.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]93[/C][C]167.9[/C][C]167.9[/C][C]0[/C][/ROW]
[ROW][C]94[/C][C]168.9[/C][C]168.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]95[/C][C]169.9[/C][C]169.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]96[/C][C]170.9[/C][C]170.9[/C][C]0[/C][/ROW]
[ROW][C]97[/C][C]171.9[/C][C]171.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]98[/C][C]172.9[/C][C]172.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]99[/C][C]173.9[/C][C]173.9[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]100[/C][C]174.9[/C][C]174.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]101[/C][C]175.9[/C][C]175.9[/C][C]0[/C][/ROW]
[ROW][C]102[/C][C]176.9[/C][C]176.9[/C][C]0[/C][/ROW]
[ROW][C]103[/C][C]177.9[/C][C]177.9[/C][C]-2.8421709430404e-14[/C][/ROW]
[ROW][C]104[/C][C]178.9[/C][C]178.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]105[/C][C]179.9[/C][C]179.9[/C][C]0[/C][/ROW]
[ROW][C]106[/C][C]180.9[/C][C]180.9[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]107[/C][C]181.9[/C][C]181.9[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]108[/C][C]182.9[/C][C]182.9[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72675&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72675&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	87.9	81.9	5.99999999999997
14	88.9	88.9	1.4210854715202e-14
15	89.9	89.9	2.8421709430404e-14
16	90.9	90.9	-1.4210854715202e-14
17	91.9	91.9	-1.4210854715202e-14
18	92.9	92.9	0
19	93.9	93.9	-1.4210854715202e-14
20	94.9	94.9	4.2632564145606e-14
21	95.9	95.9	0
22	96.9	96.9	-4.2632564145606e-14
23	97.9	97.9	4.2632564145606e-14
24	98.9	98.9	0
25	99.9	99.9	-4.2632564145606e-14
26	100.9	100.9	1.4210854715202e-14
27	101.9	101.9	2.8421709430404e-14
28	102.9	102.9	-1.4210854715202e-14
29	103.9	103.9	-1.4210854715202e-14
30	104.9	104.9	0
31	105.9	105.9	-1.4210854715202e-14
32	106.9	106.9	4.2632564145606e-14
33	107.9	107.9	0
34	108.9	108.9	-4.2632564145606e-14
35	109.9	109.9	4.2632564145606e-14
36	110.9	110.9	0
37	111.9	111.9	-4.2632564145606e-14
38	112.9	112.9	1.4210854715202e-14
39	113.9	113.9	2.8421709430404e-14
40	114.9	114.9	-1.4210854715202e-14
41	115.9	115.9	-1.4210854715202e-14
42	116.9	116.9	0
43	117.9	117.9	-1.4210854715202e-14
44	118.9	118.9	4.2632564145606e-14
45	119.9	119.9	0
46	120.9	120.9	-4.2632564145606e-14
47	121.9	121.9	4.2632564145606e-14
48	122.9	122.9	0
49	123.9	123.9	-4.2632564145606e-14
50	124.9	124.9	1.4210854715202e-14
51	125.9	125.9	2.8421709430404e-14
52	126.9	126.9	-1.4210854715202e-14
53	127.9	127.9	-1.4210854715202e-14
54	128.9	128.9	2.8421709430404e-14
55	129.9	129.9	-2.8421709430404e-14
56	130.9	130.9	5.6843418860808e-14
57	131.9	131.9	0
58	132.9	132.9	-5.6843418860808e-14
59	133.9	133.9	5.6843418860808e-14
60	134.9	134.9	0
61	135.9	135.9	-5.6843418860808e-14
62	136.9	136.9	2.8421709430404e-14
63	137.9	137.9	2.8421709430404e-14
64	138.9	138.9	-2.8421709430404e-14
65	139.9	139.9	0
66	140.9	140.9	0
67	141.9	141.9	-2.8421709430404e-14
68	142.9	142.9	5.6843418860808e-14
69	143.9	143.9	0
70	144.9	144.9	-5.6843418860808e-14
71	145.9	145.9	5.6843418860808e-14
72	146.9	146.9	0
73	147.9	147.9	-5.6843418860808e-14
74	148.9	148.9	2.8421709430404e-14
75	149.9	149.9	2.8421709430404e-14
76	150.9	150.9	-2.8421709430404e-14
77	151.9	151.9	0
78	152.9	152.9	0
79	153.9	153.9	-2.8421709430404e-14
80	154.9	154.9	5.6843418860808e-14
81	155.9	155.9	0
82	156.9	156.9	-5.6843418860808e-14
83	157.9	157.9	5.6843418860808e-14
84	158.9	158.9	0
85	159.9	159.9	-5.6843418860808e-14
86	160.9	160.9	2.8421709430404e-14
87	161.9	161.9	2.8421709430404e-14
88	162.9	162.9	-2.8421709430404e-14
89	163.9	163.9	0
90	164.9	164.9	0
91	165.9	165.9	-2.8421709430404e-14
92	166.9	166.9	5.6843418860808e-14
93	167.9	167.9	0
94	168.9	168.9	-5.6843418860808e-14
95	169.9	169.9	5.6843418860808e-14
96	170.9	170.9	0
97	171.9	171.9	-5.6843418860808e-14
98	172.9	172.9	2.8421709430404e-14
99	173.9	173.9	2.8421709430404e-14
100	174.9	174.9	-2.8421709430404e-14
101	175.9	175.9	0
102	176.9	176.9	0
103	177.9	177.9	-2.8421709430404e-14
104	178.9	178.9	5.6843418860808e-14
105	179.9	179.9	0
106	180.9	180.9	-5.6843418860808e-14
107	181.9	181.9	5.6843418860808e-14
108	182.9	182.9	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	183.9	182.699772080911	185.100227919089
110	184.9	183.202621398886	186.597378601114
111	185.9	183.821144263476	187.978855736525
112	186.9	184.499544161822	189.300455838178
113	187.9	185.216208784424	190.583791215576
114	188.9	185.96005402319	191.83994597681
115	189.9	186.724495409494	193.075504590506
116	190.9	187.505242797772	194.294757202229
117	191.9	188.299316242734	195.500683757266
118	192.9	189.104546064355	196.695453935645
119	193.9	189.919294329473	197.880705670527
120	194.9	190.742288526951	199.057711473049

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 183.9 & 182.699772080911 & 185.100227919089 \tabularnewline
110 & 184.9 & 183.202621398886 & 186.597378601114 \tabularnewline
111 & 185.9 & 183.821144263476 & 187.978855736525 \tabularnewline
112 & 186.9 & 184.499544161822 & 189.300455838178 \tabularnewline
113 & 187.9 & 185.216208784424 & 190.583791215576 \tabularnewline
114 & 188.9 & 185.96005402319 & 191.83994597681 \tabularnewline
115 & 189.9 & 186.724495409494 & 193.075504590506 \tabularnewline
116 & 190.9 & 187.505242797772 & 194.294757202229 \tabularnewline
117 & 191.9 & 188.299316242734 & 195.500683757266 \tabularnewline
118 & 192.9 & 189.104546064355 & 196.695453935645 \tabularnewline
119 & 193.9 & 189.919294329473 & 197.880705670527 \tabularnewline
120 & 194.9 & 190.742288526951 & 199.057711473049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72675&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]109[/C][C]183.9[/C][C]182.699772080911[/C][C]185.100227919089[/C][/ROW]
[ROW][C]110[/C][C]184.9[/C][C]183.202621398886[/C][C]186.597378601114[/C][/ROW]
[ROW][C]111[/C][C]185.9[/C][C]183.821144263476[/C][C]187.978855736525[/C][/ROW]
[ROW][C]112[/C][C]186.9[/C][C]184.499544161822[/C][C]189.300455838178[/C][/ROW]
[ROW][C]113[/C][C]187.9[/C][C]185.216208784424[/C][C]190.583791215576[/C][/ROW]
[ROW][C]114[/C][C]188.9[/C][C]185.96005402319[/C][C]191.83994597681[/C][/ROW]
[ROW][C]115[/C][C]189.9[/C][C]186.724495409494[/C][C]193.075504590506[/C][/ROW]
[ROW][C]116[/C][C]190.9[/C][C]187.505242797772[/C][C]194.294757202229[/C][/ROW]
[ROW][C]117[/C][C]191.9[/C][C]188.299316242734[/C][C]195.500683757266[/C][/ROW]
[ROW][C]118[/C][C]192.9[/C][C]189.104546064355[/C][C]196.695453935645[/C][/ROW]
[ROW][C]119[/C][C]193.9[/C][C]189.919294329473[/C][C]197.880705670527[/C][/ROW]
[ROW][C]120[/C][C]194.9[/C][C]190.742288526951[/C][C]199.057711473049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72675&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72675&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
109	183.9	182.699772080911	185.100227919089
110	184.9	183.202621398886	186.597378601114
111	185.9	183.821144263476	187.978855736525
112	186.9	184.499544161822	189.300455838178
113	187.9	185.216208784424	190.583791215576
114	188.9	185.96005402319	191.83994597681
115	189.9	186.724495409494	193.075504590506
116	190.9	187.505242797772	194.294757202229
117	191.9	188.299316242734	195.500683757266
118	192.9	189.104546064355	196.695453935645
119	193.9	189.919294329473	197.880705670527
120	194.9	190.742288526951	199.057711473049

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