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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, 05 Aug 2014 15:43:00 +0100

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/Aug/05/t14072498077yahayoqial6wqz.htm/, Retrieved Thu, 16 May 2024 07:23:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235413, Retrieved Thu, 16 May 2024 07:23:51 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Ines Van Dessel

Estimated Impact

124

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

-     [Histogram] [Tijdreeks 1 - Stap 3] [2014-08-03 19:11:32] [ae3d1feb555b13e324db089723206180]
- R P   [Histogram] [Tijdreeks 1 - Stap 5] [2014-08-04 09:44:37] [74be16979710d4c4e7c6647856088456]
-   P     [Histogram] [Tijdreeks 1 - Stap 5] [2014-08-04 09:47:49] [74be16979710d4c4e7c6647856088456]
- RMP       [(Partial) Autocorrelation Function] [Tijdreeks 1 - Sta...] [2014-08-04 16:49:46] [ae3d1feb555b13e324db089723206180]
- R P         [(Partial) Autocorrelation Function] [Tijdreeks 1 - Sta...] [2014-08-05 08:15:03] [74be16979710d4c4e7c6647856088456]
- RMPD          [Harrell-Davis Quantiles] [Tijdreeks 2 - Stap 6] [2014-08-05 08:50:48] [ae3d1feb555b13e324db089723206180]
- RMP             [(Partial) Autocorrelation Function] [Tijdreeks 2 - Sta...] [2014-08-05 13:41:38] [ae3d1feb555b13e324db089723206180]
- RM                  [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2014-08-05 14:43:00] [188bf81caccb86647293be436f272d1b] [Current]

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Dataseries X:

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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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235413&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235413&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235413&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235413&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235413&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235413&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
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	307	303.895032051282	3.10496794871784
14	253	250.406541375292	2.59345862470849
15	380	379.584717365967	0.415282634032508
16	320	319.55456002331	0.445439976689897
17	353	352.774402680653	0.225597319347116
18	353	352.160912004662	0.839087995337763
19	387	342.255754662005	44.7442453379952
20	280	331.850597319347	-51.8505973193475
21	387	388.07043997669	-1.07043997669018
22	307	309.165282634033	-2.16528263403285
23	347	354.593458624709	-7.59345862470877
24	427	406.063301282051	20.9366987179485
25	253	306.638111888112	-53.638111888112
26	240	252.638111888112	-12.638111888112
27	407	379.638111888112	27.361888111888
28	293	319.638111888112	-26.638111888112
29	347	352.638111888112	-5.63811188811201
30	360	352.638111888112	7.36188811188799
31	387	386.638111888112	0.361888111887993
32	240	279.638111888112	-39.638111888112
33	333	386.638111888112	-53.638111888112
34	353	306.638111888112	46.361888111888
35	313	346.638111888112	-33.638111888112
36	440	426.638111888112	13.361888111888
37	273	252.638111888112	20.361888111888
38	240	239.638111888112	0.361888111887993
39	407	406.638111888112	0.361888111887993
40	240	292.638111888112	-52.638111888112
41	360	346.638111888112	13.361888111888
42	373	359.638111888112	13.361888111888
43	387	386.638111888112	0.361888111887993
44	320	239.638111888112	80.361888111888
45	373	332.638111888112	40.361888111888
46	373	352.638111888112	20.361888111888
47	260	312.638111888112	-52.638111888112
48	420	439.638111888112	-19.638111888112
49	253	272.638111888112	-19.638111888112
50	293	239.638111888112	53.361888111888
51	413	406.638111888112	6.36188811188799
52	207	239.638111888112	-32.638111888112
53	333	359.638111888112	-26.638111888112
54	440	372.638111888112	67.361888111888
55	280	386.638111888112	-106.638111888112
56	367	319.638111888112	47.361888111888
57	380	372.638111888112	7.36188811188799
58	373	372.638111888112	0.361888111887993
59	193	259.638111888112	-66.638111888112
60	373	419.638111888112	-46.638111888112
61	213	252.638111888112	-39.638111888112
62	293	292.638111888112	0.361888111887993
63	407	412.638111888112	-5.63811188811201
64	167	206.638111888112	-39.638111888112
65	340	332.638111888112	7.36188811188799
66	447	439.638111888112	7.36188811188799
67	233	279.638111888112	-46.638111888112
68	393	366.638111888112	26.361888111888
69	333	379.638111888112	-46.638111888112
70	353	372.638111888112	-19.638111888112
71	200	192.638111888112	7.36188811188799
72	413	372.638111888112	40.361888111888
73	187	212.638111888112	-25.638111888112
74	300	292.638111888112	7.36188811188799
75	413	406.638111888112	6.36188811188799
76	213	166.638111888112	46.361888111888
77	373	339.638111888112	33.361888111888
78	453	446.638111888112	6.36188811188799
79	247	232.638111888112	14.361888111888
80	447	392.638111888112	54.361888111888
81	340	332.638111888112	7.36188811188799
82	320	352.638111888112	-32.638111888112
83	187	199.638111888112	-12.638111888112
84	380	412.638111888112	-32.638111888112
85	160	186.638111888112	-26.638111888112
86	307	299.638111888112	7.36188811188799
87	400	412.638111888112	-12.638111888112
88	213	212.638111888112	0.361888111887993
89	380	372.638111888112	7.36188811188799
90	453	452.638111888112	0.361888111887993
91	260	246.638111888112	13.361888111888
92	467	446.638111888112	20.361888111888
93	380	339.638111888112	40.361888111888
94	300	319.638111888112	-19.638111888112
95	180	186.638111888112	-6.63811188811201
96	427	379.638111888112	47.361888111888
97	153	159.638111888112	-6.63811188811201
98	327	306.638111888112	20.361888111888
99	393	399.638111888112	-6.63811188811201
100	207	212.638111888112	-5.63811188811201
101	380	379.638111888112	0.361888111887993
102	440	452.638111888112	-12.638111888112
103	247	259.638111888112	-12.638111888112
104	400	466.638111888112	-66.638111888112
105	360	379.638111888112	-19.638111888112
106	340	299.638111888112	40.361888111888
107	220	179.638111888112	40.361888111888
108	393	426.638111888112	-33.638111888112

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 307 & 303.895032051282 & 3.10496794871784 \tabularnewline
14 & 253 & 250.406541375292 & 2.59345862470849 \tabularnewline
15 & 380 & 379.584717365967 & 0.415282634032508 \tabularnewline
16 & 320 & 319.55456002331 & 0.445439976689897 \tabularnewline
17 & 353 & 352.774402680653 & 0.225597319347116 \tabularnewline
18 & 353 & 352.160912004662 & 0.839087995337763 \tabularnewline
19 & 387 & 342.255754662005 & 44.7442453379952 \tabularnewline
20 & 280 & 331.850597319347 & -51.8505973193475 \tabularnewline
21 & 387 & 388.07043997669 & -1.07043997669018 \tabularnewline
22 & 307 & 309.165282634033 & -2.16528263403285 \tabularnewline
23 & 347 & 354.593458624709 & -7.59345862470877 \tabularnewline
24 & 427 & 406.063301282051 & 20.9366987179485 \tabularnewline
25 & 253 & 306.638111888112 & -53.638111888112 \tabularnewline
26 & 240 & 252.638111888112 & -12.638111888112 \tabularnewline
27 & 407 & 379.638111888112 & 27.361888111888 \tabularnewline
28 & 293 & 319.638111888112 & -26.638111888112 \tabularnewline
29 & 347 & 352.638111888112 & -5.63811188811201 \tabularnewline
30 & 360 & 352.638111888112 & 7.36188811188799 \tabularnewline
31 & 387 & 386.638111888112 & 0.361888111887993 \tabularnewline
32 & 240 & 279.638111888112 & -39.638111888112 \tabularnewline
33 & 333 & 386.638111888112 & -53.638111888112 \tabularnewline
34 & 353 & 306.638111888112 & 46.361888111888 \tabularnewline
35 & 313 & 346.638111888112 & -33.638111888112 \tabularnewline
36 & 440 & 426.638111888112 & 13.361888111888 \tabularnewline
37 & 273 & 252.638111888112 & 20.361888111888 \tabularnewline
38 & 240 & 239.638111888112 & 0.361888111887993 \tabularnewline
39 & 407 & 406.638111888112 & 0.361888111887993 \tabularnewline
40 & 240 & 292.638111888112 & -52.638111888112 \tabularnewline
41 & 360 & 346.638111888112 & 13.361888111888 \tabularnewline
42 & 373 & 359.638111888112 & 13.361888111888 \tabularnewline
43 & 387 & 386.638111888112 & 0.361888111887993 \tabularnewline
44 & 320 & 239.638111888112 & 80.361888111888 \tabularnewline
45 & 373 & 332.638111888112 & 40.361888111888 \tabularnewline
46 & 373 & 352.638111888112 & 20.361888111888 \tabularnewline
47 & 260 & 312.638111888112 & -52.638111888112 \tabularnewline
48 & 420 & 439.638111888112 & -19.638111888112 \tabularnewline
49 & 253 & 272.638111888112 & -19.638111888112 \tabularnewline
50 & 293 & 239.638111888112 & 53.361888111888 \tabularnewline
51 & 413 & 406.638111888112 & 6.36188811188799 \tabularnewline
52 & 207 & 239.638111888112 & -32.638111888112 \tabularnewline
53 & 333 & 359.638111888112 & -26.638111888112 \tabularnewline
54 & 440 & 372.638111888112 & 67.361888111888 \tabularnewline
55 & 280 & 386.638111888112 & -106.638111888112 \tabularnewline
56 & 367 & 319.638111888112 & 47.361888111888 \tabularnewline
57 & 380 & 372.638111888112 & 7.36188811188799 \tabularnewline
58 & 373 & 372.638111888112 & 0.361888111887993 \tabularnewline
59 & 193 & 259.638111888112 & -66.638111888112 \tabularnewline
60 & 373 & 419.638111888112 & -46.638111888112 \tabularnewline
61 & 213 & 252.638111888112 & -39.638111888112 \tabularnewline
62 & 293 & 292.638111888112 & 0.361888111887993 \tabularnewline
63 & 407 & 412.638111888112 & -5.63811188811201 \tabularnewline
64 & 167 & 206.638111888112 & -39.638111888112 \tabularnewline
65 & 340 & 332.638111888112 & 7.36188811188799 \tabularnewline
66 & 447 & 439.638111888112 & 7.36188811188799 \tabularnewline
67 & 233 & 279.638111888112 & -46.638111888112 \tabularnewline
68 & 393 & 366.638111888112 & 26.361888111888 \tabularnewline
69 & 333 & 379.638111888112 & -46.638111888112 \tabularnewline
70 & 353 & 372.638111888112 & -19.638111888112 \tabularnewline
71 & 200 & 192.638111888112 & 7.36188811188799 \tabularnewline
72 & 413 & 372.638111888112 & 40.361888111888 \tabularnewline
73 & 187 & 212.638111888112 & -25.638111888112 \tabularnewline
74 & 300 & 292.638111888112 & 7.36188811188799 \tabularnewline
75 & 413 & 406.638111888112 & 6.36188811188799 \tabularnewline
76 & 213 & 166.638111888112 & 46.361888111888 \tabularnewline
77 & 373 & 339.638111888112 & 33.361888111888 \tabularnewline
78 & 453 & 446.638111888112 & 6.36188811188799 \tabularnewline
79 & 247 & 232.638111888112 & 14.361888111888 \tabularnewline
80 & 447 & 392.638111888112 & 54.361888111888 \tabularnewline
81 & 340 & 332.638111888112 & 7.36188811188799 \tabularnewline
82 & 320 & 352.638111888112 & -32.638111888112 \tabularnewline
83 & 187 & 199.638111888112 & -12.638111888112 \tabularnewline
84 & 380 & 412.638111888112 & -32.638111888112 \tabularnewline
85 & 160 & 186.638111888112 & -26.638111888112 \tabularnewline
86 & 307 & 299.638111888112 & 7.36188811188799 \tabularnewline
87 & 400 & 412.638111888112 & -12.638111888112 \tabularnewline
88 & 213 & 212.638111888112 & 0.361888111887993 \tabularnewline
89 & 380 & 372.638111888112 & 7.36188811188799 \tabularnewline
90 & 453 & 452.638111888112 & 0.361888111887993 \tabularnewline
91 & 260 & 246.638111888112 & 13.361888111888 \tabularnewline
92 & 467 & 446.638111888112 & 20.361888111888 \tabularnewline
93 & 380 & 339.638111888112 & 40.361888111888 \tabularnewline
94 & 300 & 319.638111888112 & -19.638111888112 \tabularnewline
95 & 180 & 186.638111888112 & -6.63811188811201 \tabularnewline
96 & 427 & 379.638111888112 & 47.361888111888 \tabularnewline
97 & 153 & 159.638111888112 & -6.63811188811201 \tabularnewline
98 & 327 & 306.638111888112 & 20.361888111888 \tabularnewline
99 & 393 & 399.638111888112 & -6.63811188811201 \tabularnewline
100 & 207 & 212.638111888112 & -5.63811188811201 \tabularnewline
101 & 380 & 379.638111888112 & 0.361888111887993 \tabularnewline
102 & 440 & 452.638111888112 & -12.638111888112 \tabularnewline
103 & 247 & 259.638111888112 & -12.638111888112 \tabularnewline
104 & 400 & 466.638111888112 & -66.638111888112 \tabularnewline
105 & 360 & 379.638111888112 & -19.638111888112 \tabularnewline
106 & 340 & 299.638111888112 & 40.361888111888 \tabularnewline
107 & 220 & 179.638111888112 & 40.361888111888 \tabularnewline
108 & 393 & 426.638111888112 & -33.638111888112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235413&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]307[/C][C]303.895032051282[/C][C]3.10496794871784[/C][/ROW]
[ROW][C]14[/C][C]253[/C][C]250.406541375292[/C][C]2.59345862470849[/C][/ROW]
[ROW][C]15[/C][C]380[/C][C]379.584717365967[/C][C]0.415282634032508[/C][/ROW]
[ROW][C]16[/C][C]320[/C][C]319.55456002331[/C][C]0.445439976689897[/C][/ROW]
[ROW][C]17[/C][C]353[/C][C]352.774402680653[/C][C]0.225597319347116[/C][/ROW]
[ROW][C]18[/C][C]353[/C][C]352.160912004662[/C][C]0.839087995337763[/C][/ROW]
[ROW][C]19[/C][C]387[/C][C]342.255754662005[/C][C]44.7442453379952[/C][/ROW]
[ROW][C]20[/C][C]280[/C][C]331.850597319347[/C][C]-51.8505973193475[/C][/ROW]
[ROW][C]21[/C][C]387[/C][C]388.07043997669[/C][C]-1.07043997669018[/C][/ROW]
[ROW][C]22[/C][C]307[/C][C]309.165282634033[/C][C]-2.16528263403285[/C][/ROW]
[ROW][C]23[/C][C]347[/C][C]354.593458624709[/C][C]-7.59345862470877[/C][/ROW]
[ROW][C]24[/C][C]427[/C][C]406.063301282051[/C][C]20.9366987179485[/C][/ROW]
[ROW][C]25[/C][C]253[/C][C]306.638111888112[/C][C]-53.638111888112[/C][/ROW]
[ROW][C]26[/C][C]240[/C][C]252.638111888112[/C][C]-12.638111888112[/C][/ROW]
[ROW][C]27[/C][C]407[/C][C]379.638111888112[/C][C]27.361888111888[/C][/ROW]
[ROW][C]28[/C][C]293[/C][C]319.638111888112[/C][C]-26.638111888112[/C][/ROW]
[ROW][C]29[/C][C]347[/C][C]352.638111888112[/C][C]-5.63811188811201[/C][/ROW]
[ROW][C]30[/C][C]360[/C][C]352.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]31[/C][C]387[/C][C]386.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]32[/C][C]240[/C][C]279.638111888112[/C][C]-39.638111888112[/C][/ROW]
[ROW][C]33[/C][C]333[/C][C]386.638111888112[/C][C]-53.638111888112[/C][/ROW]
[ROW][C]34[/C][C]353[/C][C]306.638111888112[/C][C]46.361888111888[/C][/ROW]
[ROW][C]35[/C][C]313[/C][C]346.638111888112[/C][C]-33.638111888112[/C][/ROW]
[ROW][C]36[/C][C]440[/C][C]426.638111888112[/C][C]13.361888111888[/C][/ROW]
[ROW][C]37[/C][C]273[/C][C]252.638111888112[/C][C]20.361888111888[/C][/ROW]
[ROW][C]38[/C][C]240[/C][C]239.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]39[/C][C]407[/C][C]406.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]40[/C][C]240[/C][C]292.638111888112[/C][C]-52.638111888112[/C][/ROW]
[ROW][C]41[/C][C]360[/C][C]346.638111888112[/C][C]13.361888111888[/C][/ROW]
[ROW][C]42[/C][C]373[/C][C]359.638111888112[/C][C]13.361888111888[/C][/ROW]
[ROW][C]43[/C][C]387[/C][C]386.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]44[/C][C]320[/C][C]239.638111888112[/C][C]80.361888111888[/C][/ROW]
[ROW][C]45[/C][C]373[/C][C]332.638111888112[/C][C]40.361888111888[/C][/ROW]
[ROW][C]46[/C][C]373[/C][C]352.638111888112[/C][C]20.361888111888[/C][/ROW]
[ROW][C]47[/C][C]260[/C][C]312.638111888112[/C][C]-52.638111888112[/C][/ROW]
[ROW][C]48[/C][C]420[/C][C]439.638111888112[/C][C]-19.638111888112[/C][/ROW]
[ROW][C]49[/C][C]253[/C][C]272.638111888112[/C][C]-19.638111888112[/C][/ROW]
[ROW][C]50[/C][C]293[/C][C]239.638111888112[/C][C]53.361888111888[/C][/ROW]
[ROW][C]51[/C][C]413[/C][C]406.638111888112[/C][C]6.36188811188799[/C][/ROW]
[ROW][C]52[/C][C]207[/C][C]239.638111888112[/C][C]-32.638111888112[/C][/ROW]
[ROW][C]53[/C][C]333[/C][C]359.638111888112[/C][C]-26.638111888112[/C][/ROW]
[ROW][C]54[/C][C]440[/C][C]372.638111888112[/C][C]67.361888111888[/C][/ROW]
[ROW][C]55[/C][C]280[/C][C]386.638111888112[/C][C]-106.638111888112[/C][/ROW]
[ROW][C]56[/C][C]367[/C][C]319.638111888112[/C][C]47.361888111888[/C][/ROW]
[ROW][C]57[/C][C]380[/C][C]372.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]58[/C][C]373[/C][C]372.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]59[/C][C]193[/C][C]259.638111888112[/C][C]-66.638111888112[/C][/ROW]
[ROW][C]60[/C][C]373[/C][C]419.638111888112[/C][C]-46.638111888112[/C][/ROW]
[ROW][C]61[/C][C]213[/C][C]252.638111888112[/C][C]-39.638111888112[/C][/ROW]
[ROW][C]62[/C][C]293[/C][C]292.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]63[/C][C]407[/C][C]412.638111888112[/C][C]-5.63811188811201[/C][/ROW]
[ROW][C]64[/C][C]167[/C][C]206.638111888112[/C][C]-39.638111888112[/C][/ROW]
[ROW][C]65[/C][C]340[/C][C]332.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]66[/C][C]447[/C][C]439.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]67[/C][C]233[/C][C]279.638111888112[/C][C]-46.638111888112[/C][/ROW]
[ROW][C]68[/C][C]393[/C][C]366.638111888112[/C][C]26.361888111888[/C][/ROW]
[ROW][C]69[/C][C]333[/C][C]379.638111888112[/C][C]-46.638111888112[/C][/ROW]
[ROW][C]70[/C][C]353[/C][C]372.638111888112[/C][C]-19.638111888112[/C][/ROW]
[ROW][C]71[/C][C]200[/C][C]192.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]72[/C][C]413[/C][C]372.638111888112[/C][C]40.361888111888[/C][/ROW]
[ROW][C]73[/C][C]187[/C][C]212.638111888112[/C][C]-25.638111888112[/C][/ROW]
[ROW][C]74[/C][C]300[/C][C]292.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]75[/C][C]413[/C][C]406.638111888112[/C][C]6.36188811188799[/C][/ROW]
[ROW][C]76[/C][C]213[/C][C]166.638111888112[/C][C]46.361888111888[/C][/ROW]
[ROW][C]77[/C][C]373[/C][C]339.638111888112[/C][C]33.361888111888[/C][/ROW]
[ROW][C]78[/C][C]453[/C][C]446.638111888112[/C][C]6.36188811188799[/C][/ROW]
[ROW][C]79[/C][C]247[/C][C]232.638111888112[/C][C]14.361888111888[/C][/ROW]
[ROW][C]80[/C][C]447[/C][C]392.638111888112[/C][C]54.361888111888[/C][/ROW]
[ROW][C]81[/C][C]340[/C][C]332.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]82[/C][C]320[/C][C]352.638111888112[/C][C]-32.638111888112[/C][/ROW]
[ROW][C]83[/C][C]187[/C][C]199.638111888112[/C][C]-12.638111888112[/C][/ROW]
[ROW][C]84[/C][C]380[/C][C]412.638111888112[/C][C]-32.638111888112[/C][/ROW]
[ROW][C]85[/C][C]160[/C][C]186.638111888112[/C][C]-26.638111888112[/C][/ROW]
[ROW][C]86[/C][C]307[/C][C]299.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]87[/C][C]400[/C][C]412.638111888112[/C][C]-12.638111888112[/C][/ROW]
[ROW][C]88[/C][C]213[/C][C]212.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]89[/C][C]380[/C][C]372.638111888112[/C][C]7.36188811188799[/C][/ROW]
[ROW][C]90[/C][C]453[/C][C]452.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]91[/C][C]260[/C][C]246.638111888112[/C][C]13.361888111888[/C][/ROW]
[ROW][C]92[/C][C]467[/C][C]446.638111888112[/C][C]20.361888111888[/C][/ROW]
[ROW][C]93[/C][C]380[/C][C]339.638111888112[/C][C]40.361888111888[/C][/ROW]
[ROW][C]94[/C][C]300[/C][C]319.638111888112[/C][C]-19.638111888112[/C][/ROW]
[ROW][C]95[/C][C]180[/C][C]186.638111888112[/C][C]-6.63811188811201[/C][/ROW]
[ROW][C]96[/C][C]427[/C][C]379.638111888112[/C][C]47.361888111888[/C][/ROW]
[ROW][C]97[/C][C]153[/C][C]159.638111888112[/C][C]-6.63811188811201[/C][/ROW]
[ROW][C]98[/C][C]327[/C][C]306.638111888112[/C][C]20.361888111888[/C][/ROW]
[ROW][C]99[/C][C]393[/C][C]399.638111888112[/C][C]-6.63811188811201[/C][/ROW]
[ROW][C]100[/C][C]207[/C][C]212.638111888112[/C][C]-5.63811188811201[/C][/ROW]
[ROW][C]101[/C][C]380[/C][C]379.638111888112[/C][C]0.361888111887993[/C][/ROW]
[ROW][C]102[/C][C]440[/C][C]452.638111888112[/C][C]-12.638111888112[/C][/ROW]
[ROW][C]103[/C][C]247[/C][C]259.638111888112[/C][C]-12.638111888112[/C][/ROW]
[ROW][C]104[/C][C]400[/C][C]466.638111888112[/C][C]-66.638111888112[/C][/ROW]
[ROW][C]105[/C][C]360[/C][C]379.638111888112[/C][C]-19.638111888112[/C][/ROW]
[ROW][C]106[/C][C]340[/C][C]299.638111888112[/C][C]40.361888111888[/C][/ROW]
[ROW][C]107[/C][C]220[/C][C]179.638111888112[/C][C]40.361888111888[/C][/ROW]
[ROW][C]108[/C][C]393[/C][C]426.638111888112[/C][C]-33.638111888112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235413&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235413&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	307	303.895032051282	3.10496794871784
14	253	250.406541375292	2.59345862470849
15	380	379.584717365967	0.415282634032508
16	320	319.55456002331	0.445439976689897
17	353	352.774402680653	0.225597319347116
18	353	352.160912004662	0.839087995337763
19	387	342.255754662005	44.7442453379952
20	280	331.850597319347	-51.8505973193475
21	387	388.07043997669	-1.07043997669018
22	307	309.165282634033	-2.16528263403285
23	347	354.593458624709	-7.59345862470877
24	427	406.063301282051	20.9366987179485
25	253	306.638111888112	-53.638111888112
26	240	252.638111888112	-12.638111888112
27	407	379.638111888112	27.361888111888
28	293	319.638111888112	-26.638111888112
29	347	352.638111888112	-5.63811188811201
30	360	352.638111888112	7.36188811188799
31	387	386.638111888112	0.361888111887993
32	240	279.638111888112	-39.638111888112
33	333	386.638111888112	-53.638111888112
34	353	306.638111888112	46.361888111888
35	313	346.638111888112	-33.638111888112
36	440	426.638111888112	13.361888111888
37	273	252.638111888112	20.361888111888
38	240	239.638111888112	0.361888111887993
39	407	406.638111888112	0.361888111887993
40	240	292.638111888112	-52.638111888112
41	360	346.638111888112	13.361888111888
42	373	359.638111888112	13.361888111888
43	387	386.638111888112	0.361888111887993
44	320	239.638111888112	80.361888111888
45	373	332.638111888112	40.361888111888
46	373	352.638111888112	20.361888111888
47	260	312.638111888112	-52.638111888112
48	420	439.638111888112	-19.638111888112
49	253	272.638111888112	-19.638111888112
50	293	239.638111888112	53.361888111888
51	413	406.638111888112	6.36188811188799
52	207	239.638111888112	-32.638111888112
53	333	359.638111888112	-26.638111888112
54	440	372.638111888112	67.361888111888
55	280	386.638111888112	-106.638111888112
56	367	319.638111888112	47.361888111888
57	380	372.638111888112	7.36188811188799
58	373	372.638111888112	0.361888111887993
59	193	259.638111888112	-66.638111888112
60	373	419.638111888112	-46.638111888112
61	213	252.638111888112	-39.638111888112
62	293	292.638111888112	0.361888111887993
63	407	412.638111888112	-5.63811188811201
64	167	206.638111888112	-39.638111888112
65	340	332.638111888112	7.36188811188799
66	447	439.638111888112	7.36188811188799
67	233	279.638111888112	-46.638111888112
68	393	366.638111888112	26.361888111888
69	333	379.638111888112	-46.638111888112
70	353	372.638111888112	-19.638111888112
71	200	192.638111888112	7.36188811188799
72	413	372.638111888112	40.361888111888
73	187	212.638111888112	-25.638111888112
74	300	292.638111888112	7.36188811188799
75	413	406.638111888112	6.36188811188799
76	213	166.638111888112	46.361888111888
77	373	339.638111888112	33.361888111888
78	453	446.638111888112	6.36188811188799
79	247	232.638111888112	14.361888111888
80	447	392.638111888112	54.361888111888
81	340	332.638111888112	7.36188811188799
82	320	352.638111888112	-32.638111888112
83	187	199.638111888112	-12.638111888112
84	380	412.638111888112	-32.638111888112
85	160	186.638111888112	-26.638111888112
86	307	299.638111888112	7.36188811188799
87	400	412.638111888112	-12.638111888112
88	213	212.638111888112	0.361888111887993
89	380	372.638111888112	7.36188811188799
90	453	452.638111888112	0.361888111887993
91	260	246.638111888112	13.361888111888
92	467	446.638111888112	20.361888111888
93	380	339.638111888112	40.361888111888
94	300	319.638111888112	-19.638111888112
95	180	186.638111888112	-6.63811188811201
96	427	379.638111888112	47.361888111888
97	153	159.638111888112	-6.63811188811201
98	327	306.638111888112	20.361888111888
99	393	399.638111888112	-6.63811188811201
100	207	212.638111888112	-5.63811188811201
101	380	379.638111888112	0.361888111887993
102	440	452.638111888112	-12.638111888112
103	247	259.638111888112	-12.638111888112
104	400	466.638111888112	-66.638111888112
105	360	379.638111888112	-19.638111888112
106	340	299.638111888112	40.361888111888
107	220	179.638111888112	40.361888111888
108	393	426.638111888112	-33.638111888112

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	152.638111888112	89.6057871026835	215.670436673541
110	326.638111888112	263.605787102683	389.67043667354
111	392.638111888112	329.605787102683	455.67043667354
112	206.638111888112	143.605787102683	269.67043667354
113	379.638111888112	316.605787102683	442.67043667354
114	439.638111888112	376.605787102683	502.67043667354
115	246.638111888112	183.605787102683	309.67043667354
116	399.638111888112	336.605787102683	462.67043667354
117	359.638111888112	296.605787102683	422.67043667354
118	339.638111888112	276.605787102683	402.67043667354
119	219.638111888112	156.605787102683	282.67043667354
120	392.638111888112	329.605787102683	455.67043667354

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 152.638111888112 & 89.6057871026835 & 215.670436673541 \tabularnewline
110 & 326.638111888112 & 263.605787102683 & 389.67043667354 \tabularnewline
111 & 392.638111888112 & 329.605787102683 & 455.67043667354 \tabularnewline
112 & 206.638111888112 & 143.605787102683 & 269.67043667354 \tabularnewline
113 & 379.638111888112 & 316.605787102683 & 442.67043667354 \tabularnewline
114 & 439.638111888112 & 376.605787102683 & 502.67043667354 \tabularnewline
115 & 246.638111888112 & 183.605787102683 & 309.67043667354 \tabularnewline
116 & 399.638111888112 & 336.605787102683 & 462.67043667354 \tabularnewline
117 & 359.638111888112 & 296.605787102683 & 422.67043667354 \tabularnewline
118 & 339.638111888112 & 276.605787102683 & 402.67043667354 \tabularnewline
119 & 219.638111888112 & 156.605787102683 & 282.67043667354 \tabularnewline
120 & 392.638111888112 & 329.605787102683 & 455.67043667354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235413&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]152.638111888112[/C][C]89.6057871026835[/C][C]215.670436673541[/C][/ROW]
[ROW][C]110[/C][C]326.638111888112[/C][C]263.605787102683[/C][C]389.67043667354[/C][/ROW]
[ROW][C]111[/C][C]392.638111888112[/C][C]329.605787102683[/C][C]455.67043667354[/C][/ROW]
[ROW][C]112[/C][C]206.638111888112[/C][C]143.605787102683[/C][C]269.67043667354[/C][/ROW]
[ROW][C]113[/C][C]379.638111888112[/C][C]316.605787102683[/C][C]442.67043667354[/C][/ROW]
[ROW][C]114[/C][C]439.638111888112[/C][C]376.605787102683[/C][C]502.67043667354[/C][/ROW]
[ROW][C]115[/C][C]246.638111888112[/C][C]183.605787102683[/C][C]309.67043667354[/C][/ROW]
[ROW][C]116[/C][C]399.638111888112[/C][C]336.605787102683[/C][C]462.67043667354[/C][/ROW]
[ROW][C]117[/C][C]359.638111888112[/C][C]296.605787102683[/C][C]422.67043667354[/C][/ROW]
[ROW][C]118[/C][C]339.638111888112[/C][C]276.605787102683[/C][C]402.67043667354[/C][/ROW]
[ROW][C]119[/C][C]219.638111888112[/C][C]156.605787102683[/C][C]282.67043667354[/C][/ROW]
[ROW][C]120[/C][C]392.638111888112[/C][C]329.605787102683[/C][C]455.67043667354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235413&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235413&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	152.638111888112	89.6057871026835	215.670436673541
110	326.638111888112	263.605787102683	389.67043667354
111	392.638111888112	329.605787102683	455.67043667354
112	206.638111888112	143.605787102683	269.67043667354
113	379.638111888112	316.605787102683	442.67043667354
114	439.638111888112	376.605787102683	502.67043667354
115	246.638111888112	183.605787102683	309.67043667354
116	399.638111888112	336.605787102683	462.67043667354
117	359.638111888112	296.605787102683	422.67043667354
118	339.638111888112	276.605787102683	402.67043667354
119	219.638111888112	156.605787102683	282.67043667354
120	392.638111888112	329.605787102683	455.67043667354

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):

Parameters (R input):

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

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

par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
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