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

Fri, 28 Nov 2014 20:18:19 +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/2014/Nov/28/t1417206575bokebnmahyfws89.htm/, Retrieved Sun, 19 May 2024 22:00:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261022, Retrieved Sun, 19 May 2024 22:00:13 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [] [2014-11-28 20:18:19] [39f63263aa230394eb25f176f7b01700] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

2,04
2,08
1,94
1,91
1,34
1,3
1,39
1,23
1,3
1,79
2,25
2,63
2,8
3,08
3,89
3,68
4,62
5,07
5,22
4,94
5,14
4,8
3,89
3,54
3,34
2,8
1,6
1,56
0,68
-0,11
-0,66
-0,2
-0,62
-0,59
-0,3
-0,26
-0,08
0,13
0,94
1,05
1,59
2,03
2,15
2,05
2,56
2,54
2,53
2,6
2,71
2,82
2,92
2,87
2,89
3,27
3,32
3,14
3,04
3,09
3,39
3,24
3,38
3,41
3,14
2,96
2,74
2,21
2,24
2,56
2,39
2,49
2,17
2,16
1,48
1,09
1,25
1,27
1,39
1,69
1,55
1,19
1,08
0,94
0,98
1,01

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261022&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261022&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261022&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999918735964482
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999918735964482 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261022&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]0.999918735964482[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261022&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261022&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	0.999918735964482
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	2.08	2.04	0.04
3	1.94	2.07999674943858	-0.139996749438579
4	1.91	1.94001137670082	-0.030011376700819
5	1.34	1.91000243884558	-0.570002438845582
6	1.3	1.34004632069844	-0.0400463206984356
7	1.39	1.30000325432563	0.0899967456743722
8	1.23	1.38999268650126	-0.159992686501263
9	1.3	1.23001300165136	0.0699869983486416
10	1.79	1.29999431257408	0.49000568742592
11	2.25	1.78996018016041	0.460039819839587
12	2.63	2.24996261530774	0.380037384692259
13	2.8	2.62996911662847	0.170030883371528
14	3.08	2.79998618260425	0.280013817395746
15	3.89	3.0799772449472	0.810022755052802
16	3.68	3.88993417428206	-0.209934174282063
17	4.62	3.6800170600982	0.939982939901805
18	5.07	4.61992361319299	0.450076386807015
19	5.22	5.06996342497652	0.150036575023482
20	4.94	5.21998780742244	-0.279987807422438
21	5.14	4.94002275293913	0.199977247060873
22	4.8	5.13998374904189	-0.339983749041892
23	3.89	4.80002762845146	-0.910027628451457
24	3.54	3.89007395251752	-0.350073952517521
25	3.34	3.54002844842211	-0.200028448422112
26	2.8	3.34001625511894	-0.540016255118938
27	1.6	2.80004388390014	-1.20004388390014
28	1.56	1.6000975204088	-0.0400975204088045
29	0.68	1.56000325848632	-0.880003258486323
30	-0.11	0.680071512616054	-0.790071512616054
31	-0.66	-0.109935795600537	-0.550064204399463
32	-0.2	-0.659955299562957	0.459955299562956
33	-0.62	-0.2000373778238	-0.4199626221762
34	-0.59	-0.619965872142555	0.0299658721425553
35	-0.3	-0.590002435147698	0.290002435147698
36	-0.26	-0.30002356676819	0.0400235667681901
37	-0.08	-0.260003252476551	0.180003252476551
38	0.13	-0.0800146277907026	0.210014627790703
39	0.94	0.129982933363828	0.810017066636172
40	1.05	0.939934174744327	0.110065825255673
41	1.59	1.04999105560687	0.540008944393133
42	2.03	1.58995611669396	0.440043883306037
43	2.15	2.02996424025824	0.120035759741763
44	2.05	2.14999024540976	-0.099990245409757
45	2.56	2.05000812561085	0.509991874389145
46	2.54	2.55995855600221	-0.019958556002206
47	2.53	2.5400016219128	-0.0100016219128043
48	2.6	2.53000081277216	0.0699991872278418
49	2.71	2.59999431158356	0.110005688416437
50	2.82	2.70999106049383	0.110008939506171
51	2.92	2.81999106022963	0.100008939770367
52	2.87	2.91999187286997	-0.0499918728699664
53	2.89	2.87000406254133	0.0199959374586673
54	3.27	2.88999837504943	0.380001624950572
55	3.32	3.26996911953445	0.0500308804655467
56	3.14	3.31999593428875	-0.179995934288752
57	3.04	3.140014627196	-0.100014627195997
58	3.09	3.04000812759222	0.0499918724077832
59	3.39	3.0899959374587	0.300004062541295
60	3.24	3.38997562045921	-0.149975620459206
61	3.38	3.24001218762415	0.139987812375852
62	3.41	3.37998862402544	0.0300113759745573
63	3.14	3.40999756115448	-0.269997561154477
64	2.96	3.1400219410914	-0.180021941091399
65	2.74	2.96001462930941	-0.220014629309414
66	2.21	2.74001787927665	-0.530017879276651
67	2.24	2.21004307139177	0.0299569286082337
68	2.56	2.23999756557909	0.32000243442091
69	2.39	2.5599739953108	-0.169973995310803
70	2.49	2.39001381277279	0.0999861872272083
71	2.17	2.48999187471893	-0.319991874718931
72	2.16	2.17002600383107	-0.0100260038310727
73	1.48	2.16000081475353	-0.680000814753531
74	1.09	1.48005525961036	-0.390055259610362
75	1.25	1.09003169746447	0.159968302535529
76	1.27	1.24998700033018	0.0200129996698191
77	1.39	1.26999837366288	0.120001626337116
78	1.69	1.38999024818357	0.300009751816425
79	1.55	1.68997561999687	-0.139975619996872
80	1.19	1.55001137498376	-0.360011374983755
81	1.08	1.19002925597716	-0.110029255977163
82	0.94	1.08000894142137	-0.140008941421366
83	0.98	0.940011377691588	0.0399886223084116
84	1.01	0.979996750363176	0.0300032496368237

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.08 & 2.04 & 0.04 \tabularnewline
3 & 1.94 & 2.07999674943858 & -0.139996749438579 \tabularnewline
4 & 1.91 & 1.94001137670082 & -0.030011376700819 \tabularnewline
5 & 1.34 & 1.91000243884558 & -0.570002438845582 \tabularnewline
6 & 1.3 & 1.34004632069844 & -0.0400463206984356 \tabularnewline
7 & 1.39 & 1.30000325432563 & 0.0899967456743722 \tabularnewline
8 & 1.23 & 1.38999268650126 & -0.159992686501263 \tabularnewline
9 & 1.3 & 1.23001300165136 & 0.0699869983486416 \tabularnewline
10 & 1.79 & 1.29999431257408 & 0.49000568742592 \tabularnewline
11 & 2.25 & 1.78996018016041 & 0.460039819839587 \tabularnewline
12 & 2.63 & 2.24996261530774 & 0.380037384692259 \tabularnewline
13 & 2.8 & 2.62996911662847 & 0.170030883371528 \tabularnewline
14 & 3.08 & 2.79998618260425 & 0.280013817395746 \tabularnewline
15 & 3.89 & 3.0799772449472 & 0.810022755052802 \tabularnewline
16 & 3.68 & 3.88993417428206 & -0.209934174282063 \tabularnewline
17 & 4.62 & 3.6800170600982 & 0.939982939901805 \tabularnewline
18 & 5.07 & 4.61992361319299 & 0.450076386807015 \tabularnewline
19 & 5.22 & 5.06996342497652 & 0.150036575023482 \tabularnewline
20 & 4.94 & 5.21998780742244 & -0.279987807422438 \tabularnewline
21 & 5.14 & 4.94002275293913 & 0.199977247060873 \tabularnewline
22 & 4.8 & 5.13998374904189 & -0.339983749041892 \tabularnewline
23 & 3.89 & 4.80002762845146 & -0.910027628451457 \tabularnewline
24 & 3.54 & 3.89007395251752 & -0.350073952517521 \tabularnewline
25 & 3.34 & 3.54002844842211 & -0.200028448422112 \tabularnewline
26 & 2.8 & 3.34001625511894 & -0.540016255118938 \tabularnewline
27 & 1.6 & 2.80004388390014 & -1.20004388390014 \tabularnewline
28 & 1.56 & 1.6000975204088 & -0.0400975204088045 \tabularnewline
29 & 0.68 & 1.56000325848632 & -0.880003258486323 \tabularnewline
30 & -0.11 & 0.680071512616054 & -0.790071512616054 \tabularnewline
31 & -0.66 & -0.109935795600537 & -0.550064204399463 \tabularnewline
32 & -0.2 & -0.659955299562957 & 0.459955299562956 \tabularnewline
33 & -0.62 & -0.2000373778238 & -0.4199626221762 \tabularnewline
34 & -0.59 & -0.619965872142555 & 0.0299658721425553 \tabularnewline
35 & -0.3 & -0.590002435147698 & 0.290002435147698 \tabularnewline
36 & -0.26 & -0.30002356676819 & 0.0400235667681901 \tabularnewline
37 & -0.08 & -0.260003252476551 & 0.180003252476551 \tabularnewline
38 & 0.13 & -0.0800146277907026 & 0.210014627790703 \tabularnewline
39 & 0.94 & 0.129982933363828 & 0.810017066636172 \tabularnewline
40 & 1.05 & 0.939934174744327 & 0.110065825255673 \tabularnewline
41 & 1.59 & 1.04999105560687 & 0.540008944393133 \tabularnewline
42 & 2.03 & 1.58995611669396 & 0.440043883306037 \tabularnewline
43 & 2.15 & 2.02996424025824 & 0.120035759741763 \tabularnewline
44 & 2.05 & 2.14999024540976 & -0.099990245409757 \tabularnewline
45 & 2.56 & 2.05000812561085 & 0.509991874389145 \tabularnewline
46 & 2.54 & 2.55995855600221 & -0.019958556002206 \tabularnewline
47 & 2.53 & 2.5400016219128 & -0.0100016219128043 \tabularnewline
48 & 2.6 & 2.53000081277216 & 0.0699991872278418 \tabularnewline
49 & 2.71 & 2.59999431158356 & 0.110005688416437 \tabularnewline
50 & 2.82 & 2.70999106049383 & 0.110008939506171 \tabularnewline
51 & 2.92 & 2.81999106022963 & 0.100008939770367 \tabularnewline
52 & 2.87 & 2.91999187286997 & -0.0499918728699664 \tabularnewline
53 & 2.89 & 2.87000406254133 & 0.0199959374586673 \tabularnewline
54 & 3.27 & 2.88999837504943 & 0.380001624950572 \tabularnewline
55 & 3.32 & 3.26996911953445 & 0.0500308804655467 \tabularnewline
56 & 3.14 & 3.31999593428875 & -0.179995934288752 \tabularnewline
57 & 3.04 & 3.140014627196 & -0.100014627195997 \tabularnewline
58 & 3.09 & 3.04000812759222 & 0.0499918724077832 \tabularnewline
59 & 3.39 & 3.0899959374587 & 0.300004062541295 \tabularnewline
60 & 3.24 & 3.38997562045921 & -0.149975620459206 \tabularnewline
61 & 3.38 & 3.24001218762415 & 0.139987812375852 \tabularnewline
62 & 3.41 & 3.37998862402544 & 0.0300113759745573 \tabularnewline
63 & 3.14 & 3.40999756115448 & -0.269997561154477 \tabularnewline
64 & 2.96 & 3.1400219410914 & -0.180021941091399 \tabularnewline
65 & 2.74 & 2.96001462930941 & -0.220014629309414 \tabularnewline
66 & 2.21 & 2.74001787927665 & -0.530017879276651 \tabularnewline
67 & 2.24 & 2.21004307139177 & 0.0299569286082337 \tabularnewline
68 & 2.56 & 2.23999756557909 & 0.32000243442091 \tabularnewline
69 & 2.39 & 2.5599739953108 & -0.169973995310803 \tabularnewline
70 & 2.49 & 2.39001381277279 & 0.0999861872272083 \tabularnewline
71 & 2.17 & 2.48999187471893 & -0.319991874718931 \tabularnewline
72 & 2.16 & 2.17002600383107 & -0.0100260038310727 \tabularnewline
73 & 1.48 & 2.16000081475353 & -0.680000814753531 \tabularnewline
74 & 1.09 & 1.48005525961036 & -0.390055259610362 \tabularnewline
75 & 1.25 & 1.09003169746447 & 0.159968302535529 \tabularnewline
76 & 1.27 & 1.24998700033018 & 0.0200129996698191 \tabularnewline
77 & 1.39 & 1.26999837366288 & 0.120001626337116 \tabularnewline
78 & 1.69 & 1.38999024818357 & 0.300009751816425 \tabularnewline
79 & 1.55 & 1.68997561999687 & -0.139975619996872 \tabularnewline
80 & 1.19 & 1.55001137498376 & -0.360011374983755 \tabularnewline
81 & 1.08 & 1.19002925597716 & -0.110029255977163 \tabularnewline
82 & 0.94 & 1.08000894142137 & -0.140008941421366 \tabularnewline
83 & 0.98 & 0.940011377691588 & 0.0399886223084116 \tabularnewline
84 & 1.01 & 0.979996750363176 & 0.0300032496368237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261022&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]2.08[/C][C]2.04[/C][C]0.04[/C][/ROW]
[ROW][C]3[/C][C]1.94[/C][C]2.07999674943858[/C][C]-0.139996749438579[/C][/ROW]
[ROW][C]4[/C][C]1.91[/C][C]1.94001137670082[/C][C]-0.030011376700819[/C][/ROW]
[ROW][C]5[/C][C]1.34[/C][C]1.91000243884558[/C][C]-0.570002438845582[/C][/ROW]
[ROW][C]6[/C][C]1.3[/C][C]1.34004632069844[/C][C]-0.0400463206984356[/C][/ROW]
[ROW][C]7[/C][C]1.39[/C][C]1.30000325432563[/C][C]0.0899967456743722[/C][/ROW]
[ROW][C]8[/C][C]1.23[/C][C]1.38999268650126[/C][C]-0.159992686501263[/C][/ROW]
[ROW][C]9[/C][C]1.3[/C][C]1.23001300165136[/C][C]0.0699869983486416[/C][/ROW]
[ROW][C]10[/C][C]1.79[/C][C]1.29999431257408[/C][C]0.49000568742592[/C][/ROW]
[ROW][C]11[/C][C]2.25[/C][C]1.78996018016041[/C][C]0.460039819839587[/C][/ROW]
[ROW][C]12[/C][C]2.63[/C][C]2.24996261530774[/C][C]0.380037384692259[/C][/ROW]
[ROW][C]13[/C][C]2.8[/C][C]2.62996911662847[/C][C]0.170030883371528[/C][/ROW]
[ROW][C]14[/C][C]3.08[/C][C]2.79998618260425[/C][C]0.280013817395746[/C][/ROW]
[ROW][C]15[/C][C]3.89[/C][C]3.0799772449472[/C][C]0.810022755052802[/C][/ROW]
[ROW][C]16[/C][C]3.68[/C][C]3.88993417428206[/C][C]-0.209934174282063[/C][/ROW]
[ROW][C]17[/C][C]4.62[/C][C]3.6800170600982[/C][C]0.939982939901805[/C][/ROW]
[ROW][C]18[/C][C]5.07[/C][C]4.61992361319299[/C][C]0.450076386807015[/C][/ROW]
[ROW][C]19[/C][C]5.22[/C][C]5.06996342497652[/C][C]0.150036575023482[/C][/ROW]
[ROW][C]20[/C][C]4.94[/C][C]5.21998780742244[/C][C]-0.279987807422438[/C][/ROW]
[ROW][C]21[/C][C]5.14[/C][C]4.94002275293913[/C][C]0.199977247060873[/C][/ROW]
[ROW][C]22[/C][C]4.8[/C][C]5.13998374904189[/C][C]-0.339983749041892[/C][/ROW]
[ROW][C]23[/C][C]3.89[/C][C]4.80002762845146[/C][C]-0.910027628451457[/C][/ROW]
[ROW][C]24[/C][C]3.54[/C][C]3.89007395251752[/C][C]-0.350073952517521[/C][/ROW]
[ROW][C]25[/C][C]3.34[/C][C]3.54002844842211[/C][C]-0.200028448422112[/C][/ROW]
[ROW][C]26[/C][C]2.8[/C][C]3.34001625511894[/C][C]-0.540016255118938[/C][/ROW]
[ROW][C]27[/C][C]1.6[/C][C]2.80004388390014[/C][C]-1.20004388390014[/C][/ROW]
[ROW][C]28[/C][C]1.56[/C][C]1.6000975204088[/C][C]-0.0400975204088045[/C][/ROW]
[ROW][C]29[/C][C]0.68[/C][C]1.56000325848632[/C][C]-0.880003258486323[/C][/ROW]
[ROW][C]30[/C][C]-0.11[/C][C]0.680071512616054[/C][C]-0.790071512616054[/C][/ROW]
[ROW][C]31[/C][C]-0.66[/C][C]-0.109935795600537[/C][C]-0.550064204399463[/C][/ROW]
[ROW][C]32[/C][C]-0.2[/C][C]-0.659955299562957[/C][C]0.459955299562956[/C][/ROW]
[ROW][C]33[/C][C]-0.62[/C][C]-0.2000373778238[/C][C]-0.4199626221762[/C][/ROW]
[ROW][C]34[/C][C]-0.59[/C][C]-0.619965872142555[/C][C]0.0299658721425553[/C][/ROW]
[ROW][C]35[/C][C]-0.3[/C][C]-0.590002435147698[/C][C]0.290002435147698[/C][/ROW]
[ROW][C]36[/C][C]-0.26[/C][C]-0.30002356676819[/C][C]0.0400235667681901[/C][/ROW]
[ROW][C]37[/C][C]-0.08[/C][C]-0.260003252476551[/C][C]0.180003252476551[/C][/ROW]
[ROW][C]38[/C][C]0.13[/C][C]-0.0800146277907026[/C][C]0.210014627790703[/C][/ROW]
[ROW][C]39[/C][C]0.94[/C][C]0.129982933363828[/C][C]0.810017066636172[/C][/ROW]
[ROW][C]40[/C][C]1.05[/C][C]0.939934174744327[/C][C]0.110065825255673[/C][/ROW]
[ROW][C]41[/C][C]1.59[/C][C]1.04999105560687[/C][C]0.540008944393133[/C][/ROW]
[ROW][C]42[/C][C]2.03[/C][C]1.58995611669396[/C][C]0.440043883306037[/C][/ROW]
[ROW][C]43[/C][C]2.15[/C][C]2.02996424025824[/C][C]0.120035759741763[/C][/ROW]
[ROW][C]44[/C][C]2.05[/C][C]2.14999024540976[/C][C]-0.099990245409757[/C][/ROW]
[ROW][C]45[/C][C]2.56[/C][C]2.05000812561085[/C][C]0.509991874389145[/C][/ROW]
[ROW][C]46[/C][C]2.54[/C][C]2.55995855600221[/C][C]-0.019958556002206[/C][/ROW]
[ROW][C]47[/C][C]2.53[/C][C]2.5400016219128[/C][C]-0.0100016219128043[/C][/ROW]
[ROW][C]48[/C][C]2.6[/C][C]2.53000081277216[/C][C]0.0699991872278418[/C][/ROW]
[ROW][C]49[/C][C]2.71[/C][C]2.59999431158356[/C][C]0.110005688416437[/C][/ROW]
[ROW][C]50[/C][C]2.82[/C][C]2.70999106049383[/C][C]0.110008939506171[/C][/ROW]
[ROW][C]51[/C][C]2.92[/C][C]2.81999106022963[/C][C]0.100008939770367[/C][/ROW]
[ROW][C]52[/C][C]2.87[/C][C]2.91999187286997[/C][C]-0.0499918728699664[/C][/ROW]
[ROW][C]53[/C][C]2.89[/C][C]2.87000406254133[/C][C]0.0199959374586673[/C][/ROW]
[ROW][C]54[/C][C]3.27[/C][C]2.88999837504943[/C][C]0.380001624950572[/C][/ROW]
[ROW][C]55[/C][C]3.32[/C][C]3.26996911953445[/C][C]0.0500308804655467[/C][/ROW]
[ROW][C]56[/C][C]3.14[/C][C]3.31999593428875[/C][C]-0.179995934288752[/C][/ROW]
[ROW][C]57[/C][C]3.04[/C][C]3.140014627196[/C][C]-0.100014627195997[/C][/ROW]
[ROW][C]58[/C][C]3.09[/C][C]3.04000812759222[/C][C]0.0499918724077832[/C][/ROW]
[ROW][C]59[/C][C]3.39[/C][C]3.0899959374587[/C][C]0.300004062541295[/C][/ROW]
[ROW][C]60[/C][C]3.24[/C][C]3.38997562045921[/C][C]-0.149975620459206[/C][/ROW]
[ROW][C]61[/C][C]3.38[/C][C]3.24001218762415[/C][C]0.139987812375852[/C][/ROW]
[ROW][C]62[/C][C]3.41[/C][C]3.37998862402544[/C][C]0.0300113759745573[/C][/ROW]
[ROW][C]63[/C][C]3.14[/C][C]3.40999756115448[/C][C]-0.269997561154477[/C][/ROW]
[ROW][C]64[/C][C]2.96[/C][C]3.1400219410914[/C][C]-0.180021941091399[/C][/ROW]
[ROW][C]65[/C][C]2.74[/C][C]2.96001462930941[/C][C]-0.220014629309414[/C][/ROW]
[ROW][C]66[/C][C]2.21[/C][C]2.74001787927665[/C][C]-0.530017879276651[/C][/ROW]
[ROW][C]67[/C][C]2.24[/C][C]2.21004307139177[/C][C]0.0299569286082337[/C][/ROW]
[ROW][C]68[/C][C]2.56[/C][C]2.23999756557909[/C][C]0.32000243442091[/C][/ROW]
[ROW][C]69[/C][C]2.39[/C][C]2.5599739953108[/C][C]-0.169973995310803[/C][/ROW]
[ROW][C]70[/C][C]2.49[/C][C]2.39001381277279[/C][C]0.0999861872272083[/C][/ROW]
[ROW][C]71[/C][C]2.17[/C][C]2.48999187471893[/C][C]-0.319991874718931[/C][/ROW]
[ROW][C]72[/C][C]2.16[/C][C]2.17002600383107[/C][C]-0.0100260038310727[/C][/ROW]
[ROW][C]73[/C][C]1.48[/C][C]2.16000081475353[/C][C]-0.680000814753531[/C][/ROW]
[ROW][C]74[/C][C]1.09[/C][C]1.48005525961036[/C][C]-0.390055259610362[/C][/ROW]
[ROW][C]75[/C][C]1.25[/C][C]1.09003169746447[/C][C]0.159968302535529[/C][/ROW]
[ROW][C]76[/C][C]1.27[/C][C]1.24998700033018[/C][C]0.0200129996698191[/C][/ROW]
[ROW][C]77[/C][C]1.39[/C][C]1.26999837366288[/C][C]0.120001626337116[/C][/ROW]
[ROW][C]78[/C][C]1.69[/C][C]1.38999024818357[/C][C]0.300009751816425[/C][/ROW]
[ROW][C]79[/C][C]1.55[/C][C]1.68997561999687[/C][C]-0.139975619996872[/C][/ROW]
[ROW][C]80[/C][C]1.19[/C][C]1.55001137498376[/C][C]-0.360011374983755[/C][/ROW]
[ROW][C]81[/C][C]1.08[/C][C]1.19002925597716[/C][C]-0.110029255977163[/C][/ROW]
[ROW][C]82[/C][C]0.94[/C][C]1.08000894142137[/C][C]-0.140008941421366[/C][/ROW]
[ROW][C]83[/C][C]0.98[/C][C]0.940011377691588[/C][C]0.0399886223084116[/C][/ROW]
[ROW][C]84[/C][C]1.01[/C][C]0.979996750363176[/C][C]0.0300032496368237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261022&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261022&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	2.08	2.04	0.04
3	1.94	2.07999674943858	-0.139996749438579
4	1.91	1.94001137670082	-0.030011376700819
5	1.34	1.91000243884558	-0.570002438845582
6	1.3	1.34004632069844	-0.0400463206984356
7	1.39	1.30000325432563	0.0899967456743722
8	1.23	1.38999268650126	-0.159992686501263
9	1.3	1.23001300165136	0.0699869983486416
10	1.79	1.29999431257408	0.49000568742592
11	2.25	1.78996018016041	0.460039819839587
12	2.63	2.24996261530774	0.380037384692259
13	2.8	2.62996911662847	0.170030883371528
14	3.08	2.79998618260425	0.280013817395746
15	3.89	3.0799772449472	0.810022755052802
16	3.68	3.88993417428206	-0.209934174282063
17	4.62	3.6800170600982	0.939982939901805
18	5.07	4.61992361319299	0.450076386807015
19	5.22	5.06996342497652	0.150036575023482
20	4.94	5.21998780742244	-0.279987807422438
21	5.14	4.94002275293913	0.199977247060873
22	4.8	5.13998374904189	-0.339983749041892
23	3.89	4.80002762845146	-0.910027628451457
24	3.54	3.89007395251752	-0.350073952517521
25	3.34	3.54002844842211	-0.200028448422112
26	2.8	3.34001625511894	-0.540016255118938
27	1.6	2.80004388390014	-1.20004388390014
28	1.56	1.6000975204088	-0.0400975204088045
29	0.68	1.56000325848632	-0.880003258486323
30	-0.11	0.680071512616054	-0.790071512616054
31	-0.66	-0.109935795600537	-0.550064204399463
32	-0.2	-0.659955299562957	0.459955299562956
33	-0.62	-0.2000373778238	-0.4199626221762
34	-0.59	-0.619965872142555	0.0299658721425553
35	-0.3	-0.590002435147698	0.290002435147698
36	-0.26	-0.30002356676819	0.0400235667681901
37	-0.08	-0.260003252476551	0.180003252476551
38	0.13	-0.0800146277907026	0.210014627790703
39	0.94	0.129982933363828	0.810017066636172
40	1.05	0.939934174744327	0.110065825255673
41	1.59	1.04999105560687	0.540008944393133
42	2.03	1.58995611669396	0.440043883306037
43	2.15	2.02996424025824	0.120035759741763
44	2.05	2.14999024540976	-0.099990245409757
45	2.56	2.05000812561085	0.509991874389145
46	2.54	2.55995855600221	-0.019958556002206
47	2.53	2.5400016219128	-0.0100016219128043
48	2.6	2.53000081277216	0.0699991872278418
49	2.71	2.59999431158356	0.110005688416437
50	2.82	2.70999106049383	0.110008939506171
51	2.92	2.81999106022963	0.100008939770367
52	2.87	2.91999187286997	-0.0499918728699664
53	2.89	2.87000406254133	0.0199959374586673
54	3.27	2.88999837504943	0.380001624950572
55	3.32	3.26996911953445	0.0500308804655467
56	3.14	3.31999593428875	-0.179995934288752
57	3.04	3.140014627196	-0.100014627195997
58	3.09	3.04000812759222	0.0499918724077832
59	3.39	3.0899959374587	0.300004062541295
60	3.24	3.38997562045921	-0.149975620459206
61	3.38	3.24001218762415	0.139987812375852
62	3.41	3.37998862402544	0.0300113759745573
63	3.14	3.40999756115448	-0.269997561154477
64	2.96	3.1400219410914	-0.180021941091399
65	2.74	2.96001462930941	-0.220014629309414
66	2.21	2.74001787927665	-0.530017879276651
67	2.24	2.21004307139177	0.0299569286082337
68	2.56	2.23999756557909	0.32000243442091
69	2.39	2.5599739953108	-0.169973995310803
70	2.49	2.39001381277279	0.0999861872272083
71	2.17	2.48999187471893	-0.319991874718931
72	2.16	2.17002600383107	-0.0100260038310727
73	1.48	2.16000081475353	-0.680000814753531
74	1.09	1.48005525961036	-0.390055259610362
75	1.25	1.09003169746447	0.159968302535529
76	1.27	1.24998700033018	0.0200129996698191
77	1.39	1.26999837366288	0.120001626337116
78	1.69	1.38999024818357	0.300009751816425
79	1.55	1.68997561999687	-0.139975619996872
80	1.19	1.55001137498376	-0.360011374983755
81	1.08	1.19002925597716	-0.110029255977163
82	0.94	1.08000894142137	-0.140008941421366
83	0.98	0.940011377691588	0.0399886223084116
84	1.01	0.979996750363176	0.0300032496368237

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.00999756181486	0.275689903077591	1.74430522055212
86	1.00999756181486	-0.0284280939389676	2.04842321756868
87	1.00999756181486	-0.261791708219812	2.28178683184952
88	1.00999756181486	-0.458528247363474	2.47852337099319
89	1.00999756181486	-0.631857534431589	2.6518526580613
90	1.00999756181486	-0.788559710533728	2.80855483416344
91	1.00999756181486	-0.932662564600862	2.95265768823057
92	1.00999756181486	-1.0667904561622	3.08678557979192
93	1.00999756181486	-1.19276628763897	3.21276141126868
94	1.00999756181486	-1.31191731201411	3.33191243564382
95	1.00999756181486	-1.42524550329297	3.44524062692268
96	1.00999756181486	-1.53352929886567	3.55352442249538

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.00999756181486 & 0.275689903077591 & 1.74430522055212 \tabularnewline
86 & 1.00999756181486 & -0.0284280939389676 & 2.04842321756868 \tabularnewline
87 & 1.00999756181486 & -0.261791708219812 & 2.28178683184952 \tabularnewline
88 & 1.00999756181486 & -0.458528247363474 & 2.47852337099319 \tabularnewline
89 & 1.00999756181486 & -0.631857534431589 & 2.6518526580613 \tabularnewline
90 & 1.00999756181486 & -0.788559710533728 & 2.80855483416344 \tabularnewline
91 & 1.00999756181486 & -0.932662564600862 & 2.95265768823057 \tabularnewline
92 & 1.00999756181486 & -1.0667904561622 & 3.08678557979192 \tabularnewline
93 & 1.00999756181486 & -1.19276628763897 & 3.21276141126868 \tabularnewline
94 & 1.00999756181486 & -1.31191731201411 & 3.33191243564382 \tabularnewline
95 & 1.00999756181486 & -1.42524550329297 & 3.44524062692268 \tabularnewline
96 & 1.00999756181486 & -1.53352929886567 & 3.55352442249538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261022&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]1.00999756181486[/C][C]0.275689903077591[/C][C]1.74430522055212[/C][/ROW]
[ROW][C]86[/C][C]1.00999756181486[/C][C]-0.0284280939389676[/C][C]2.04842321756868[/C][/ROW]
[ROW][C]87[/C][C]1.00999756181486[/C][C]-0.261791708219812[/C][C]2.28178683184952[/C][/ROW]
[ROW][C]88[/C][C]1.00999756181486[/C][C]-0.458528247363474[/C][C]2.47852337099319[/C][/ROW]
[ROW][C]89[/C][C]1.00999756181486[/C][C]-0.631857534431589[/C][C]2.6518526580613[/C][/ROW]
[ROW][C]90[/C][C]1.00999756181486[/C][C]-0.788559710533728[/C][C]2.80855483416344[/C][/ROW]
[ROW][C]91[/C][C]1.00999756181486[/C][C]-0.932662564600862[/C][C]2.95265768823057[/C][/ROW]
[ROW][C]92[/C][C]1.00999756181486[/C][C]-1.0667904561622[/C][C]3.08678557979192[/C][/ROW]
[ROW][C]93[/C][C]1.00999756181486[/C][C]-1.19276628763897[/C][C]3.21276141126868[/C][/ROW]
[ROW][C]94[/C][C]1.00999756181486[/C][C]-1.31191731201411[/C][C]3.33191243564382[/C][/ROW]
[ROW][C]95[/C][C]1.00999756181486[/C][C]-1.42524550329297[/C][C]3.44524062692268[/C][/ROW]
[ROW][C]96[/C][C]1.00999756181486[/C][C]-1.53352929886567[/C][C]3.55352442249538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261022&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261022&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.00999756181486	0.275689903077591	1.74430522055212
86	1.00999756181486	-0.0284280939389676	2.04842321756868
87	1.00999756181486	-0.261791708219812	2.28178683184952
88	1.00999756181486	-0.458528247363474	2.47852337099319
89	1.00999756181486	-0.631857534431589	2.6518526580613
90	1.00999756181486	-0.788559710533728	2.80855483416344
91	1.00999756181486	-0.932662564600862	2.95265768823057
92	1.00999756181486	-1.0667904561622	3.08678557979192
93	1.00999756181486	-1.19276628763897	3.21276141126868
94	1.00999756181486	-1.31191731201411	3.33191243564382
95	1.00999756181486	-1.42524550329297	3.44524062692268
96	1.00999756181486	-1.53352929886567	3.55352442249538

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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