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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 31 Dec 2014 13:48:57 +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/Dec/31/t1420033765n5v72r8tdv3qsby.htm/, Retrieved Thu, 31 Oct 2024 22:46:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271816, Retrieved Thu, 31 Oct 2024 22:46:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Simon Dewilde

Estimated Impact

158

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

-       [Exponential Smoothing] [] [2014-12-31 13:48:57] [1a08c6aa6bf9a3504070a6066c5cb670] [Current]

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Dataseries X:

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1,64
1,65
1,65
1,66
1,67
1,67
1,68
1,68
1,69
1,7
1,71
1,72
1,72
1,73
1,73
1,73
1,73
1,74
1,75
1,75
1,75
1,76
1,76
1,76
1,77
1,78
1,78
1,79
1,79
1,79
1,79
1,79
1,83
1,83
1,83
1,83
1,84
1,84
1,84
1,85
1,85
1,85
1,86
1,86
1,86
1,87
1,87
1,88
1,88
1,88
1,89
1,89
1,9
1,91
1,91
1,91
1,91
1,91
1,92
1,92
1,92
1,93
1,94
1,94
1,94
1,95
1,95
1,95
1,95
1,96
1,96
1,97

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=271816&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=271816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271816&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	0.668625017373185
beta	0.11119640039078
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.668625017373185 \tabularnewline
beta & 0.11119640039078 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271816&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]0.668625017373185[/C][/ROW]
[ROW][C]beta[/C][C]0.11119640039078[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271816&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	0.668625017373185
beta	0.11119640039078
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.65	1.66	-0.01
4	1.66	1.66257026287484	-0.00257026287483697
5	1.67	1.66991713817315	8.28618268546855e-05
6	1.67	1.67904411968992	-0.00904411968991936
7	1.68	1.68139615453381	-0.00139615453381192
8	1.68	1.68875800794527	-0.00875800794526915
9	1.69	1.69054639552881	-0.000546395528808308
10	1.7	1.69778464881237	0.00221535118763394
11	1.71	1.70703418351227	0.00296581648772998
12	1.72	1.71700600267239	0.00299399732761474
13	1.72	1.72721926404163	-0.00721926404162798
14	1.73	1.73006694048904	-6.69404890352165e-05
15	1.73	1.73769186245804	-0.00769186245804154
16	1.73	1.73964669090608	-0.00964669090607595
17	1.73	1.73957725326777	-0.00957725326776626
18	1.74	1.73884218708806	0.00115781291193606
19	1.75	1.74537093659849	0.00462906340151026
20	1.75	1.75456481585145	-0.00456481585145108
21	1.75	1.75727204932705	-0.00727204932704995
22	1.76	1.75762849139451	0.00237150860548896
23	1.76	1.76460917612249	-0.00460917612249379
24	1.76	1.76657971417256	-0.00657971417256031
25	1.77	1.76674350802152	0.0032564919784781
26	1.78	1.77372615130845	0.00627384869154834
27	1.78	1.78319272724382	-0.00319272724382125
28	1.79	1.78609233857541	0.0039076614245861
29	1.79	1.79402997693176	-0.00402997693175555
30	1.79	1.79636068817785	-0.00636068817785329
31	1.79	1.7966601187103	-0.00666011871030148
32	1.79	1.79626417136218	-0.00626417136218005
33	1.83	1.79566723134964	0.0343327686503558
34	1.83	1.82476701760809	0.00523298239190706
35	1.83	1.83479902418648	-0.00479902418647571
36	1.83	1.83776657900587	-0.00776657900587474
37	1.84	1.83817251741778	0.00182748258221577
38	1.84	1.84512915637109	-0.00512915637109468
39	1.84	1.84705306640001	-0.00705306640001302
40	1.85	1.84716621576882	0.00283378423117719
41	1.85	1.85410064897258	-0.00410064897258322
42	1.85	1.85609366875465	-0.00609366875465445
43	1.86	1.85630104932977	0.00369895067022963
44	1.86	1.86333103239371	-0.00333103239370902
45	1.86	1.86541293499744	-0.00541293499743634
46	1.87	1.86570038078262	0.00429961921737654
47	1.87	1.87280155437685	-0.00280155437685226
48	1.88	1.87494641374098	0.0050535862590213
49	1.88	1.88271914419339	-0.00271914419338604
50	1.88	1.88509266778933	-0.00509266778933126
51	1.89	1.88550056092477	0.00449943907523243
52	1.89	1.89265650410329	-0.00265650410328777
53	1.9	1.89483029703603	0.00516970296397345
54	1.91	1.90262124847473	0.0073787515252719
55	1.91	1.9124378255938	-0.00243782559379535
56	1.91	1.9155095445142	-0.00550954451419572
57	1.91	1.91611780787261	-0.00611780787261473
58	1.91	1.91586452009998	-0.00586452009997784
59	1.92	1.91534456745165	0.00465543254835299
60	1.92	1.92220464366087	-0.00220464366086826
61	1.92	1.92431398891608	-0.00431398891607659
62	1.93	1.9246922337166	0.00530776628339691
63	1.94	1.93189845025183	0.00810154974816713
64	1.94	1.94157499995714	-0.00157499995714505
65	1.94	1.94466446725597	-0.00466446725596614
66	1.95	1.94534144237442	0.00465855762557976
67	1.95	1.95259838284698	-0.00259838284697955
68	1.95	1.95480996499584	-0.00480996499584263
69	1.95	1.95518521337087	-0.00518521337087496
70	1.96	1.95492404744647	0.00507595255353133
71	1.96	1.9619011442155	-0.00190114421550103
72	1.97	1.96407183194442	0.0059281680555765

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.65 & 1.66 & -0.01 \tabularnewline
4 & 1.66 & 1.66257026287484 & -0.00257026287483697 \tabularnewline
5 & 1.67 & 1.66991713817315 & 8.28618268546855e-05 \tabularnewline
6 & 1.67 & 1.67904411968992 & -0.00904411968991936 \tabularnewline
7 & 1.68 & 1.68139615453381 & -0.00139615453381192 \tabularnewline
8 & 1.68 & 1.68875800794527 & -0.00875800794526915 \tabularnewline
9 & 1.69 & 1.69054639552881 & -0.000546395528808308 \tabularnewline
10 & 1.7 & 1.69778464881237 & 0.00221535118763394 \tabularnewline
11 & 1.71 & 1.70703418351227 & 0.00296581648772998 \tabularnewline
12 & 1.72 & 1.71700600267239 & 0.00299399732761474 \tabularnewline
13 & 1.72 & 1.72721926404163 & -0.00721926404162798 \tabularnewline
14 & 1.73 & 1.73006694048904 & -6.69404890352165e-05 \tabularnewline
15 & 1.73 & 1.73769186245804 & -0.00769186245804154 \tabularnewline
16 & 1.73 & 1.73964669090608 & -0.00964669090607595 \tabularnewline
17 & 1.73 & 1.73957725326777 & -0.00957725326776626 \tabularnewline
18 & 1.74 & 1.73884218708806 & 0.00115781291193606 \tabularnewline
19 & 1.75 & 1.74537093659849 & 0.00462906340151026 \tabularnewline
20 & 1.75 & 1.75456481585145 & -0.00456481585145108 \tabularnewline
21 & 1.75 & 1.75727204932705 & -0.00727204932704995 \tabularnewline
22 & 1.76 & 1.75762849139451 & 0.00237150860548896 \tabularnewline
23 & 1.76 & 1.76460917612249 & -0.00460917612249379 \tabularnewline
24 & 1.76 & 1.76657971417256 & -0.00657971417256031 \tabularnewline
25 & 1.77 & 1.76674350802152 & 0.0032564919784781 \tabularnewline
26 & 1.78 & 1.77372615130845 & 0.00627384869154834 \tabularnewline
27 & 1.78 & 1.78319272724382 & -0.00319272724382125 \tabularnewline
28 & 1.79 & 1.78609233857541 & 0.0039076614245861 \tabularnewline
29 & 1.79 & 1.79402997693176 & -0.00402997693175555 \tabularnewline
30 & 1.79 & 1.79636068817785 & -0.00636068817785329 \tabularnewline
31 & 1.79 & 1.7966601187103 & -0.00666011871030148 \tabularnewline
32 & 1.79 & 1.79626417136218 & -0.00626417136218005 \tabularnewline
33 & 1.83 & 1.79566723134964 & 0.0343327686503558 \tabularnewline
34 & 1.83 & 1.82476701760809 & 0.00523298239190706 \tabularnewline
35 & 1.83 & 1.83479902418648 & -0.00479902418647571 \tabularnewline
36 & 1.83 & 1.83776657900587 & -0.00776657900587474 \tabularnewline
37 & 1.84 & 1.83817251741778 & 0.00182748258221577 \tabularnewline
38 & 1.84 & 1.84512915637109 & -0.00512915637109468 \tabularnewline
39 & 1.84 & 1.84705306640001 & -0.00705306640001302 \tabularnewline
40 & 1.85 & 1.84716621576882 & 0.00283378423117719 \tabularnewline
41 & 1.85 & 1.85410064897258 & -0.00410064897258322 \tabularnewline
42 & 1.85 & 1.85609366875465 & -0.00609366875465445 \tabularnewline
43 & 1.86 & 1.85630104932977 & 0.00369895067022963 \tabularnewline
44 & 1.86 & 1.86333103239371 & -0.00333103239370902 \tabularnewline
45 & 1.86 & 1.86541293499744 & -0.00541293499743634 \tabularnewline
46 & 1.87 & 1.86570038078262 & 0.00429961921737654 \tabularnewline
47 & 1.87 & 1.87280155437685 & -0.00280155437685226 \tabularnewline
48 & 1.88 & 1.87494641374098 & 0.0050535862590213 \tabularnewline
49 & 1.88 & 1.88271914419339 & -0.00271914419338604 \tabularnewline
50 & 1.88 & 1.88509266778933 & -0.00509266778933126 \tabularnewline
51 & 1.89 & 1.88550056092477 & 0.00449943907523243 \tabularnewline
52 & 1.89 & 1.89265650410329 & -0.00265650410328777 \tabularnewline
53 & 1.9 & 1.89483029703603 & 0.00516970296397345 \tabularnewline
54 & 1.91 & 1.90262124847473 & 0.0073787515252719 \tabularnewline
55 & 1.91 & 1.9124378255938 & -0.00243782559379535 \tabularnewline
56 & 1.91 & 1.9155095445142 & -0.00550954451419572 \tabularnewline
57 & 1.91 & 1.91611780787261 & -0.00611780787261473 \tabularnewline
58 & 1.91 & 1.91586452009998 & -0.00586452009997784 \tabularnewline
59 & 1.92 & 1.91534456745165 & 0.00465543254835299 \tabularnewline
60 & 1.92 & 1.92220464366087 & -0.00220464366086826 \tabularnewline
61 & 1.92 & 1.92431398891608 & -0.00431398891607659 \tabularnewline
62 & 1.93 & 1.9246922337166 & 0.00530776628339691 \tabularnewline
63 & 1.94 & 1.93189845025183 & 0.00810154974816713 \tabularnewline
64 & 1.94 & 1.94157499995714 & -0.00157499995714505 \tabularnewline
65 & 1.94 & 1.94466446725597 & -0.00466446725596614 \tabularnewline
66 & 1.95 & 1.94534144237442 & 0.00465855762557976 \tabularnewline
67 & 1.95 & 1.95259838284698 & -0.00259838284697955 \tabularnewline
68 & 1.95 & 1.95480996499584 & -0.00480996499584263 \tabularnewline
69 & 1.95 & 1.95518521337087 & -0.00518521337087496 \tabularnewline
70 & 1.96 & 1.95492404744647 & 0.00507595255353133 \tabularnewline
71 & 1.96 & 1.9619011442155 & -0.00190114421550103 \tabularnewline
72 & 1.97 & 1.96407183194442 & 0.0059281680555765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271816&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]1.65[/C][C]1.66[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]1.66[/C][C]1.66257026287484[/C][C]-0.00257026287483697[/C][/ROW]
[ROW][C]5[/C][C]1.67[/C][C]1.66991713817315[/C][C]8.28618268546855e-05[/C][/ROW]
[ROW][C]6[/C][C]1.67[/C][C]1.67904411968992[/C][C]-0.00904411968991936[/C][/ROW]
[ROW][C]7[/C][C]1.68[/C][C]1.68139615453381[/C][C]-0.00139615453381192[/C][/ROW]
[ROW][C]8[/C][C]1.68[/C][C]1.68875800794527[/C][C]-0.00875800794526915[/C][/ROW]
[ROW][C]9[/C][C]1.69[/C][C]1.69054639552881[/C][C]-0.000546395528808308[/C][/ROW]
[ROW][C]10[/C][C]1.7[/C][C]1.69778464881237[/C][C]0.00221535118763394[/C][/ROW]
[ROW][C]11[/C][C]1.71[/C][C]1.70703418351227[/C][C]0.00296581648772998[/C][/ROW]
[ROW][C]12[/C][C]1.72[/C][C]1.71700600267239[/C][C]0.00299399732761474[/C][/ROW]
[ROW][C]13[/C][C]1.72[/C][C]1.72721926404163[/C][C]-0.00721926404162798[/C][/ROW]
[ROW][C]14[/C][C]1.73[/C][C]1.73006694048904[/C][C]-6.69404890352165e-05[/C][/ROW]
[ROW][C]15[/C][C]1.73[/C][C]1.73769186245804[/C][C]-0.00769186245804154[/C][/ROW]
[ROW][C]16[/C][C]1.73[/C][C]1.73964669090608[/C][C]-0.00964669090607595[/C][/ROW]
[ROW][C]17[/C][C]1.73[/C][C]1.73957725326777[/C][C]-0.00957725326776626[/C][/ROW]
[ROW][C]18[/C][C]1.74[/C][C]1.73884218708806[/C][C]0.00115781291193606[/C][/ROW]
[ROW][C]19[/C][C]1.75[/C][C]1.74537093659849[/C][C]0.00462906340151026[/C][/ROW]
[ROW][C]20[/C][C]1.75[/C][C]1.75456481585145[/C][C]-0.00456481585145108[/C][/ROW]
[ROW][C]21[/C][C]1.75[/C][C]1.75727204932705[/C][C]-0.00727204932704995[/C][/ROW]
[ROW][C]22[/C][C]1.76[/C][C]1.75762849139451[/C][C]0.00237150860548896[/C][/ROW]
[ROW][C]23[/C][C]1.76[/C][C]1.76460917612249[/C][C]-0.00460917612249379[/C][/ROW]
[ROW][C]24[/C][C]1.76[/C][C]1.76657971417256[/C][C]-0.00657971417256031[/C][/ROW]
[ROW][C]25[/C][C]1.77[/C][C]1.76674350802152[/C][C]0.0032564919784781[/C][/ROW]
[ROW][C]26[/C][C]1.78[/C][C]1.77372615130845[/C][C]0.00627384869154834[/C][/ROW]
[ROW][C]27[/C][C]1.78[/C][C]1.78319272724382[/C][C]-0.00319272724382125[/C][/ROW]
[ROW][C]28[/C][C]1.79[/C][C]1.78609233857541[/C][C]0.0039076614245861[/C][/ROW]
[ROW][C]29[/C][C]1.79[/C][C]1.79402997693176[/C][C]-0.00402997693175555[/C][/ROW]
[ROW][C]30[/C][C]1.79[/C][C]1.79636068817785[/C][C]-0.00636068817785329[/C][/ROW]
[ROW][C]31[/C][C]1.79[/C][C]1.7966601187103[/C][C]-0.00666011871030148[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.79626417136218[/C][C]-0.00626417136218005[/C][/ROW]
[ROW][C]33[/C][C]1.83[/C][C]1.79566723134964[/C][C]0.0343327686503558[/C][/ROW]
[ROW][C]34[/C][C]1.83[/C][C]1.82476701760809[/C][C]0.00523298239190706[/C][/ROW]
[ROW][C]35[/C][C]1.83[/C][C]1.83479902418648[/C][C]-0.00479902418647571[/C][/ROW]
[ROW][C]36[/C][C]1.83[/C][C]1.83776657900587[/C][C]-0.00776657900587474[/C][/ROW]
[ROW][C]37[/C][C]1.84[/C][C]1.83817251741778[/C][C]0.00182748258221577[/C][/ROW]
[ROW][C]38[/C][C]1.84[/C][C]1.84512915637109[/C][C]-0.00512915637109468[/C][/ROW]
[ROW][C]39[/C][C]1.84[/C][C]1.84705306640001[/C][C]-0.00705306640001302[/C][/ROW]
[ROW][C]40[/C][C]1.85[/C][C]1.84716621576882[/C][C]0.00283378423117719[/C][/ROW]
[ROW][C]41[/C][C]1.85[/C][C]1.85410064897258[/C][C]-0.00410064897258322[/C][/ROW]
[ROW][C]42[/C][C]1.85[/C][C]1.85609366875465[/C][C]-0.00609366875465445[/C][/ROW]
[ROW][C]43[/C][C]1.86[/C][C]1.85630104932977[/C][C]0.00369895067022963[/C][/ROW]
[ROW][C]44[/C][C]1.86[/C][C]1.86333103239371[/C][C]-0.00333103239370902[/C][/ROW]
[ROW][C]45[/C][C]1.86[/C][C]1.86541293499744[/C][C]-0.00541293499743634[/C][/ROW]
[ROW][C]46[/C][C]1.87[/C][C]1.86570038078262[/C][C]0.00429961921737654[/C][/ROW]
[ROW][C]47[/C][C]1.87[/C][C]1.87280155437685[/C][C]-0.00280155437685226[/C][/ROW]
[ROW][C]48[/C][C]1.88[/C][C]1.87494641374098[/C][C]0.0050535862590213[/C][/ROW]
[ROW][C]49[/C][C]1.88[/C][C]1.88271914419339[/C][C]-0.00271914419338604[/C][/ROW]
[ROW][C]50[/C][C]1.88[/C][C]1.88509266778933[/C][C]-0.00509266778933126[/C][/ROW]
[ROW][C]51[/C][C]1.89[/C][C]1.88550056092477[/C][C]0.00449943907523243[/C][/ROW]
[ROW][C]52[/C][C]1.89[/C][C]1.89265650410329[/C][C]-0.00265650410328777[/C][/ROW]
[ROW][C]53[/C][C]1.9[/C][C]1.89483029703603[/C][C]0.00516970296397345[/C][/ROW]
[ROW][C]54[/C][C]1.91[/C][C]1.90262124847473[/C][C]0.0073787515252719[/C][/ROW]
[ROW][C]55[/C][C]1.91[/C][C]1.9124378255938[/C][C]-0.00243782559379535[/C][/ROW]
[ROW][C]56[/C][C]1.91[/C][C]1.9155095445142[/C][C]-0.00550954451419572[/C][/ROW]
[ROW][C]57[/C][C]1.91[/C][C]1.91611780787261[/C][C]-0.00611780787261473[/C][/ROW]
[ROW][C]58[/C][C]1.91[/C][C]1.91586452009998[/C][C]-0.00586452009997784[/C][/ROW]
[ROW][C]59[/C][C]1.92[/C][C]1.91534456745165[/C][C]0.00465543254835299[/C][/ROW]
[ROW][C]60[/C][C]1.92[/C][C]1.92220464366087[/C][C]-0.00220464366086826[/C][/ROW]
[ROW][C]61[/C][C]1.92[/C][C]1.92431398891608[/C][C]-0.00431398891607659[/C][/ROW]
[ROW][C]62[/C][C]1.93[/C][C]1.9246922337166[/C][C]0.00530776628339691[/C][/ROW]
[ROW][C]63[/C][C]1.94[/C][C]1.93189845025183[/C][C]0.00810154974816713[/C][/ROW]
[ROW][C]64[/C][C]1.94[/C][C]1.94157499995714[/C][C]-0.00157499995714505[/C][/ROW]
[ROW][C]65[/C][C]1.94[/C][C]1.94466446725597[/C][C]-0.00466446725596614[/C][/ROW]
[ROW][C]66[/C][C]1.95[/C][C]1.94534144237442[/C][C]0.00465855762557976[/C][/ROW]
[ROW][C]67[/C][C]1.95[/C][C]1.95259838284698[/C][C]-0.00259838284697955[/C][/ROW]
[ROW][C]68[/C][C]1.95[/C][C]1.95480996499584[/C][C]-0.00480996499584263[/C][/ROW]
[ROW][C]69[/C][C]1.95[/C][C]1.95518521337087[/C][C]-0.00518521337087496[/C][/ROW]
[ROW][C]70[/C][C]1.96[/C][C]1.95492404744647[/C][C]0.00507595255353133[/C][/ROW]
[ROW][C]71[/C][C]1.96[/C][C]1.9619011442155[/C][C]-0.00190114421550103[/C][/ROW]
[ROW][C]72[/C][C]1.97[/C][C]1.96407183194442[/C][C]0.0059281680555765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271816&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271816&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.65	1.66	-0.01
4	1.66	1.66257026287484	-0.00257026287483697
5	1.67	1.66991713817315	8.28618268546855e-05
6	1.67	1.67904411968992	-0.00904411968991936
7	1.68	1.68139615453381	-0.00139615453381192
8	1.68	1.68875800794527	-0.00875800794526915
9	1.69	1.69054639552881	-0.000546395528808308
10	1.7	1.69778464881237	0.00221535118763394
11	1.71	1.70703418351227	0.00296581648772998
12	1.72	1.71700600267239	0.00299399732761474
13	1.72	1.72721926404163	-0.00721926404162798
14	1.73	1.73006694048904	-6.69404890352165e-05
15	1.73	1.73769186245804	-0.00769186245804154
16	1.73	1.73964669090608	-0.00964669090607595
17	1.73	1.73957725326777	-0.00957725326776626
18	1.74	1.73884218708806	0.00115781291193606
19	1.75	1.74537093659849	0.00462906340151026
20	1.75	1.75456481585145	-0.00456481585145108
21	1.75	1.75727204932705	-0.00727204932704995
22	1.76	1.75762849139451	0.00237150860548896
23	1.76	1.76460917612249	-0.00460917612249379
24	1.76	1.76657971417256	-0.00657971417256031
25	1.77	1.76674350802152	0.0032564919784781
26	1.78	1.77372615130845	0.00627384869154834
27	1.78	1.78319272724382	-0.00319272724382125
28	1.79	1.78609233857541	0.0039076614245861
29	1.79	1.79402997693176	-0.00402997693175555
30	1.79	1.79636068817785	-0.00636068817785329
31	1.79	1.7966601187103	-0.00666011871030148
32	1.79	1.79626417136218	-0.00626417136218005
33	1.83	1.79566723134964	0.0343327686503558
34	1.83	1.82476701760809	0.00523298239190706
35	1.83	1.83479902418648	-0.00479902418647571
36	1.83	1.83776657900587	-0.00776657900587474
37	1.84	1.83817251741778	0.00182748258221577
38	1.84	1.84512915637109	-0.00512915637109468
39	1.84	1.84705306640001	-0.00705306640001302
40	1.85	1.84716621576882	0.00283378423117719
41	1.85	1.85410064897258	-0.00410064897258322
42	1.85	1.85609366875465	-0.00609366875465445
43	1.86	1.85630104932977	0.00369895067022963
44	1.86	1.86333103239371	-0.00333103239370902
45	1.86	1.86541293499744	-0.00541293499743634
46	1.87	1.86570038078262	0.00429961921737654
47	1.87	1.87280155437685	-0.00280155437685226
48	1.88	1.87494641374098	0.0050535862590213
49	1.88	1.88271914419339	-0.00271914419338604
50	1.88	1.88509266778933	-0.00509266778933126
51	1.89	1.88550056092477	0.00449943907523243
52	1.89	1.89265650410329	-0.00265650410328777
53	1.9	1.89483029703603	0.00516970296397345
54	1.91	1.90262124847473	0.0073787515252719
55	1.91	1.9124378255938	-0.00243782559379535
56	1.91	1.9155095445142	-0.00550954451419572
57	1.91	1.91611780787261	-0.00611780787261473
58	1.91	1.91586452009998	-0.00586452009997784
59	1.92	1.91534456745165	0.00465543254835299
60	1.92	1.92220464366087	-0.00220464366086826
61	1.92	1.92431398891608	-0.00431398891607659
62	1.93	1.9246922337166	0.00530776628339691
63	1.94	1.93189845025183	0.00810154974816713
64	1.94	1.94157499995714	-0.00157499995714505
65	1.94	1.94466446725597	-0.00466446725596614
66	1.95	1.94534144237442	0.00465855762557976
67	1.95	1.95259838284698	-0.00259838284697955
68	1.95	1.95480996499584	-0.00480996499584263
69	1.95	1.95518521337087	-0.00518521337087496
70	1.96	1.95492404744647	0.00507595255353133
71	1.96	1.9619011442155	-0.00190114421550103
72	1.97	1.96407183194442	0.0059281680555765

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.97191814528614	1.95907085982118	1.98476543075109
74	1.9758007371587	1.95979562864249	1.99180584567491
75	1.97968332903126	1.96054119334044	1.99882546472208
76	1.98356592090382	1.96125782690431	2.00587401490333
77	1.98744851277638	1.96192054126723	2.01297648428554
78	1.99133110464895	1.96251574577989	2.020146463518
79	1.99521369652151	1.96303577670787	2.02739161633515
80	1.99909628839407	1.96347630926415	2.03471626752399
81	2.00297888026663	1.96383500706401	2.04212275346925
82	2.00686147213919	1.96411076518251	2.04961217909588
83	2.01074406401176	1.96430326239617	2.05718486562734
84	2.01462665588432	1.96441268500957	2.06484062675907

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.97191814528614 & 1.95907085982118 & 1.98476543075109 \tabularnewline
74 & 1.9758007371587 & 1.95979562864249 & 1.99180584567491 \tabularnewline
75 & 1.97968332903126 & 1.96054119334044 & 1.99882546472208 \tabularnewline
76 & 1.98356592090382 & 1.96125782690431 & 2.00587401490333 \tabularnewline
77 & 1.98744851277638 & 1.96192054126723 & 2.01297648428554 \tabularnewline
78 & 1.99133110464895 & 1.96251574577989 & 2.020146463518 \tabularnewline
79 & 1.99521369652151 & 1.96303577670787 & 2.02739161633515 \tabularnewline
80 & 1.99909628839407 & 1.96347630926415 & 2.03471626752399 \tabularnewline
81 & 2.00297888026663 & 1.96383500706401 & 2.04212275346925 \tabularnewline
82 & 2.00686147213919 & 1.96411076518251 & 2.04961217909588 \tabularnewline
83 & 2.01074406401176 & 1.96430326239617 & 2.05718486562734 \tabularnewline
84 & 2.01462665588432 & 1.96441268500957 & 2.06484062675907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271816&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]73[/C][C]1.97191814528614[/C][C]1.95907085982118[/C][C]1.98476543075109[/C][/ROW]
[ROW][C]74[/C][C]1.9758007371587[/C][C]1.95979562864249[/C][C]1.99180584567491[/C][/ROW]
[ROW][C]75[/C][C]1.97968332903126[/C][C]1.96054119334044[/C][C]1.99882546472208[/C][/ROW]
[ROW][C]76[/C][C]1.98356592090382[/C][C]1.96125782690431[/C][C]2.00587401490333[/C][/ROW]
[ROW][C]77[/C][C]1.98744851277638[/C][C]1.96192054126723[/C][C]2.01297648428554[/C][/ROW]
[ROW][C]78[/C][C]1.99133110464895[/C][C]1.96251574577989[/C][C]2.020146463518[/C][/ROW]
[ROW][C]79[/C][C]1.99521369652151[/C][C]1.96303577670787[/C][C]2.02739161633515[/C][/ROW]
[ROW][C]80[/C][C]1.99909628839407[/C][C]1.96347630926415[/C][C]2.03471626752399[/C][/ROW]
[ROW][C]81[/C][C]2.00297888026663[/C][C]1.96383500706401[/C][C]2.04212275346925[/C][/ROW]
[ROW][C]82[/C][C]2.00686147213919[/C][C]1.96411076518251[/C][C]2.04961217909588[/C][/ROW]
[ROW][C]83[/C][C]2.01074406401176[/C][C]1.96430326239617[/C][C]2.05718486562734[/C][/ROW]
[ROW][C]84[/C][C]2.01462665588432[/C][C]1.96441268500957[/C][C]2.06484062675907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271816&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271816&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
73	1.97191814528614	1.95907085982118	1.98476543075109
74	1.9758007371587	1.95979562864249	1.99180584567491
75	1.97968332903126	1.96054119334044	1.99882546472208
76	1.98356592090382	1.96125782690431	2.00587401490333
77	1.98744851277638	1.96192054126723	2.01297648428554
78	1.99133110464895	1.96251574577989	2.020146463518
79	1.99521369652151	1.96303577670787	2.02739161633515
80	1.99909628839407	1.96347630926415	2.03471626752399
81	2.00297888026663	1.96383500706401	2.04212275346925
82	2.00686147213919	1.96411076518251	2.04961217909588
83	2.01074406401176	1.96430326239617	2.05718486562734
84	2.01462665588432	1.96441268500957	2.06484062675907

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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