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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 21 May 2013 16:32:41 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/21/t1369168393djalghrx95fldnt.htm/, Retrieved Thu, 02 May 2024 00:57:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209296, Retrieved Thu, 02 May 2024 00:57:37 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [Opgave 10: eigen ...] [2013-05-21 20:32:41] [7bf0202b24d13a3918d58b8a1b5b6350] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	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=209296&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=209296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209296&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	1
beta	0.125332141259147
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.125332141259147 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209296&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.125332141259147[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209296&T=1

As an alternative you can also use a QR Code:

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.125332141259147
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	39.55	39.44	0.109999999999999
4	39.64	39.6437865355385	-0.00378653553850228
5	39.8	39.7333119609315	0.0666880390684881
6	39.79	39.9016701156643	-0.111670115664339
7	39.79	39.8776742609535	-0.0876742609534702
8	39.86	39.8666858580949	-0.00668585809485478
9	39.91	39.9358479051837	-0.0258479051836744
10	40	39.9826083318799	0.0173916681200623
11	40.01	40.0747880668855	-0.0647880668854981
12	40.01	40.0766680397347	-0.0666680397346937
13	40.01	40.0683123915612	-0.0583123915611949
14	39.96	40.0610039746649	-0.101003974664884
15	40	39.9983449302445	0.00165506975554308
16	39.76	40.0385523636809	-0.278552363680852
17	39.68	39.7636407994879	-0.0836407994879309
18	39.7	39.6731579189915	0.0268420810085175
19	39.7	39.6965220944801	0.00347790551986549
20	39.73	39.696957987826	0.0330420121739579
21	39.64	39.7310992139633	-0.0910992139633038
22	39.56	39.6296815544103	-0.0696815544102591
23	39.67	39.5409482159898	0.129051784010244
24	39.66	39.6671225524131	-0.00712255241307957
25	39.66	39.6562298676679	0.00377013233208601
26	40.05	39.6567023864259	0.393297613574077
27	39.99	40.0959952184873	-0.105995218487273
28	40.06	40.022710610791	0.037289389208965
29	40.08	40.0973841697868	-0.017384169786844
30	40.1	40.1152053745634	-0.0152053745634362
31	40.1	40.1332996524108	-0.0332996524107614
32	40.12	40.1291261356709	-0.00912613567093956
33	40.07	40.1479823375459	-0.077982337545869
34	40.24	40.0882086442009	0.151791355799148
35	40.58	40.2772329798478	0.302767020152203
36	40.72	40.6551794187861	0.0648205812138798
37	40.72	40.8033035210273	-0.0833035210273181
38	40.89	40.7928629123625	0.0971370876374635
39	40.9	40.9750373115518	-0.0750373115518173
40	41.04	40.9756327246207	0.0643672753793041
41	41.27	41.123700013071	0.146299986929002
42	41.29	41.372036103699	-0.0820361036990036
43	41.29	41.3817543431618	-0.0917543431618455
44	41.33	41.3702545748635	-0.0402545748635461
45	41.34	41.4052093828004	-0.0652093828004183
46	41.37	41.4070365512239	-0.0370365512238635
47	41.33	41.4323946809541	-0.102394680954113
48	41.37	41.3795613363366	-0.00956133633658851
49	41.37	41.4183629935802	-0.048362993580227
50	41.42	41.4123015560371	0.00769844396288732
51	41.61	41.4632664185034	0.146733581496648
52	41.58	41.6716568524669	-0.0916568524669472
53	41.75	41.6301693028862	0.119830697113812
54	41.75	41.815187940744	-0.065187940744039
55	41.75	41.8070177965463	-0.0570177965463117
56	41.85	41.7998716340153	0.0501283659847118
57	41.84	41.906154329462	-0.0661543294619733
58	41.97	41.8878630656969	0.0821369343030511
59	42.01	42.0281574635496	-0.0181574635496062
60	42.04	42.0658817497631	-0.0258817497630943
61	42.04	42.0926379346458	-0.0526379346457588
62	42.06	42.0860407095851	-0.0260407095851392
63	41.93	42.1027769716929	-0.172776971692933
64	41.93	41.9511224638704	-0.021122463870384
65	41.99	41.9484751402448	0.0415248597551638
66	42.03	42.0136795398334	0.0163204601665612
67	42.03	42.0557250180524	-0.025725018052448
68	42.12	42.052500846456	0.0674991535439915
69	42.22	42.1509606599029	0.0690393400971487
70	42.21	42.2596135082283	-0.0496135082283473
71	42.23	42.2433953410067	-0.0133953410067136
72	42.22	42.2617164742354	-0.041716474235443

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 39.55 & 39.44 & 0.109999999999999 \tabularnewline
4 & 39.64 & 39.6437865355385 & -0.00378653553850228 \tabularnewline
5 & 39.8 & 39.7333119609315 & 0.0666880390684881 \tabularnewline
6 & 39.79 & 39.9016701156643 & -0.111670115664339 \tabularnewline
7 & 39.79 & 39.8776742609535 & -0.0876742609534702 \tabularnewline
8 & 39.86 & 39.8666858580949 & -0.00668585809485478 \tabularnewline
9 & 39.91 & 39.9358479051837 & -0.0258479051836744 \tabularnewline
10 & 40 & 39.9826083318799 & 0.0173916681200623 \tabularnewline
11 & 40.01 & 40.0747880668855 & -0.0647880668854981 \tabularnewline
12 & 40.01 & 40.0766680397347 & -0.0666680397346937 \tabularnewline
13 & 40.01 & 40.0683123915612 & -0.0583123915611949 \tabularnewline
14 & 39.96 & 40.0610039746649 & -0.101003974664884 \tabularnewline
15 & 40 & 39.9983449302445 & 0.00165506975554308 \tabularnewline
16 & 39.76 & 40.0385523636809 & -0.278552363680852 \tabularnewline
17 & 39.68 & 39.7636407994879 & -0.0836407994879309 \tabularnewline
18 & 39.7 & 39.6731579189915 & 0.0268420810085175 \tabularnewline
19 & 39.7 & 39.6965220944801 & 0.00347790551986549 \tabularnewline
20 & 39.73 & 39.696957987826 & 0.0330420121739579 \tabularnewline
21 & 39.64 & 39.7310992139633 & -0.0910992139633038 \tabularnewline
22 & 39.56 & 39.6296815544103 & -0.0696815544102591 \tabularnewline
23 & 39.67 & 39.5409482159898 & 0.129051784010244 \tabularnewline
24 & 39.66 & 39.6671225524131 & -0.00712255241307957 \tabularnewline
25 & 39.66 & 39.6562298676679 & 0.00377013233208601 \tabularnewline
26 & 40.05 & 39.6567023864259 & 0.393297613574077 \tabularnewline
27 & 39.99 & 40.0959952184873 & -0.105995218487273 \tabularnewline
28 & 40.06 & 40.022710610791 & 0.037289389208965 \tabularnewline
29 & 40.08 & 40.0973841697868 & -0.017384169786844 \tabularnewline
30 & 40.1 & 40.1152053745634 & -0.0152053745634362 \tabularnewline
31 & 40.1 & 40.1332996524108 & -0.0332996524107614 \tabularnewline
32 & 40.12 & 40.1291261356709 & -0.00912613567093956 \tabularnewline
33 & 40.07 & 40.1479823375459 & -0.077982337545869 \tabularnewline
34 & 40.24 & 40.0882086442009 & 0.151791355799148 \tabularnewline
35 & 40.58 & 40.2772329798478 & 0.302767020152203 \tabularnewline
36 & 40.72 & 40.6551794187861 & 0.0648205812138798 \tabularnewline
37 & 40.72 & 40.8033035210273 & -0.0833035210273181 \tabularnewline
38 & 40.89 & 40.7928629123625 & 0.0971370876374635 \tabularnewline
39 & 40.9 & 40.9750373115518 & -0.0750373115518173 \tabularnewline
40 & 41.04 & 40.9756327246207 & 0.0643672753793041 \tabularnewline
41 & 41.27 & 41.123700013071 & 0.146299986929002 \tabularnewline
42 & 41.29 & 41.372036103699 & -0.0820361036990036 \tabularnewline
43 & 41.29 & 41.3817543431618 & -0.0917543431618455 \tabularnewline
44 & 41.33 & 41.3702545748635 & -0.0402545748635461 \tabularnewline
45 & 41.34 & 41.4052093828004 & -0.0652093828004183 \tabularnewline
46 & 41.37 & 41.4070365512239 & -0.0370365512238635 \tabularnewline
47 & 41.33 & 41.4323946809541 & -0.102394680954113 \tabularnewline
48 & 41.37 & 41.3795613363366 & -0.00956133633658851 \tabularnewline
49 & 41.37 & 41.4183629935802 & -0.048362993580227 \tabularnewline
50 & 41.42 & 41.4123015560371 & 0.00769844396288732 \tabularnewline
51 & 41.61 & 41.4632664185034 & 0.146733581496648 \tabularnewline
52 & 41.58 & 41.6716568524669 & -0.0916568524669472 \tabularnewline
53 & 41.75 & 41.6301693028862 & 0.119830697113812 \tabularnewline
54 & 41.75 & 41.815187940744 & -0.065187940744039 \tabularnewline
55 & 41.75 & 41.8070177965463 & -0.0570177965463117 \tabularnewline
56 & 41.85 & 41.7998716340153 & 0.0501283659847118 \tabularnewline
57 & 41.84 & 41.906154329462 & -0.0661543294619733 \tabularnewline
58 & 41.97 & 41.8878630656969 & 0.0821369343030511 \tabularnewline
59 & 42.01 & 42.0281574635496 & -0.0181574635496062 \tabularnewline
60 & 42.04 & 42.0658817497631 & -0.0258817497630943 \tabularnewline
61 & 42.04 & 42.0926379346458 & -0.0526379346457588 \tabularnewline
62 & 42.06 & 42.0860407095851 & -0.0260407095851392 \tabularnewline
63 & 41.93 & 42.1027769716929 & -0.172776971692933 \tabularnewline
64 & 41.93 & 41.9511224638704 & -0.021122463870384 \tabularnewline
65 & 41.99 & 41.9484751402448 & 0.0415248597551638 \tabularnewline
66 & 42.03 & 42.0136795398334 & 0.0163204601665612 \tabularnewline
67 & 42.03 & 42.0557250180524 & -0.025725018052448 \tabularnewline
68 & 42.12 & 42.052500846456 & 0.0674991535439915 \tabularnewline
69 & 42.22 & 42.1509606599029 & 0.0690393400971487 \tabularnewline
70 & 42.21 & 42.2596135082283 & -0.0496135082283473 \tabularnewline
71 & 42.23 & 42.2433953410067 & -0.0133953410067136 \tabularnewline
72 & 42.22 & 42.2617164742354 & -0.041716474235443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209296&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]39.55[/C][C]39.44[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]4[/C][C]39.64[/C][C]39.6437865355385[/C][C]-0.00378653553850228[/C][/ROW]
[ROW][C]5[/C][C]39.8[/C][C]39.7333119609315[/C][C]0.0666880390684881[/C][/ROW]
[ROW][C]6[/C][C]39.79[/C][C]39.9016701156643[/C][C]-0.111670115664339[/C][/ROW]
[ROW][C]7[/C][C]39.79[/C][C]39.8776742609535[/C][C]-0.0876742609534702[/C][/ROW]
[ROW][C]8[/C][C]39.86[/C][C]39.8666858580949[/C][C]-0.00668585809485478[/C][/ROW]
[ROW][C]9[/C][C]39.91[/C][C]39.9358479051837[/C][C]-0.0258479051836744[/C][/ROW]
[ROW][C]10[/C][C]40[/C][C]39.9826083318799[/C][C]0.0173916681200623[/C][/ROW]
[ROW][C]11[/C][C]40.01[/C][C]40.0747880668855[/C][C]-0.0647880668854981[/C][/ROW]
[ROW][C]12[/C][C]40.01[/C][C]40.0766680397347[/C][C]-0.0666680397346937[/C][/ROW]
[ROW][C]13[/C][C]40.01[/C][C]40.0683123915612[/C][C]-0.0583123915611949[/C][/ROW]
[ROW][C]14[/C][C]39.96[/C][C]40.0610039746649[/C][C]-0.101003974664884[/C][/ROW]
[ROW][C]15[/C][C]40[/C][C]39.9983449302445[/C][C]0.00165506975554308[/C][/ROW]
[ROW][C]16[/C][C]39.76[/C][C]40.0385523636809[/C][C]-0.278552363680852[/C][/ROW]
[ROW][C]17[/C][C]39.68[/C][C]39.7636407994879[/C][C]-0.0836407994879309[/C][/ROW]
[ROW][C]18[/C][C]39.7[/C][C]39.6731579189915[/C][C]0.0268420810085175[/C][/ROW]
[ROW][C]19[/C][C]39.7[/C][C]39.6965220944801[/C][C]0.00347790551986549[/C][/ROW]
[ROW][C]20[/C][C]39.73[/C][C]39.696957987826[/C][C]0.0330420121739579[/C][/ROW]
[ROW][C]21[/C][C]39.64[/C][C]39.7310992139633[/C][C]-0.0910992139633038[/C][/ROW]
[ROW][C]22[/C][C]39.56[/C][C]39.6296815544103[/C][C]-0.0696815544102591[/C][/ROW]
[ROW][C]23[/C][C]39.67[/C][C]39.5409482159898[/C][C]0.129051784010244[/C][/ROW]
[ROW][C]24[/C][C]39.66[/C][C]39.6671225524131[/C][C]-0.00712255241307957[/C][/ROW]
[ROW][C]25[/C][C]39.66[/C][C]39.6562298676679[/C][C]0.00377013233208601[/C][/ROW]
[ROW][C]26[/C][C]40.05[/C][C]39.6567023864259[/C][C]0.393297613574077[/C][/ROW]
[ROW][C]27[/C][C]39.99[/C][C]40.0959952184873[/C][C]-0.105995218487273[/C][/ROW]
[ROW][C]28[/C][C]40.06[/C][C]40.022710610791[/C][C]0.037289389208965[/C][/ROW]
[ROW][C]29[/C][C]40.08[/C][C]40.0973841697868[/C][C]-0.017384169786844[/C][/ROW]
[ROW][C]30[/C][C]40.1[/C][C]40.1152053745634[/C][C]-0.0152053745634362[/C][/ROW]
[ROW][C]31[/C][C]40.1[/C][C]40.1332996524108[/C][C]-0.0332996524107614[/C][/ROW]
[ROW][C]32[/C][C]40.12[/C][C]40.1291261356709[/C][C]-0.00912613567093956[/C][/ROW]
[ROW][C]33[/C][C]40.07[/C][C]40.1479823375459[/C][C]-0.077982337545869[/C][/ROW]
[ROW][C]34[/C][C]40.24[/C][C]40.0882086442009[/C][C]0.151791355799148[/C][/ROW]
[ROW][C]35[/C][C]40.58[/C][C]40.2772329798478[/C][C]0.302767020152203[/C][/ROW]
[ROW][C]36[/C][C]40.72[/C][C]40.6551794187861[/C][C]0.0648205812138798[/C][/ROW]
[ROW][C]37[/C][C]40.72[/C][C]40.8033035210273[/C][C]-0.0833035210273181[/C][/ROW]
[ROW][C]38[/C][C]40.89[/C][C]40.7928629123625[/C][C]0.0971370876374635[/C][/ROW]
[ROW][C]39[/C][C]40.9[/C][C]40.9750373115518[/C][C]-0.0750373115518173[/C][/ROW]
[ROW][C]40[/C][C]41.04[/C][C]40.9756327246207[/C][C]0.0643672753793041[/C][/ROW]
[ROW][C]41[/C][C]41.27[/C][C]41.123700013071[/C][C]0.146299986929002[/C][/ROW]
[ROW][C]42[/C][C]41.29[/C][C]41.372036103699[/C][C]-0.0820361036990036[/C][/ROW]
[ROW][C]43[/C][C]41.29[/C][C]41.3817543431618[/C][C]-0.0917543431618455[/C][/ROW]
[ROW][C]44[/C][C]41.33[/C][C]41.3702545748635[/C][C]-0.0402545748635461[/C][/ROW]
[ROW][C]45[/C][C]41.34[/C][C]41.4052093828004[/C][C]-0.0652093828004183[/C][/ROW]
[ROW][C]46[/C][C]41.37[/C][C]41.4070365512239[/C][C]-0.0370365512238635[/C][/ROW]
[ROW][C]47[/C][C]41.33[/C][C]41.4323946809541[/C][C]-0.102394680954113[/C][/ROW]
[ROW][C]48[/C][C]41.37[/C][C]41.3795613363366[/C][C]-0.00956133633658851[/C][/ROW]
[ROW][C]49[/C][C]41.37[/C][C]41.4183629935802[/C][C]-0.048362993580227[/C][/ROW]
[ROW][C]50[/C][C]41.42[/C][C]41.4123015560371[/C][C]0.00769844396288732[/C][/ROW]
[ROW][C]51[/C][C]41.61[/C][C]41.4632664185034[/C][C]0.146733581496648[/C][/ROW]
[ROW][C]52[/C][C]41.58[/C][C]41.6716568524669[/C][C]-0.0916568524669472[/C][/ROW]
[ROW][C]53[/C][C]41.75[/C][C]41.6301693028862[/C][C]0.119830697113812[/C][/ROW]
[ROW][C]54[/C][C]41.75[/C][C]41.815187940744[/C][C]-0.065187940744039[/C][/ROW]
[ROW][C]55[/C][C]41.75[/C][C]41.8070177965463[/C][C]-0.0570177965463117[/C][/ROW]
[ROW][C]56[/C][C]41.85[/C][C]41.7998716340153[/C][C]0.0501283659847118[/C][/ROW]
[ROW][C]57[/C][C]41.84[/C][C]41.906154329462[/C][C]-0.0661543294619733[/C][/ROW]
[ROW][C]58[/C][C]41.97[/C][C]41.8878630656969[/C][C]0.0821369343030511[/C][/ROW]
[ROW][C]59[/C][C]42.01[/C][C]42.0281574635496[/C][C]-0.0181574635496062[/C][/ROW]
[ROW][C]60[/C][C]42.04[/C][C]42.0658817497631[/C][C]-0.0258817497630943[/C][/ROW]
[ROW][C]61[/C][C]42.04[/C][C]42.0926379346458[/C][C]-0.0526379346457588[/C][/ROW]
[ROW][C]62[/C][C]42.06[/C][C]42.0860407095851[/C][C]-0.0260407095851392[/C][/ROW]
[ROW][C]63[/C][C]41.93[/C][C]42.1027769716929[/C][C]-0.172776971692933[/C][/ROW]
[ROW][C]64[/C][C]41.93[/C][C]41.9511224638704[/C][C]-0.021122463870384[/C][/ROW]
[ROW][C]65[/C][C]41.99[/C][C]41.9484751402448[/C][C]0.0415248597551638[/C][/ROW]
[ROW][C]66[/C][C]42.03[/C][C]42.0136795398334[/C][C]0.0163204601665612[/C][/ROW]
[ROW][C]67[/C][C]42.03[/C][C]42.0557250180524[/C][C]-0.025725018052448[/C][/ROW]
[ROW][C]68[/C][C]42.12[/C][C]42.052500846456[/C][C]0.0674991535439915[/C][/ROW]
[ROW][C]69[/C][C]42.22[/C][C]42.1509606599029[/C][C]0.0690393400971487[/C][/ROW]
[ROW][C]70[/C][C]42.21[/C][C]42.2596135082283[/C][C]-0.0496135082283473[/C][/ROW]
[ROW][C]71[/C][C]42.23[/C][C]42.2433953410067[/C][C]-0.0133953410067136[/C][/ROW]
[ROW][C]72[/C][C]42.22[/C][C]42.2617164742354[/C][C]-0.041716474235443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209296&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	39.55	39.44	0.109999999999999
4	39.64	39.6437865355385	-0.00378653553850228
5	39.8	39.7333119609315	0.0666880390684881
6	39.79	39.9016701156643	-0.111670115664339
7	39.79	39.8776742609535	-0.0876742609534702
8	39.86	39.8666858580949	-0.00668585809485478
9	39.91	39.9358479051837	-0.0258479051836744
10	40	39.9826083318799	0.0173916681200623
11	40.01	40.0747880668855	-0.0647880668854981
12	40.01	40.0766680397347	-0.0666680397346937
13	40.01	40.0683123915612	-0.0583123915611949
14	39.96	40.0610039746649	-0.101003974664884
15	40	39.9983449302445	0.00165506975554308
16	39.76	40.0385523636809	-0.278552363680852
17	39.68	39.7636407994879	-0.0836407994879309
18	39.7	39.6731579189915	0.0268420810085175
19	39.7	39.6965220944801	0.00347790551986549
20	39.73	39.696957987826	0.0330420121739579
21	39.64	39.7310992139633	-0.0910992139633038
22	39.56	39.6296815544103	-0.0696815544102591
23	39.67	39.5409482159898	0.129051784010244
24	39.66	39.6671225524131	-0.00712255241307957
25	39.66	39.6562298676679	0.00377013233208601
26	40.05	39.6567023864259	0.393297613574077
27	39.99	40.0959952184873	-0.105995218487273
28	40.06	40.022710610791	0.037289389208965
29	40.08	40.0973841697868	-0.017384169786844
30	40.1	40.1152053745634	-0.0152053745634362
31	40.1	40.1332996524108	-0.0332996524107614
32	40.12	40.1291261356709	-0.00912613567093956
33	40.07	40.1479823375459	-0.077982337545869
34	40.24	40.0882086442009	0.151791355799148
35	40.58	40.2772329798478	0.302767020152203
36	40.72	40.6551794187861	0.0648205812138798
37	40.72	40.8033035210273	-0.0833035210273181
38	40.89	40.7928629123625	0.0971370876374635
39	40.9	40.9750373115518	-0.0750373115518173
40	41.04	40.9756327246207	0.0643672753793041
41	41.27	41.123700013071	0.146299986929002
42	41.29	41.372036103699	-0.0820361036990036
43	41.29	41.3817543431618	-0.0917543431618455
44	41.33	41.3702545748635	-0.0402545748635461
45	41.34	41.4052093828004	-0.0652093828004183
46	41.37	41.4070365512239	-0.0370365512238635
47	41.33	41.4323946809541	-0.102394680954113
48	41.37	41.3795613363366	-0.00956133633658851
49	41.37	41.4183629935802	-0.048362993580227
50	41.42	41.4123015560371	0.00769844396288732
51	41.61	41.4632664185034	0.146733581496648
52	41.58	41.6716568524669	-0.0916568524669472
53	41.75	41.6301693028862	0.119830697113812
54	41.75	41.815187940744	-0.065187940744039
55	41.75	41.8070177965463	-0.0570177965463117
56	41.85	41.7998716340153	0.0501283659847118
57	41.84	41.906154329462	-0.0661543294619733
58	41.97	41.8878630656969	0.0821369343030511
59	42.01	42.0281574635496	-0.0181574635496062
60	42.04	42.0658817497631	-0.0258817497630943
61	42.04	42.0926379346458	-0.0526379346457588
62	42.06	42.0860407095851	-0.0260407095851392
63	41.93	42.1027769716929	-0.172776971692933
64	41.93	41.9511224638704	-0.021122463870384
65	41.99	41.9484751402448	0.0415248597551638
66	42.03	42.0136795398334	0.0163204601665612
67	42.03	42.0557250180524	-0.025725018052448
68	42.12	42.052500846456	0.0674991535439915
69	42.22	42.1509606599029	0.0690393400971487
70	42.21	42.2596135082283	-0.0496135082283473
71	42.23	42.2433953410067	-0.0133953410067136
72	42.22	42.2617164742354	-0.041716474235443

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	42.2464880591937	42.0537660610706	42.4392100573169
74	42.2729761183875	41.9828432519306	42.5631089848443
75	42.2994641775812	41.92227352084	42.6766548343224
76	42.3259522367749	41.8648711601919	42.787033313358
77	42.3524402959687	41.8080940460798	42.8967865458575
78	42.3789283551624	41.7507636554958	43.007093054829
79	42.4054164143561	41.6922567083858	43.1185761203264
80	42.4319044735499	41.6322187069361	43.2315902401636
81	42.4583925327436	41.5704401557315	43.3463449097557
82	42.4848805919373	41.5067957702633	43.4629654136113
83	42.5113686511311	41.4412118095481	43.5815254927141
84	42.5378567103248	41.3736473124697	43.7020661081799

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 42.2464880591937 & 42.0537660610706 & 42.4392100573169 \tabularnewline
74 & 42.2729761183875 & 41.9828432519306 & 42.5631089848443 \tabularnewline
75 & 42.2994641775812 & 41.92227352084 & 42.6766548343224 \tabularnewline
76 & 42.3259522367749 & 41.8648711601919 & 42.787033313358 \tabularnewline
77 & 42.3524402959687 & 41.8080940460798 & 42.8967865458575 \tabularnewline
78 & 42.3789283551624 & 41.7507636554958 & 43.007093054829 \tabularnewline
79 & 42.4054164143561 & 41.6922567083858 & 43.1185761203264 \tabularnewline
80 & 42.4319044735499 & 41.6322187069361 & 43.2315902401636 \tabularnewline
81 & 42.4583925327436 & 41.5704401557315 & 43.3463449097557 \tabularnewline
82 & 42.4848805919373 & 41.5067957702633 & 43.4629654136113 \tabularnewline
83 & 42.5113686511311 & 41.4412118095481 & 43.5815254927141 \tabularnewline
84 & 42.5378567103248 & 41.3736473124697 & 43.7020661081799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209296&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]42.2464880591937[/C][C]42.0537660610706[/C][C]42.4392100573169[/C][/ROW]
[ROW][C]74[/C][C]42.2729761183875[/C][C]41.9828432519306[/C][C]42.5631089848443[/C][/ROW]
[ROW][C]75[/C][C]42.2994641775812[/C][C]41.92227352084[/C][C]42.6766548343224[/C][/ROW]
[ROW][C]76[/C][C]42.3259522367749[/C][C]41.8648711601919[/C][C]42.787033313358[/C][/ROW]
[ROW][C]77[/C][C]42.3524402959687[/C][C]41.8080940460798[/C][C]42.8967865458575[/C][/ROW]
[ROW][C]78[/C][C]42.3789283551624[/C][C]41.7507636554958[/C][C]43.007093054829[/C][/ROW]
[ROW][C]79[/C][C]42.4054164143561[/C][C]41.6922567083858[/C][C]43.1185761203264[/C][/ROW]
[ROW][C]80[/C][C]42.4319044735499[/C][C]41.6322187069361[/C][C]43.2315902401636[/C][/ROW]
[ROW][C]81[/C][C]42.4583925327436[/C][C]41.5704401557315[/C][C]43.3463449097557[/C][/ROW]
[ROW][C]82[/C][C]42.4848805919373[/C][C]41.5067957702633[/C][C]43.4629654136113[/C][/ROW]
[ROW][C]83[/C][C]42.5113686511311[/C][C]41.4412118095481[/C][C]43.5815254927141[/C][/ROW]
[ROW][C]84[/C][C]42.5378567103248[/C][C]41.3736473124697[/C][C]43.7020661081799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209296&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209296&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	42.2464880591937	42.0537660610706	42.4392100573169
74	42.2729761183875	41.9828432519306	42.5631089848443
75	42.2994641775812	41.92227352084	42.6766548343224
76	42.3259522367749	41.8648711601919	42.787033313358
77	42.3524402959687	41.8080940460798	42.8967865458575
78	42.3789283551624	41.7507636554958	43.007093054829
79	42.4054164143561	41.6922567083858	43.1185761203264
80	42.4319044735499	41.6322187069361	43.2315902401636
81	42.4583925327436	41.5704401557315	43.3463449097557
82	42.4848805919373	41.5067957702633	43.4629654136113
83	42.5113686511311	41.4412118095481	43.5815254927141
84	42.5378567103248	41.3736473124697	43.7020661081799

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