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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 27 Nov 2016 15:26:15 +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/2016/Nov/27/t1480260454z6k4hs8hwu5qtc3.htm/, Retrieved Mon, 29 Apr 2024 23:20:00 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 23:20:00 +0200

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Estimated Impact

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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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.894316694477335
beta	0.0554592401396707
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.894316694477335 \tabularnewline
beta & 0.0554592401396707 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.894316694477335[/C][/ROW]
[ROW][C]beta[/C][C]0.0554592401396707[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.894316694477335
beta	0.0554592401396707
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	100	100	0
4	100	100	0
5	100	100	0
6	100	100	0
7	100	100	0
8	100	100	0
9	100	100	0
10	100	100	0
11	100	100	0
12	100	100	0
13	100.4	100	0.400000000000006
14	100.4	100.377565927519	0.0224340724810901
15	100.4	100.418581030708	-0.0185810307077645
16	100.4	100.421994058118	-0.021994058118068
17	100.4	100.421263894108	-0.021263894107804
18	100.4	100.420132078698	-0.0201320786981398
19	100.4	100.419013951362	-0.0190139513623109
20	100.4	100.417952727646	-0.0179527276459766
21	100.4	100.416950152398	-0.0169501523980671
22	100.4	100.416003501166	-0.0160035011659687
23	101.4	100.415109712294	0.984890287705809
24	101.4	101.35818065914	0.041819340859746
25	102	101.459921675012	0.540078324987732
26	102	102.034050890468	-0.0340508904684924
27	102.6	102.093037903456	0.506962096543603
28	102.6	102.661006231748	-0.0610062317481237
29	102.6	102.718005207448	-0.118005207447652
30	102.6	102.718176210662	-0.118176210661602
31	102.6	102.712332964458	-0.112332964458446
32	102.6	102.706143926548	-0.106143926548285
33	102.3	102.700225308899	-0.400225308899181
34	102.4	102.411454376852	-0.0114543768519155
35	102.4	102.469799664055	-0.0697996640549263
36	102.4	102.472503854453	-0.0725038544529184
37	102.9	102.469193587046	0.430806412953899
38	102.9	102.937369284311	-0.0373692843105857
39	102.9	102.984994193154	-0.0849941931538893
40	104.9	102.985811798387	1.91418820161286
41	104.9	104.869471738961	0.0305282610391657
42	105.5	105.070057292448	0.429942707552414
43	105.5	105.649170205326	-0.149170205326186
44	105.5	105.702974209841	-0.202974209841443
45	105.5	105.698593254796	-0.198593254795526
46	105.5	105.688280408044	-0.188280408044477
47	105.5	105.677852157225	-0.177852157225288
48	105.5	105.667928931803	-0.16792893180326
49	105.5	105.658551252503	-0.158551252502718
50	106.8	105.649696343623	1.15030365637661
51	106.8	106.868425134158	-0.0684251341581046
52	106.8	106.993830662967	-0.19383066296686
53	106.9	106.997470296463	-0.0974702964633423
54	107.5	107.082452270528	0.417547729471607
55	107.6	107.64873304734	-0.0487330473396668
56	107.6	107.795594073394	-0.195594073394318
57	107.6	107.801413732912	-0.201413732911774
58	107.8	107.792039030402	0.007960969598102
59	107.8	107.970306468908	-0.170306468907654
60	107.8	107.980699479659	-0.180699479658642

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 100 & 100 & 0 \tabularnewline
4 & 100 & 100 & 0 \tabularnewline
5 & 100 & 100 & 0 \tabularnewline
6 & 100 & 100 & 0 \tabularnewline
7 & 100 & 100 & 0 \tabularnewline
8 & 100 & 100 & 0 \tabularnewline
9 & 100 & 100 & 0 \tabularnewline
10 & 100 & 100 & 0 \tabularnewline
11 & 100 & 100 & 0 \tabularnewline
12 & 100 & 100 & 0 \tabularnewline
13 & 100.4 & 100 & 0.400000000000006 \tabularnewline
14 & 100.4 & 100.377565927519 & 0.0224340724810901 \tabularnewline
15 & 100.4 & 100.418581030708 & -0.0185810307077645 \tabularnewline
16 & 100.4 & 100.421994058118 & -0.021994058118068 \tabularnewline
17 & 100.4 & 100.421263894108 & -0.021263894107804 \tabularnewline
18 & 100.4 & 100.420132078698 & -0.0201320786981398 \tabularnewline
19 & 100.4 & 100.419013951362 & -0.0190139513623109 \tabularnewline
20 & 100.4 & 100.417952727646 & -0.0179527276459766 \tabularnewline
21 & 100.4 & 100.416950152398 & -0.0169501523980671 \tabularnewline
22 & 100.4 & 100.416003501166 & -0.0160035011659687 \tabularnewline
23 & 101.4 & 100.415109712294 & 0.984890287705809 \tabularnewline
24 & 101.4 & 101.35818065914 & 0.041819340859746 \tabularnewline
25 & 102 & 101.459921675012 & 0.540078324987732 \tabularnewline
26 & 102 & 102.034050890468 & -0.0340508904684924 \tabularnewline
27 & 102.6 & 102.093037903456 & 0.506962096543603 \tabularnewline
28 & 102.6 & 102.661006231748 & -0.0610062317481237 \tabularnewline
29 & 102.6 & 102.718005207448 & -0.118005207447652 \tabularnewline
30 & 102.6 & 102.718176210662 & -0.118176210661602 \tabularnewline
31 & 102.6 & 102.712332964458 & -0.112332964458446 \tabularnewline
32 & 102.6 & 102.706143926548 & -0.106143926548285 \tabularnewline
33 & 102.3 & 102.700225308899 & -0.400225308899181 \tabularnewline
34 & 102.4 & 102.411454376852 & -0.0114543768519155 \tabularnewline
35 & 102.4 & 102.469799664055 & -0.0697996640549263 \tabularnewline
36 & 102.4 & 102.472503854453 & -0.0725038544529184 \tabularnewline
37 & 102.9 & 102.469193587046 & 0.430806412953899 \tabularnewline
38 & 102.9 & 102.937369284311 & -0.0373692843105857 \tabularnewline
39 & 102.9 & 102.984994193154 & -0.0849941931538893 \tabularnewline
40 & 104.9 & 102.985811798387 & 1.91418820161286 \tabularnewline
41 & 104.9 & 104.869471738961 & 0.0305282610391657 \tabularnewline
42 & 105.5 & 105.070057292448 & 0.429942707552414 \tabularnewline
43 & 105.5 & 105.649170205326 & -0.149170205326186 \tabularnewline
44 & 105.5 & 105.702974209841 & -0.202974209841443 \tabularnewline
45 & 105.5 & 105.698593254796 & -0.198593254795526 \tabularnewline
46 & 105.5 & 105.688280408044 & -0.188280408044477 \tabularnewline
47 & 105.5 & 105.677852157225 & -0.177852157225288 \tabularnewline
48 & 105.5 & 105.667928931803 & -0.16792893180326 \tabularnewline
49 & 105.5 & 105.658551252503 & -0.158551252502718 \tabularnewline
50 & 106.8 & 105.649696343623 & 1.15030365637661 \tabularnewline
51 & 106.8 & 106.868425134158 & -0.0684251341581046 \tabularnewline
52 & 106.8 & 106.993830662967 & -0.19383066296686 \tabularnewline
53 & 106.9 & 106.997470296463 & -0.0974702964633423 \tabularnewline
54 & 107.5 & 107.082452270528 & 0.417547729471607 \tabularnewline
55 & 107.6 & 107.64873304734 & -0.0487330473396668 \tabularnewline
56 & 107.6 & 107.795594073394 & -0.195594073394318 \tabularnewline
57 & 107.6 & 107.801413732912 & -0.201413732911774 \tabularnewline
58 & 107.8 & 107.792039030402 & 0.007960969598102 \tabularnewline
59 & 107.8 & 107.970306468908 & -0.170306468907654 \tabularnewline
60 & 107.8 & 107.980699479659 & -0.180699479658642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]100.4[/C][C]100[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]14[/C][C]100.4[/C][C]100.377565927519[/C][C]0.0224340724810901[/C][/ROW]
[ROW][C]15[/C][C]100.4[/C][C]100.418581030708[/C][C]-0.0185810307077645[/C][/ROW]
[ROW][C]16[/C][C]100.4[/C][C]100.421994058118[/C][C]-0.021994058118068[/C][/ROW]
[ROW][C]17[/C][C]100.4[/C][C]100.421263894108[/C][C]-0.021263894107804[/C][/ROW]
[ROW][C]18[/C][C]100.4[/C][C]100.420132078698[/C][C]-0.0201320786981398[/C][/ROW]
[ROW][C]19[/C][C]100.4[/C][C]100.419013951362[/C][C]-0.0190139513623109[/C][/ROW]
[ROW][C]20[/C][C]100.4[/C][C]100.417952727646[/C][C]-0.0179527276459766[/C][/ROW]
[ROW][C]21[/C][C]100.4[/C][C]100.416950152398[/C][C]-0.0169501523980671[/C][/ROW]
[ROW][C]22[/C][C]100.4[/C][C]100.416003501166[/C][C]-0.0160035011659687[/C][/ROW]
[ROW][C]23[/C][C]101.4[/C][C]100.415109712294[/C][C]0.984890287705809[/C][/ROW]
[ROW][C]24[/C][C]101.4[/C][C]101.35818065914[/C][C]0.041819340859746[/C][/ROW]
[ROW][C]25[/C][C]102[/C][C]101.459921675012[/C][C]0.540078324987732[/C][/ROW]
[ROW][C]26[/C][C]102[/C][C]102.034050890468[/C][C]-0.0340508904684924[/C][/ROW]
[ROW][C]27[/C][C]102.6[/C][C]102.093037903456[/C][C]0.506962096543603[/C][/ROW]
[ROW][C]28[/C][C]102.6[/C][C]102.661006231748[/C][C]-0.0610062317481237[/C][/ROW]
[ROW][C]29[/C][C]102.6[/C][C]102.718005207448[/C][C]-0.118005207447652[/C][/ROW]
[ROW][C]30[/C][C]102.6[/C][C]102.718176210662[/C][C]-0.118176210661602[/C][/ROW]
[ROW][C]31[/C][C]102.6[/C][C]102.712332964458[/C][C]-0.112332964458446[/C][/ROW]
[ROW][C]32[/C][C]102.6[/C][C]102.706143926548[/C][C]-0.106143926548285[/C][/ROW]
[ROW][C]33[/C][C]102.3[/C][C]102.700225308899[/C][C]-0.400225308899181[/C][/ROW]
[ROW][C]34[/C][C]102.4[/C][C]102.411454376852[/C][C]-0.0114543768519155[/C][/ROW]
[ROW][C]35[/C][C]102.4[/C][C]102.469799664055[/C][C]-0.0697996640549263[/C][/ROW]
[ROW][C]36[/C][C]102.4[/C][C]102.472503854453[/C][C]-0.0725038544529184[/C][/ROW]
[ROW][C]37[/C][C]102.9[/C][C]102.469193587046[/C][C]0.430806412953899[/C][/ROW]
[ROW][C]38[/C][C]102.9[/C][C]102.937369284311[/C][C]-0.0373692843105857[/C][/ROW]
[ROW][C]39[/C][C]102.9[/C][C]102.984994193154[/C][C]-0.0849941931538893[/C][/ROW]
[ROW][C]40[/C][C]104.9[/C][C]102.985811798387[/C][C]1.91418820161286[/C][/ROW]
[ROW][C]41[/C][C]104.9[/C][C]104.869471738961[/C][C]0.0305282610391657[/C][/ROW]
[ROW][C]42[/C][C]105.5[/C][C]105.070057292448[/C][C]0.429942707552414[/C][/ROW]
[ROW][C]43[/C][C]105.5[/C][C]105.649170205326[/C][C]-0.149170205326186[/C][/ROW]
[ROW][C]44[/C][C]105.5[/C][C]105.702974209841[/C][C]-0.202974209841443[/C][/ROW]
[ROW][C]45[/C][C]105.5[/C][C]105.698593254796[/C][C]-0.198593254795526[/C][/ROW]
[ROW][C]46[/C][C]105.5[/C][C]105.688280408044[/C][C]-0.188280408044477[/C][/ROW]
[ROW][C]47[/C][C]105.5[/C][C]105.677852157225[/C][C]-0.177852157225288[/C][/ROW]
[ROW][C]48[/C][C]105.5[/C][C]105.667928931803[/C][C]-0.16792893180326[/C][/ROW]
[ROW][C]49[/C][C]105.5[/C][C]105.658551252503[/C][C]-0.158551252502718[/C][/ROW]
[ROW][C]50[/C][C]106.8[/C][C]105.649696343623[/C][C]1.15030365637661[/C][/ROW]
[ROW][C]51[/C][C]106.8[/C][C]106.868425134158[/C][C]-0.0684251341581046[/C][/ROW]
[ROW][C]52[/C][C]106.8[/C][C]106.993830662967[/C][C]-0.19383066296686[/C][/ROW]
[ROW][C]53[/C][C]106.9[/C][C]106.997470296463[/C][C]-0.0974702964633423[/C][/ROW]
[ROW][C]54[/C][C]107.5[/C][C]107.082452270528[/C][C]0.417547729471607[/C][/ROW]
[ROW][C]55[/C][C]107.6[/C][C]107.64873304734[/C][C]-0.0487330473396668[/C][/ROW]
[ROW][C]56[/C][C]107.6[/C][C]107.795594073394[/C][C]-0.195594073394318[/C][/ROW]
[ROW][C]57[/C][C]107.6[/C][C]107.801413732912[/C][C]-0.201413732911774[/C][/ROW]
[ROW][C]58[/C][C]107.8[/C][C]107.792039030402[/C][C]0.007960969598102[/C][/ROW]
[ROW][C]59[/C][C]107.8[/C][C]107.970306468908[/C][C]-0.170306468907654[/C][/ROW]
[ROW][C]60[/C][C]107.8[/C][C]107.980699479659[/C][C]-0.180699479658642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	100	100	0
4	100	100	0
5	100	100	0
6	100	100	0
7	100	100	0
8	100	100	0
9	100	100	0
10	100	100	0
11	100	100	0
12	100	100	0
13	100.4	100	0.400000000000006
14	100.4	100.377565927519	0.0224340724810901
15	100.4	100.418581030708	-0.0185810307077645
16	100.4	100.421994058118	-0.021994058118068
17	100.4	100.421263894108	-0.021263894107804
18	100.4	100.420132078698	-0.0201320786981398
19	100.4	100.419013951362	-0.0190139513623109
20	100.4	100.417952727646	-0.0179527276459766
21	100.4	100.416950152398	-0.0169501523980671
22	100.4	100.416003501166	-0.0160035011659687
23	101.4	100.415109712294	0.984890287705809
24	101.4	101.35818065914	0.041819340859746
25	102	101.459921675012	0.540078324987732
26	102	102.034050890468	-0.0340508904684924
27	102.6	102.093037903456	0.506962096543603
28	102.6	102.661006231748	-0.0610062317481237
29	102.6	102.718005207448	-0.118005207447652
30	102.6	102.718176210662	-0.118176210661602
31	102.6	102.712332964458	-0.112332964458446
32	102.6	102.706143926548	-0.106143926548285
33	102.3	102.700225308899	-0.400225308899181
34	102.4	102.411454376852	-0.0114543768519155
35	102.4	102.469799664055	-0.0697996640549263
36	102.4	102.472503854453	-0.0725038544529184
37	102.9	102.469193587046	0.430806412953899
38	102.9	102.937369284311	-0.0373692843105857
39	102.9	102.984994193154	-0.0849941931538893
40	104.9	102.985811798387	1.91418820161286
41	104.9	104.869471738961	0.0305282610391657
42	105.5	105.070057292448	0.429942707552414
43	105.5	105.649170205326	-0.149170205326186
44	105.5	105.702974209841	-0.202974209841443
45	105.5	105.698593254796	-0.198593254795526
46	105.5	105.688280408044	-0.188280408044477
47	105.5	105.677852157225	-0.177852157225288
48	105.5	105.667928931803	-0.16792893180326
49	105.5	105.658551252503	-0.158551252502718
50	106.8	105.649696343623	1.15030365637661
51	106.8	106.868425134158	-0.0684251341581046
52	106.8	106.993830662967	-0.19383066296686
53	106.9	106.997470296463	-0.0974702964633423
54	107.5	107.082452270528	0.417547729471607
55	107.6	107.64873304734	-0.0487330473396668
56	107.6	107.795594073394	-0.195594073394318
57	107.6	107.801413732912	-0.201413732911774
58	107.8	107.792039030402	0.007960969598102
59	107.8	107.970306468908	-0.170306468907654
60	107.8	107.980699479659	-0.180699479658642

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	107.972835492132	107.252233249902	108.693437734363
62	108.126574065948	107.135654225603	109.117493906294
63	108.280312639764	107.057825610606	109.502799668923
64	108.43405121358	106.998962512349	109.869139914811
65	108.587789787396	106.950874386011	110.224705188782
66	108.741528361212	106.909298392399	110.573758330025
67	108.895266935028	106.871716038248	110.918817831808
68	109.049005508844	106.836513357333	111.261497660354
69	109.20274408266	106.802595900982	111.602892264338
70	109.356482656476	106.769190187138	111.943775125813
71	109.510221230292	106.735732201009	112.284710259575
72	109.663959804108	106.701800588492	112.626119019723

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 107.972835492132 & 107.252233249902 & 108.693437734363 \tabularnewline
62 & 108.126574065948 & 107.135654225603 & 109.117493906294 \tabularnewline
63 & 108.280312639764 & 107.057825610606 & 109.502799668923 \tabularnewline
64 & 108.43405121358 & 106.998962512349 & 109.869139914811 \tabularnewline
65 & 108.587789787396 & 106.950874386011 & 110.224705188782 \tabularnewline
66 & 108.741528361212 & 106.909298392399 & 110.573758330025 \tabularnewline
67 & 108.895266935028 & 106.871716038248 & 110.918817831808 \tabularnewline
68 & 109.049005508844 & 106.836513357333 & 111.261497660354 \tabularnewline
69 & 109.20274408266 & 106.802595900982 & 111.602892264338 \tabularnewline
70 & 109.356482656476 & 106.769190187138 & 111.943775125813 \tabularnewline
71 & 109.510221230292 & 106.735732201009 & 112.284710259575 \tabularnewline
72 & 109.663959804108 & 106.701800588492 & 112.626119019723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]107.972835492132[/C][C]107.252233249902[/C][C]108.693437734363[/C][/ROW]
[ROW][C]62[/C][C]108.126574065948[/C][C]107.135654225603[/C][C]109.117493906294[/C][/ROW]
[ROW][C]63[/C][C]108.280312639764[/C][C]107.057825610606[/C][C]109.502799668923[/C][/ROW]
[ROW][C]64[/C][C]108.43405121358[/C][C]106.998962512349[/C][C]109.869139914811[/C][/ROW]
[ROW][C]65[/C][C]108.587789787396[/C][C]106.950874386011[/C][C]110.224705188782[/C][/ROW]
[ROW][C]66[/C][C]108.741528361212[/C][C]106.909298392399[/C][C]110.573758330025[/C][/ROW]
[ROW][C]67[/C][C]108.895266935028[/C][C]106.871716038248[/C][C]110.918817831808[/C][/ROW]
[ROW][C]68[/C][C]109.049005508844[/C][C]106.836513357333[/C][C]111.261497660354[/C][/ROW]
[ROW][C]69[/C][C]109.20274408266[/C][C]106.802595900982[/C][C]111.602892264338[/C][/ROW]
[ROW][C]70[/C][C]109.356482656476[/C][C]106.769190187138[/C][C]111.943775125813[/C][/ROW]
[ROW][C]71[/C][C]109.510221230292[/C][C]106.735732201009[/C][C]112.284710259575[/C][/ROW]
[ROW][C]72[/C][C]109.663959804108[/C][C]106.701800588492[/C][C]112.626119019723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61	107.972835492132	107.252233249902	108.693437734363
62	108.126574065948	107.135654225603	109.117493906294
63	108.280312639764	107.057825610606	109.502799668923
64	108.43405121358	106.998962512349	109.869139914811
65	108.587789787396	106.950874386011	110.224705188782
66	108.741528361212	106.909298392399	110.573758330025
67	108.895266935028	106.871716038248	110.918817831808
68	109.049005508844	106.836513357333	111.261497660354
69	109.20274408266	106.802595900982	111.602892264338
70	109.356482656476	106.769190187138	111.943775125813
71	109.510221230292	106.735732201009	112.284710259575
72	109.663959804108	106.701800588492	112.626119019723

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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