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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 12 Dec 2011 15:03:37 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/12/t1323720274vfj9c5pbjyc40tb.htm/, Retrieved Fri, 03 May 2024 08:28:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154189, Retrieved Fri, 03 May 2024 08:28:54 +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] [Exponential Smoot...] [2011-12-12 20:03:37] [82ceb5b481b3a9ad89a8151bb4a3670f] [Current]

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Dataseries X:

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1.35
1.91
1.31
1.19
1.3
1.14
1.1
1.02
1.11
1.18
1.24
1.36
1.29
1.73
1.41
1.15
1.31
1.15
1.08
1.1
1.14
1.24
1.33
1.49
1.38
1.96
1.36
1.24
1.35
1.23
1.09
1.08
1.33
1.35
1.38
1.5
1.47
2.09
1.52
1.29
1.52
1.27
1.35
1.29
1.41
1.39
1.45
1.53
1.45
2.11
1.53
1.38
1.54
1.35
1.29
1.33
1.47
1.47
1.54
1.59
1.5
2
1.51
1.4
1.62
1.44
1.29
1.28
1.4
1.39
1.46
1.49

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	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154189&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154189&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154189&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.259326530458147
beta	0
gamma	0.48255780916394

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.259326530458147 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.48255780916394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154189&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]0.259326530458147[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.48255780916394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154189&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154189&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	0.259326530458147
beta	0
gamma	0.48255780916394

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.29	1.29367788461538	-0.00367788461538443
14	1.73	1.73171449617404	-0.00171449617403585
15	1.41	1.40817693311179	0.0018230668882091
16	1.15	1.14639008733809	0.00360991266191202
17	1.31	1.30256661807934	0.0074333819206569
18	1.15	1.13681800917112	0.0131819908288846
19	1.08	1.10631016706602	-0.0263101670660191
20	1.1	1.0309776273404	0.0690223726596013
21	1.14	1.14370067771492	-0.00370067771492044
22	1.24	1.21173137841815	0.0282686215818491
23	1.33	1.28180256658919	0.0481974334108093
24	1.49	1.41495849105466	0.0750415089453449
25	1.38	1.36501125518619	0.0149887448138144
26	1.96	1.80859036890206	0.151409631097936
27	1.36	1.5260263423842	-0.166026342384199
28	1.24	1.22135034209043	0.018649657909571
29	1.35	1.3827936536295	-0.0327936536295004
30	1.23	1.20866776211944	0.0213322378805649
31	1.09	1.16615829642498	-0.0761582964249834
32	1.08	1.11197235771192	-0.031972357711924
33	1.33	1.17251228480723	0.157487715192774
34	1.35	1.29376980775312	0.0562301922468784
35	1.38	1.37821508444913	0.00178491555086979
36	1.5	1.50892956121665	-0.00892956121665378
37	1.47	1.41574247422008	0.0542575257799198
38	2.09	1.9182642731754	0.171735726824602
39	1.52	1.52751408580629	-0.00751408580628832
40	1.29	1.3299510026466	-0.0399510026465997
41	1.52	1.45781085467564	0.0621891453243599
42	1.27	1.32766207813934	-0.057662078139336
43	1.35	1.22982244149302	0.120177558506977
44	1.29	1.24234443838137	0.0476555616186285
45	1.41	1.39125039367356	0.018749606326439
46	1.39	1.44033820648505	-0.0503382064850468
47	1.45	1.47768776087367	-0.0276877608736728
48	1.53	1.59692964636237	-0.0669296463623688
49	1.45	1.51128578604157	-0.0612857860415685
50	2.11	2.02583293508588	0.0841670649141153
51	1.53	1.54830680272256	-0.0183068027225557
52	1.38	1.33635135135285	0.0436486486471477
53	1.54	1.52239751448454	0.0176024855154584
54	1.35	1.33784927752047	0.0121507224795259
55	1.29	1.32167699801317	-0.0316769980131701
56	1.33	1.2688984294555	0.0611015705444995
57	1.47	1.41095978960412	0.0590402103958836
58	1.47	1.44580281321303	0.0241971867869708
59	1.54	1.51057704422194	0.0294229557780621
60	1.59	1.63060350663677	-0.0406035066367723
61	1.5	1.55380392874318	-0.0538039287431782
62	2	2.12227875504068	-0.122278755040684
63	1.51	1.55458976353811	-0.0445897635381141
64	1.4	1.35796242219761	0.0420375778023947
65	1.62	1.5342814304574	0.0857185695426004
66	1.44	1.36544894426324	0.0745510557367643
67	1.29	1.34979392069793	-0.059793920697933
68	1.28	1.32288459691108	-0.0428845969110754
69	1.4	1.43724281829697	-0.0372428182969744
70	1.39	1.43466358244722	-0.0446635824472248
71	1.46	1.48344817176839	-0.0234481717683914
72	1.49	1.56473504630422	-0.0747350463042225

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.29 & 1.29367788461538 & -0.00367788461538443 \tabularnewline
14 & 1.73 & 1.73171449617404 & -0.00171449617403585 \tabularnewline
15 & 1.41 & 1.40817693311179 & 0.0018230668882091 \tabularnewline
16 & 1.15 & 1.14639008733809 & 0.00360991266191202 \tabularnewline
17 & 1.31 & 1.30256661807934 & 0.0074333819206569 \tabularnewline
18 & 1.15 & 1.13681800917112 & 0.0131819908288846 \tabularnewline
19 & 1.08 & 1.10631016706602 & -0.0263101670660191 \tabularnewline
20 & 1.1 & 1.0309776273404 & 0.0690223726596013 \tabularnewline
21 & 1.14 & 1.14370067771492 & -0.00370067771492044 \tabularnewline
22 & 1.24 & 1.21173137841815 & 0.0282686215818491 \tabularnewline
23 & 1.33 & 1.28180256658919 & 0.0481974334108093 \tabularnewline
24 & 1.49 & 1.41495849105466 & 0.0750415089453449 \tabularnewline
25 & 1.38 & 1.36501125518619 & 0.0149887448138144 \tabularnewline
26 & 1.96 & 1.80859036890206 & 0.151409631097936 \tabularnewline
27 & 1.36 & 1.5260263423842 & -0.166026342384199 \tabularnewline
28 & 1.24 & 1.22135034209043 & 0.018649657909571 \tabularnewline
29 & 1.35 & 1.3827936536295 & -0.0327936536295004 \tabularnewline
30 & 1.23 & 1.20866776211944 & 0.0213322378805649 \tabularnewline
31 & 1.09 & 1.16615829642498 & -0.0761582964249834 \tabularnewline
32 & 1.08 & 1.11197235771192 & -0.031972357711924 \tabularnewline
33 & 1.33 & 1.17251228480723 & 0.157487715192774 \tabularnewline
34 & 1.35 & 1.29376980775312 & 0.0562301922468784 \tabularnewline
35 & 1.38 & 1.37821508444913 & 0.00178491555086979 \tabularnewline
36 & 1.5 & 1.50892956121665 & -0.00892956121665378 \tabularnewline
37 & 1.47 & 1.41574247422008 & 0.0542575257799198 \tabularnewline
38 & 2.09 & 1.9182642731754 & 0.171735726824602 \tabularnewline
39 & 1.52 & 1.52751408580629 & -0.00751408580628832 \tabularnewline
40 & 1.29 & 1.3299510026466 & -0.0399510026465997 \tabularnewline
41 & 1.52 & 1.45781085467564 & 0.0621891453243599 \tabularnewline
42 & 1.27 & 1.32766207813934 & -0.057662078139336 \tabularnewline
43 & 1.35 & 1.22982244149302 & 0.120177558506977 \tabularnewline
44 & 1.29 & 1.24234443838137 & 0.0476555616186285 \tabularnewline
45 & 1.41 & 1.39125039367356 & 0.018749606326439 \tabularnewline
46 & 1.39 & 1.44033820648505 & -0.0503382064850468 \tabularnewline
47 & 1.45 & 1.47768776087367 & -0.0276877608736728 \tabularnewline
48 & 1.53 & 1.59692964636237 & -0.0669296463623688 \tabularnewline
49 & 1.45 & 1.51128578604157 & -0.0612857860415685 \tabularnewline
50 & 2.11 & 2.02583293508588 & 0.0841670649141153 \tabularnewline
51 & 1.53 & 1.54830680272256 & -0.0183068027225557 \tabularnewline
52 & 1.38 & 1.33635135135285 & 0.0436486486471477 \tabularnewline
53 & 1.54 & 1.52239751448454 & 0.0176024855154584 \tabularnewline
54 & 1.35 & 1.33784927752047 & 0.0121507224795259 \tabularnewline
55 & 1.29 & 1.32167699801317 & -0.0316769980131701 \tabularnewline
56 & 1.33 & 1.2688984294555 & 0.0611015705444995 \tabularnewline
57 & 1.47 & 1.41095978960412 & 0.0590402103958836 \tabularnewline
58 & 1.47 & 1.44580281321303 & 0.0241971867869708 \tabularnewline
59 & 1.54 & 1.51057704422194 & 0.0294229557780621 \tabularnewline
60 & 1.59 & 1.63060350663677 & -0.0406035066367723 \tabularnewline
61 & 1.5 & 1.55380392874318 & -0.0538039287431782 \tabularnewline
62 & 2 & 2.12227875504068 & -0.122278755040684 \tabularnewline
63 & 1.51 & 1.55458976353811 & -0.0445897635381141 \tabularnewline
64 & 1.4 & 1.35796242219761 & 0.0420375778023947 \tabularnewline
65 & 1.62 & 1.5342814304574 & 0.0857185695426004 \tabularnewline
66 & 1.44 & 1.36544894426324 & 0.0745510557367643 \tabularnewline
67 & 1.29 & 1.34979392069793 & -0.059793920697933 \tabularnewline
68 & 1.28 & 1.32288459691108 & -0.0428845969110754 \tabularnewline
69 & 1.4 & 1.43724281829697 & -0.0372428182969744 \tabularnewline
70 & 1.39 & 1.43466358244722 & -0.0446635824472248 \tabularnewline
71 & 1.46 & 1.48344817176839 & -0.0234481717683914 \tabularnewline
72 & 1.49 & 1.56473504630422 & -0.0747350463042225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154189&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1.29[/C][C]1.29367788461538[/C][C]-0.00367788461538443[/C][/ROW]
[ROW][C]14[/C][C]1.73[/C][C]1.73171449617404[/C][C]-0.00171449617403585[/C][/ROW]
[ROW][C]15[/C][C]1.41[/C][C]1.40817693311179[/C][C]0.0018230668882091[/C][/ROW]
[ROW][C]16[/C][C]1.15[/C][C]1.14639008733809[/C][C]0.00360991266191202[/C][/ROW]
[ROW][C]17[/C][C]1.31[/C][C]1.30256661807934[/C][C]0.0074333819206569[/C][/ROW]
[ROW][C]18[/C][C]1.15[/C][C]1.13681800917112[/C][C]0.0131819908288846[/C][/ROW]
[ROW][C]19[/C][C]1.08[/C][C]1.10631016706602[/C][C]-0.0263101670660191[/C][/ROW]
[ROW][C]20[/C][C]1.1[/C][C]1.0309776273404[/C][C]0.0690223726596013[/C][/ROW]
[ROW][C]21[/C][C]1.14[/C][C]1.14370067771492[/C][C]-0.00370067771492044[/C][/ROW]
[ROW][C]22[/C][C]1.24[/C][C]1.21173137841815[/C][C]0.0282686215818491[/C][/ROW]
[ROW][C]23[/C][C]1.33[/C][C]1.28180256658919[/C][C]0.0481974334108093[/C][/ROW]
[ROW][C]24[/C][C]1.49[/C][C]1.41495849105466[/C][C]0.0750415089453449[/C][/ROW]
[ROW][C]25[/C][C]1.38[/C][C]1.36501125518619[/C][C]0.0149887448138144[/C][/ROW]
[ROW][C]26[/C][C]1.96[/C][C]1.80859036890206[/C][C]0.151409631097936[/C][/ROW]
[ROW][C]27[/C][C]1.36[/C][C]1.5260263423842[/C][C]-0.166026342384199[/C][/ROW]
[ROW][C]28[/C][C]1.24[/C][C]1.22135034209043[/C][C]0.018649657909571[/C][/ROW]
[ROW][C]29[/C][C]1.35[/C][C]1.3827936536295[/C][C]-0.0327936536295004[/C][/ROW]
[ROW][C]30[/C][C]1.23[/C][C]1.20866776211944[/C][C]0.0213322378805649[/C][/ROW]
[ROW][C]31[/C][C]1.09[/C][C]1.16615829642498[/C][C]-0.0761582964249834[/C][/ROW]
[ROW][C]32[/C][C]1.08[/C][C]1.11197235771192[/C][C]-0.031972357711924[/C][/ROW]
[ROW][C]33[/C][C]1.33[/C][C]1.17251228480723[/C][C]0.157487715192774[/C][/ROW]
[ROW][C]34[/C][C]1.35[/C][C]1.29376980775312[/C][C]0.0562301922468784[/C][/ROW]
[ROW][C]35[/C][C]1.38[/C][C]1.37821508444913[/C][C]0.00178491555086979[/C][/ROW]
[ROW][C]36[/C][C]1.5[/C][C]1.50892956121665[/C][C]-0.00892956121665378[/C][/ROW]
[ROW][C]37[/C][C]1.47[/C][C]1.41574247422008[/C][C]0.0542575257799198[/C][/ROW]
[ROW][C]38[/C][C]2.09[/C][C]1.9182642731754[/C][C]0.171735726824602[/C][/ROW]
[ROW][C]39[/C][C]1.52[/C][C]1.52751408580629[/C][C]-0.00751408580628832[/C][/ROW]
[ROW][C]40[/C][C]1.29[/C][C]1.3299510026466[/C][C]-0.0399510026465997[/C][/ROW]
[ROW][C]41[/C][C]1.52[/C][C]1.45781085467564[/C][C]0.0621891453243599[/C][/ROW]
[ROW][C]42[/C][C]1.27[/C][C]1.32766207813934[/C][C]-0.057662078139336[/C][/ROW]
[ROW][C]43[/C][C]1.35[/C][C]1.22982244149302[/C][C]0.120177558506977[/C][/ROW]
[ROW][C]44[/C][C]1.29[/C][C]1.24234443838137[/C][C]0.0476555616186285[/C][/ROW]
[ROW][C]45[/C][C]1.41[/C][C]1.39125039367356[/C][C]0.018749606326439[/C][/ROW]
[ROW][C]46[/C][C]1.39[/C][C]1.44033820648505[/C][C]-0.0503382064850468[/C][/ROW]
[ROW][C]47[/C][C]1.45[/C][C]1.47768776087367[/C][C]-0.0276877608736728[/C][/ROW]
[ROW][C]48[/C][C]1.53[/C][C]1.59692964636237[/C][C]-0.0669296463623688[/C][/ROW]
[ROW][C]49[/C][C]1.45[/C][C]1.51128578604157[/C][C]-0.0612857860415685[/C][/ROW]
[ROW][C]50[/C][C]2.11[/C][C]2.02583293508588[/C][C]0.0841670649141153[/C][/ROW]
[ROW][C]51[/C][C]1.53[/C][C]1.54830680272256[/C][C]-0.0183068027225557[/C][/ROW]
[ROW][C]52[/C][C]1.38[/C][C]1.33635135135285[/C][C]0.0436486486471477[/C][/ROW]
[ROW][C]53[/C][C]1.54[/C][C]1.52239751448454[/C][C]0.0176024855154584[/C][/ROW]
[ROW][C]54[/C][C]1.35[/C][C]1.33784927752047[/C][C]0.0121507224795259[/C][/ROW]
[ROW][C]55[/C][C]1.29[/C][C]1.32167699801317[/C][C]-0.0316769980131701[/C][/ROW]
[ROW][C]56[/C][C]1.33[/C][C]1.2688984294555[/C][C]0.0611015705444995[/C][/ROW]
[ROW][C]57[/C][C]1.47[/C][C]1.41095978960412[/C][C]0.0590402103958836[/C][/ROW]
[ROW][C]58[/C][C]1.47[/C][C]1.44580281321303[/C][C]0.0241971867869708[/C][/ROW]
[ROW][C]59[/C][C]1.54[/C][C]1.51057704422194[/C][C]0.0294229557780621[/C][/ROW]
[ROW][C]60[/C][C]1.59[/C][C]1.63060350663677[/C][C]-0.0406035066367723[/C][/ROW]
[ROW][C]61[/C][C]1.5[/C][C]1.55380392874318[/C][C]-0.0538039287431782[/C][/ROW]
[ROW][C]62[/C][C]2[/C][C]2.12227875504068[/C][C]-0.122278755040684[/C][/ROW]
[ROW][C]63[/C][C]1.51[/C][C]1.55458976353811[/C][C]-0.0445897635381141[/C][/ROW]
[ROW][C]64[/C][C]1.4[/C][C]1.35796242219761[/C][C]0.0420375778023947[/C][/ROW]
[ROW][C]65[/C][C]1.62[/C][C]1.5342814304574[/C][C]0.0857185695426004[/C][/ROW]
[ROW][C]66[/C][C]1.44[/C][C]1.36544894426324[/C][C]0.0745510557367643[/C][/ROW]
[ROW][C]67[/C][C]1.29[/C][C]1.34979392069793[/C][C]-0.059793920697933[/C][/ROW]
[ROW][C]68[/C][C]1.28[/C][C]1.32288459691108[/C][C]-0.0428845969110754[/C][/ROW]
[ROW][C]69[/C][C]1.4[/C][C]1.43724281829697[/C][C]-0.0372428182969744[/C][/ROW]
[ROW][C]70[/C][C]1.39[/C][C]1.43466358244722[/C][C]-0.0446635824472248[/C][/ROW]
[ROW][C]71[/C][C]1.46[/C][C]1.48344817176839[/C][C]-0.0234481717683914[/C][/ROW]
[ROW][C]72[/C][C]1.49[/C][C]1.56473504630422[/C][C]-0.0747350463042225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154189&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154189&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.29	1.29367788461538	-0.00367788461538443
14	1.73	1.73171449617404	-0.00171449617403585
15	1.41	1.40817693311179	0.0018230668882091
16	1.15	1.14639008733809	0.00360991266191202
17	1.31	1.30256661807934	0.0074333819206569
18	1.15	1.13681800917112	0.0131819908288846
19	1.08	1.10631016706602	-0.0263101670660191
20	1.1	1.0309776273404	0.0690223726596013
21	1.14	1.14370067771492	-0.00370067771492044
22	1.24	1.21173137841815	0.0282686215818491
23	1.33	1.28180256658919	0.0481974334108093
24	1.49	1.41495849105466	0.0750415089453449
25	1.38	1.36501125518619	0.0149887448138144
26	1.96	1.80859036890206	0.151409631097936
27	1.36	1.5260263423842	-0.166026342384199
28	1.24	1.22135034209043	0.018649657909571
29	1.35	1.3827936536295	-0.0327936536295004
30	1.23	1.20866776211944	0.0213322378805649
31	1.09	1.16615829642498	-0.0761582964249834
32	1.08	1.11197235771192	-0.031972357711924
33	1.33	1.17251228480723	0.157487715192774
34	1.35	1.29376980775312	0.0562301922468784
35	1.38	1.37821508444913	0.00178491555086979
36	1.5	1.50892956121665	-0.00892956121665378
37	1.47	1.41574247422008	0.0542575257799198
38	2.09	1.9182642731754	0.171735726824602
39	1.52	1.52751408580629	-0.00751408580628832
40	1.29	1.3299510026466	-0.0399510026465997
41	1.52	1.45781085467564	0.0621891453243599
42	1.27	1.32766207813934	-0.057662078139336
43	1.35	1.22982244149302	0.120177558506977
44	1.29	1.24234443838137	0.0476555616186285
45	1.41	1.39125039367356	0.018749606326439
46	1.39	1.44033820648505	-0.0503382064850468
47	1.45	1.47768776087367	-0.0276877608736728
48	1.53	1.59692964636237	-0.0669296463623688
49	1.45	1.51128578604157	-0.0612857860415685
50	2.11	2.02583293508588	0.0841670649141153
51	1.53	1.54830680272256	-0.0183068027225557
52	1.38	1.33635135135285	0.0436486486471477
53	1.54	1.52239751448454	0.0176024855154584
54	1.35	1.33784927752047	0.0121507224795259
55	1.29	1.32167699801317	-0.0316769980131701
56	1.33	1.2688984294555	0.0611015705444995
57	1.47	1.41095978960412	0.0590402103958836
58	1.47	1.44580281321303	0.0241971867869708
59	1.54	1.51057704422194	0.0294229557780621
60	1.59	1.63060350663677	-0.0406035066367723
61	1.5	1.55380392874318	-0.0538039287431782
62	2	2.12227875504068	-0.122278755040684
63	1.51	1.55458976353811	-0.0445897635381141
64	1.4	1.35796242219761	0.0420375778023947
65	1.62	1.5342814304574	0.0857185695426004
66	1.44	1.36544894426324	0.0745510557367643
67	1.29	1.34979392069793	-0.059793920697933
68	1.28	1.32288459691108	-0.0428845969110754
69	1.4	1.43724281829697	-0.0372428182969744
70	1.39	1.43466358244722	-0.0446635824472248
71	1.46	1.48344817176839	-0.0234481717683914
72	1.49	1.56473504630422	-0.0747350463042225

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.47436618925981	1.34950920795588	1.59922317056373
74	2.03231968222822	1.90333267593685	2.16130668851959
75	1.5241082418644	1.3911194084847	1.65709707524409
76	1.37000636007915	1.23313265254051	1.50688006761779
77	1.55103627165658	1.41038495162347	1.69168759168968
78	1.35598321838226	1.21165312505888	1.50031331170565
79	1.27297784673697	1.12506044461532	1.42089524885862
80	1.26761836569265	1.11619861842665	1.41903811295865
81	1.39511417271845	1.24027127855219	1.5499570668847
82	1.39954067477184	1.24134869050758	1.5577326590361
83	1.46749048067277	1.30601885500081	1.62896210634473
84	1.53652724807778	1.37184128052491	1.70121321563065

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.47436618925981 & 1.34950920795588 & 1.59922317056373 \tabularnewline
74 & 2.03231968222822 & 1.90333267593685 & 2.16130668851959 \tabularnewline
75 & 1.5241082418644 & 1.3911194084847 & 1.65709707524409 \tabularnewline
76 & 1.37000636007915 & 1.23313265254051 & 1.50688006761779 \tabularnewline
77 & 1.55103627165658 & 1.41038495162347 & 1.69168759168968 \tabularnewline
78 & 1.35598321838226 & 1.21165312505888 & 1.50031331170565 \tabularnewline
79 & 1.27297784673697 & 1.12506044461532 & 1.42089524885862 \tabularnewline
80 & 1.26761836569265 & 1.11619861842665 & 1.41903811295865 \tabularnewline
81 & 1.39511417271845 & 1.24027127855219 & 1.5499570668847 \tabularnewline
82 & 1.39954067477184 & 1.24134869050758 & 1.5577326590361 \tabularnewline
83 & 1.46749048067277 & 1.30601885500081 & 1.62896210634473 \tabularnewline
84 & 1.53652724807778 & 1.37184128052491 & 1.70121321563065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154189&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]1.47436618925981[/C][C]1.34950920795588[/C][C]1.59922317056373[/C][/ROW]
[ROW][C]74[/C][C]2.03231968222822[/C][C]1.90333267593685[/C][C]2.16130668851959[/C][/ROW]
[ROW][C]75[/C][C]1.5241082418644[/C][C]1.3911194084847[/C][C]1.65709707524409[/C][/ROW]
[ROW][C]76[/C][C]1.37000636007915[/C][C]1.23313265254051[/C][C]1.50688006761779[/C][/ROW]
[ROW][C]77[/C][C]1.55103627165658[/C][C]1.41038495162347[/C][C]1.69168759168968[/C][/ROW]
[ROW][C]78[/C][C]1.35598321838226[/C][C]1.21165312505888[/C][C]1.50031331170565[/C][/ROW]
[ROW][C]79[/C][C]1.27297784673697[/C][C]1.12506044461532[/C][C]1.42089524885862[/C][/ROW]
[ROW][C]80[/C][C]1.26761836569265[/C][C]1.11619861842665[/C][C]1.41903811295865[/C][/ROW]
[ROW][C]81[/C][C]1.39511417271845[/C][C]1.24027127855219[/C][C]1.5499570668847[/C][/ROW]
[ROW][C]82[/C][C]1.39954067477184[/C][C]1.24134869050758[/C][C]1.5577326590361[/C][/ROW]
[ROW][C]83[/C][C]1.46749048067277[/C][C]1.30601885500081[/C][C]1.62896210634473[/C][/ROW]
[ROW][C]84[/C][C]1.53652724807778[/C][C]1.37184128052491[/C][C]1.70121321563065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154189&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154189&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	1.47436618925981	1.34950920795588	1.59922317056373
74	2.03231968222822	1.90333267593685	2.16130668851959
75	1.5241082418644	1.3911194084847	1.65709707524409
76	1.37000636007915	1.23313265254051	1.50688006761779
77	1.55103627165658	1.41038495162347	1.69168759168968
78	1.35598321838226	1.21165312505888	1.50031331170565
79	1.27297784673697	1.12506044461532	1.42089524885862
80	1.26761836569265	1.11619861842665	1.41903811295865
81	1.39511417271845	1.24027127855219	1.5499570668847
82	1.39954067477184	1.24134869050758	1.5577326590361
83	1.46749048067277	1.30601885500081	1.62896210634473
84	1.53652724807778	1.37184128052491	1.70121321563065

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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