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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 17 Dec 2012 03:09:55 -0500

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/2012/Dec/17/t13557318712b1pzbkpe7pfeqx.htm/, Retrieved Thu, 25 Apr 2024 14:44:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200696, Retrieved Thu, 25 Apr 2024 14:44:19 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [exponential smoot...] [2012-12-17 08:09:55] [f824ea295e177f9d3dd7528a75f4b680] [Current]

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Dataseries X:

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1.58
1.58
1.58
1.58
1.59
1.59
1.6
1.6
1.61
1.62
1.62
1.63
1.63
1.63
1.63
1.63
1.63
1.64
1.64
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

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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200696&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200696&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.752890942654235
beta	0.0947903596727852
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.752890942654235 \tabularnewline
beta & 0.0947903596727852 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200696&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]0.752890942654235[/C][/ROW]
[ROW][C]beta[/C][C]0.0947903596727852[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200696&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	0.752890942654235
beta	0.0947903596727852
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.58	1.58	0
4	1.58	1.58	0
5	1.59	1.58	0.01
6	1.59	1.58824257745903	0.001757422540972
7	1.6	1.59040481463373	0.00959518536626591
8	1.6	1.59915281015644	0.000847189843556029
9	1.61	1.60137498031461	0.00862501968539497
10	1.62	1.6100685481971	0.00993145180290478
11	1.62	1.62045449295484	-0.00045449295484179
12	1.63	1.62298851826429	0.00701148173571209
13	1.63	1.63164399533385	-0.00164399533385118
14	1.63	1.63366551542186	-0.00366551542185611
15	1.63	1.63390345522729	-0.00390345522729252
16	1.63	1.63368367518712	-0.0036836751871232
17	1.63	1.63336647342626	-0.0033664734262624
18	1.64	1.63304783555149	0.00695216444850622
19	1.64	1.64099416042552	-0.000994160425515922
20	1.64	1.64288681922301	-0.00288681922301315
21	1.65	1.64314848929484	0.00685151070516299
22	1.65	1.65123103018261	-0.00123103018261417
23	1.66	1.65314044455352	0.00685955544648431
24	1.67	1.66163073210926	0.0083692678907441
25	1.67	1.67185495638519	-0.00185495638518529
26	1.68	1.67424907250073	0.00575092749927442
27	1.68	1.68278001501509	-0.00278001501509295
28	1.69	1.68468968739348	0.00531031260652104
29	1.7	1.69306947419626	0.00693052580373843
30	1.71	1.70316371431184	0.00683628568815764
31	1.72	1.71367488575363	0.00632511424637427
32	1.72	1.72425260403069	-0.00425260403069272
33	1.73	1.72656295926786	0.0034370407321449
34	1.73	1.73490806900887	-0.00490806900887497
35	1.73	1.73661994801514	-0.00661994801513832
36	1.73	1.73657052429515	-0.00657052429515392
37	1.74	1.73608939393169	0.00391060606831406
38	1.75	1.74377849914151	0.00622150085848872
39	1.75	1.75365146473596	-0.00365146473596467
40	1.75	1.75583057059184	-0.00583057059183645
41	1.76	1.75595293820148	0.00404706179851688
42	1.76	1.7638009116358	-0.00380091163580443
43	1.76	1.76546895804036	-0.00546895804035641
44	1.77	1.76549084536255	0.0045091546374465
45	1.78	1.77334696729648	0.00665303270352013
46	1.78	1.78329200128447	-0.00329200128446661
47	1.79	1.78551456965055	0.00448543034945303
48	1.79	1.79391280667615	-0.00391280667615268
49	1.79	1.79570884260671	-0.00570884260670956
50	1.79	1.79574523750538	-0.00574523750537836
51	1.79	1.79534421177982	-0.00534421177981814
52	1.83	1.79486371538019	0.0351362846198056
53	1.83	1.82736818238534	0.00263181761465736
54	1.83	1.8355881549964	-0.00558815499640275
55	1.83	1.83722057592158	-0.00722057592157888
56	1.84	1.83710865249645	0.00289134750354614
57	1.84	1.84481625085933	-0.00481625085932746
58	1.84	1.8463771477977	-0.00637714779770349
59	1.85	1.84630774291659	0.00369225708340615
60	1.85	1.8540830063532	-0.00408300635320469
61	1.85	1.85571295326057	-0.00571295326056842
62	1.86	1.85570801269306	0.00429198730694447
63	1.86	1.8635420066743	-0.00354200667429727
64	1.86	1.86522507584882	-0.00522507584882459
65	1.87	1.86526808052593	0.00473191947407225
66	1.87	1.87314531876378	-0.00314531876378465
67	1.88	1.87486738433386	0.00513261566613932
68	1.88	1.88318813013251	-0.00318813013250763
69	1.88	1.88501673512733	-0.00501673512732759
70	1.89	1.88511057163507	0.00488942836492678
71	1.89	1.89301161178471	-0.00301161178470699
72	1.9	1.89474910126243	0.00525089873756635

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.58 & 1.58 & 0 \tabularnewline
4 & 1.58 & 1.58 & 0 \tabularnewline
5 & 1.59 & 1.58 & 0.01 \tabularnewline
6 & 1.59 & 1.58824257745903 & 0.001757422540972 \tabularnewline
7 & 1.6 & 1.59040481463373 & 0.00959518536626591 \tabularnewline
8 & 1.6 & 1.59915281015644 & 0.000847189843556029 \tabularnewline
9 & 1.61 & 1.60137498031461 & 0.00862501968539497 \tabularnewline
10 & 1.62 & 1.6100685481971 & 0.00993145180290478 \tabularnewline
11 & 1.62 & 1.62045449295484 & -0.00045449295484179 \tabularnewline
12 & 1.63 & 1.62298851826429 & 0.00701148173571209 \tabularnewline
13 & 1.63 & 1.63164399533385 & -0.00164399533385118 \tabularnewline
14 & 1.63 & 1.63366551542186 & -0.00366551542185611 \tabularnewline
15 & 1.63 & 1.63390345522729 & -0.00390345522729252 \tabularnewline
16 & 1.63 & 1.63368367518712 & -0.0036836751871232 \tabularnewline
17 & 1.63 & 1.63336647342626 & -0.0033664734262624 \tabularnewline
18 & 1.64 & 1.63304783555149 & 0.00695216444850622 \tabularnewline
19 & 1.64 & 1.64099416042552 & -0.000994160425515922 \tabularnewline
20 & 1.64 & 1.64288681922301 & -0.00288681922301315 \tabularnewline
21 & 1.65 & 1.64314848929484 & 0.00685151070516299 \tabularnewline
22 & 1.65 & 1.65123103018261 & -0.00123103018261417 \tabularnewline
23 & 1.66 & 1.65314044455352 & 0.00685955544648431 \tabularnewline
24 & 1.67 & 1.66163073210926 & 0.0083692678907441 \tabularnewline
25 & 1.67 & 1.67185495638519 & -0.00185495638518529 \tabularnewline
26 & 1.68 & 1.67424907250073 & 0.00575092749927442 \tabularnewline
27 & 1.68 & 1.68278001501509 & -0.00278001501509295 \tabularnewline
28 & 1.69 & 1.68468968739348 & 0.00531031260652104 \tabularnewline
29 & 1.7 & 1.69306947419626 & 0.00693052580373843 \tabularnewline
30 & 1.71 & 1.70316371431184 & 0.00683628568815764 \tabularnewline
31 & 1.72 & 1.71367488575363 & 0.00632511424637427 \tabularnewline
32 & 1.72 & 1.72425260403069 & -0.00425260403069272 \tabularnewline
33 & 1.73 & 1.72656295926786 & 0.0034370407321449 \tabularnewline
34 & 1.73 & 1.73490806900887 & -0.00490806900887497 \tabularnewline
35 & 1.73 & 1.73661994801514 & -0.00661994801513832 \tabularnewline
36 & 1.73 & 1.73657052429515 & -0.00657052429515392 \tabularnewline
37 & 1.74 & 1.73608939393169 & 0.00391060606831406 \tabularnewline
38 & 1.75 & 1.74377849914151 & 0.00622150085848872 \tabularnewline
39 & 1.75 & 1.75365146473596 & -0.00365146473596467 \tabularnewline
40 & 1.75 & 1.75583057059184 & -0.00583057059183645 \tabularnewline
41 & 1.76 & 1.75595293820148 & 0.00404706179851688 \tabularnewline
42 & 1.76 & 1.7638009116358 & -0.00380091163580443 \tabularnewline
43 & 1.76 & 1.76546895804036 & -0.00546895804035641 \tabularnewline
44 & 1.77 & 1.76549084536255 & 0.0045091546374465 \tabularnewline
45 & 1.78 & 1.77334696729648 & 0.00665303270352013 \tabularnewline
46 & 1.78 & 1.78329200128447 & -0.00329200128446661 \tabularnewline
47 & 1.79 & 1.78551456965055 & 0.00448543034945303 \tabularnewline
48 & 1.79 & 1.79391280667615 & -0.00391280667615268 \tabularnewline
49 & 1.79 & 1.79570884260671 & -0.00570884260670956 \tabularnewline
50 & 1.79 & 1.79574523750538 & -0.00574523750537836 \tabularnewline
51 & 1.79 & 1.79534421177982 & -0.00534421177981814 \tabularnewline
52 & 1.83 & 1.79486371538019 & 0.0351362846198056 \tabularnewline
53 & 1.83 & 1.82736818238534 & 0.00263181761465736 \tabularnewline
54 & 1.83 & 1.8355881549964 & -0.00558815499640275 \tabularnewline
55 & 1.83 & 1.83722057592158 & -0.00722057592157888 \tabularnewline
56 & 1.84 & 1.83710865249645 & 0.00289134750354614 \tabularnewline
57 & 1.84 & 1.84481625085933 & -0.00481625085932746 \tabularnewline
58 & 1.84 & 1.8463771477977 & -0.00637714779770349 \tabularnewline
59 & 1.85 & 1.84630774291659 & 0.00369225708340615 \tabularnewline
60 & 1.85 & 1.8540830063532 & -0.00408300635320469 \tabularnewline
61 & 1.85 & 1.85571295326057 & -0.00571295326056842 \tabularnewline
62 & 1.86 & 1.85570801269306 & 0.00429198730694447 \tabularnewline
63 & 1.86 & 1.8635420066743 & -0.00354200667429727 \tabularnewline
64 & 1.86 & 1.86522507584882 & -0.00522507584882459 \tabularnewline
65 & 1.87 & 1.86526808052593 & 0.00473191947407225 \tabularnewline
66 & 1.87 & 1.87314531876378 & -0.00314531876378465 \tabularnewline
67 & 1.88 & 1.87486738433386 & 0.00513261566613932 \tabularnewline
68 & 1.88 & 1.88318813013251 & -0.00318813013250763 \tabularnewline
69 & 1.88 & 1.88501673512733 & -0.00501673512732759 \tabularnewline
70 & 1.89 & 1.88511057163507 & 0.00488942836492678 \tabularnewline
71 & 1.89 & 1.89301161178471 & -0.00301161178470699 \tabularnewline
72 & 1.9 & 1.89474910126243 & 0.00525089873756635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200696&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]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]1.59[/C][C]1.58[/C][C]0.01[/C][/ROW]
[ROW][C]6[/C][C]1.59[/C][C]1.58824257745903[/C][C]0.001757422540972[/C][/ROW]
[ROW][C]7[/C][C]1.6[/C][C]1.59040481463373[/C][C]0.00959518536626591[/C][/ROW]
[ROW][C]8[/C][C]1.6[/C][C]1.59915281015644[/C][C]0.000847189843556029[/C][/ROW]
[ROW][C]9[/C][C]1.61[/C][C]1.60137498031461[/C][C]0.00862501968539497[/C][/ROW]
[ROW][C]10[/C][C]1.62[/C][C]1.6100685481971[/C][C]0.00993145180290478[/C][/ROW]
[ROW][C]11[/C][C]1.62[/C][C]1.62045449295484[/C][C]-0.00045449295484179[/C][/ROW]
[ROW][C]12[/C][C]1.63[/C][C]1.62298851826429[/C][C]0.00701148173571209[/C][/ROW]
[ROW][C]13[/C][C]1.63[/C][C]1.63164399533385[/C][C]-0.00164399533385118[/C][/ROW]
[ROW][C]14[/C][C]1.63[/C][C]1.63366551542186[/C][C]-0.00366551542185611[/C][/ROW]
[ROW][C]15[/C][C]1.63[/C][C]1.63390345522729[/C][C]-0.00390345522729252[/C][/ROW]
[ROW][C]16[/C][C]1.63[/C][C]1.63368367518712[/C][C]-0.0036836751871232[/C][/ROW]
[ROW][C]17[/C][C]1.63[/C][C]1.63336647342626[/C][C]-0.0033664734262624[/C][/ROW]
[ROW][C]18[/C][C]1.64[/C][C]1.63304783555149[/C][C]0.00695216444850622[/C][/ROW]
[ROW][C]19[/C][C]1.64[/C][C]1.64099416042552[/C][C]-0.000994160425515922[/C][/ROW]
[ROW][C]20[/C][C]1.64[/C][C]1.64288681922301[/C][C]-0.00288681922301315[/C][/ROW]
[ROW][C]21[/C][C]1.65[/C][C]1.64314848929484[/C][C]0.00685151070516299[/C][/ROW]
[ROW][C]22[/C][C]1.65[/C][C]1.65123103018261[/C][C]-0.00123103018261417[/C][/ROW]
[ROW][C]23[/C][C]1.66[/C][C]1.65314044455352[/C][C]0.00685955544648431[/C][/ROW]
[ROW][C]24[/C][C]1.67[/C][C]1.66163073210926[/C][C]0.0083692678907441[/C][/ROW]
[ROW][C]25[/C][C]1.67[/C][C]1.67185495638519[/C][C]-0.00185495638518529[/C][/ROW]
[ROW][C]26[/C][C]1.68[/C][C]1.67424907250073[/C][C]0.00575092749927442[/C][/ROW]
[ROW][C]27[/C][C]1.68[/C][C]1.68278001501509[/C][C]-0.00278001501509295[/C][/ROW]
[ROW][C]28[/C][C]1.69[/C][C]1.68468968739348[/C][C]0.00531031260652104[/C][/ROW]
[ROW][C]29[/C][C]1.7[/C][C]1.69306947419626[/C][C]0.00693052580373843[/C][/ROW]
[ROW][C]30[/C][C]1.71[/C][C]1.70316371431184[/C][C]0.00683628568815764[/C][/ROW]
[ROW][C]31[/C][C]1.72[/C][C]1.71367488575363[/C][C]0.00632511424637427[/C][/ROW]
[ROW][C]32[/C][C]1.72[/C][C]1.72425260403069[/C][C]-0.00425260403069272[/C][/ROW]
[ROW][C]33[/C][C]1.73[/C][C]1.72656295926786[/C][C]0.0034370407321449[/C][/ROW]
[ROW][C]34[/C][C]1.73[/C][C]1.73490806900887[/C][C]-0.00490806900887497[/C][/ROW]
[ROW][C]35[/C][C]1.73[/C][C]1.73661994801514[/C][C]-0.00661994801513832[/C][/ROW]
[ROW][C]36[/C][C]1.73[/C][C]1.73657052429515[/C][C]-0.00657052429515392[/C][/ROW]
[ROW][C]37[/C][C]1.74[/C][C]1.73608939393169[/C][C]0.00391060606831406[/C][/ROW]
[ROW][C]38[/C][C]1.75[/C][C]1.74377849914151[/C][C]0.00622150085848872[/C][/ROW]
[ROW][C]39[/C][C]1.75[/C][C]1.75365146473596[/C][C]-0.00365146473596467[/C][/ROW]
[ROW][C]40[/C][C]1.75[/C][C]1.75583057059184[/C][C]-0.00583057059183645[/C][/ROW]
[ROW][C]41[/C][C]1.76[/C][C]1.75595293820148[/C][C]0.00404706179851688[/C][/ROW]
[ROW][C]42[/C][C]1.76[/C][C]1.7638009116358[/C][C]-0.00380091163580443[/C][/ROW]
[ROW][C]43[/C][C]1.76[/C][C]1.76546895804036[/C][C]-0.00546895804035641[/C][/ROW]
[ROW][C]44[/C][C]1.77[/C][C]1.76549084536255[/C][C]0.0045091546374465[/C][/ROW]
[ROW][C]45[/C][C]1.78[/C][C]1.77334696729648[/C][C]0.00665303270352013[/C][/ROW]
[ROW][C]46[/C][C]1.78[/C][C]1.78329200128447[/C][C]-0.00329200128446661[/C][/ROW]
[ROW][C]47[/C][C]1.79[/C][C]1.78551456965055[/C][C]0.00448543034945303[/C][/ROW]
[ROW][C]48[/C][C]1.79[/C][C]1.79391280667615[/C][C]-0.00391280667615268[/C][/ROW]
[ROW][C]49[/C][C]1.79[/C][C]1.79570884260671[/C][C]-0.00570884260670956[/C][/ROW]
[ROW][C]50[/C][C]1.79[/C][C]1.79574523750538[/C][C]-0.00574523750537836[/C][/ROW]
[ROW][C]51[/C][C]1.79[/C][C]1.79534421177982[/C][C]-0.00534421177981814[/C][/ROW]
[ROW][C]52[/C][C]1.83[/C][C]1.79486371538019[/C][C]0.0351362846198056[/C][/ROW]
[ROW][C]53[/C][C]1.83[/C][C]1.82736818238534[/C][C]0.00263181761465736[/C][/ROW]
[ROW][C]54[/C][C]1.83[/C][C]1.8355881549964[/C][C]-0.00558815499640275[/C][/ROW]
[ROW][C]55[/C][C]1.83[/C][C]1.83722057592158[/C][C]-0.00722057592157888[/C][/ROW]
[ROW][C]56[/C][C]1.84[/C][C]1.83710865249645[/C][C]0.00289134750354614[/C][/ROW]
[ROW][C]57[/C][C]1.84[/C][C]1.84481625085933[/C][C]-0.00481625085932746[/C][/ROW]
[ROW][C]58[/C][C]1.84[/C][C]1.8463771477977[/C][C]-0.00637714779770349[/C][/ROW]
[ROW][C]59[/C][C]1.85[/C][C]1.84630774291659[/C][C]0.00369225708340615[/C][/ROW]
[ROW][C]60[/C][C]1.85[/C][C]1.8540830063532[/C][C]-0.00408300635320469[/C][/ROW]
[ROW][C]61[/C][C]1.85[/C][C]1.85571295326057[/C][C]-0.00571295326056842[/C][/ROW]
[ROW][C]62[/C][C]1.86[/C][C]1.85570801269306[/C][C]0.00429198730694447[/C][/ROW]
[ROW][C]63[/C][C]1.86[/C][C]1.8635420066743[/C][C]-0.00354200667429727[/C][/ROW]
[ROW][C]64[/C][C]1.86[/C][C]1.86522507584882[/C][C]-0.00522507584882459[/C][/ROW]
[ROW][C]65[/C][C]1.87[/C][C]1.86526808052593[/C][C]0.00473191947407225[/C][/ROW]
[ROW][C]66[/C][C]1.87[/C][C]1.87314531876378[/C][C]-0.00314531876378465[/C][/ROW]
[ROW][C]67[/C][C]1.88[/C][C]1.87486738433386[/C][C]0.00513261566613932[/C][/ROW]
[ROW][C]68[/C][C]1.88[/C][C]1.88318813013251[/C][C]-0.00318813013250763[/C][/ROW]
[ROW][C]69[/C][C]1.88[/C][C]1.88501673512733[/C][C]-0.00501673512732759[/C][/ROW]
[ROW][C]70[/C][C]1.89[/C][C]1.88511057163507[/C][C]0.00488942836492678[/C][/ROW]
[ROW][C]71[/C][C]1.89[/C][C]1.89301161178471[/C][C]-0.00301161178470699[/C][/ROW]
[ROW][C]72[/C][C]1.9[/C][C]1.89474910126243[/C][C]0.00525089873756635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200696&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	1.58	1.58	0
4	1.58	1.58	0
5	1.59	1.58	0.01
6	1.59	1.58824257745903	0.001757422540972
7	1.6	1.59040481463373	0.00959518536626591
8	1.6	1.59915281015644	0.000847189843556029
9	1.61	1.60137498031461	0.00862501968539497
10	1.62	1.6100685481971	0.00993145180290478
11	1.62	1.62045449295484	-0.00045449295484179
12	1.63	1.62298851826429	0.00701148173571209
13	1.63	1.63164399533385	-0.00164399533385118
14	1.63	1.63366551542186	-0.00366551542185611
15	1.63	1.63390345522729	-0.00390345522729252
16	1.63	1.63368367518712	-0.0036836751871232
17	1.63	1.63336647342626	-0.0033664734262624
18	1.64	1.63304783555149	0.00695216444850622
19	1.64	1.64099416042552	-0.000994160425515922
20	1.64	1.64288681922301	-0.00288681922301315
21	1.65	1.64314848929484	0.00685151070516299
22	1.65	1.65123103018261	-0.00123103018261417
23	1.66	1.65314044455352	0.00685955544648431
24	1.67	1.66163073210926	0.0083692678907441
25	1.67	1.67185495638519	-0.00185495638518529
26	1.68	1.67424907250073	0.00575092749927442
27	1.68	1.68278001501509	-0.00278001501509295
28	1.69	1.68468968739348	0.00531031260652104
29	1.7	1.69306947419626	0.00693052580373843
30	1.71	1.70316371431184	0.00683628568815764
31	1.72	1.71367488575363	0.00632511424637427
32	1.72	1.72425260403069	-0.00425260403069272
33	1.73	1.72656295926786	0.0034370407321449
34	1.73	1.73490806900887	-0.00490806900887497
35	1.73	1.73661994801514	-0.00661994801513832
36	1.73	1.73657052429515	-0.00657052429515392
37	1.74	1.73608939393169	0.00391060606831406
38	1.75	1.74377849914151	0.00622150085848872
39	1.75	1.75365146473596	-0.00365146473596467
40	1.75	1.75583057059184	-0.00583057059183645
41	1.76	1.75595293820148	0.00404706179851688
42	1.76	1.7638009116358	-0.00380091163580443
43	1.76	1.76546895804036	-0.00546895804035641
44	1.77	1.76549084536255	0.0045091546374465
45	1.78	1.77334696729648	0.00665303270352013
46	1.78	1.78329200128447	-0.00329200128446661
47	1.79	1.78551456965055	0.00448543034945303
48	1.79	1.79391280667615	-0.00391280667615268
49	1.79	1.79570884260671	-0.00570884260670956
50	1.79	1.79574523750538	-0.00574523750537836
51	1.79	1.79534421177982	-0.00534421177981814
52	1.83	1.79486371538019	0.0351362846198056
53	1.83	1.82736818238534	0.00263181761465736
54	1.83	1.8355881549964	-0.00558815499640275
55	1.83	1.83722057592158	-0.00722057592157888
56	1.84	1.83710865249645	0.00289134750354614
57	1.84	1.84481625085933	-0.00481625085932746
58	1.84	1.8463771477977	-0.00637714779770349
59	1.85	1.84630774291659	0.00369225708340615
60	1.85	1.8540830063532	-0.00408300635320469
61	1.85	1.85571295326057	-0.00571295326056842
62	1.86	1.85570801269306	0.00429198730694447
63	1.86	1.8635420066743	-0.00354200667429727
64	1.86	1.86522507584882	-0.00522507584882459
65	1.87	1.86526808052593	0.00473191947407225
66	1.87	1.87314531876378	-0.00314531876378465
67	1.88	1.87486738433386	0.00513261566613932
68	1.88	1.88318813013251	-0.00318813013250763
69	1.88	1.88501673512733	-0.00501673512732759
70	1.89	1.88511057163507	0.00488942836492678
71	1.89	1.89301161178471	-0.00301161178470699
72	1.9	1.89474910126243	0.00525089873756635

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.90308209993305	1.89008967364679	1.91607452621931
74	1.90746174450335	1.89062463860428	1.92429885040242
75	1.91184138907366	1.8913745268557	1.93230825129162
76	1.91622103364396	1.89220571382407	1.94023635346386
77	1.92060067821427	1.89305549625199	1.94814586017654
78	1.92498032278457	1.89388986858769	1.95607077698146
79	1.92935996735488	1.89468875497598	1.96403117973378
80	1.93373961192519	1.8954396585366	1.97203956531377
81	1.93811925649549	1.89613454224525	1.98010397074573
82	1.9424989010658	1.89676814692362	1.98822965520797
83	1.9468785456361	1.89733701897361	1.9964200722986
84	1.95125819020641	1.89783891744029	2.00467746297253

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.90308209993305 & 1.89008967364679 & 1.91607452621931 \tabularnewline
74 & 1.90746174450335 & 1.89062463860428 & 1.92429885040242 \tabularnewline
75 & 1.91184138907366 & 1.8913745268557 & 1.93230825129162 \tabularnewline
76 & 1.91622103364396 & 1.89220571382407 & 1.94023635346386 \tabularnewline
77 & 1.92060067821427 & 1.89305549625199 & 1.94814586017654 \tabularnewline
78 & 1.92498032278457 & 1.89388986858769 & 1.95607077698146 \tabularnewline
79 & 1.92935996735488 & 1.89468875497598 & 1.96403117973378 \tabularnewline
80 & 1.93373961192519 & 1.8954396585366 & 1.97203956531377 \tabularnewline
81 & 1.93811925649549 & 1.89613454224525 & 1.98010397074573 \tabularnewline
82 & 1.9424989010658 & 1.89676814692362 & 1.98822965520797 \tabularnewline
83 & 1.9468785456361 & 1.89733701897361 & 1.9964200722986 \tabularnewline
84 & 1.95125819020641 & 1.89783891744029 & 2.00467746297253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200696&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]1.90308209993305[/C][C]1.89008967364679[/C][C]1.91607452621931[/C][/ROW]
[ROW][C]74[/C][C]1.90746174450335[/C][C]1.89062463860428[/C][C]1.92429885040242[/C][/ROW]
[ROW][C]75[/C][C]1.91184138907366[/C][C]1.8913745268557[/C][C]1.93230825129162[/C][/ROW]
[ROW][C]76[/C][C]1.91622103364396[/C][C]1.89220571382407[/C][C]1.94023635346386[/C][/ROW]
[ROW][C]77[/C][C]1.92060067821427[/C][C]1.89305549625199[/C][C]1.94814586017654[/C][/ROW]
[ROW][C]78[/C][C]1.92498032278457[/C][C]1.89388986858769[/C][C]1.95607077698146[/C][/ROW]
[ROW][C]79[/C][C]1.92935996735488[/C][C]1.89468875497598[/C][C]1.96403117973378[/C][/ROW]
[ROW][C]80[/C][C]1.93373961192519[/C][C]1.8954396585366[/C][C]1.97203956531377[/C][/ROW]
[ROW][C]81[/C][C]1.93811925649549[/C][C]1.89613454224525[/C][C]1.98010397074573[/C][/ROW]
[ROW][C]82[/C][C]1.9424989010658[/C][C]1.89676814692362[/C][C]1.98822965520797[/C][/ROW]
[ROW][C]83[/C][C]1.9468785456361[/C][C]1.89733701897361[/C][C]1.9964200722986[/C][/ROW]
[ROW][C]84[/C][C]1.95125819020641[/C][C]1.89783891744029[/C][C]2.00467746297253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200696&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200696&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	1.90308209993305	1.89008967364679	1.91607452621931
74	1.90746174450335	1.89062463860428	1.92429885040242
75	1.91184138907366	1.8913745268557	1.93230825129162
76	1.91622103364396	1.89220571382407	1.94023635346386
77	1.92060067821427	1.89305549625199	1.94814586017654
78	1.92498032278457	1.89388986858769	1.95607077698146
79	1.92935996735488	1.89468875497598	1.96403117973378
80	1.93373961192519	1.8954396585366	1.97203956531377
81	1.93811925649549	1.89613454224525	1.98010397074573
82	1.9424989010658	1.89676814692362	1.98822965520797
83	1.9468785456361	1.89733701897361	1.9964200722986
84	1.95125819020641	1.89783891744029	2.00467746297253

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