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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 27 Nov 2016 14:38:19 +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/t1480257835ppbvao421w2ixfg.htm/, Retrieved Mon, 29 Apr 2024 22:47:03 +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 22:47:03 +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	0.882411060037558
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.882411060037558 \tabularnewline
beta & FALSE \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]0.882411060037558[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/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	0.882411060037558
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	103.66	102.8	0.859999999999999
3	103.55	103.558873511632	-0.008873511632288
4	103.87	103.551043426827	0.318956573173423
5	104.03	103.832494234666	0.197505765333517
6	104.02	104.006775506418	0.0132244935820296
7	104.02	104.018444945818	0.00155505418184987
8	102.97	104.019817142827	-1.04981714282717
9	103.18	103.093446884979	0.0865531150205641
10	103.53	103.169822310954	0.360177689045699
11	103.78	103.487647087347	0.292352912653001
12	103.85	103.745622530906	0.104377469093791
13	103.85	103.837726364053	0.0122736359466984
14	104.78	103.84855675616	0.931443243840462
15	104.76	104.670472576322	0.0895274236783763
16	104.84	104.749472565152	0.0905274348478997
17	104.85	104.829354974899	0.0206450251012882
18	104.83	104.847572373383	-0.0175723733828335
19	104.83	104.832066316759	-0.00206631675871449
20	103.71	104.830242975997	-1.12024297599729
21	103.84	103.841728184048	-0.00172818404789155
22	104.37	103.84020321533	0.529796784669756
23	104.44	104.307701757695	0.132298242304827
24	104.4	104.424443189928	-0.0244431899284621
25	99.54	104.402874248793	-4.86287424879299
26	100.42	100.111820228086	0.308179771913771
27	100.34	100.383761467303	-0.0437614673027866
28	100.36	100.345145864551	0.0148541354486582
29	100.37	100.358253317959	0.011746682041462
30	100.42	100.368618720111	0.0513812798893269
31	100.41	100.413958129764	-0.00395812976390175
32	99.13	100.410465432283	-1.28046543228318
33	99.42	99.2805685728407	0.139431427159266
34	99.76	99.4036044062829	0.35639559371711
35	99.92	99.7180918199275	0.201908180072465
36	99.92	99.8962578311355	0.023742168864473
37	100.47	99.9172081835308	0.552791816469181
38	100.44	100.404997796281	0.035002203718534
39	100.47	100.435884127968	0.0341158720316059
40	100.61	100.465988350772	0.144011649228091
41	100.73	100.593065822825	0.136934177174979
42	100.64	100.713898055261	-0.0738980552613668
43	99.99	100.648689593983	-0.658689593983482
44	99.74	100.067454611121	-0.327454611120814
45	99.49	99.7785050406075	-0.288505040607504
46	99.41	99.5239250018988	-0.113925001898849
47	99.49	99.4233963202085	0.0666036797914842
48	99.53	99.4821681438957	0.0478318561042954
49	99.91	99.5243755027443	0.385624497255733
50	99.84	99.8646548241442	-0.0246548241441502
51	99.67	99.8428991346361	-0.172899134636069
52	99.39	99.6903310259623	-0.300331025962279
53	99.38	99.4253156069807	-0.0453156069807363
54	99.29	99.3853286141886	-0.0953286141886167
55	97.91	99.3012095906905	-1.39120959069054
56	97.62	98.0735908610349	-0.453590861034868
57	97.67	97.6733372685258	-0.00333726852575467
58	97.64	97.6703924258683	-0.0303924258683139
59	97.63	97.6435738131407	-0.0135738131407521
60	97.66	97.6315961302985	0.0284038697015347

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 103.66 & 102.8 & 0.859999999999999 \tabularnewline
3 & 103.55 & 103.558873511632 & -0.008873511632288 \tabularnewline
4 & 103.87 & 103.551043426827 & 0.318956573173423 \tabularnewline
5 & 104.03 & 103.832494234666 & 0.197505765333517 \tabularnewline
6 & 104.02 & 104.006775506418 & 0.0132244935820296 \tabularnewline
7 & 104.02 & 104.018444945818 & 0.00155505418184987 \tabularnewline
8 & 102.97 & 104.019817142827 & -1.04981714282717 \tabularnewline
9 & 103.18 & 103.093446884979 & 0.0865531150205641 \tabularnewline
10 & 103.53 & 103.169822310954 & 0.360177689045699 \tabularnewline
11 & 103.78 & 103.487647087347 & 0.292352912653001 \tabularnewline
12 & 103.85 & 103.745622530906 & 0.104377469093791 \tabularnewline
13 & 103.85 & 103.837726364053 & 0.0122736359466984 \tabularnewline
14 & 104.78 & 103.84855675616 & 0.931443243840462 \tabularnewline
15 & 104.76 & 104.670472576322 & 0.0895274236783763 \tabularnewline
16 & 104.84 & 104.749472565152 & 0.0905274348478997 \tabularnewline
17 & 104.85 & 104.829354974899 & 0.0206450251012882 \tabularnewline
18 & 104.83 & 104.847572373383 & -0.0175723733828335 \tabularnewline
19 & 104.83 & 104.832066316759 & -0.00206631675871449 \tabularnewline
20 & 103.71 & 104.830242975997 & -1.12024297599729 \tabularnewline
21 & 103.84 & 103.841728184048 & -0.00172818404789155 \tabularnewline
22 & 104.37 & 103.84020321533 & 0.529796784669756 \tabularnewline
23 & 104.44 & 104.307701757695 & 0.132298242304827 \tabularnewline
24 & 104.4 & 104.424443189928 & -0.0244431899284621 \tabularnewline
25 & 99.54 & 104.402874248793 & -4.86287424879299 \tabularnewline
26 & 100.42 & 100.111820228086 & 0.308179771913771 \tabularnewline
27 & 100.34 & 100.383761467303 & -0.0437614673027866 \tabularnewline
28 & 100.36 & 100.345145864551 & 0.0148541354486582 \tabularnewline
29 & 100.37 & 100.358253317959 & 0.011746682041462 \tabularnewline
30 & 100.42 & 100.368618720111 & 0.0513812798893269 \tabularnewline
31 & 100.41 & 100.413958129764 & -0.00395812976390175 \tabularnewline
32 & 99.13 & 100.410465432283 & -1.28046543228318 \tabularnewline
33 & 99.42 & 99.2805685728407 & 0.139431427159266 \tabularnewline
34 & 99.76 & 99.4036044062829 & 0.35639559371711 \tabularnewline
35 & 99.92 & 99.7180918199275 & 0.201908180072465 \tabularnewline
36 & 99.92 & 99.8962578311355 & 0.023742168864473 \tabularnewline
37 & 100.47 & 99.9172081835308 & 0.552791816469181 \tabularnewline
38 & 100.44 & 100.404997796281 & 0.035002203718534 \tabularnewline
39 & 100.47 & 100.435884127968 & 0.0341158720316059 \tabularnewline
40 & 100.61 & 100.465988350772 & 0.144011649228091 \tabularnewline
41 & 100.73 & 100.593065822825 & 0.136934177174979 \tabularnewline
42 & 100.64 & 100.713898055261 & -0.0738980552613668 \tabularnewline
43 & 99.99 & 100.648689593983 & -0.658689593983482 \tabularnewline
44 & 99.74 & 100.067454611121 & -0.327454611120814 \tabularnewline
45 & 99.49 & 99.7785050406075 & -0.288505040607504 \tabularnewline
46 & 99.41 & 99.5239250018988 & -0.113925001898849 \tabularnewline
47 & 99.49 & 99.4233963202085 & 0.0666036797914842 \tabularnewline
48 & 99.53 & 99.4821681438957 & 0.0478318561042954 \tabularnewline
49 & 99.91 & 99.5243755027443 & 0.385624497255733 \tabularnewline
50 & 99.84 & 99.8646548241442 & -0.0246548241441502 \tabularnewline
51 & 99.67 & 99.8428991346361 & -0.172899134636069 \tabularnewline
52 & 99.39 & 99.6903310259623 & -0.300331025962279 \tabularnewline
53 & 99.38 & 99.4253156069807 & -0.0453156069807363 \tabularnewline
54 & 99.29 & 99.3853286141886 & -0.0953286141886167 \tabularnewline
55 & 97.91 & 99.3012095906905 & -1.39120959069054 \tabularnewline
56 & 97.62 & 98.0735908610349 & -0.453590861034868 \tabularnewline
57 & 97.67 & 97.6733372685258 & -0.00333726852575467 \tabularnewline
58 & 97.64 & 97.6703924258683 & -0.0303924258683139 \tabularnewline
59 & 97.63 & 97.6435738131407 & -0.0135738131407521 \tabularnewline
60 & 97.66 & 97.6315961302985 & 0.0284038697015347 \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]2[/C][C]103.66[/C][C]102.8[/C][C]0.859999999999999[/C][/ROW]
[ROW][C]3[/C][C]103.55[/C][C]103.558873511632[/C][C]-0.008873511632288[/C][/ROW]
[ROW][C]4[/C][C]103.87[/C][C]103.551043426827[/C][C]0.318956573173423[/C][/ROW]
[ROW][C]5[/C][C]104.03[/C][C]103.832494234666[/C][C]0.197505765333517[/C][/ROW]
[ROW][C]6[/C][C]104.02[/C][C]104.006775506418[/C][C]0.0132244935820296[/C][/ROW]
[ROW][C]7[/C][C]104.02[/C][C]104.018444945818[/C][C]0.00155505418184987[/C][/ROW]
[ROW][C]8[/C][C]102.97[/C][C]104.019817142827[/C][C]-1.04981714282717[/C][/ROW]
[ROW][C]9[/C][C]103.18[/C][C]103.093446884979[/C][C]0.0865531150205641[/C][/ROW]
[ROW][C]10[/C][C]103.53[/C][C]103.169822310954[/C][C]0.360177689045699[/C][/ROW]
[ROW][C]11[/C][C]103.78[/C][C]103.487647087347[/C][C]0.292352912653001[/C][/ROW]
[ROW][C]12[/C][C]103.85[/C][C]103.745622530906[/C][C]0.104377469093791[/C][/ROW]
[ROW][C]13[/C][C]103.85[/C][C]103.837726364053[/C][C]0.0122736359466984[/C][/ROW]
[ROW][C]14[/C][C]104.78[/C][C]103.84855675616[/C][C]0.931443243840462[/C][/ROW]
[ROW][C]15[/C][C]104.76[/C][C]104.670472576322[/C][C]0.0895274236783763[/C][/ROW]
[ROW][C]16[/C][C]104.84[/C][C]104.749472565152[/C][C]0.0905274348478997[/C][/ROW]
[ROW][C]17[/C][C]104.85[/C][C]104.829354974899[/C][C]0.0206450251012882[/C][/ROW]
[ROW][C]18[/C][C]104.83[/C][C]104.847572373383[/C][C]-0.0175723733828335[/C][/ROW]
[ROW][C]19[/C][C]104.83[/C][C]104.832066316759[/C][C]-0.00206631675871449[/C][/ROW]
[ROW][C]20[/C][C]103.71[/C][C]104.830242975997[/C][C]-1.12024297599729[/C][/ROW]
[ROW][C]21[/C][C]103.84[/C][C]103.841728184048[/C][C]-0.00172818404789155[/C][/ROW]
[ROW][C]22[/C][C]104.37[/C][C]103.84020321533[/C][C]0.529796784669756[/C][/ROW]
[ROW][C]23[/C][C]104.44[/C][C]104.307701757695[/C][C]0.132298242304827[/C][/ROW]
[ROW][C]24[/C][C]104.4[/C][C]104.424443189928[/C][C]-0.0244431899284621[/C][/ROW]
[ROW][C]25[/C][C]99.54[/C][C]104.402874248793[/C][C]-4.86287424879299[/C][/ROW]
[ROW][C]26[/C][C]100.42[/C][C]100.111820228086[/C][C]0.308179771913771[/C][/ROW]
[ROW][C]27[/C][C]100.34[/C][C]100.383761467303[/C][C]-0.0437614673027866[/C][/ROW]
[ROW][C]28[/C][C]100.36[/C][C]100.345145864551[/C][C]0.0148541354486582[/C][/ROW]
[ROW][C]29[/C][C]100.37[/C][C]100.358253317959[/C][C]0.011746682041462[/C][/ROW]
[ROW][C]30[/C][C]100.42[/C][C]100.368618720111[/C][C]0.0513812798893269[/C][/ROW]
[ROW][C]31[/C][C]100.41[/C][C]100.413958129764[/C][C]-0.00395812976390175[/C][/ROW]
[ROW][C]32[/C][C]99.13[/C][C]100.410465432283[/C][C]-1.28046543228318[/C][/ROW]
[ROW][C]33[/C][C]99.42[/C][C]99.2805685728407[/C][C]0.139431427159266[/C][/ROW]
[ROW][C]34[/C][C]99.76[/C][C]99.4036044062829[/C][C]0.35639559371711[/C][/ROW]
[ROW][C]35[/C][C]99.92[/C][C]99.7180918199275[/C][C]0.201908180072465[/C][/ROW]
[ROW][C]36[/C][C]99.92[/C][C]99.8962578311355[/C][C]0.023742168864473[/C][/ROW]
[ROW][C]37[/C][C]100.47[/C][C]99.9172081835308[/C][C]0.552791816469181[/C][/ROW]
[ROW][C]38[/C][C]100.44[/C][C]100.404997796281[/C][C]0.035002203718534[/C][/ROW]
[ROW][C]39[/C][C]100.47[/C][C]100.435884127968[/C][C]0.0341158720316059[/C][/ROW]
[ROW][C]40[/C][C]100.61[/C][C]100.465988350772[/C][C]0.144011649228091[/C][/ROW]
[ROW][C]41[/C][C]100.73[/C][C]100.593065822825[/C][C]0.136934177174979[/C][/ROW]
[ROW][C]42[/C][C]100.64[/C][C]100.713898055261[/C][C]-0.0738980552613668[/C][/ROW]
[ROW][C]43[/C][C]99.99[/C][C]100.648689593983[/C][C]-0.658689593983482[/C][/ROW]
[ROW][C]44[/C][C]99.74[/C][C]100.067454611121[/C][C]-0.327454611120814[/C][/ROW]
[ROW][C]45[/C][C]99.49[/C][C]99.7785050406075[/C][C]-0.288505040607504[/C][/ROW]
[ROW][C]46[/C][C]99.41[/C][C]99.5239250018988[/C][C]-0.113925001898849[/C][/ROW]
[ROW][C]47[/C][C]99.49[/C][C]99.4233963202085[/C][C]0.0666036797914842[/C][/ROW]
[ROW][C]48[/C][C]99.53[/C][C]99.4821681438957[/C][C]0.0478318561042954[/C][/ROW]
[ROW][C]49[/C][C]99.91[/C][C]99.5243755027443[/C][C]0.385624497255733[/C][/ROW]
[ROW][C]50[/C][C]99.84[/C][C]99.8646548241442[/C][C]-0.0246548241441502[/C][/ROW]
[ROW][C]51[/C][C]99.67[/C][C]99.8428991346361[/C][C]-0.172899134636069[/C][/ROW]
[ROW][C]52[/C][C]99.39[/C][C]99.6903310259623[/C][C]-0.300331025962279[/C][/ROW]
[ROW][C]53[/C][C]99.38[/C][C]99.4253156069807[/C][C]-0.0453156069807363[/C][/ROW]
[ROW][C]54[/C][C]99.29[/C][C]99.3853286141886[/C][C]-0.0953286141886167[/C][/ROW]
[ROW][C]55[/C][C]97.91[/C][C]99.3012095906905[/C][C]-1.39120959069054[/C][/ROW]
[ROW][C]56[/C][C]97.62[/C][C]98.0735908610349[/C][C]-0.453590861034868[/C][/ROW]
[ROW][C]57[/C][C]97.67[/C][C]97.6733372685258[/C][C]-0.00333726852575467[/C][/ROW]
[ROW][C]58[/C][C]97.64[/C][C]97.6703924258683[/C][C]-0.0303924258683139[/C][/ROW]
[ROW][C]59[/C][C]97.63[/C][C]97.6435738131407[/C][C]-0.0135738131407521[/C][/ROW]
[ROW][C]60[/C][C]97.66[/C][C]97.6315961302985[/C][C]0.0284038697015347[/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
2	103.66	102.8	0.859999999999999
3	103.55	103.558873511632	-0.008873511632288
4	103.87	103.551043426827	0.318956573173423
5	104.03	103.832494234666	0.197505765333517
6	104.02	104.006775506418	0.0132244935820296
7	104.02	104.018444945818	0.00155505418184987
8	102.97	104.019817142827	-1.04981714282717
9	103.18	103.093446884979	0.0865531150205641
10	103.53	103.169822310954	0.360177689045699
11	103.78	103.487647087347	0.292352912653001
12	103.85	103.745622530906	0.104377469093791
13	103.85	103.837726364053	0.0122736359466984
14	104.78	103.84855675616	0.931443243840462
15	104.76	104.670472576322	0.0895274236783763
16	104.84	104.749472565152	0.0905274348478997
17	104.85	104.829354974899	0.0206450251012882
18	104.83	104.847572373383	-0.0175723733828335
19	104.83	104.832066316759	-0.00206631675871449
20	103.71	104.830242975997	-1.12024297599729
21	103.84	103.841728184048	-0.00172818404789155
22	104.37	103.84020321533	0.529796784669756
23	104.44	104.307701757695	0.132298242304827
24	104.4	104.424443189928	-0.0244431899284621
25	99.54	104.402874248793	-4.86287424879299
26	100.42	100.111820228086	0.308179771913771
27	100.34	100.383761467303	-0.0437614673027866
28	100.36	100.345145864551	0.0148541354486582
29	100.37	100.358253317959	0.011746682041462
30	100.42	100.368618720111	0.0513812798893269
31	100.41	100.413958129764	-0.00395812976390175
32	99.13	100.410465432283	-1.28046543228318
33	99.42	99.2805685728407	0.139431427159266
34	99.76	99.4036044062829	0.35639559371711
35	99.92	99.7180918199275	0.201908180072465
36	99.92	99.8962578311355	0.023742168864473
37	100.47	99.9172081835308	0.552791816469181
38	100.44	100.404997796281	0.035002203718534
39	100.47	100.435884127968	0.0341158720316059
40	100.61	100.465988350772	0.144011649228091
41	100.73	100.593065822825	0.136934177174979
42	100.64	100.713898055261	-0.0738980552613668
43	99.99	100.648689593983	-0.658689593983482
44	99.74	100.067454611121	-0.327454611120814
45	99.49	99.7785050406075	-0.288505040607504
46	99.41	99.5239250018988	-0.113925001898849
47	99.49	99.4233963202085	0.0666036797914842
48	99.53	99.4821681438957	0.0478318561042954
49	99.91	99.5243755027443	0.385624497255733
50	99.84	99.8646548241442	-0.0246548241441502
51	99.67	99.8428991346361	-0.172899134636069
52	99.39	99.6903310259623	-0.300331025962279
53	99.38	99.4253156069807	-0.0453156069807363
54	99.29	99.3853286141886	-0.0953286141886167
55	97.91	99.3012095906905	-1.39120959069054
56	97.62	98.0735908610349	-0.453590861034868
57	97.67	97.6733372685258	-0.00333726852575467
58	97.64	97.6703924258683	-0.0303924258683139
59	97.63	97.6435738131407	-0.0135738131407521
60	97.66	97.6315961302985	0.0284038697015347

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	97.656660019071	96.176598461686	99.1367215764559
62	97.656660019071	95.6827609652624	99.6305590728795
63	97.656660019071	95.2898113260608	100.023508712081
64	97.656660019071	94.9533901478628	100.359929890279
65	97.656660019071	94.6544336356083	100.658886402534
66	97.656660019071	94.3826626888129	100.930657349329
67	97.656660019071	94.131783598611	101.181536439531
68	97.656660019071	93.8976110648151	101.415708973327
69	97.656660019071	93.6771946904785	101.636125347663
70	97.656660019071	93.4683620876378	101.844957950504
71	97.656660019071	93.2694587673132	102.043861270829
72	97.656660019071	93.079190184719	102.234129853423

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 97.656660019071 & 96.176598461686 & 99.1367215764559 \tabularnewline
62 & 97.656660019071 & 95.6827609652624 & 99.6305590728795 \tabularnewline
63 & 97.656660019071 & 95.2898113260608 & 100.023508712081 \tabularnewline
64 & 97.656660019071 & 94.9533901478628 & 100.359929890279 \tabularnewline
65 & 97.656660019071 & 94.6544336356083 & 100.658886402534 \tabularnewline
66 & 97.656660019071 & 94.3826626888129 & 100.930657349329 \tabularnewline
67 & 97.656660019071 & 94.131783598611 & 101.181536439531 \tabularnewline
68 & 97.656660019071 & 93.8976110648151 & 101.415708973327 \tabularnewline
69 & 97.656660019071 & 93.6771946904785 & 101.636125347663 \tabularnewline
70 & 97.656660019071 & 93.4683620876378 & 101.844957950504 \tabularnewline
71 & 97.656660019071 & 93.2694587673132 & 102.043861270829 \tabularnewline
72 & 97.656660019071 & 93.079190184719 & 102.234129853423 \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]97.656660019071[/C][C]96.176598461686[/C][C]99.1367215764559[/C][/ROW]
[ROW][C]62[/C][C]97.656660019071[/C][C]95.6827609652624[/C][C]99.6305590728795[/C][/ROW]
[ROW][C]63[/C][C]97.656660019071[/C][C]95.2898113260608[/C][C]100.023508712081[/C][/ROW]
[ROW][C]64[/C][C]97.656660019071[/C][C]94.9533901478628[/C][C]100.359929890279[/C][/ROW]
[ROW][C]65[/C][C]97.656660019071[/C][C]94.6544336356083[/C][C]100.658886402534[/C][/ROW]
[ROW][C]66[/C][C]97.656660019071[/C][C]94.3826626888129[/C][C]100.930657349329[/C][/ROW]
[ROW][C]67[/C][C]97.656660019071[/C][C]94.131783598611[/C][C]101.181536439531[/C][/ROW]
[ROW][C]68[/C][C]97.656660019071[/C][C]93.8976110648151[/C][C]101.415708973327[/C][/ROW]
[ROW][C]69[/C][C]97.656660019071[/C][C]93.6771946904785[/C][C]101.636125347663[/C][/ROW]
[ROW][C]70[/C][C]97.656660019071[/C][C]93.4683620876378[/C][C]101.844957950504[/C][/ROW]
[ROW][C]71[/C][C]97.656660019071[/C][C]93.2694587673132[/C][C]102.043861270829[/C][/ROW]
[ROW][C]72[/C][C]97.656660019071[/C][C]93.079190184719[/C][C]102.234129853423[/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	97.656660019071	96.176598461686	99.1367215764559
62	97.656660019071	95.6827609652624	99.6305590728795
63	97.656660019071	95.2898113260608	100.023508712081
64	97.656660019071	94.9533901478628	100.359929890279
65	97.656660019071	94.6544336356083	100.658886402534
66	97.656660019071	94.3826626888129	100.930657349329
67	97.656660019071	94.131783598611	101.181536439531
68	97.656660019071	93.8976110648151	101.415708973327
69	97.656660019071	93.6771946904785	101.636125347663
70	97.656660019071	93.4683620876378	101.844957950504
71	97.656660019071	93.2694587673132	102.043861270829
72	97.656660019071	93.079190184719	102.234129853423

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

R code (references can be found in the software module):

par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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