Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 28 Apr 2017 13:45:03 +0100

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/2017/Apr/28/t1493383692pq13q6qc0b30heu.htm/, Retrieved Fri, 10 May 2024 18:09:06 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 18:09:06 +0200

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Opdracht10_oef2

Estimated Impact

Dataseries X:

Download CSV

Histogram

Boxplots

3.65
3.66
3.36
3.19
2.81
2.25
2.32
2.85
2.75
2.78
2.26
2.23
1.46
1.19
1.11
1
1.18
1.59
1.51
1.01
0.9
0.63
0.81
0.97
1.14
0.97
0.89
0.62
0.36
0.27
0.34
0.02
-0.12
0.09
-0.11
-0.38
-0.65
-0.4
-0.4
0.29
0.56
0.63
0.46
0.91
1.06
1.28
1.52
1.5
1.74
1.39
2.24
2.04
2.2
2.16
2.28
2.16
1.87
1.81
1.77
2.03
2.65

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999927022282636
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999927022282636 \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]0.999927022282636[/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	0.999927022282636
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	3.66	3.65	0.0100000000000002
3	3.36	3.65999927022283	-0.299999270222826
4	3.19	3.36002189326195	-0.170021893261952
5	2.81	3.19001240780967	-0.380012407809672
6	2.25	2.81002773243809	-0.560027732438092
7	2.32	2.25004086954557	0.0699591304544258
8	2.85	2.31999489454235	0.53000510545765
9	2.75	2.84996132143721	-0.0999613214372124
10	2.78	2.75000729494906	0.0299927050509363
11	2.26	2.77999781120085	-0.519997811200848
12	2.23	2.2600379482533	-0.0300379482532955
13	1.46	2.2300021921009	-0.770002192100898
14	1.19	1.46005619300235	-0.270056193002345
15	1.11	1.19001970808453	-0.0800197080845253
16	1	1.11000583965564	-0.11000583965564
17	1.18	1.00000802797507	0.179991972024925
18	1.59	1.17998686459674	0.410013135403262
19	1.51	1.58997007817729	-0.079970078177289
20	1.01	1.51000583603376	-0.500005836033763
21	0.9	1.01003648928458	-0.110036489284583
22	0.63	0.900008030211815	-0.270008030211815
23	0.81	0.630019704569715	0.179980295430285
24	0.97	0.809986865448869	0.160013134551131
25	1.14	0.969988322606692	0.170011677393308
26	0.97	1.13998759293586	-0.169987592935859
27	0.89	0.970012405306513	-0.0800124053065128
28	0.62	0.8900058391227	-0.2700058391227
29	0.36	0.620019704409814	-0.260019704409814
30	0.27	0.360018975644498	-0.0900189756444976
31	0.34	0.270006569379362	0.069993430620638
32	0.02	0.339994892039203	-0.319994892039203
33	-0.12	0.0200233524967893	-0.140023352496789
34	0.09	-0.119989781415357	0.209989781415357
35	-0.11	0.0899846754250824	-0.199984675425082
36	-0.38	-0.10998540557488	-0.27001459442512
37	-0.65	-0.379980294951244	-0.270019705048756
38	-0.4	-0.649980294578282	0.249980294578282
39	-0.4	-0.400018242991284	1.82429912844451e-05
40	0.29	-0.400000001331332	0.690000001331332
41	0.56	0.289949645374921	0.270050354625079
42	0.63	0.559980292341546	0.0700197076584539
43	0.46	0.629994890121565	-0.169994890121564
44	0.91	0.460012405839045	0.449987594160955
45	1.06	0.909967160932536	0.150032839067464
46	1.28	1.05998905094588	0.220010949054125
47	1.52	1.27998394410314	0.240016055896857
48	1.5	1.51998248417611	-0.0199824841761098
49	1.74	1.50000145827608	0.239998541723918
50	1.39	1.73998248545425	-0.349982485454254
51	2.24	1.39002554092291	0.849974459077094
52	2.04	2.23993797080416	-0.199937970804159
53	2.2	2.04001459101672	0.159985408983276
54	2.16	2.19998832463004	-0.0399883246300408
55	2.28	2.16000291825665	0.119997081743347
56	2.16	2.27999124288688	-0.119991242886884
57	1.87	2.16000875668701	-0.29000875668701
58	1.81	1.87002116417708	-0.0600211641770789
59	1.77	1.81000438020756	-0.0400043802075554
60	2.03	1.77000291942835	0.259997080571648
61	2.65	2.02998102600654	0.620018973993462

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3.66 & 3.65 & 0.0100000000000002 \tabularnewline
3 & 3.36 & 3.65999927022283 & -0.299999270222826 \tabularnewline
4 & 3.19 & 3.36002189326195 & -0.170021893261952 \tabularnewline
5 & 2.81 & 3.19001240780967 & -0.380012407809672 \tabularnewline
6 & 2.25 & 2.81002773243809 & -0.560027732438092 \tabularnewline
7 & 2.32 & 2.25004086954557 & 0.0699591304544258 \tabularnewline
8 & 2.85 & 2.31999489454235 & 0.53000510545765 \tabularnewline
9 & 2.75 & 2.84996132143721 & -0.0999613214372124 \tabularnewline
10 & 2.78 & 2.75000729494906 & 0.0299927050509363 \tabularnewline
11 & 2.26 & 2.77999781120085 & -0.519997811200848 \tabularnewline
12 & 2.23 & 2.2600379482533 & -0.0300379482532955 \tabularnewline
13 & 1.46 & 2.2300021921009 & -0.770002192100898 \tabularnewline
14 & 1.19 & 1.46005619300235 & -0.270056193002345 \tabularnewline
15 & 1.11 & 1.19001970808453 & -0.0800197080845253 \tabularnewline
16 & 1 & 1.11000583965564 & -0.11000583965564 \tabularnewline
17 & 1.18 & 1.00000802797507 & 0.179991972024925 \tabularnewline
18 & 1.59 & 1.17998686459674 & 0.410013135403262 \tabularnewline
19 & 1.51 & 1.58997007817729 & -0.079970078177289 \tabularnewline
20 & 1.01 & 1.51000583603376 & -0.500005836033763 \tabularnewline
21 & 0.9 & 1.01003648928458 & -0.110036489284583 \tabularnewline
22 & 0.63 & 0.900008030211815 & -0.270008030211815 \tabularnewline
23 & 0.81 & 0.630019704569715 & 0.179980295430285 \tabularnewline
24 & 0.97 & 0.809986865448869 & 0.160013134551131 \tabularnewline
25 & 1.14 & 0.969988322606692 & 0.170011677393308 \tabularnewline
26 & 0.97 & 1.13998759293586 & -0.169987592935859 \tabularnewline
27 & 0.89 & 0.970012405306513 & -0.0800124053065128 \tabularnewline
28 & 0.62 & 0.8900058391227 & -0.2700058391227 \tabularnewline
29 & 0.36 & 0.620019704409814 & -0.260019704409814 \tabularnewline
30 & 0.27 & 0.360018975644498 & -0.0900189756444976 \tabularnewline
31 & 0.34 & 0.270006569379362 & 0.069993430620638 \tabularnewline
32 & 0.02 & 0.339994892039203 & -0.319994892039203 \tabularnewline
33 & -0.12 & 0.0200233524967893 & -0.140023352496789 \tabularnewline
34 & 0.09 & -0.119989781415357 & 0.209989781415357 \tabularnewline
35 & -0.11 & 0.0899846754250824 & -0.199984675425082 \tabularnewline
36 & -0.38 & -0.10998540557488 & -0.27001459442512 \tabularnewline
37 & -0.65 & -0.379980294951244 & -0.270019705048756 \tabularnewline
38 & -0.4 & -0.649980294578282 & 0.249980294578282 \tabularnewline
39 & -0.4 & -0.400018242991284 & 1.82429912844451e-05 \tabularnewline
40 & 0.29 & -0.400000001331332 & 0.690000001331332 \tabularnewline
41 & 0.56 & 0.289949645374921 & 0.270050354625079 \tabularnewline
42 & 0.63 & 0.559980292341546 & 0.0700197076584539 \tabularnewline
43 & 0.46 & 0.629994890121565 & -0.169994890121564 \tabularnewline
44 & 0.91 & 0.460012405839045 & 0.449987594160955 \tabularnewline
45 & 1.06 & 0.909967160932536 & 0.150032839067464 \tabularnewline
46 & 1.28 & 1.05998905094588 & 0.220010949054125 \tabularnewline
47 & 1.52 & 1.27998394410314 & 0.240016055896857 \tabularnewline
48 & 1.5 & 1.51998248417611 & -0.0199824841761098 \tabularnewline
49 & 1.74 & 1.50000145827608 & 0.239998541723918 \tabularnewline
50 & 1.39 & 1.73998248545425 & -0.349982485454254 \tabularnewline
51 & 2.24 & 1.39002554092291 & 0.849974459077094 \tabularnewline
52 & 2.04 & 2.23993797080416 & -0.199937970804159 \tabularnewline
53 & 2.2 & 2.04001459101672 & 0.159985408983276 \tabularnewline
54 & 2.16 & 2.19998832463004 & -0.0399883246300408 \tabularnewline
55 & 2.28 & 2.16000291825665 & 0.119997081743347 \tabularnewline
56 & 2.16 & 2.27999124288688 & -0.119991242886884 \tabularnewline
57 & 1.87 & 2.16000875668701 & -0.29000875668701 \tabularnewline
58 & 1.81 & 1.87002116417708 & -0.0600211641770789 \tabularnewline
59 & 1.77 & 1.81000438020756 & -0.0400043802075554 \tabularnewline
60 & 2.03 & 1.77000291942835 & 0.259997080571648 \tabularnewline
61 & 2.65 & 2.02998102600654 & 0.620018973993462 \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]3.66[/C][C]3.65[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]3[/C][C]3.36[/C][C]3.65999927022283[/C][C]-0.299999270222826[/C][/ROW]
[ROW][C]4[/C][C]3.19[/C][C]3.36002189326195[/C][C]-0.170021893261952[/C][/ROW]
[ROW][C]5[/C][C]2.81[/C][C]3.19001240780967[/C][C]-0.380012407809672[/C][/ROW]
[ROW][C]6[/C][C]2.25[/C][C]2.81002773243809[/C][C]-0.560027732438092[/C][/ROW]
[ROW][C]7[/C][C]2.32[/C][C]2.25004086954557[/C][C]0.0699591304544258[/C][/ROW]
[ROW][C]8[/C][C]2.85[/C][C]2.31999489454235[/C][C]0.53000510545765[/C][/ROW]
[ROW][C]9[/C][C]2.75[/C][C]2.84996132143721[/C][C]-0.0999613214372124[/C][/ROW]
[ROW][C]10[/C][C]2.78[/C][C]2.75000729494906[/C][C]0.0299927050509363[/C][/ROW]
[ROW][C]11[/C][C]2.26[/C][C]2.77999781120085[/C][C]-0.519997811200848[/C][/ROW]
[ROW][C]12[/C][C]2.23[/C][C]2.2600379482533[/C][C]-0.0300379482532955[/C][/ROW]
[ROW][C]13[/C][C]1.46[/C][C]2.2300021921009[/C][C]-0.770002192100898[/C][/ROW]
[ROW][C]14[/C][C]1.19[/C][C]1.46005619300235[/C][C]-0.270056193002345[/C][/ROW]
[ROW][C]15[/C][C]1.11[/C][C]1.19001970808453[/C][C]-0.0800197080845253[/C][/ROW]
[ROW][C]16[/C][C]1[/C][C]1.11000583965564[/C][C]-0.11000583965564[/C][/ROW]
[ROW][C]17[/C][C]1.18[/C][C]1.00000802797507[/C][C]0.179991972024925[/C][/ROW]
[ROW][C]18[/C][C]1.59[/C][C]1.17998686459674[/C][C]0.410013135403262[/C][/ROW]
[ROW][C]19[/C][C]1.51[/C][C]1.58997007817729[/C][C]-0.079970078177289[/C][/ROW]
[ROW][C]20[/C][C]1.01[/C][C]1.51000583603376[/C][C]-0.500005836033763[/C][/ROW]
[ROW][C]21[/C][C]0.9[/C][C]1.01003648928458[/C][C]-0.110036489284583[/C][/ROW]
[ROW][C]22[/C][C]0.63[/C][C]0.900008030211815[/C][C]-0.270008030211815[/C][/ROW]
[ROW][C]23[/C][C]0.81[/C][C]0.630019704569715[/C][C]0.179980295430285[/C][/ROW]
[ROW][C]24[/C][C]0.97[/C][C]0.809986865448869[/C][C]0.160013134551131[/C][/ROW]
[ROW][C]25[/C][C]1.14[/C][C]0.969988322606692[/C][C]0.170011677393308[/C][/ROW]
[ROW][C]26[/C][C]0.97[/C][C]1.13998759293586[/C][C]-0.169987592935859[/C][/ROW]
[ROW][C]27[/C][C]0.89[/C][C]0.970012405306513[/C][C]-0.0800124053065128[/C][/ROW]
[ROW][C]28[/C][C]0.62[/C][C]0.8900058391227[/C][C]-0.2700058391227[/C][/ROW]
[ROW][C]29[/C][C]0.36[/C][C]0.620019704409814[/C][C]-0.260019704409814[/C][/ROW]
[ROW][C]30[/C][C]0.27[/C][C]0.360018975644498[/C][C]-0.0900189756444976[/C][/ROW]
[ROW][C]31[/C][C]0.34[/C][C]0.270006569379362[/C][C]0.069993430620638[/C][/ROW]
[ROW][C]32[/C][C]0.02[/C][C]0.339994892039203[/C][C]-0.319994892039203[/C][/ROW]
[ROW][C]33[/C][C]-0.12[/C][C]0.0200233524967893[/C][C]-0.140023352496789[/C][/ROW]
[ROW][C]34[/C][C]0.09[/C][C]-0.119989781415357[/C][C]0.209989781415357[/C][/ROW]
[ROW][C]35[/C][C]-0.11[/C][C]0.0899846754250824[/C][C]-0.199984675425082[/C][/ROW]
[ROW][C]36[/C][C]-0.38[/C][C]-0.10998540557488[/C][C]-0.27001459442512[/C][/ROW]
[ROW][C]37[/C][C]-0.65[/C][C]-0.379980294951244[/C][C]-0.270019705048756[/C][/ROW]
[ROW][C]38[/C][C]-0.4[/C][C]-0.649980294578282[/C][C]0.249980294578282[/C][/ROW]
[ROW][C]39[/C][C]-0.4[/C][C]-0.400018242991284[/C][C]1.82429912844451e-05[/C][/ROW]
[ROW][C]40[/C][C]0.29[/C][C]-0.400000001331332[/C][C]0.690000001331332[/C][/ROW]
[ROW][C]41[/C][C]0.56[/C][C]0.289949645374921[/C][C]0.270050354625079[/C][/ROW]
[ROW][C]42[/C][C]0.63[/C][C]0.559980292341546[/C][C]0.0700197076584539[/C][/ROW]
[ROW][C]43[/C][C]0.46[/C][C]0.629994890121565[/C][C]-0.169994890121564[/C][/ROW]
[ROW][C]44[/C][C]0.91[/C][C]0.460012405839045[/C][C]0.449987594160955[/C][/ROW]
[ROW][C]45[/C][C]1.06[/C][C]0.909967160932536[/C][C]0.150032839067464[/C][/ROW]
[ROW][C]46[/C][C]1.28[/C][C]1.05998905094588[/C][C]0.220010949054125[/C][/ROW]
[ROW][C]47[/C][C]1.52[/C][C]1.27998394410314[/C][C]0.240016055896857[/C][/ROW]
[ROW][C]48[/C][C]1.5[/C][C]1.51998248417611[/C][C]-0.0199824841761098[/C][/ROW]
[ROW][C]49[/C][C]1.74[/C][C]1.50000145827608[/C][C]0.239998541723918[/C][/ROW]
[ROW][C]50[/C][C]1.39[/C][C]1.73998248545425[/C][C]-0.349982485454254[/C][/ROW]
[ROW][C]51[/C][C]2.24[/C][C]1.39002554092291[/C][C]0.849974459077094[/C][/ROW]
[ROW][C]52[/C][C]2.04[/C][C]2.23993797080416[/C][C]-0.199937970804159[/C][/ROW]
[ROW][C]53[/C][C]2.2[/C][C]2.04001459101672[/C][C]0.159985408983276[/C][/ROW]
[ROW][C]54[/C][C]2.16[/C][C]2.19998832463004[/C][C]-0.0399883246300408[/C][/ROW]
[ROW][C]55[/C][C]2.28[/C][C]2.16000291825665[/C][C]0.119997081743347[/C][/ROW]
[ROW][C]56[/C][C]2.16[/C][C]2.27999124288688[/C][C]-0.119991242886884[/C][/ROW]
[ROW][C]57[/C][C]1.87[/C][C]2.16000875668701[/C][C]-0.29000875668701[/C][/ROW]
[ROW][C]58[/C][C]1.81[/C][C]1.87002116417708[/C][C]-0.0600211641770789[/C][/ROW]
[ROW][C]59[/C][C]1.77[/C][C]1.81000438020756[/C][C]-0.0400043802075554[/C][/ROW]
[ROW][C]60[/C][C]2.03[/C][C]1.77000291942835[/C][C]0.259997080571648[/C][/ROW]
[ROW][C]61[/C][C]2.65[/C][C]2.02998102600654[/C][C]0.620018973993462[/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	3.66	3.65	0.0100000000000002
3	3.36	3.65999927022283	-0.299999270222826
4	3.19	3.36002189326195	-0.170021893261952
5	2.81	3.19001240780967	-0.380012407809672
6	2.25	2.81002773243809	-0.560027732438092
7	2.32	2.25004086954557	0.0699591304544258
8	2.85	2.31999489454235	0.53000510545765
9	2.75	2.84996132143721	-0.0999613214372124
10	2.78	2.75000729494906	0.0299927050509363
11	2.26	2.77999781120085	-0.519997811200848
12	2.23	2.2600379482533	-0.0300379482532955
13	1.46	2.2300021921009	-0.770002192100898
14	1.19	1.46005619300235	-0.270056193002345
15	1.11	1.19001970808453	-0.0800197080845253
16	1	1.11000583965564	-0.11000583965564
17	1.18	1.00000802797507	0.179991972024925
18	1.59	1.17998686459674	0.410013135403262
19	1.51	1.58997007817729	-0.079970078177289
20	1.01	1.51000583603376	-0.500005836033763
21	0.9	1.01003648928458	-0.110036489284583
22	0.63	0.900008030211815	-0.270008030211815
23	0.81	0.630019704569715	0.179980295430285
24	0.97	0.809986865448869	0.160013134551131
25	1.14	0.969988322606692	0.170011677393308
26	0.97	1.13998759293586	-0.169987592935859
27	0.89	0.970012405306513	-0.0800124053065128
28	0.62	0.8900058391227	-0.2700058391227
29	0.36	0.620019704409814	-0.260019704409814
30	0.27	0.360018975644498	-0.0900189756444976
31	0.34	0.270006569379362	0.069993430620638
32	0.02	0.339994892039203	-0.319994892039203
33	-0.12	0.0200233524967893	-0.140023352496789
34	0.09	-0.119989781415357	0.209989781415357
35	-0.11	0.0899846754250824	-0.199984675425082
36	-0.38	-0.10998540557488	-0.27001459442512
37	-0.65	-0.379980294951244	-0.270019705048756
38	-0.4	-0.649980294578282	0.249980294578282
39	-0.4	-0.400018242991284	1.82429912844451e-05
40	0.29	-0.400000001331332	0.690000001331332
41	0.56	0.289949645374921	0.270050354625079
42	0.63	0.559980292341546	0.0700197076584539
43	0.46	0.629994890121565	-0.169994890121564
44	0.91	0.460012405839045	0.449987594160955
45	1.06	0.909967160932536	0.150032839067464
46	1.28	1.05998905094588	0.220010949054125
47	1.52	1.27998394410314	0.240016055896857
48	1.5	1.51998248417611	-0.0199824841761098
49	1.74	1.50000145827608	0.239998541723918
50	1.39	1.73998248545425	-0.349982485454254
51	2.24	1.39002554092291	0.849974459077094
52	2.04	2.23993797080416	-0.199937970804159
53	2.2	2.04001459101672	0.159985408983276
54	2.16	2.19998832463004	-0.0399883246300408
55	2.28	2.16000291825665	0.119997081743347
56	2.16	2.27999124288688	-0.119991242886884
57	1.87	2.16000875668701	-0.29000875668701
58	1.81	1.87002116417708	-0.0600211641770789
59	1.77	1.81000438020756	-0.0400043802075554
60	2.03	1.77000291942835	0.259997080571648
61	2.65	2.02998102600654	0.620018973993462

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
62	2.64995475243056	2.05160245162742	3.24830705323369
63	2.64995475243056	1.80378768979128	3.49612181506983
64	2.64995475243056	1.61362858759886	3.68628091726225
65	2.64995475243056	1.45331564980439	3.84659385505672
66	2.64995475243056	1.31207644557558	3.98783305928553
67	2.64995475243056	1.18438606213579	4.11552344272532
68	2.64995475243056	1.0669623936393	4.23294711122181
69	2.64995475243056	0.957666942981267	4.34224256187984
70	2.64995475243056	0.855014293242605	4.44489521161851
71	2.64995475243056	0.757922914947625	4.54198658991348
72	2.64995475243056	0.665576336888748	4.63433316797236
73	2.64995475243056	0.577340239770907	4.7225692650902

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 2.64995475243056 & 2.05160245162742 & 3.24830705323369 \tabularnewline
63 & 2.64995475243056 & 1.80378768979128 & 3.49612181506983 \tabularnewline
64 & 2.64995475243056 & 1.61362858759886 & 3.68628091726225 \tabularnewline
65 & 2.64995475243056 & 1.45331564980439 & 3.84659385505672 \tabularnewline
66 & 2.64995475243056 & 1.31207644557558 & 3.98783305928553 \tabularnewline
67 & 2.64995475243056 & 1.18438606213579 & 4.11552344272532 \tabularnewline
68 & 2.64995475243056 & 1.0669623936393 & 4.23294711122181 \tabularnewline
69 & 2.64995475243056 & 0.957666942981267 & 4.34224256187984 \tabularnewline
70 & 2.64995475243056 & 0.855014293242605 & 4.44489521161851 \tabularnewline
71 & 2.64995475243056 & 0.757922914947625 & 4.54198658991348 \tabularnewline
72 & 2.64995475243056 & 0.665576336888748 & 4.63433316797236 \tabularnewline
73 & 2.64995475243056 & 0.577340239770907 & 4.7225692650902 \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]62[/C][C]2.64995475243056[/C][C]2.05160245162742[/C][C]3.24830705323369[/C][/ROW]
[ROW][C]63[/C][C]2.64995475243056[/C][C]1.80378768979128[/C][C]3.49612181506983[/C][/ROW]
[ROW][C]64[/C][C]2.64995475243056[/C][C]1.61362858759886[/C][C]3.68628091726225[/C][/ROW]
[ROW][C]65[/C][C]2.64995475243056[/C][C]1.45331564980439[/C][C]3.84659385505672[/C][/ROW]
[ROW][C]66[/C][C]2.64995475243056[/C][C]1.31207644557558[/C][C]3.98783305928553[/C][/ROW]
[ROW][C]67[/C][C]2.64995475243056[/C][C]1.18438606213579[/C][C]4.11552344272532[/C][/ROW]
[ROW][C]68[/C][C]2.64995475243056[/C][C]1.0669623936393[/C][C]4.23294711122181[/C][/ROW]
[ROW][C]69[/C][C]2.64995475243056[/C][C]0.957666942981267[/C][C]4.34224256187984[/C][/ROW]
[ROW][C]70[/C][C]2.64995475243056[/C][C]0.855014293242605[/C][C]4.44489521161851[/C][/ROW]
[ROW][C]71[/C][C]2.64995475243056[/C][C]0.757922914947625[/C][C]4.54198658991348[/C][/ROW]
[ROW][C]72[/C][C]2.64995475243056[/C][C]0.665576336888748[/C][C]4.63433316797236[/C][/ROW]
[ROW][C]73[/C][C]2.64995475243056[/C][C]0.577340239770907[/C][C]4.7225692650902[/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
62	2.64995475243056	2.05160245162742	3.24830705323369
63	2.64995475243056	1.80378768979128	3.49612181506983
64	2.64995475243056	1.61362858759886	3.68628091726225
65	2.64995475243056	1.45331564980439	3.84659385505672
66	2.64995475243056	1.31207644557558	3.98783305928553
67	2.64995475243056	1.18438606213579	4.11552344272532
68	2.64995475243056	1.0669623936393	4.23294711122181
69	2.64995475243056	0.957666942981267	4.34224256187984
70	2.64995475243056	0.855014293242605	4.44489521161851
71	2.64995475243056	0.757922914947625	4.54198658991348
72	2.64995475243056	0.665576336888748	4.63433316797236
73	2.64995475243056	0.577340239770907	4.7225692650902

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):

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