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

Sat, 15 Jan 2011 15:33:55 +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/2011/Jan/15/t1295105532khhb5u9s5qmuzn2.htm/, Retrieved Thu, 16 May 2024 08:04:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117342, Retrieved Thu, 16 May 2024 08:04:53 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

159

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

-       [Exponential Smoothing] [] [2011-01-15 15:33:55] [5cd570406d143ae5f29e48ad26074e87] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117342&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117342&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.253682747786366
beta	0.000800115960723572
gamma	0.477115909808832

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.253682747786366 \tabularnewline
beta & 0.000800115960723572 \tabularnewline
gamma & 0.477115909808832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117342&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]0.253682747786366[/C][/ROW]
[ROW][C]beta[/C][C]0.000800115960723572[/C][/ROW]
[ROW][C]gamma[/C][C]0.477115909808832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117342&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	0.253682747786366
beta	0.000800115960723572
gamma	0.477115909808832

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.29	1.29367788461538	-0.00367788461538465
14	1.73	1.73173450683460	-0.00173450683460397
15	1.41	1.40820044507331	0.00179955492668693
16	1.15	1.14639661240958	0.00360338759042489
17	1.31	1.30255111237233	0.00744888762766527
18	1.15	1.13676599462704	0.0132340053729614
19	1.08	1.10620114762802	-0.0262011476280224
20	1.1	1.03104363112894	0.0689563688710586
21	1.14	1.14337326468262	-0.00337326468261945
22	1.24	1.21152010002621	0.0284798999737896
23	1.33	1.28150331443076	0.0484966855692428
24	1.49	1.41449095231828	0.0755090476817237
25	1.38	1.36428686639987	0.0157131336001277
26	1.96	1.80800172959252	0.151998270407481
27	1.36	1.52480370987104	-0.164803709871041
28	1.24	1.22142227579602	0.0185777242039793
29	1.35	1.38279231521622	-0.0327923152162248
30	1.23	1.20889799792844	0.02110200207156
31	1.09	1.16632799579539	-0.0763279957953855
32	1.08	1.11236859355169	-0.0323685935516942
33	1.33	1.17324889983714	0.156751100162864
34	1.35	1.29340148657753	0.0565985134224749
35	1.38	1.37769388213319	0.00230611786680979
36	1.5	1.50862135208323	-0.00862135208323411
37	1.47	1.41580466431340	0.0541953356865976
38	2.09	1.91783994656133	0.172160053438669
39	1.52	1.52698367819881	-0.00698367819880663
40	1.29	1.32900277942220	-0.0390027794221977
41	1.52	1.45752800113321	0.0624719988667861
42	1.27	1.32706481055688	-0.0570648105568776
43	1.35	1.23003004726162	0.119969952738380
44	1.29	1.24161861656809	0.0483813834319089
45	1.41	1.39043941036186	0.0195605896381372
46	1.39	1.44021287072182	-0.0502128707218179
47	1.45	1.47814100934692	-0.0281410093469177
48	1.53	1.59751171241841	-0.0675117124184088
49	1.45	1.51216955442677	-0.0621695544267717
50	2.11	2.02671255198124	0.0832874480187589
51	1.53	1.54952595070233	-0.0195259507023304
52	1.38	1.33696397591979	0.0430360240802086
53	1.54	1.52245283931432	0.0175471606856790
54	1.35	1.33803791664287	0.0119620833571257
55	1.29	1.32157617716061	-0.03157617716061
56	1.33	1.26922168414342	0.0607783158565791
57	1.47	1.41092020085845	0.0590797991415499
58	1.47	1.44587744060575	0.0241225593942467
59	1.54	1.51054098840056	0.0294590115994395
60	1.59	1.63053484926045	-0.0405348492604511
61	1.5	1.55397410606957	-0.0539741060695722
62	2	2.12242773165260	-0.122427731652603
63	1.51	1.55644048390593	-0.0464404839059258
64	1.4	1.35931787464009	0.0406821253599117
65	1.62	1.53512310709864	0.084876892901357
66	1.44	1.36580309161081	0.0741969083891871
67	1.29	1.34964203821004	-0.0596420382100389
68	1.28	1.32306347764545	-0.0430634776454544
69	1.4	1.43780342253298	-0.0378034225329817
70	1.39	1.43570493454025	-0.0457049345402489
71	1.46	1.48450992384668	-0.0245099238466782
72	1.49	1.56583370910222	-0.0758337091022239

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.29 & 1.29367788461538 & -0.00367788461538465 \tabularnewline
14 & 1.73 & 1.73173450683460 & -0.00173450683460397 \tabularnewline
15 & 1.41 & 1.40820044507331 & 0.00179955492668693 \tabularnewline
16 & 1.15 & 1.14639661240958 & 0.00360338759042489 \tabularnewline
17 & 1.31 & 1.30255111237233 & 0.00744888762766527 \tabularnewline
18 & 1.15 & 1.13676599462704 & 0.0132340053729614 \tabularnewline
19 & 1.08 & 1.10620114762802 & -0.0262011476280224 \tabularnewline
20 & 1.1 & 1.03104363112894 & 0.0689563688710586 \tabularnewline
21 & 1.14 & 1.14337326468262 & -0.00337326468261945 \tabularnewline
22 & 1.24 & 1.21152010002621 & 0.0284798999737896 \tabularnewline
23 & 1.33 & 1.28150331443076 & 0.0484966855692428 \tabularnewline
24 & 1.49 & 1.41449095231828 & 0.0755090476817237 \tabularnewline
25 & 1.38 & 1.36428686639987 & 0.0157131336001277 \tabularnewline
26 & 1.96 & 1.80800172959252 & 0.151998270407481 \tabularnewline
27 & 1.36 & 1.52480370987104 & -0.164803709871041 \tabularnewline
28 & 1.24 & 1.22142227579602 & 0.0185777242039793 \tabularnewline
29 & 1.35 & 1.38279231521622 & -0.0327923152162248 \tabularnewline
30 & 1.23 & 1.20889799792844 & 0.02110200207156 \tabularnewline
31 & 1.09 & 1.16632799579539 & -0.0763279957953855 \tabularnewline
32 & 1.08 & 1.11236859355169 & -0.0323685935516942 \tabularnewline
33 & 1.33 & 1.17324889983714 & 0.156751100162864 \tabularnewline
34 & 1.35 & 1.29340148657753 & 0.0565985134224749 \tabularnewline
35 & 1.38 & 1.37769388213319 & 0.00230611786680979 \tabularnewline
36 & 1.5 & 1.50862135208323 & -0.00862135208323411 \tabularnewline
37 & 1.47 & 1.41580466431340 & 0.0541953356865976 \tabularnewline
38 & 2.09 & 1.91783994656133 & 0.172160053438669 \tabularnewline
39 & 1.52 & 1.52698367819881 & -0.00698367819880663 \tabularnewline
40 & 1.29 & 1.32900277942220 & -0.0390027794221977 \tabularnewline
41 & 1.52 & 1.45752800113321 & 0.0624719988667861 \tabularnewline
42 & 1.27 & 1.32706481055688 & -0.0570648105568776 \tabularnewline
43 & 1.35 & 1.23003004726162 & 0.119969952738380 \tabularnewline
44 & 1.29 & 1.24161861656809 & 0.0483813834319089 \tabularnewline
45 & 1.41 & 1.39043941036186 & 0.0195605896381372 \tabularnewline
46 & 1.39 & 1.44021287072182 & -0.0502128707218179 \tabularnewline
47 & 1.45 & 1.47814100934692 & -0.0281410093469177 \tabularnewline
48 & 1.53 & 1.59751171241841 & -0.0675117124184088 \tabularnewline
49 & 1.45 & 1.51216955442677 & -0.0621695544267717 \tabularnewline
50 & 2.11 & 2.02671255198124 & 0.0832874480187589 \tabularnewline
51 & 1.53 & 1.54952595070233 & -0.0195259507023304 \tabularnewline
52 & 1.38 & 1.33696397591979 & 0.0430360240802086 \tabularnewline
53 & 1.54 & 1.52245283931432 & 0.0175471606856790 \tabularnewline
54 & 1.35 & 1.33803791664287 & 0.0119620833571257 \tabularnewline
55 & 1.29 & 1.32157617716061 & -0.03157617716061 \tabularnewline
56 & 1.33 & 1.26922168414342 & 0.0607783158565791 \tabularnewline
57 & 1.47 & 1.41092020085845 & 0.0590797991415499 \tabularnewline
58 & 1.47 & 1.44587744060575 & 0.0241225593942467 \tabularnewline
59 & 1.54 & 1.51054098840056 & 0.0294590115994395 \tabularnewline
60 & 1.59 & 1.63053484926045 & -0.0405348492604511 \tabularnewline
61 & 1.5 & 1.55397410606957 & -0.0539741060695722 \tabularnewline
62 & 2 & 2.12242773165260 & -0.122427731652603 \tabularnewline
63 & 1.51 & 1.55644048390593 & -0.0464404839059258 \tabularnewline
64 & 1.4 & 1.35931787464009 & 0.0406821253599117 \tabularnewline
65 & 1.62 & 1.53512310709864 & 0.084876892901357 \tabularnewline
66 & 1.44 & 1.36580309161081 & 0.0741969083891871 \tabularnewline
67 & 1.29 & 1.34964203821004 & -0.0596420382100389 \tabularnewline
68 & 1.28 & 1.32306347764545 & -0.0430634776454544 \tabularnewline
69 & 1.4 & 1.43780342253298 & -0.0378034225329817 \tabularnewline
70 & 1.39 & 1.43570493454025 & -0.0457049345402489 \tabularnewline
71 & 1.46 & 1.48450992384668 & -0.0245099238466782 \tabularnewline
72 & 1.49 & 1.56583370910222 & -0.0758337091022239 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117342&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]-0.00367788461538465[/C][/ROW]
[ROW][C]14[/C][C]1.73[/C][C]1.73173450683460[/C][C]-0.00173450683460397[/C][/ROW]
[ROW][C]15[/C][C]1.41[/C][C]1.40820044507331[/C][C]0.00179955492668693[/C][/ROW]
[ROW][C]16[/C][C]1.15[/C][C]1.14639661240958[/C][C]0.00360338759042489[/C][/ROW]
[ROW][C]17[/C][C]1.31[/C][C]1.30255111237233[/C][C]0.00744888762766527[/C][/ROW]
[ROW][C]18[/C][C]1.15[/C][C]1.13676599462704[/C][C]0.0132340053729614[/C][/ROW]
[ROW][C]19[/C][C]1.08[/C][C]1.10620114762802[/C][C]-0.0262011476280224[/C][/ROW]
[ROW][C]20[/C][C]1.1[/C][C]1.03104363112894[/C][C]0.0689563688710586[/C][/ROW]
[ROW][C]21[/C][C]1.14[/C][C]1.14337326468262[/C][C]-0.00337326468261945[/C][/ROW]
[ROW][C]22[/C][C]1.24[/C][C]1.21152010002621[/C][C]0.0284798999737896[/C][/ROW]
[ROW][C]23[/C][C]1.33[/C][C]1.28150331443076[/C][C]0.0484966855692428[/C][/ROW]
[ROW][C]24[/C][C]1.49[/C][C]1.41449095231828[/C][C]0.0755090476817237[/C][/ROW]
[ROW][C]25[/C][C]1.38[/C][C]1.36428686639987[/C][C]0.0157131336001277[/C][/ROW]
[ROW][C]26[/C][C]1.96[/C][C]1.80800172959252[/C][C]0.151998270407481[/C][/ROW]
[ROW][C]27[/C][C]1.36[/C][C]1.52480370987104[/C][C]-0.164803709871041[/C][/ROW]
[ROW][C]28[/C][C]1.24[/C][C]1.22142227579602[/C][C]0.0185777242039793[/C][/ROW]
[ROW][C]29[/C][C]1.35[/C][C]1.38279231521622[/C][C]-0.0327923152162248[/C][/ROW]
[ROW][C]30[/C][C]1.23[/C][C]1.20889799792844[/C][C]0.02110200207156[/C][/ROW]
[ROW][C]31[/C][C]1.09[/C][C]1.16632799579539[/C][C]-0.0763279957953855[/C][/ROW]
[ROW][C]32[/C][C]1.08[/C][C]1.11236859355169[/C][C]-0.0323685935516942[/C][/ROW]
[ROW][C]33[/C][C]1.33[/C][C]1.17324889983714[/C][C]0.156751100162864[/C][/ROW]
[ROW][C]34[/C][C]1.35[/C][C]1.29340148657753[/C][C]0.0565985134224749[/C][/ROW]
[ROW][C]35[/C][C]1.38[/C][C]1.37769388213319[/C][C]0.00230611786680979[/C][/ROW]
[ROW][C]36[/C][C]1.5[/C][C]1.50862135208323[/C][C]-0.00862135208323411[/C][/ROW]
[ROW][C]37[/C][C]1.47[/C][C]1.41580466431340[/C][C]0.0541953356865976[/C][/ROW]
[ROW][C]38[/C][C]2.09[/C][C]1.91783994656133[/C][C]0.172160053438669[/C][/ROW]
[ROW][C]39[/C][C]1.52[/C][C]1.52698367819881[/C][C]-0.00698367819880663[/C][/ROW]
[ROW][C]40[/C][C]1.29[/C][C]1.32900277942220[/C][C]-0.0390027794221977[/C][/ROW]
[ROW][C]41[/C][C]1.52[/C][C]1.45752800113321[/C][C]0.0624719988667861[/C][/ROW]
[ROW][C]42[/C][C]1.27[/C][C]1.32706481055688[/C][C]-0.0570648105568776[/C][/ROW]
[ROW][C]43[/C][C]1.35[/C][C]1.23003004726162[/C][C]0.119969952738380[/C][/ROW]
[ROW][C]44[/C][C]1.29[/C][C]1.24161861656809[/C][C]0.0483813834319089[/C][/ROW]
[ROW][C]45[/C][C]1.41[/C][C]1.39043941036186[/C][C]0.0195605896381372[/C][/ROW]
[ROW][C]46[/C][C]1.39[/C][C]1.44021287072182[/C][C]-0.0502128707218179[/C][/ROW]
[ROW][C]47[/C][C]1.45[/C][C]1.47814100934692[/C][C]-0.0281410093469177[/C][/ROW]
[ROW][C]48[/C][C]1.53[/C][C]1.59751171241841[/C][C]-0.0675117124184088[/C][/ROW]
[ROW][C]49[/C][C]1.45[/C][C]1.51216955442677[/C][C]-0.0621695544267717[/C][/ROW]
[ROW][C]50[/C][C]2.11[/C][C]2.02671255198124[/C][C]0.0832874480187589[/C][/ROW]
[ROW][C]51[/C][C]1.53[/C][C]1.54952595070233[/C][C]-0.0195259507023304[/C][/ROW]
[ROW][C]52[/C][C]1.38[/C][C]1.33696397591979[/C][C]0.0430360240802086[/C][/ROW]
[ROW][C]53[/C][C]1.54[/C][C]1.52245283931432[/C][C]0.0175471606856790[/C][/ROW]
[ROW][C]54[/C][C]1.35[/C][C]1.33803791664287[/C][C]0.0119620833571257[/C][/ROW]
[ROW][C]55[/C][C]1.29[/C][C]1.32157617716061[/C][C]-0.03157617716061[/C][/ROW]
[ROW][C]56[/C][C]1.33[/C][C]1.26922168414342[/C][C]0.0607783158565791[/C][/ROW]
[ROW][C]57[/C][C]1.47[/C][C]1.41092020085845[/C][C]0.0590797991415499[/C][/ROW]
[ROW][C]58[/C][C]1.47[/C][C]1.44587744060575[/C][C]0.0241225593942467[/C][/ROW]
[ROW][C]59[/C][C]1.54[/C][C]1.51054098840056[/C][C]0.0294590115994395[/C][/ROW]
[ROW][C]60[/C][C]1.59[/C][C]1.63053484926045[/C][C]-0.0405348492604511[/C][/ROW]
[ROW][C]61[/C][C]1.5[/C][C]1.55397410606957[/C][C]-0.0539741060695722[/C][/ROW]
[ROW][C]62[/C][C]2[/C][C]2.12242773165260[/C][C]-0.122427731652603[/C][/ROW]
[ROW][C]63[/C][C]1.51[/C][C]1.55644048390593[/C][C]-0.0464404839059258[/C][/ROW]
[ROW][C]64[/C][C]1.4[/C][C]1.35931787464009[/C][C]0.0406821253599117[/C][/ROW]
[ROW][C]65[/C][C]1.62[/C][C]1.53512310709864[/C][C]0.084876892901357[/C][/ROW]
[ROW][C]66[/C][C]1.44[/C][C]1.36580309161081[/C][C]0.0741969083891871[/C][/ROW]
[ROW][C]67[/C][C]1.29[/C][C]1.34964203821004[/C][C]-0.0596420382100389[/C][/ROW]
[ROW][C]68[/C][C]1.28[/C][C]1.32306347764545[/C][C]-0.0430634776454544[/C][/ROW]
[ROW][C]69[/C][C]1.4[/C][C]1.43780342253298[/C][C]-0.0378034225329817[/C][/ROW]
[ROW][C]70[/C][C]1.39[/C][C]1.43570493454025[/C][C]-0.0457049345402489[/C][/ROW]
[ROW][C]71[/C][C]1.46[/C][C]1.48450992384668[/C][C]-0.0245099238466782[/C][/ROW]
[ROW][C]72[/C][C]1.49[/C][C]1.56583370910222[/C][C]-0.0758337091022239[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117342&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	-0.00367788461538465
14	1.73	1.73173450683460	-0.00173450683460397
15	1.41	1.40820044507331	0.00179955492668693
16	1.15	1.14639661240958	0.00360338759042489
17	1.31	1.30255111237233	0.00744888762766527
18	1.15	1.13676599462704	0.0132340053729614
19	1.08	1.10620114762802	-0.0262011476280224
20	1.1	1.03104363112894	0.0689563688710586
21	1.14	1.14337326468262	-0.00337326468261945
22	1.24	1.21152010002621	0.0284798999737896
23	1.33	1.28150331443076	0.0484966855692428
24	1.49	1.41449095231828	0.0755090476817237
25	1.38	1.36428686639987	0.0157131336001277
26	1.96	1.80800172959252	0.151998270407481
27	1.36	1.52480370987104	-0.164803709871041
28	1.24	1.22142227579602	0.0185777242039793
29	1.35	1.38279231521622	-0.0327923152162248
30	1.23	1.20889799792844	0.02110200207156
31	1.09	1.16632799579539	-0.0763279957953855
32	1.08	1.11236859355169	-0.0323685935516942
33	1.33	1.17324889983714	0.156751100162864
34	1.35	1.29340148657753	0.0565985134224749
35	1.38	1.37769388213319	0.00230611786680979
36	1.5	1.50862135208323	-0.00862135208323411
37	1.47	1.41580466431340	0.0541953356865976
38	2.09	1.91783994656133	0.172160053438669
39	1.52	1.52698367819881	-0.00698367819880663
40	1.29	1.32900277942220	-0.0390027794221977
41	1.52	1.45752800113321	0.0624719988667861
42	1.27	1.32706481055688	-0.0570648105568776
43	1.35	1.23003004726162	0.119969952738380
44	1.29	1.24161861656809	0.0483813834319089
45	1.41	1.39043941036186	0.0195605896381372
46	1.39	1.44021287072182	-0.0502128707218179
47	1.45	1.47814100934692	-0.0281410093469177
48	1.53	1.59751171241841	-0.0675117124184088
49	1.45	1.51216955442677	-0.0621695544267717
50	2.11	2.02671255198124	0.0832874480187589
51	1.53	1.54952595070233	-0.0195259507023304
52	1.38	1.33696397591979	0.0430360240802086
53	1.54	1.52245283931432	0.0175471606856790
54	1.35	1.33803791664287	0.0119620833571257
55	1.29	1.32157617716061	-0.03157617716061
56	1.33	1.26922168414342	0.0607783158565791
57	1.47	1.41092020085845	0.0590797991415499
58	1.47	1.44587744060575	0.0241225593942467
59	1.54	1.51054098840056	0.0294590115994395
60	1.59	1.63053484926045	-0.0405348492604511
61	1.5	1.55397410606957	-0.0539741060695722
62	2	2.12242773165260	-0.122427731652603
63	1.51	1.55644048390593	-0.0464404839059258
64	1.4	1.35931787464009	0.0406821253599117
65	1.62	1.53512310709864	0.084876892901357
66	1.44	1.36580309161081	0.0741969083891871
67	1.29	1.34964203821004	-0.0596420382100389
68	1.28	1.32306347764545	-0.0430634776454544
69	1.4	1.43780342253298	-0.0378034225329817
70	1.39	1.43570493454025	-0.0457049345402489
71	1.46	1.48450992384668	-0.0245099238466782
72	1.49	1.56583370910222	-0.0758337091022239

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.47546995564724	1.35057403958556	1.60036587170891
74	2.03318903034457	1.90433070146691	2.16204735922222
75	1.52529006770324	1.39258152860566	1.65799860680082
76	1.37095359371359	1.23449754430929	1.50740964311789
77	1.55214946226665	1.41204035686905	1.69225856766426
78	1.35745161222035	1.21377669574706	1.50112652869363
79	1.27475256904171	1.12759273984494	1.42191239823849
80	1.26916139741412	1.11859193232407	1.41973086250416
81	1.39666148572462	1.24275265435434	1.55057031709490
82	1.40130986044772	1.24412744958904	1.55849227130640
83	1.46923615173132	1.30884191607564	1.62963038738701
84	1.53848692444765	1.37493897642088	1.70203487247443

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.47546995564724 & 1.35057403958556 & 1.60036587170891 \tabularnewline
74 & 2.03318903034457 & 1.90433070146691 & 2.16204735922222 \tabularnewline
75 & 1.52529006770324 & 1.39258152860566 & 1.65799860680082 \tabularnewline
76 & 1.37095359371359 & 1.23449754430929 & 1.50740964311789 \tabularnewline
77 & 1.55214946226665 & 1.41204035686905 & 1.69225856766426 \tabularnewline
78 & 1.35745161222035 & 1.21377669574706 & 1.50112652869363 \tabularnewline
79 & 1.27475256904171 & 1.12759273984494 & 1.42191239823849 \tabularnewline
80 & 1.26916139741412 & 1.11859193232407 & 1.41973086250416 \tabularnewline
81 & 1.39666148572462 & 1.24275265435434 & 1.55057031709490 \tabularnewline
82 & 1.40130986044772 & 1.24412744958904 & 1.55849227130640 \tabularnewline
83 & 1.46923615173132 & 1.30884191607564 & 1.62963038738701 \tabularnewline
84 & 1.53848692444765 & 1.37493897642088 & 1.70203487247443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117342&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]1.47546995564724[/C][C]1.35057403958556[/C][C]1.60036587170891[/C][/ROW]
[ROW][C]74[/C][C]2.03318903034457[/C][C]1.90433070146691[/C][C]2.16204735922222[/C][/ROW]
[ROW][C]75[/C][C]1.52529006770324[/C][C]1.39258152860566[/C][C]1.65799860680082[/C][/ROW]
[ROW][C]76[/C][C]1.37095359371359[/C][C]1.23449754430929[/C][C]1.50740964311789[/C][/ROW]
[ROW][C]77[/C][C]1.55214946226665[/C][C]1.41204035686905[/C][C]1.69225856766426[/C][/ROW]
[ROW][C]78[/C][C]1.35745161222035[/C][C]1.21377669574706[/C][C]1.50112652869363[/C][/ROW]
[ROW][C]79[/C][C]1.27475256904171[/C][C]1.12759273984494[/C][C]1.42191239823849[/C][/ROW]
[ROW][C]80[/C][C]1.26916139741412[/C][C]1.11859193232407[/C][C]1.41973086250416[/C][/ROW]
[ROW][C]81[/C][C]1.39666148572462[/C][C]1.24275265435434[/C][C]1.55057031709490[/C][/ROW]
[ROW][C]82[/C][C]1.40130986044772[/C][C]1.24412744958904[/C][C]1.55849227130640[/C][/ROW]
[ROW][C]83[/C][C]1.46923615173132[/C][C]1.30884191607564[/C][C]1.62963038738701[/C][/ROW]
[ROW][C]84[/C][C]1.53848692444765[/C][C]1.37493897642088[/C][C]1.70203487247443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117342&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117342&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	1.47546995564724	1.35057403958556	1.60036587170891
74	2.03318903034457	1.90433070146691	2.16204735922222
75	1.52529006770324	1.39258152860566	1.65799860680082
76	1.37095359371359	1.23449754430929	1.50740964311789
77	1.55214946226665	1.41204035686905	1.69225856766426
78	1.35745161222035	1.21377669574706	1.50112652869363
79	1.27475256904171	1.12759273984494	1.42191239823849
80	1.26916139741412	1.11859193232407	1.41973086250416
81	1.39666148572462	1.24275265435434	1.55057031709490
82	1.40130986044772	1.24412744958904	1.55849227130640
83	1.46923615173132	1.30884191607564	1.62963038738701
84	1.53848692444765	1.37493897642088	1.70203487247443

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