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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 25 Jan 2009 05:50:17 -0700

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/2009/Jan/25/t1232887851sgafbbxvzo8n9gd.htm/, Retrieved Tue, 10 Feb 2026 02:26:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36958, Retrieved Tue, 10 Feb 2026 02:26:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

498

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

-     [Classical Decomposition] [Nieuwe personenwa...] [2009-01-13 17:37:29] [74be16979710d4c4e7c6647856088456]
-       [Classical Decomposition] [roger dirkx oefen...] [2009-01-14 16:39:03] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [roger dirkx oef 10] [2009-01-24 20:53:30] [74be16979710d4c4e7c6647856088456]
-           [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:25:31] [2097edf1f094fab6879a8cb46df74ec2]
-             [Exponential Smoothing] [Dennis Collin oef 2] [2009-01-25 12:34:26] [2097edf1f094fab6879a8cb46df74ec2]
-               [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:39:06] [2097edf1f094fab6879a8cb46df74ec2]
-   PD              [Exponential Smoothing] [Dennis Collin oef...] [2009-01-25 12:50:17] [06e57c0cb32e2f613cf343ab1a0ac99f] [Current]

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Dataseries X:

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Histogram

Boxplots

1,29
1,29
1,3
1,3
1,3
1,3
1,31
1,31
1,31
1,31
1,31
1,32
1,32
1,32
1,32
1,33
1,33
1,33
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,35
1,36
1,36
1,36
1,37
1,37
1,37
1,37
1,37
1,37
1,37
1,38
1,38
1,38
1,39
1,4
1,4
1,4
1,4
1,41
1,42
1,43
1,43
1,43
1,44
1,45
1,45
1,46
1,46
1,47
1,47
1,47
1,48
1,49
1,49
1,49
1,5
1,51
1,51
1,51
1,52
1,52
1,52
1,52
1,53
1,53
1,53
1,53
1,54
1,54
1,55
1,55
1,55
1,56
1,56
1,58
1,58
1,58
1,58
1,58
1,58
1,59
1,59
1,6
1,6
1,6
1,61
1,62
1,62
1,63
1,63

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36958&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36958&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.693880469628355
beta	0.087046697378327
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.693880469628355 \tabularnewline
beta & 0.087046697378327 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36958&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]0.693880469628355[/C][/ROW]
[ROW][C]beta[/C][C]0.087046697378327[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36958&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	0.693880469628355
beta	0.087046697378327
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.3	1.29	0.01
4	1.3	1.29754280472885	0.00245719527115185
5	1.3	1.30000021917251	-2.19172507698318e-07
6	1.3	1.30075246848991	-0.000752468489908953
7	1.31	1.30093729759843	0.0090627024015666
8	1.31	1.30848006934918	0.00151993065081557
9	1.31	1.31088086291148	-0.000880862911483815
10	1.31	1.31156258858657	-0.00156258858657199
11	1.31	1.31167689777435	-0.00167689777435487
12	1.32	1.31161060541820	0.00838939458179566
13	1.32	1.31903583618962	0.000964163810384111
14	1.32	1.32136707984355	-0.00136707984354878
15	1.32	1.32199814742907	-0.00199814742907023
16	1.33	1.32207064143076	0.00792935856923993
17	1.33	1.3295105712402	0.000489428759800514
18	1.33	1.33181764055815	-0.00181764055814893
19	1.34	1.33241409403866	0.00758590596133701
20	1.34	1.33999367353906	6.32646094178568e-06
21	1.34	1.34231431297440	-0.00231431297439522
22	1.34	1.34288492151731	-0.00288492151731257
23	1.34	1.34288534666746	-0.0028853466674561
24	1.34	1.34271120186611	-0.00271120186610796
25	1.34	1.34249413613976	-0.00249413613976057
26	1.35	1.34227704225059	0.007722957749412
27	1.36	1.34961585694069	0.0103841430593148
28	1.36	1.35942841841798	0.000571581582015757
29	1.36	1.36246675865857	-0.00246675865857293
30	1.37	1.36324786171512	0.00675213828487942
31	1.37	1.37083360648664	-0.000833606486641436
32	1.37	1.37310540127911	-0.00310540127911074
33	1.37	1.37361327578671	-0.00361327578671133
34	1.37	1.37355050422318	-0.00355050422318159
35	1.37	1.37331683815499	-0.00331683815499084
36	1.37	1.37304497137257	-0.00304497137257020
37	1.38	1.37277783135999	0.00722216864000713
38	1.38	1.38007107829046	-7.10782904578267e-05
39	1.38	1.38229939048672	-0.00229939048672101
40	1.39	1.38284263717688	0.0071573628231234
41	1.4	1.39038004503265	0.00961995496734902
42	1.4	1.40020724279332	-0.000207242793318629
43	1.4	1.40320302249129	-0.00320302249129223
44	1.4	1.40392662659663	-0.00392662659662824
45	1.41	1.40391096768631	0.00608903231369462
46	1.42	1.41121275645589	0.0087872435441092
47	1.43	1.42091753083987	0.0090824691601279
48	1.43	1.43137573767979	-0.0013757376797916
49	1.43	1.43449410448582	-0.00449410448581755
50	1.44	1.43517725354243	0.00482274645757341
51	1.45	1.44261647740884	0.00738352259116426
52	1.45	1.45227853860998	-0.00227853860998461
53	1.46	1.45509866050784	0.00490133949216065
54	1.46	1.46319680051637	-0.0031968005163725
55	1.47	1.46548271257107	0.00451728742893054
56	1.47	1.47339412376743	-0.00339412376742532
57	1.47	1.47561095616083	-0.00561095616082552
58	1.48	1.47595067008162	0.00404932991838014
59	1.49	1.48323804738405	0.0067619526159457
60	1.49	1.49281608255782	-0.00281608255782362
61	1.49	1.49557801479144	-0.00557801479143771
62	1.5	1.49608658407814	0.00391341592185745
63	1.51	1.50341744210006	0.00658255789994211
64	1.51	1.51299795212982	-0.00299795212982357
65	1.51	1.51574965704245	-0.00574965704245223
66	1.52	1.51624472835394	0.00375527164606027
67	1.52	1.52356190246725	-0.0035619024672473
68	1.52	1.52558669344984	-0.00558669344983964
69	1.52	1.52586908521197	-0.00586908521196827
70	1.53	1.52560103807966	0.0043989619203435
71	1.53	1.53272348562799	-0.00272348562799318
72	1.53	1.53473930738579	-0.00473930738578709
73	1.53	1.53507013561406	-0.005070135614061
74	1.54	1.53486517238833	0.00513482761166628
75	1.54	1.54205137744268	-0.00205137744268025
76	1.55	1.54412731195485	0.00587268804514696
77	1.55	1.55205631112614	-0.00205631112613647
78	1.55	1.55435933143005	-0.00435933143005185
79	1.56	1.55480102729135	0.00519897270864855
80	1.56	1.56218906168580	-0.00218906168579602
81	1.58	1.56431846397204	0.0156815360279579
82	1.58	1.57979508981960	0.000204910180397588
83	1.58	1.58454516383136	-0.0045451638313585
84	1.58	1.58572472634685	-0.0057247263468525
85	1.58	1.58574003998015	-0.00574003998014727
86	1.58	1.58539802934889	-0.00539802934888645
87	1.59	1.58496729222481	0.00503270777518838
88	1.59	1.59207821544097	-0.00207821544096998
89	1.6	1.59412948369701	0.00587051630299285
90	1.6	1.60205080087231	-0.00205080087231280
91	1.6	1.60435180238658	-0.00435180238657606
92	1.61	1.60479333501119	0.00520666498881384
93	1.62	1.61218178404944	0.00781821595056109
94	1.62	1.62185455756436	-0.00185455756436070
95	1.63	1.62470356716721	0.00529643283278647
96	1.63	1.63283441390549	-0.00283441390549433

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.3 & 1.29 & 0.01 \tabularnewline
4 & 1.3 & 1.29754280472885 & 0.00245719527115185 \tabularnewline
5 & 1.3 & 1.30000021917251 & -2.19172507698318e-07 \tabularnewline
6 & 1.3 & 1.30075246848991 & -0.000752468489908953 \tabularnewline
7 & 1.31 & 1.30093729759843 & 0.0090627024015666 \tabularnewline
8 & 1.31 & 1.30848006934918 & 0.00151993065081557 \tabularnewline
9 & 1.31 & 1.31088086291148 & -0.000880862911483815 \tabularnewline
10 & 1.31 & 1.31156258858657 & -0.00156258858657199 \tabularnewline
11 & 1.31 & 1.31167689777435 & -0.00167689777435487 \tabularnewline
12 & 1.32 & 1.31161060541820 & 0.00838939458179566 \tabularnewline
13 & 1.32 & 1.31903583618962 & 0.000964163810384111 \tabularnewline
14 & 1.32 & 1.32136707984355 & -0.00136707984354878 \tabularnewline
15 & 1.32 & 1.32199814742907 & -0.00199814742907023 \tabularnewline
16 & 1.33 & 1.32207064143076 & 0.00792935856923993 \tabularnewline
17 & 1.33 & 1.3295105712402 & 0.000489428759800514 \tabularnewline
18 & 1.33 & 1.33181764055815 & -0.00181764055814893 \tabularnewline
19 & 1.34 & 1.33241409403866 & 0.00758590596133701 \tabularnewline
20 & 1.34 & 1.33999367353906 & 6.32646094178568e-06 \tabularnewline
21 & 1.34 & 1.34231431297440 & -0.00231431297439522 \tabularnewline
22 & 1.34 & 1.34288492151731 & -0.00288492151731257 \tabularnewline
23 & 1.34 & 1.34288534666746 & -0.0028853466674561 \tabularnewline
24 & 1.34 & 1.34271120186611 & -0.00271120186610796 \tabularnewline
25 & 1.34 & 1.34249413613976 & -0.00249413613976057 \tabularnewline
26 & 1.35 & 1.34227704225059 & 0.007722957749412 \tabularnewline
27 & 1.36 & 1.34961585694069 & 0.0103841430593148 \tabularnewline
28 & 1.36 & 1.35942841841798 & 0.000571581582015757 \tabularnewline
29 & 1.36 & 1.36246675865857 & -0.00246675865857293 \tabularnewline
30 & 1.37 & 1.36324786171512 & 0.00675213828487942 \tabularnewline
31 & 1.37 & 1.37083360648664 & -0.000833606486641436 \tabularnewline
32 & 1.37 & 1.37310540127911 & -0.00310540127911074 \tabularnewline
33 & 1.37 & 1.37361327578671 & -0.00361327578671133 \tabularnewline
34 & 1.37 & 1.37355050422318 & -0.00355050422318159 \tabularnewline
35 & 1.37 & 1.37331683815499 & -0.00331683815499084 \tabularnewline
36 & 1.37 & 1.37304497137257 & -0.00304497137257020 \tabularnewline
37 & 1.38 & 1.37277783135999 & 0.00722216864000713 \tabularnewline
38 & 1.38 & 1.38007107829046 & -7.10782904578267e-05 \tabularnewline
39 & 1.38 & 1.38229939048672 & -0.00229939048672101 \tabularnewline
40 & 1.39 & 1.38284263717688 & 0.0071573628231234 \tabularnewline
41 & 1.4 & 1.39038004503265 & 0.00961995496734902 \tabularnewline
42 & 1.4 & 1.40020724279332 & -0.000207242793318629 \tabularnewline
43 & 1.4 & 1.40320302249129 & -0.00320302249129223 \tabularnewline
44 & 1.4 & 1.40392662659663 & -0.00392662659662824 \tabularnewline
45 & 1.41 & 1.40391096768631 & 0.00608903231369462 \tabularnewline
46 & 1.42 & 1.41121275645589 & 0.0087872435441092 \tabularnewline
47 & 1.43 & 1.42091753083987 & 0.0090824691601279 \tabularnewline
48 & 1.43 & 1.43137573767979 & -0.0013757376797916 \tabularnewline
49 & 1.43 & 1.43449410448582 & -0.00449410448581755 \tabularnewline
50 & 1.44 & 1.43517725354243 & 0.00482274645757341 \tabularnewline
51 & 1.45 & 1.44261647740884 & 0.00738352259116426 \tabularnewline
52 & 1.45 & 1.45227853860998 & -0.00227853860998461 \tabularnewline
53 & 1.46 & 1.45509866050784 & 0.00490133949216065 \tabularnewline
54 & 1.46 & 1.46319680051637 & -0.0031968005163725 \tabularnewline
55 & 1.47 & 1.46548271257107 & 0.00451728742893054 \tabularnewline
56 & 1.47 & 1.47339412376743 & -0.00339412376742532 \tabularnewline
57 & 1.47 & 1.47561095616083 & -0.00561095616082552 \tabularnewline
58 & 1.48 & 1.47595067008162 & 0.00404932991838014 \tabularnewline
59 & 1.49 & 1.48323804738405 & 0.0067619526159457 \tabularnewline
60 & 1.49 & 1.49281608255782 & -0.00281608255782362 \tabularnewline
61 & 1.49 & 1.49557801479144 & -0.00557801479143771 \tabularnewline
62 & 1.5 & 1.49608658407814 & 0.00391341592185745 \tabularnewline
63 & 1.51 & 1.50341744210006 & 0.00658255789994211 \tabularnewline
64 & 1.51 & 1.51299795212982 & -0.00299795212982357 \tabularnewline
65 & 1.51 & 1.51574965704245 & -0.00574965704245223 \tabularnewline
66 & 1.52 & 1.51624472835394 & 0.00375527164606027 \tabularnewline
67 & 1.52 & 1.52356190246725 & -0.0035619024672473 \tabularnewline
68 & 1.52 & 1.52558669344984 & -0.00558669344983964 \tabularnewline
69 & 1.52 & 1.52586908521197 & -0.00586908521196827 \tabularnewline
70 & 1.53 & 1.52560103807966 & 0.0043989619203435 \tabularnewline
71 & 1.53 & 1.53272348562799 & -0.00272348562799318 \tabularnewline
72 & 1.53 & 1.53473930738579 & -0.00473930738578709 \tabularnewline
73 & 1.53 & 1.53507013561406 & -0.005070135614061 \tabularnewline
74 & 1.54 & 1.53486517238833 & 0.00513482761166628 \tabularnewline
75 & 1.54 & 1.54205137744268 & -0.00205137744268025 \tabularnewline
76 & 1.55 & 1.54412731195485 & 0.00587268804514696 \tabularnewline
77 & 1.55 & 1.55205631112614 & -0.00205631112613647 \tabularnewline
78 & 1.55 & 1.55435933143005 & -0.00435933143005185 \tabularnewline
79 & 1.56 & 1.55480102729135 & 0.00519897270864855 \tabularnewline
80 & 1.56 & 1.56218906168580 & -0.00218906168579602 \tabularnewline
81 & 1.58 & 1.56431846397204 & 0.0156815360279579 \tabularnewline
82 & 1.58 & 1.57979508981960 & 0.000204910180397588 \tabularnewline
83 & 1.58 & 1.58454516383136 & -0.0045451638313585 \tabularnewline
84 & 1.58 & 1.58572472634685 & -0.0057247263468525 \tabularnewline
85 & 1.58 & 1.58574003998015 & -0.00574003998014727 \tabularnewline
86 & 1.58 & 1.58539802934889 & -0.00539802934888645 \tabularnewline
87 & 1.59 & 1.58496729222481 & 0.00503270777518838 \tabularnewline
88 & 1.59 & 1.59207821544097 & -0.00207821544096998 \tabularnewline
89 & 1.6 & 1.59412948369701 & 0.00587051630299285 \tabularnewline
90 & 1.6 & 1.60205080087231 & -0.00205080087231280 \tabularnewline
91 & 1.6 & 1.60435180238658 & -0.00435180238657606 \tabularnewline
92 & 1.61 & 1.60479333501119 & 0.00520666498881384 \tabularnewline
93 & 1.62 & 1.61218178404944 & 0.00781821595056109 \tabularnewline
94 & 1.62 & 1.62185455756436 & -0.00185455756436070 \tabularnewline
95 & 1.63 & 1.62470356716721 & 0.00529643283278647 \tabularnewline
96 & 1.63 & 1.63283441390549 & -0.00283441390549433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36958&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]1.3[/C][C]1.29[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]1.3[/C][C]1.29754280472885[/C][C]0.00245719527115185[/C][/ROW]
[ROW][C]5[/C][C]1.3[/C][C]1.30000021917251[/C][C]-2.19172507698318e-07[/C][/ROW]
[ROW][C]6[/C][C]1.3[/C][C]1.30075246848991[/C][C]-0.000752468489908953[/C][/ROW]
[ROW][C]7[/C][C]1.31[/C][C]1.30093729759843[/C][C]0.0090627024015666[/C][/ROW]
[ROW][C]8[/C][C]1.31[/C][C]1.30848006934918[/C][C]0.00151993065081557[/C][/ROW]
[ROW][C]9[/C][C]1.31[/C][C]1.31088086291148[/C][C]-0.000880862911483815[/C][/ROW]
[ROW][C]10[/C][C]1.31[/C][C]1.31156258858657[/C][C]-0.00156258858657199[/C][/ROW]
[ROW][C]11[/C][C]1.31[/C][C]1.31167689777435[/C][C]-0.00167689777435487[/C][/ROW]
[ROW][C]12[/C][C]1.32[/C][C]1.31161060541820[/C][C]0.00838939458179566[/C][/ROW]
[ROW][C]13[/C][C]1.32[/C][C]1.31903583618962[/C][C]0.000964163810384111[/C][/ROW]
[ROW][C]14[/C][C]1.32[/C][C]1.32136707984355[/C][C]-0.00136707984354878[/C][/ROW]
[ROW][C]15[/C][C]1.32[/C][C]1.32199814742907[/C][C]-0.00199814742907023[/C][/ROW]
[ROW][C]16[/C][C]1.33[/C][C]1.32207064143076[/C][C]0.00792935856923993[/C][/ROW]
[ROW][C]17[/C][C]1.33[/C][C]1.3295105712402[/C][C]0.000489428759800514[/C][/ROW]
[ROW][C]18[/C][C]1.33[/C][C]1.33181764055815[/C][C]-0.00181764055814893[/C][/ROW]
[ROW][C]19[/C][C]1.34[/C][C]1.33241409403866[/C][C]0.00758590596133701[/C][/ROW]
[ROW][C]20[/C][C]1.34[/C][C]1.33999367353906[/C][C]6.32646094178568e-06[/C][/ROW]
[ROW][C]21[/C][C]1.34[/C][C]1.34231431297440[/C][C]-0.00231431297439522[/C][/ROW]
[ROW][C]22[/C][C]1.34[/C][C]1.34288492151731[/C][C]-0.00288492151731257[/C][/ROW]
[ROW][C]23[/C][C]1.34[/C][C]1.34288534666746[/C][C]-0.0028853466674561[/C][/ROW]
[ROW][C]24[/C][C]1.34[/C][C]1.34271120186611[/C][C]-0.00271120186610796[/C][/ROW]
[ROW][C]25[/C][C]1.34[/C][C]1.34249413613976[/C][C]-0.00249413613976057[/C][/ROW]
[ROW][C]26[/C][C]1.35[/C][C]1.34227704225059[/C][C]0.007722957749412[/C][/ROW]
[ROW][C]27[/C][C]1.36[/C][C]1.34961585694069[/C][C]0.0103841430593148[/C][/ROW]
[ROW][C]28[/C][C]1.36[/C][C]1.35942841841798[/C][C]0.000571581582015757[/C][/ROW]
[ROW][C]29[/C][C]1.36[/C][C]1.36246675865857[/C][C]-0.00246675865857293[/C][/ROW]
[ROW][C]30[/C][C]1.37[/C][C]1.36324786171512[/C][C]0.00675213828487942[/C][/ROW]
[ROW][C]31[/C][C]1.37[/C][C]1.37083360648664[/C][C]-0.000833606486641436[/C][/ROW]
[ROW][C]32[/C][C]1.37[/C][C]1.37310540127911[/C][C]-0.00310540127911074[/C][/ROW]
[ROW][C]33[/C][C]1.37[/C][C]1.37361327578671[/C][C]-0.00361327578671133[/C][/ROW]
[ROW][C]34[/C][C]1.37[/C][C]1.37355050422318[/C][C]-0.00355050422318159[/C][/ROW]
[ROW][C]35[/C][C]1.37[/C][C]1.37331683815499[/C][C]-0.00331683815499084[/C][/ROW]
[ROW][C]36[/C][C]1.37[/C][C]1.37304497137257[/C][C]-0.00304497137257020[/C][/ROW]
[ROW][C]37[/C][C]1.38[/C][C]1.37277783135999[/C][C]0.00722216864000713[/C][/ROW]
[ROW][C]38[/C][C]1.38[/C][C]1.38007107829046[/C][C]-7.10782904578267e-05[/C][/ROW]
[ROW][C]39[/C][C]1.38[/C][C]1.38229939048672[/C][C]-0.00229939048672101[/C][/ROW]
[ROW][C]40[/C][C]1.39[/C][C]1.38284263717688[/C][C]0.0071573628231234[/C][/ROW]
[ROW][C]41[/C][C]1.4[/C][C]1.39038004503265[/C][C]0.00961995496734902[/C][/ROW]
[ROW][C]42[/C][C]1.4[/C][C]1.40020724279332[/C][C]-0.000207242793318629[/C][/ROW]
[ROW][C]43[/C][C]1.4[/C][C]1.40320302249129[/C][C]-0.00320302249129223[/C][/ROW]
[ROW][C]44[/C][C]1.4[/C][C]1.40392662659663[/C][C]-0.00392662659662824[/C][/ROW]
[ROW][C]45[/C][C]1.41[/C][C]1.40391096768631[/C][C]0.00608903231369462[/C][/ROW]
[ROW][C]46[/C][C]1.42[/C][C]1.41121275645589[/C][C]0.0087872435441092[/C][/ROW]
[ROW][C]47[/C][C]1.43[/C][C]1.42091753083987[/C][C]0.0090824691601279[/C][/ROW]
[ROW][C]48[/C][C]1.43[/C][C]1.43137573767979[/C][C]-0.0013757376797916[/C][/ROW]
[ROW][C]49[/C][C]1.43[/C][C]1.43449410448582[/C][C]-0.00449410448581755[/C][/ROW]
[ROW][C]50[/C][C]1.44[/C][C]1.43517725354243[/C][C]0.00482274645757341[/C][/ROW]
[ROW][C]51[/C][C]1.45[/C][C]1.44261647740884[/C][C]0.00738352259116426[/C][/ROW]
[ROW][C]52[/C][C]1.45[/C][C]1.45227853860998[/C][C]-0.00227853860998461[/C][/ROW]
[ROW][C]53[/C][C]1.46[/C][C]1.45509866050784[/C][C]0.00490133949216065[/C][/ROW]
[ROW][C]54[/C][C]1.46[/C][C]1.46319680051637[/C][C]-0.0031968005163725[/C][/ROW]
[ROW][C]55[/C][C]1.47[/C][C]1.46548271257107[/C][C]0.00451728742893054[/C][/ROW]
[ROW][C]56[/C][C]1.47[/C][C]1.47339412376743[/C][C]-0.00339412376742532[/C][/ROW]
[ROW][C]57[/C][C]1.47[/C][C]1.47561095616083[/C][C]-0.00561095616082552[/C][/ROW]
[ROW][C]58[/C][C]1.48[/C][C]1.47595067008162[/C][C]0.00404932991838014[/C][/ROW]
[ROW][C]59[/C][C]1.49[/C][C]1.48323804738405[/C][C]0.0067619526159457[/C][/ROW]
[ROW][C]60[/C][C]1.49[/C][C]1.49281608255782[/C][C]-0.00281608255782362[/C][/ROW]
[ROW][C]61[/C][C]1.49[/C][C]1.49557801479144[/C][C]-0.00557801479143771[/C][/ROW]
[ROW][C]62[/C][C]1.5[/C][C]1.49608658407814[/C][C]0.00391341592185745[/C][/ROW]
[ROW][C]63[/C][C]1.51[/C][C]1.50341744210006[/C][C]0.00658255789994211[/C][/ROW]
[ROW][C]64[/C][C]1.51[/C][C]1.51299795212982[/C][C]-0.00299795212982357[/C][/ROW]
[ROW][C]65[/C][C]1.51[/C][C]1.51574965704245[/C][C]-0.00574965704245223[/C][/ROW]
[ROW][C]66[/C][C]1.52[/C][C]1.51624472835394[/C][C]0.00375527164606027[/C][/ROW]
[ROW][C]67[/C][C]1.52[/C][C]1.52356190246725[/C][C]-0.0035619024672473[/C][/ROW]
[ROW][C]68[/C][C]1.52[/C][C]1.52558669344984[/C][C]-0.00558669344983964[/C][/ROW]
[ROW][C]69[/C][C]1.52[/C][C]1.52586908521197[/C][C]-0.00586908521196827[/C][/ROW]
[ROW][C]70[/C][C]1.53[/C][C]1.52560103807966[/C][C]0.0043989619203435[/C][/ROW]
[ROW][C]71[/C][C]1.53[/C][C]1.53272348562799[/C][C]-0.00272348562799318[/C][/ROW]
[ROW][C]72[/C][C]1.53[/C][C]1.53473930738579[/C][C]-0.00473930738578709[/C][/ROW]
[ROW][C]73[/C][C]1.53[/C][C]1.53507013561406[/C][C]-0.005070135614061[/C][/ROW]
[ROW][C]74[/C][C]1.54[/C][C]1.53486517238833[/C][C]0.00513482761166628[/C][/ROW]
[ROW][C]75[/C][C]1.54[/C][C]1.54205137744268[/C][C]-0.00205137744268025[/C][/ROW]
[ROW][C]76[/C][C]1.55[/C][C]1.54412731195485[/C][C]0.00587268804514696[/C][/ROW]
[ROW][C]77[/C][C]1.55[/C][C]1.55205631112614[/C][C]-0.00205631112613647[/C][/ROW]
[ROW][C]78[/C][C]1.55[/C][C]1.55435933143005[/C][C]-0.00435933143005185[/C][/ROW]
[ROW][C]79[/C][C]1.56[/C][C]1.55480102729135[/C][C]0.00519897270864855[/C][/ROW]
[ROW][C]80[/C][C]1.56[/C][C]1.56218906168580[/C][C]-0.00218906168579602[/C][/ROW]
[ROW][C]81[/C][C]1.58[/C][C]1.56431846397204[/C][C]0.0156815360279579[/C][/ROW]
[ROW][C]82[/C][C]1.58[/C][C]1.57979508981960[/C][C]0.000204910180397588[/C][/ROW]
[ROW][C]83[/C][C]1.58[/C][C]1.58454516383136[/C][C]-0.0045451638313585[/C][/ROW]
[ROW][C]84[/C][C]1.58[/C][C]1.58572472634685[/C][C]-0.0057247263468525[/C][/ROW]
[ROW][C]85[/C][C]1.58[/C][C]1.58574003998015[/C][C]-0.00574003998014727[/C][/ROW]
[ROW][C]86[/C][C]1.58[/C][C]1.58539802934889[/C][C]-0.00539802934888645[/C][/ROW]
[ROW][C]87[/C][C]1.59[/C][C]1.58496729222481[/C][C]0.00503270777518838[/C][/ROW]
[ROW][C]88[/C][C]1.59[/C][C]1.59207821544097[/C][C]-0.00207821544096998[/C][/ROW]
[ROW][C]89[/C][C]1.6[/C][C]1.59412948369701[/C][C]0.00587051630299285[/C][/ROW]
[ROW][C]90[/C][C]1.6[/C][C]1.60205080087231[/C][C]-0.00205080087231280[/C][/ROW]
[ROW][C]91[/C][C]1.6[/C][C]1.60435180238658[/C][C]-0.00435180238657606[/C][/ROW]
[ROW][C]92[/C][C]1.61[/C][C]1.60479333501119[/C][C]0.00520666498881384[/C][/ROW]
[ROW][C]93[/C][C]1.62[/C][C]1.61218178404944[/C][C]0.00781821595056109[/C][/ROW]
[ROW][C]94[/C][C]1.62[/C][C]1.62185455756436[/C][C]-0.00185455756436070[/C][/ROW]
[ROW][C]95[/C][C]1.63[/C][C]1.62470356716721[/C][C]0.00529643283278647[/C][/ROW]
[ROW][C]96[/C][C]1.63[/C][C]1.63283441390549[/C][C]-0.00283441390549433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36958&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	1.3	1.29	0.01
4	1.3	1.29754280472885	0.00245719527115185
5	1.3	1.30000021917251	-2.19172507698318e-07
6	1.3	1.30075246848991	-0.000752468489908953
7	1.31	1.30093729759843	0.0090627024015666
8	1.31	1.30848006934918	0.00151993065081557
9	1.31	1.31088086291148	-0.000880862911483815
10	1.31	1.31156258858657	-0.00156258858657199
11	1.31	1.31167689777435	-0.00167689777435487
12	1.32	1.31161060541820	0.00838939458179566
13	1.32	1.31903583618962	0.000964163810384111
14	1.32	1.32136707984355	-0.00136707984354878
15	1.32	1.32199814742907	-0.00199814742907023
16	1.33	1.32207064143076	0.00792935856923993
17	1.33	1.3295105712402	0.000489428759800514
18	1.33	1.33181764055815	-0.00181764055814893
19	1.34	1.33241409403866	0.00758590596133701
20	1.34	1.33999367353906	6.32646094178568e-06
21	1.34	1.34231431297440	-0.00231431297439522
22	1.34	1.34288492151731	-0.00288492151731257
23	1.34	1.34288534666746	-0.0028853466674561
24	1.34	1.34271120186611	-0.00271120186610796
25	1.34	1.34249413613976	-0.00249413613976057
26	1.35	1.34227704225059	0.007722957749412
27	1.36	1.34961585694069	0.0103841430593148
28	1.36	1.35942841841798	0.000571581582015757
29	1.36	1.36246675865857	-0.00246675865857293
30	1.37	1.36324786171512	0.00675213828487942
31	1.37	1.37083360648664	-0.000833606486641436
32	1.37	1.37310540127911	-0.00310540127911074
33	1.37	1.37361327578671	-0.00361327578671133
34	1.37	1.37355050422318	-0.00355050422318159
35	1.37	1.37331683815499	-0.00331683815499084
36	1.37	1.37304497137257	-0.00304497137257020
37	1.38	1.37277783135999	0.00722216864000713
38	1.38	1.38007107829046	-7.10782904578267e-05
39	1.38	1.38229939048672	-0.00229939048672101
40	1.39	1.38284263717688	0.0071573628231234
41	1.4	1.39038004503265	0.00961995496734902
42	1.4	1.40020724279332	-0.000207242793318629
43	1.4	1.40320302249129	-0.00320302249129223
44	1.4	1.40392662659663	-0.00392662659662824
45	1.41	1.40391096768631	0.00608903231369462
46	1.42	1.41121275645589	0.0087872435441092
47	1.43	1.42091753083987	0.0090824691601279
48	1.43	1.43137573767979	-0.0013757376797916
49	1.43	1.43449410448582	-0.00449410448581755
50	1.44	1.43517725354243	0.00482274645757341
51	1.45	1.44261647740884	0.00738352259116426
52	1.45	1.45227853860998	-0.00227853860998461
53	1.46	1.45509866050784	0.00490133949216065
54	1.46	1.46319680051637	-0.0031968005163725
55	1.47	1.46548271257107	0.00451728742893054
56	1.47	1.47339412376743	-0.00339412376742532
57	1.47	1.47561095616083	-0.00561095616082552
58	1.48	1.47595067008162	0.00404932991838014
59	1.49	1.48323804738405	0.0067619526159457
60	1.49	1.49281608255782	-0.00281608255782362
61	1.49	1.49557801479144	-0.00557801479143771
62	1.5	1.49608658407814	0.00391341592185745
63	1.51	1.50341744210006	0.00658255789994211
64	1.51	1.51299795212982	-0.00299795212982357
65	1.51	1.51574965704245	-0.00574965704245223
66	1.52	1.51624472835394	0.00375527164606027
67	1.52	1.52356190246725	-0.0035619024672473
68	1.52	1.52558669344984	-0.00558669344983964
69	1.52	1.52586908521197	-0.00586908521196827
70	1.53	1.52560103807966	0.0043989619203435
71	1.53	1.53272348562799	-0.00272348562799318
72	1.53	1.53473930738579	-0.00473930738578709
73	1.53	1.53507013561406	-0.005070135614061
74	1.54	1.53486517238833	0.00513482761166628
75	1.54	1.54205137744268	-0.00205137744268025
76	1.55	1.54412731195485	0.00587268804514696
77	1.55	1.55205631112614	-0.00205631112613647
78	1.55	1.55435933143005	-0.00435933143005185
79	1.56	1.55480102729135	0.00519897270864855
80	1.56	1.56218906168580	-0.00218906168579602
81	1.58	1.56431846397204	0.0156815360279579
82	1.58	1.57979508981960	0.000204910180397588
83	1.58	1.58454516383136	-0.0045451638313585
84	1.58	1.58572472634685	-0.0057247263468525
85	1.58	1.58574003998015	-0.00574003998014727
86	1.58	1.58539802934889	-0.00539802934888645
87	1.59	1.58496729222481	0.00503270777518838
88	1.59	1.59207821544097	-0.00207821544096998
89	1.6	1.59412948369701	0.00587051630299285
90	1.6	1.60205080087231	-0.00205080087231280
91	1.6	1.60435180238658	-0.00435180238657606
92	1.61	1.60479333501119	0.00520666498881384
93	1.62	1.61218178404944	0.00781821595056109
94	1.62	1.62185455756436	-0.00185455756436070
95	1.63	1.62470356716721	0.00529643283278647
96	1.63	1.63283441390549	-0.00283441390549433

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	1.63515222628142	1.62530346020719	1.64500099235564
98	1.63943678310921	1.62710048498946	1.65177308122896
99	1.64372133993700	1.62900528179991	1.65843739807409
100	1.64800589676479	1.63095185705266	1.66505993647692
101	1.65229045359258	1.63290680864488	1.67167409854028
102	1.65657501042037	1.63485114428438	1.67829887655635
103	1.66085956724816	1.63677326396718	1.68494587052913
104	1.66514412407595	1.63866574876819	1.69162249938371
105	1.66942868090374	1.64052371334773	1.69833364845975
106	1.67371323773153	1.64234388792790	1.70508258753515
107	1.67799779455932	1.64412407374308	1.71187151537556
108	1.68228235138711	1.64586280383569	1.71870189893853

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1.63515222628142 & 1.62530346020719 & 1.64500099235564 \tabularnewline
98 & 1.63943678310921 & 1.62710048498946 & 1.65177308122896 \tabularnewline
99 & 1.64372133993700 & 1.62900528179991 & 1.65843739807409 \tabularnewline
100 & 1.64800589676479 & 1.63095185705266 & 1.66505993647692 \tabularnewline
101 & 1.65229045359258 & 1.63290680864488 & 1.67167409854028 \tabularnewline
102 & 1.65657501042037 & 1.63485114428438 & 1.67829887655635 \tabularnewline
103 & 1.66085956724816 & 1.63677326396718 & 1.68494587052913 \tabularnewline
104 & 1.66514412407595 & 1.63866574876819 & 1.69162249938371 \tabularnewline
105 & 1.66942868090374 & 1.64052371334773 & 1.69833364845975 \tabularnewline
106 & 1.67371323773153 & 1.64234388792790 & 1.70508258753515 \tabularnewline
107 & 1.67799779455932 & 1.64412407374308 & 1.71187151537556 \tabularnewline
108 & 1.68228235138711 & 1.64586280383569 & 1.71870189893853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36958&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]97[/C][C]1.63515222628142[/C][C]1.62530346020719[/C][C]1.64500099235564[/C][/ROW]
[ROW][C]98[/C][C]1.63943678310921[/C][C]1.62710048498946[/C][C]1.65177308122896[/C][/ROW]
[ROW][C]99[/C][C]1.64372133993700[/C][C]1.62900528179991[/C][C]1.65843739807409[/C][/ROW]
[ROW][C]100[/C][C]1.64800589676479[/C][C]1.63095185705266[/C][C]1.66505993647692[/C][/ROW]
[ROW][C]101[/C][C]1.65229045359258[/C][C]1.63290680864488[/C][C]1.67167409854028[/C][/ROW]
[ROW][C]102[/C][C]1.65657501042037[/C][C]1.63485114428438[/C][C]1.67829887655635[/C][/ROW]
[ROW][C]103[/C][C]1.66085956724816[/C][C]1.63677326396718[/C][C]1.68494587052913[/C][/ROW]
[ROW][C]104[/C][C]1.66514412407595[/C][C]1.63866574876819[/C][C]1.69162249938371[/C][/ROW]
[ROW][C]105[/C][C]1.66942868090374[/C][C]1.64052371334773[/C][C]1.69833364845975[/C][/ROW]
[ROW][C]106[/C][C]1.67371323773153[/C][C]1.64234388792790[/C][C]1.70508258753515[/C][/ROW]
[ROW][C]107[/C][C]1.67799779455932[/C][C]1.64412407374308[/C][C]1.71187151537556[/C][/ROW]
[ROW][C]108[/C][C]1.68228235138711[/C][C]1.64586280383569[/C][C]1.71870189893853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36958&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
97	1.63515222628142	1.62530346020719	1.64500099235564
98	1.63943678310921	1.62710048498946	1.65177308122896
99	1.64372133993700	1.62900528179991	1.65843739807409
100	1.64800589676479	1.63095185705266	1.66505993647692
101	1.65229045359258	1.63290680864488	1.67167409854028
102	1.65657501042037	1.63485114428438	1.67829887655635
103	1.66085956724816	1.63677326396718	1.68494587052913
104	1.66514412407595	1.63866574876819	1.69162249938371
105	1.66942868090374	1.64052371334773	1.69833364845975
106	1.67371323773153	1.64234388792790	1.70508258753515
107	1.67799779455932	1.64412407374308	1.71187151537556
108	1.68228235138711	1.64586280383569	1.71870189893853

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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