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, 16 Jan 2010 07:56:57 -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/2010/Jan/16/t1263653911oomg26k81ahrc82.htm/, Retrieved Fri, 03 May 2024 13:45:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72235, Retrieved Fri, 03 May 2024 13:45:16 +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

KDGP2W62

Estimated Impact

140

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

-       [Exponential Smoothing] [] [2010-01-16 14:56:57] [b64bb1ef3dba20c1e1ef56758a8a991a] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72235&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72235&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0963474453290963
beta	0.343443065425805
gamma	0.235170688807855

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0963474453290963 \tabularnewline
beta & 0.343443065425805 \tabularnewline
gamma & 0.235170688807855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72235&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]0.0963474453290963[/C][/ROW]
[ROW][C]beta[/C][C]0.343443065425805[/C][/ROW]
[ROW][C]gamma[/C][C]0.235170688807855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72235&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	0.0963474453290963
beta	0.343443065425805
gamma	0.235170688807855

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	101.8	101.277287425462	0.522712574538346
14	102.9	102.252139067473	0.647860932527124
15	119	118.518061280529	0.481938719470818
16	112.8	112.466915237244	0.333084762755533
17	120.9	120.404675682050	0.49532431794988
18	123.1	122.655194166115	0.444805833884828
19	121.9	117.395196072577	4.50480392742267
20	119.4	118.839009955928	0.560990044072028
21	110.9	116.433708685718	-5.5337086857179
22	116.8	113.178578254901	3.62142174509883
23	120.6	120.337964576642	0.262035423357545
24	143.3	145.590981100622	-2.29098110062182
25	106.4	104.913320222304	1.48667977769622
26	106.9	106.203322696405	0.696677303595152
27	125.6	123.228854121050	2.37114587895019
28	110.9	117.316165731205	-6.41616573120494
29	127	124.942719534639	2.05728046536133
30	124.3	127.481482263572	-3.18148226357204
31	121.3	122.520167586333	-1.22016758633264
32	124.4	122.333551608785	2.06644839121475
33	113.2	118.472074619633	-5.27207461963347
34	120.2	116.988041226851	3.21195877314879
35	122.6	123.352083403192	-0.75208340319216
36	143.3	148.268458737549	-4.96845873754907
37	106.5	107.073400127399	-0.573400127398642
38	105.9	107.676024966410	-1.77602496641025
39	114	124.512357215434	-10.5123572154341
40	121.6	114.672142810139	6.92785718986075
41	119.7	124.946482739439	-5.24648273943873
42	122.5	124.973556227158	-2.47355622715817
43	126.5	119.920465493495	6.57953450650491
44	118.2	120.795164474322	-2.59516447432230
45	115.5	114.524973804509	0.97502619549131
46	120.1	115.121695811683	4.97830418831667
47	115.3	120.451306748820	-5.15130674882023
48	146.5	142.944858182845	3.55514181715455
49	107.7	104.290950679179	3.40904932082121
50	106.3	104.995350736643	1.30464926335661
51	121.8	120.065442417401	1.73455758259944
52	115.8	115.619359551648	0.180640448352392
53	115.4	122.844863691546	-7.44486369154588
54	124.3	123.427368486299	0.872631513700611
55	121.7	120.924668764043	0.77533123595687
56	118.7	119.402754965216	-0.702754965215661
57	113.5	114.257885189853	-0.757885189853411
58	113.4	115.626155831230	-2.22615583122963
59	115.1	117.932674009311	-2.83267400931095
60	144.2	142.163025097462	2.03697490253779
61	100.9	103.687844119812	-2.78784411981181
62	103.2	103.046644107937	0.153355892062962
63	121.3	117.375343143529	3.92465685647123
64	111.9	112.625617659283	-0.725617659282904
65	117.3	117.637213121795	-0.337213121795472
66	124.2	120.473389731657	3.72661026834345
67	122	118.257337941230	3.74266205876971
68	119.6	116.817228224179	2.78277177582108
69	114.9	112.263465188583	2.63653481141705
70	112.2	113.92404484476	-1.72404484475999
71	115.3	116.440135139821	-1.14013513982114
72	143	142.163290190717	0.836709809283263
73	104	102.998584803698	1.00141519630225
74	105.3	103.777631362056	1.52236863794367
75	124.3	119.706660516196	4.59333948380412
76	114.1	114.493415203007	-0.393415203007493
77	124.8	120.294008143440	4.50599185656037
78	131.9	125.327666993841	6.57233300615901
79	125.8	124.137266206681	1.66273379331872
80	125.2	122.96485063182	2.23514936818000
81	119.8	118.800987089810	0.999012910189592
82	116.2	120.045641988447	-3.84564198844703
83	120.2	123.226948746746	-3.02694874674629
84	148.6	151.385830782402	-2.7858307824018
85	109.4	109.894663681849	-0.494663681848593
86	109.6	111.022121009392	-1.42212100939206
87	135.2	128.629941140805	6.5700588591946
88	115.2	122.398097210631	-7.19809721063108
89	129.1	129.104716185616	-0.00471618561613241
90	138.8	134.364285581255	4.43571441874542
91	126	131.598390430252	-5.59839043025167
92	130.7	129.39422936014	1.30577063985996
93	120.5	124.253997514669	-3.75399751466911
94	126.5	123.459716653618	3.04028334638184
95	128	127.299860757428	0.700139242571694
96	151.7	156.800869115537	-5.10086911553734
97	114.8	113.774958224513	1.02504177548667
98	118.9	114.705292845492	4.19470715450844
99	131.5	135.345341936157	-3.84534193615750
100	124.8	124.532732914897	0.267267085102603
101	137	133.739601269251	3.2603987307493
102	137.1	140.527534084171	-3.42753408417053
103	137	134.473150154057	2.52684984594291
104	131.3	134.56431364795	-3.26431364794996
105	126	127.594985554761	-1.59498555476145
106	129.7	128.467604706045	1.23239529395485
107	125.1	131.654687024155	-6.55468702415473
108	157.8	159.60355805447	-1.80355805446990

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.8 & 101.277287425462 & 0.522712574538346 \tabularnewline
14 & 102.9 & 102.252139067473 & 0.647860932527124 \tabularnewline
15 & 119 & 118.518061280529 & 0.481938719470818 \tabularnewline
16 & 112.8 & 112.466915237244 & 0.333084762755533 \tabularnewline
17 & 120.9 & 120.404675682050 & 0.49532431794988 \tabularnewline
18 & 123.1 & 122.655194166115 & 0.444805833884828 \tabularnewline
19 & 121.9 & 117.395196072577 & 4.50480392742267 \tabularnewline
20 & 119.4 & 118.839009955928 & 0.560990044072028 \tabularnewline
21 & 110.9 & 116.433708685718 & -5.5337086857179 \tabularnewline
22 & 116.8 & 113.178578254901 & 3.62142174509883 \tabularnewline
23 & 120.6 & 120.337964576642 & 0.262035423357545 \tabularnewline
24 & 143.3 & 145.590981100622 & -2.29098110062182 \tabularnewline
25 & 106.4 & 104.913320222304 & 1.48667977769622 \tabularnewline
26 & 106.9 & 106.203322696405 & 0.696677303595152 \tabularnewline
27 & 125.6 & 123.228854121050 & 2.37114587895019 \tabularnewline
28 & 110.9 & 117.316165731205 & -6.41616573120494 \tabularnewline
29 & 127 & 124.942719534639 & 2.05728046536133 \tabularnewline
30 & 124.3 & 127.481482263572 & -3.18148226357204 \tabularnewline
31 & 121.3 & 122.520167586333 & -1.22016758633264 \tabularnewline
32 & 124.4 & 122.333551608785 & 2.06644839121475 \tabularnewline
33 & 113.2 & 118.472074619633 & -5.27207461963347 \tabularnewline
34 & 120.2 & 116.988041226851 & 3.21195877314879 \tabularnewline
35 & 122.6 & 123.352083403192 & -0.75208340319216 \tabularnewline
36 & 143.3 & 148.268458737549 & -4.96845873754907 \tabularnewline
37 & 106.5 & 107.073400127399 & -0.573400127398642 \tabularnewline
38 & 105.9 & 107.676024966410 & -1.77602496641025 \tabularnewline
39 & 114 & 124.512357215434 & -10.5123572154341 \tabularnewline
40 & 121.6 & 114.672142810139 & 6.92785718986075 \tabularnewline
41 & 119.7 & 124.946482739439 & -5.24648273943873 \tabularnewline
42 & 122.5 & 124.973556227158 & -2.47355622715817 \tabularnewline
43 & 126.5 & 119.920465493495 & 6.57953450650491 \tabularnewline
44 & 118.2 & 120.795164474322 & -2.59516447432230 \tabularnewline
45 & 115.5 & 114.524973804509 & 0.97502619549131 \tabularnewline
46 & 120.1 & 115.121695811683 & 4.97830418831667 \tabularnewline
47 & 115.3 & 120.451306748820 & -5.15130674882023 \tabularnewline
48 & 146.5 & 142.944858182845 & 3.55514181715455 \tabularnewline
49 & 107.7 & 104.290950679179 & 3.40904932082121 \tabularnewline
50 & 106.3 & 104.995350736643 & 1.30464926335661 \tabularnewline
51 & 121.8 & 120.065442417401 & 1.73455758259944 \tabularnewline
52 & 115.8 & 115.619359551648 & 0.180640448352392 \tabularnewline
53 & 115.4 & 122.844863691546 & -7.44486369154588 \tabularnewline
54 & 124.3 & 123.427368486299 & 0.872631513700611 \tabularnewline
55 & 121.7 & 120.924668764043 & 0.77533123595687 \tabularnewline
56 & 118.7 & 119.402754965216 & -0.702754965215661 \tabularnewline
57 & 113.5 & 114.257885189853 & -0.757885189853411 \tabularnewline
58 & 113.4 & 115.626155831230 & -2.22615583122963 \tabularnewline
59 & 115.1 & 117.932674009311 & -2.83267400931095 \tabularnewline
60 & 144.2 & 142.163025097462 & 2.03697490253779 \tabularnewline
61 & 100.9 & 103.687844119812 & -2.78784411981181 \tabularnewline
62 & 103.2 & 103.046644107937 & 0.153355892062962 \tabularnewline
63 & 121.3 & 117.375343143529 & 3.92465685647123 \tabularnewline
64 & 111.9 & 112.625617659283 & -0.725617659282904 \tabularnewline
65 & 117.3 & 117.637213121795 & -0.337213121795472 \tabularnewline
66 & 124.2 & 120.473389731657 & 3.72661026834345 \tabularnewline
67 & 122 & 118.257337941230 & 3.74266205876971 \tabularnewline
68 & 119.6 & 116.817228224179 & 2.78277177582108 \tabularnewline
69 & 114.9 & 112.263465188583 & 2.63653481141705 \tabularnewline
70 & 112.2 & 113.92404484476 & -1.72404484475999 \tabularnewline
71 & 115.3 & 116.440135139821 & -1.14013513982114 \tabularnewline
72 & 143 & 142.163290190717 & 0.836709809283263 \tabularnewline
73 & 104 & 102.998584803698 & 1.00141519630225 \tabularnewline
74 & 105.3 & 103.777631362056 & 1.52236863794367 \tabularnewline
75 & 124.3 & 119.706660516196 & 4.59333948380412 \tabularnewline
76 & 114.1 & 114.493415203007 & -0.393415203007493 \tabularnewline
77 & 124.8 & 120.294008143440 & 4.50599185656037 \tabularnewline
78 & 131.9 & 125.327666993841 & 6.57233300615901 \tabularnewline
79 & 125.8 & 124.137266206681 & 1.66273379331872 \tabularnewline
80 & 125.2 & 122.96485063182 & 2.23514936818000 \tabularnewline
81 & 119.8 & 118.800987089810 & 0.999012910189592 \tabularnewline
82 & 116.2 & 120.045641988447 & -3.84564198844703 \tabularnewline
83 & 120.2 & 123.226948746746 & -3.02694874674629 \tabularnewline
84 & 148.6 & 151.385830782402 & -2.7858307824018 \tabularnewline
85 & 109.4 & 109.894663681849 & -0.494663681848593 \tabularnewline
86 & 109.6 & 111.022121009392 & -1.42212100939206 \tabularnewline
87 & 135.2 & 128.629941140805 & 6.5700588591946 \tabularnewline
88 & 115.2 & 122.398097210631 & -7.19809721063108 \tabularnewline
89 & 129.1 & 129.104716185616 & -0.00471618561613241 \tabularnewline
90 & 138.8 & 134.364285581255 & 4.43571441874542 \tabularnewline
91 & 126 & 131.598390430252 & -5.59839043025167 \tabularnewline
92 & 130.7 & 129.39422936014 & 1.30577063985996 \tabularnewline
93 & 120.5 & 124.253997514669 & -3.75399751466911 \tabularnewline
94 & 126.5 & 123.459716653618 & 3.04028334638184 \tabularnewline
95 & 128 & 127.299860757428 & 0.700139242571694 \tabularnewline
96 & 151.7 & 156.800869115537 & -5.10086911553734 \tabularnewline
97 & 114.8 & 113.774958224513 & 1.02504177548667 \tabularnewline
98 & 118.9 & 114.705292845492 & 4.19470715450844 \tabularnewline
99 & 131.5 & 135.345341936157 & -3.84534193615750 \tabularnewline
100 & 124.8 & 124.532732914897 & 0.267267085102603 \tabularnewline
101 & 137 & 133.739601269251 & 3.2603987307493 \tabularnewline
102 & 137.1 & 140.527534084171 & -3.42753408417053 \tabularnewline
103 & 137 & 134.473150154057 & 2.52684984594291 \tabularnewline
104 & 131.3 & 134.56431364795 & -3.26431364794996 \tabularnewline
105 & 126 & 127.594985554761 & -1.59498555476145 \tabularnewline
106 & 129.7 & 128.467604706045 & 1.23239529395485 \tabularnewline
107 & 125.1 & 131.654687024155 & -6.55468702415473 \tabularnewline
108 & 157.8 & 159.60355805447 & -1.80355805446990 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72235&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]101.8[/C][C]101.277287425462[/C][C]0.522712574538346[/C][/ROW]
[ROW][C]14[/C][C]102.9[/C][C]102.252139067473[/C][C]0.647860932527124[/C][/ROW]
[ROW][C]15[/C][C]119[/C][C]118.518061280529[/C][C]0.481938719470818[/C][/ROW]
[ROW][C]16[/C][C]112.8[/C][C]112.466915237244[/C][C]0.333084762755533[/C][/ROW]
[ROW][C]17[/C][C]120.9[/C][C]120.404675682050[/C][C]0.49532431794988[/C][/ROW]
[ROW][C]18[/C][C]123.1[/C][C]122.655194166115[/C][C]0.444805833884828[/C][/ROW]
[ROW][C]19[/C][C]121.9[/C][C]117.395196072577[/C][C]4.50480392742267[/C][/ROW]
[ROW][C]20[/C][C]119.4[/C][C]118.839009955928[/C][C]0.560990044072028[/C][/ROW]
[ROW][C]21[/C][C]110.9[/C][C]116.433708685718[/C][C]-5.5337086857179[/C][/ROW]
[ROW][C]22[/C][C]116.8[/C][C]113.178578254901[/C][C]3.62142174509883[/C][/ROW]
[ROW][C]23[/C][C]120.6[/C][C]120.337964576642[/C][C]0.262035423357545[/C][/ROW]
[ROW][C]24[/C][C]143.3[/C][C]145.590981100622[/C][C]-2.29098110062182[/C][/ROW]
[ROW][C]25[/C][C]106.4[/C][C]104.913320222304[/C][C]1.48667977769622[/C][/ROW]
[ROW][C]26[/C][C]106.9[/C][C]106.203322696405[/C][C]0.696677303595152[/C][/ROW]
[ROW][C]27[/C][C]125.6[/C][C]123.228854121050[/C][C]2.37114587895019[/C][/ROW]
[ROW][C]28[/C][C]110.9[/C][C]117.316165731205[/C][C]-6.41616573120494[/C][/ROW]
[ROW][C]29[/C][C]127[/C][C]124.942719534639[/C][C]2.05728046536133[/C][/ROW]
[ROW][C]30[/C][C]124.3[/C][C]127.481482263572[/C][C]-3.18148226357204[/C][/ROW]
[ROW][C]31[/C][C]121.3[/C][C]122.520167586333[/C][C]-1.22016758633264[/C][/ROW]
[ROW][C]32[/C][C]124.4[/C][C]122.333551608785[/C][C]2.06644839121475[/C][/ROW]
[ROW][C]33[/C][C]113.2[/C][C]118.472074619633[/C][C]-5.27207461963347[/C][/ROW]
[ROW][C]34[/C][C]120.2[/C][C]116.988041226851[/C][C]3.21195877314879[/C][/ROW]
[ROW][C]35[/C][C]122.6[/C][C]123.352083403192[/C][C]-0.75208340319216[/C][/ROW]
[ROW][C]36[/C][C]143.3[/C][C]148.268458737549[/C][C]-4.96845873754907[/C][/ROW]
[ROW][C]37[/C][C]106.5[/C][C]107.073400127399[/C][C]-0.573400127398642[/C][/ROW]
[ROW][C]38[/C][C]105.9[/C][C]107.676024966410[/C][C]-1.77602496641025[/C][/ROW]
[ROW][C]39[/C][C]114[/C][C]124.512357215434[/C][C]-10.5123572154341[/C][/ROW]
[ROW][C]40[/C][C]121.6[/C][C]114.672142810139[/C][C]6.92785718986075[/C][/ROW]
[ROW][C]41[/C][C]119.7[/C][C]124.946482739439[/C][C]-5.24648273943873[/C][/ROW]
[ROW][C]42[/C][C]122.5[/C][C]124.973556227158[/C][C]-2.47355622715817[/C][/ROW]
[ROW][C]43[/C][C]126.5[/C][C]119.920465493495[/C][C]6.57953450650491[/C][/ROW]
[ROW][C]44[/C][C]118.2[/C][C]120.795164474322[/C][C]-2.59516447432230[/C][/ROW]
[ROW][C]45[/C][C]115.5[/C][C]114.524973804509[/C][C]0.97502619549131[/C][/ROW]
[ROW][C]46[/C][C]120.1[/C][C]115.121695811683[/C][C]4.97830418831667[/C][/ROW]
[ROW][C]47[/C][C]115.3[/C][C]120.451306748820[/C][C]-5.15130674882023[/C][/ROW]
[ROW][C]48[/C][C]146.5[/C][C]142.944858182845[/C][C]3.55514181715455[/C][/ROW]
[ROW][C]49[/C][C]107.7[/C][C]104.290950679179[/C][C]3.40904932082121[/C][/ROW]
[ROW][C]50[/C][C]106.3[/C][C]104.995350736643[/C][C]1.30464926335661[/C][/ROW]
[ROW][C]51[/C][C]121.8[/C][C]120.065442417401[/C][C]1.73455758259944[/C][/ROW]
[ROW][C]52[/C][C]115.8[/C][C]115.619359551648[/C][C]0.180640448352392[/C][/ROW]
[ROW][C]53[/C][C]115.4[/C][C]122.844863691546[/C][C]-7.44486369154588[/C][/ROW]
[ROW][C]54[/C][C]124.3[/C][C]123.427368486299[/C][C]0.872631513700611[/C][/ROW]
[ROW][C]55[/C][C]121.7[/C][C]120.924668764043[/C][C]0.77533123595687[/C][/ROW]
[ROW][C]56[/C][C]118.7[/C][C]119.402754965216[/C][C]-0.702754965215661[/C][/ROW]
[ROW][C]57[/C][C]113.5[/C][C]114.257885189853[/C][C]-0.757885189853411[/C][/ROW]
[ROW][C]58[/C][C]113.4[/C][C]115.626155831230[/C][C]-2.22615583122963[/C][/ROW]
[ROW][C]59[/C][C]115.1[/C][C]117.932674009311[/C][C]-2.83267400931095[/C][/ROW]
[ROW][C]60[/C][C]144.2[/C][C]142.163025097462[/C][C]2.03697490253779[/C][/ROW]
[ROW][C]61[/C][C]100.9[/C][C]103.687844119812[/C][C]-2.78784411981181[/C][/ROW]
[ROW][C]62[/C][C]103.2[/C][C]103.046644107937[/C][C]0.153355892062962[/C][/ROW]
[ROW][C]63[/C][C]121.3[/C][C]117.375343143529[/C][C]3.92465685647123[/C][/ROW]
[ROW][C]64[/C][C]111.9[/C][C]112.625617659283[/C][C]-0.725617659282904[/C][/ROW]
[ROW][C]65[/C][C]117.3[/C][C]117.637213121795[/C][C]-0.337213121795472[/C][/ROW]
[ROW][C]66[/C][C]124.2[/C][C]120.473389731657[/C][C]3.72661026834345[/C][/ROW]
[ROW][C]67[/C][C]122[/C][C]118.257337941230[/C][C]3.74266205876971[/C][/ROW]
[ROW][C]68[/C][C]119.6[/C][C]116.817228224179[/C][C]2.78277177582108[/C][/ROW]
[ROW][C]69[/C][C]114.9[/C][C]112.263465188583[/C][C]2.63653481141705[/C][/ROW]
[ROW][C]70[/C][C]112.2[/C][C]113.92404484476[/C][C]-1.72404484475999[/C][/ROW]
[ROW][C]71[/C][C]115.3[/C][C]116.440135139821[/C][C]-1.14013513982114[/C][/ROW]
[ROW][C]72[/C][C]143[/C][C]142.163290190717[/C][C]0.836709809283263[/C][/ROW]
[ROW][C]73[/C][C]104[/C][C]102.998584803698[/C][C]1.00141519630225[/C][/ROW]
[ROW][C]74[/C][C]105.3[/C][C]103.777631362056[/C][C]1.52236863794367[/C][/ROW]
[ROW][C]75[/C][C]124.3[/C][C]119.706660516196[/C][C]4.59333948380412[/C][/ROW]
[ROW][C]76[/C][C]114.1[/C][C]114.493415203007[/C][C]-0.393415203007493[/C][/ROW]
[ROW][C]77[/C][C]124.8[/C][C]120.294008143440[/C][C]4.50599185656037[/C][/ROW]
[ROW][C]78[/C][C]131.9[/C][C]125.327666993841[/C][C]6.57233300615901[/C][/ROW]
[ROW][C]79[/C][C]125.8[/C][C]124.137266206681[/C][C]1.66273379331872[/C][/ROW]
[ROW][C]80[/C][C]125.2[/C][C]122.96485063182[/C][C]2.23514936818000[/C][/ROW]
[ROW][C]81[/C][C]119.8[/C][C]118.800987089810[/C][C]0.999012910189592[/C][/ROW]
[ROW][C]82[/C][C]116.2[/C][C]120.045641988447[/C][C]-3.84564198844703[/C][/ROW]
[ROW][C]83[/C][C]120.2[/C][C]123.226948746746[/C][C]-3.02694874674629[/C][/ROW]
[ROW][C]84[/C][C]148.6[/C][C]151.385830782402[/C][C]-2.7858307824018[/C][/ROW]
[ROW][C]85[/C][C]109.4[/C][C]109.894663681849[/C][C]-0.494663681848593[/C][/ROW]
[ROW][C]86[/C][C]109.6[/C][C]111.022121009392[/C][C]-1.42212100939206[/C][/ROW]
[ROW][C]87[/C][C]135.2[/C][C]128.629941140805[/C][C]6.5700588591946[/C][/ROW]
[ROW][C]88[/C][C]115.2[/C][C]122.398097210631[/C][C]-7.19809721063108[/C][/ROW]
[ROW][C]89[/C][C]129.1[/C][C]129.104716185616[/C][C]-0.00471618561613241[/C][/ROW]
[ROW][C]90[/C][C]138.8[/C][C]134.364285581255[/C][C]4.43571441874542[/C][/ROW]
[ROW][C]91[/C][C]126[/C][C]131.598390430252[/C][C]-5.59839043025167[/C][/ROW]
[ROW][C]92[/C][C]130.7[/C][C]129.39422936014[/C][C]1.30577063985996[/C][/ROW]
[ROW][C]93[/C][C]120.5[/C][C]124.253997514669[/C][C]-3.75399751466911[/C][/ROW]
[ROW][C]94[/C][C]126.5[/C][C]123.459716653618[/C][C]3.04028334638184[/C][/ROW]
[ROW][C]95[/C][C]128[/C][C]127.299860757428[/C][C]0.700139242571694[/C][/ROW]
[ROW][C]96[/C][C]151.7[/C][C]156.800869115537[/C][C]-5.10086911553734[/C][/ROW]
[ROW][C]97[/C][C]114.8[/C][C]113.774958224513[/C][C]1.02504177548667[/C][/ROW]
[ROW][C]98[/C][C]118.9[/C][C]114.705292845492[/C][C]4.19470715450844[/C][/ROW]
[ROW][C]99[/C][C]131.5[/C][C]135.345341936157[/C][C]-3.84534193615750[/C][/ROW]
[ROW][C]100[/C][C]124.8[/C][C]124.532732914897[/C][C]0.267267085102603[/C][/ROW]
[ROW][C]101[/C][C]137[/C][C]133.739601269251[/C][C]3.2603987307493[/C][/ROW]
[ROW][C]102[/C][C]137.1[/C][C]140.527534084171[/C][C]-3.42753408417053[/C][/ROW]
[ROW][C]103[/C][C]137[/C][C]134.473150154057[/C][C]2.52684984594291[/C][/ROW]
[ROW][C]104[/C][C]131.3[/C][C]134.56431364795[/C][C]-3.26431364794996[/C][/ROW]
[ROW][C]105[/C][C]126[/C][C]127.594985554761[/C][C]-1.59498555476145[/C][/ROW]
[ROW][C]106[/C][C]129.7[/C][C]128.467604706045[/C][C]1.23239529395485[/C][/ROW]
[ROW][C]107[/C][C]125.1[/C][C]131.654687024155[/C][C]-6.55468702415473[/C][/ROW]
[ROW][C]108[/C][C]157.8[/C][C]159.60355805447[/C][C]-1.80355805446990[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72235&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72235&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	101.8	101.277287425462	0.522712574538346
14	102.9	102.252139067473	0.647860932527124
15	119	118.518061280529	0.481938719470818
16	112.8	112.466915237244	0.333084762755533
17	120.9	120.404675682050	0.49532431794988
18	123.1	122.655194166115	0.444805833884828
19	121.9	117.395196072577	4.50480392742267
20	119.4	118.839009955928	0.560990044072028
21	110.9	116.433708685718	-5.5337086857179
22	116.8	113.178578254901	3.62142174509883
23	120.6	120.337964576642	0.262035423357545
24	143.3	145.590981100622	-2.29098110062182
25	106.4	104.913320222304	1.48667977769622
26	106.9	106.203322696405	0.696677303595152
27	125.6	123.228854121050	2.37114587895019
28	110.9	117.316165731205	-6.41616573120494
29	127	124.942719534639	2.05728046536133
30	124.3	127.481482263572	-3.18148226357204
31	121.3	122.520167586333	-1.22016758633264
32	124.4	122.333551608785	2.06644839121475
33	113.2	118.472074619633	-5.27207461963347
34	120.2	116.988041226851	3.21195877314879
35	122.6	123.352083403192	-0.75208340319216
36	143.3	148.268458737549	-4.96845873754907
37	106.5	107.073400127399	-0.573400127398642
38	105.9	107.676024966410	-1.77602496641025
39	114	124.512357215434	-10.5123572154341
40	121.6	114.672142810139	6.92785718986075
41	119.7	124.946482739439	-5.24648273943873
42	122.5	124.973556227158	-2.47355622715817
43	126.5	119.920465493495	6.57953450650491
44	118.2	120.795164474322	-2.59516447432230
45	115.5	114.524973804509	0.97502619549131
46	120.1	115.121695811683	4.97830418831667
47	115.3	120.451306748820	-5.15130674882023
48	146.5	142.944858182845	3.55514181715455
49	107.7	104.290950679179	3.40904932082121
50	106.3	104.995350736643	1.30464926335661
51	121.8	120.065442417401	1.73455758259944
52	115.8	115.619359551648	0.180640448352392
53	115.4	122.844863691546	-7.44486369154588
54	124.3	123.427368486299	0.872631513700611
55	121.7	120.924668764043	0.77533123595687
56	118.7	119.402754965216	-0.702754965215661
57	113.5	114.257885189853	-0.757885189853411
58	113.4	115.626155831230	-2.22615583122963
59	115.1	117.932674009311	-2.83267400931095
60	144.2	142.163025097462	2.03697490253779
61	100.9	103.687844119812	-2.78784411981181
62	103.2	103.046644107937	0.153355892062962
63	121.3	117.375343143529	3.92465685647123
64	111.9	112.625617659283	-0.725617659282904
65	117.3	117.637213121795	-0.337213121795472
66	124.2	120.473389731657	3.72661026834345
67	122	118.257337941230	3.74266205876971
68	119.6	116.817228224179	2.78277177582108
69	114.9	112.263465188583	2.63653481141705
70	112.2	113.92404484476	-1.72404484475999
71	115.3	116.440135139821	-1.14013513982114
72	143	142.163290190717	0.836709809283263
73	104	102.998584803698	1.00141519630225
74	105.3	103.777631362056	1.52236863794367
75	124.3	119.706660516196	4.59333948380412
76	114.1	114.493415203007	-0.393415203007493
77	124.8	120.294008143440	4.50599185656037
78	131.9	125.327666993841	6.57233300615901
79	125.8	124.137266206681	1.66273379331872
80	125.2	122.96485063182	2.23514936818000
81	119.8	118.800987089810	0.999012910189592
82	116.2	120.045641988447	-3.84564198844703
83	120.2	123.226948746746	-3.02694874674629
84	148.6	151.385830782402	-2.7858307824018
85	109.4	109.894663681849	-0.494663681848593
86	109.6	111.022121009392	-1.42212100939206
87	135.2	128.629941140805	6.5700588591946
88	115.2	122.398097210631	-7.19809721063108
89	129.1	129.104716185616	-0.00471618561613241
90	138.8	134.364285581255	4.43571441874542
91	126	131.598390430252	-5.59839043025167
92	130.7	129.39422936014	1.30577063985996
93	120.5	124.253997514669	-3.75399751466911
94	126.5	123.459716653618	3.04028334638184
95	128	127.299860757428	0.700139242571694
96	151.7	156.800869115537	-5.10086911553734
97	114.8	113.774958224513	1.02504177548667
98	118.9	114.705292845492	4.19470715450844
99	131.5	135.345341936157	-3.84534193615750
100	124.8	124.532732914897	0.267267085102603
101	137	133.739601269251	3.2603987307493
102	137.1	140.527534084171	-3.42753408417053
103	137	134.473150154057	2.52684984594291
104	131.3	134.56431364795	-3.26431364794996
105	126	127.594985554761	-1.59498555476145
106	129.7	128.467604706045	1.23239529395485
107	125.1	131.654687024155	-6.55468702415473
108	157.8	159.60355805447	-1.80355805446990

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	116.875154931201	114.788675712536	118.961634149867
110	118.172143695526	115.906233084753	120.438054306299
111	136.601904778109	133.952754809723	139.251054746495
112	126.569537428808	123.665702292737	129.473372564879
113	136.218444136065	132.757197211304	139.679691060827
114	140.881517332329	136.82945040822	144.933584256437
115	136.059447407979	131.574283642735	140.544611173223
116	134.271964059335	129.261572316064	139.282355802606
117	127.665606808959	122.282097997682	133.049115620235
118	129.078457649881	123.020688463827	135.136226835936
119	130.224076872719	123.456852988829	136.991300756609
120	159.889159926174	116.120048171011	203.658271681337

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 116.875154931201 & 114.788675712536 & 118.961634149867 \tabularnewline
110 & 118.172143695526 & 115.906233084753 & 120.438054306299 \tabularnewline
111 & 136.601904778109 & 133.952754809723 & 139.251054746495 \tabularnewline
112 & 126.569537428808 & 123.665702292737 & 129.473372564879 \tabularnewline
113 & 136.218444136065 & 132.757197211304 & 139.679691060827 \tabularnewline
114 & 140.881517332329 & 136.82945040822 & 144.933584256437 \tabularnewline
115 & 136.059447407979 & 131.574283642735 & 140.544611173223 \tabularnewline
116 & 134.271964059335 & 129.261572316064 & 139.282355802606 \tabularnewline
117 & 127.665606808959 & 122.282097997682 & 133.049115620235 \tabularnewline
118 & 129.078457649881 & 123.020688463827 & 135.136226835936 \tabularnewline
119 & 130.224076872719 & 123.456852988829 & 136.991300756609 \tabularnewline
120 & 159.889159926174 & 116.120048171011 & 203.658271681337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72235&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]109[/C][C]116.875154931201[/C][C]114.788675712536[/C][C]118.961634149867[/C][/ROW]
[ROW][C]110[/C][C]118.172143695526[/C][C]115.906233084753[/C][C]120.438054306299[/C][/ROW]
[ROW][C]111[/C][C]136.601904778109[/C][C]133.952754809723[/C][C]139.251054746495[/C][/ROW]
[ROW][C]112[/C][C]126.569537428808[/C][C]123.665702292737[/C][C]129.473372564879[/C][/ROW]
[ROW][C]113[/C][C]136.218444136065[/C][C]132.757197211304[/C][C]139.679691060827[/C][/ROW]
[ROW][C]114[/C][C]140.881517332329[/C][C]136.82945040822[/C][C]144.933584256437[/C][/ROW]
[ROW][C]115[/C][C]136.059447407979[/C][C]131.574283642735[/C][C]140.544611173223[/C][/ROW]
[ROW][C]116[/C][C]134.271964059335[/C][C]129.261572316064[/C][C]139.282355802606[/C][/ROW]
[ROW][C]117[/C][C]127.665606808959[/C][C]122.282097997682[/C][C]133.049115620235[/C][/ROW]
[ROW][C]118[/C][C]129.078457649881[/C][C]123.020688463827[/C][C]135.136226835936[/C][/ROW]
[ROW][C]119[/C][C]130.224076872719[/C][C]123.456852988829[/C][C]136.991300756609[/C][/ROW]
[ROW][C]120[/C][C]159.889159926174[/C][C]116.120048171011[/C][C]203.658271681337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72235&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72235&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
109	116.875154931201	114.788675712536	118.961634149867
110	118.172143695526	115.906233084753	120.438054306299
111	136.601904778109	133.952754809723	139.251054746495
112	126.569537428808	123.665702292737	129.473372564879
113	136.218444136065	132.757197211304	139.679691060827
114	140.881517332329	136.82945040822	144.933584256437
115	136.059447407979	131.574283642735	140.544611173223
116	134.271964059335	129.261572316064	139.282355802606
117	127.665606808959	122.282097997682	133.049115620235
118	129.078457649881	123.020688463827	135.136226835936
119	130.224076872719	123.456852988829	136.991300756609
120	159.889159926174	116.120048171011	203.658271681337

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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