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, 29 Apr 2017 13:37:55 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/29/t1493470054vqs1np4rcl9dja4.htm/, Retrieved Mon, 13 May 2024 07:51:26 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 13 May 2024 07:51:26 +0200

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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	'Gertrude Mary Cox' @ cox.wessa.net

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

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

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

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.974487445048262
beta	0.322684263837289
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.974487445048262 \tabularnewline
beta & 0.322684263837289 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.974487445048262[/C][/ROW]
[ROW][C]beta[/C][C]0.322684263837289[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.974487445048262
beta	0.322684263837289
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	99.69	99.28	0.409999999999997
4	99.45	99.3584650756377	0.0915349243623496
5	99.47	99.1553732517973	0.314626748202699
6	99.56	99.2686165453009	0.29138345469913
7	99.54	99.4508355823829	0.0891644176170843
8	99.87	99.4640326150688	0.405967384931174
9	99.73	99.913607322203	-0.183607322203002
10	99.86	99.7309132329992	0.129086767000842
11	99.91	99.893527169435	0.0164728305649788
12	99.91	99.951580149303	-0.0415801493030159
13	99.91	99.9399862778536	-0.0299862778535953
14	99.87	99.9302612506096	-0.0602612506095568
15	99.77	99.8720843859712	-0.102084385971253
16	100.14	99.7410507857828	0.398949214217154
17	100.04	100.223718422612	-0.183718422612174
18	100.11	100.080813180678	0.0291868193219784
19	100.13	100.15455927081	-0.0245592708098883
20	100.22	100.168207764863	0.0517922351366167
21	100.59	100.272546002563	0.317453997436616
22	100.25	100.735592261681	-0.485592261681091
23	99.94	100.263384680311	-0.323384680310667
24	99.85	99.84755746736	0.00244253264000349
25	99.85	99.7500128413817	0.0999871586183332
26	99.85	99.7789653671384	0.0710346328615685
27	100.15	99.8020409856387	0.347959014361294
28	100.34	100.204392262943	0.135607737057384
29	100.72	100.44245197868	0.2775480213202
30	100.61	100.906106184228	-0.296106184227696
31	100.61	100.71763045676	-0.107630456760418
32	100.52	100.678977372437	-0.158977372436837
33	100.64	100.540296648274	0.099703351726248
34	100.57	100.685048936893	-0.115048936893089
35	100.16	100.584350475325	-0.424350475325369
36	100.2	100.048803792376	0.151196207624366
37	100.2	100.121664040171	0.0783359598294169
38	99.99	100.148155771985	-0.158155771985463
39	99.69	99.8944569188292	-0.204456918829237
40	99.85	99.5313463406305	0.318653659369488
41	99.54	99.7782016584961	-0.238201658496109
42	99.67	99.4075055287334	0.262494471266578
43	99.72	99.6072733406925	0.112726659307455
44	99.74	99.6965413970744	0.0434586029255826
45	99.97	99.7319742365125	0.238025763487499
46	100.29	100.031857952301	0.258142047698911
47	100.57	100.432517956711	0.137482043289168
48	100.77	100.75882777271	0.0111722272897907
49	100.3	100.965563385409	-0.665563385408959
50	100.32	100.303541059437	0.0164589405628419
51	100.32	100.311316470258	0.00868352974185882
52	100.37	100.314245392098	0.0557546079024718
53	100.47	100.380576623426	0.0894233765744161
54	100.68	100.507836985606	0.172163014394414
55	100.7	100.769863049591	-0.0698630495906372
56	100.62	100.774069193678	-0.154069193677884
57	100.52	100.647770177853	-0.127770177853236
58	100.62	100.506921664977	0.113078335023232
59	100.52	100.636334685955	-0.116334685955309
60	100.57	100.505605951067	0.0643940489328969
61	100.59	100.571243921554	0.0187560784463869
62	100.59	100.598306144733	-0.00830614473343871
63	100.56	100.596384689327	-0.03638468932742
64	100.44	100.555659815004	-0.11565981500415
65	100.39	100.401312893173	-0.0113128931726578
66	100.51	100.345093377383	0.164906622616712
67	100.4	100.512452745651	-0.11245274565124
68	100.45	100.374167927559	0.0758320724413295
69	100.42	100.443209829724	-0.0232098297241237
70	100.38	100.408438269801	-0.0284382698008159
71	100.25	100.359629196567	-0.109629196566615
72	100.34	100.19722749032	0.142772509679688

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99.69 & 99.28 & 0.409999999999997 \tabularnewline
4 & 99.45 & 99.3584650756377 & 0.0915349243623496 \tabularnewline
5 & 99.47 & 99.1553732517973 & 0.314626748202699 \tabularnewline
6 & 99.56 & 99.2686165453009 & 0.29138345469913 \tabularnewline
7 & 99.54 & 99.4508355823829 & 0.0891644176170843 \tabularnewline
8 & 99.87 & 99.4640326150688 & 0.405967384931174 \tabularnewline
9 & 99.73 & 99.913607322203 & -0.183607322203002 \tabularnewline
10 & 99.86 & 99.7309132329992 & 0.129086767000842 \tabularnewline
11 & 99.91 & 99.893527169435 & 0.0164728305649788 \tabularnewline
12 & 99.91 & 99.951580149303 & -0.0415801493030159 \tabularnewline
13 & 99.91 & 99.9399862778536 & -0.0299862778535953 \tabularnewline
14 & 99.87 & 99.9302612506096 & -0.0602612506095568 \tabularnewline
15 & 99.77 & 99.8720843859712 & -0.102084385971253 \tabularnewline
16 & 100.14 & 99.7410507857828 & 0.398949214217154 \tabularnewline
17 & 100.04 & 100.223718422612 & -0.183718422612174 \tabularnewline
18 & 100.11 & 100.080813180678 & 0.0291868193219784 \tabularnewline
19 & 100.13 & 100.15455927081 & -0.0245592708098883 \tabularnewline
20 & 100.22 & 100.168207764863 & 0.0517922351366167 \tabularnewline
21 & 100.59 & 100.272546002563 & 0.317453997436616 \tabularnewline
22 & 100.25 & 100.735592261681 & -0.485592261681091 \tabularnewline
23 & 99.94 & 100.263384680311 & -0.323384680310667 \tabularnewline
24 & 99.85 & 99.84755746736 & 0.00244253264000349 \tabularnewline
25 & 99.85 & 99.7500128413817 & 0.0999871586183332 \tabularnewline
26 & 99.85 & 99.7789653671384 & 0.0710346328615685 \tabularnewline
27 & 100.15 & 99.8020409856387 & 0.347959014361294 \tabularnewline
28 & 100.34 & 100.204392262943 & 0.135607737057384 \tabularnewline
29 & 100.72 & 100.44245197868 & 0.2775480213202 \tabularnewline
30 & 100.61 & 100.906106184228 & -0.296106184227696 \tabularnewline
31 & 100.61 & 100.71763045676 & -0.107630456760418 \tabularnewline
32 & 100.52 & 100.678977372437 & -0.158977372436837 \tabularnewline
33 & 100.64 & 100.540296648274 & 0.099703351726248 \tabularnewline
34 & 100.57 & 100.685048936893 & -0.115048936893089 \tabularnewline
35 & 100.16 & 100.584350475325 & -0.424350475325369 \tabularnewline
36 & 100.2 & 100.048803792376 & 0.151196207624366 \tabularnewline
37 & 100.2 & 100.121664040171 & 0.0783359598294169 \tabularnewline
38 & 99.99 & 100.148155771985 & -0.158155771985463 \tabularnewline
39 & 99.69 & 99.8944569188292 & -0.204456918829237 \tabularnewline
40 & 99.85 & 99.5313463406305 & 0.318653659369488 \tabularnewline
41 & 99.54 & 99.7782016584961 & -0.238201658496109 \tabularnewline
42 & 99.67 & 99.4075055287334 & 0.262494471266578 \tabularnewline
43 & 99.72 & 99.6072733406925 & 0.112726659307455 \tabularnewline
44 & 99.74 & 99.6965413970744 & 0.0434586029255826 \tabularnewline
45 & 99.97 & 99.7319742365125 & 0.238025763487499 \tabularnewline
46 & 100.29 & 100.031857952301 & 0.258142047698911 \tabularnewline
47 & 100.57 & 100.432517956711 & 0.137482043289168 \tabularnewline
48 & 100.77 & 100.75882777271 & 0.0111722272897907 \tabularnewline
49 & 100.3 & 100.965563385409 & -0.665563385408959 \tabularnewline
50 & 100.32 & 100.303541059437 & 0.0164589405628419 \tabularnewline
51 & 100.32 & 100.311316470258 & 0.00868352974185882 \tabularnewline
52 & 100.37 & 100.314245392098 & 0.0557546079024718 \tabularnewline
53 & 100.47 & 100.380576623426 & 0.0894233765744161 \tabularnewline
54 & 100.68 & 100.507836985606 & 0.172163014394414 \tabularnewline
55 & 100.7 & 100.769863049591 & -0.0698630495906372 \tabularnewline
56 & 100.62 & 100.774069193678 & -0.154069193677884 \tabularnewline
57 & 100.52 & 100.647770177853 & -0.127770177853236 \tabularnewline
58 & 100.62 & 100.506921664977 & 0.113078335023232 \tabularnewline
59 & 100.52 & 100.636334685955 & -0.116334685955309 \tabularnewline
60 & 100.57 & 100.505605951067 & 0.0643940489328969 \tabularnewline
61 & 100.59 & 100.571243921554 & 0.0187560784463869 \tabularnewline
62 & 100.59 & 100.598306144733 & -0.00830614473343871 \tabularnewline
63 & 100.56 & 100.596384689327 & -0.03638468932742 \tabularnewline
64 & 100.44 & 100.555659815004 & -0.11565981500415 \tabularnewline
65 & 100.39 & 100.401312893173 & -0.0113128931726578 \tabularnewline
66 & 100.51 & 100.345093377383 & 0.164906622616712 \tabularnewline
67 & 100.4 & 100.512452745651 & -0.11245274565124 \tabularnewline
68 & 100.45 & 100.374167927559 & 0.0758320724413295 \tabularnewline
69 & 100.42 & 100.443209829724 & -0.0232098297241237 \tabularnewline
70 & 100.38 & 100.408438269801 & -0.0284382698008159 \tabularnewline
71 & 100.25 & 100.359629196567 & -0.109629196566615 \tabularnewline
72 & 100.34 & 100.19722749032 & 0.142772509679688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]99.69[/C][C]99.28[/C][C]0.409999999999997[/C][/ROW]
[ROW][C]4[/C][C]99.45[/C][C]99.3584650756377[/C][C]0.0915349243623496[/C][/ROW]
[ROW][C]5[/C][C]99.47[/C][C]99.1553732517973[/C][C]0.314626748202699[/C][/ROW]
[ROW][C]6[/C][C]99.56[/C][C]99.2686165453009[/C][C]0.29138345469913[/C][/ROW]
[ROW][C]7[/C][C]99.54[/C][C]99.4508355823829[/C][C]0.0891644176170843[/C][/ROW]
[ROW][C]8[/C][C]99.87[/C][C]99.4640326150688[/C][C]0.405967384931174[/C][/ROW]
[ROW][C]9[/C][C]99.73[/C][C]99.913607322203[/C][C]-0.183607322203002[/C][/ROW]
[ROW][C]10[/C][C]99.86[/C][C]99.7309132329992[/C][C]0.129086767000842[/C][/ROW]
[ROW][C]11[/C][C]99.91[/C][C]99.893527169435[/C][C]0.0164728305649788[/C][/ROW]
[ROW][C]12[/C][C]99.91[/C][C]99.951580149303[/C][C]-0.0415801493030159[/C][/ROW]
[ROW][C]13[/C][C]99.91[/C][C]99.9399862778536[/C][C]-0.0299862778535953[/C][/ROW]
[ROW][C]14[/C][C]99.87[/C][C]99.9302612506096[/C][C]-0.0602612506095568[/C][/ROW]
[ROW][C]15[/C][C]99.77[/C][C]99.8720843859712[/C][C]-0.102084385971253[/C][/ROW]
[ROW][C]16[/C][C]100.14[/C][C]99.7410507857828[/C][C]0.398949214217154[/C][/ROW]
[ROW][C]17[/C][C]100.04[/C][C]100.223718422612[/C][C]-0.183718422612174[/C][/ROW]
[ROW][C]18[/C][C]100.11[/C][C]100.080813180678[/C][C]0.0291868193219784[/C][/ROW]
[ROW][C]19[/C][C]100.13[/C][C]100.15455927081[/C][C]-0.0245592708098883[/C][/ROW]
[ROW][C]20[/C][C]100.22[/C][C]100.168207764863[/C][C]0.0517922351366167[/C][/ROW]
[ROW][C]21[/C][C]100.59[/C][C]100.272546002563[/C][C]0.317453997436616[/C][/ROW]
[ROW][C]22[/C][C]100.25[/C][C]100.735592261681[/C][C]-0.485592261681091[/C][/ROW]
[ROW][C]23[/C][C]99.94[/C][C]100.263384680311[/C][C]-0.323384680310667[/C][/ROW]
[ROW][C]24[/C][C]99.85[/C][C]99.84755746736[/C][C]0.00244253264000349[/C][/ROW]
[ROW][C]25[/C][C]99.85[/C][C]99.7500128413817[/C][C]0.0999871586183332[/C][/ROW]
[ROW][C]26[/C][C]99.85[/C][C]99.7789653671384[/C][C]0.0710346328615685[/C][/ROW]
[ROW][C]27[/C][C]100.15[/C][C]99.8020409856387[/C][C]0.347959014361294[/C][/ROW]
[ROW][C]28[/C][C]100.34[/C][C]100.204392262943[/C][C]0.135607737057384[/C][/ROW]
[ROW][C]29[/C][C]100.72[/C][C]100.44245197868[/C][C]0.2775480213202[/C][/ROW]
[ROW][C]30[/C][C]100.61[/C][C]100.906106184228[/C][C]-0.296106184227696[/C][/ROW]
[ROW][C]31[/C][C]100.61[/C][C]100.71763045676[/C][C]-0.107630456760418[/C][/ROW]
[ROW][C]32[/C][C]100.52[/C][C]100.678977372437[/C][C]-0.158977372436837[/C][/ROW]
[ROW][C]33[/C][C]100.64[/C][C]100.540296648274[/C][C]0.099703351726248[/C][/ROW]
[ROW][C]34[/C][C]100.57[/C][C]100.685048936893[/C][C]-0.115048936893089[/C][/ROW]
[ROW][C]35[/C][C]100.16[/C][C]100.584350475325[/C][C]-0.424350475325369[/C][/ROW]
[ROW][C]36[/C][C]100.2[/C][C]100.048803792376[/C][C]0.151196207624366[/C][/ROW]
[ROW][C]37[/C][C]100.2[/C][C]100.121664040171[/C][C]0.0783359598294169[/C][/ROW]
[ROW][C]38[/C][C]99.99[/C][C]100.148155771985[/C][C]-0.158155771985463[/C][/ROW]
[ROW][C]39[/C][C]99.69[/C][C]99.8944569188292[/C][C]-0.204456918829237[/C][/ROW]
[ROW][C]40[/C][C]99.85[/C][C]99.5313463406305[/C][C]0.318653659369488[/C][/ROW]
[ROW][C]41[/C][C]99.54[/C][C]99.7782016584961[/C][C]-0.238201658496109[/C][/ROW]
[ROW][C]42[/C][C]99.67[/C][C]99.4075055287334[/C][C]0.262494471266578[/C][/ROW]
[ROW][C]43[/C][C]99.72[/C][C]99.6072733406925[/C][C]0.112726659307455[/C][/ROW]
[ROW][C]44[/C][C]99.74[/C][C]99.6965413970744[/C][C]0.0434586029255826[/C][/ROW]
[ROW][C]45[/C][C]99.97[/C][C]99.7319742365125[/C][C]0.238025763487499[/C][/ROW]
[ROW][C]46[/C][C]100.29[/C][C]100.031857952301[/C][C]0.258142047698911[/C][/ROW]
[ROW][C]47[/C][C]100.57[/C][C]100.432517956711[/C][C]0.137482043289168[/C][/ROW]
[ROW][C]48[/C][C]100.77[/C][C]100.75882777271[/C][C]0.0111722272897907[/C][/ROW]
[ROW][C]49[/C][C]100.3[/C][C]100.965563385409[/C][C]-0.665563385408959[/C][/ROW]
[ROW][C]50[/C][C]100.32[/C][C]100.303541059437[/C][C]0.0164589405628419[/C][/ROW]
[ROW][C]51[/C][C]100.32[/C][C]100.311316470258[/C][C]0.00868352974185882[/C][/ROW]
[ROW][C]52[/C][C]100.37[/C][C]100.314245392098[/C][C]0.0557546079024718[/C][/ROW]
[ROW][C]53[/C][C]100.47[/C][C]100.380576623426[/C][C]0.0894233765744161[/C][/ROW]
[ROW][C]54[/C][C]100.68[/C][C]100.507836985606[/C][C]0.172163014394414[/C][/ROW]
[ROW][C]55[/C][C]100.7[/C][C]100.769863049591[/C][C]-0.0698630495906372[/C][/ROW]
[ROW][C]56[/C][C]100.62[/C][C]100.774069193678[/C][C]-0.154069193677884[/C][/ROW]
[ROW][C]57[/C][C]100.52[/C][C]100.647770177853[/C][C]-0.127770177853236[/C][/ROW]
[ROW][C]58[/C][C]100.62[/C][C]100.506921664977[/C][C]0.113078335023232[/C][/ROW]
[ROW][C]59[/C][C]100.52[/C][C]100.636334685955[/C][C]-0.116334685955309[/C][/ROW]
[ROW][C]60[/C][C]100.57[/C][C]100.505605951067[/C][C]0.0643940489328969[/C][/ROW]
[ROW][C]61[/C][C]100.59[/C][C]100.571243921554[/C][C]0.0187560784463869[/C][/ROW]
[ROW][C]62[/C][C]100.59[/C][C]100.598306144733[/C][C]-0.00830614473343871[/C][/ROW]
[ROW][C]63[/C][C]100.56[/C][C]100.596384689327[/C][C]-0.03638468932742[/C][/ROW]
[ROW][C]64[/C][C]100.44[/C][C]100.555659815004[/C][C]-0.11565981500415[/C][/ROW]
[ROW][C]65[/C][C]100.39[/C][C]100.401312893173[/C][C]-0.0113128931726578[/C][/ROW]
[ROW][C]66[/C][C]100.51[/C][C]100.345093377383[/C][C]0.164906622616712[/C][/ROW]
[ROW][C]67[/C][C]100.4[/C][C]100.512452745651[/C][C]-0.11245274565124[/C][/ROW]
[ROW][C]68[/C][C]100.45[/C][C]100.374167927559[/C][C]0.0758320724413295[/C][/ROW]
[ROW][C]69[/C][C]100.42[/C][C]100.443209829724[/C][C]-0.0232098297241237[/C][/ROW]
[ROW][C]70[/C][C]100.38[/C][C]100.408438269801[/C][C]-0.0284382698008159[/C][/ROW]
[ROW][C]71[/C][C]100.25[/C][C]100.359629196567[/C][C]-0.109629196566615[/C][/ROW]
[ROW][C]72[/C][C]100.34[/C][C]100.19722749032[/C][C]0.142772509679688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	99.69	99.28	0.409999999999997
4	99.45	99.3584650756377	0.0915349243623496
5	99.47	99.1553732517973	0.314626748202699
6	99.56	99.2686165453009	0.29138345469913
7	99.54	99.4508355823829	0.0891644176170843
8	99.87	99.4640326150688	0.405967384931174
9	99.73	99.913607322203	-0.183607322203002
10	99.86	99.7309132329992	0.129086767000842
11	99.91	99.893527169435	0.0164728305649788
12	99.91	99.951580149303	-0.0415801493030159
13	99.91	99.9399862778536	-0.0299862778535953
14	99.87	99.9302612506096	-0.0602612506095568
15	99.77	99.8720843859712	-0.102084385971253
16	100.14	99.7410507857828	0.398949214217154
17	100.04	100.223718422612	-0.183718422612174
18	100.11	100.080813180678	0.0291868193219784
19	100.13	100.15455927081	-0.0245592708098883
20	100.22	100.168207764863	0.0517922351366167
21	100.59	100.272546002563	0.317453997436616
22	100.25	100.735592261681	-0.485592261681091
23	99.94	100.263384680311	-0.323384680310667
24	99.85	99.84755746736	0.00244253264000349
25	99.85	99.7500128413817	0.0999871586183332
26	99.85	99.7789653671384	0.0710346328615685
27	100.15	99.8020409856387	0.347959014361294
28	100.34	100.204392262943	0.135607737057384
29	100.72	100.44245197868	0.2775480213202
30	100.61	100.906106184228	-0.296106184227696
31	100.61	100.71763045676	-0.107630456760418
32	100.52	100.678977372437	-0.158977372436837
33	100.64	100.540296648274	0.099703351726248
34	100.57	100.685048936893	-0.115048936893089
35	100.16	100.584350475325	-0.424350475325369
36	100.2	100.048803792376	0.151196207624366
37	100.2	100.121664040171	0.0783359598294169
38	99.99	100.148155771985	-0.158155771985463
39	99.69	99.8944569188292	-0.204456918829237
40	99.85	99.5313463406305	0.318653659369488
41	99.54	99.7782016584961	-0.238201658496109
42	99.67	99.4075055287334	0.262494471266578
43	99.72	99.6072733406925	0.112726659307455
44	99.74	99.6965413970744	0.0434586029255826
45	99.97	99.7319742365125	0.238025763487499
46	100.29	100.031857952301	0.258142047698911
47	100.57	100.432517956711	0.137482043289168
48	100.77	100.75882777271	0.0111722272897907
49	100.3	100.965563385409	-0.665563385408959
50	100.32	100.303541059437	0.0164589405628419
51	100.32	100.311316470258	0.00868352974185882
52	100.37	100.314245392098	0.0557546079024718
53	100.47	100.380576623426	0.0894233765744161
54	100.68	100.507836985606	0.172163014394414
55	100.7	100.769863049591	-0.0698630495906372
56	100.62	100.774069193678	-0.154069193677884
57	100.52	100.647770177853	-0.127770177853236
58	100.62	100.506921664977	0.113078335023232
59	100.52	100.636334685955	-0.116334685955309
60	100.57	100.505605951067	0.0643940489328969
61	100.59	100.571243921554	0.0187560784463869
62	100.59	100.598306144733	-0.00830614473343871
63	100.56	100.596384689327	-0.03638468932742
64	100.44	100.555659815004	-0.11565981500415
65	100.39	100.401312893173	-0.0113128931726578
66	100.51	100.345093377383	0.164906622616712
67	100.4	100.512452745651	-0.11245274565124
68	100.45	100.374167927559	0.0758320724413295
69	100.42	100.443209829724	-0.0232098297241237
70	100.38	100.408438269801	-0.0284382698008159
71	100.25	100.359629196567	-0.109629196566615
72	100.34	100.19722749032	0.142772509679688

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	100.325683145414	99.9235880141735	100.727778276655
74	100.315008782327	99.6590433154857	100.970974249169
75	100.30433441924	99.3845795431169	101.224089295363
76	100.293660056153	99.0933978281231	101.493922284183
77	100.282985693066	98.7842176151388	101.781753770993
78	100.272311329979	98.4571110808706	102.087511579087
79	100.261636966892	98.1125576521713	102.410716281613
80	100.250962603805	97.7511527055764	102.750772502034
81	100.240288240718	97.3735045499937	103.107071931442
82	100.229613877631	96.9801964816352	103.479031273627
83	100.218939514544	96.5717738361918	103.866105192896
84	100.208265151457	96.1487411828951	104.267789120019

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 100.325683145414 & 99.9235880141735 & 100.727778276655 \tabularnewline
74 & 100.315008782327 & 99.6590433154857 & 100.970974249169 \tabularnewline
75 & 100.30433441924 & 99.3845795431169 & 101.224089295363 \tabularnewline
76 & 100.293660056153 & 99.0933978281231 & 101.493922284183 \tabularnewline
77 & 100.282985693066 & 98.7842176151388 & 101.781753770993 \tabularnewline
78 & 100.272311329979 & 98.4571110808706 & 102.087511579087 \tabularnewline
79 & 100.261636966892 & 98.1125576521713 & 102.410716281613 \tabularnewline
80 & 100.250962603805 & 97.7511527055764 & 102.750772502034 \tabularnewline
81 & 100.240288240718 & 97.3735045499937 & 103.107071931442 \tabularnewline
82 & 100.229613877631 & 96.9801964816352 & 103.479031273627 \tabularnewline
83 & 100.218939514544 & 96.5717738361918 & 103.866105192896 \tabularnewline
84 & 100.208265151457 & 96.1487411828951 & 104.267789120019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]100.325683145414[/C][C]99.9235880141735[/C][C]100.727778276655[/C][/ROW]
[ROW][C]74[/C][C]100.315008782327[/C][C]99.6590433154857[/C][C]100.970974249169[/C][/ROW]
[ROW][C]75[/C][C]100.30433441924[/C][C]99.3845795431169[/C][C]101.224089295363[/C][/ROW]
[ROW][C]76[/C][C]100.293660056153[/C][C]99.0933978281231[/C][C]101.493922284183[/C][/ROW]
[ROW][C]77[/C][C]100.282985693066[/C][C]98.7842176151388[/C][C]101.781753770993[/C][/ROW]
[ROW][C]78[/C][C]100.272311329979[/C][C]98.4571110808706[/C][C]102.087511579087[/C][/ROW]
[ROW][C]79[/C][C]100.261636966892[/C][C]98.1125576521713[/C][C]102.410716281613[/C][/ROW]
[ROW][C]80[/C][C]100.250962603805[/C][C]97.7511527055764[/C][C]102.750772502034[/C][/ROW]
[ROW][C]81[/C][C]100.240288240718[/C][C]97.3735045499937[/C][C]103.107071931442[/C][/ROW]
[ROW][C]82[/C][C]100.229613877631[/C][C]96.9801964816352[/C][C]103.479031273627[/C][/ROW]
[ROW][C]83[/C][C]100.218939514544[/C][C]96.5717738361918[/C][C]103.866105192896[/C][/ROW]
[ROW][C]84[/C][C]100.208265151457[/C][C]96.1487411828951[/C][C]104.267789120019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	100.325683145414	99.9235880141735	100.727778276655
74	100.315008782327	99.6590433154857	100.970974249169
75	100.30433441924	99.3845795431169	101.224089295363
76	100.293660056153	99.0933978281231	101.493922284183
77	100.282985693066	98.7842176151388	101.781753770993
78	100.272311329979	98.4571110808706	102.087511579087
79	100.261636966892	98.1125576521713	102.410716281613
80	100.250962603805	97.7511527055764	102.750772502034
81	100.240288240718	97.3735045499937	103.107071931442
82	100.229613877631	96.9801964816352	103.479031273627
83	100.218939514544	96.5717738361918	103.866105192896
84	100.208265151457	96.1487411828951	104.267789120019

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):

par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code