Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 30 Dec 2016 11:33:15 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/30/t14830976480ztzc42w26pgd2m.htm/, Retrieved Fri, 03 May 2024 23:23:30 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 23:23:30 +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

-0.4
0
0.2
-0.6
0.5
-0.3
-1.2
0
0.9
0.5
-0.5
0.1
-0.9
1.1
-0.6
-0.2
0.1
-0.2
3.5
-0.9
-1.3
-0.3
-0.4
1.3
-0.7
0.5
-0.6
0.8
-0.2
0.3
3.8
-1.1
-1.7
0.1
-0.9
1.9
-1.4
1.4
-0.2
0.6
0.5
0.6
3.4
-1.4
-1.6
-1.2
-1.7
1.9
-0.8
1
-0.9
1.1
-0.6
0.6
4.1
-1.1
-2
-1.3
-1.7
1.6
-1.2
1.2
-0.8
0.7
1.2
-0.2
4.4
-1.1
-2.2
-0.7
-1.7
1.6

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.108696406028489
beta	0.406355813593699
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.108696406028489 \tabularnewline
beta & 0.406355813593699 \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]0.108696406028489[/C][/ROW]
[ROW][C]beta[/C][C]0.406355813593699[/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	0.108696406028489
beta	0.406355813593699
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.2	0.4	-0.2
4	-0.6	0.769426835493018	-1.36942683549302
5	0.5	0.951254392582719	-0.451254392582719
6	-0.3	1.21295235111483	-1.51295235111483
7	-1.2	1.29242133471596	-2.49242133471596
8	0	1.15533676394072	-1.15533676394072
9	0.9	1.11255792983322	-0.212557929833223
10	0.5	1.16286720693839	-0.662867206938391
11	-0.5	1.13495102626923	-1.63495102626923
12	0.1	0.929157995233484	-0.829157995233484
13	-0.9	0.774328345833029	-1.67432834583303
14	1.1	0.453677610764965	0.646322389235035
15	-0.6	0.413820953053717	-1.01382095305372
16	-0.2	0.148732800605194	-0.348732800605194
17	0.1	-0.0594659842994269	0.159465984299427
18	-0.2	-0.205381868257743	0.00538186825774281
19	3.5	-0.367808427875208	3.86780842787521
20	-0.9	0.0604357395045823	-0.960435739504582
21	-1.3	-0.0785547677436544	-1.22144523225635
22	-0.3	-0.299866591996636	-0.00013340800336431
23	-0.4	-0.388432102866886	-0.0115678971331143
24	1.3	-0.478751448876887	1.77875144887689
25	-0.7	-0.295903102725489	-0.404096897274511
26	0.5	-0.368171250870648	0.868171250870648
27	-0.6	-0.263801806229303	-0.336198193770697
28	0.8	-0.305192669800364	1.10519266980036
29	-0.2	-0.141093811466697	-0.0589061885333027
30	0.3	-0.106130167271901	0.406130167271901
31	3.8	-0.00268021001443911	3.80268021001444
32	-1.1	0.637924695821889	-1.73792469582189
33	-1.7	0.599522641423445	-2.29952264142344
34	0.1	0.398508335390158	-0.298508335390158
35	-0.9	0.401812153837796	-1.3018121538378
36	1.9	0.238560169829537	1.66143983017046
37	-1.4	0.470787854498917	-1.87078785449892
38	1.4	0.236443476629894	1.16355652337011
39	-0.2	0.383315039997479	-0.583315039997479
40	0.6	0.314543257677533	0.285456742322467
41	0.5	0.352812303500936	0.147187696499064
42	0.6	0.382553195649635	0.217446804350365
43	3.4	0.429535498781878	2.97046450121812
44	-1.4	0.906964615068308	-2.30696461506831
45	-1.6	0.708858872395777	-2.30885887239578
46	-1.2	0.408566281570268	-1.60856628157027
47	-1.7	0.113343544467015	-1.81334354446702
48	1.9	-0.284232071434253	2.18423207143425
49	-0.8	-0.150809328950073	-0.649190671049927
50	1	-0.354043828474994	1.35404382847499
51	-0.9	-0.279726611641421	-0.620273388358579
52	1.1	-0.447407694276083	1.54740769427608
53	-0.6	-0.311121538858697	-0.288878461141303
54	0.6	-0.387192682044936	0.987192682044936
55	4.1	-0.280955753384834	4.38095575338483
56	-1.1	0.387675283409564	-1.48767528340956
57	-2	0.352697468977944	-2.35269746897794
58	-1.3	0.11977757741925	-1.41977757741925
59	-1.7	-0.0744480219780294	-1.62555197802197
60	1.6	-0.362840241543575	1.96284024154358
61	-1.2	-0.174489615257456	-1.02551038474254
62	1.2	-0.356258157316974	1.55625815731697
63	-0.8	-0.188658722915166	-0.611341277084834
64	0.7	-0.283672144237346	0.983672144237346
65	1.2	-0.161865114450019	1.36186511445002
66	-0.2	0.0612029194503674	-0.261202919450367
67	4.4	0.0963121107841602	4.30368788921584
68	-1.1	0.817699909824855	-1.91769990982486
69	-2.2	0.778141528548959	-2.97814152854896
70	-0.7	0.49177418092518	-1.19177418092518
71	-1.7	0.346938573655871	-2.04693857365587
72	1.6	0.018737587910342	1.58126241208966

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.2 & 0.4 & -0.2 \tabularnewline
4 & -0.6 & 0.769426835493018 & -1.36942683549302 \tabularnewline
5 & 0.5 & 0.951254392582719 & -0.451254392582719 \tabularnewline
6 & -0.3 & 1.21295235111483 & -1.51295235111483 \tabularnewline
7 & -1.2 & 1.29242133471596 & -2.49242133471596 \tabularnewline
8 & 0 & 1.15533676394072 & -1.15533676394072 \tabularnewline
9 & 0.9 & 1.11255792983322 & -0.212557929833223 \tabularnewline
10 & 0.5 & 1.16286720693839 & -0.662867206938391 \tabularnewline
11 & -0.5 & 1.13495102626923 & -1.63495102626923 \tabularnewline
12 & 0.1 & 0.929157995233484 & -0.829157995233484 \tabularnewline
13 & -0.9 & 0.774328345833029 & -1.67432834583303 \tabularnewline
14 & 1.1 & 0.453677610764965 & 0.646322389235035 \tabularnewline
15 & -0.6 & 0.413820953053717 & -1.01382095305372 \tabularnewline
16 & -0.2 & 0.148732800605194 & -0.348732800605194 \tabularnewline
17 & 0.1 & -0.0594659842994269 & 0.159465984299427 \tabularnewline
18 & -0.2 & -0.205381868257743 & 0.00538186825774281 \tabularnewline
19 & 3.5 & -0.367808427875208 & 3.86780842787521 \tabularnewline
20 & -0.9 & 0.0604357395045823 & -0.960435739504582 \tabularnewline
21 & -1.3 & -0.0785547677436544 & -1.22144523225635 \tabularnewline
22 & -0.3 & -0.299866591996636 & -0.00013340800336431 \tabularnewline
23 & -0.4 & -0.388432102866886 & -0.0115678971331143 \tabularnewline
24 & 1.3 & -0.478751448876887 & 1.77875144887689 \tabularnewline
25 & -0.7 & -0.295903102725489 & -0.404096897274511 \tabularnewline
26 & 0.5 & -0.368171250870648 & 0.868171250870648 \tabularnewline
27 & -0.6 & -0.263801806229303 & -0.336198193770697 \tabularnewline
28 & 0.8 & -0.305192669800364 & 1.10519266980036 \tabularnewline
29 & -0.2 & -0.141093811466697 & -0.0589061885333027 \tabularnewline
30 & 0.3 & -0.106130167271901 & 0.406130167271901 \tabularnewline
31 & 3.8 & -0.00268021001443911 & 3.80268021001444 \tabularnewline
32 & -1.1 & 0.637924695821889 & -1.73792469582189 \tabularnewline
33 & -1.7 & 0.599522641423445 & -2.29952264142344 \tabularnewline
34 & 0.1 & 0.398508335390158 & -0.298508335390158 \tabularnewline
35 & -0.9 & 0.401812153837796 & -1.3018121538378 \tabularnewline
36 & 1.9 & 0.238560169829537 & 1.66143983017046 \tabularnewline
37 & -1.4 & 0.470787854498917 & -1.87078785449892 \tabularnewline
38 & 1.4 & 0.236443476629894 & 1.16355652337011 \tabularnewline
39 & -0.2 & 0.383315039997479 & -0.583315039997479 \tabularnewline
40 & 0.6 & 0.314543257677533 & 0.285456742322467 \tabularnewline
41 & 0.5 & 0.352812303500936 & 0.147187696499064 \tabularnewline
42 & 0.6 & 0.382553195649635 & 0.217446804350365 \tabularnewline
43 & 3.4 & 0.429535498781878 & 2.97046450121812 \tabularnewline
44 & -1.4 & 0.906964615068308 & -2.30696461506831 \tabularnewline
45 & -1.6 & 0.708858872395777 & -2.30885887239578 \tabularnewline
46 & -1.2 & 0.408566281570268 & -1.60856628157027 \tabularnewline
47 & -1.7 & 0.113343544467015 & -1.81334354446702 \tabularnewline
48 & 1.9 & -0.284232071434253 & 2.18423207143425 \tabularnewline
49 & -0.8 & -0.150809328950073 & -0.649190671049927 \tabularnewline
50 & 1 & -0.354043828474994 & 1.35404382847499 \tabularnewline
51 & -0.9 & -0.279726611641421 & -0.620273388358579 \tabularnewline
52 & 1.1 & -0.447407694276083 & 1.54740769427608 \tabularnewline
53 & -0.6 & -0.311121538858697 & -0.288878461141303 \tabularnewline
54 & 0.6 & -0.387192682044936 & 0.987192682044936 \tabularnewline
55 & 4.1 & -0.280955753384834 & 4.38095575338483 \tabularnewline
56 & -1.1 & 0.387675283409564 & -1.48767528340956 \tabularnewline
57 & -2 & 0.352697468977944 & -2.35269746897794 \tabularnewline
58 & -1.3 & 0.11977757741925 & -1.41977757741925 \tabularnewline
59 & -1.7 & -0.0744480219780294 & -1.62555197802197 \tabularnewline
60 & 1.6 & -0.362840241543575 & 1.96284024154358 \tabularnewline
61 & -1.2 & -0.174489615257456 & -1.02551038474254 \tabularnewline
62 & 1.2 & -0.356258157316974 & 1.55625815731697 \tabularnewline
63 & -0.8 & -0.188658722915166 & -0.611341277084834 \tabularnewline
64 & 0.7 & -0.283672144237346 & 0.983672144237346 \tabularnewline
65 & 1.2 & -0.161865114450019 & 1.36186511445002 \tabularnewline
66 & -0.2 & 0.0612029194503674 & -0.261202919450367 \tabularnewline
67 & 4.4 & 0.0963121107841602 & 4.30368788921584 \tabularnewline
68 & -1.1 & 0.817699909824855 & -1.91769990982486 \tabularnewline
69 & -2.2 & 0.778141528548959 & -2.97814152854896 \tabularnewline
70 & -0.7 & 0.49177418092518 & -1.19177418092518 \tabularnewline
71 & -1.7 & 0.346938573655871 & -2.04693857365587 \tabularnewline
72 & 1.6 & 0.018737587910342 & 1.58126241208966 \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]0.2[/C][C]0.4[/C][C]-0.2[/C][/ROW]
[ROW][C]4[/C][C]-0.6[/C][C]0.769426835493018[/C][C]-1.36942683549302[/C][/ROW]
[ROW][C]5[/C][C]0.5[/C][C]0.951254392582719[/C][C]-0.451254392582719[/C][/ROW]
[ROW][C]6[/C][C]-0.3[/C][C]1.21295235111483[/C][C]-1.51295235111483[/C][/ROW]
[ROW][C]7[/C][C]-1.2[/C][C]1.29242133471596[/C][C]-2.49242133471596[/C][/ROW]
[ROW][C]8[/C][C]0[/C][C]1.15533676394072[/C][C]-1.15533676394072[/C][/ROW]
[ROW][C]9[/C][C]0.9[/C][C]1.11255792983322[/C][C]-0.212557929833223[/C][/ROW]
[ROW][C]10[/C][C]0.5[/C][C]1.16286720693839[/C][C]-0.662867206938391[/C][/ROW]
[ROW][C]11[/C][C]-0.5[/C][C]1.13495102626923[/C][C]-1.63495102626923[/C][/ROW]
[ROW][C]12[/C][C]0.1[/C][C]0.929157995233484[/C][C]-0.829157995233484[/C][/ROW]
[ROW][C]13[/C][C]-0.9[/C][C]0.774328345833029[/C][C]-1.67432834583303[/C][/ROW]
[ROW][C]14[/C][C]1.1[/C][C]0.453677610764965[/C][C]0.646322389235035[/C][/ROW]
[ROW][C]15[/C][C]-0.6[/C][C]0.413820953053717[/C][C]-1.01382095305372[/C][/ROW]
[ROW][C]16[/C][C]-0.2[/C][C]0.148732800605194[/C][C]-0.348732800605194[/C][/ROW]
[ROW][C]17[/C][C]0.1[/C][C]-0.0594659842994269[/C][C]0.159465984299427[/C][/ROW]
[ROW][C]18[/C][C]-0.2[/C][C]-0.205381868257743[/C][C]0.00538186825774281[/C][/ROW]
[ROW][C]19[/C][C]3.5[/C][C]-0.367808427875208[/C][C]3.86780842787521[/C][/ROW]
[ROW][C]20[/C][C]-0.9[/C][C]0.0604357395045823[/C][C]-0.960435739504582[/C][/ROW]
[ROW][C]21[/C][C]-1.3[/C][C]-0.0785547677436544[/C][C]-1.22144523225635[/C][/ROW]
[ROW][C]22[/C][C]-0.3[/C][C]-0.299866591996636[/C][C]-0.00013340800336431[/C][/ROW]
[ROW][C]23[/C][C]-0.4[/C][C]-0.388432102866886[/C][C]-0.0115678971331143[/C][/ROW]
[ROW][C]24[/C][C]1.3[/C][C]-0.478751448876887[/C][C]1.77875144887689[/C][/ROW]
[ROW][C]25[/C][C]-0.7[/C][C]-0.295903102725489[/C][C]-0.404096897274511[/C][/ROW]
[ROW][C]26[/C][C]0.5[/C][C]-0.368171250870648[/C][C]0.868171250870648[/C][/ROW]
[ROW][C]27[/C][C]-0.6[/C][C]-0.263801806229303[/C][C]-0.336198193770697[/C][/ROW]
[ROW][C]28[/C][C]0.8[/C][C]-0.305192669800364[/C][C]1.10519266980036[/C][/ROW]
[ROW][C]29[/C][C]-0.2[/C][C]-0.141093811466697[/C][C]-0.0589061885333027[/C][/ROW]
[ROW][C]30[/C][C]0.3[/C][C]-0.106130167271901[/C][C]0.406130167271901[/C][/ROW]
[ROW][C]31[/C][C]3.8[/C][C]-0.00268021001443911[/C][C]3.80268021001444[/C][/ROW]
[ROW][C]32[/C][C]-1.1[/C][C]0.637924695821889[/C][C]-1.73792469582189[/C][/ROW]
[ROW][C]33[/C][C]-1.7[/C][C]0.599522641423445[/C][C]-2.29952264142344[/C][/ROW]
[ROW][C]34[/C][C]0.1[/C][C]0.398508335390158[/C][C]-0.298508335390158[/C][/ROW]
[ROW][C]35[/C][C]-0.9[/C][C]0.401812153837796[/C][C]-1.3018121538378[/C][/ROW]
[ROW][C]36[/C][C]1.9[/C][C]0.238560169829537[/C][C]1.66143983017046[/C][/ROW]
[ROW][C]37[/C][C]-1.4[/C][C]0.470787854498917[/C][C]-1.87078785449892[/C][/ROW]
[ROW][C]38[/C][C]1.4[/C][C]0.236443476629894[/C][C]1.16355652337011[/C][/ROW]
[ROW][C]39[/C][C]-0.2[/C][C]0.383315039997479[/C][C]-0.583315039997479[/C][/ROW]
[ROW][C]40[/C][C]0.6[/C][C]0.314543257677533[/C][C]0.285456742322467[/C][/ROW]
[ROW][C]41[/C][C]0.5[/C][C]0.352812303500936[/C][C]0.147187696499064[/C][/ROW]
[ROW][C]42[/C][C]0.6[/C][C]0.382553195649635[/C][C]0.217446804350365[/C][/ROW]
[ROW][C]43[/C][C]3.4[/C][C]0.429535498781878[/C][C]2.97046450121812[/C][/ROW]
[ROW][C]44[/C][C]-1.4[/C][C]0.906964615068308[/C][C]-2.30696461506831[/C][/ROW]
[ROW][C]45[/C][C]-1.6[/C][C]0.708858872395777[/C][C]-2.30885887239578[/C][/ROW]
[ROW][C]46[/C][C]-1.2[/C][C]0.408566281570268[/C][C]-1.60856628157027[/C][/ROW]
[ROW][C]47[/C][C]-1.7[/C][C]0.113343544467015[/C][C]-1.81334354446702[/C][/ROW]
[ROW][C]48[/C][C]1.9[/C][C]-0.284232071434253[/C][C]2.18423207143425[/C][/ROW]
[ROW][C]49[/C][C]-0.8[/C][C]-0.150809328950073[/C][C]-0.649190671049927[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]-0.354043828474994[/C][C]1.35404382847499[/C][/ROW]
[ROW][C]51[/C][C]-0.9[/C][C]-0.279726611641421[/C][C]-0.620273388358579[/C][/ROW]
[ROW][C]52[/C][C]1.1[/C][C]-0.447407694276083[/C][C]1.54740769427608[/C][/ROW]
[ROW][C]53[/C][C]-0.6[/C][C]-0.311121538858697[/C][C]-0.288878461141303[/C][/ROW]
[ROW][C]54[/C][C]0.6[/C][C]-0.387192682044936[/C][C]0.987192682044936[/C][/ROW]
[ROW][C]55[/C][C]4.1[/C][C]-0.280955753384834[/C][C]4.38095575338483[/C][/ROW]
[ROW][C]56[/C][C]-1.1[/C][C]0.387675283409564[/C][C]-1.48767528340956[/C][/ROW]
[ROW][C]57[/C][C]-2[/C][C]0.352697468977944[/C][C]-2.35269746897794[/C][/ROW]
[ROW][C]58[/C][C]-1.3[/C][C]0.11977757741925[/C][C]-1.41977757741925[/C][/ROW]
[ROW][C]59[/C][C]-1.7[/C][C]-0.0744480219780294[/C][C]-1.62555197802197[/C][/ROW]
[ROW][C]60[/C][C]1.6[/C][C]-0.362840241543575[/C][C]1.96284024154358[/C][/ROW]
[ROW][C]61[/C][C]-1.2[/C][C]-0.174489615257456[/C][C]-1.02551038474254[/C][/ROW]
[ROW][C]62[/C][C]1.2[/C][C]-0.356258157316974[/C][C]1.55625815731697[/C][/ROW]
[ROW][C]63[/C][C]-0.8[/C][C]-0.188658722915166[/C][C]-0.611341277084834[/C][/ROW]
[ROW][C]64[/C][C]0.7[/C][C]-0.283672144237346[/C][C]0.983672144237346[/C][/ROW]
[ROW][C]65[/C][C]1.2[/C][C]-0.161865114450019[/C][C]1.36186511445002[/C][/ROW]
[ROW][C]66[/C][C]-0.2[/C][C]0.0612029194503674[/C][C]-0.261202919450367[/C][/ROW]
[ROW][C]67[/C][C]4.4[/C][C]0.0963121107841602[/C][C]4.30368788921584[/C][/ROW]
[ROW][C]68[/C][C]-1.1[/C][C]0.817699909824855[/C][C]-1.91769990982486[/C][/ROW]
[ROW][C]69[/C][C]-2.2[/C][C]0.778141528548959[/C][C]-2.97814152854896[/C][/ROW]
[ROW][C]70[/C][C]-0.7[/C][C]0.49177418092518[/C][C]-1.19177418092518[/C][/ROW]
[ROW][C]71[/C][C]-1.7[/C][C]0.346938573655871[/C][C]-2.04693857365587[/C][/ROW]
[ROW][C]72[/C][C]1.6[/C][C]0.018737587910342[/C][C]1.58126241208966[/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	0.2	0.4	-0.2
4	-0.6	0.769426835493018	-1.36942683549302
5	0.5	0.951254392582719	-0.451254392582719
6	-0.3	1.21295235111483	-1.51295235111483
7	-1.2	1.29242133471596	-2.49242133471596
8	0	1.15533676394072	-1.15533676394072
9	0.9	1.11255792983322	-0.212557929833223
10	0.5	1.16286720693839	-0.662867206938391
11	-0.5	1.13495102626923	-1.63495102626923
12	0.1	0.929157995233484	-0.829157995233484
13	-0.9	0.774328345833029	-1.67432834583303
14	1.1	0.453677610764965	0.646322389235035
15	-0.6	0.413820953053717	-1.01382095305372
16	-0.2	0.148732800605194	-0.348732800605194
17	0.1	-0.0594659842994269	0.159465984299427
18	-0.2	-0.205381868257743	0.00538186825774281
19	3.5	-0.367808427875208	3.86780842787521
20	-0.9	0.0604357395045823	-0.960435739504582
21	-1.3	-0.0785547677436544	-1.22144523225635
22	-0.3	-0.299866591996636	-0.00013340800336431
23	-0.4	-0.388432102866886	-0.0115678971331143
24	1.3	-0.478751448876887	1.77875144887689
25	-0.7	-0.295903102725489	-0.404096897274511
26	0.5	-0.368171250870648	0.868171250870648
27	-0.6	-0.263801806229303	-0.336198193770697
28	0.8	-0.305192669800364	1.10519266980036
29	-0.2	-0.141093811466697	-0.0589061885333027
30	0.3	-0.106130167271901	0.406130167271901
31	3.8	-0.00268021001443911	3.80268021001444
32	-1.1	0.637924695821889	-1.73792469582189
33	-1.7	0.599522641423445	-2.29952264142344
34	0.1	0.398508335390158	-0.298508335390158
35	-0.9	0.401812153837796	-1.3018121538378
36	1.9	0.238560169829537	1.66143983017046
37	-1.4	0.470787854498917	-1.87078785449892
38	1.4	0.236443476629894	1.16355652337011
39	-0.2	0.383315039997479	-0.583315039997479
40	0.6	0.314543257677533	0.285456742322467
41	0.5	0.352812303500936	0.147187696499064
42	0.6	0.382553195649635	0.217446804350365
43	3.4	0.429535498781878	2.97046450121812
44	-1.4	0.906964615068308	-2.30696461506831
45	-1.6	0.708858872395777	-2.30885887239578
46	-1.2	0.408566281570268	-1.60856628157027
47	-1.7	0.113343544467015	-1.81334354446702
48	1.9	-0.284232071434253	2.18423207143425
49	-0.8	-0.150809328950073	-0.649190671049927
50	1	-0.354043828474994	1.35404382847499
51	-0.9	-0.279726611641421	-0.620273388358579
52	1.1	-0.447407694276083	1.54740769427608
53	-0.6	-0.311121538858697	-0.288878461141303
54	0.6	-0.387192682044936	0.987192682044936
55	4.1	-0.280955753384834	4.38095575338483
56	-1.1	0.387675283409564	-1.48767528340956
57	-2	0.352697468977944	-2.35269746897794
58	-1.3	0.11977757741925	-1.41977757741925
59	-1.7	-0.0744480219780294	-1.62555197802197
60	1.6	-0.362840241543575	1.96284024154358
61	-1.2	-0.174489615257456	-1.02551038474254
62	1.2	-0.356258157316974	1.55625815731697
63	-0.8	-0.188658722915166	-0.611341277084834
64	0.7	-0.283672144237346	0.983672144237346
65	1.2	-0.161865114450019	1.36186511445002
66	-0.2	0.0612029194503674	-0.261202919450367
67	4.4	0.0963121107841602	4.30368788921584
68	-1.1	0.817699909824855	-1.91769990982486
69	-2.2	0.778141528548959	-2.97814152854896
70	-0.7	0.49177418092518	-1.19177418092518
71	-1.7	0.346938573655871	-2.04693857365587
72	1.6	0.018737587910342	1.58126241208966

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.154752447749905	-3.11473565373517	3.42424054923498
74	0.118889766407382	-3.1885783704774	3.42635790329217
75	0.0830270850648596	-3.28659377585468	3.4526479459844
76	0.0471644037223368	-3.41350887608893	3.5078376835336
77	0.011301722379814	-3.57294145862975	3.59554490338938
78	-0.0245609589627089	-3.76724354418481	3.7181216262594
79	-0.0604236403052316	-3.99750251978841	3.87665523917794
80	-0.0962863216477544	-4.2636907876908	4.07111814439529
81	-0.132149002990277	-4.56491246036457	4.30061445438401
82	-0.1680116843328	-4.89968105717824	4.56365768851264
83	-0.203874365675323	-5.2661741229602	4.85842539160955
84	-0.239737047017846	-5.66243494561231	5.18296085157662

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.154752447749905 & -3.11473565373517 & 3.42424054923498 \tabularnewline
74 & 0.118889766407382 & -3.1885783704774 & 3.42635790329217 \tabularnewline
75 & 0.0830270850648596 & -3.28659377585468 & 3.4526479459844 \tabularnewline
76 & 0.0471644037223368 & -3.41350887608893 & 3.5078376835336 \tabularnewline
77 & 0.011301722379814 & -3.57294145862975 & 3.59554490338938 \tabularnewline
78 & -0.0245609589627089 & -3.76724354418481 & 3.7181216262594 \tabularnewline
79 & -0.0604236403052316 & -3.99750251978841 & 3.87665523917794 \tabularnewline
80 & -0.0962863216477544 & -4.2636907876908 & 4.07111814439529 \tabularnewline
81 & -0.132149002990277 & -4.56491246036457 & 4.30061445438401 \tabularnewline
82 & -0.1680116843328 & -4.89968105717824 & 4.56365768851264 \tabularnewline
83 & -0.203874365675323 & -5.2661741229602 & 4.85842539160955 \tabularnewline
84 & -0.239737047017846 & -5.66243494561231 & 5.18296085157662 \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]0.154752447749905[/C][C]-3.11473565373517[/C][C]3.42424054923498[/C][/ROW]
[ROW][C]74[/C][C]0.118889766407382[/C][C]-3.1885783704774[/C][C]3.42635790329217[/C][/ROW]
[ROW][C]75[/C][C]0.0830270850648596[/C][C]-3.28659377585468[/C][C]3.4526479459844[/C][/ROW]
[ROW][C]76[/C][C]0.0471644037223368[/C][C]-3.41350887608893[/C][C]3.5078376835336[/C][/ROW]
[ROW][C]77[/C][C]0.011301722379814[/C][C]-3.57294145862975[/C][C]3.59554490338938[/C][/ROW]
[ROW][C]78[/C][C]-0.0245609589627089[/C][C]-3.76724354418481[/C][C]3.7181216262594[/C][/ROW]
[ROW][C]79[/C][C]-0.0604236403052316[/C][C]-3.99750251978841[/C][C]3.87665523917794[/C][/ROW]
[ROW][C]80[/C][C]-0.0962863216477544[/C][C]-4.2636907876908[/C][C]4.07111814439529[/C][/ROW]
[ROW][C]81[/C][C]-0.132149002990277[/C][C]-4.56491246036457[/C][C]4.30061445438401[/C][/ROW]
[ROW][C]82[/C][C]-0.1680116843328[/C][C]-4.89968105717824[/C][C]4.56365768851264[/C][/ROW]
[ROW][C]83[/C][C]-0.203874365675323[/C][C]-5.2661741229602[/C][C]4.85842539160955[/C][/ROW]
[ROW][C]84[/C][C]-0.239737047017846[/C][C]-5.66243494561231[/C][C]5.18296085157662[/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	0.154752447749905	-3.11473565373517	3.42424054923498
74	0.118889766407382	-3.1885783704774	3.42635790329217
75	0.0830270850648596	-3.28659377585468	3.4526479459844
76	0.0471644037223368	-3.41350887608893	3.5078376835336
77	0.011301722379814	-3.57294145862975	3.59554490338938
78	-0.0245609589627089	-3.76724354418481	3.7181216262594
79	-0.0604236403052316	-3.99750251978841	3.87665523917794
80	-0.0962863216477544	-4.2636907876908	4.07111814439529
81	-0.132149002990277	-4.56491246036457	4.30061445438401
82	-0.1680116843328	-4.89968105717824	4.56365768851264
83	-0.203874365675323	-5.2661741229602	4.85842539160955
84	-0.239737047017846	-5.66243494561231	5.18296085157662

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code