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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 26 Nov 2016 00:03:31 +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/Nov/26/t1480118636i42e75hl1hyvdug.htm/, Retrieved Fri, 03 May 2024 22:14:46 +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 22:14:46 +0200

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

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Boxplots

-5
-3
-7
-10
-10
-11
-11
-19
-30
-38
-36
-40
-34
-35
-38
-32
-37
-39
-31
-30
-29
-36
-41
-42
-33
-43
-41
-34
-32
-36
-37
-30
-32
-30
-21
-19
-9
-8
-6
-4
-1
-2
-1
-4
-8
-6
-11
-11
-3
-6
2
2
4
8
6
8
5
3
5
3

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	'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 & 1 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]1 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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999928905996714
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999928905996714 \tabularnewline
beta & FALSE \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]0.999928905996714[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/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	0.999928905996714
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	-3	-5	2
3	-7	-3.00014218800657	-3.99985781199343
4	-10	-6.99971563409557	-3.00028436590443
5	-10	-9.99978669777343	-0.000213302226567791
6	-11	-9.99999998483549	-1.00000001516451
7	-11	-10.9999289059956	-7.10940043635588e-05
8	-19	-10.9999999949456	-8.00000000505436
9	-30	-18.9994312479734	-11.0005687520266
10	-38	-29.999217925529	-8.000782074471
11	-36	-37.9994311923729	1.99943119237291
12	-40	-36.0001421475678	-3.99985785243224
13	-34	-39.9997156340927	5.9997156340927
14	-35	-34.000426543803	-0.999573456196998
15	-38	-34.9999289363214	-3.00007106367858
16	-32	-37.9997867129379	5.99978671293795
17	-37	-32.0004265488563	-4.99957345114372
18	-39	-36.9996445603086	-2.00035543969136
19	-31	-38.9998577867238	7.99985778672379
20	-30	-31.0005687419158	1.00056874191577
21	-29	-30.0000711344374	1.00007113443742
22	-36	-29.0000710990605	-6.99992890093948
23	-41	-35.9995023470317	-5.00049765296828
24	-42	-40.9996444946034	-1.00035550539657
25	-33	-41.9999288807224	8.99992888072241
26	-43	-33.0006398409734	-9.99936015902659
27	-41	-42.999289105456	1.999289105456
28	-34	-41.0001421374662	7.00014213746623
29	-32	-34.0004976681281	2.00049766812812
30	-36	-32.0001422233878	-3.99985777661221
31	-37	-35.9997156340981	-1.00028436590191
32	-30	-36.99992888578	6.99992888578
33	-32	-30.0004976529672	-1.9995023470328
34	-30	-31.9998578473736	1.99985784737357
35	-21	-30.0001421779004	9.00014217790037
36	-19	-21.0006398561376	2.00063985613757
37	-9	-19.0001422334965	10.0001422334965
38	-8	-9.00071095014481	1.00071095014481
39	-6	-8.00007114454758	2.00007114454758
40	-4	-6.00014219306452	2.00014219306452
41	-1	-4.00014219811565	3.00014219811565
42	-2	-1.00021329211929	-0.999786707880709
43	-1	-1.9999289211605	0.999928921160505
44	-4	-1.00007108895001	-2.99992891104999
45	-8	-3.99978672304414	-4.00021327695586
46	-6	-7.99971560882414	1.99971560882414
47	-11	-6.00014216778806	-4.99985783221194
48	-11	-10.9996445400908	-0.000355459909151534
49	-3	-10.9999999747289	7.99999997472893
50	-6	-3.00056875202449	-2.99943124797551
51	2	-5.999786758425	7.999786758425
52	2	1.99943126313391	0.000568736866088715
53	4	1.99999995956622	2.00000004043378
54	8	3.99985781199055	4.00014218800945
55	6	7.99971561387814	-1.99971561387814
56	8	6.00014216778842	1.99985783221158
57	5	7.99985782210071	-2.99985782210071
58	3	5.00021327190186	-2.00021327190186
59	5	3.00014220316892	1.99985779683108
60	3	4.99985782210322	-1.99985782210322

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & -3 & -5 & 2 \tabularnewline
3 & -7 & -3.00014218800657 & -3.99985781199343 \tabularnewline
4 & -10 & -6.99971563409557 & -3.00028436590443 \tabularnewline
5 & -10 & -9.99978669777343 & -0.000213302226567791 \tabularnewline
6 & -11 & -9.99999998483549 & -1.00000001516451 \tabularnewline
7 & -11 & -10.9999289059956 & -7.10940043635588e-05 \tabularnewline
8 & -19 & -10.9999999949456 & -8.00000000505436 \tabularnewline
9 & -30 & -18.9994312479734 & -11.0005687520266 \tabularnewline
10 & -38 & -29.999217925529 & -8.000782074471 \tabularnewline
11 & -36 & -37.9994311923729 & 1.99943119237291 \tabularnewline
12 & -40 & -36.0001421475678 & -3.99985785243224 \tabularnewline
13 & -34 & -39.9997156340927 & 5.9997156340927 \tabularnewline
14 & -35 & -34.000426543803 & -0.999573456196998 \tabularnewline
15 & -38 & -34.9999289363214 & -3.00007106367858 \tabularnewline
16 & -32 & -37.9997867129379 & 5.99978671293795 \tabularnewline
17 & -37 & -32.0004265488563 & -4.99957345114372 \tabularnewline
18 & -39 & -36.9996445603086 & -2.00035543969136 \tabularnewline
19 & -31 & -38.9998577867238 & 7.99985778672379 \tabularnewline
20 & -30 & -31.0005687419158 & 1.00056874191577 \tabularnewline
21 & -29 & -30.0000711344374 & 1.00007113443742 \tabularnewline
22 & -36 & -29.0000710990605 & -6.99992890093948 \tabularnewline
23 & -41 & -35.9995023470317 & -5.00049765296828 \tabularnewline
24 & -42 & -40.9996444946034 & -1.00035550539657 \tabularnewline
25 & -33 & -41.9999288807224 & 8.99992888072241 \tabularnewline
26 & -43 & -33.0006398409734 & -9.99936015902659 \tabularnewline
27 & -41 & -42.999289105456 & 1.999289105456 \tabularnewline
28 & -34 & -41.0001421374662 & 7.00014213746623 \tabularnewline
29 & -32 & -34.0004976681281 & 2.00049766812812 \tabularnewline
30 & -36 & -32.0001422233878 & -3.99985777661221 \tabularnewline
31 & -37 & -35.9997156340981 & -1.00028436590191 \tabularnewline
32 & -30 & -36.99992888578 & 6.99992888578 \tabularnewline
33 & -32 & -30.0004976529672 & -1.9995023470328 \tabularnewline
34 & -30 & -31.9998578473736 & 1.99985784737357 \tabularnewline
35 & -21 & -30.0001421779004 & 9.00014217790037 \tabularnewline
36 & -19 & -21.0006398561376 & 2.00063985613757 \tabularnewline
37 & -9 & -19.0001422334965 & 10.0001422334965 \tabularnewline
38 & -8 & -9.00071095014481 & 1.00071095014481 \tabularnewline
39 & -6 & -8.00007114454758 & 2.00007114454758 \tabularnewline
40 & -4 & -6.00014219306452 & 2.00014219306452 \tabularnewline
41 & -1 & -4.00014219811565 & 3.00014219811565 \tabularnewline
42 & -2 & -1.00021329211929 & -0.999786707880709 \tabularnewline
43 & -1 & -1.9999289211605 & 0.999928921160505 \tabularnewline
44 & -4 & -1.00007108895001 & -2.99992891104999 \tabularnewline
45 & -8 & -3.99978672304414 & -4.00021327695586 \tabularnewline
46 & -6 & -7.99971560882414 & 1.99971560882414 \tabularnewline
47 & -11 & -6.00014216778806 & -4.99985783221194 \tabularnewline
48 & -11 & -10.9996445400908 & -0.000355459909151534 \tabularnewline
49 & -3 & -10.9999999747289 & 7.99999997472893 \tabularnewline
50 & -6 & -3.00056875202449 & -2.99943124797551 \tabularnewline
51 & 2 & -5.999786758425 & 7.999786758425 \tabularnewline
52 & 2 & 1.99943126313391 & 0.000568736866088715 \tabularnewline
53 & 4 & 1.99999995956622 & 2.00000004043378 \tabularnewline
54 & 8 & 3.99985781199055 & 4.00014218800945 \tabularnewline
55 & 6 & 7.99971561387814 & -1.99971561387814 \tabularnewline
56 & 8 & 6.00014216778842 & 1.99985783221158 \tabularnewline
57 & 5 & 7.99985782210071 & -2.99985782210071 \tabularnewline
58 & 3 & 5.00021327190186 & -2.00021327190186 \tabularnewline
59 & 5 & 3.00014220316892 & 1.99985779683108 \tabularnewline
60 & 3 & 4.99985782210322 & -1.99985782210322 \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]2[/C][C]-3[/C][C]-5[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]-7[/C][C]-3.00014218800657[/C][C]-3.99985781199343[/C][/ROW]
[ROW][C]4[/C][C]-10[/C][C]-6.99971563409557[/C][C]-3.00028436590443[/C][/ROW]
[ROW][C]5[/C][C]-10[/C][C]-9.99978669777343[/C][C]-0.000213302226567791[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-9.99999998483549[/C][C]-1.00000001516451[/C][/ROW]
[ROW][C]7[/C][C]-11[/C][C]-10.9999289059956[/C][C]-7.10940043635588e-05[/C][/ROW]
[ROW][C]8[/C][C]-19[/C][C]-10.9999999949456[/C][C]-8.00000000505436[/C][/ROW]
[ROW][C]9[/C][C]-30[/C][C]-18.9994312479734[/C][C]-11.0005687520266[/C][/ROW]
[ROW][C]10[/C][C]-38[/C][C]-29.999217925529[/C][C]-8.000782074471[/C][/ROW]
[ROW][C]11[/C][C]-36[/C][C]-37.9994311923729[/C][C]1.99943119237291[/C][/ROW]
[ROW][C]12[/C][C]-40[/C][C]-36.0001421475678[/C][C]-3.99985785243224[/C][/ROW]
[ROW][C]13[/C][C]-34[/C][C]-39.9997156340927[/C][C]5.9997156340927[/C][/ROW]
[ROW][C]14[/C][C]-35[/C][C]-34.000426543803[/C][C]-0.999573456196998[/C][/ROW]
[ROW][C]15[/C][C]-38[/C][C]-34.9999289363214[/C][C]-3.00007106367858[/C][/ROW]
[ROW][C]16[/C][C]-32[/C][C]-37.9997867129379[/C][C]5.99978671293795[/C][/ROW]
[ROW][C]17[/C][C]-37[/C][C]-32.0004265488563[/C][C]-4.99957345114372[/C][/ROW]
[ROW][C]18[/C][C]-39[/C][C]-36.9996445603086[/C][C]-2.00035543969136[/C][/ROW]
[ROW][C]19[/C][C]-31[/C][C]-38.9998577867238[/C][C]7.99985778672379[/C][/ROW]
[ROW][C]20[/C][C]-30[/C][C]-31.0005687419158[/C][C]1.00056874191577[/C][/ROW]
[ROW][C]21[/C][C]-29[/C][C]-30.0000711344374[/C][C]1.00007113443742[/C][/ROW]
[ROW][C]22[/C][C]-36[/C][C]-29.0000710990605[/C][C]-6.99992890093948[/C][/ROW]
[ROW][C]23[/C][C]-41[/C][C]-35.9995023470317[/C][C]-5.00049765296828[/C][/ROW]
[ROW][C]24[/C][C]-42[/C][C]-40.9996444946034[/C][C]-1.00035550539657[/C][/ROW]
[ROW][C]25[/C][C]-33[/C][C]-41.9999288807224[/C][C]8.99992888072241[/C][/ROW]
[ROW][C]26[/C][C]-43[/C][C]-33.0006398409734[/C][C]-9.99936015902659[/C][/ROW]
[ROW][C]27[/C][C]-41[/C][C]-42.999289105456[/C][C]1.999289105456[/C][/ROW]
[ROW][C]28[/C][C]-34[/C][C]-41.0001421374662[/C][C]7.00014213746623[/C][/ROW]
[ROW][C]29[/C][C]-32[/C][C]-34.0004976681281[/C][C]2.00049766812812[/C][/ROW]
[ROW][C]30[/C][C]-36[/C][C]-32.0001422233878[/C][C]-3.99985777661221[/C][/ROW]
[ROW][C]31[/C][C]-37[/C][C]-35.9997156340981[/C][C]-1.00028436590191[/C][/ROW]
[ROW][C]32[/C][C]-30[/C][C]-36.99992888578[/C][C]6.99992888578[/C][/ROW]
[ROW][C]33[/C][C]-32[/C][C]-30.0004976529672[/C][C]-1.9995023470328[/C][/ROW]
[ROW][C]34[/C][C]-30[/C][C]-31.9998578473736[/C][C]1.99985784737357[/C][/ROW]
[ROW][C]35[/C][C]-21[/C][C]-30.0001421779004[/C][C]9.00014217790037[/C][/ROW]
[ROW][C]36[/C][C]-19[/C][C]-21.0006398561376[/C][C]2.00063985613757[/C][/ROW]
[ROW][C]37[/C][C]-9[/C][C]-19.0001422334965[/C][C]10.0001422334965[/C][/ROW]
[ROW][C]38[/C][C]-8[/C][C]-9.00071095014481[/C][C]1.00071095014481[/C][/ROW]
[ROW][C]39[/C][C]-6[/C][C]-8.00007114454758[/C][C]2.00007114454758[/C][/ROW]
[ROW][C]40[/C][C]-4[/C][C]-6.00014219306452[/C][C]2.00014219306452[/C][/ROW]
[ROW][C]41[/C][C]-1[/C][C]-4.00014219811565[/C][C]3.00014219811565[/C][/ROW]
[ROW][C]42[/C][C]-2[/C][C]-1.00021329211929[/C][C]-0.999786707880709[/C][/ROW]
[ROW][C]43[/C][C]-1[/C][C]-1.9999289211605[/C][C]0.999928921160505[/C][/ROW]
[ROW][C]44[/C][C]-4[/C][C]-1.00007108895001[/C][C]-2.99992891104999[/C][/ROW]
[ROW][C]45[/C][C]-8[/C][C]-3.99978672304414[/C][C]-4.00021327695586[/C][/ROW]
[ROW][C]46[/C][C]-6[/C][C]-7.99971560882414[/C][C]1.99971560882414[/C][/ROW]
[ROW][C]47[/C][C]-11[/C][C]-6.00014216778806[/C][C]-4.99985783221194[/C][/ROW]
[ROW][C]48[/C][C]-11[/C][C]-10.9996445400908[/C][C]-0.000355459909151534[/C][/ROW]
[ROW][C]49[/C][C]-3[/C][C]-10.9999999747289[/C][C]7.99999997472893[/C][/ROW]
[ROW][C]50[/C][C]-6[/C][C]-3.00056875202449[/C][C]-2.99943124797551[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]-5.999786758425[/C][C]7.999786758425[/C][/ROW]
[ROW][C]52[/C][C]2[/C][C]1.99943126313391[/C][C]0.000568736866088715[/C][/ROW]
[ROW][C]53[/C][C]4[/C][C]1.99999995956622[/C][C]2.00000004043378[/C][/ROW]
[ROW][C]54[/C][C]8[/C][C]3.99985781199055[/C][C]4.00014218800945[/C][/ROW]
[ROW][C]55[/C][C]6[/C][C]7.99971561387814[/C][C]-1.99971561387814[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]6.00014216778842[/C][C]1.99985783221158[/C][/ROW]
[ROW][C]57[/C][C]5[/C][C]7.99985782210071[/C][C]-2.99985782210071[/C][/ROW]
[ROW][C]58[/C][C]3[/C][C]5.00021327190186[/C][C]-2.00021327190186[/C][/ROW]
[ROW][C]59[/C][C]5[/C][C]3.00014220316892[/C][C]1.99985779683108[/C][/ROW]
[ROW][C]60[/C][C]3[/C][C]4.99985782210322[/C][C]-1.99985782210322[/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
2	-3	-5	2
3	-7	-3.00014218800657	-3.99985781199343
4	-10	-6.99971563409557	-3.00028436590443
5	-10	-9.99978669777343	-0.000213302226567791
6	-11	-9.99999998483549	-1.00000001516451
7	-11	-10.9999289059956	-7.10940043635588e-05
8	-19	-10.9999999949456	-8.00000000505436
9	-30	-18.9994312479734	-11.0005687520266
10	-38	-29.999217925529	-8.000782074471
11	-36	-37.9994311923729	1.99943119237291
12	-40	-36.0001421475678	-3.99985785243224
13	-34	-39.9997156340927	5.9997156340927
14	-35	-34.000426543803	-0.999573456196998
15	-38	-34.9999289363214	-3.00007106367858
16	-32	-37.9997867129379	5.99978671293795
17	-37	-32.0004265488563	-4.99957345114372
18	-39	-36.9996445603086	-2.00035543969136
19	-31	-38.9998577867238	7.99985778672379
20	-30	-31.0005687419158	1.00056874191577
21	-29	-30.0000711344374	1.00007113443742
22	-36	-29.0000710990605	-6.99992890093948
23	-41	-35.9995023470317	-5.00049765296828
24	-42	-40.9996444946034	-1.00035550539657
25	-33	-41.9999288807224	8.99992888072241
26	-43	-33.0006398409734	-9.99936015902659
27	-41	-42.999289105456	1.999289105456
28	-34	-41.0001421374662	7.00014213746623
29	-32	-34.0004976681281	2.00049766812812
30	-36	-32.0001422233878	-3.99985777661221
31	-37	-35.9997156340981	-1.00028436590191
32	-30	-36.99992888578	6.99992888578
33	-32	-30.0004976529672	-1.9995023470328
34	-30	-31.9998578473736	1.99985784737357
35	-21	-30.0001421779004	9.00014217790037
36	-19	-21.0006398561376	2.00063985613757
37	-9	-19.0001422334965	10.0001422334965
38	-8	-9.00071095014481	1.00071095014481
39	-6	-8.00007114454758	2.00007114454758
40	-4	-6.00014219306452	2.00014219306452
41	-1	-4.00014219811565	3.00014219811565
42	-2	-1.00021329211929	-0.999786707880709
43	-1	-1.9999289211605	0.999928921160505
44	-4	-1.00007108895001	-2.99992891104999
45	-8	-3.99978672304414	-4.00021327695586
46	-6	-7.99971560882414	1.99971560882414
47	-11	-6.00014216778806	-4.99985783221194
48	-11	-10.9996445400908	-0.000355459909151534
49	-3	-10.9999999747289	7.99999997472893
50	-6	-3.00056875202449	-2.99943124797551
51	2	-5.999786758425	7.999786758425
52	2	1.99943126313391	0.000568736866088715
53	4	1.99999995956622	2.00000004043378
54	8	3.99985781199055	4.00014218800945
55	6	7.99971561387814	-1.99971561387814
56	8	6.00014216778842	1.99985783221158
57	5	7.99985782210071	-2.99985782210071
58	3	5.00021327190186	-2.00021327190186
59	5	3.00014220316892	1.99985779683108
60	3	4.99985782210322	-1.99985782210322

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	3.00014217789858	-6.30360337040843	12.3038877262056
62	3.00014217789858	-10.156873256624	16.1571576124212
63	3.00014217789858	-13.1136540557916	19.1139384115888
64	3.00014217789858	-15.6063567667581	21.6066411225553
65	3.00014217789858	-17.8024821011229	23.8027664569201
66	3.00014217789858	-19.7879369603429	25.7882213161401
67	3.00014217789858	-21.6137548058661	27.6140391616632
68	3.00014217789858	-23.3131871181826	29.3134714739797
69	3.00014217789858	-24.9093306326119	30.9096149884091
70	3.00014217789858	-26.4190020393836	32.4192863951808
71	3.00014217789858	-27.8548966390252	33.8551809948223
72	3.00014217789858	-29.226877453313	35.2271618091101

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.00014217789858 & -6.30360337040843 & 12.3038877262056 \tabularnewline
62 & 3.00014217789858 & -10.156873256624 & 16.1571576124212 \tabularnewline
63 & 3.00014217789858 & -13.1136540557916 & 19.1139384115888 \tabularnewline
64 & 3.00014217789858 & -15.6063567667581 & 21.6066411225553 \tabularnewline
65 & 3.00014217789858 & -17.8024821011229 & 23.8027664569201 \tabularnewline
66 & 3.00014217789858 & -19.7879369603429 & 25.7882213161401 \tabularnewline
67 & 3.00014217789858 & -21.6137548058661 & 27.6140391616632 \tabularnewline
68 & 3.00014217789858 & -23.3131871181826 & 29.3134714739797 \tabularnewline
69 & 3.00014217789858 & -24.9093306326119 & 30.9096149884091 \tabularnewline
70 & 3.00014217789858 & -26.4190020393836 & 32.4192863951808 \tabularnewline
71 & 3.00014217789858 & -27.8548966390252 & 33.8551809948223 \tabularnewline
72 & 3.00014217789858 & -29.226877453313 & 35.2271618091101 \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]61[/C][C]3.00014217789858[/C][C]-6.30360337040843[/C][C]12.3038877262056[/C][/ROW]
[ROW][C]62[/C][C]3.00014217789858[/C][C]-10.156873256624[/C][C]16.1571576124212[/C][/ROW]
[ROW][C]63[/C][C]3.00014217789858[/C][C]-13.1136540557916[/C][C]19.1139384115888[/C][/ROW]
[ROW][C]64[/C][C]3.00014217789858[/C][C]-15.6063567667581[/C][C]21.6066411225553[/C][/ROW]
[ROW][C]65[/C][C]3.00014217789858[/C][C]-17.8024821011229[/C][C]23.8027664569201[/C][/ROW]
[ROW][C]66[/C][C]3.00014217789858[/C][C]-19.7879369603429[/C][C]25.7882213161401[/C][/ROW]
[ROW][C]67[/C][C]3.00014217789858[/C][C]-21.6137548058661[/C][C]27.6140391616632[/C][/ROW]
[ROW][C]68[/C][C]3.00014217789858[/C][C]-23.3131871181826[/C][C]29.3134714739797[/C][/ROW]
[ROW][C]69[/C][C]3.00014217789858[/C][C]-24.9093306326119[/C][C]30.9096149884091[/C][/ROW]
[ROW][C]70[/C][C]3.00014217789858[/C][C]-26.4190020393836[/C][C]32.4192863951808[/C][/ROW]
[ROW][C]71[/C][C]3.00014217789858[/C][C]-27.8548966390252[/C][C]33.8551809948223[/C][/ROW]
[ROW][C]72[/C][C]3.00014217789858[/C][C]-29.226877453313[/C][C]35.2271618091101[/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
61	3.00014217789858	-6.30360337040843	12.3038877262056
62	3.00014217789858	-10.156873256624	16.1571576124212
63	3.00014217789858	-13.1136540557916	19.1139384115888
64	3.00014217789858	-15.6063567667581	21.6066411225553
65	3.00014217789858	-17.8024821011229	23.8027664569201
66	3.00014217789858	-19.7879369603429	25.7882213161401
67	3.00014217789858	-21.6137548058661	27.6140391616632
68	3.00014217789858	-23.3131871181826	29.3134714739797
69	3.00014217789858	-24.9093306326119	30.9096149884091
70	3.00014217789858	-26.4190020393836	32.4192863951808
71	3.00014217789858	-27.8548966390252	33.8551809948223
72	3.00014217789858	-29.226877453313	35.2271618091101

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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