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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 00:06:02 +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/t1480118782rvtkon8o5ab1rhw.htm/, Retrieved Fri, 03 May 2024 20:34:41 +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 20:34:41 +0200

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No (this computation is public)

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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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.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]'Sir Maurice George Kendall' @ kendall.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	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.982041012729787
beta	0.0921305872438814
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.982041012729787 \tabularnewline
beta & 0.0921305872438814 \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]0.982041012729787[/C][/ROW]
[ROW][C]beta[/C][C]0.0921305872438814[/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	0.982041012729787
beta	0.0921305872438814
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	-7	-1	-6
4	-10	-5.43510216758095	-4.56489783241905
5	-10	-8.87388891481408	-1.12611108518592
6	-11	-9.0375320858932	-1.9624679141068
7	-11	-10.2000682410762	-0.799931758923776
8	-19	-10.293320851068	-8.70667914893203
9	-30	-18.9390693103656	-11.0609306896344
10	-38	-30.8975382701208	-7.10246172987919
11	-36	-39.6112307992112	3.61123079921119
12	-40	-37.4769080942766	-2.52309190572338
13	-34	-41.5950211725215	7.59502117252149
14	-35	-35.0895649854401	0.0895649854400702
15	-38	-35.946671110335	-2.05332888966496
16	-32	-39.0939639223433	7.09396392234329
17	-37	-32.6164064498422	-4.38359355015776
18	-39	-37.8068912179768	-1.19310878202322
19	-31	-39.9721368216116	8.97213682161156
20	-30	-31.3429311505539	1.34293115055388
21	-29	-30.0844152838349	1.08441528383495
22	-36	-28.9816590269716	-7.01834097302837
23	-41	-36.4711332550581	-4.52886674494191
24	-42	-41.9255955074856	-0.0744044925143612
25	-33	-43.0123249603683	10.0123249603683
26	-43	-33.2875971409054	-9.71240285909461
27	-41	-43.8121005137988	2.81210051379881
28	-34	-41.7826002616069	7.78260026160692
29	-32	-34.1677267437368	2.16772674373684
30	-36	-31.870762023889	-4.12923797611104
31	-37	-36.1312719125368	-0.868728087463197
32	-30	-37.2684264237677	7.26842642376775
33	-32	-29.7569432184511	-2.24305678154889
34	-30	-31.7890694521087	1.7890694521087
35	-21	-29.6996144808673	8.69961448086734
36	-19	-20.0366144190607	1.03661441906073
37	-9	-17.8052059565632	8.80520595656324
38	-8	-7.14806204512432	-0.851937954875684
39	-6	-6.05170947190727	0.0517094719072739
40	-4	-4.06325959757534	0.0632595975753434
41	-1	-2.05774354982339	1.05774354982339
42	-2	1.02009694702967	-3.02009694702967
43	-1	-0.179915504683435	-0.820084495316565
44	-4	0.706376522438088	-4.70637652243809
45	-8	-2.64964380230128	-5.35035619769872
46	-6	-7.12215748818139	1.12215748818139
47	-11	-5.13686894111448	-5.86313105888552
48	-11	-10.5418929678244	-0.458107032175564
49	-3	-10.6804094243218	7.68040942432183
50	-6	-2.13167609794247	-3.86832390205753
51	2	-5.27426307530946	7.27426307530946
52	2	3.18377368357997	-1.18377368357997
53	4	3.22856833227448	0.771431667725524
54	8	5.26325088755491	2.73674911244509
55	6	9.47556593088045	-3.47556593088045
56	8	7.27267746166985	0.727322538330146
57	5	9.26300308618671	-4.26300308618671
58	3	5.96692474852656	-2.96692474852656
59	5	3.67521296551328	1.32478703448672
60	3	5.7179996201042	-2.7179996201042

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -7 & -1 & -6 \tabularnewline
4 & -10 & -5.43510216758095 & -4.56489783241905 \tabularnewline
5 & -10 & -8.87388891481408 & -1.12611108518592 \tabularnewline
6 & -11 & -9.0375320858932 & -1.9624679141068 \tabularnewline
7 & -11 & -10.2000682410762 & -0.799931758923776 \tabularnewline
8 & -19 & -10.293320851068 & -8.70667914893203 \tabularnewline
9 & -30 & -18.9390693103656 & -11.0609306896344 \tabularnewline
10 & -38 & -30.8975382701208 & -7.10246172987919 \tabularnewline
11 & -36 & -39.6112307992112 & 3.61123079921119 \tabularnewline
12 & -40 & -37.4769080942766 & -2.52309190572338 \tabularnewline
13 & -34 & -41.5950211725215 & 7.59502117252149 \tabularnewline
14 & -35 & -35.0895649854401 & 0.0895649854400702 \tabularnewline
15 & -38 & -35.946671110335 & -2.05332888966496 \tabularnewline
16 & -32 & -39.0939639223433 & 7.09396392234329 \tabularnewline
17 & -37 & -32.6164064498422 & -4.38359355015776 \tabularnewline
18 & -39 & -37.8068912179768 & -1.19310878202322 \tabularnewline
19 & -31 & -39.9721368216116 & 8.97213682161156 \tabularnewline
20 & -30 & -31.3429311505539 & 1.34293115055388 \tabularnewline
21 & -29 & -30.0844152838349 & 1.08441528383495 \tabularnewline
22 & -36 & -28.9816590269716 & -7.01834097302837 \tabularnewline
23 & -41 & -36.4711332550581 & -4.52886674494191 \tabularnewline
24 & -42 & -41.9255955074856 & -0.0744044925143612 \tabularnewline
25 & -33 & -43.0123249603683 & 10.0123249603683 \tabularnewline
26 & -43 & -33.2875971409054 & -9.71240285909461 \tabularnewline
27 & -41 & -43.8121005137988 & 2.81210051379881 \tabularnewline
28 & -34 & -41.7826002616069 & 7.78260026160692 \tabularnewline
29 & -32 & -34.1677267437368 & 2.16772674373684 \tabularnewline
30 & -36 & -31.870762023889 & -4.12923797611104 \tabularnewline
31 & -37 & -36.1312719125368 & -0.868728087463197 \tabularnewline
32 & -30 & -37.2684264237677 & 7.26842642376775 \tabularnewline
33 & -32 & -29.7569432184511 & -2.24305678154889 \tabularnewline
34 & -30 & -31.7890694521087 & 1.7890694521087 \tabularnewline
35 & -21 & -29.6996144808673 & 8.69961448086734 \tabularnewline
36 & -19 & -20.0366144190607 & 1.03661441906073 \tabularnewline
37 & -9 & -17.8052059565632 & 8.80520595656324 \tabularnewline
38 & -8 & -7.14806204512432 & -0.851937954875684 \tabularnewline
39 & -6 & -6.05170947190727 & 0.0517094719072739 \tabularnewline
40 & -4 & -4.06325959757534 & 0.0632595975753434 \tabularnewline
41 & -1 & -2.05774354982339 & 1.05774354982339 \tabularnewline
42 & -2 & 1.02009694702967 & -3.02009694702967 \tabularnewline
43 & -1 & -0.179915504683435 & -0.820084495316565 \tabularnewline
44 & -4 & 0.706376522438088 & -4.70637652243809 \tabularnewline
45 & -8 & -2.64964380230128 & -5.35035619769872 \tabularnewline
46 & -6 & -7.12215748818139 & 1.12215748818139 \tabularnewline
47 & -11 & -5.13686894111448 & -5.86313105888552 \tabularnewline
48 & -11 & -10.5418929678244 & -0.458107032175564 \tabularnewline
49 & -3 & -10.6804094243218 & 7.68040942432183 \tabularnewline
50 & -6 & -2.13167609794247 & -3.86832390205753 \tabularnewline
51 & 2 & -5.27426307530946 & 7.27426307530946 \tabularnewline
52 & 2 & 3.18377368357997 & -1.18377368357997 \tabularnewline
53 & 4 & 3.22856833227448 & 0.771431667725524 \tabularnewline
54 & 8 & 5.26325088755491 & 2.73674911244509 \tabularnewline
55 & 6 & 9.47556593088045 & -3.47556593088045 \tabularnewline
56 & 8 & 7.27267746166985 & 0.727322538330146 \tabularnewline
57 & 5 & 9.26300308618671 & -4.26300308618671 \tabularnewline
58 & 3 & 5.96692474852656 & -2.96692474852656 \tabularnewline
59 & 5 & 3.67521296551328 & 1.32478703448672 \tabularnewline
60 & 3 & 5.7179996201042 & -2.7179996201042 \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]-7[/C][C]-1[/C][C]-6[/C][/ROW]
[ROW][C]4[/C][C]-10[/C][C]-5.43510216758095[/C][C]-4.56489783241905[/C][/ROW]
[ROW][C]5[/C][C]-10[/C][C]-8.87388891481408[/C][C]-1.12611108518592[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-9.0375320858932[/C][C]-1.9624679141068[/C][/ROW]
[ROW][C]7[/C][C]-11[/C][C]-10.2000682410762[/C][C]-0.799931758923776[/C][/ROW]
[ROW][C]8[/C][C]-19[/C][C]-10.293320851068[/C][C]-8.70667914893203[/C][/ROW]
[ROW][C]9[/C][C]-30[/C][C]-18.9390693103656[/C][C]-11.0609306896344[/C][/ROW]
[ROW][C]10[/C][C]-38[/C][C]-30.8975382701208[/C][C]-7.10246172987919[/C][/ROW]
[ROW][C]11[/C][C]-36[/C][C]-39.6112307992112[/C][C]3.61123079921119[/C][/ROW]
[ROW][C]12[/C][C]-40[/C][C]-37.4769080942766[/C][C]-2.52309190572338[/C][/ROW]
[ROW][C]13[/C][C]-34[/C][C]-41.5950211725215[/C][C]7.59502117252149[/C][/ROW]
[ROW][C]14[/C][C]-35[/C][C]-35.0895649854401[/C][C]0.0895649854400702[/C][/ROW]
[ROW][C]15[/C][C]-38[/C][C]-35.946671110335[/C][C]-2.05332888966496[/C][/ROW]
[ROW][C]16[/C][C]-32[/C][C]-39.0939639223433[/C][C]7.09396392234329[/C][/ROW]
[ROW][C]17[/C][C]-37[/C][C]-32.6164064498422[/C][C]-4.38359355015776[/C][/ROW]
[ROW][C]18[/C][C]-39[/C][C]-37.8068912179768[/C][C]-1.19310878202322[/C][/ROW]
[ROW][C]19[/C][C]-31[/C][C]-39.9721368216116[/C][C]8.97213682161156[/C][/ROW]
[ROW][C]20[/C][C]-30[/C][C]-31.3429311505539[/C][C]1.34293115055388[/C][/ROW]
[ROW][C]21[/C][C]-29[/C][C]-30.0844152838349[/C][C]1.08441528383495[/C][/ROW]
[ROW][C]22[/C][C]-36[/C][C]-28.9816590269716[/C][C]-7.01834097302837[/C][/ROW]
[ROW][C]23[/C][C]-41[/C][C]-36.4711332550581[/C][C]-4.52886674494191[/C][/ROW]
[ROW][C]24[/C][C]-42[/C][C]-41.9255955074856[/C][C]-0.0744044925143612[/C][/ROW]
[ROW][C]25[/C][C]-33[/C][C]-43.0123249603683[/C][C]10.0123249603683[/C][/ROW]
[ROW][C]26[/C][C]-43[/C][C]-33.2875971409054[/C][C]-9.71240285909461[/C][/ROW]
[ROW][C]27[/C][C]-41[/C][C]-43.8121005137988[/C][C]2.81210051379881[/C][/ROW]
[ROW][C]28[/C][C]-34[/C][C]-41.7826002616069[/C][C]7.78260026160692[/C][/ROW]
[ROW][C]29[/C][C]-32[/C][C]-34.1677267437368[/C][C]2.16772674373684[/C][/ROW]
[ROW][C]30[/C][C]-36[/C][C]-31.870762023889[/C][C]-4.12923797611104[/C][/ROW]
[ROW][C]31[/C][C]-37[/C][C]-36.1312719125368[/C][C]-0.868728087463197[/C][/ROW]
[ROW][C]32[/C][C]-30[/C][C]-37.2684264237677[/C][C]7.26842642376775[/C][/ROW]
[ROW][C]33[/C][C]-32[/C][C]-29.7569432184511[/C][C]-2.24305678154889[/C][/ROW]
[ROW][C]34[/C][C]-30[/C][C]-31.7890694521087[/C][C]1.7890694521087[/C][/ROW]
[ROW][C]35[/C][C]-21[/C][C]-29.6996144808673[/C][C]8.69961448086734[/C][/ROW]
[ROW][C]36[/C][C]-19[/C][C]-20.0366144190607[/C][C]1.03661441906073[/C][/ROW]
[ROW][C]37[/C][C]-9[/C][C]-17.8052059565632[/C][C]8.80520595656324[/C][/ROW]
[ROW][C]38[/C][C]-8[/C][C]-7.14806204512432[/C][C]-0.851937954875684[/C][/ROW]
[ROW][C]39[/C][C]-6[/C][C]-6.05170947190727[/C][C]0.0517094719072739[/C][/ROW]
[ROW][C]40[/C][C]-4[/C][C]-4.06325959757534[/C][C]0.0632595975753434[/C][/ROW]
[ROW][C]41[/C][C]-1[/C][C]-2.05774354982339[/C][C]1.05774354982339[/C][/ROW]
[ROW][C]42[/C][C]-2[/C][C]1.02009694702967[/C][C]-3.02009694702967[/C][/ROW]
[ROW][C]43[/C][C]-1[/C][C]-0.179915504683435[/C][C]-0.820084495316565[/C][/ROW]
[ROW][C]44[/C][C]-4[/C][C]0.706376522438088[/C][C]-4.70637652243809[/C][/ROW]
[ROW][C]45[/C][C]-8[/C][C]-2.64964380230128[/C][C]-5.35035619769872[/C][/ROW]
[ROW][C]46[/C][C]-6[/C][C]-7.12215748818139[/C][C]1.12215748818139[/C][/ROW]
[ROW][C]47[/C][C]-11[/C][C]-5.13686894111448[/C][C]-5.86313105888552[/C][/ROW]
[ROW][C]48[/C][C]-11[/C][C]-10.5418929678244[/C][C]-0.458107032175564[/C][/ROW]
[ROW][C]49[/C][C]-3[/C][C]-10.6804094243218[/C][C]7.68040942432183[/C][/ROW]
[ROW][C]50[/C][C]-6[/C][C]-2.13167609794247[/C][C]-3.86832390205753[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]-5.27426307530946[/C][C]7.27426307530946[/C][/ROW]
[ROW][C]52[/C][C]2[/C][C]3.18377368357997[/C][C]-1.18377368357997[/C][/ROW]
[ROW][C]53[/C][C]4[/C][C]3.22856833227448[/C][C]0.771431667725524[/C][/ROW]
[ROW][C]54[/C][C]8[/C][C]5.26325088755491[/C][C]2.73674911244509[/C][/ROW]
[ROW][C]55[/C][C]6[/C][C]9.47556593088045[/C][C]-3.47556593088045[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]7.27267746166985[/C][C]0.727322538330146[/C][/ROW]
[ROW][C]57[/C][C]5[/C][C]9.26300308618671[/C][C]-4.26300308618671[/C][/ROW]
[ROW][C]58[/C][C]3[/C][C]5.96692474852656[/C][C]-2.96692474852656[/C][/ROW]
[ROW][C]59[/C][C]5[/C][C]3.67521296551328[/C][C]1.32478703448672[/C][/ROW]
[ROW][C]60[/C][C]3[/C][C]5.7179996201042[/C][C]-2.7179996201042[/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	-7	-1	-6
4	-10	-5.43510216758095	-4.56489783241905
5	-10	-8.87388891481408	-1.12611108518592
6	-11	-9.0375320858932	-1.9624679141068
7	-11	-10.2000682410762	-0.799931758923776
8	-19	-10.293320851068	-8.70667914893203
9	-30	-18.9390693103656	-11.0609306896344
10	-38	-30.8975382701208	-7.10246172987919
11	-36	-39.6112307992112	3.61123079921119
12	-40	-37.4769080942766	-2.52309190572338
13	-34	-41.5950211725215	7.59502117252149
14	-35	-35.0895649854401	0.0895649854400702
15	-38	-35.946671110335	-2.05332888966496
16	-32	-39.0939639223433	7.09396392234329
17	-37	-32.6164064498422	-4.38359355015776
18	-39	-37.8068912179768	-1.19310878202322
19	-31	-39.9721368216116	8.97213682161156
20	-30	-31.3429311505539	1.34293115055388
21	-29	-30.0844152838349	1.08441528383495
22	-36	-28.9816590269716	-7.01834097302837
23	-41	-36.4711332550581	-4.52886674494191
24	-42	-41.9255955074856	-0.0744044925143612
25	-33	-43.0123249603683	10.0123249603683
26	-43	-33.2875971409054	-9.71240285909461
27	-41	-43.8121005137988	2.81210051379881
28	-34	-41.7826002616069	7.78260026160692
29	-32	-34.1677267437368	2.16772674373684
30	-36	-31.870762023889	-4.12923797611104
31	-37	-36.1312719125368	-0.868728087463197
32	-30	-37.2684264237677	7.26842642376775
33	-32	-29.7569432184511	-2.24305678154889
34	-30	-31.7890694521087	1.7890694521087
35	-21	-29.6996144808673	8.69961448086734
36	-19	-20.0366144190607	1.03661441906073
37	-9	-17.8052059565632	8.80520595656324
38	-8	-7.14806204512432	-0.851937954875684
39	-6	-6.05170947190727	0.0517094719072739
40	-4	-4.06325959757534	0.0632595975753434
41	-1	-2.05774354982339	1.05774354982339
42	-2	1.02009694702967	-3.02009694702967
43	-1	-0.179915504683435	-0.820084495316565
44	-4	0.706376522438088	-4.70637652243809
45	-8	-2.64964380230128	-5.35035619769872
46	-6	-7.12215748818139	1.12215748818139
47	-11	-5.13686894111448	-5.86313105888552
48	-11	-10.5418929678244	-0.458107032175564
49	-3	-10.6804094243218	7.68040942432183
50	-6	-2.13167609794247	-3.86832390205753
51	2	-5.27426307530946	7.27426307530946
52	2	3.18377368357997	-1.18377368357997
53	4	3.22856833227448	0.771431667725524
54	8	5.26325088755491	2.73674911244509
55	6	9.47556593088045	-3.47556593088045
56	8	7.27267746166985	0.727322538330146
57	5	9.26300308618671	-4.26300308618671
58	3	5.96692474852656	-2.96692474852656
59	5	3.67521296551328	1.32478703448672
60	3	5.7179996201042	-2.7179996201042

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	3.54469019922703	-6.15565166107018	13.2450320595242
62	4.04056787787617	-10.1838937430285	18.2650294987809
63	4.5364455565253	-13.618608106155	22.6914992192056
64	5.03232323517444	-16.8182868358422	26.8829333061911
65	5.52820091382358	-19.9159615275968	30.9723633552439
66	6.02407859247271	-22.9761840287945	35.0243412137399
67	6.51995627112185	-26.0349079237295	39.0748204659732
68	7.01583394977098	-29.1139015498417	43.1455694493836
69	7.51171162842012	-32.227080233954	47.2505034907943
70	8.00758930706925	-35.3836666089669	51.3988452231054
71	8.50346698571839	-38.5899174131529	55.5968513845897
72	8.99934466436753	-41.8501332502206	59.8488225789557

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.54469019922703 & -6.15565166107018 & 13.2450320595242 \tabularnewline
62 & 4.04056787787617 & -10.1838937430285 & 18.2650294987809 \tabularnewline
63 & 4.5364455565253 & -13.618608106155 & 22.6914992192056 \tabularnewline
64 & 5.03232323517444 & -16.8182868358422 & 26.8829333061911 \tabularnewline
65 & 5.52820091382358 & -19.9159615275968 & 30.9723633552439 \tabularnewline
66 & 6.02407859247271 & -22.9761840287945 & 35.0243412137399 \tabularnewline
67 & 6.51995627112185 & -26.0349079237295 & 39.0748204659732 \tabularnewline
68 & 7.01583394977098 & -29.1139015498417 & 43.1455694493836 \tabularnewline
69 & 7.51171162842012 & -32.227080233954 & 47.2505034907943 \tabularnewline
70 & 8.00758930706925 & -35.3836666089669 & 51.3988452231054 \tabularnewline
71 & 8.50346698571839 & -38.5899174131529 & 55.5968513845897 \tabularnewline
72 & 8.99934466436753 & -41.8501332502206 & 59.8488225789557 \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]3.54469019922703[/C][C]-6.15565166107018[/C][C]13.2450320595242[/C][/ROW]
[ROW][C]62[/C][C]4.04056787787617[/C][C]-10.1838937430285[/C][C]18.2650294987809[/C][/ROW]
[ROW][C]63[/C][C]4.5364455565253[/C][C]-13.618608106155[/C][C]22.6914992192056[/C][/ROW]
[ROW][C]64[/C][C]5.03232323517444[/C][C]-16.8182868358422[/C][C]26.8829333061911[/C][/ROW]
[ROW][C]65[/C][C]5.52820091382358[/C][C]-19.9159615275968[/C][C]30.9723633552439[/C][/ROW]
[ROW][C]66[/C][C]6.02407859247271[/C][C]-22.9761840287945[/C][C]35.0243412137399[/C][/ROW]
[ROW][C]67[/C][C]6.51995627112185[/C][C]-26.0349079237295[/C][C]39.0748204659732[/C][/ROW]
[ROW][C]68[/C][C]7.01583394977098[/C][C]-29.1139015498417[/C][C]43.1455694493836[/C][/ROW]
[ROW][C]69[/C][C]7.51171162842012[/C][C]-32.227080233954[/C][C]47.2505034907943[/C][/ROW]
[ROW][C]70[/C][C]8.00758930706925[/C][C]-35.3836666089669[/C][C]51.3988452231054[/C][/ROW]
[ROW][C]71[/C][C]8.50346698571839[/C][C]-38.5899174131529[/C][C]55.5968513845897[/C][/ROW]
[ROW][C]72[/C][C]8.99934466436753[/C][C]-41.8501332502206[/C][C]59.8488225789557[/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	3.54469019922703	-6.15565166107018	13.2450320595242
62	4.04056787787617	-10.1838937430285	18.2650294987809
63	4.5364455565253	-13.618608106155	22.6914992192056
64	5.03232323517444	-16.8182868358422	26.8829333061911
65	5.52820091382358	-19.9159615275968	30.9723633552439
66	6.02407859247271	-22.9761840287945	35.0243412137399
67	6.51995627112185	-26.0349079237295	39.0748204659732
68	7.01583394977098	-29.1139015498417	43.1455694493836
69	7.51171162842012	-32.227080233954	47.2505034907943
70	8.00758930706925	-35.3836666089669	51.3988452231054
71	8.50346698571839	-38.5899174131529	55.5968513845897
72	8.99934466436753	-41.8501332502206	59.8488225789557

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