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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 14 Dec 2013 15:07:20 -0500

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/2013/Dec/14/t1387051709ekhvq2rj23551zb.htm/, Retrieved Wed, 24 Apr 2024 09:19:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232335, Retrieved Wed, 24 Apr 2024 09:19:45 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

152

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

-       [Exponential Smoothing] [] [2013-12-14 20:07:20] [d2dbc91554044d1d1a55d99248130a60] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232335&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]5 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=232335&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232335&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	5 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.630518605848567
beta	0.0171001057019711
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.630518605848567 \tabularnewline
beta & 0.0171001057019711 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232335&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]0.630518605848567[/C][/ROW]
[ROW][C]beta[/C][C]0.0171001057019711[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232335&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232335&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	0.630518605848567
beta	0.0171001057019711
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	38.97	38.926124465812	0.043875534188011
14	38.95	38.9293099465314	0.0206900534686127
15	38.95	38.9380996290793	0.011900370920678
16	38.92	38.9285588955981	-0.00855889559805689
17	38.96	38.990192599127	-0.0301925991270195
18	38.97	39.0011936487655	-0.0311936487654521
19	38.97	38.8878938567608	0.082106143239244
20	38.95	38.9331669547375	0.0168330452625369
21	38.93	38.9174656427751	0.0125343572248937
22	38.76	39.1762724059801	-0.41627240598006
23	38.81	38.8723036380606	-0.0623036380606408
24	38.81	38.7391803437733	0.0708196562267389
25	38.81	38.7915518631967	0.0184481368033289
26	38.78	38.7667399412009	0.0132600587991476
27	38.77	38.7641187881626	0.00588121183736945
28	38.61	38.7396801848465	-0.129680184846549
29	38.69	38.7121021294304	-0.0221021294304364
30	38.69	38.7230724508744	-0.0330724508744282
31	38.68	38.6456678965162	0.0343321034837558
32	38.74	38.6314039739534	0.108596026046584
33	38.73	38.6676646215747	0.0623353784252672
34	38.62	38.7956646640305	-0.175664664030535
35	38.57	38.7730115744505	-0.203011574450493
36	38.57	38.5976619313212	-0.0276619313211555
37	38.57	38.5648328960702	0.00516710392984265
38	38.57	38.5258311628366	0.0441688371634186
39	38.56	38.5364065047995	0.0235934952004797
40	38.55	38.4696736663617	0.0803263336383324
41	38.42	38.613146249192	-0.193146249191969
42	38.47	38.5092620855925	-0.0392620855924903
43	38.47	38.4498381884082	0.0201618115918478
44	38.48	38.450904595948	0.0290954040519651
45	38.45	38.4159148282715	0.0340851717285489
46	38.43	38.4338300650281	-0.00383006502806893
47	38.43	38.5069344848408	-0.0769344848407911
48	38.48	38.4747433502307	0.00525664976929363
49	38.48	38.4740308636855	0.00596913631446938
50	38.48	38.4491849421603	0.0308150578397246
51	38.51	38.4428339927874	0.0671660072126201
52	38.48	38.4241016791206	0.0558983208794217
53	38.55	38.4504310499988	0.0995689500012205
54	38.55	38.5904247729672	-0.0404247729671923
55	38.55	38.5546694400758	-0.00466944007578007
56	38.49	38.5455579846309	-0.0555579846308802
57	38.37	38.4603014863425	-0.0903014863425327
58	38.14	38.3857036971746	-0.245703697174648
59	38.08	38.2766077538154	-0.196607753815449
60	38.04	38.1953543672242	-0.155354367224206
61	38.04	38.0879310748953	-0.0479310748953381
62	38.03	38.0319932027169	-0.00199320271686076
63	37.98	38.0117463272137	-0.0317463272136891
64	38.03	37.9187775726697	0.111222427330326
65	38.05	37.9890146346393	0.0609853653607288
66	38.05	38.0454289356732	0.00457106432675403
67	38.05	38.0442137098073	0.00578629019268817
68	38.05	38.0159636136288	0.0340363863711843
69	38.02	37.9683981536366	0.0516018463633898
70	38.06	37.9214220207916	0.138577979208414
71	38.01	38.0724733521928	-0.0624733521927539
72	38	38.0921932789885	-0.0921932789884963
73	38	38.0661228531959	-0.0661228531959068
74	38	38.0173294902387	-0.0173294902386516
75	37.99	37.977895794193	0.0121042058069989
76	37.96	37.9673489249363	-0.00734892493632344
77	37.96	37.9449334684888	0.0150665315111596
78	38.02	37.951726546955	0.0682734530450375
79	38.02	37.9919881918916	0.0280118081084453
80	38.02	37.9892915434212	0.0307084565787648
81	38	37.9471839511174	0.0528160488825549
82	37.93	37.9341886285206	-0.00418862852055923
83	38	37.9204781011225	0.0795218988774806
84	38	38.0198185691035	-0.0198185691034709
85	38	38.0508654745878	-0.0508654745877664
86	38	38.0317361093852	-0.0317361093851929
87	38	37.9959543406368	0.0040456593631788
88	38.01	37.9749123169877	0.0350876830122644
89	37.98	37.9897670532042	-0.00976705320420024
90	38	38.0025243355973	-0.00252433559729326
91	38	37.9844706652914	0.0155293347085887
92	38	37.9759652977689	0.0240347022311482
93	37.95	37.9388115184565	0.0111884815435133
94	37.87	37.8790516419916	-0.00905164199157582
95	37.75	37.893696513329	-0.143696513329033
96	37.75	37.8136745751137	-0.0636745751136942

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 38.97 & 38.926124465812 & 0.043875534188011 \tabularnewline
14 & 38.95 & 38.9293099465314 & 0.0206900534686127 \tabularnewline
15 & 38.95 & 38.9380996290793 & 0.011900370920678 \tabularnewline
16 & 38.92 & 38.9285588955981 & -0.00855889559805689 \tabularnewline
17 & 38.96 & 38.990192599127 & -0.0301925991270195 \tabularnewline
18 & 38.97 & 39.0011936487655 & -0.0311936487654521 \tabularnewline
19 & 38.97 & 38.8878938567608 & 0.082106143239244 \tabularnewline
20 & 38.95 & 38.9331669547375 & 0.0168330452625369 \tabularnewline
21 & 38.93 & 38.9174656427751 & 0.0125343572248937 \tabularnewline
22 & 38.76 & 39.1762724059801 & -0.41627240598006 \tabularnewline
23 & 38.81 & 38.8723036380606 & -0.0623036380606408 \tabularnewline
24 & 38.81 & 38.7391803437733 & 0.0708196562267389 \tabularnewline
25 & 38.81 & 38.7915518631967 & 0.0184481368033289 \tabularnewline
26 & 38.78 & 38.7667399412009 & 0.0132600587991476 \tabularnewline
27 & 38.77 & 38.7641187881626 & 0.00588121183736945 \tabularnewline
28 & 38.61 & 38.7396801848465 & -0.129680184846549 \tabularnewline
29 & 38.69 & 38.7121021294304 & -0.0221021294304364 \tabularnewline
30 & 38.69 & 38.7230724508744 & -0.0330724508744282 \tabularnewline
31 & 38.68 & 38.6456678965162 & 0.0343321034837558 \tabularnewline
32 & 38.74 & 38.6314039739534 & 0.108596026046584 \tabularnewline
33 & 38.73 & 38.6676646215747 & 0.0623353784252672 \tabularnewline
34 & 38.62 & 38.7956646640305 & -0.175664664030535 \tabularnewline
35 & 38.57 & 38.7730115744505 & -0.203011574450493 \tabularnewline
36 & 38.57 & 38.5976619313212 & -0.0276619313211555 \tabularnewline
37 & 38.57 & 38.5648328960702 & 0.00516710392984265 \tabularnewline
38 & 38.57 & 38.5258311628366 & 0.0441688371634186 \tabularnewline
39 & 38.56 & 38.5364065047995 & 0.0235934952004797 \tabularnewline
40 & 38.55 & 38.4696736663617 & 0.0803263336383324 \tabularnewline
41 & 38.42 & 38.613146249192 & -0.193146249191969 \tabularnewline
42 & 38.47 & 38.5092620855925 & -0.0392620855924903 \tabularnewline
43 & 38.47 & 38.4498381884082 & 0.0201618115918478 \tabularnewline
44 & 38.48 & 38.450904595948 & 0.0290954040519651 \tabularnewline
45 & 38.45 & 38.4159148282715 & 0.0340851717285489 \tabularnewline
46 & 38.43 & 38.4338300650281 & -0.00383006502806893 \tabularnewline
47 & 38.43 & 38.5069344848408 & -0.0769344848407911 \tabularnewline
48 & 38.48 & 38.4747433502307 & 0.00525664976929363 \tabularnewline
49 & 38.48 & 38.4740308636855 & 0.00596913631446938 \tabularnewline
50 & 38.48 & 38.4491849421603 & 0.0308150578397246 \tabularnewline
51 & 38.51 & 38.4428339927874 & 0.0671660072126201 \tabularnewline
52 & 38.48 & 38.4241016791206 & 0.0558983208794217 \tabularnewline
53 & 38.55 & 38.4504310499988 & 0.0995689500012205 \tabularnewline
54 & 38.55 & 38.5904247729672 & -0.0404247729671923 \tabularnewline
55 & 38.55 & 38.5546694400758 & -0.00466944007578007 \tabularnewline
56 & 38.49 & 38.5455579846309 & -0.0555579846308802 \tabularnewline
57 & 38.37 & 38.4603014863425 & -0.0903014863425327 \tabularnewline
58 & 38.14 & 38.3857036971746 & -0.245703697174648 \tabularnewline
59 & 38.08 & 38.2766077538154 & -0.196607753815449 \tabularnewline
60 & 38.04 & 38.1953543672242 & -0.155354367224206 \tabularnewline
61 & 38.04 & 38.0879310748953 & -0.0479310748953381 \tabularnewline
62 & 38.03 & 38.0319932027169 & -0.00199320271686076 \tabularnewline
63 & 37.98 & 38.0117463272137 & -0.0317463272136891 \tabularnewline
64 & 38.03 & 37.9187775726697 & 0.111222427330326 \tabularnewline
65 & 38.05 & 37.9890146346393 & 0.0609853653607288 \tabularnewline
66 & 38.05 & 38.0454289356732 & 0.00457106432675403 \tabularnewline
67 & 38.05 & 38.0442137098073 & 0.00578629019268817 \tabularnewline
68 & 38.05 & 38.0159636136288 & 0.0340363863711843 \tabularnewline
69 & 38.02 & 37.9683981536366 & 0.0516018463633898 \tabularnewline
70 & 38.06 & 37.9214220207916 & 0.138577979208414 \tabularnewline
71 & 38.01 & 38.0724733521928 & -0.0624733521927539 \tabularnewline
72 & 38 & 38.0921932789885 & -0.0921932789884963 \tabularnewline
73 & 38 & 38.0661228531959 & -0.0661228531959068 \tabularnewline
74 & 38 & 38.0173294902387 & -0.0173294902386516 \tabularnewline
75 & 37.99 & 37.977895794193 & 0.0121042058069989 \tabularnewline
76 & 37.96 & 37.9673489249363 & -0.00734892493632344 \tabularnewline
77 & 37.96 & 37.9449334684888 & 0.0150665315111596 \tabularnewline
78 & 38.02 & 37.951726546955 & 0.0682734530450375 \tabularnewline
79 & 38.02 & 37.9919881918916 & 0.0280118081084453 \tabularnewline
80 & 38.02 & 37.9892915434212 & 0.0307084565787648 \tabularnewline
81 & 38 & 37.9471839511174 & 0.0528160488825549 \tabularnewline
82 & 37.93 & 37.9341886285206 & -0.00418862852055923 \tabularnewline
83 & 38 & 37.9204781011225 & 0.0795218988774806 \tabularnewline
84 & 38 & 38.0198185691035 & -0.0198185691034709 \tabularnewline
85 & 38 & 38.0508654745878 & -0.0508654745877664 \tabularnewline
86 & 38 & 38.0317361093852 & -0.0317361093851929 \tabularnewline
87 & 38 & 37.9959543406368 & 0.0040456593631788 \tabularnewline
88 & 38.01 & 37.9749123169877 & 0.0350876830122644 \tabularnewline
89 & 37.98 & 37.9897670532042 & -0.00976705320420024 \tabularnewline
90 & 38 & 38.0025243355973 & -0.00252433559729326 \tabularnewline
91 & 38 & 37.9844706652914 & 0.0155293347085887 \tabularnewline
92 & 38 & 37.9759652977689 & 0.0240347022311482 \tabularnewline
93 & 37.95 & 37.9388115184565 & 0.0111884815435133 \tabularnewline
94 & 37.87 & 37.8790516419916 & -0.00905164199157582 \tabularnewline
95 & 37.75 & 37.893696513329 & -0.143696513329033 \tabularnewline
96 & 37.75 & 37.8136745751137 & -0.0636745751136942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232335&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]38.97[/C][C]38.926124465812[/C][C]0.043875534188011[/C][/ROW]
[ROW][C]14[/C][C]38.95[/C][C]38.9293099465314[/C][C]0.0206900534686127[/C][/ROW]
[ROW][C]15[/C][C]38.95[/C][C]38.9380996290793[/C][C]0.011900370920678[/C][/ROW]
[ROW][C]16[/C][C]38.92[/C][C]38.9285588955981[/C][C]-0.00855889559805689[/C][/ROW]
[ROW][C]17[/C][C]38.96[/C][C]38.990192599127[/C][C]-0.0301925991270195[/C][/ROW]
[ROW][C]18[/C][C]38.97[/C][C]39.0011936487655[/C][C]-0.0311936487654521[/C][/ROW]
[ROW][C]19[/C][C]38.97[/C][C]38.8878938567608[/C][C]0.082106143239244[/C][/ROW]
[ROW][C]20[/C][C]38.95[/C][C]38.9331669547375[/C][C]0.0168330452625369[/C][/ROW]
[ROW][C]21[/C][C]38.93[/C][C]38.9174656427751[/C][C]0.0125343572248937[/C][/ROW]
[ROW][C]22[/C][C]38.76[/C][C]39.1762724059801[/C][C]-0.41627240598006[/C][/ROW]
[ROW][C]23[/C][C]38.81[/C][C]38.8723036380606[/C][C]-0.0623036380606408[/C][/ROW]
[ROW][C]24[/C][C]38.81[/C][C]38.7391803437733[/C][C]0.0708196562267389[/C][/ROW]
[ROW][C]25[/C][C]38.81[/C][C]38.7915518631967[/C][C]0.0184481368033289[/C][/ROW]
[ROW][C]26[/C][C]38.78[/C][C]38.7667399412009[/C][C]0.0132600587991476[/C][/ROW]
[ROW][C]27[/C][C]38.77[/C][C]38.7641187881626[/C][C]0.00588121183736945[/C][/ROW]
[ROW][C]28[/C][C]38.61[/C][C]38.7396801848465[/C][C]-0.129680184846549[/C][/ROW]
[ROW][C]29[/C][C]38.69[/C][C]38.7121021294304[/C][C]-0.0221021294304364[/C][/ROW]
[ROW][C]30[/C][C]38.69[/C][C]38.7230724508744[/C][C]-0.0330724508744282[/C][/ROW]
[ROW][C]31[/C][C]38.68[/C][C]38.6456678965162[/C][C]0.0343321034837558[/C][/ROW]
[ROW][C]32[/C][C]38.74[/C][C]38.6314039739534[/C][C]0.108596026046584[/C][/ROW]
[ROW][C]33[/C][C]38.73[/C][C]38.6676646215747[/C][C]0.0623353784252672[/C][/ROW]
[ROW][C]34[/C][C]38.62[/C][C]38.7956646640305[/C][C]-0.175664664030535[/C][/ROW]
[ROW][C]35[/C][C]38.57[/C][C]38.7730115744505[/C][C]-0.203011574450493[/C][/ROW]
[ROW][C]36[/C][C]38.57[/C][C]38.5976619313212[/C][C]-0.0276619313211555[/C][/ROW]
[ROW][C]37[/C][C]38.57[/C][C]38.5648328960702[/C][C]0.00516710392984265[/C][/ROW]
[ROW][C]38[/C][C]38.57[/C][C]38.5258311628366[/C][C]0.0441688371634186[/C][/ROW]
[ROW][C]39[/C][C]38.56[/C][C]38.5364065047995[/C][C]0.0235934952004797[/C][/ROW]
[ROW][C]40[/C][C]38.55[/C][C]38.4696736663617[/C][C]0.0803263336383324[/C][/ROW]
[ROW][C]41[/C][C]38.42[/C][C]38.613146249192[/C][C]-0.193146249191969[/C][/ROW]
[ROW][C]42[/C][C]38.47[/C][C]38.5092620855925[/C][C]-0.0392620855924903[/C][/ROW]
[ROW][C]43[/C][C]38.47[/C][C]38.4498381884082[/C][C]0.0201618115918478[/C][/ROW]
[ROW][C]44[/C][C]38.48[/C][C]38.450904595948[/C][C]0.0290954040519651[/C][/ROW]
[ROW][C]45[/C][C]38.45[/C][C]38.4159148282715[/C][C]0.0340851717285489[/C][/ROW]
[ROW][C]46[/C][C]38.43[/C][C]38.4338300650281[/C][C]-0.00383006502806893[/C][/ROW]
[ROW][C]47[/C][C]38.43[/C][C]38.5069344848408[/C][C]-0.0769344848407911[/C][/ROW]
[ROW][C]48[/C][C]38.48[/C][C]38.4747433502307[/C][C]0.00525664976929363[/C][/ROW]
[ROW][C]49[/C][C]38.48[/C][C]38.4740308636855[/C][C]0.00596913631446938[/C][/ROW]
[ROW][C]50[/C][C]38.48[/C][C]38.4491849421603[/C][C]0.0308150578397246[/C][/ROW]
[ROW][C]51[/C][C]38.51[/C][C]38.4428339927874[/C][C]0.0671660072126201[/C][/ROW]
[ROW][C]52[/C][C]38.48[/C][C]38.4241016791206[/C][C]0.0558983208794217[/C][/ROW]
[ROW][C]53[/C][C]38.55[/C][C]38.4504310499988[/C][C]0.0995689500012205[/C][/ROW]
[ROW][C]54[/C][C]38.55[/C][C]38.5904247729672[/C][C]-0.0404247729671923[/C][/ROW]
[ROW][C]55[/C][C]38.55[/C][C]38.5546694400758[/C][C]-0.00466944007578007[/C][/ROW]
[ROW][C]56[/C][C]38.49[/C][C]38.5455579846309[/C][C]-0.0555579846308802[/C][/ROW]
[ROW][C]57[/C][C]38.37[/C][C]38.4603014863425[/C][C]-0.0903014863425327[/C][/ROW]
[ROW][C]58[/C][C]38.14[/C][C]38.3857036971746[/C][C]-0.245703697174648[/C][/ROW]
[ROW][C]59[/C][C]38.08[/C][C]38.2766077538154[/C][C]-0.196607753815449[/C][/ROW]
[ROW][C]60[/C][C]38.04[/C][C]38.1953543672242[/C][C]-0.155354367224206[/C][/ROW]
[ROW][C]61[/C][C]38.04[/C][C]38.0879310748953[/C][C]-0.0479310748953381[/C][/ROW]
[ROW][C]62[/C][C]38.03[/C][C]38.0319932027169[/C][C]-0.00199320271686076[/C][/ROW]
[ROW][C]63[/C][C]37.98[/C][C]38.0117463272137[/C][C]-0.0317463272136891[/C][/ROW]
[ROW][C]64[/C][C]38.03[/C][C]37.9187775726697[/C][C]0.111222427330326[/C][/ROW]
[ROW][C]65[/C][C]38.05[/C][C]37.9890146346393[/C][C]0.0609853653607288[/C][/ROW]
[ROW][C]66[/C][C]38.05[/C][C]38.0454289356732[/C][C]0.00457106432675403[/C][/ROW]
[ROW][C]67[/C][C]38.05[/C][C]38.0442137098073[/C][C]0.00578629019268817[/C][/ROW]
[ROW][C]68[/C][C]38.05[/C][C]38.0159636136288[/C][C]0.0340363863711843[/C][/ROW]
[ROW][C]69[/C][C]38.02[/C][C]37.9683981536366[/C][C]0.0516018463633898[/C][/ROW]
[ROW][C]70[/C][C]38.06[/C][C]37.9214220207916[/C][C]0.138577979208414[/C][/ROW]
[ROW][C]71[/C][C]38.01[/C][C]38.0724733521928[/C][C]-0.0624733521927539[/C][/ROW]
[ROW][C]72[/C][C]38[/C][C]38.0921932789885[/C][C]-0.0921932789884963[/C][/ROW]
[ROW][C]73[/C][C]38[/C][C]38.0661228531959[/C][C]-0.0661228531959068[/C][/ROW]
[ROW][C]74[/C][C]38[/C][C]38.0173294902387[/C][C]-0.0173294902386516[/C][/ROW]
[ROW][C]75[/C][C]37.99[/C][C]37.977895794193[/C][C]0.0121042058069989[/C][/ROW]
[ROW][C]76[/C][C]37.96[/C][C]37.9673489249363[/C][C]-0.00734892493632344[/C][/ROW]
[ROW][C]77[/C][C]37.96[/C][C]37.9449334684888[/C][C]0.0150665315111596[/C][/ROW]
[ROW][C]78[/C][C]38.02[/C][C]37.951726546955[/C][C]0.0682734530450375[/C][/ROW]
[ROW][C]79[/C][C]38.02[/C][C]37.9919881918916[/C][C]0.0280118081084453[/C][/ROW]
[ROW][C]80[/C][C]38.02[/C][C]37.9892915434212[/C][C]0.0307084565787648[/C][/ROW]
[ROW][C]81[/C][C]38[/C][C]37.9471839511174[/C][C]0.0528160488825549[/C][/ROW]
[ROW][C]82[/C][C]37.93[/C][C]37.9341886285206[/C][C]-0.00418862852055923[/C][/ROW]
[ROW][C]83[/C][C]38[/C][C]37.9204781011225[/C][C]0.0795218988774806[/C][/ROW]
[ROW][C]84[/C][C]38[/C][C]38.0198185691035[/C][C]-0.0198185691034709[/C][/ROW]
[ROW][C]85[/C][C]38[/C][C]38.0508654745878[/C][C]-0.0508654745877664[/C][/ROW]
[ROW][C]86[/C][C]38[/C][C]38.0317361093852[/C][C]-0.0317361093851929[/C][/ROW]
[ROW][C]87[/C][C]38[/C][C]37.9959543406368[/C][C]0.0040456593631788[/C][/ROW]
[ROW][C]88[/C][C]38.01[/C][C]37.9749123169877[/C][C]0.0350876830122644[/C][/ROW]
[ROW][C]89[/C][C]37.98[/C][C]37.9897670532042[/C][C]-0.00976705320420024[/C][/ROW]
[ROW][C]90[/C][C]38[/C][C]38.0025243355973[/C][C]-0.00252433559729326[/C][/ROW]
[ROW][C]91[/C][C]38[/C][C]37.9844706652914[/C][C]0.0155293347085887[/C][/ROW]
[ROW][C]92[/C][C]38[/C][C]37.9759652977689[/C][C]0.0240347022311482[/C][/ROW]
[ROW][C]93[/C][C]37.95[/C][C]37.9388115184565[/C][C]0.0111884815435133[/C][/ROW]
[ROW][C]94[/C][C]37.87[/C][C]37.8790516419916[/C][C]-0.00905164199157582[/C][/ROW]
[ROW][C]95[/C][C]37.75[/C][C]37.893696513329[/C][C]-0.143696513329033[/C][/ROW]
[ROW][C]96[/C][C]37.75[/C][C]37.8136745751137[/C][C]-0.0636745751136942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232335&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232335&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	38.97	38.926124465812	0.043875534188011
14	38.95	38.9293099465314	0.0206900534686127
15	38.95	38.9380996290793	0.011900370920678
16	38.92	38.9285588955981	-0.00855889559805689
17	38.96	38.990192599127	-0.0301925991270195
18	38.97	39.0011936487655	-0.0311936487654521
19	38.97	38.8878938567608	0.082106143239244
20	38.95	38.9331669547375	0.0168330452625369
21	38.93	38.9174656427751	0.0125343572248937
22	38.76	39.1762724059801	-0.41627240598006
23	38.81	38.8723036380606	-0.0623036380606408
24	38.81	38.7391803437733	0.0708196562267389
25	38.81	38.7915518631967	0.0184481368033289
26	38.78	38.7667399412009	0.0132600587991476
27	38.77	38.7641187881626	0.00588121183736945
28	38.61	38.7396801848465	-0.129680184846549
29	38.69	38.7121021294304	-0.0221021294304364
30	38.69	38.7230724508744	-0.0330724508744282
31	38.68	38.6456678965162	0.0343321034837558
32	38.74	38.6314039739534	0.108596026046584
33	38.73	38.6676646215747	0.0623353784252672
34	38.62	38.7956646640305	-0.175664664030535
35	38.57	38.7730115744505	-0.203011574450493
36	38.57	38.5976619313212	-0.0276619313211555
37	38.57	38.5648328960702	0.00516710392984265
38	38.57	38.5258311628366	0.0441688371634186
39	38.56	38.5364065047995	0.0235934952004797
40	38.55	38.4696736663617	0.0803263336383324
41	38.42	38.613146249192	-0.193146249191969
42	38.47	38.5092620855925	-0.0392620855924903
43	38.47	38.4498381884082	0.0201618115918478
44	38.48	38.450904595948	0.0290954040519651
45	38.45	38.4159148282715	0.0340851717285489
46	38.43	38.4338300650281	-0.00383006502806893
47	38.43	38.5069344848408	-0.0769344848407911
48	38.48	38.4747433502307	0.00525664976929363
49	38.48	38.4740308636855	0.00596913631446938
50	38.48	38.4491849421603	0.0308150578397246
51	38.51	38.4428339927874	0.0671660072126201
52	38.48	38.4241016791206	0.0558983208794217
53	38.55	38.4504310499988	0.0995689500012205
54	38.55	38.5904247729672	-0.0404247729671923
55	38.55	38.5546694400758	-0.00466944007578007
56	38.49	38.5455579846309	-0.0555579846308802
57	38.37	38.4603014863425	-0.0903014863425327
58	38.14	38.3857036971746	-0.245703697174648
59	38.08	38.2766077538154	-0.196607753815449
60	38.04	38.1953543672242	-0.155354367224206
61	38.04	38.0879310748953	-0.0479310748953381
62	38.03	38.0319932027169	-0.00199320271686076
63	37.98	38.0117463272137	-0.0317463272136891
64	38.03	37.9187775726697	0.111222427330326
65	38.05	37.9890146346393	0.0609853653607288
66	38.05	38.0454289356732	0.00457106432675403
67	38.05	38.0442137098073	0.00578629019268817
68	38.05	38.0159636136288	0.0340363863711843
69	38.02	37.9683981536366	0.0516018463633898
70	38.06	37.9214220207916	0.138577979208414
71	38.01	38.0724733521928	-0.0624733521927539
72	38	38.0921932789885	-0.0921932789884963
73	38	38.0661228531959	-0.0661228531959068
74	38	38.0173294902387	-0.0173294902386516
75	37.99	37.977895794193	0.0121042058069989
76	37.96	37.9673489249363	-0.00734892493632344
77	37.96	37.9449334684888	0.0150665315111596
78	38.02	37.951726546955	0.0682734530450375
79	38.02	37.9919881918916	0.0280118081084453
80	38.02	37.9892915434212	0.0307084565787648
81	38	37.9471839511174	0.0528160488825549
82	37.93	37.9341886285206	-0.00418862852055923
83	38	37.9204781011225	0.0795218988774806
84	38	38.0198185691035	-0.0198185691034709
85	38	38.0508654745878	-0.0508654745877664
86	38	38.0317361093852	-0.0317361093851929
87	38	37.9959543406368	0.0040456593631788
88	38.01	37.9749123169877	0.0350876830122644
89	37.98	37.9897670532042	-0.00976705320420024
90	38	38.0025243355973	-0.00252433559729326
91	38	37.9844706652914	0.0155293347085887
92	38	37.9759652977689	0.0240347022311482
93	37.95	37.9388115184565	0.0111884815435133
94	37.87	37.8790516419916	-0.00905164199157582
95	37.75	37.893696513329	-0.143696513329033
96	37.75	37.8136745751137	-0.0636745751136942

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	37.8032107567834	37.6358828439836	37.9705386695831
98	37.8213819503343	37.6226018560876	38.0201620445811
99	37.8173342496017	37.5905769629837	38.0440915362198
100	37.8036703553597	37.5512398429666	38.0561008677527
101	37.7779098937518	37.5014556928164	38.0543640946871
102	37.7976880716667	37.4984512731174	38.0969248702159
103	37.7861102917717	37.4650575197097	38.1071630638338
104	37.7690022831298	37.4269056631067	38.1110989031529
105	37.7097349150537	37.3472230997406	38.0722467303668
106	37.6331086879726	37.250701119313	38.0155162566322
107	37.6014761516656	37.1996070136381	38.0033452896931
108	37.6409376208766	37.2199731419448	38.0619020998083

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 37.8032107567834 & 37.6358828439836 & 37.9705386695831 \tabularnewline
98 & 37.8213819503343 & 37.6226018560876 & 38.0201620445811 \tabularnewline
99 & 37.8173342496017 & 37.5905769629837 & 38.0440915362198 \tabularnewline
100 & 37.8036703553597 & 37.5512398429666 & 38.0561008677527 \tabularnewline
101 & 37.7779098937518 & 37.5014556928164 & 38.0543640946871 \tabularnewline
102 & 37.7976880716667 & 37.4984512731174 & 38.0969248702159 \tabularnewline
103 & 37.7861102917717 & 37.4650575197097 & 38.1071630638338 \tabularnewline
104 & 37.7690022831298 & 37.4269056631067 & 38.1110989031529 \tabularnewline
105 & 37.7097349150537 & 37.3472230997406 & 38.0722467303668 \tabularnewline
106 & 37.6331086879726 & 37.250701119313 & 38.0155162566322 \tabularnewline
107 & 37.6014761516656 & 37.1996070136381 & 38.0033452896931 \tabularnewline
108 & 37.6409376208766 & 37.2199731419448 & 38.0619020998083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232335&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]97[/C][C]37.8032107567834[/C][C]37.6358828439836[/C][C]37.9705386695831[/C][/ROW]
[ROW][C]98[/C][C]37.8213819503343[/C][C]37.6226018560876[/C][C]38.0201620445811[/C][/ROW]
[ROW][C]99[/C][C]37.8173342496017[/C][C]37.5905769629837[/C][C]38.0440915362198[/C][/ROW]
[ROW][C]100[/C][C]37.8036703553597[/C][C]37.5512398429666[/C][C]38.0561008677527[/C][/ROW]
[ROW][C]101[/C][C]37.7779098937518[/C][C]37.5014556928164[/C][C]38.0543640946871[/C][/ROW]
[ROW][C]102[/C][C]37.7976880716667[/C][C]37.4984512731174[/C][C]38.0969248702159[/C][/ROW]
[ROW][C]103[/C][C]37.7861102917717[/C][C]37.4650575197097[/C][C]38.1071630638338[/C][/ROW]
[ROW][C]104[/C][C]37.7690022831298[/C][C]37.4269056631067[/C][C]38.1110989031529[/C][/ROW]
[ROW][C]105[/C][C]37.7097349150537[/C][C]37.3472230997406[/C][C]38.0722467303668[/C][/ROW]
[ROW][C]106[/C][C]37.6331086879726[/C][C]37.250701119313[/C][C]38.0155162566322[/C][/ROW]
[ROW][C]107[/C][C]37.6014761516656[/C][C]37.1996070136381[/C][C]38.0033452896931[/C][/ROW]
[ROW][C]108[/C][C]37.6409376208766[/C][C]37.2199731419448[/C][C]38.0619020998083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232335&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232335&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
97	37.8032107567834	37.6358828439836	37.9705386695831
98	37.8213819503343	37.6226018560876	38.0201620445811
99	37.8173342496017	37.5905769629837	38.0440915362198
100	37.8036703553597	37.5512398429666	38.0561008677527
101	37.7779098937518	37.5014556928164	38.0543640946871
102	37.7976880716667	37.4984512731174	38.0969248702159
103	37.7861102917717	37.4650575197097	38.1071630638338
104	37.7690022831298	37.4269056631067	38.1110989031529
105	37.7097349150537	37.3472230997406	38.0722467303668
106	37.6331086879726	37.250701119313	38.0155162566322
107	37.6014761516656	37.1996070136381	38.0033452896931
108	37.6409376208766	37.2199731419448	38.0619020998083

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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