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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 29 Nov 2015 12:29:23 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448800206ja1asg3wnoirql5.htm/, Retrieved Wed, 15 May 2024 05:36:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284418, Retrieved Wed, 15 May 2024 05:36:36 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-11-29 12:29:23] [e897088c3d9e15a1e92009c0481cb133] [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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284418&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284418&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284418&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0214832940592476
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0214832940592476 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284418&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0214832940592476[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284418&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284418&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	1
beta	0.0214832940592476
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	97.33	97.23	0.100000000000009
4	97.38	97.2421483294059	0.137851670594074
5	97.47	97.2951098373818	0.174890162618155
6	97.5	97.3888670541734	0.111132945826554
7	97.5	97.4212545559283	0.0787454440716857
8	97.58	97.4229462674591	0.157053732540874
9	97.7	97.5063202989784	0.193679701021594
10	97.9	97.6304811769488	0.269518823051243
11	97.98	97.8362713290789	0.143728670921121
12	98.03	97.919359094381	0.110640905618979
13	98.03	97.9717360254914	0.0582639745085913
14	97.94	97.9729877275888	-0.0329877275888464
15	98.12	97.8822790425367	0.23772095746331
16	98.19	98.0673860717699	0.122613928230066
17	98.34	98.1400202228458	0.199979777154155
18	98.42	98.2943164472044	0.125683552795635
19	98.43	98.3770165439275	0.0529834560725249
20	98.45	98.3881548030946	0.0618451969054377
21	98.77	98.4094834416458	0.360516558354163
22	99.24	98.7372285248822	0.502771475117811
23	99.46	99.2180297123267	0.241970287673254
24	99.54	99.4432280311704	0.0967719688295858
25	99.55	99.5253070118335	0.0246929881665068
26	99.24	99.5358374985595	-0.295837498559465
27	99.43	99.2194819345842	0.210518065415854
28	99.47	99.4140045560883	0.0559954439117121
29	99.57	99.4552075226758	0.114792477324187
30	99.62	99.5576736432219	0.0623263567780583
31	99.64	99.6090126186723	0.0309873813277335
32	99.75	99.6296783296975	0.120321670302545
33	99.85	99.7422632355223	0.107736764477735
34	100.28	99.8445777761145	0.435422223885482
35	100.52	100.28393207979	0.236067920209805
36	100.57	100.529003596338	0.0409964036619925
37	100.57	100.579884334133	-0.00988433413324685
38	100.27	100.579671986076	-0.309671986076481
39	100.27	100.273019211738	-0.00301921173769415
40	100.18	100.272954349124	-0.0929543491240992
41	100.16	100.180957383508	-0.0209573835078061
42	100.18	100.160507149875	0.0194928501248341
43	100.18	100.180925920506	-0.000925920506460898
44	100.59	100.180906028684	0.409093971316054
45	100.69	100.599694714768	0.0903052852324038
46	101.06	100.701634769765	0.358365230234654
47	101.15	101.079333635387	0.0706663646129186
48	101.16	101.170851781678	-0.0108517816781699
49	101.16	101.180618649661	-0.0206186496613014
50	100.81	101.180175693148	-0.370175693147516
51	100.94	100.822223099878	0.117776900121939
52	101.13	100.954753335657	0.175246664343234
53	101.29	101.14851821128	0.141481788720256
54	101.34	101.311557706151	0.0284422938491389
55	101.35	101.362168740313	-0.0121687403133421
56	101.7	101.371907315687	0.328092684313162
57	102.05	101.728955827303	0.321044172697356
58	102.48	102.085852913671	0.394147086329298
59	102.66	102.524320491429	0.135679508571073
60	102.72	102.707235334209	0.0127646657906411
61	102.73	102.767509561278	-0.0375095612780996
62	102.18	102.776703732343	-0.59670373234313
63	102.22	102.213884570595	0.00611542940502829
64	102.37	102.254015950163	0.11598404983684
65	102.53	102.406507669612	0.123492330388004
66	102.61	102.56916069166	0.0408393083402103
67	102.62	102.65003805453	-0.0300380545300243
68	103	102.659392738172	0.340607261828396
69	103.17	103.046710104136	0.123289895863834
70	103.52	103.219358777224	0.300641222776449
71	103.69	103.575817541019	0.114182458981219
72	103.73	103.748270556361	-0.0182705563614718
73	99.57	103.787878044627	-4.21787804462656
74	99.09	99.5372641302878	-0.447264130287778
75	99.14	99.0476554234547	0.0923445765453295
76	99.36	99.0996392891474	0.260360710852638
77	99.6	99.3252326948601	0.274767305139903
78	99.65	99.5711356016743	0.0788643983257344
79	99.8	99.6228298687343	0.177170131265683
80	100.15	99.7766360667628	0.373363933237201
81	100.45	100.134657153932	0.315342846068333
82	100.89	100.441431757023	0.448568242976776
83	101.13	100.891068480493	0.238931519507261
84	101.17	101.136201516586	0.0337984834136762
85	101.21	101.176927619344	0.0330723806557245
86	101.1	101.217638123023	-0.117638123023127
87	101.17	101.105110868634	0.0648891313663569
88	101.11	101.176504900924	-0.0665049009240448
89	101.2	101.115076156581	0.0849238434188919
90	101.15	101.206900600482	-0.0569006004819101
91	100.92	101.15567818815	-0.23567818814962
92	101.1	100.92061504433	0.179384955669747
93	101.22	101.104468824083	0.115531175917297
94	101.25	101.226950814308	0.0230491856920594
95	101.39	101.257445986742	0.132554013258002
96	101.43	101.400293683588	0.029706316412458

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 97.33 & 97.23 & 0.100000000000009 \tabularnewline
4 & 97.38 & 97.2421483294059 & 0.137851670594074 \tabularnewline
5 & 97.47 & 97.2951098373818 & 0.174890162618155 \tabularnewline
6 & 97.5 & 97.3888670541734 & 0.111132945826554 \tabularnewline
7 & 97.5 & 97.4212545559283 & 0.0787454440716857 \tabularnewline
8 & 97.58 & 97.4229462674591 & 0.157053732540874 \tabularnewline
9 & 97.7 & 97.5063202989784 & 0.193679701021594 \tabularnewline
10 & 97.9 & 97.6304811769488 & 0.269518823051243 \tabularnewline
11 & 97.98 & 97.8362713290789 & 0.143728670921121 \tabularnewline
12 & 98.03 & 97.919359094381 & 0.110640905618979 \tabularnewline
13 & 98.03 & 97.9717360254914 & 0.0582639745085913 \tabularnewline
14 & 97.94 & 97.9729877275888 & -0.0329877275888464 \tabularnewline
15 & 98.12 & 97.8822790425367 & 0.23772095746331 \tabularnewline
16 & 98.19 & 98.0673860717699 & 0.122613928230066 \tabularnewline
17 & 98.34 & 98.1400202228458 & 0.199979777154155 \tabularnewline
18 & 98.42 & 98.2943164472044 & 0.125683552795635 \tabularnewline
19 & 98.43 & 98.3770165439275 & 0.0529834560725249 \tabularnewline
20 & 98.45 & 98.3881548030946 & 0.0618451969054377 \tabularnewline
21 & 98.77 & 98.4094834416458 & 0.360516558354163 \tabularnewline
22 & 99.24 & 98.7372285248822 & 0.502771475117811 \tabularnewline
23 & 99.46 & 99.2180297123267 & 0.241970287673254 \tabularnewline
24 & 99.54 & 99.4432280311704 & 0.0967719688295858 \tabularnewline
25 & 99.55 & 99.5253070118335 & 0.0246929881665068 \tabularnewline
26 & 99.24 & 99.5358374985595 & -0.295837498559465 \tabularnewline
27 & 99.43 & 99.2194819345842 & 0.210518065415854 \tabularnewline
28 & 99.47 & 99.4140045560883 & 0.0559954439117121 \tabularnewline
29 & 99.57 & 99.4552075226758 & 0.114792477324187 \tabularnewline
30 & 99.62 & 99.5576736432219 & 0.0623263567780583 \tabularnewline
31 & 99.64 & 99.6090126186723 & 0.0309873813277335 \tabularnewline
32 & 99.75 & 99.6296783296975 & 0.120321670302545 \tabularnewline
33 & 99.85 & 99.7422632355223 & 0.107736764477735 \tabularnewline
34 & 100.28 & 99.8445777761145 & 0.435422223885482 \tabularnewline
35 & 100.52 & 100.28393207979 & 0.236067920209805 \tabularnewline
36 & 100.57 & 100.529003596338 & 0.0409964036619925 \tabularnewline
37 & 100.57 & 100.579884334133 & -0.00988433413324685 \tabularnewline
38 & 100.27 & 100.579671986076 & -0.309671986076481 \tabularnewline
39 & 100.27 & 100.273019211738 & -0.00301921173769415 \tabularnewline
40 & 100.18 & 100.272954349124 & -0.0929543491240992 \tabularnewline
41 & 100.16 & 100.180957383508 & -0.0209573835078061 \tabularnewline
42 & 100.18 & 100.160507149875 & 0.0194928501248341 \tabularnewline
43 & 100.18 & 100.180925920506 & -0.000925920506460898 \tabularnewline
44 & 100.59 & 100.180906028684 & 0.409093971316054 \tabularnewline
45 & 100.69 & 100.599694714768 & 0.0903052852324038 \tabularnewline
46 & 101.06 & 100.701634769765 & 0.358365230234654 \tabularnewline
47 & 101.15 & 101.079333635387 & 0.0706663646129186 \tabularnewline
48 & 101.16 & 101.170851781678 & -0.0108517816781699 \tabularnewline
49 & 101.16 & 101.180618649661 & -0.0206186496613014 \tabularnewline
50 & 100.81 & 101.180175693148 & -0.370175693147516 \tabularnewline
51 & 100.94 & 100.822223099878 & 0.117776900121939 \tabularnewline
52 & 101.13 & 100.954753335657 & 0.175246664343234 \tabularnewline
53 & 101.29 & 101.14851821128 & 0.141481788720256 \tabularnewline
54 & 101.34 & 101.311557706151 & 0.0284422938491389 \tabularnewline
55 & 101.35 & 101.362168740313 & -0.0121687403133421 \tabularnewline
56 & 101.7 & 101.371907315687 & 0.328092684313162 \tabularnewline
57 & 102.05 & 101.728955827303 & 0.321044172697356 \tabularnewline
58 & 102.48 & 102.085852913671 & 0.394147086329298 \tabularnewline
59 & 102.66 & 102.524320491429 & 0.135679508571073 \tabularnewline
60 & 102.72 & 102.707235334209 & 0.0127646657906411 \tabularnewline
61 & 102.73 & 102.767509561278 & -0.0375095612780996 \tabularnewline
62 & 102.18 & 102.776703732343 & -0.59670373234313 \tabularnewline
63 & 102.22 & 102.213884570595 & 0.00611542940502829 \tabularnewline
64 & 102.37 & 102.254015950163 & 0.11598404983684 \tabularnewline
65 & 102.53 & 102.406507669612 & 0.123492330388004 \tabularnewline
66 & 102.61 & 102.56916069166 & 0.0408393083402103 \tabularnewline
67 & 102.62 & 102.65003805453 & -0.0300380545300243 \tabularnewline
68 & 103 & 102.659392738172 & 0.340607261828396 \tabularnewline
69 & 103.17 & 103.046710104136 & 0.123289895863834 \tabularnewline
70 & 103.52 & 103.219358777224 & 0.300641222776449 \tabularnewline
71 & 103.69 & 103.575817541019 & 0.114182458981219 \tabularnewline
72 & 103.73 & 103.748270556361 & -0.0182705563614718 \tabularnewline
73 & 99.57 & 103.787878044627 & -4.21787804462656 \tabularnewline
74 & 99.09 & 99.5372641302878 & -0.447264130287778 \tabularnewline
75 & 99.14 & 99.0476554234547 & 0.0923445765453295 \tabularnewline
76 & 99.36 & 99.0996392891474 & 0.260360710852638 \tabularnewline
77 & 99.6 & 99.3252326948601 & 0.274767305139903 \tabularnewline
78 & 99.65 & 99.5711356016743 & 0.0788643983257344 \tabularnewline
79 & 99.8 & 99.6228298687343 & 0.177170131265683 \tabularnewline
80 & 100.15 & 99.7766360667628 & 0.373363933237201 \tabularnewline
81 & 100.45 & 100.134657153932 & 0.315342846068333 \tabularnewline
82 & 100.89 & 100.441431757023 & 0.448568242976776 \tabularnewline
83 & 101.13 & 100.891068480493 & 0.238931519507261 \tabularnewline
84 & 101.17 & 101.136201516586 & 0.0337984834136762 \tabularnewline
85 & 101.21 & 101.176927619344 & 0.0330723806557245 \tabularnewline
86 & 101.1 & 101.217638123023 & -0.117638123023127 \tabularnewline
87 & 101.17 & 101.105110868634 & 0.0648891313663569 \tabularnewline
88 & 101.11 & 101.176504900924 & -0.0665049009240448 \tabularnewline
89 & 101.2 & 101.115076156581 & 0.0849238434188919 \tabularnewline
90 & 101.15 & 101.206900600482 & -0.0569006004819101 \tabularnewline
91 & 100.92 & 101.15567818815 & -0.23567818814962 \tabularnewline
92 & 101.1 & 100.92061504433 & 0.179384955669747 \tabularnewline
93 & 101.22 & 101.104468824083 & 0.115531175917297 \tabularnewline
94 & 101.25 & 101.226950814308 & 0.0230491856920594 \tabularnewline
95 & 101.39 & 101.257445986742 & 0.132554013258002 \tabularnewline
96 & 101.43 & 101.400293683588 & 0.029706316412458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284418&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]97.33[/C][C]97.23[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]4[/C][C]97.38[/C][C]97.2421483294059[/C][C]0.137851670594074[/C][/ROW]
[ROW][C]5[/C][C]97.47[/C][C]97.2951098373818[/C][C]0.174890162618155[/C][/ROW]
[ROW][C]6[/C][C]97.5[/C][C]97.3888670541734[/C][C]0.111132945826554[/C][/ROW]
[ROW][C]7[/C][C]97.5[/C][C]97.4212545559283[/C][C]0.0787454440716857[/C][/ROW]
[ROW][C]8[/C][C]97.58[/C][C]97.4229462674591[/C][C]0.157053732540874[/C][/ROW]
[ROW][C]9[/C][C]97.7[/C][C]97.5063202989784[/C][C]0.193679701021594[/C][/ROW]
[ROW][C]10[/C][C]97.9[/C][C]97.6304811769488[/C][C]0.269518823051243[/C][/ROW]
[ROW][C]11[/C][C]97.98[/C][C]97.8362713290789[/C][C]0.143728670921121[/C][/ROW]
[ROW][C]12[/C][C]98.03[/C][C]97.919359094381[/C][C]0.110640905618979[/C][/ROW]
[ROW][C]13[/C][C]98.03[/C][C]97.9717360254914[/C][C]0.0582639745085913[/C][/ROW]
[ROW][C]14[/C][C]97.94[/C][C]97.9729877275888[/C][C]-0.0329877275888464[/C][/ROW]
[ROW][C]15[/C][C]98.12[/C][C]97.8822790425367[/C][C]0.23772095746331[/C][/ROW]
[ROW][C]16[/C][C]98.19[/C][C]98.0673860717699[/C][C]0.122613928230066[/C][/ROW]
[ROW][C]17[/C][C]98.34[/C][C]98.1400202228458[/C][C]0.199979777154155[/C][/ROW]
[ROW][C]18[/C][C]98.42[/C][C]98.2943164472044[/C][C]0.125683552795635[/C][/ROW]
[ROW][C]19[/C][C]98.43[/C][C]98.3770165439275[/C][C]0.0529834560725249[/C][/ROW]
[ROW][C]20[/C][C]98.45[/C][C]98.3881548030946[/C][C]0.0618451969054377[/C][/ROW]
[ROW][C]21[/C][C]98.77[/C][C]98.4094834416458[/C][C]0.360516558354163[/C][/ROW]
[ROW][C]22[/C][C]99.24[/C][C]98.7372285248822[/C][C]0.502771475117811[/C][/ROW]
[ROW][C]23[/C][C]99.46[/C][C]99.2180297123267[/C][C]0.241970287673254[/C][/ROW]
[ROW][C]24[/C][C]99.54[/C][C]99.4432280311704[/C][C]0.0967719688295858[/C][/ROW]
[ROW][C]25[/C][C]99.55[/C][C]99.5253070118335[/C][C]0.0246929881665068[/C][/ROW]
[ROW][C]26[/C][C]99.24[/C][C]99.5358374985595[/C][C]-0.295837498559465[/C][/ROW]
[ROW][C]27[/C][C]99.43[/C][C]99.2194819345842[/C][C]0.210518065415854[/C][/ROW]
[ROW][C]28[/C][C]99.47[/C][C]99.4140045560883[/C][C]0.0559954439117121[/C][/ROW]
[ROW][C]29[/C][C]99.57[/C][C]99.4552075226758[/C][C]0.114792477324187[/C][/ROW]
[ROW][C]30[/C][C]99.62[/C][C]99.5576736432219[/C][C]0.0623263567780583[/C][/ROW]
[ROW][C]31[/C][C]99.64[/C][C]99.6090126186723[/C][C]0.0309873813277335[/C][/ROW]
[ROW][C]32[/C][C]99.75[/C][C]99.6296783296975[/C][C]0.120321670302545[/C][/ROW]
[ROW][C]33[/C][C]99.85[/C][C]99.7422632355223[/C][C]0.107736764477735[/C][/ROW]
[ROW][C]34[/C][C]100.28[/C][C]99.8445777761145[/C][C]0.435422223885482[/C][/ROW]
[ROW][C]35[/C][C]100.52[/C][C]100.28393207979[/C][C]0.236067920209805[/C][/ROW]
[ROW][C]36[/C][C]100.57[/C][C]100.529003596338[/C][C]0.0409964036619925[/C][/ROW]
[ROW][C]37[/C][C]100.57[/C][C]100.579884334133[/C][C]-0.00988433413324685[/C][/ROW]
[ROW][C]38[/C][C]100.27[/C][C]100.579671986076[/C][C]-0.309671986076481[/C][/ROW]
[ROW][C]39[/C][C]100.27[/C][C]100.273019211738[/C][C]-0.00301921173769415[/C][/ROW]
[ROW][C]40[/C][C]100.18[/C][C]100.272954349124[/C][C]-0.0929543491240992[/C][/ROW]
[ROW][C]41[/C][C]100.16[/C][C]100.180957383508[/C][C]-0.0209573835078061[/C][/ROW]
[ROW][C]42[/C][C]100.18[/C][C]100.160507149875[/C][C]0.0194928501248341[/C][/ROW]
[ROW][C]43[/C][C]100.18[/C][C]100.180925920506[/C][C]-0.000925920506460898[/C][/ROW]
[ROW][C]44[/C][C]100.59[/C][C]100.180906028684[/C][C]0.409093971316054[/C][/ROW]
[ROW][C]45[/C][C]100.69[/C][C]100.599694714768[/C][C]0.0903052852324038[/C][/ROW]
[ROW][C]46[/C][C]101.06[/C][C]100.701634769765[/C][C]0.358365230234654[/C][/ROW]
[ROW][C]47[/C][C]101.15[/C][C]101.079333635387[/C][C]0.0706663646129186[/C][/ROW]
[ROW][C]48[/C][C]101.16[/C][C]101.170851781678[/C][C]-0.0108517816781699[/C][/ROW]
[ROW][C]49[/C][C]101.16[/C][C]101.180618649661[/C][C]-0.0206186496613014[/C][/ROW]
[ROW][C]50[/C][C]100.81[/C][C]101.180175693148[/C][C]-0.370175693147516[/C][/ROW]
[ROW][C]51[/C][C]100.94[/C][C]100.822223099878[/C][C]0.117776900121939[/C][/ROW]
[ROW][C]52[/C][C]101.13[/C][C]100.954753335657[/C][C]0.175246664343234[/C][/ROW]
[ROW][C]53[/C][C]101.29[/C][C]101.14851821128[/C][C]0.141481788720256[/C][/ROW]
[ROW][C]54[/C][C]101.34[/C][C]101.311557706151[/C][C]0.0284422938491389[/C][/ROW]
[ROW][C]55[/C][C]101.35[/C][C]101.362168740313[/C][C]-0.0121687403133421[/C][/ROW]
[ROW][C]56[/C][C]101.7[/C][C]101.371907315687[/C][C]0.328092684313162[/C][/ROW]
[ROW][C]57[/C][C]102.05[/C][C]101.728955827303[/C][C]0.321044172697356[/C][/ROW]
[ROW][C]58[/C][C]102.48[/C][C]102.085852913671[/C][C]0.394147086329298[/C][/ROW]
[ROW][C]59[/C][C]102.66[/C][C]102.524320491429[/C][C]0.135679508571073[/C][/ROW]
[ROW][C]60[/C][C]102.72[/C][C]102.707235334209[/C][C]0.0127646657906411[/C][/ROW]
[ROW][C]61[/C][C]102.73[/C][C]102.767509561278[/C][C]-0.0375095612780996[/C][/ROW]
[ROW][C]62[/C][C]102.18[/C][C]102.776703732343[/C][C]-0.59670373234313[/C][/ROW]
[ROW][C]63[/C][C]102.22[/C][C]102.213884570595[/C][C]0.00611542940502829[/C][/ROW]
[ROW][C]64[/C][C]102.37[/C][C]102.254015950163[/C][C]0.11598404983684[/C][/ROW]
[ROW][C]65[/C][C]102.53[/C][C]102.406507669612[/C][C]0.123492330388004[/C][/ROW]
[ROW][C]66[/C][C]102.61[/C][C]102.56916069166[/C][C]0.0408393083402103[/C][/ROW]
[ROW][C]67[/C][C]102.62[/C][C]102.65003805453[/C][C]-0.0300380545300243[/C][/ROW]
[ROW][C]68[/C][C]103[/C][C]102.659392738172[/C][C]0.340607261828396[/C][/ROW]
[ROW][C]69[/C][C]103.17[/C][C]103.046710104136[/C][C]0.123289895863834[/C][/ROW]
[ROW][C]70[/C][C]103.52[/C][C]103.219358777224[/C][C]0.300641222776449[/C][/ROW]
[ROW][C]71[/C][C]103.69[/C][C]103.575817541019[/C][C]0.114182458981219[/C][/ROW]
[ROW][C]72[/C][C]103.73[/C][C]103.748270556361[/C][C]-0.0182705563614718[/C][/ROW]
[ROW][C]73[/C][C]99.57[/C][C]103.787878044627[/C][C]-4.21787804462656[/C][/ROW]
[ROW][C]74[/C][C]99.09[/C][C]99.5372641302878[/C][C]-0.447264130287778[/C][/ROW]
[ROW][C]75[/C][C]99.14[/C][C]99.0476554234547[/C][C]0.0923445765453295[/C][/ROW]
[ROW][C]76[/C][C]99.36[/C][C]99.0996392891474[/C][C]0.260360710852638[/C][/ROW]
[ROW][C]77[/C][C]99.6[/C][C]99.3252326948601[/C][C]0.274767305139903[/C][/ROW]
[ROW][C]78[/C][C]99.65[/C][C]99.5711356016743[/C][C]0.0788643983257344[/C][/ROW]
[ROW][C]79[/C][C]99.8[/C][C]99.6228298687343[/C][C]0.177170131265683[/C][/ROW]
[ROW][C]80[/C][C]100.15[/C][C]99.7766360667628[/C][C]0.373363933237201[/C][/ROW]
[ROW][C]81[/C][C]100.45[/C][C]100.134657153932[/C][C]0.315342846068333[/C][/ROW]
[ROW][C]82[/C][C]100.89[/C][C]100.441431757023[/C][C]0.448568242976776[/C][/ROW]
[ROW][C]83[/C][C]101.13[/C][C]100.891068480493[/C][C]0.238931519507261[/C][/ROW]
[ROW][C]84[/C][C]101.17[/C][C]101.136201516586[/C][C]0.0337984834136762[/C][/ROW]
[ROW][C]85[/C][C]101.21[/C][C]101.176927619344[/C][C]0.0330723806557245[/C][/ROW]
[ROW][C]86[/C][C]101.1[/C][C]101.217638123023[/C][C]-0.117638123023127[/C][/ROW]
[ROW][C]87[/C][C]101.17[/C][C]101.105110868634[/C][C]0.0648891313663569[/C][/ROW]
[ROW][C]88[/C][C]101.11[/C][C]101.176504900924[/C][C]-0.0665049009240448[/C][/ROW]
[ROW][C]89[/C][C]101.2[/C][C]101.115076156581[/C][C]0.0849238434188919[/C][/ROW]
[ROW][C]90[/C][C]101.15[/C][C]101.206900600482[/C][C]-0.0569006004819101[/C][/ROW]
[ROW][C]91[/C][C]100.92[/C][C]101.15567818815[/C][C]-0.23567818814962[/C][/ROW]
[ROW][C]92[/C][C]101.1[/C][C]100.92061504433[/C][C]0.179384955669747[/C][/ROW]
[ROW][C]93[/C][C]101.22[/C][C]101.104468824083[/C][C]0.115531175917297[/C][/ROW]
[ROW][C]94[/C][C]101.25[/C][C]101.226950814308[/C][C]0.0230491856920594[/C][/ROW]
[ROW][C]95[/C][C]101.39[/C][C]101.257445986742[/C][C]0.132554013258002[/C][/ROW]
[ROW][C]96[/C][C]101.43[/C][C]101.400293683588[/C][C]0.029706316412458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284418&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284418&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	97.33	97.23	0.100000000000009
4	97.38	97.2421483294059	0.137851670594074
5	97.47	97.2951098373818	0.174890162618155
6	97.5	97.3888670541734	0.111132945826554
7	97.5	97.4212545559283	0.0787454440716857
8	97.58	97.4229462674591	0.157053732540874
9	97.7	97.5063202989784	0.193679701021594
10	97.9	97.6304811769488	0.269518823051243
11	97.98	97.8362713290789	0.143728670921121
12	98.03	97.919359094381	0.110640905618979
13	98.03	97.9717360254914	0.0582639745085913
14	97.94	97.9729877275888	-0.0329877275888464
15	98.12	97.8822790425367	0.23772095746331
16	98.19	98.0673860717699	0.122613928230066
17	98.34	98.1400202228458	0.199979777154155
18	98.42	98.2943164472044	0.125683552795635
19	98.43	98.3770165439275	0.0529834560725249
20	98.45	98.3881548030946	0.0618451969054377
21	98.77	98.4094834416458	0.360516558354163
22	99.24	98.7372285248822	0.502771475117811
23	99.46	99.2180297123267	0.241970287673254
24	99.54	99.4432280311704	0.0967719688295858
25	99.55	99.5253070118335	0.0246929881665068
26	99.24	99.5358374985595	-0.295837498559465
27	99.43	99.2194819345842	0.210518065415854
28	99.47	99.4140045560883	0.0559954439117121
29	99.57	99.4552075226758	0.114792477324187
30	99.62	99.5576736432219	0.0623263567780583
31	99.64	99.6090126186723	0.0309873813277335
32	99.75	99.6296783296975	0.120321670302545
33	99.85	99.7422632355223	0.107736764477735
34	100.28	99.8445777761145	0.435422223885482
35	100.52	100.28393207979	0.236067920209805
36	100.57	100.529003596338	0.0409964036619925
37	100.57	100.579884334133	-0.00988433413324685
38	100.27	100.579671986076	-0.309671986076481
39	100.27	100.273019211738	-0.00301921173769415
40	100.18	100.272954349124	-0.0929543491240992
41	100.16	100.180957383508	-0.0209573835078061
42	100.18	100.160507149875	0.0194928501248341
43	100.18	100.180925920506	-0.000925920506460898
44	100.59	100.180906028684	0.409093971316054
45	100.69	100.599694714768	0.0903052852324038
46	101.06	100.701634769765	0.358365230234654
47	101.15	101.079333635387	0.0706663646129186
48	101.16	101.170851781678	-0.0108517816781699
49	101.16	101.180618649661	-0.0206186496613014
50	100.81	101.180175693148	-0.370175693147516
51	100.94	100.822223099878	0.117776900121939
52	101.13	100.954753335657	0.175246664343234
53	101.29	101.14851821128	0.141481788720256
54	101.34	101.311557706151	0.0284422938491389
55	101.35	101.362168740313	-0.0121687403133421
56	101.7	101.371907315687	0.328092684313162
57	102.05	101.728955827303	0.321044172697356
58	102.48	102.085852913671	0.394147086329298
59	102.66	102.524320491429	0.135679508571073
60	102.72	102.707235334209	0.0127646657906411
61	102.73	102.767509561278	-0.0375095612780996
62	102.18	102.776703732343	-0.59670373234313
63	102.22	102.213884570595	0.00611542940502829
64	102.37	102.254015950163	0.11598404983684
65	102.53	102.406507669612	0.123492330388004
66	102.61	102.56916069166	0.0408393083402103
67	102.62	102.65003805453	-0.0300380545300243
68	103	102.659392738172	0.340607261828396
69	103.17	103.046710104136	0.123289895863834
70	103.52	103.219358777224	0.300641222776449
71	103.69	103.575817541019	0.114182458981219
72	103.73	103.748270556361	-0.0182705563614718
73	99.57	103.787878044627	-4.21787804462656
74	99.09	99.5372641302878	-0.447264130287778
75	99.14	99.0476554234547	0.0923445765453295
76	99.36	99.0996392891474	0.260360710852638
77	99.6	99.3252326948601	0.274767305139903
78	99.65	99.5711356016743	0.0788643983257344
79	99.8	99.6228298687343	0.177170131265683
80	100.15	99.7766360667628	0.373363933237201
81	100.45	100.134657153932	0.315342846068333
82	100.89	100.441431757023	0.448568242976776
83	101.13	100.891068480493	0.238931519507261
84	101.17	101.136201516586	0.0337984834136762
85	101.21	101.176927619344	0.0330723806557245
86	101.1	101.217638123023	-0.117638123023127
87	101.17	101.105110868634	0.0648891313663569
88	101.11	101.176504900924	-0.0665049009240448
89	101.2	101.115076156581	0.0849238434188919
90	101.15	101.206900600482	-0.0569006004819101
91	100.92	101.15567818815	-0.23567818814962
92	101.1	100.92061504433	0.179384955669747
93	101.22	101.104468824083	0.115531175917297
94	101.25	101.226950814308	0.0230491856920594
95	101.39	101.257445986742	0.132554013258002
96	101.43	101.400293683588	0.029706316412458

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	101.440931873118	100.49887952903	102.382984217207
98	101.451863746237	100.10521380243	102.798513690044
99	101.462795619355	99.795813453548	103.129777785163
100	101.473727492474	99.5283811959103	103.419073789037
101	101.484659365592	99.2867255010013	103.682593230183
102	101.495591238711	99.0626358539025	103.928546623519
103	101.506523111829	98.8512891687902	104.161757054868
104	101.517454984948	98.6495779615777	104.385332008318
105	101.528386858066	98.4553679717189	104.601405744413
106	101.539318731185	98.2671228567073	104.811514605662
107	101.550250604303	98.0836961043519	105.016805104254
108	101.561182477421	97.9042073556765	105.218157599167

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 101.440931873118 & 100.49887952903 & 102.382984217207 \tabularnewline
98 & 101.451863746237 & 100.10521380243 & 102.798513690044 \tabularnewline
99 & 101.462795619355 & 99.795813453548 & 103.129777785163 \tabularnewline
100 & 101.473727492474 & 99.5283811959103 & 103.419073789037 \tabularnewline
101 & 101.484659365592 & 99.2867255010013 & 103.682593230183 \tabularnewline
102 & 101.495591238711 & 99.0626358539025 & 103.928546623519 \tabularnewline
103 & 101.506523111829 & 98.8512891687902 & 104.161757054868 \tabularnewline
104 & 101.517454984948 & 98.6495779615777 & 104.385332008318 \tabularnewline
105 & 101.528386858066 & 98.4553679717189 & 104.601405744413 \tabularnewline
106 & 101.539318731185 & 98.2671228567073 & 104.811514605662 \tabularnewline
107 & 101.550250604303 & 98.0836961043519 & 105.016805104254 \tabularnewline
108 & 101.561182477421 & 97.9042073556765 & 105.218157599167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284418&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]101.440931873118[/C][C]100.49887952903[/C][C]102.382984217207[/C][/ROW]
[ROW][C]98[/C][C]101.451863746237[/C][C]100.10521380243[/C][C]102.798513690044[/C][/ROW]
[ROW][C]99[/C][C]101.462795619355[/C][C]99.795813453548[/C][C]103.129777785163[/C][/ROW]
[ROW][C]100[/C][C]101.473727492474[/C][C]99.5283811959103[/C][C]103.419073789037[/C][/ROW]
[ROW][C]101[/C][C]101.484659365592[/C][C]99.2867255010013[/C][C]103.682593230183[/C][/ROW]
[ROW][C]102[/C][C]101.495591238711[/C][C]99.0626358539025[/C][C]103.928546623519[/C][/ROW]
[ROW][C]103[/C][C]101.506523111829[/C][C]98.8512891687902[/C][C]104.161757054868[/C][/ROW]
[ROW][C]104[/C][C]101.517454984948[/C][C]98.6495779615777[/C][C]104.385332008318[/C][/ROW]
[ROW][C]105[/C][C]101.528386858066[/C][C]98.4553679717189[/C][C]104.601405744413[/C][/ROW]
[ROW][C]106[/C][C]101.539318731185[/C][C]98.2671228567073[/C][C]104.811514605662[/C][/ROW]
[ROW][C]107[/C][C]101.550250604303[/C][C]98.0836961043519[/C][C]105.016805104254[/C][/ROW]
[ROW][C]108[/C][C]101.561182477421[/C][C]97.9042073556765[/C][C]105.218157599167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284418&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284418&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	101.440931873118	100.49887952903	102.382984217207
98	101.451863746237	100.10521380243	102.798513690044
99	101.462795619355	99.795813453548	103.129777785163
100	101.473727492474	99.5283811959103	103.419073789037
101	101.484659365592	99.2867255010013	103.682593230183
102	101.495591238711	99.0626358539025	103.928546623519
103	101.506523111829	98.8512891687902	104.161757054868
104	101.517454984948	98.6495779615777	104.385332008318
105	101.528386858066	98.4553679717189	104.601405744413
106	101.539318731185	98.2671228567073	104.811514605662
107	101.550250604303	98.0836961043519	105.016805104254
108	101.561182477421	97.9042073556765	105.218157599167

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