Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 29 Nov 2015 10:05:57 +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/2015/Nov/29/t14487915927sbsydaplwq6358.htm/, Retrieved Wed, 22 May 2024 03:05:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284401, Retrieved Wed, 22 May 2024 03:05:43 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

146

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

-       [Exponential Smoothing] [] [2015-11-29 10:05:57] [9337274ae6f8d164202b783ce953e57d] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=284401&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=284401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284401&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	0.910656099546388
beta	0.0308404236024571
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.910656099546388 \tabularnewline
beta & 0.0308404236024571 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284401&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]0.910656099546388[/C][/ROW]
[ROW][C]beta[/C][C]0.0308404236024571[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284401&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	0.910656099546388
beta	0.0308404236024571
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	81.03	81.36	-0.330000000000013
4	81.6	81.5102154305939	0.0897845694061346
5	81.56	82.0452318412283	-0.485231841228313
6	82.08	82.0429783042787	0.0370216957213358
7	83.44	82.5173578913217	0.922642108678318
8	83.55	83.8241455312584	-0.27414553125837
9	82.63	84.0333718243334	-1.40337182433338
10	82.43	83.1748475802854	-0.744847580285423
11	82.42	82.8950933966893	-0.475093396689346
12	82.48	82.8476494982789	-0.36764949827888
13	82.51	82.887724597852	-0.377724597851994
14	83.23	82.9080163437107	0.321983656289305
15	83.41	83.5745445964896	-0.164544596489606
16	83.88	83.7933916900125	0.0866083099875397
17	83.96	84.2433851058441	-0.283385105844118
18	84.32	84.3484828844293	-0.0284828844292662
19	85.82	84.6849089833587	1.13509101664127
20	85.72	86.1128298063233	-0.392829806323334
21	84.36	86.1383075793167	-1.77830757931666
22	84.36	84.8521477638544	-0.492147763854419
23	84.36	84.7234152496094	-0.363415249609375
24	85.08	84.7017072601666	0.378292739833427
25	84.95	85.3660645345056	-0.416064534505594
26	85.62	85.2953503310315	0.324649668968476
27	86.22	85.9082898273743	0.311710172625681
28	86.4	86.5182002788382	-0.11820027883816
29	86.71	86.7332904982384	-0.0232904982383673
30	87.51	87.0341567741426	0.475843225857361
31	89.22	87.8029262868354	1.4170737131646
32	89.43	89.4686316272596	-0.0386316272595479
33	88.24	89.8076050502652	-1.56760505026517
34	88.9	88.7101832805874	0.189816719412619
35	88.78	89.2184993712779	-0.438499371277928
36	89.25	89.1423203179843	0.107679682015657
37	88.8	89.5665467370256	-0.766546737025621
38	89.46	89.1731250548446	0.286874945155347
39	89.66	89.74706514147	-0.0870651414699921
40	90.29	89.9780291811172	0.311970818882784
41	90.08	90.581139458644	-0.501139458644047
42	90.42	90.4297113906855	-0.00971139068548155
43	92.14	90.7255325457013	1.41446745429866
44	92.09	92.358016199301	-0.268016199300959
45	91.35	92.4508086110812	-1.10080861108118
46	91.22	91.7542973017067	-0.534297301706715
47	90.99	91.5586772213432	-0.56867722134325
48	91.48	91.315777546402	0.164222453598001
49	90.98	91.7449096216733	-0.76490962167334
50	91.52	91.3064394033941	0.213560596605873
51	91.62	91.7650169112137	-0.145016911213659
52	92.12	91.8929808215448	0.22701917845518
53	92.26	92.3661175043212	-0.106117504321219
54	92.18	92.5329009227276	-0.352900922727628
55	94.12	92.4650382864697	1.65496171353027
56	93.82	94.2721276395736	-0.452127639573646
57	93.2	94.1476852072447	-0.947685207244731
58	93.34	93.5453444953674	-0.205344495367427
59	93.11	93.613253776471	-0.503253776471013
60	93.63	93.3957362613162	0.234263738683779
61	93.29	93.8564228716143	-0.566422871614279
62	93.69	93.5720513388174	0.117948661182638
63	94.19	93.9142195072103	0.27578049278965
64	94.82	94.4078634963776	0.412136503622435
65	94.52	95.0372557804113	-0.517255780411261
66	94.94	94.8057641732496	0.134235826750412
67	96.87	95.171327387814	1.698672612186
68	96.6	97.0092617574495	-0.409261757449471
69	95.43	96.9160987113445	-1.48609871134447
70	95.56	95.8005704131269	-0.240570413126861
71	95.37	95.8125336320068	-0.442533632006842
72	96	95.6281492478834	0.3718507521166
73	95.6	96.1958324062977	-0.595832406297745
74	96.17	95.865555029106	0.304444970894025
75	96.26	96.3636710797932	-0.103671079793202
76	97.2	96.4872221552638	0.712777844736209
77	97.23	97.3742958037548	-0.144295803754773
78	97.74	97.4768175559719	0.263182444028089
79	99.37	97.9578033441339	1.41219665586607
80	99.37	99.5248075039066	-0.154807503906639
81	98.22	99.6604619957451	-1.44046199574512
82	98.27	98.5848719789147	-0.314871978914724
83	97.98	98.5254641907163	-0.545464190716302
84	98.53	98.2407468257003	0.28925317429966
85	97.98	98.72429360168	-0.744293601680013
86	98.63	98.2457312013578	0.384268798642154
87	98.74	98.8056932314516	-0.0656932314515757
88	99.37	98.9540495985658	0.415950401434216
89	99.51	99.5526996530628	-0.0426996530627548
90	99.66	99.7324780172702	-0.0724780172702424
91	101.62	99.8831029859228	1.73689701407724
92	101.71	101.730227150385	-0.0202271503846561
93	100.49	101.976647396899	-1.48664739689858
94	100.81	100.84591057975	-0.0359105797503787
95	100.48	101.035287544629	-0.55528754462901
96	101.01	100.736095446755	0.273904553245316
97	100.62	101.199704805325	-0.579704805324596
98	101.12	100.869688573909	0.250311426091102
99	101.45	101.302561687729	0.147438312271092
100	101.34	101.645893580899	-0.305893580898555
101	101.39	101.567804993138	-0.177804993137883
102	101.93	101.601367402339	0.328632597660842
103	102.42	102.105349945675	0.314650054325128
104	102.18	102.605436153661	-0.425436153661352
105	102.72	102.419609959327	0.300390040672568
106	102.43	102.903198276334	-0.473198276334102
107	102.35	102.669023890929	-0.319023890929358
108	102.69	102.566289557673	0.12371044232728

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 81.03 & 81.36 & -0.330000000000013 \tabularnewline
4 & 81.6 & 81.5102154305939 & 0.0897845694061346 \tabularnewline
5 & 81.56 & 82.0452318412283 & -0.485231841228313 \tabularnewline
6 & 82.08 & 82.0429783042787 & 0.0370216957213358 \tabularnewline
7 & 83.44 & 82.5173578913217 & 0.922642108678318 \tabularnewline
8 & 83.55 & 83.8241455312584 & -0.27414553125837 \tabularnewline
9 & 82.63 & 84.0333718243334 & -1.40337182433338 \tabularnewline
10 & 82.43 & 83.1748475802854 & -0.744847580285423 \tabularnewline
11 & 82.42 & 82.8950933966893 & -0.475093396689346 \tabularnewline
12 & 82.48 & 82.8476494982789 & -0.36764949827888 \tabularnewline
13 & 82.51 & 82.887724597852 & -0.377724597851994 \tabularnewline
14 & 83.23 & 82.9080163437107 & 0.321983656289305 \tabularnewline
15 & 83.41 & 83.5745445964896 & -0.164544596489606 \tabularnewline
16 & 83.88 & 83.7933916900125 & 0.0866083099875397 \tabularnewline
17 & 83.96 & 84.2433851058441 & -0.283385105844118 \tabularnewline
18 & 84.32 & 84.3484828844293 & -0.0284828844292662 \tabularnewline
19 & 85.82 & 84.6849089833587 & 1.13509101664127 \tabularnewline
20 & 85.72 & 86.1128298063233 & -0.392829806323334 \tabularnewline
21 & 84.36 & 86.1383075793167 & -1.77830757931666 \tabularnewline
22 & 84.36 & 84.8521477638544 & -0.492147763854419 \tabularnewline
23 & 84.36 & 84.7234152496094 & -0.363415249609375 \tabularnewline
24 & 85.08 & 84.7017072601666 & 0.378292739833427 \tabularnewline
25 & 84.95 & 85.3660645345056 & -0.416064534505594 \tabularnewline
26 & 85.62 & 85.2953503310315 & 0.324649668968476 \tabularnewline
27 & 86.22 & 85.9082898273743 & 0.311710172625681 \tabularnewline
28 & 86.4 & 86.5182002788382 & -0.11820027883816 \tabularnewline
29 & 86.71 & 86.7332904982384 & -0.0232904982383673 \tabularnewline
30 & 87.51 & 87.0341567741426 & 0.475843225857361 \tabularnewline
31 & 89.22 & 87.8029262868354 & 1.4170737131646 \tabularnewline
32 & 89.43 & 89.4686316272596 & -0.0386316272595479 \tabularnewline
33 & 88.24 & 89.8076050502652 & -1.56760505026517 \tabularnewline
34 & 88.9 & 88.7101832805874 & 0.189816719412619 \tabularnewline
35 & 88.78 & 89.2184993712779 & -0.438499371277928 \tabularnewline
36 & 89.25 & 89.1423203179843 & 0.107679682015657 \tabularnewline
37 & 88.8 & 89.5665467370256 & -0.766546737025621 \tabularnewline
38 & 89.46 & 89.1731250548446 & 0.286874945155347 \tabularnewline
39 & 89.66 & 89.74706514147 & -0.0870651414699921 \tabularnewline
40 & 90.29 & 89.9780291811172 & 0.311970818882784 \tabularnewline
41 & 90.08 & 90.581139458644 & -0.501139458644047 \tabularnewline
42 & 90.42 & 90.4297113906855 & -0.00971139068548155 \tabularnewline
43 & 92.14 & 90.7255325457013 & 1.41446745429866 \tabularnewline
44 & 92.09 & 92.358016199301 & -0.268016199300959 \tabularnewline
45 & 91.35 & 92.4508086110812 & -1.10080861108118 \tabularnewline
46 & 91.22 & 91.7542973017067 & -0.534297301706715 \tabularnewline
47 & 90.99 & 91.5586772213432 & -0.56867722134325 \tabularnewline
48 & 91.48 & 91.315777546402 & 0.164222453598001 \tabularnewline
49 & 90.98 & 91.7449096216733 & -0.76490962167334 \tabularnewline
50 & 91.52 & 91.3064394033941 & 0.213560596605873 \tabularnewline
51 & 91.62 & 91.7650169112137 & -0.145016911213659 \tabularnewline
52 & 92.12 & 91.8929808215448 & 0.22701917845518 \tabularnewline
53 & 92.26 & 92.3661175043212 & -0.106117504321219 \tabularnewline
54 & 92.18 & 92.5329009227276 & -0.352900922727628 \tabularnewline
55 & 94.12 & 92.4650382864697 & 1.65496171353027 \tabularnewline
56 & 93.82 & 94.2721276395736 & -0.452127639573646 \tabularnewline
57 & 93.2 & 94.1476852072447 & -0.947685207244731 \tabularnewline
58 & 93.34 & 93.5453444953674 & -0.205344495367427 \tabularnewline
59 & 93.11 & 93.613253776471 & -0.503253776471013 \tabularnewline
60 & 93.63 & 93.3957362613162 & 0.234263738683779 \tabularnewline
61 & 93.29 & 93.8564228716143 & -0.566422871614279 \tabularnewline
62 & 93.69 & 93.5720513388174 & 0.117948661182638 \tabularnewline
63 & 94.19 & 93.9142195072103 & 0.27578049278965 \tabularnewline
64 & 94.82 & 94.4078634963776 & 0.412136503622435 \tabularnewline
65 & 94.52 & 95.0372557804113 & -0.517255780411261 \tabularnewline
66 & 94.94 & 94.8057641732496 & 0.134235826750412 \tabularnewline
67 & 96.87 & 95.171327387814 & 1.698672612186 \tabularnewline
68 & 96.6 & 97.0092617574495 & -0.409261757449471 \tabularnewline
69 & 95.43 & 96.9160987113445 & -1.48609871134447 \tabularnewline
70 & 95.56 & 95.8005704131269 & -0.240570413126861 \tabularnewline
71 & 95.37 & 95.8125336320068 & -0.442533632006842 \tabularnewline
72 & 96 & 95.6281492478834 & 0.3718507521166 \tabularnewline
73 & 95.6 & 96.1958324062977 & -0.595832406297745 \tabularnewline
74 & 96.17 & 95.865555029106 & 0.304444970894025 \tabularnewline
75 & 96.26 & 96.3636710797932 & -0.103671079793202 \tabularnewline
76 & 97.2 & 96.4872221552638 & 0.712777844736209 \tabularnewline
77 & 97.23 & 97.3742958037548 & -0.144295803754773 \tabularnewline
78 & 97.74 & 97.4768175559719 & 0.263182444028089 \tabularnewline
79 & 99.37 & 97.9578033441339 & 1.41219665586607 \tabularnewline
80 & 99.37 & 99.5248075039066 & -0.154807503906639 \tabularnewline
81 & 98.22 & 99.6604619957451 & -1.44046199574512 \tabularnewline
82 & 98.27 & 98.5848719789147 & -0.314871978914724 \tabularnewline
83 & 97.98 & 98.5254641907163 & -0.545464190716302 \tabularnewline
84 & 98.53 & 98.2407468257003 & 0.28925317429966 \tabularnewline
85 & 97.98 & 98.72429360168 & -0.744293601680013 \tabularnewline
86 & 98.63 & 98.2457312013578 & 0.384268798642154 \tabularnewline
87 & 98.74 & 98.8056932314516 & -0.0656932314515757 \tabularnewline
88 & 99.37 & 98.9540495985658 & 0.415950401434216 \tabularnewline
89 & 99.51 & 99.5526996530628 & -0.0426996530627548 \tabularnewline
90 & 99.66 & 99.7324780172702 & -0.0724780172702424 \tabularnewline
91 & 101.62 & 99.8831029859228 & 1.73689701407724 \tabularnewline
92 & 101.71 & 101.730227150385 & -0.0202271503846561 \tabularnewline
93 & 100.49 & 101.976647396899 & -1.48664739689858 \tabularnewline
94 & 100.81 & 100.84591057975 & -0.0359105797503787 \tabularnewline
95 & 100.48 & 101.035287544629 & -0.55528754462901 \tabularnewline
96 & 101.01 & 100.736095446755 & 0.273904553245316 \tabularnewline
97 & 100.62 & 101.199704805325 & -0.579704805324596 \tabularnewline
98 & 101.12 & 100.869688573909 & 0.250311426091102 \tabularnewline
99 & 101.45 & 101.302561687729 & 0.147438312271092 \tabularnewline
100 & 101.34 & 101.645893580899 & -0.305893580898555 \tabularnewline
101 & 101.39 & 101.567804993138 & -0.177804993137883 \tabularnewline
102 & 101.93 & 101.601367402339 & 0.328632597660842 \tabularnewline
103 & 102.42 & 102.105349945675 & 0.314650054325128 \tabularnewline
104 & 102.18 & 102.605436153661 & -0.425436153661352 \tabularnewline
105 & 102.72 & 102.419609959327 & 0.300390040672568 \tabularnewline
106 & 102.43 & 102.903198276334 & -0.473198276334102 \tabularnewline
107 & 102.35 & 102.669023890929 & -0.319023890929358 \tabularnewline
108 & 102.69 & 102.566289557673 & 0.12371044232728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284401&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]81.03[/C][C]81.36[/C][C]-0.330000000000013[/C][/ROW]
[ROW][C]4[/C][C]81.6[/C][C]81.5102154305939[/C][C]0.0897845694061346[/C][/ROW]
[ROW][C]5[/C][C]81.56[/C][C]82.0452318412283[/C][C]-0.485231841228313[/C][/ROW]
[ROW][C]6[/C][C]82.08[/C][C]82.0429783042787[/C][C]0.0370216957213358[/C][/ROW]
[ROW][C]7[/C][C]83.44[/C][C]82.5173578913217[/C][C]0.922642108678318[/C][/ROW]
[ROW][C]8[/C][C]83.55[/C][C]83.8241455312584[/C][C]-0.27414553125837[/C][/ROW]
[ROW][C]9[/C][C]82.63[/C][C]84.0333718243334[/C][C]-1.40337182433338[/C][/ROW]
[ROW][C]10[/C][C]82.43[/C][C]83.1748475802854[/C][C]-0.744847580285423[/C][/ROW]
[ROW][C]11[/C][C]82.42[/C][C]82.8950933966893[/C][C]-0.475093396689346[/C][/ROW]
[ROW][C]12[/C][C]82.48[/C][C]82.8476494982789[/C][C]-0.36764949827888[/C][/ROW]
[ROW][C]13[/C][C]82.51[/C][C]82.887724597852[/C][C]-0.377724597851994[/C][/ROW]
[ROW][C]14[/C][C]83.23[/C][C]82.9080163437107[/C][C]0.321983656289305[/C][/ROW]
[ROW][C]15[/C][C]83.41[/C][C]83.5745445964896[/C][C]-0.164544596489606[/C][/ROW]
[ROW][C]16[/C][C]83.88[/C][C]83.7933916900125[/C][C]0.0866083099875397[/C][/ROW]
[ROW][C]17[/C][C]83.96[/C][C]84.2433851058441[/C][C]-0.283385105844118[/C][/ROW]
[ROW][C]18[/C][C]84.32[/C][C]84.3484828844293[/C][C]-0.0284828844292662[/C][/ROW]
[ROW][C]19[/C][C]85.82[/C][C]84.6849089833587[/C][C]1.13509101664127[/C][/ROW]
[ROW][C]20[/C][C]85.72[/C][C]86.1128298063233[/C][C]-0.392829806323334[/C][/ROW]
[ROW][C]21[/C][C]84.36[/C][C]86.1383075793167[/C][C]-1.77830757931666[/C][/ROW]
[ROW][C]22[/C][C]84.36[/C][C]84.8521477638544[/C][C]-0.492147763854419[/C][/ROW]
[ROW][C]23[/C][C]84.36[/C][C]84.7234152496094[/C][C]-0.363415249609375[/C][/ROW]
[ROW][C]24[/C][C]85.08[/C][C]84.7017072601666[/C][C]0.378292739833427[/C][/ROW]
[ROW][C]25[/C][C]84.95[/C][C]85.3660645345056[/C][C]-0.416064534505594[/C][/ROW]
[ROW][C]26[/C][C]85.62[/C][C]85.2953503310315[/C][C]0.324649668968476[/C][/ROW]
[ROW][C]27[/C][C]86.22[/C][C]85.9082898273743[/C][C]0.311710172625681[/C][/ROW]
[ROW][C]28[/C][C]86.4[/C][C]86.5182002788382[/C][C]-0.11820027883816[/C][/ROW]
[ROW][C]29[/C][C]86.71[/C][C]86.7332904982384[/C][C]-0.0232904982383673[/C][/ROW]
[ROW][C]30[/C][C]87.51[/C][C]87.0341567741426[/C][C]0.475843225857361[/C][/ROW]
[ROW][C]31[/C][C]89.22[/C][C]87.8029262868354[/C][C]1.4170737131646[/C][/ROW]
[ROW][C]32[/C][C]89.43[/C][C]89.4686316272596[/C][C]-0.0386316272595479[/C][/ROW]
[ROW][C]33[/C][C]88.24[/C][C]89.8076050502652[/C][C]-1.56760505026517[/C][/ROW]
[ROW][C]34[/C][C]88.9[/C][C]88.7101832805874[/C][C]0.189816719412619[/C][/ROW]
[ROW][C]35[/C][C]88.78[/C][C]89.2184993712779[/C][C]-0.438499371277928[/C][/ROW]
[ROW][C]36[/C][C]89.25[/C][C]89.1423203179843[/C][C]0.107679682015657[/C][/ROW]
[ROW][C]37[/C][C]88.8[/C][C]89.5665467370256[/C][C]-0.766546737025621[/C][/ROW]
[ROW][C]38[/C][C]89.46[/C][C]89.1731250548446[/C][C]0.286874945155347[/C][/ROW]
[ROW][C]39[/C][C]89.66[/C][C]89.74706514147[/C][C]-0.0870651414699921[/C][/ROW]
[ROW][C]40[/C][C]90.29[/C][C]89.9780291811172[/C][C]0.311970818882784[/C][/ROW]
[ROW][C]41[/C][C]90.08[/C][C]90.581139458644[/C][C]-0.501139458644047[/C][/ROW]
[ROW][C]42[/C][C]90.42[/C][C]90.4297113906855[/C][C]-0.00971139068548155[/C][/ROW]
[ROW][C]43[/C][C]92.14[/C][C]90.7255325457013[/C][C]1.41446745429866[/C][/ROW]
[ROW][C]44[/C][C]92.09[/C][C]92.358016199301[/C][C]-0.268016199300959[/C][/ROW]
[ROW][C]45[/C][C]91.35[/C][C]92.4508086110812[/C][C]-1.10080861108118[/C][/ROW]
[ROW][C]46[/C][C]91.22[/C][C]91.7542973017067[/C][C]-0.534297301706715[/C][/ROW]
[ROW][C]47[/C][C]90.99[/C][C]91.5586772213432[/C][C]-0.56867722134325[/C][/ROW]
[ROW][C]48[/C][C]91.48[/C][C]91.315777546402[/C][C]0.164222453598001[/C][/ROW]
[ROW][C]49[/C][C]90.98[/C][C]91.7449096216733[/C][C]-0.76490962167334[/C][/ROW]
[ROW][C]50[/C][C]91.52[/C][C]91.3064394033941[/C][C]0.213560596605873[/C][/ROW]
[ROW][C]51[/C][C]91.62[/C][C]91.7650169112137[/C][C]-0.145016911213659[/C][/ROW]
[ROW][C]52[/C][C]92.12[/C][C]91.8929808215448[/C][C]0.22701917845518[/C][/ROW]
[ROW][C]53[/C][C]92.26[/C][C]92.3661175043212[/C][C]-0.106117504321219[/C][/ROW]
[ROW][C]54[/C][C]92.18[/C][C]92.5329009227276[/C][C]-0.352900922727628[/C][/ROW]
[ROW][C]55[/C][C]94.12[/C][C]92.4650382864697[/C][C]1.65496171353027[/C][/ROW]
[ROW][C]56[/C][C]93.82[/C][C]94.2721276395736[/C][C]-0.452127639573646[/C][/ROW]
[ROW][C]57[/C][C]93.2[/C][C]94.1476852072447[/C][C]-0.947685207244731[/C][/ROW]
[ROW][C]58[/C][C]93.34[/C][C]93.5453444953674[/C][C]-0.205344495367427[/C][/ROW]
[ROW][C]59[/C][C]93.11[/C][C]93.613253776471[/C][C]-0.503253776471013[/C][/ROW]
[ROW][C]60[/C][C]93.63[/C][C]93.3957362613162[/C][C]0.234263738683779[/C][/ROW]
[ROW][C]61[/C][C]93.29[/C][C]93.8564228716143[/C][C]-0.566422871614279[/C][/ROW]
[ROW][C]62[/C][C]93.69[/C][C]93.5720513388174[/C][C]0.117948661182638[/C][/ROW]
[ROW][C]63[/C][C]94.19[/C][C]93.9142195072103[/C][C]0.27578049278965[/C][/ROW]
[ROW][C]64[/C][C]94.82[/C][C]94.4078634963776[/C][C]0.412136503622435[/C][/ROW]
[ROW][C]65[/C][C]94.52[/C][C]95.0372557804113[/C][C]-0.517255780411261[/C][/ROW]
[ROW][C]66[/C][C]94.94[/C][C]94.8057641732496[/C][C]0.134235826750412[/C][/ROW]
[ROW][C]67[/C][C]96.87[/C][C]95.171327387814[/C][C]1.698672612186[/C][/ROW]
[ROW][C]68[/C][C]96.6[/C][C]97.0092617574495[/C][C]-0.409261757449471[/C][/ROW]
[ROW][C]69[/C][C]95.43[/C][C]96.9160987113445[/C][C]-1.48609871134447[/C][/ROW]
[ROW][C]70[/C][C]95.56[/C][C]95.8005704131269[/C][C]-0.240570413126861[/C][/ROW]
[ROW][C]71[/C][C]95.37[/C][C]95.8125336320068[/C][C]-0.442533632006842[/C][/ROW]
[ROW][C]72[/C][C]96[/C][C]95.6281492478834[/C][C]0.3718507521166[/C][/ROW]
[ROW][C]73[/C][C]95.6[/C][C]96.1958324062977[/C][C]-0.595832406297745[/C][/ROW]
[ROW][C]74[/C][C]96.17[/C][C]95.865555029106[/C][C]0.304444970894025[/C][/ROW]
[ROW][C]75[/C][C]96.26[/C][C]96.3636710797932[/C][C]-0.103671079793202[/C][/ROW]
[ROW][C]76[/C][C]97.2[/C][C]96.4872221552638[/C][C]0.712777844736209[/C][/ROW]
[ROW][C]77[/C][C]97.23[/C][C]97.3742958037548[/C][C]-0.144295803754773[/C][/ROW]
[ROW][C]78[/C][C]97.74[/C][C]97.4768175559719[/C][C]0.263182444028089[/C][/ROW]
[ROW][C]79[/C][C]99.37[/C][C]97.9578033441339[/C][C]1.41219665586607[/C][/ROW]
[ROW][C]80[/C][C]99.37[/C][C]99.5248075039066[/C][C]-0.154807503906639[/C][/ROW]
[ROW][C]81[/C][C]98.22[/C][C]99.6604619957451[/C][C]-1.44046199574512[/C][/ROW]
[ROW][C]82[/C][C]98.27[/C][C]98.5848719789147[/C][C]-0.314871978914724[/C][/ROW]
[ROW][C]83[/C][C]97.98[/C][C]98.5254641907163[/C][C]-0.545464190716302[/C][/ROW]
[ROW][C]84[/C][C]98.53[/C][C]98.2407468257003[/C][C]0.28925317429966[/C][/ROW]
[ROW][C]85[/C][C]97.98[/C][C]98.72429360168[/C][C]-0.744293601680013[/C][/ROW]
[ROW][C]86[/C][C]98.63[/C][C]98.2457312013578[/C][C]0.384268798642154[/C][/ROW]
[ROW][C]87[/C][C]98.74[/C][C]98.8056932314516[/C][C]-0.0656932314515757[/C][/ROW]
[ROW][C]88[/C][C]99.37[/C][C]98.9540495985658[/C][C]0.415950401434216[/C][/ROW]
[ROW][C]89[/C][C]99.51[/C][C]99.5526996530628[/C][C]-0.0426996530627548[/C][/ROW]
[ROW][C]90[/C][C]99.66[/C][C]99.7324780172702[/C][C]-0.0724780172702424[/C][/ROW]
[ROW][C]91[/C][C]101.62[/C][C]99.8831029859228[/C][C]1.73689701407724[/C][/ROW]
[ROW][C]92[/C][C]101.71[/C][C]101.730227150385[/C][C]-0.0202271503846561[/C][/ROW]
[ROW][C]93[/C][C]100.49[/C][C]101.976647396899[/C][C]-1.48664739689858[/C][/ROW]
[ROW][C]94[/C][C]100.81[/C][C]100.84591057975[/C][C]-0.0359105797503787[/C][/ROW]
[ROW][C]95[/C][C]100.48[/C][C]101.035287544629[/C][C]-0.55528754462901[/C][/ROW]
[ROW][C]96[/C][C]101.01[/C][C]100.736095446755[/C][C]0.273904553245316[/C][/ROW]
[ROW][C]97[/C][C]100.62[/C][C]101.199704805325[/C][C]-0.579704805324596[/C][/ROW]
[ROW][C]98[/C][C]101.12[/C][C]100.869688573909[/C][C]0.250311426091102[/C][/ROW]
[ROW][C]99[/C][C]101.45[/C][C]101.302561687729[/C][C]0.147438312271092[/C][/ROW]
[ROW][C]100[/C][C]101.34[/C][C]101.645893580899[/C][C]-0.305893580898555[/C][/ROW]
[ROW][C]101[/C][C]101.39[/C][C]101.567804993138[/C][C]-0.177804993137883[/C][/ROW]
[ROW][C]102[/C][C]101.93[/C][C]101.601367402339[/C][C]0.328632597660842[/C][/ROW]
[ROW][C]103[/C][C]102.42[/C][C]102.105349945675[/C][C]0.314650054325128[/C][/ROW]
[ROW][C]104[/C][C]102.18[/C][C]102.605436153661[/C][C]-0.425436153661352[/C][/ROW]
[ROW][C]105[/C][C]102.72[/C][C]102.419609959327[/C][C]0.300390040672568[/C][/ROW]
[ROW][C]106[/C][C]102.43[/C][C]102.903198276334[/C][C]-0.473198276334102[/C][/ROW]
[ROW][C]107[/C][C]102.35[/C][C]102.669023890929[/C][C]-0.319023890929358[/C][/ROW]
[ROW][C]108[/C][C]102.69[/C][C]102.566289557673[/C][C]0.12371044232728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284401&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284401&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	81.03	81.36	-0.330000000000013
4	81.6	81.5102154305939	0.0897845694061346
5	81.56	82.0452318412283	-0.485231841228313
6	82.08	82.0429783042787	0.0370216957213358
7	83.44	82.5173578913217	0.922642108678318
8	83.55	83.8241455312584	-0.27414553125837
9	82.63	84.0333718243334	-1.40337182433338
10	82.43	83.1748475802854	-0.744847580285423
11	82.42	82.8950933966893	-0.475093396689346
12	82.48	82.8476494982789	-0.36764949827888
13	82.51	82.887724597852	-0.377724597851994
14	83.23	82.9080163437107	0.321983656289305
15	83.41	83.5745445964896	-0.164544596489606
16	83.88	83.7933916900125	0.0866083099875397
17	83.96	84.2433851058441	-0.283385105844118
18	84.32	84.3484828844293	-0.0284828844292662
19	85.82	84.6849089833587	1.13509101664127
20	85.72	86.1128298063233	-0.392829806323334
21	84.36	86.1383075793167	-1.77830757931666
22	84.36	84.8521477638544	-0.492147763854419
23	84.36	84.7234152496094	-0.363415249609375
24	85.08	84.7017072601666	0.378292739833427
25	84.95	85.3660645345056	-0.416064534505594
26	85.62	85.2953503310315	0.324649668968476
27	86.22	85.9082898273743	0.311710172625681
28	86.4	86.5182002788382	-0.11820027883816
29	86.71	86.7332904982384	-0.0232904982383673
30	87.51	87.0341567741426	0.475843225857361
31	89.22	87.8029262868354	1.4170737131646
32	89.43	89.4686316272596	-0.0386316272595479
33	88.24	89.8076050502652	-1.56760505026517
34	88.9	88.7101832805874	0.189816719412619
35	88.78	89.2184993712779	-0.438499371277928
36	89.25	89.1423203179843	0.107679682015657
37	88.8	89.5665467370256	-0.766546737025621
38	89.46	89.1731250548446	0.286874945155347
39	89.66	89.74706514147	-0.0870651414699921
40	90.29	89.9780291811172	0.311970818882784
41	90.08	90.581139458644	-0.501139458644047
42	90.42	90.4297113906855	-0.00971139068548155
43	92.14	90.7255325457013	1.41446745429866
44	92.09	92.358016199301	-0.268016199300959
45	91.35	92.4508086110812	-1.10080861108118
46	91.22	91.7542973017067	-0.534297301706715
47	90.99	91.5586772213432	-0.56867722134325
48	91.48	91.315777546402	0.164222453598001
49	90.98	91.7449096216733	-0.76490962167334
50	91.52	91.3064394033941	0.213560596605873
51	91.62	91.7650169112137	-0.145016911213659
52	92.12	91.8929808215448	0.22701917845518
53	92.26	92.3661175043212	-0.106117504321219
54	92.18	92.5329009227276	-0.352900922727628
55	94.12	92.4650382864697	1.65496171353027
56	93.82	94.2721276395736	-0.452127639573646
57	93.2	94.1476852072447	-0.947685207244731
58	93.34	93.5453444953674	-0.205344495367427
59	93.11	93.613253776471	-0.503253776471013
60	93.63	93.3957362613162	0.234263738683779
61	93.29	93.8564228716143	-0.566422871614279
62	93.69	93.5720513388174	0.117948661182638
63	94.19	93.9142195072103	0.27578049278965
64	94.82	94.4078634963776	0.412136503622435
65	94.52	95.0372557804113	-0.517255780411261
66	94.94	94.8057641732496	0.134235826750412
67	96.87	95.171327387814	1.698672612186
68	96.6	97.0092617574495	-0.409261757449471
69	95.43	96.9160987113445	-1.48609871134447
70	95.56	95.8005704131269	-0.240570413126861
71	95.37	95.8125336320068	-0.442533632006842
72	96	95.6281492478834	0.3718507521166
73	95.6	96.1958324062977	-0.595832406297745
74	96.17	95.865555029106	0.304444970894025
75	96.26	96.3636710797932	-0.103671079793202
76	97.2	96.4872221552638	0.712777844736209
77	97.23	97.3742958037548	-0.144295803754773
78	97.74	97.4768175559719	0.263182444028089
79	99.37	97.9578033441339	1.41219665586607
80	99.37	99.5248075039066	-0.154807503906639
81	98.22	99.6604619957451	-1.44046199574512
82	98.27	98.5848719789147	-0.314871978914724
83	97.98	98.5254641907163	-0.545464190716302
84	98.53	98.2407468257003	0.28925317429966
85	97.98	98.72429360168	-0.744293601680013
86	98.63	98.2457312013578	0.384268798642154
87	98.74	98.8056932314516	-0.0656932314515757
88	99.37	98.9540495985658	0.415950401434216
89	99.51	99.5526996530628	-0.0426996530627548
90	99.66	99.7324780172702	-0.0724780172702424
91	101.62	99.8831029859228	1.73689701407724
92	101.71	101.730227150385	-0.0202271503846561
93	100.49	101.976647396899	-1.48664739689858
94	100.81	100.84591057975	-0.0359105797503787
95	100.48	101.035287544629	-0.55528754462901
96	101.01	100.736095446755	0.273904553245316
97	100.62	101.199704805325	-0.579704805324596
98	101.12	100.869688573909	0.250311426091102
99	101.45	101.302561687729	0.147438312271092
100	101.34	101.645893580899	-0.305893580898555
101	101.39	101.567804993138	-0.177804993137883
102	101.93	101.601367402339	0.328632597660842
103	102.42	102.105349945675	0.314650054325128
104	102.18	102.605436153661	-0.425436153661352
105	102.72	102.419609959327	0.300390040672568
106	102.43	102.903198276334	-0.473198276334102
107	102.35	102.669023890929	-0.319023890929358
108	102.69	102.566289557673	0.12371044232728

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	102.870208355705	101.600016318931	104.140400392479
110	103.061469484855	101.319298012629	104.803640957081
111	103.252730614004	101.121233444099	105.38422778391
112	103.443991743154	100.966031043553	105.921952442755
113	103.635252872304	100.837265426398	106.43324031821
114	103.826514001453	100.726327084539	106.926700918368
115	104.017775130603	100.6280686648	107.407481596406
116	104.209036259753	100.539140901655	107.87893161785
117	104.400297388902	100.457231304812	108.343363472992
118	104.591558518052	100.38067147194	108.802445564163
119	104.782819647201	100.308216219783	109.25742307462
120	104.974080776351	100.238910908795	109.709250643907

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 102.870208355705 & 101.600016318931 & 104.140400392479 \tabularnewline
110 & 103.061469484855 & 101.319298012629 & 104.803640957081 \tabularnewline
111 & 103.252730614004 & 101.121233444099 & 105.38422778391 \tabularnewline
112 & 103.443991743154 & 100.966031043553 & 105.921952442755 \tabularnewline
113 & 103.635252872304 & 100.837265426398 & 106.43324031821 \tabularnewline
114 & 103.826514001453 & 100.726327084539 & 106.926700918368 \tabularnewline
115 & 104.017775130603 & 100.6280686648 & 107.407481596406 \tabularnewline
116 & 104.209036259753 & 100.539140901655 & 107.87893161785 \tabularnewline
117 & 104.400297388902 & 100.457231304812 & 108.343363472992 \tabularnewline
118 & 104.591558518052 & 100.38067147194 & 108.802445564163 \tabularnewline
119 & 104.782819647201 & 100.308216219783 & 109.25742307462 \tabularnewline
120 & 104.974080776351 & 100.238910908795 & 109.709250643907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284401&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]109[/C][C]102.870208355705[/C][C]101.600016318931[/C][C]104.140400392479[/C][/ROW]
[ROW][C]110[/C][C]103.061469484855[/C][C]101.319298012629[/C][C]104.803640957081[/C][/ROW]
[ROW][C]111[/C][C]103.252730614004[/C][C]101.121233444099[/C][C]105.38422778391[/C][/ROW]
[ROW][C]112[/C][C]103.443991743154[/C][C]100.966031043553[/C][C]105.921952442755[/C][/ROW]
[ROW][C]113[/C][C]103.635252872304[/C][C]100.837265426398[/C][C]106.43324031821[/C][/ROW]
[ROW][C]114[/C][C]103.826514001453[/C][C]100.726327084539[/C][C]106.926700918368[/C][/ROW]
[ROW][C]115[/C][C]104.017775130603[/C][C]100.6280686648[/C][C]107.407481596406[/C][/ROW]
[ROW][C]116[/C][C]104.209036259753[/C][C]100.539140901655[/C][C]107.87893161785[/C][/ROW]
[ROW][C]117[/C][C]104.400297388902[/C][C]100.457231304812[/C][C]108.343363472992[/C][/ROW]
[ROW][C]118[/C][C]104.591558518052[/C][C]100.38067147194[/C][C]108.802445564163[/C][/ROW]
[ROW][C]119[/C][C]104.782819647201[/C][C]100.308216219783[/C][C]109.25742307462[/C][/ROW]
[ROW][C]120[/C][C]104.974080776351[/C][C]100.238910908795[/C][C]109.709250643907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284401&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284401&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
109	102.870208355705	101.600016318931	104.140400392479
110	103.061469484855	101.319298012629	104.803640957081
111	103.252730614004	101.121233444099	105.38422778391
112	103.443991743154	100.966031043553	105.921952442755
113	103.635252872304	100.837265426398	106.43324031821
114	103.826514001453	100.726327084539	106.926700918368
115	104.017775130603	100.6280686648	107.407481596406
116	104.209036259753	100.539140901655	107.87893161785
117	104.400297388902	100.457231304812	108.343363472992
118	104.591558518052	100.38067147194	108.802445564163
119	104.782819647201	100.308216219783	109.25742307462
120	104.974080776351	100.238910908795	109.709250643907

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