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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 24 Dec 2010 14:48:17 +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/2010/Dec/24/t1293201976z95ip0evnpqoeub.htm/, Retrieved Tue, 30 Apr 2024 07:07:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115029, Retrieved Tue, 30 Apr 2024 07:07:15 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

114

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

-       [Exponential Smoothing] [10.2] [2010-12-24 14:48:17] [836c64735fc21f091fd80eb090cba4d6] [Current]

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Dataseries X:

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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115029&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115029&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.238478317886849
beta	0.0332524755449531
gamma	0.786856072763765

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.238478317886849 \tabularnewline
beta & 0.0332524755449531 \tabularnewline
gamma & 0.786856072763765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115029&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]0.238478317886849[/C][/ROW]
[ROW][C]beta[/C][C]0.0332524755449531[/C][/ROW]
[ROW][C]gamma[/C][C]0.786856072763765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115029&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	0.238478317886849
beta	0.0332524755449531
gamma	0.786856072763765

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	74	76.1609807081855	-2.16098070818548
14	77.6	79.0715192698551	-1.47151926985515
15	75.1	75.9320633301454	-0.83206333014536
16	85	85.3702471707489	-0.370247170748897
17	75.4	75.2330732961018	0.16692670389817
18	63.2	62.7602291643611	0.439770835638889
19	64.7	59.9747603108474	4.72523968915258
20	77	76.9857929700979	0.0142070299020816
21	82.6	80.737854397984	1.862145602016
22	97.6	98.590085292572	-0.99008529257209
23	99	95.3036784097252	3.69632159027485
24	75.3	77.0443186004388	-1.7443186004388
25	71.6	73.9638293823682	-2.36382938236817
26	76.8	77.2147861428936	-0.414786142893647
27	83.9	74.7678706727276	9.13212932727244
28	79.7	87.221791561436	-7.52179156143598
29	77.5	75.7272089028127	1.77279109718732
30	73.1	63.7419643602922	9.35803563970784
31	65.6	65.7266265579438	-0.126626557943766
32	85.2	79.2392222151445	5.96077778485555
33	98.3	85.923694277481	12.376305722519
34	98	106.148503406018	-8.1485034060185
35	100.6	104.187778000516	-3.58777800051568
36	84.1	79.9568905416234	4.14310945837656
37	76.7	77.8784201026497	-1.17842010264968
38	82.4	83.1904662296599	-0.79046622965987
39	95.5	86.705936204537	8.79406379546302
40	79.9	89.2371047653084	-9.33710476530837
41	82.4	82.75425249186	-0.354252491859938
42	83.6	74.2039821018118	9.3960178981882
43	73.1	70.2437180091495	2.85628199085046
44	91.1	89.6339225146001	1.46607748539991
45	118.6	99.6214602990688	18.9785397009312
46	102.9	109.646879399444	-6.74687939944442
47	111.8	111.20817886582	0.59182113417981
48	93.9	90.9098801962	2.99011980379998
49	91.6	84.9414952417987	6.65850475820132
50	92	93.3551953110195	-1.3551953110195
51	91.1	103.838593280986	-12.7385932809861
52	97.5	89.578106760884	7.92189323911596
53	94.7	92.9771154747697	1.7228845252303
54	96.7	90.4818649150129	6.21813508498714
55	78.7	80.792937942156	-2.09293794215606
56	103.5	100.231119765343	3.26888023465663
57	113.8	123.074772075817	-9.27477207581728
58	106.1	110.425674864106	-4.32567486410616
59	120.3	117.373090491436	2.92690950856441
60	114.2	98.0002142902896	16.1997857097104
61	106.3	97.0108623302688	9.28913766973125
62	98.8	101.5715103602	-2.77151036020022
63	113.1	105.144676842999	7.95532315700119
64	97.7	108.537492182488	-10.8374921824884
65	116.3	103.648649972666	12.6513500273344
66	107.2	106.560862008207	0.639137991792992
67	94.5	88.821026272786	5.67897372721407
68	123.5	116.807493792395	6.69250620760509
69	126.6	135.306892493306	-8.70689249330616
70	126.5	124.849835511515	1.65016448848509
71	141.4	140.04766311641	1.35233688358954
72	124.3	126.053479973353	-1.75347997335339
73	124.9	115.508293700746	9.39170629925364
74	108.9	112.372600800479	-3.47260080047873
75	126.7	123.562341312867	3.13765868713308
76	107.7	113.357500396483	-5.65750039648297
77	121.8	125.153856399775	-3.35385639977471
78	118.3	116.411184433191	1.88881556680887
79	122.8	100.589716017468	22.2102839825317
80	149.5	136.795936209635	12.7040637903651
81	147	148.689573475122	-1.68957347512176
82	139.3	145.99850723732	-6.69850723732011
83	162.1	161.325666058821	0.774333941179265
84	142.2	143.165877883393	-0.965877883392778
85	141.4	139.02279915057	2.37720084943001
86	124.7	124.864928135823	-0.164928135823189
87	114	143.170115879426	-29.1701158794258
88	126.6	118.590286921694	8.00971307830588
89	121.9	136.628867189686	-14.7288671896856
90	125.1	127.843674456522	-2.7436744565224
91	122.1	121.985461586875	0.114538413125246
92	135.9	147.364252207196	-11.4642522071958
93	148.4	144.42242866009	3.97757133991038
94	137.5	139.721582528843	-2.22158252884333
95	145.3	160.004715605443	-14.7047156054434
96	139.9	137.327183895329	2.57281610467101
97	128.2	135.68006196386	-7.48006196386035
98	115.4	118.06081079513	-2.66081079512979
99	124.7	117.075888338417	7.62411166158346
100	111.5	123.266342255578	-11.7663422555776
101	121.1	122.295704578738	-1.1957045787378
102	122.5	123.608740001927	-1.10874000192676
103	127.4	119.66695035705	7.73304964294964
104	143.7	139.486618516595	4.21338148340496
105	157.8	149.575133025594	8.22486697440613
106	148.8	141.838162915263	6.96183708473666
107	162.9	157.143153892183	5.75684610781713
108	153.9	149.151505063144	4.74849493685602

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 74 & 76.1609807081855 & -2.16098070818548 \tabularnewline
14 & 77.6 & 79.0715192698551 & -1.47151926985515 \tabularnewline
15 & 75.1 & 75.9320633301454 & -0.83206333014536 \tabularnewline
16 & 85 & 85.3702471707489 & -0.370247170748897 \tabularnewline
17 & 75.4 & 75.2330732961018 & 0.16692670389817 \tabularnewline
18 & 63.2 & 62.7602291643611 & 0.439770835638889 \tabularnewline
19 & 64.7 & 59.9747603108474 & 4.72523968915258 \tabularnewline
20 & 77 & 76.9857929700979 & 0.0142070299020816 \tabularnewline
21 & 82.6 & 80.737854397984 & 1.862145602016 \tabularnewline
22 & 97.6 & 98.590085292572 & -0.99008529257209 \tabularnewline
23 & 99 & 95.3036784097252 & 3.69632159027485 \tabularnewline
24 & 75.3 & 77.0443186004388 & -1.7443186004388 \tabularnewline
25 & 71.6 & 73.9638293823682 & -2.36382938236817 \tabularnewline
26 & 76.8 & 77.2147861428936 & -0.414786142893647 \tabularnewline
27 & 83.9 & 74.7678706727276 & 9.13212932727244 \tabularnewline
28 & 79.7 & 87.221791561436 & -7.52179156143598 \tabularnewline
29 & 77.5 & 75.7272089028127 & 1.77279109718732 \tabularnewline
30 & 73.1 & 63.7419643602922 & 9.35803563970784 \tabularnewline
31 & 65.6 & 65.7266265579438 & -0.126626557943766 \tabularnewline
32 & 85.2 & 79.2392222151445 & 5.96077778485555 \tabularnewline
33 & 98.3 & 85.923694277481 & 12.376305722519 \tabularnewline
34 & 98 & 106.148503406018 & -8.1485034060185 \tabularnewline
35 & 100.6 & 104.187778000516 & -3.58777800051568 \tabularnewline
36 & 84.1 & 79.9568905416234 & 4.14310945837656 \tabularnewline
37 & 76.7 & 77.8784201026497 & -1.17842010264968 \tabularnewline
38 & 82.4 & 83.1904662296599 & -0.79046622965987 \tabularnewline
39 & 95.5 & 86.705936204537 & 8.79406379546302 \tabularnewline
40 & 79.9 & 89.2371047653084 & -9.33710476530837 \tabularnewline
41 & 82.4 & 82.75425249186 & -0.354252491859938 \tabularnewline
42 & 83.6 & 74.2039821018118 & 9.3960178981882 \tabularnewline
43 & 73.1 & 70.2437180091495 & 2.85628199085046 \tabularnewline
44 & 91.1 & 89.6339225146001 & 1.46607748539991 \tabularnewline
45 & 118.6 & 99.6214602990688 & 18.9785397009312 \tabularnewline
46 & 102.9 & 109.646879399444 & -6.74687939944442 \tabularnewline
47 & 111.8 & 111.20817886582 & 0.59182113417981 \tabularnewline
48 & 93.9 & 90.9098801962 & 2.99011980379998 \tabularnewline
49 & 91.6 & 84.9414952417987 & 6.65850475820132 \tabularnewline
50 & 92 & 93.3551953110195 & -1.3551953110195 \tabularnewline
51 & 91.1 & 103.838593280986 & -12.7385932809861 \tabularnewline
52 & 97.5 & 89.578106760884 & 7.92189323911596 \tabularnewline
53 & 94.7 & 92.9771154747697 & 1.7228845252303 \tabularnewline
54 & 96.7 & 90.4818649150129 & 6.21813508498714 \tabularnewline
55 & 78.7 & 80.792937942156 & -2.09293794215606 \tabularnewline
56 & 103.5 & 100.231119765343 & 3.26888023465663 \tabularnewline
57 & 113.8 & 123.074772075817 & -9.27477207581728 \tabularnewline
58 & 106.1 & 110.425674864106 & -4.32567486410616 \tabularnewline
59 & 120.3 & 117.373090491436 & 2.92690950856441 \tabularnewline
60 & 114.2 & 98.0002142902896 & 16.1997857097104 \tabularnewline
61 & 106.3 & 97.0108623302688 & 9.28913766973125 \tabularnewline
62 & 98.8 & 101.5715103602 & -2.77151036020022 \tabularnewline
63 & 113.1 & 105.144676842999 & 7.95532315700119 \tabularnewline
64 & 97.7 & 108.537492182488 & -10.8374921824884 \tabularnewline
65 & 116.3 & 103.648649972666 & 12.6513500273344 \tabularnewline
66 & 107.2 & 106.560862008207 & 0.639137991792992 \tabularnewline
67 & 94.5 & 88.821026272786 & 5.67897372721407 \tabularnewline
68 & 123.5 & 116.807493792395 & 6.69250620760509 \tabularnewline
69 & 126.6 & 135.306892493306 & -8.70689249330616 \tabularnewline
70 & 126.5 & 124.849835511515 & 1.65016448848509 \tabularnewline
71 & 141.4 & 140.04766311641 & 1.35233688358954 \tabularnewline
72 & 124.3 & 126.053479973353 & -1.75347997335339 \tabularnewline
73 & 124.9 & 115.508293700746 & 9.39170629925364 \tabularnewline
74 & 108.9 & 112.372600800479 & -3.47260080047873 \tabularnewline
75 & 126.7 & 123.562341312867 & 3.13765868713308 \tabularnewline
76 & 107.7 & 113.357500396483 & -5.65750039648297 \tabularnewline
77 & 121.8 & 125.153856399775 & -3.35385639977471 \tabularnewline
78 & 118.3 & 116.411184433191 & 1.88881556680887 \tabularnewline
79 & 122.8 & 100.589716017468 & 22.2102839825317 \tabularnewline
80 & 149.5 & 136.795936209635 & 12.7040637903651 \tabularnewline
81 & 147 & 148.689573475122 & -1.68957347512176 \tabularnewline
82 & 139.3 & 145.99850723732 & -6.69850723732011 \tabularnewline
83 & 162.1 & 161.325666058821 & 0.774333941179265 \tabularnewline
84 & 142.2 & 143.165877883393 & -0.965877883392778 \tabularnewline
85 & 141.4 & 139.02279915057 & 2.37720084943001 \tabularnewline
86 & 124.7 & 124.864928135823 & -0.164928135823189 \tabularnewline
87 & 114 & 143.170115879426 & -29.1701158794258 \tabularnewline
88 & 126.6 & 118.590286921694 & 8.00971307830588 \tabularnewline
89 & 121.9 & 136.628867189686 & -14.7288671896856 \tabularnewline
90 & 125.1 & 127.843674456522 & -2.7436744565224 \tabularnewline
91 & 122.1 & 121.985461586875 & 0.114538413125246 \tabularnewline
92 & 135.9 & 147.364252207196 & -11.4642522071958 \tabularnewline
93 & 148.4 & 144.42242866009 & 3.97757133991038 \tabularnewline
94 & 137.5 & 139.721582528843 & -2.22158252884333 \tabularnewline
95 & 145.3 & 160.004715605443 & -14.7047156054434 \tabularnewline
96 & 139.9 & 137.327183895329 & 2.57281610467101 \tabularnewline
97 & 128.2 & 135.68006196386 & -7.48006196386035 \tabularnewline
98 & 115.4 & 118.06081079513 & -2.66081079512979 \tabularnewline
99 & 124.7 & 117.075888338417 & 7.62411166158346 \tabularnewline
100 & 111.5 & 123.266342255578 & -11.7663422555776 \tabularnewline
101 & 121.1 & 122.295704578738 & -1.1957045787378 \tabularnewline
102 & 122.5 & 123.608740001927 & -1.10874000192676 \tabularnewline
103 & 127.4 & 119.66695035705 & 7.73304964294964 \tabularnewline
104 & 143.7 & 139.486618516595 & 4.21338148340496 \tabularnewline
105 & 157.8 & 149.575133025594 & 8.22486697440613 \tabularnewline
106 & 148.8 & 141.838162915263 & 6.96183708473666 \tabularnewline
107 & 162.9 & 157.143153892183 & 5.75684610781713 \tabularnewline
108 & 153.9 & 149.151505063144 & 4.74849493685602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115029&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]74[/C][C]76.1609807081855[/C][C]-2.16098070818548[/C][/ROW]
[ROW][C]14[/C][C]77.6[/C][C]79.0715192698551[/C][C]-1.47151926985515[/C][/ROW]
[ROW][C]15[/C][C]75.1[/C][C]75.9320633301454[/C][C]-0.83206333014536[/C][/ROW]
[ROW][C]16[/C][C]85[/C][C]85.3702471707489[/C][C]-0.370247170748897[/C][/ROW]
[ROW][C]17[/C][C]75.4[/C][C]75.2330732961018[/C][C]0.16692670389817[/C][/ROW]
[ROW][C]18[/C][C]63.2[/C][C]62.7602291643611[/C][C]0.439770835638889[/C][/ROW]
[ROW][C]19[/C][C]64.7[/C][C]59.9747603108474[/C][C]4.72523968915258[/C][/ROW]
[ROW][C]20[/C][C]77[/C][C]76.9857929700979[/C][C]0.0142070299020816[/C][/ROW]
[ROW][C]21[/C][C]82.6[/C][C]80.737854397984[/C][C]1.862145602016[/C][/ROW]
[ROW][C]22[/C][C]97.6[/C][C]98.590085292572[/C][C]-0.99008529257209[/C][/ROW]
[ROW][C]23[/C][C]99[/C][C]95.3036784097252[/C][C]3.69632159027485[/C][/ROW]
[ROW][C]24[/C][C]75.3[/C][C]77.0443186004388[/C][C]-1.7443186004388[/C][/ROW]
[ROW][C]25[/C][C]71.6[/C][C]73.9638293823682[/C][C]-2.36382938236817[/C][/ROW]
[ROW][C]26[/C][C]76.8[/C][C]77.2147861428936[/C][C]-0.414786142893647[/C][/ROW]
[ROW][C]27[/C][C]83.9[/C][C]74.7678706727276[/C][C]9.13212932727244[/C][/ROW]
[ROW][C]28[/C][C]79.7[/C][C]87.221791561436[/C][C]-7.52179156143598[/C][/ROW]
[ROW][C]29[/C][C]77.5[/C][C]75.7272089028127[/C][C]1.77279109718732[/C][/ROW]
[ROW][C]30[/C][C]73.1[/C][C]63.7419643602922[/C][C]9.35803563970784[/C][/ROW]
[ROW][C]31[/C][C]65.6[/C][C]65.7266265579438[/C][C]-0.126626557943766[/C][/ROW]
[ROW][C]32[/C][C]85.2[/C][C]79.2392222151445[/C][C]5.96077778485555[/C][/ROW]
[ROW][C]33[/C][C]98.3[/C][C]85.923694277481[/C][C]12.376305722519[/C][/ROW]
[ROW][C]34[/C][C]98[/C][C]106.148503406018[/C][C]-8.1485034060185[/C][/ROW]
[ROW][C]35[/C][C]100.6[/C][C]104.187778000516[/C][C]-3.58777800051568[/C][/ROW]
[ROW][C]36[/C][C]84.1[/C][C]79.9568905416234[/C][C]4.14310945837656[/C][/ROW]
[ROW][C]37[/C][C]76.7[/C][C]77.8784201026497[/C][C]-1.17842010264968[/C][/ROW]
[ROW][C]38[/C][C]82.4[/C][C]83.1904662296599[/C][C]-0.79046622965987[/C][/ROW]
[ROW][C]39[/C][C]95.5[/C][C]86.705936204537[/C][C]8.79406379546302[/C][/ROW]
[ROW][C]40[/C][C]79.9[/C][C]89.2371047653084[/C][C]-9.33710476530837[/C][/ROW]
[ROW][C]41[/C][C]82.4[/C][C]82.75425249186[/C][C]-0.354252491859938[/C][/ROW]
[ROW][C]42[/C][C]83.6[/C][C]74.2039821018118[/C][C]9.3960178981882[/C][/ROW]
[ROW][C]43[/C][C]73.1[/C][C]70.2437180091495[/C][C]2.85628199085046[/C][/ROW]
[ROW][C]44[/C][C]91.1[/C][C]89.6339225146001[/C][C]1.46607748539991[/C][/ROW]
[ROW][C]45[/C][C]118.6[/C][C]99.6214602990688[/C][C]18.9785397009312[/C][/ROW]
[ROW][C]46[/C][C]102.9[/C][C]109.646879399444[/C][C]-6.74687939944442[/C][/ROW]
[ROW][C]47[/C][C]111.8[/C][C]111.20817886582[/C][C]0.59182113417981[/C][/ROW]
[ROW][C]48[/C][C]93.9[/C][C]90.9098801962[/C][C]2.99011980379998[/C][/ROW]
[ROW][C]49[/C][C]91.6[/C][C]84.9414952417987[/C][C]6.65850475820132[/C][/ROW]
[ROW][C]50[/C][C]92[/C][C]93.3551953110195[/C][C]-1.3551953110195[/C][/ROW]
[ROW][C]51[/C][C]91.1[/C][C]103.838593280986[/C][C]-12.7385932809861[/C][/ROW]
[ROW][C]52[/C][C]97.5[/C][C]89.578106760884[/C][C]7.92189323911596[/C][/ROW]
[ROW][C]53[/C][C]94.7[/C][C]92.9771154747697[/C][C]1.7228845252303[/C][/ROW]
[ROW][C]54[/C][C]96.7[/C][C]90.4818649150129[/C][C]6.21813508498714[/C][/ROW]
[ROW][C]55[/C][C]78.7[/C][C]80.792937942156[/C][C]-2.09293794215606[/C][/ROW]
[ROW][C]56[/C][C]103.5[/C][C]100.231119765343[/C][C]3.26888023465663[/C][/ROW]
[ROW][C]57[/C][C]113.8[/C][C]123.074772075817[/C][C]-9.27477207581728[/C][/ROW]
[ROW][C]58[/C][C]106.1[/C][C]110.425674864106[/C][C]-4.32567486410616[/C][/ROW]
[ROW][C]59[/C][C]120.3[/C][C]117.373090491436[/C][C]2.92690950856441[/C][/ROW]
[ROW][C]60[/C][C]114.2[/C][C]98.0002142902896[/C][C]16.1997857097104[/C][/ROW]
[ROW][C]61[/C][C]106.3[/C][C]97.0108623302688[/C][C]9.28913766973125[/C][/ROW]
[ROW][C]62[/C][C]98.8[/C][C]101.5715103602[/C][C]-2.77151036020022[/C][/ROW]
[ROW][C]63[/C][C]113.1[/C][C]105.144676842999[/C][C]7.95532315700119[/C][/ROW]
[ROW][C]64[/C][C]97.7[/C][C]108.537492182488[/C][C]-10.8374921824884[/C][/ROW]
[ROW][C]65[/C][C]116.3[/C][C]103.648649972666[/C][C]12.6513500273344[/C][/ROW]
[ROW][C]66[/C][C]107.2[/C][C]106.560862008207[/C][C]0.639137991792992[/C][/ROW]
[ROW][C]67[/C][C]94.5[/C][C]88.821026272786[/C][C]5.67897372721407[/C][/ROW]
[ROW][C]68[/C][C]123.5[/C][C]116.807493792395[/C][C]6.69250620760509[/C][/ROW]
[ROW][C]69[/C][C]126.6[/C][C]135.306892493306[/C][C]-8.70689249330616[/C][/ROW]
[ROW][C]70[/C][C]126.5[/C][C]124.849835511515[/C][C]1.65016448848509[/C][/ROW]
[ROW][C]71[/C][C]141.4[/C][C]140.04766311641[/C][C]1.35233688358954[/C][/ROW]
[ROW][C]72[/C][C]124.3[/C][C]126.053479973353[/C][C]-1.75347997335339[/C][/ROW]
[ROW][C]73[/C][C]124.9[/C][C]115.508293700746[/C][C]9.39170629925364[/C][/ROW]
[ROW][C]74[/C][C]108.9[/C][C]112.372600800479[/C][C]-3.47260080047873[/C][/ROW]
[ROW][C]75[/C][C]126.7[/C][C]123.562341312867[/C][C]3.13765868713308[/C][/ROW]
[ROW][C]76[/C][C]107.7[/C][C]113.357500396483[/C][C]-5.65750039648297[/C][/ROW]
[ROW][C]77[/C][C]121.8[/C][C]125.153856399775[/C][C]-3.35385639977471[/C][/ROW]
[ROW][C]78[/C][C]118.3[/C][C]116.411184433191[/C][C]1.88881556680887[/C][/ROW]
[ROW][C]79[/C][C]122.8[/C][C]100.589716017468[/C][C]22.2102839825317[/C][/ROW]
[ROW][C]80[/C][C]149.5[/C][C]136.795936209635[/C][C]12.7040637903651[/C][/ROW]
[ROW][C]81[/C][C]147[/C][C]148.689573475122[/C][C]-1.68957347512176[/C][/ROW]
[ROW][C]82[/C][C]139.3[/C][C]145.99850723732[/C][C]-6.69850723732011[/C][/ROW]
[ROW][C]83[/C][C]162.1[/C][C]161.325666058821[/C][C]0.774333941179265[/C][/ROW]
[ROW][C]84[/C][C]142.2[/C][C]143.165877883393[/C][C]-0.965877883392778[/C][/ROW]
[ROW][C]85[/C][C]141.4[/C][C]139.02279915057[/C][C]2.37720084943001[/C][/ROW]
[ROW][C]86[/C][C]124.7[/C][C]124.864928135823[/C][C]-0.164928135823189[/C][/ROW]
[ROW][C]87[/C][C]114[/C][C]143.170115879426[/C][C]-29.1701158794258[/C][/ROW]
[ROW][C]88[/C][C]126.6[/C][C]118.590286921694[/C][C]8.00971307830588[/C][/ROW]
[ROW][C]89[/C][C]121.9[/C][C]136.628867189686[/C][C]-14.7288671896856[/C][/ROW]
[ROW][C]90[/C][C]125.1[/C][C]127.843674456522[/C][C]-2.7436744565224[/C][/ROW]
[ROW][C]91[/C][C]122.1[/C][C]121.985461586875[/C][C]0.114538413125246[/C][/ROW]
[ROW][C]92[/C][C]135.9[/C][C]147.364252207196[/C][C]-11.4642522071958[/C][/ROW]
[ROW][C]93[/C][C]148.4[/C][C]144.42242866009[/C][C]3.97757133991038[/C][/ROW]
[ROW][C]94[/C][C]137.5[/C][C]139.721582528843[/C][C]-2.22158252884333[/C][/ROW]
[ROW][C]95[/C][C]145.3[/C][C]160.004715605443[/C][C]-14.7047156054434[/C][/ROW]
[ROW][C]96[/C][C]139.9[/C][C]137.327183895329[/C][C]2.57281610467101[/C][/ROW]
[ROW][C]97[/C][C]128.2[/C][C]135.68006196386[/C][C]-7.48006196386035[/C][/ROW]
[ROW][C]98[/C][C]115.4[/C][C]118.06081079513[/C][C]-2.66081079512979[/C][/ROW]
[ROW][C]99[/C][C]124.7[/C][C]117.075888338417[/C][C]7.62411166158346[/C][/ROW]
[ROW][C]100[/C][C]111.5[/C][C]123.266342255578[/C][C]-11.7663422555776[/C][/ROW]
[ROW][C]101[/C][C]121.1[/C][C]122.295704578738[/C][C]-1.1957045787378[/C][/ROW]
[ROW][C]102[/C][C]122.5[/C][C]123.608740001927[/C][C]-1.10874000192676[/C][/ROW]
[ROW][C]103[/C][C]127.4[/C][C]119.66695035705[/C][C]7.73304964294964[/C][/ROW]
[ROW][C]104[/C][C]143.7[/C][C]139.486618516595[/C][C]4.21338148340496[/C][/ROW]
[ROW][C]105[/C][C]157.8[/C][C]149.575133025594[/C][C]8.22486697440613[/C][/ROW]
[ROW][C]106[/C][C]148.8[/C][C]141.838162915263[/C][C]6.96183708473666[/C][/ROW]
[ROW][C]107[/C][C]162.9[/C][C]157.143153892183[/C][C]5.75684610781713[/C][/ROW]
[ROW][C]108[/C][C]153.9[/C][C]149.151505063144[/C][C]4.74849493685602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115029&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	74	76.1609807081855	-2.16098070818548
14	77.6	79.0715192698551	-1.47151926985515
15	75.1	75.9320633301454	-0.83206333014536
16	85	85.3702471707489	-0.370247170748897
17	75.4	75.2330732961018	0.16692670389817
18	63.2	62.7602291643611	0.439770835638889
19	64.7	59.9747603108474	4.72523968915258
20	77	76.9857929700979	0.0142070299020816
21	82.6	80.737854397984	1.862145602016
22	97.6	98.590085292572	-0.99008529257209
23	99	95.3036784097252	3.69632159027485
24	75.3	77.0443186004388	-1.7443186004388
25	71.6	73.9638293823682	-2.36382938236817
26	76.8	77.2147861428936	-0.414786142893647
27	83.9	74.7678706727276	9.13212932727244
28	79.7	87.221791561436	-7.52179156143598
29	77.5	75.7272089028127	1.77279109718732
30	73.1	63.7419643602922	9.35803563970784
31	65.6	65.7266265579438	-0.126626557943766
32	85.2	79.2392222151445	5.96077778485555
33	98.3	85.923694277481	12.376305722519
34	98	106.148503406018	-8.1485034060185
35	100.6	104.187778000516	-3.58777800051568
36	84.1	79.9568905416234	4.14310945837656
37	76.7	77.8784201026497	-1.17842010264968
38	82.4	83.1904662296599	-0.79046622965987
39	95.5	86.705936204537	8.79406379546302
40	79.9	89.2371047653084	-9.33710476530837
41	82.4	82.75425249186	-0.354252491859938
42	83.6	74.2039821018118	9.3960178981882
43	73.1	70.2437180091495	2.85628199085046
44	91.1	89.6339225146001	1.46607748539991
45	118.6	99.6214602990688	18.9785397009312
46	102.9	109.646879399444	-6.74687939944442
47	111.8	111.20817886582	0.59182113417981
48	93.9	90.9098801962	2.99011980379998
49	91.6	84.9414952417987	6.65850475820132
50	92	93.3551953110195	-1.3551953110195
51	91.1	103.838593280986	-12.7385932809861
52	97.5	89.578106760884	7.92189323911596
53	94.7	92.9771154747697	1.7228845252303
54	96.7	90.4818649150129	6.21813508498714
55	78.7	80.792937942156	-2.09293794215606
56	103.5	100.231119765343	3.26888023465663
57	113.8	123.074772075817	-9.27477207581728
58	106.1	110.425674864106	-4.32567486410616
59	120.3	117.373090491436	2.92690950856441
60	114.2	98.0002142902896	16.1997857097104
61	106.3	97.0108623302688	9.28913766973125
62	98.8	101.5715103602	-2.77151036020022
63	113.1	105.144676842999	7.95532315700119
64	97.7	108.537492182488	-10.8374921824884
65	116.3	103.648649972666	12.6513500273344
66	107.2	106.560862008207	0.639137991792992
67	94.5	88.821026272786	5.67897372721407
68	123.5	116.807493792395	6.69250620760509
69	126.6	135.306892493306	-8.70689249330616
70	126.5	124.849835511515	1.65016448848509
71	141.4	140.04766311641	1.35233688358954
72	124.3	126.053479973353	-1.75347997335339
73	124.9	115.508293700746	9.39170629925364
74	108.9	112.372600800479	-3.47260080047873
75	126.7	123.562341312867	3.13765868713308
76	107.7	113.357500396483	-5.65750039648297
77	121.8	125.153856399775	-3.35385639977471
78	118.3	116.411184433191	1.88881556680887
79	122.8	100.589716017468	22.2102839825317
80	149.5	136.795936209635	12.7040637903651
81	147	148.689573475122	-1.68957347512176
82	139.3	145.99850723732	-6.69850723732011
83	162.1	161.325666058821	0.774333941179265
84	142.2	143.165877883393	-0.965877883392778
85	141.4	139.02279915057	2.37720084943001
86	124.7	124.864928135823	-0.164928135823189
87	114	143.170115879426	-29.1701158794258
88	126.6	118.590286921694	8.00971307830588
89	121.9	136.628867189686	-14.7288671896856
90	125.1	127.843674456522	-2.7436744565224
91	122.1	121.985461586875	0.114538413125246
92	135.9	147.364252207196	-11.4642522071958
93	148.4	144.42242866009	3.97757133991038
94	137.5	139.721582528843	-2.22158252884333
95	145.3	160.004715605443	-14.7047156054434
96	139.9	137.327183895329	2.57281610467101
97	128.2	135.68006196386	-7.48006196386035
98	115.4	118.06081079513	-2.66081079512979
99	124.7	117.075888338417	7.62411166158346
100	111.5	123.266342255578	-11.7663422555776
101	121.1	122.295704578738	-1.1957045787378
102	122.5	123.608740001927	-1.10874000192676
103	127.4	119.66695035705	7.73304964294964
104	143.7	139.486618516595	4.21338148340496
105	157.8	149.575133025594	8.22486697440613
106	148.8	141.838162915263	6.96183708473666
107	162.9	157.143153892183	5.75684610781713
108	153.9	149.151505063144	4.74849493685602

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	141.406617179124	129.050372233495	153.762862124753
110	127.400448551296	114.621471934327	140.179425168265
111	133.89525133318	120.496490331273	147.294012335088
112	125.967364911902	112.207592956421	139.727136867383
113	135.248587930581	120.678153390128	149.819022471035
114	137.307558410042	122.113058613373	152.502058206711
115	139.273724885247	123.437805739424	155.109644031071
116	156.957822687201	139.630152314849	174.285493059552
117	169.65855869907	150.976538992097	188.340578406043
118	158.359978394713	139.825673108269	176.894283681157
119	172.225506261968	152.108321390685	192.342691133252
120	161.598571755364	134.580639386293	188.616504124436

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 141.406617179124 & 129.050372233495 & 153.762862124753 \tabularnewline
110 & 127.400448551296 & 114.621471934327 & 140.179425168265 \tabularnewline
111 & 133.89525133318 & 120.496490331273 & 147.294012335088 \tabularnewline
112 & 125.967364911902 & 112.207592956421 & 139.727136867383 \tabularnewline
113 & 135.248587930581 & 120.678153390128 & 149.819022471035 \tabularnewline
114 & 137.307558410042 & 122.113058613373 & 152.502058206711 \tabularnewline
115 & 139.273724885247 & 123.437805739424 & 155.109644031071 \tabularnewline
116 & 156.957822687201 & 139.630152314849 & 174.285493059552 \tabularnewline
117 & 169.65855869907 & 150.976538992097 & 188.340578406043 \tabularnewline
118 & 158.359978394713 & 139.825673108269 & 176.894283681157 \tabularnewline
119 & 172.225506261968 & 152.108321390685 & 192.342691133252 \tabularnewline
120 & 161.598571755364 & 134.580639386293 & 188.616504124436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115029&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]141.406617179124[/C][C]129.050372233495[/C][C]153.762862124753[/C][/ROW]
[ROW][C]110[/C][C]127.400448551296[/C][C]114.621471934327[/C][C]140.179425168265[/C][/ROW]
[ROW][C]111[/C][C]133.89525133318[/C][C]120.496490331273[/C][C]147.294012335088[/C][/ROW]
[ROW][C]112[/C][C]125.967364911902[/C][C]112.207592956421[/C][C]139.727136867383[/C][/ROW]
[ROW][C]113[/C][C]135.248587930581[/C][C]120.678153390128[/C][C]149.819022471035[/C][/ROW]
[ROW][C]114[/C][C]137.307558410042[/C][C]122.113058613373[/C][C]152.502058206711[/C][/ROW]
[ROW][C]115[/C][C]139.273724885247[/C][C]123.437805739424[/C][C]155.109644031071[/C][/ROW]
[ROW][C]116[/C][C]156.957822687201[/C][C]139.630152314849[/C][C]174.285493059552[/C][/ROW]
[ROW][C]117[/C][C]169.65855869907[/C][C]150.976538992097[/C][C]188.340578406043[/C][/ROW]
[ROW][C]118[/C][C]158.359978394713[/C][C]139.825673108269[/C][C]176.894283681157[/C][/ROW]
[ROW][C]119[/C][C]172.225506261968[/C][C]152.108321390685[/C][C]192.342691133252[/C][/ROW]
[ROW][C]120[/C][C]161.598571755364[/C][C]134.580639386293[/C][C]188.616504124436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115029&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115029&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	141.406617179124	129.050372233495	153.762862124753
110	127.400448551296	114.621471934327	140.179425168265
111	133.89525133318	120.496490331273	147.294012335088
112	125.967364911902	112.207592956421	139.727136867383
113	135.248587930581	120.678153390128	149.819022471035
114	137.307558410042	122.113058613373	152.502058206711
115	139.273724885247	123.437805739424	155.109644031071
116	156.957822687201	139.630152314849	174.285493059552
117	169.65855869907	150.976538992097	188.340578406043
118	158.359978394713	139.825673108269	176.894283681157
119	172.225506261968	152.108321390685	192.342691133252
120	161.598571755364	134.580639386293	188.616504124436

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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