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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

Sun, 16 Jan 2011 15:29:18 +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/2011/Jan/16/t1295193489i9tqs3fu90gc33w.htm/, Retrieved Thu, 16 May 2024 14:24:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117436, Retrieved Thu, 16 May 2024 14:24:50 +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] [] [2011-01-16 15:29:18] [465c6c9df074117d1de4b3f3c25f0c87] [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	'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117436&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117436&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	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.422780569694171
beta	0.0509407545878842
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.422780569694171 \tabularnewline
beta & 0.0509407545878842 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117436&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]0.422780569694171[/C][/ROW]
[ROW][C]beta[/C][C]0.0509407545878842[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117436&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	0.422780569694171
beta	0.0509407545878842
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	74.2	97.4696531217023	-23.2696531217022
14	76	87.494643728192	-11.4946437281919
15	76.2	80.5631398801289	-4.36313988012893
16	74.9	75.1529736755632	-0.25297367556324
17	74.1	71.7930050109392	2.30699498906077
18	76.5	72.4569462108016	4.04305378919841
19	57.8	43.4471419389714	14.3528580610286
20	59.2	51.4946239093631	7.70537609063691
21	57.3	59.101675497228	-1.80167549722803
22	57.5	58.1160143828865	-0.616014382886526
23	60.4	59.1048617310509	1.29513826894911
24	59.9	58.9378089807861	0.962191019213911
25	59.9	49.2410214183594	10.6589785816406
26	60	58.11389568684	1.88610431315995
27	60.2	60.6656652120729	-0.465665212072849
28	65.4	59.8770816284178	5.52291837158225
29	62.4	61.3599374102099	1.04006258979014
30	78.8	63.0021589681363	15.7978410318637
31	65.6	47.068164004859	18.531835995141
32	64.4	53.931982432364	10.468017567636
33	67.4	58.4281170915968	8.97188290840322
34	65.3	64.4808305409199	0.819169459080115
35	66.7	69.5370952029573	-2.83709520295727
36	66.8	69.3524718183228	-2.55247181832276
37	69.4	64.4603096253617	4.93969037463829
38	71.7	67.4631420442994	4.23685795570059
39	77.1	71.6590574828285	5.44094251717152
40	81.1	79.8081370274108	1.29186297258923
41	82.1	78.4444658027555	3.65553419724452
42	92.1	94.3248915968475	-2.22489159684748
43	77.1	68.2647984671459	8.83520153285413
44	78.2	66.3514391174274	11.8485608825726
45	77.7	71.156824800966	6.54317519903393
46	77.3	72.1395446909289	5.16045530907108
47	78.5	78.3365070265643	0.16349297343568
48	78.8	81.0048785672222	-2.20487856722218
49	78.7	81.8921236100645	-3.19212361006447
50	79.8	82.1544281846514	-2.35442818465143
51	82.2	85.5143976129973	-3.31439761299734
52	84	88.6262144761773	-4.62621447617728
53	81.7	86.6457532719863	-4.94575327198626
54	77.6	96.239005014121	-18.639005014121
55	64.3	70.1333206186518	-5.83332061865181
56	72.6	63.4624986972499	9.13750130275007
57	73.8	64.0016828876833	9.79831711231674
58	73.8	65.5090869489537	8.29091305104627
59	70.1	69.8042648005846	0.295735199415404
60	70	70.7937736619488	-0.79377366194879
61	72.3	71.3494766967108	0.950523303289202
62	72.1	73.5281505906217	-1.42815059062174
63	73.3	76.2605680300349	-2.96056803003492
64	79.1	78.267108947801	0.832891052198917
65	77	78.358877753979	-1.35887775397902
66	76.1	80.5495677278125	-4.44956772781251
67	66.4	67.885605728391	-1.48560572839101
68	72.7	72.0588653647302	0.641134635269779
69	73.2	69.2796355213542	3.92036447864582
70	70.7	67.3949520038613	3.30504799613865
71	73.6	65.1698645081275	8.43013549187245
72	74.2	69.0949301414909	5.1050698585091
73	72.6	73.459453684245	-0.859453684244997
74	73.6	73.7354950191562	-0.135495019156181
75	79.1	76.4336433340664	2.66635666593362
76	79.6	83.7697271094478	-4.16972710944778
77	78	80.7440313801815	-2.74403138018148
78	85.4	80.8340233625048	4.56597663749523
79	82	73.3508484401147	8.64915155988534
80	91.9	84.7850352535039	7.11496474649613
81	89.4	87.2707003936192	2.1292996063808
82	92.1	84.2659208350583	7.83407916494174
83	93.8	87.3626639769617	6.43733602303834
84	93.6	88.866557136	4.73344286399994
85	95.6	90.09840708052	5.50159291947995
86	99.9	94.6739229356168	5.22607706438323
87	103.7	103.691943733467	0.00805626653330194
88	99.2	107.626946895424	-8.42694689542438
89	93.7	104.41953270131	-10.7195327013104
90	93.5	107.672460848824	-14.1724608488235
91	80.7	93.3824335894013	-12.6824335894013
92	91.8	95.1567553518504	-3.35675535185038
93	105.8	89.9339205628948	15.8660794371052
94	111.3	95.744127996031	15.555872003969
95	110.3	101.135236452591	9.16476354740917
96	109.4	102.580164763613	6.81983523638668
97	111.4	105.130156951341	6.26984304865859
98	111.6	110.182035361365	1.41796463863541
99	111.8	115.032988744125	-3.23298874412546
100	106.6	112.441452563164	-5.84145256316397
101	104.3	108.625099541743	-4.32509954174287
102	105.5	113.022136945463	-7.52213694546255
103	98.5	100.870763698647	-2.37076369864693
104	108.5	115.935183891023	-7.43518389102304
105	106	121.547081317978	-15.5470813179784
106	101.8	113.018661503138	-11.2186615031376
107	101.3	102.670528322464	-1.37052832246422
108	92.4	97.6663895177743	-5.26638951777433
109	88.9	93.7881508284179	-4.88815082841788
110	84.9	90.2287038185965	-5.3287038185965
111	86.4	87.9298778453421	-1.5298778453421
112	90.7	83.9011693165611	6.79883068343888
113	86.8	85.3892315225562	1.41076847744381
114	90.6	88.5927152913846	2.00728470861539
115	88.3	83.6465598875715	4.65344011242854
116	95.4	96.2940503355499	-0.894050335549878
117	93.6	98.5150288102285	-4.91502881022848
118	91.3	96.2854850042793	-4.98548500427928
119	91.3	93.9583231648315	-2.65832316483147
120	89.3	86.3559410050502	2.94405899494976

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 74.2 & 97.4696531217023 & -23.2696531217022 \tabularnewline
14 & 76 & 87.494643728192 & -11.4946437281919 \tabularnewline
15 & 76.2 & 80.5631398801289 & -4.36313988012893 \tabularnewline
16 & 74.9 & 75.1529736755632 & -0.25297367556324 \tabularnewline
17 & 74.1 & 71.7930050109392 & 2.30699498906077 \tabularnewline
18 & 76.5 & 72.4569462108016 & 4.04305378919841 \tabularnewline
19 & 57.8 & 43.4471419389714 & 14.3528580610286 \tabularnewline
20 & 59.2 & 51.4946239093631 & 7.70537609063691 \tabularnewline
21 & 57.3 & 59.101675497228 & -1.80167549722803 \tabularnewline
22 & 57.5 & 58.1160143828865 & -0.616014382886526 \tabularnewline
23 & 60.4 & 59.1048617310509 & 1.29513826894911 \tabularnewline
24 & 59.9 & 58.9378089807861 & 0.962191019213911 \tabularnewline
25 & 59.9 & 49.2410214183594 & 10.6589785816406 \tabularnewline
26 & 60 & 58.11389568684 & 1.88610431315995 \tabularnewline
27 & 60.2 & 60.6656652120729 & -0.465665212072849 \tabularnewline
28 & 65.4 & 59.8770816284178 & 5.52291837158225 \tabularnewline
29 & 62.4 & 61.3599374102099 & 1.04006258979014 \tabularnewline
30 & 78.8 & 63.0021589681363 & 15.7978410318637 \tabularnewline
31 & 65.6 & 47.068164004859 & 18.531835995141 \tabularnewline
32 & 64.4 & 53.931982432364 & 10.468017567636 \tabularnewline
33 & 67.4 & 58.4281170915968 & 8.97188290840322 \tabularnewline
34 & 65.3 & 64.4808305409199 & 0.819169459080115 \tabularnewline
35 & 66.7 & 69.5370952029573 & -2.83709520295727 \tabularnewline
36 & 66.8 & 69.3524718183228 & -2.55247181832276 \tabularnewline
37 & 69.4 & 64.4603096253617 & 4.93969037463829 \tabularnewline
38 & 71.7 & 67.4631420442994 & 4.23685795570059 \tabularnewline
39 & 77.1 & 71.6590574828285 & 5.44094251717152 \tabularnewline
40 & 81.1 & 79.8081370274108 & 1.29186297258923 \tabularnewline
41 & 82.1 & 78.4444658027555 & 3.65553419724452 \tabularnewline
42 & 92.1 & 94.3248915968475 & -2.22489159684748 \tabularnewline
43 & 77.1 & 68.2647984671459 & 8.83520153285413 \tabularnewline
44 & 78.2 & 66.3514391174274 & 11.8485608825726 \tabularnewline
45 & 77.7 & 71.156824800966 & 6.54317519903393 \tabularnewline
46 & 77.3 & 72.1395446909289 & 5.16045530907108 \tabularnewline
47 & 78.5 & 78.3365070265643 & 0.16349297343568 \tabularnewline
48 & 78.8 & 81.0048785672222 & -2.20487856722218 \tabularnewline
49 & 78.7 & 81.8921236100645 & -3.19212361006447 \tabularnewline
50 & 79.8 & 82.1544281846514 & -2.35442818465143 \tabularnewline
51 & 82.2 & 85.5143976129973 & -3.31439761299734 \tabularnewline
52 & 84 & 88.6262144761773 & -4.62621447617728 \tabularnewline
53 & 81.7 & 86.6457532719863 & -4.94575327198626 \tabularnewline
54 & 77.6 & 96.239005014121 & -18.639005014121 \tabularnewline
55 & 64.3 & 70.1333206186518 & -5.83332061865181 \tabularnewline
56 & 72.6 & 63.4624986972499 & 9.13750130275007 \tabularnewline
57 & 73.8 & 64.0016828876833 & 9.79831711231674 \tabularnewline
58 & 73.8 & 65.5090869489537 & 8.29091305104627 \tabularnewline
59 & 70.1 & 69.8042648005846 & 0.295735199415404 \tabularnewline
60 & 70 & 70.7937736619488 & -0.79377366194879 \tabularnewline
61 & 72.3 & 71.3494766967108 & 0.950523303289202 \tabularnewline
62 & 72.1 & 73.5281505906217 & -1.42815059062174 \tabularnewline
63 & 73.3 & 76.2605680300349 & -2.96056803003492 \tabularnewline
64 & 79.1 & 78.267108947801 & 0.832891052198917 \tabularnewline
65 & 77 & 78.358877753979 & -1.35887775397902 \tabularnewline
66 & 76.1 & 80.5495677278125 & -4.44956772781251 \tabularnewline
67 & 66.4 & 67.885605728391 & -1.48560572839101 \tabularnewline
68 & 72.7 & 72.0588653647302 & 0.641134635269779 \tabularnewline
69 & 73.2 & 69.2796355213542 & 3.92036447864582 \tabularnewline
70 & 70.7 & 67.3949520038613 & 3.30504799613865 \tabularnewline
71 & 73.6 & 65.1698645081275 & 8.43013549187245 \tabularnewline
72 & 74.2 & 69.0949301414909 & 5.1050698585091 \tabularnewline
73 & 72.6 & 73.459453684245 & -0.859453684244997 \tabularnewline
74 & 73.6 & 73.7354950191562 & -0.135495019156181 \tabularnewline
75 & 79.1 & 76.4336433340664 & 2.66635666593362 \tabularnewline
76 & 79.6 & 83.7697271094478 & -4.16972710944778 \tabularnewline
77 & 78 & 80.7440313801815 & -2.74403138018148 \tabularnewline
78 & 85.4 & 80.8340233625048 & 4.56597663749523 \tabularnewline
79 & 82 & 73.3508484401147 & 8.64915155988534 \tabularnewline
80 & 91.9 & 84.7850352535039 & 7.11496474649613 \tabularnewline
81 & 89.4 & 87.2707003936192 & 2.1292996063808 \tabularnewline
82 & 92.1 & 84.2659208350583 & 7.83407916494174 \tabularnewline
83 & 93.8 & 87.3626639769617 & 6.43733602303834 \tabularnewline
84 & 93.6 & 88.866557136 & 4.73344286399994 \tabularnewline
85 & 95.6 & 90.09840708052 & 5.50159291947995 \tabularnewline
86 & 99.9 & 94.6739229356168 & 5.22607706438323 \tabularnewline
87 & 103.7 & 103.691943733467 & 0.00805626653330194 \tabularnewline
88 & 99.2 & 107.626946895424 & -8.42694689542438 \tabularnewline
89 & 93.7 & 104.41953270131 & -10.7195327013104 \tabularnewline
90 & 93.5 & 107.672460848824 & -14.1724608488235 \tabularnewline
91 & 80.7 & 93.3824335894013 & -12.6824335894013 \tabularnewline
92 & 91.8 & 95.1567553518504 & -3.35675535185038 \tabularnewline
93 & 105.8 & 89.9339205628948 & 15.8660794371052 \tabularnewline
94 & 111.3 & 95.744127996031 & 15.555872003969 \tabularnewline
95 & 110.3 & 101.135236452591 & 9.16476354740917 \tabularnewline
96 & 109.4 & 102.580164763613 & 6.81983523638668 \tabularnewline
97 & 111.4 & 105.130156951341 & 6.26984304865859 \tabularnewline
98 & 111.6 & 110.182035361365 & 1.41796463863541 \tabularnewline
99 & 111.8 & 115.032988744125 & -3.23298874412546 \tabularnewline
100 & 106.6 & 112.441452563164 & -5.84145256316397 \tabularnewline
101 & 104.3 & 108.625099541743 & -4.32509954174287 \tabularnewline
102 & 105.5 & 113.022136945463 & -7.52213694546255 \tabularnewline
103 & 98.5 & 100.870763698647 & -2.37076369864693 \tabularnewline
104 & 108.5 & 115.935183891023 & -7.43518389102304 \tabularnewline
105 & 106 & 121.547081317978 & -15.5470813179784 \tabularnewline
106 & 101.8 & 113.018661503138 & -11.2186615031376 \tabularnewline
107 & 101.3 & 102.670528322464 & -1.37052832246422 \tabularnewline
108 & 92.4 & 97.6663895177743 & -5.26638951777433 \tabularnewline
109 & 88.9 & 93.7881508284179 & -4.88815082841788 \tabularnewline
110 & 84.9 & 90.2287038185965 & -5.3287038185965 \tabularnewline
111 & 86.4 & 87.9298778453421 & -1.5298778453421 \tabularnewline
112 & 90.7 & 83.9011693165611 & 6.79883068343888 \tabularnewline
113 & 86.8 & 85.3892315225562 & 1.41076847744381 \tabularnewline
114 & 90.6 & 88.5927152913846 & 2.00728470861539 \tabularnewline
115 & 88.3 & 83.6465598875715 & 4.65344011242854 \tabularnewline
116 & 95.4 & 96.2940503355499 & -0.894050335549878 \tabularnewline
117 & 93.6 & 98.5150288102285 & -4.91502881022848 \tabularnewline
118 & 91.3 & 96.2854850042793 & -4.98548500427928 \tabularnewline
119 & 91.3 & 93.9583231648315 & -2.65832316483147 \tabularnewline
120 & 89.3 & 86.3559410050502 & 2.94405899494976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117436&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]74.2[/C][C]97.4696531217023[/C][C]-23.2696531217022[/C][/ROW]
[ROW][C]14[/C][C]76[/C][C]87.494643728192[/C][C]-11.4946437281919[/C][/ROW]
[ROW][C]15[/C][C]76.2[/C][C]80.5631398801289[/C][C]-4.36313988012893[/C][/ROW]
[ROW][C]16[/C][C]74.9[/C][C]75.1529736755632[/C][C]-0.25297367556324[/C][/ROW]
[ROW][C]17[/C][C]74.1[/C][C]71.7930050109392[/C][C]2.30699498906077[/C][/ROW]
[ROW][C]18[/C][C]76.5[/C][C]72.4569462108016[/C][C]4.04305378919841[/C][/ROW]
[ROW][C]19[/C][C]57.8[/C][C]43.4471419389714[/C][C]14.3528580610286[/C][/ROW]
[ROW][C]20[/C][C]59.2[/C][C]51.4946239093631[/C][C]7.70537609063691[/C][/ROW]
[ROW][C]21[/C][C]57.3[/C][C]59.101675497228[/C][C]-1.80167549722803[/C][/ROW]
[ROW][C]22[/C][C]57.5[/C][C]58.1160143828865[/C][C]-0.616014382886526[/C][/ROW]
[ROW][C]23[/C][C]60.4[/C][C]59.1048617310509[/C][C]1.29513826894911[/C][/ROW]
[ROW][C]24[/C][C]59.9[/C][C]58.9378089807861[/C][C]0.962191019213911[/C][/ROW]
[ROW][C]25[/C][C]59.9[/C][C]49.2410214183594[/C][C]10.6589785816406[/C][/ROW]
[ROW][C]26[/C][C]60[/C][C]58.11389568684[/C][C]1.88610431315995[/C][/ROW]
[ROW][C]27[/C][C]60.2[/C][C]60.6656652120729[/C][C]-0.465665212072849[/C][/ROW]
[ROW][C]28[/C][C]65.4[/C][C]59.8770816284178[/C][C]5.52291837158225[/C][/ROW]
[ROW][C]29[/C][C]62.4[/C][C]61.3599374102099[/C][C]1.04006258979014[/C][/ROW]
[ROW][C]30[/C][C]78.8[/C][C]63.0021589681363[/C][C]15.7978410318637[/C][/ROW]
[ROW][C]31[/C][C]65.6[/C][C]47.068164004859[/C][C]18.531835995141[/C][/ROW]
[ROW][C]32[/C][C]64.4[/C][C]53.931982432364[/C][C]10.468017567636[/C][/ROW]
[ROW][C]33[/C][C]67.4[/C][C]58.4281170915968[/C][C]8.97188290840322[/C][/ROW]
[ROW][C]34[/C][C]65.3[/C][C]64.4808305409199[/C][C]0.819169459080115[/C][/ROW]
[ROW][C]35[/C][C]66.7[/C][C]69.5370952029573[/C][C]-2.83709520295727[/C][/ROW]
[ROW][C]36[/C][C]66.8[/C][C]69.3524718183228[/C][C]-2.55247181832276[/C][/ROW]
[ROW][C]37[/C][C]69.4[/C][C]64.4603096253617[/C][C]4.93969037463829[/C][/ROW]
[ROW][C]38[/C][C]71.7[/C][C]67.4631420442994[/C][C]4.23685795570059[/C][/ROW]
[ROW][C]39[/C][C]77.1[/C][C]71.6590574828285[/C][C]5.44094251717152[/C][/ROW]
[ROW][C]40[/C][C]81.1[/C][C]79.8081370274108[/C][C]1.29186297258923[/C][/ROW]
[ROW][C]41[/C][C]82.1[/C][C]78.4444658027555[/C][C]3.65553419724452[/C][/ROW]
[ROW][C]42[/C][C]92.1[/C][C]94.3248915968475[/C][C]-2.22489159684748[/C][/ROW]
[ROW][C]43[/C][C]77.1[/C][C]68.2647984671459[/C][C]8.83520153285413[/C][/ROW]
[ROW][C]44[/C][C]78.2[/C][C]66.3514391174274[/C][C]11.8485608825726[/C][/ROW]
[ROW][C]45[/C][C]77.7[/C][C]71.156824800966[/C][C]6.54317519903393[/C][/ROW]
[ROW][C]46[/C][C]77.3[/C][C]72.1395446909289[/C][C]5.16045530907108[/C][/ROW]
[ROW][C]47[/C][C]78.5[/C][C]78.3365070265643[/C][C]0.16349297343568[/C][/ROW]
[ROW][C]48[/C][C]78.8[/C][C]81.0048785672222[/C][C]-2.20487856722218[/C][/ROW]
[ROW][C]49[/C][C]78.7[/C][C]81.8921236100645[/C][C]-3.19212361006447[/C][/ROW]
[ROW][C]50[/C][C]79.8[/C][C]82.1544281846514[/C][C]-2.35442818465143[/C][/ROW]
[ROW][C]51[/C][C]82.2[/C][C]85.5143976129973[/C][C]-3.31439761299734[/C][/ROW]
[ROW][C]52[/C][C]84[/C][C]88.6262144761773[/C][C]-4.62621447617728[/C][/ROW]
[ROW][C]53[/C][C]81.7[/C][C]86.6457532719863[/C][C]-4.94575327198626[/C][/ROW]
[ROW][C]54[/C][C]77.6[/C][C]96.239005014121[/C][C]-18.639005014121[/C][/ROW]
[ROW][C]55[/C][C]64.3[/C][C]70.1333206186518[/C][C]-5.83332061865181[/C][/ROW]
[ROW][C]56[/C][C]72.6[/C][C]63.4624986972499[/C][C]9.13750130275007[/C][/ROW]
[ROW][C]57[/C][C]73.8[/C][C]64.0016828876833[/C][C]9.79831711231674[/C][/ROW]
[ROW][C]58[/C][C]73.8[/C][C]65.5090869489537[/C][C]8.29091305104627[/C][/ROW]
[ROW][C]59[/C][C]70.1[/C][C]69.8042648005846[/C][C]0.295735199415404[/C][/ROW]
[ROW][C]60[/C][C]70[/C][C]70.7937736619488[/C][C]-0.79377366194879[/C][/ROW]
[ROW][C]61[/C][C]72.3[/C][C]71.3494766967108[/C][C]0.950523303289202[/C][/ROW]
[ROW][C]62[/C][C]72.1[/C][C]73.5281505906217[/C][C]-1.42815059062174[/C][/ROW]
[ROW][C]63[/C][C]73.3[/C][C]76.2605680300349[/C][C]-2.96056803003492[/C][/ROW]
[ROW][C]64[/C][C]79.1[/C][C]78.267108947801[/C][C]0.832891052198917[/C][/ROW]
[ROW][C]65[/C][C]77[/C][C]78.358877753979[/C][C]-1.35887775397902[/C][/ROW]
[ROW][C]66[/C][C]76.1[/C][C]80.5495677278125[/C][C]-4.44956772781251[/C][/ROW]
[ROW][C]67[/C][C]66.4[/C][C]67.885605728391[/C][C]-1.48560572839101[/C][/ROW]
[ROW][C]68[/C][C]72.7[/C][C]72.0588653647302[/C][C]0.641134635269779[/C][/ROW]
[ROW][C]69[/C][C]73.2[/C][C]69.2796355213542[/C][C]3.92036447864582[/C][/ROW]
[ROW][C]70[/C][C]70.7[/C][C]67.3949520038613[/C][C]3.30504799613865[/C][/ROW]
[ROW][C]71[/C][C]73.6[/C][C]65.1698645081275[/C][C]8.43013549187245[/C][/ROW]
[ROW][C]72[/C][C]74.2[/C][C]69.0949301414909[/C][C]5.1050698585091[/C][/ROW]
[ROW][C]73[/C][C]72.6[/C][C]73.459453684245[/C][C]-0.859453684244997[/C][/ROW]
[ROW][C]74[/C][C]73.6[/C][C]73.7354950191562[/C][C]-0.135495019156181[/C][/ROW]
[ROW][C]75[/C][C]79.1[/C][C]76.4336433340664[/C][C]2.66635666593362[/C][/ROW]
[ROW][C]76[/C][C]79.6[/C][C]83.7697271094478[/C][C]-4.16972710944778[/C][/ROW]
[ROW][C]77[/C][C]78[/C][C]80.7440313801815[/C][C]-2.74403138018148[/C][/ROW]
[ROW][C]78[/C][C]85.4[/C][C]80.8340233625048[/C][C]4.56597663749523[/C][/ROW]
[ROW][C]79[/C][C]82[/C][C]73.3508484401147[/C][C]8.64915155988534[/C][/ROW]
[ROW][C]80[/C][C]91.9[/C][C]84.7850352535039[/C][C]7.11496474649613[/C][/ROW]
[ROW][C]81[/C][C]89.4[/C][C]87.2707003936192[/C][C]2.1292996063808[/C][/ROW]
[ROW][C]82[/C][C]92.1[/C][C]84.2659208350583[/C][C]7.83407916494174[/C][/ROW]
[ROW][C]83[/C][C]93.8[/C][C]87.3626639769617[/C][C]6.43733602303834[/C][/ROW]
[ROW][C]84[/C][C]93.6[/C][C]88.866557136[/C][C]4.73344286399994[/C][/ROW]
[ROW][C]85[/C][C]95.6[/C][C]90.09840708052[/C][C]5.50159291947995[/C][/ROW]
[ROW][C]86[/C][C]99.9[/C][C]94.6739229356168[/C][C]5.22607706438323[/C][/ROW]
[ROW][C]87[/C][C]103.7[/C][C]103.691943733467[/C][C]0.00805626653330194[/C][/ROW]
[ROW][C]88[/C][C]99.2[/C][C]107.626946895424[/C][C]-8.42694689542438[/C][/ROW]
[ROW][C]89[/C][C]93.7[/C][C]104.41953270131[/C][C]-10.7195327013104[/C][/ROW]
[ROW][C]90[/C][C]93.5[/C][C]107.672460848824[/C][C]-14.1724608488235[/C][/ROW]
[ROW][C]91[/C][C]80.7[/C][C]93.3824335894013[/C][C]-12.6824335894013[/C][/ROW]
[ROW][C]92[/C][C]91.8[/C][C]95.1567553518504[/C][C]-3.35675535185038[/C][/ROW]
[ROW][C]93[/C][C]105.8[/C][C]89.9339205628948[/C][C]15.8660794371052[/C][/ROW]
[ROW][C]94[/C][C]111.3[/C][C]95.744127996031[/C][C]15.555872003969[/C][/ROW]
[ROW][C]95[/C][C]110.3[/C][C]101.135236452591[/C][C]9.16476354740917[/C][/ROW]
[ROW][C]96[/C][C]109.4[/C][C]102.580164763613[/C][C]6.81983523638668[/C][/ROW]
[ROW][C]97[/C][C]111.4[/C][C]105.130156951341[/C][C]6.26984304865859[/C][/ROW]
[ROW][C]98[/C][C]111.6[/C][C]110.182035361365[/C][C]1.41796463863541[/C][/ROW]
[ROW][C]99[/C][C]111.8[/C][C]115.032988744125[/C][C]-3.23298874412546[/C][/ROW]
[ROW][C]100[/C][C]106.6[/C][C]112.441452563164[/C][C]-5.84145256316397[/C][/ROW]
[ROW][C]101[/C][C]104.3[/C][C]108.625099541743[/C][C]-4.32509954174287[/C][/ROW]
[ROW][C]102[/C][C]105.5[/C][C]113.022136945463[/C][C]-7.52213694546255[/C][/ROW]
[ROW][C]103[/C][C]98.5[/C][C]100.870763698647[/C][C]-2.37076369864693[/C][/ROW]
[ROW][C]104[/C][C]108.5[/C][C]115.935183891023[/C][C]-7.43518389102304[/C][/ROW]
[ROW][C]105[/C][C]106[/C][C]121.547081317978[/C][C]-15.5470813179784[/C][/ROW]
[ROW][C]106[/C][C]101.8[/C][C]113.018661503138[/C][C]-11.2186615031376[/C][/ROW]
[ROW][C]107[/C][C]101.3[/C][C]102.670528322464[/C][C]-1.37052832246422[/C][/ROW]
[ROW][C]108[/C][C]92.4[/C][C]97.6663895177743[/C][C]-5.26638951777433[/C][/ROW]
[ROW][C]109[/C][C]88.9[/C][C]93.7881508284179[/C][C]-4.88815082841788[/C][/ROW]
[ROW][C]110[/C][C]84.9[/C][C]90.2287038185965[/C][C]-5.3287038185965[/C][/ROW]
[ROW][C]111[/C][C]86.4[/C][C]87.9298778453421[/C][C]-1.5298778453421[/C][/ROW]
[ROW][C]112[/C][C]90.7[/C][C]83.9011693165611[/C][C]6.79883068343888[/C][/ROW]
[ROW][C]113[/C][C]86.8[/C][C]85.3892315225562[/C][C]1.41076847744381[/C][/ROW]
[ROW][C]114[/C][C]90.6[/C][C]88.5927152913846[/C][C]2.00728470861539[/C][/ROW]
[ROW][C]115[/C][C]88.3[/C][C]83.6465598875715[/C][C]4.65344011242854[/C][/ROW]
[ROW][C]116[/C][C]95.4[/C][C]96.2940503355499[/C][C]-0.894050335549878[/C][/ROW]
[ROW][C]117[/C][C]93.6[/C][C]98.5150288102285[/C][C]-4.91502881022848[/C][/ROW]
[ROW][C]118[/C][C]91.3[/C][C]96.2854850042793[/C][C]-4.98548500427928[/C][/ROW]
[ROW][C]119[/C][C]91.3[/C][C]93.9583231648315[/C][C]-2.65832316483147[/C][/ROW]
[ROW][C]120[/C][C]89.3[/C][C]86.3559410050502[/C][C]2.94405899494976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117436&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117436&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	74.2	97.4696531217023	-23.2696531217022
14	76	87.494643728192	-11.4946437281919
15	76.2	80.5631398801289	-4.36313988012893
16	74.9	75.1529736755632	-0.25297367556324
17	74.1	71.7930050109392	2.30699498906077
18	76.5	72.4569462108016	4.04305378919841
19	57.8	43.4471419389714	14.3528580610286
20	59.2	51.4946239093631	7.70537609063691
21	57.3	59.101675497228	-1.80167549722803
22	57.5	58.1160143828865	-0.616014382886526
23	60.4	59.1048617310509	1.29513826894911
24	59.9	58.9378089807861	0.962191019213911
25	59.9	49.2410214183594	10.6589785816406
26	60	58.11389568684	1.88610431315995
27	60.2	60.6656652120729	-0.465665212072849
28	65.4	59.8770816284178	5.52291837158225
29	62.4	61.3599374102099	1.04006258979014
30	78.8	63.0021589681363	15.7978410318637
31	65.6	47.068164004859	18.531835995141
32	64.4	53.931982432364	10.468017567636
33	67.4	58.4281170915968	8.97188290840322
34	65.3	64.4808305409199	0.819169459080115
35	66.7	69.5370952029573	-2.83709520295727
36	66.8	69.3524718183228	-2.55247181832276
37	69.4	64.4603096253617	4.93969037463829
38	71.7	67.4631420442994	4.23685795570059
39	77.1	71.6590574828285	5.44094251717152
40	81.1	79.8081370274108	1.29186297258923
41	82.1	78.4444658027555	3.65553419724452
42	92.1	94.3248915968475	-2.22489159684748
43	77.1	68.2647984671459	8.83520153285413
44	78.2	66.3514391174274	11.8485608825726
45	77.7	71.156824800966	6.54317519903393
46	77.3	72.1395446909289	5.16045530907108
47	78.5	78.3365070265643	0.16349297343568
48	78.8	81.0048785672222	-2.20487856722218
49	78.7	81.8921236100645	-3.19212361006447
50	79.8	82.1544281846514	-2.35442818465143
51	82.2	85.5143976129973	-3.31439761299734
52	84	88.6262144761773	-4.62621447617728
53	81.7	86.6457532719863	-4.94575327198626
54	77.6	96.239005014121	-18.639005014121
55	64.3	70.1333206186518	-5.83332061865181
56	72.6	63.4624986972499	9.13750130275007
57	73.8	64.0016828876833	9.79831711231674
58	73.8	65.5090869489537	8.29091305104627
59	70.1	69.8042648005846	0.295735199415404
60	70	70.7937736619488	-0.79377366194879
61	72.3	71.3494766967108	0.950523303289202
62	72.1	73.5281505906217	-1.42815059062174
63	73.3	76.2605680300349	-2.96056803003492
64	79.1	78.267108947801	0.832891052198917
65	77	78.358877753979	-1.35887775397902
66	76.1	80.5495677278125	-4.44956772781251
67	66.4	67.885605728391	-1.48560572839101
68	72.7	72.0588653647302	0.641134635269779
69	73.2	69.2796355213542	3.92036447864582
70	70.7	67.3949520038613	3.30504799613865
71	73.6	65.1698645081275	8.43013549187245
72	74.2	69.0949301414909	5.1050698585091
73	72.6	73.459453684245	-0.859453684244997
74	73.6	73.7354950191562	-0.135495019156181
75	79.1	76.4336433340664	2.66635666593362
76	79.6	83.7697271094478	-4.16972710944778
77	78	80.7440313801815	-2.74403138018148
78	85.4	80.8340233625048	4.56597663749523
79	82	73.3508484401147	8.64915155988534
80	91.9	84.7850352535039	7.11496474649613
81	89.4	87.2707003936192	2.1292996063808
82	92.1	84.2659208350583	7.83407916494174
83	93.8	87.3626639769617	6.43733602303834
84	93.6	88.866557136	4.73344286399994
85	95.6	90.09840708052	5.50159291947995
86	99.9	94.6739229356168	5.22607706438323
87	103.7	103.691943733467	0.00805626653330194
88	99.2	107.626946895424	-8.42694689542438
89	93.7	104.41953270131	-10.7195327013104
90	93.5	107.672460848824	-14.1724608488235
91	80.7	93.3824335894013	-12.6824335894013
92	91.8	95.1567553518504	-3.35675535185038
93	105.8	89.9339205628948	15.8660794371052
94	111.3	95.744127996031	15.555872003969
95	110.3	101.135236452591	9.16476354740917
96	109.4	102.580164763613	6.81983523638668
97	111.4	105.130156951341	6.26984304865859
98	111.6	110.182035361365	1.41796463863541
99	111.8	115.032988744125	-3.23298874412546
100	106.6	112.441452563164	-5.84145256316397
101	104.3	108.625099541743	-4.32509954174287
102	105.5	113.022136945463	-7.52213694546255
103	98.5	100.870763698647	-2.37076369864693
104	108.5	115.935183891023	-7.43518389102304
105	106	121.547081317978	-15.5470813179784
106	101.8	113.018661503138	-11.2186615031376
107	101.3	102.670528322464	-1.37052832246422
108	92.4	97.6663895177743	-5.26638951777433
109	88.9	93.7881508284179	-4.88815082841788
110	84.9	90.2287038185965	-5.3287038185965
111	86.4	87.9298778453421	-1.5298778453421
112	90.7	83.9011693165611	6.79883068343888
113	86.8	85.3892315225562	1.41076847744381
114	90.6	88.5927152913846	2.00728470861539
115	88.3	83.6465598875715	4.65344011242854
116	95.4	96.2940503355499	-0.894050335549878
117	93.6	98.5150288102285	-4.91502881022848
118	91.3	96.2854850042793	-4.98548500427928
119	91.3	93.9583231648315	-2.65832316483147
120	89.3	86.3559410050502	2.94405899494976

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	86.0533563820287	72.0227301067477	100.08398265731
122	84.2593975087075	68.9517499275693	99.5670450898457
123	86.4746720629798	69.6925754801267	103.256768645833
124	87.900433675216	69.6287167864192	106.172150564013
125	83.5076857222329	64.318977658555	102.696393785911
126	86.2737415646314	65.3116470751294	107.235836054133
127	82.0499789792314	60.309161865594	103.790796092869
128	88.7792020357376	64.369524411365	113.18887966011
129	88.780734081546	62.8649961024594	114.696472060633
130	88.4355510896264	61.0667205537393	115.804381625514
131	89.5084121283924	60.3147844651656	118.702039791619
132	86.3622832810063	14.1923432461477	158.532223315865

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 86.0533563820287 & 72.0227301067477 & 100.08398265731 \tabularnewline
122 & 84.2593975087075 & 68.9517499275693 & 99.5670450898457 \tabularnewline
123 & 86.4746720629798 & 69.6925754801267 & 103.256768645833 \tabularnewline
124 & 87.900433675216 & 69.6287167864192 & 106.172150564013 \tabularnewline
125 & 83.5076857222329 & 64.318977658555 & 102.696393785911 \tabularnewline
126 & 86.2737415646314 & 65.3116470751294 & 107.235836054133 \tabularnewline
127 & 82.0499789792314 & 60.309161865594 & 103.790796092869 \tabularnewline
128 & 88.7792020357376 & 64.369524411365 & 113.18887966011 \tabularnewline
129 & 88.780734081546 & 62.8649961024594 & 114.696472060633 \tabularnewline
130 & 88.4355510896264 & 61.0667205537393 & 115.804381625514 \tabularnewline
131 & 89.5084121283924 & 60.3147844651656 & 118.702039791619 \tabularnewline
132 & 86.3622832810063 & 14.1923432461477 & 158.532223315865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117436&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]121[/C][C]86.0533563820287[/C][C]72.0227301067477[/C][C]100.08398265731[/C][/ROW]
[ROW][C]122[/C][C]84.2593975087075[/C][C]68.9517499275693[/C][C]99.5670450898457[/C][/ROW]
[ROW][C]123[/C][C]86.4746720629798[/C][C]69.6925754801267[/C][C]103.256768645833[/C][/ROW]
[ROW][C]124[/C][C]87.900433675216[/C][C]69.6287167864192[/C][C]106.172150564013[/C][/ROW]
[ROW][C]125[/C][C]83.5076857222329[/C][C]64.318977658555[/C][C]102.696393785911[/C][/ROW]
[ROW][C]126[/C][C]86.2737415646314[/C][C]65.3116470751294[/C][C]107.235836054133[/C][/ROW]
[ROW][C]127[/C][C]82.0499789792314[/C][C]60.309161865594[/C][C]103.790796092869[/C][/ROW]
[ROW][C]128[/C][C]88.7792020357376[/C][C]64.369524411365[/C][C]113.18887966011[/C][/ROW]
[ROW][C]129[/C][C]88.780734081546[/C][C]62.8649961024594[/C][C]114.696472060633[/C][/ROW]
[ROW][C]130[/C][C]88.4355510896264[/C][C]61.0667205537393[/C][C]115.804381625514[/C][/ROW]
[ROW][C]131[/C][C]89.5084121283924[/C][C]60.3147844651656[/C][C]118.702039791619[/C][/ROW]
[ROW][C]132[/C][C]86.3622832810063[/C][C]14.1923432461477[/C][C]158.532223315865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117436&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117436&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
121	86.0533563820287	72.0227301067477	100.08398265731
122	84.2593975087075	68.9517499275693	99.5670450898457
123	86.4746720629798	69.6925754801267	103.256768645833
124	87.900433675216	69.6287167864192	106.172150564013
125	83.5076857222329	64.318977658555	102.696393785911
126	86.2737415646314	65.3116470751294	107.235836054133
127	82.0499789792314	60.309161865594	103.790796092869
128	88.7792020357376	64.369524411365	113.18887966011
129	88.780734081546	62.8649961024594	114.696472060633
130	88.4355510896264	61.0667205537393	115.804381625514
131	89.5084121283924	60.3147844651656	118.702039791619
132	86.3622832810063	14.1923432461477	158.532223315865

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