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

Tue, 28 Dec 2010 17:41:10 +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/28/t1293558073qc9hu3tp3d82yxp.htm/, Retrieved Sun, 05 May 2024 03:49:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116443, Retrieved Sun, 05 May 2024 03:49:31 +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

KDGP2W102

Estimated Impact

106

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

-       [Exponential Smoothing] [opdracht 10 oefen...] [2010-12-28 17:41:10] [72a344459e5b13eacf7bf474aa92c893] [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	7 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116443&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116443&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	7 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.316980625774965
beta	0
gamma	0.600837245360393

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.316980625774965 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.600837245360393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116443&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]0.316980625774965[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.600837245360393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116443&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	0.316980625774965
beta	0
gamma	0.600837245360393

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	143.6	142.513755341880	1.08624465811960
14	134.9	134.505699144731	0.394300855268853
15	135.6	135.765810167953	-0.165810167953197
16	105.3	105.610876848531	-0.310876848530825
17	86.4	86.2974602019199	0.102539798080130
18	74.6	73.8942552893241	0.705744710675887
19	67.6	72.5822546473935	-4.98225464739348
20	73.4	76.3672684095344	-2.9672684095344
21	78.5	81.5159937702799	-3.01599377027989
22	98.2	92.4034408023518	5.7965591976482
23	118.6	109.609296388873	8.9907036111274
24	136.9	128.181800537060	8.71819946293971
25	137.9	148.180369678706	-10.2803696787063
26	115.6	136.285354650808	-20.6853546508077
27	119.3	130.633762970068	-11.3337629700679
28	98.5	96.8792720136946	1.62072798630540
29	84.3	78.3477960382321	5.95220396176789
30	73.5	68.0463666635998	5.45363333640022
31	60.7	65.9050937623291	-5.20509376232911
32	69.5	70.4463889054797	-0.946388905479694
33	77.9	76.2156978329615	1.68430216703848
34	113.9	92.2095737613934	21.6904262386066
35	126.3	115.764301366450	10.5356986335498
36	135.1	134.714707803197	0.38529219680251
37	130.5	144.275207878323	-13.7752078783225
38	113.1	127.002362915626	-13.9023629156255
39	110	127.338586931013	-17.3385869310125
40	90.8	96.9969921895486	-6.19699218954861
41	85.4	77.7650165620859	7.6349834379141
42	72.5	67.79239053091	4.70760946909
43	64.7	61.0404770052546	3.65952299474542
44	67.2	70.1393860319418	-2.93938603194177
45	77.9	76.3565456385111	1.54345436148887
46	105.2	100.515958345942	4.68404165405832
47	107.2	114.102275597597	-6.90227559759728
48	120.7	123.359622940109	-2.6596229401093
49	121.3	126.143708619721	-4.8437086197206
50	107.9	111.649793554500	-3.74979355450022
51	105.6	113.794015791984	-8.1940157919841
52	81.3	90.9233993479795	-9.62339934797954
53	71.7	76.2817333193824	-4.58173331938238
54	64.8	61.2352988509161	3.5647011490839
55	57.3	53.690988156794	3.60901184320601
56	61.9	60.0658028808564	1.83419711914360
57	70.1	69.6357794998148	0.464220500185192
58	88.8	94.7419411228185	-5.94194112281848
59	106.8	100.205194517947	6.59480548205279
60	110.7	115.481969626421	-4.78196962642106
61	114.1	116.696999844925	-2.59699984492451
62	108	103.364172603638	4.63582739636243
63	111.5	106.342638832871	5.15736116712863
64	86.8	87.117554815307	-0.317554815307091
65	78.4	77.4946776565126	0.905322343487413
66	68	67.5306956470861	0.46930435291388
67	57.3	59.0233885163179	-1.72338851631790
68	65.3	62.9795809958962	2.32041900410375
69	73.3	72.1414647607161	1.15853523928389
70	88.6	94.8387278081597	-6.2387278081597
71	101.3	105.352779265323	-4.05277926532256
72	122.9	112.585635744930	10.3143642550704
73	126.6	119.482586825273	7.11741317472689
74	114.1	112.197273110716	1.90272688928439
75	124.7	114.523428274349	10.1765717256512
76	93.3	94.6425216905708	-1.34252169057078
77	77.2	85.1965984734846	-7.99659847348461
78	66.5	72.23194545287	-5.73194545287001
79	57.9	60.8591173492844	-2.95911734928442
80	63.7	66.0831195301012	-2.38311953010123
81	65.8	73.277254805	-7.47725480500002
82	85	90.2014251731632	-5.20142517316324
83	101	101.941358637347	-0.94135863734678
84	105.3	116.056513520694	-10.7565135206938
85	121	114.962428670426	6.03757132957429
86	117.9	105.194804910582	12.7051950894179
87	106	114.340582435652	-8.34058243565171
88	86.6	83.8628511032936	2.73714889670643
89	79.9	72.9793812399695	6.92061876003049
90	65.2	65.6725732589468	-0.472573258946824
91	61.2	57.1047870893277	4.09521291067226
92	67.6	64.8012552794959	2.79874472050409
93	78.9	71.5473921689054	7.35260783109459
94	95.5	94.1063045583064	1.39369544169355
95	113.1	109.685024409225	3.41497559077521
96	124.4	121.153075431026	3.24692456897415
97	122	131.389824122558	-9.38982412255803
98	110.3	119.468297535695	-9.16829753569536
99	114	113.043762274479	0.956237725521177
100	93.3	90.0590607418619	3.24093925813813
101	75.5	81.0521095807769	-5.55210958077686
102	65.4	66.7576445010084	-1.35764450100837
103	59.2	59.7838518763816	-0.583851876381573
104	63.8	65.4650980555767	-1.66509805557668
105	74.2	72.6651134562123	1.53488654378775
106	91.7	90.9344817119508	0.765518288049208
107	107	107.143581555905	-0.143581555904632
108	120.7	117.414673543462	3.28532645653773
109	127.4	122.477681993805	4.92231800619484
110	119.7	115.183738026577	4.5162619734228
111	112.7	117.251885009185	-4.55188500918538
112	84.4	93.458819049478	-9.05881904947807
113	75.6	76.9445608266687	-1.34456082666867
114	66.5	65.7051463573496	0.794853642650367
115	59.9	59.731205650859	0.168794349140995
116	64.8	65.2073005325693	-0.407300532569323
117	74.3	74.1192341928584	0.180765807141555
118	100.4	91.6436363884385	8.75636361156154
119	105.9	110.012599826484	-4.11259982648355
120	131.1	120.432757119394	10.6672428806060

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 143.6 & 142.513755341880 & 1.08624465811960 \tabularnewline
14 & 134.9 & 134.505699144731 & 0.394300855268853 \tabularnewline
15 & 135.6 & 135.765810167953 & -0.165810167953197 \tabularnewline
16 & 105.3 & 105.610876848531 & -0.310876848530825 \tabularnewline
17 & 86.4 & 86.2974602019199 & 0.102539798080130 \tabularnewline
18 & 74.6 & 73.8942552893241 & 0.705744710675887 \tabularnewline
19 & 67.6 & 72.5822546473935 & -4.98225464739348 \tabularnewline
20 & 73.4 & 76.3672684095344 & -2.9672684095344 \tabularnewline
21 & 78.5 & 81.5159937702799 & -3.01599377027989 \tabularnewline
22 & 98.2 & 92.4034408023518 & 5.7965591976482 \tabularnewline
23 & 118.6 & 109.609296388873 & 8.9907036111274 \tabularnewline
24 & 136.9 & 128.181800537060 & 8.71819946293971 \tabularnewline
25 & 137.9 & 148.180369678706 & -10.2803696787063 \tabularnewline
26 & 115.6 & 136.285354650808 & -20.6853546508077 \tabularnewline
27 & 119.3 & 130.633762970068 & -11.3337629700679 \tabularnewline
28 & 98.5 & 96.8792720136946 & 1.62072798630540 \tabularnewline
29 & 84.3 & 78.3477960382321 & 5.95220396176789 \tabularnewline
30 & 73.5 & 68.0463666635998 & 5.45363333640022 \tabularnewline
31 & 60.7 & 65.9050937623291 & -5.20509376232911 \tabularnewline
32 & 69.5 & 70.4463889054797 & -0.946388905479694 \tabularnewline
33 & 77.9 & 76.2156978329615 & 1.68430216703848 \tabularnewline
34 & 113.9 & 92.2095737613934 & 21.6904262386066 \tabularnewline
35 & 126.3 & 115.764301366450 & 10.5356986335498 \tabularnewline
36 & 135.1 & 134.714707803197 & 0.38529219680251 \tabularnewline
37 & 130.5 & 144.275207878323 & -13.7752078783225 \tabularnewline
38 & 113.1 & 127.002362915626 & -13.9023629156255 \tabularnewline
39 & 110 & 127.338586931013 & -17.3385869310125 \tabularnewline
40 & 90.8 & 96.9969921895486 & -6.19699218954861 \tabularnewline
41 & 85.4 & 77.7650165620859 & 7.6349834379141 \tabularnewline
42 & 72.5 & 67.79239053091 & 4.70760946909 \tabularnewline
43 & 64.7 & 61.0404770052546 & 3.65952299474542 \tabularnewline
44 & 67.2 & 70.1393860319418 & -2.93938603194177 \tabularnewline
45 & 77.9 & 76.3565456385111 & 1.54345436148887 \tabularnewline
46 & 105.2 & 100.515958345942 & 4.68404165405832 \tabularnewline
47 & 107.2 & 114.102275597597 & -6.90227559759728 \tabularnewline
48 & 120.7 & 123.359622940109 & -2.6596229401093 \tabularnewline
49 & 121.3 & 126.143708619721 & -4.8437086197206 \tabularnewline
50 & 107.9 & 111.649793554500 & -3.74979355450022 \tabularnewline
51 & 105.6 & 113.794015791984 & -8.1940157919841 \tabularnewline
52 & 81.3 & 90.9233993479795 & -9.62339934797954 \tabularnewline
53 & 71.7 & 76.2817333193824 & -4.58173331938238 \tabularnewline
54 & 64.8 & 61.2352988509161 & 3.5647011490839 \tabularnewline
55 & 57.3 & 53.690988156794 & 3.60901184320601 \tabularnewline
56 & 61.9 & 60.0658028808564 & 1.83419711914360 \tabularnewline
57 & 70.1 & 69.6357794998148 & 0.464220500185192 \tabularnewline
58 & 88.8 & 94.7419411228185 & -5.94194112281848 \tabularnewline
59 & 106.8 & 100.205194517947 & 6.59480548205279 \tabularnewline
60 & 110.7 & 115.481969626421 & -4.78196962642106 \tabularnewline
61 & 114.1 & 116.696999844925 & -2.59699984492451 \tabularnewline
62 & 108 & 103.364172603638 & 4.63582739636243 \tabularnewline
63 & 111.5 & 106.342638832871 & 5.15736116712863 \tabularnewline
64 & 86.8 & 87.117554815307 & -0.317554815307091 \tabularnewline
65 & 78.4 & 77.4946776565126 & 0.905322343487413 \tabularnewline
66 & 68 & 67.5306956470861 & 0.46930435291388 \tabularnewline
67 & 57.3 & 59.0233885163179 & -1.72338851631790 \tabularnewline
68 & 65.3 & 62.9795809958962 & 2.32041900410375 \tabularnewline
69 & 73.3 & 72.1414647607161 & 1.15853523928389 \tabularnewline
70 & 88.6 & 94.8387278081597 & -6.2387278081597 \tabularnewline
71 & 101.3 & 105.352779265323 & -4.05277926532256 \tabularnewline
72 & 122.9 & 112.585635744930 & 10.3143642550704 \tabularnewline
73 & 126.6 & 119.482586825273 & 7.11741317472689 \tabularnewline
74 & 114.1 & 112.197273110716 & 1.90272688928439 \tabularnewline
75 & 124.7 & 114.523428274349 & 10.1765717256512 \tabularnewline
76 & 93.3 & 94.6425216905708 & -1.34252169057078 \tabularnewline
77 & 77.2 & 85.1965984734846 & -7.99659847348461 \tabularnewline
78 & 66.5 & 72.23194545287 & -5.73194545287001 \tabularnewline
79 & 57.9 & 60.8591173492844 & -2.95911734928442 \tabularnewline
80 & 63.7 & 66.0831195301012 & -2.38311953010123 \tabularnewline
81 & 65.8 & 73.277254805 & -7.47725480500002 \tabularnewline
82 & 85 & 90.2014251731632 & -5.20142517316324 \tabularnewline
83 & 101 & 101.941358637347 & -0.94135863734678 \tabularnewline
84 & 105.3 & 116.056513520694 & -10.7565135206938 \tabularnewline
85 & 121 & 114.962428670426 & 6.03757132957429 \tabularnewline
86 & 117.9 & 105.194804910582 & 12.7051950894179 \tabularnewline
87 & 106 & 114.340582435652 & -8.34058243565171 \tabularnewline
88 & 86.6 & 83.8628511032936 & 2.73714889670643 \tabularnewline
89 & 79.9 & 72.9793812399695 & 6.92061876003049 \tabularnewline
90 & 65.2 & 65.6725732589468 & -0.472573258946824 \tabularnewline
91 & 61.2 & 57.1047870893277 & 4.09521291067226 \tabularnewline
92 & 67.6 & 64.8012552794959 & 2.79874472050409 \tabularnewline
93 & 78.9 & 71.5473921689054 & 7.35260783109459 \tabularnewline
94 & 95.5 & 94.1063045583064 & 1.39369544169355 \tabularnewline
95 & 113.1 & 109.685024409225 & 3.41497559077521 \tabularnewline
96 & 124.4 & 121.153075431026 & 3.24692456897415 \tabularnewline
97 & 122 & 131.389824122558 & -9.38982412255803 \tabularnewline
98 & 110.3 & 119.468297535695 & -9.16829753569536 \tabularnewline
99 & 114 & 113.043762274479 & 0.956237725521177 \tabularnewline
100 & 93.3 & 90.0590607418619 & 3.24093925813813 \tabularnewline
101 & 75.5 & 81.0521095807769 & -5.55210958077686 \tabularnewline
102 & 65.4 & 66.7576445010084 & -1.35764450100837 \tabularnewline
103 & 59.2 & 59.7838518763816 & -0.583851876381573 \tabularnewline
104 & 63.8 & 65.4650980555767 & -1.66509805557668 \tabularnewline
105 & 74.2 & 72.6651134562123 & 1.53488654378775 \tabularnewline
106 & 91.7 & 90.9344817119508 & 0.765518288049208 \tabularnewline
107 & 107 & 107.143581555905 & -0.143581555904632 \tabularnewline
108 & 120.7 & 117.414673543462 & 3.28532645653773 \tabularnewline
109 & 127.4 & 122.477681993805 & 4.92231800619484 \tabularnewline
110 & 119.7 & 115.183738026577 & 4.5162619734228 \tabularnewline
111 & 112.7 & 117.251885009185 & -4.55188500918538 \tabularnewline
112 & 84.4 & 93.458819049478 & -9.05881904947807 \tabularnewline
113 & 75.6 & 76.9445608266687 & -1.34456082666867 \tabularnewline
114 & 66.5 & 65.7051463573496 & 0.794853642650367 \tabularnewline
115 & 59.9 & 59.731205650859 & 0.168794349140995 \tabularnewline
116 & 64.8 & 65.2073005325693 & -0.407300532569323 \tabularnewline
117 & 74.3 & 74.1192341928584 & 0.180765807141555 \tabularnewline
118 & 100.4 & 91.6436363884385 & 8.75636361156154 \tabularnewline
119 & 105.9 & 110.012599826484 & -4.11259982648355 \tabularnewline
120 & 131.1 & 120.432757119394 & 10.6672428806060 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116443&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]143.6[/C][C]142.513755341880[/C][C]1.08624465811960[/C][/ROW]
[ROW][C]14[/C][C]134.9[/C][C]134.505699144731[/C][C]0.394300855268853[/C][/ROW]
[ROW][C]15[/C][C]135.6[/C][C]135.765810167953[/C][C]-0.165810167953197[/C][/ROW]
[ROW][C]16[/C][C]105.3[/C][C]105.610876848531[/C][C]-0.310876848530825[/C][/ROW]
[ROW][C]17[/C][C]86.4[/C][C]86.2974602019199[/C][C]0.102539798080130[/C][/ROW]
[ROW][C]18[/C][C]74.6[/C][C]73.8942552893241[/C][C]0.705744710675887[/C][/ROW]
[ROW][C]19[/C][C]67.6[/C][C]72.5822546473935[/C][C]-4.98225464739348[/C][/ROW]
[ROW][C]20[/C][C]73.4[/C][C]76.3672684095344[/C][C]-2.9672684095344[/C][/ROW]
[ROW][C]21[/C][C]78.5[/C][C]81.5159937702799[/C][C]-3.01599377027989[/C][/ROW]
[ROW][C]22[/C][C]98.2[/C][C]92.4034408023518[/C][C]5.7965591976482[/C][/ROW]
[ROW][C]23[/C][C]118.6[/C][C]109.609296388873[/C][C]8.9907036111274[/C][/ROW]
[ROW][C]24[/C][C]136.9[/C][C]128.181800537060[/C][C]8.71819946293971[/C][/ROW]
[ROW][C]25[/C][C]137.9[/C][C]148.180369678706[/C][C]-10.2803696787063[/C][/ROW]
[ROW][C]26[/C][C]115.6[/C][C]136.285354650808[/C][C]-20.6853546508077[/C][/ROW]
[ROW][C]27[/C][C]119.3[/C][C]130.633762970068[/C][C]-11.3337629700679[/C][/ROW]
[ROW][C]28[/C][C]98.5[/C][C]96.8792720136946[/C][C]1.62072798630540[/C][/ROW]
[ROW][C]29[/C][C]84.3[/C][C]78.3477960382321[/C][C]5.95220396176789[/C][/ROW]
[ROW][C]30[/C][C]73.5[/C][C]68.0463666635998[/C][C]5.45363333640022[/C][/ROW]
[ROW][C]31[/C][C]60.7[/C][C]65.9050937623291[/C][C]-5.20509376232911[/C][/ROW]
[ROW][C]32[/C][C]69.5[/C][C]70.4463889054797[/C][C]-0.946388905479694[/C][/ROW]
[ROW][C]33[/C][C]77.9[/C][C]76.2156978329615[/C][C]1.68430216703848[/C][/ROW]
[ROW][C]34[/C][C]113.9[/C][C]92.2095737613934[/C][C]21.6904262386066[/C][/ROW]
[ROW][C]35[/C][C]126.3[/C][C]115.764301366450[/C][C]10.5356986335498[/C][/ROW]
[ROW][C]36[/C][C]135.1[/C][C]134.714707803197[/C][C]0.38529219680251[/C][/ROW]
[ROW][C]37[/C][C]130.5[/C][C]144.275207878323[/C][C]-13.7752078783225[/C][/ROW]
[ROW][C]38[/C][C]113.1[/C][C]127.002362915626[/C][C]-13.9023629156255[/C][/ROW]
[ROW][C]39[/C][C]110[/C][C]127.338586931013[/C][C]-17.3385869310125[/C][/ROW]
[ROW][C]40[/C][C]90.8[/C][C]96.9969921895486[/C][C]-6.19699218954861[/C][/ROW]
[ROW][C]41[/C][C]85.4[/C][C]77.7650165620859[/C][C]7.6349834379141[/C][/ROW]
[ROW][C]42[/C][C]72.5[/C][C]67.79239053091[/C][C]4.70760946909[/C][/ROW]
[ROW][C]43[/C][C]64.7[/C][C]61.0404770052546[/C][C]3.65952299474542[/C][/ROW]
[ROW][C]44[/C][C]67.2[/C][C]70.1393860319418[/C][C]-2.93938603194177[/C][/ROW]
[ROW][C]45[/C][C]77.9[/C][C]76.3565456385111[/C][C]1.54345436148887[/C][/ROW]
[ROW][C]46[/C][C]105.2[/C][C]100.515958345942[/C][C]4.68404165405832[/C][/ROW]
[ROW][C]47[/C][C]107.2[/C][C]114.102275597597[/C][C]-6.90227559759728[/C][/ROW]
[ROW][C]48[/C][C]120.7[/C][C]123.359622940109[/C][C]-2.6596229401093[/C][/ROW]
[ROW][C]49[/C][C]121.3[/C][C]126.143708619721[/C][C]-4.8437086197206[/C][/ROW]
[ROW][C]50[/C][C]107.9[/C][C]111.649793554500[/C][C]-3.74979355450022[/C][/ROW]
[ROW][C]51[/C][C]105.6[/C][C]113.794015791984[/C][C]-8.1940157919841[/C][/ROW]
[ROW][C]52[/C][C]81.3[/C][C]90.9233993479795[/C][C]-9.62339934797954[/C][/ROW]
[ROW][C]53[/C][C]71.7[/C][C]76.2817333193824[/C][C]-4.58173331938238[/C][/ROW]
[ROW][C]54[/C][C]64.8[/C][C]61.2352988509161[/C][C]3.5647011490839[/C][/ROW]
[ROW][C]55[/C][C]57.3[/C][C]53.690988156794[/C][C]3.60901184320601[/C][/ROW]
[ROW][C]56[/C][C]61.9[/C][C]60.0658028808564[/C][C]1.83419711914360[/C][/ROW]
[ROW][C]57[/C][C]70.1[/C][C]69.6357794998148[/C][C]0.464220500185192[/C][/ROW]
[ROW][C]58[/C][C]88.8[/C][C]94.7419411228185[/C][C]-5.94194112281848[/C][/ROW]
[ROW][C]59[/C][C]106.8[/C][C]100.205194517947[/C][C]6.59480548205279[/C][/ROW]
[ROW][C]60[/C][C]110.7[/C][C]115.481969626421[/C][C]-4.78196962642106[/C][/ROW]
[ROW][C]61[/C][C]114.1[/C][C]116.696999844925[/C][C]-2.59699984492451[/C][/ROW]
[ROW][C]62[/C][C]108[/C][C]103.364172603638[/C][C]4.63582739636243[/C][/ROW]
[ROW][C]63[/C][C]111.5[/C][C]106.342638832871[/C][C]5.15736116712863[/C][/ROW]
[ROW][C]64[/C][C]86.8[/C][C]87.117554815307[/C][C]-0.317554815307091[/C][/ROW]
[ROW][C]65[/C][C]78.4[/C][C]77.4946776565126[/C][C]0.905322343487413[/C][/ROW]
[ROW][C]66[/C][C]68[/C][C]67.5306956470861[/C][C]0.46930435291388[/C][/ROW]
[ROW][C]67[/C][C]57.3[/C][C]59.0233885163179[/C][C]-1.72338851631790[/C][/ROW]
[ROW][C]68[/C][C]65.3[/C][C]62.9795809958962[/C][C]2.32041900410375[/C][/ROW]
[ROW][C]69[/C][C]73.3[/C][C]72.1414647607161[/C][C]1.15853523928389[/C][/ROW]
[ROW][C]70[/C][C]88.6[/C][C]94.8387278081597[/C][C]-6.2387278081597[/C][/ROW]
[ROW][C]71[/C][C]101.3[/C][C]105.352779265323[/C][C]-4.05277926532256[/C][/ROW]
[ROW][C]72[/C][C]122.9[/C][C]112.585635744930[/C][C]10.3143642550704[/C][/ROW]
[ROW][C]73[/C][C]126.6[/C][C]119.482586825273[/C][C]7.11741317472689[/C][/ROW]
[ROW][C]74[/C][C]114.1[/C][C]112.197273110716[/C][C]1.90272688928439[/C][/ROW]
[ROW][C]75[/C][C]124.7[/C][C]114.523428274349[/C][C]10.1765717256512[/C][/ROW]
[ROW][C]76[/C][C]93.3[/C][C]94.6425216905708[/C][C]-1.34252169057078[/C][/ROW]
[ROW][C]77[/C][C]77.2[/C][C]85.1965984734846[/C][C]-7.99659847348461[/C][/ROW]
[ROW][C]78[/C][C]66.5[/C][C]72.23194545287[/C][C]-5.73194545287001[/C][/ROW]
[ROW][C]79[/C][C]57.9[/C][C]60.8591173492844[/C][C]-2.95911734928442[/C][/ROW]
[ROW][C]80[/C][C]63.7[/C][C]66.0831195301012[/C][C]-2.38311953010123[/C][/ROW]
[ROW][C]81[/C][C]65.8[/C][C]73.277254805[/C][C]-7.47725480500002[/C][/ROW]
[ROW][C]82[/C][C]85[/C][C]90.2014251731632[/C][C]-5.20142517316324[/C][/ROW]
[ROW][C]83[/C][C]101[/C][C]101.941358637347[/C][C]-0.94135863734678[/C][/ROW]
[ROW][C]84[/C][C]105.3[/C][C]116.056513520694[/C][C]-10.7565135206938[/C][/ROW]
[ROW][C]85[/C][C]121[/C][C]114.962428670426[/C][C]6.03757132957429[/C][/ROW]
[ROW][C]86[/C][C]117.9[/C][C]105.194804910582[/C][C]12.7051950894179[/C][/ROW]
[ROW][C]87[/C][C]106[/C][C]114.340582435652[/C][C]-8.34058243565171[/C][/ROW]
[ROW][C]88[/C][C]86.6[/C][C]83.8628511032936[/C][C]2.73714889670643[/C][/ROW]
[ROW][C]89[/C][C]79.9[/C][C]72.9793812399695[/C][C]6.92061876003049[/C][/ROW]
[ROW][C]90[/C][C]65.2[/C][C]65.6725732589468[/C][C]-0.472573258946824[/C][/ROW]
[ROW][C]91[/C][C]61.2[/C][C]57.1047870893277[/C][C]4.09521291067226[/C][/ROW]
[ROW][C]92[/C][C]67.6[/C][C]64.8012552794959[/C][C]2.79874472050409[/C][/ROW]
[ROW][C]93[/C][C]78.9[/C][C]71.5473921689054[/C][C]7.35260783109459[/C][/ROW]
[ROW][C]94[/C][C]95.5[/C][C]94.1063045583064[/C][C]1.39369544169355[/C][/ROW]
[ROW][C]95[/C][C]113.1[/C][C]109.685024409225[/C][C]3.41497559077521[/C][/ROW]
[ROW][C]96[/C][C]124.4[/C][C]121.153075431026[/C][C]3.24692456897415[/C][/ROW]
[ROW][C]97[/C][C]122[/C][C]131.389824122558[/C][C]-9.38982412255803[/C][/ROW]
[ROW][C]98[/C][C]110.3[/C][C]119.468297535695[/C][C]-9.16829753569536[/C][/ROW]
[ROW][C]99[/C][C]114[/C][C]113.043762274479[/C][C]0.956237725521177[/C][/ROW]
[ROW][C]100[/C][C]93.3[/C][C]90.0590607418619[/C][C]3.24093925813813[/C][/ROW]
[ROW][C]101[/C][C]75.5[/C][C]81.0521095807769[/C][C]-5.55210958077686[/C][/ROW]
[ROW][C]102[/C][C]65.4[/C][C]66.7576445010084[/C][C]-1.35764450100837[/C][/ROW]
[ROW][C]103[/C][C]59.2[/C][C]59.7838518763816[/C][C]-0.583851876381573[/C][/ROW]
[ROW][C]104[/C][C]63.8[/C][C]65.4650980555767[/C][C]-1.66509805557668[/C][/ROW]
[ROW][C]105[/C][C]74.2[/C][C]72.6651134562123[/C][C]1.53488654378775[/C][/ROW]
[ROW][C]106[/C][C]91.7[/C][C]90.9344817119508[/C][C]0.765518288049208[/C][/ROW]
[ROW][C]107[/C][C]107[/C][C]107.143581555905[/C][C]-0.143581555904632[/C][/ROW]
[ROW][C]108[/C][C]120.7[/C][C]117.414673543462[/C][C]3.28532645653773[/C][/ROW]
[ROW][C]109[/C][C]127.4[/C][C]122.477681993805[/C][C]4.92231800619484[/C][/ROW]
[ROW][C]110[/C][C]119.7[/C][C]115.183738026577[/C][C]4.5162619734228[/C][/ROW]
[ROW][C]111[/C][C]112.7[/C][C]117.251885009185[/C][C]-4.55188500918538[/C][/ROW]
[ROW][C]112[/C][C]84.4[/C][C]93.458819049478[/C][C]-9.05881904947807[/C][/ROW]
[ROW][C]113[/C][C]75.6[/C][C]76.9445608266687[/C][C]-1.34456082666867[/C][/ROW]
[ROW][C]114[/C][C]66.5[/C][C]65.7051463573496[/C][C]0.794853642650367[/C][/ROW]
[ROW][C]115[/C][C]59.9[/C][C]59.731205650859[/C][C]0.168794349140995[/C][/ROW]
[ROW][C]116[/C][C]64.8[/C][C]65.2073005325693[/C][C]-0.407300532569323[/C][/ROW]
[ROW][C]117[/C][C]74.3[/C][C]74.1192341928584[/C][C]0.180765807141555[/C][/ROW]
[ROW][C]118[/C][C]100.4[/C][C]91.6436363884385[/C][C]8.75636361156154[/C][/ROW]
[ROW][C]119[/C][C]105.9[/C][C]110.012599826484[/C][C]-4.11259982648355[/C][/ROW]
[ROW][C]120[/C][C]131.1[/C][C]120.432757119394[/C][C]10.6672428806060[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116443&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116443&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	143.6	142.513755341880	1.08624465811960
14	134.9	134.505699144731	0.394300855268853
15	135.6	135.765810167953	-0.165810167953197
16	105.3	105.610876848531	-0.310876848530825
17	86.4	86.2974602019199	0.102539798080130
18	74.6	73.8942552893241	0.705744710675887
19	67.6	72.5822546473935	-4.98225464739348
20	73.4	76.3672684095344	-2.9672684095344
21	78.5	81.5159937702799	-3.01599377027989
22	98.2	92.4034408023518	5.7965591976482
23	118.6	109.609296388873	8.9907036111274
24	136.9	128.181800537060	8.71819946293971
25	137.9	148.180369678706	-10.2803696787063
26	115.6	136.285354650808	-20.6853546508077
27	119.3	130.633762970068	-11.3337629700679
28	98.5	96.8792720136946	1.62072798630540
29	84.3	78.3477960382321	5.95220396176789
30	73.5	68.0463666635998	5.45363333640022
31	60.7	65.9050937623291	-5.20509376232911
32	69.5	70.4463889054797	-0.946388905479694
33	77.9	76.2156978329615	1.68430216703848
34	113.9	92.2095737613934	21.6904262386066
35	126.3	115.764301366450	10.5356986335498
36	135.1	134.714707803197	0.38529219680251
37	130.5	144.275207878323	-13.7752078783225
38	113.1	127.002362915626	-13.9023629156255
39	110	127.338586931013	-17.3385869310125
40	90.8	96.9969921895486	-6.19699218954861
41	85.4	77.7650165620859	7.6349834379141
42	72.5	67.79239053091	4.70760946909
43	64.7	61.0404770052546	3.65952299474542
44	67.2	70.1393860319418	-2.93938603194177
45	77.9	76.3565456385111	1.54345436148887
46	105.2	100.515958345942	4.68404165405832
47	107.2	114.102275597597	-6.90227559759728
48	120.7	123.359622940109	-2.6596229401093
49	121.3	126.143708619721	-4.8437086197206
50	107.9	111.649793554500	-3.74979355450022
51	105.6	113.794015791984	-8.1940157919841
52	81.3	90.9233993479795	-9.62339934797954
53	71.7	76.2817333193824	-4.58173331938238
54	64.8	61.2352988509161	3.5647011490839
55	57.3	53.690988156794	3.60901184320601
56	61.9	60.0658028808564	1.83419711914360
57	70.1	69.6357794998148	0.464220500185192
58	88.8	94.7419411228185	-5.94194112281848
59	106.8	100.205194517947	6.59480548205279
60	110.7	115.481969626421	-4.78196962642106
61	114.1	116.696999844925	-2.59699984492451
62	108	103.364172603638	4.63582739636243
63	111.5	106.342638832871	5.15736116712863
64	86.8	87.117554815307	-0.317554815307091
65	78.4	77.4946776565126	0.905322343487413
66	68	67.5306956470861	0.46930435291388
67	57.3	59.0233885163179	-1.72338851631790
68	65.3	62.9795809958962	2.32041900410375
69	73.3	72.1414647607161	1.15853523928389
70	88.6	94.8387278081597	-6.2387278081597
71	101.3	105.352779265323	-4.05277926532256
72	122.9	112.585635744930	10.3143642550704
73	126.6	119.482586825273	7.11741317472689
74	114.1	112.197273110716	1.90272688928439
75	124.7	114.523428274349	10.1765717256512
76	93.3	94.6425216905708	-1.34252169057078
77	77.2	85.1965984734846	-7.99659847348461
78	66.5	72.23194545287	-5.73194545287001
79	57.9	60.8591173492844	-2.95911734928442
80	63.7	66.0831195301012	-2.38311953010123
81	65.8	73.277254805	-7.47725480500002
82	85	90.2014251731632	-5.20142517316324
83	101	101.941358637347	-0.94135863734678
84	105.3	116.056513520694	-10.7565135206938
85	121	114.962428670426	6.03757132957429
86	117.9	105.194804910582	12.7051950894179
87	106	114.340582435652	-8.34058243565171
88	86.6	83.8628511032936	2.73714889670643
89	79.9	72.9793812399695	6.92061876003049
90	65.2	65.6725732589468	-0.472573258946824
91	61.2	57.1047870893277	4.09521291067226
92	67.6	64.8012552794959	2.79874472050409
93	78.9	71.5473921689054	7.35260783109459
94	95.5	94.1063045583064	1.39369544169355
95	113.1	109.685024409225	3.41497559077521
96	124.4	121.153075431026	3.24692456897415
97	122	131.389824122558	-9.38982412255803
98	110.3	119.468297535695	-9.16829753569536
99	114	113.043762274479	0.956237725521177
100	93.3	90.0590607418619	3.24093925813813
101	75.5	81.0521095807769	-5.55210958077686
102	65.4	66.7576445010084	-1.35764450100837
103	59.2	59.7838518763816	-0.583851876381573
104	63.8	65.4650980555767	-1.66509805557668
105	74.2	72.6651134562123	1.53488654378775
106	91.7	90.9344817119508	0.765518288049208
107	107	107.143581555905	-0.143581555904632
108	120.7	117.414673543462	3.28532645653773
109	127.4	122.477681993805	4.92231800619484
110	119.7	115.183738026577	4.5162619734228
111	112.7	117.251885009185	-4.55188500918538
112	84.4	93.458819049478	-9.05881904947807
113	75.6	76.9445608266687	-1.34456082666867
114	66.5	65.7051463573496	0.794853642650367
115	59.9	59.731205650859	0.168794349140995
116	64.8	65.2073005325693	-0.407300532569323
117	74.3	74.1192341928584	0.180765807141555
118	100.4	91.6436363884385	8.75636361156154
119	105.9	110.012599826484	-4.11259982648355
120	131.1	120.432757119394	10.6672428806060

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	128.507484345050	115.750275241454	141.264693448647
122	119.486622248420	106.103849497187	132.869394999654
123	116.401783974666	102.421410985742	130.382156963590
124	92.2020061010276	77.6485511398265	106.755461062229
125	81.7250221392856	66.6202125176459	96.8298317609254
126	71.7897877558599	56.1530522876026	87.4265232241172
127	65.3069694531807	49.1558172186641	81.4581216876973
128	70.4931399744884	53.8434570675738	87.142822881403
129	79.7755127230415	62.641798493515	96.909226952568
130	100.761899324329	83.1574571094403	118.366341539218
131	111.074055154101	93.01114818718	129.136962121021
132	128.863230187763	110.353210455361	147.373249920165

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 128.507484345050 & 115.750275241454 & 141.264693448647 \tabularnewline
122 & 119.486622248420 & 106.103849497187 & 132.869394999654 \tabularnewline
123 & 116.401783974666 & 102.421410985742 & 130.382156963590 \tabularnewline
124 & 92.2020061010276 & 77.6485511398265 & 106.755461062229 \tabularnewline
125 & 81.7250221392856 & 66.6202125176459 & 96.8298317609254 \tabularnewline
126 & 71.7897877558599 & 56.1530522876026 & 87.4265232241172 \tabularnewline
127 & 65.3069694531807 & 49.1558172186641 & 81.4581216876973 \tabularnewline
128 & 70.4931399744884 & 53.8434570675738 & 87.142822881403 \tabularnewline
129 & 79.7755127230415 & 62.641798493515 & 96.909226952568 \tabularnewline
130 & 100.761899324329 & 83.1574571094403 & 118.366341539218 \tabularnewline
131 & 111.074055154101 & 93.01114818718 & 129.136962121021 \tabularnewline
132 & 128.863230187763 & 110.353210455361 & 147.373249920165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116443&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]128.507484345050[/C][C]115.750275241454[/C][C]141.264693448647[/C][/ROW]
[ROW][C]122[/C][C]119.486622248420[/C][C]106.103849497187[/C][C]132.869394999654[/C][/ROW]
[ROW][C]123[/C][C]116.401783974666[/C][C]102.421410985742[/C][C]130.382156963590[/C][/ROW]
[ROW][C]124[/C][C]92.2020061010276[/C][C]77.6485511398265[/C][C]106.755461062229[/C][/ROW]
[ROW][C]125[/C][C]81.7250221392856[/C][C]66.6202125176459[/C][C]96.8298317609254[/C][/ROW]
[ROW][C]126[/C][C]71.7897877558599[/C][C]56.1530522876026[/C][C]87.4265232241172[/C][/ROW]
[ROW][C]127[/C][C]65.3069694531807[/C][C]49.1558172186641[/C][C]81.4581216876973[/C][/ROW]
[ROW][C]128[/C][C]70.4931399744884[/C][C]53.8434570675738[/C][C]87.142822881403[/C][/ROW]
[ROW][C]129[/C][C]79.7755127230415[/C][C]62.641798493515[/C][C]96.909226952568[/C][/ROW]
[ROW][C]130[/C][C]100.761899324329[/C][C]83.1574571094403[/C][C]118.366341539218[/C][/ROW]
[ROW][C]131[/C][C]111.074055154101[/C][C]93.01114818718[/C][C]129.136962121021[/C][/ROW]
[ROW][C]132[/C][C]128.863230187763[/C][C]110.353210455361[/C][C]147.373249920165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116443&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116443&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	128.507484345050	115.750275241454	141.264693448647
122	119.486622248420	106.103849497187	132.869394999654
123	116.401783974666	102.421410985742	130.382156963590
124	92.2020061010276	77.6485511398265	106.755461062229
125	81.7250221392856	66.6202125176459	96.8298317609254
126	71.7897877558599	56.1530522876026	87.4265232241172
127	65.3069694531807	49.1558172186641	81.4581216876973
128	70.4931399744884	53.8434570675738	87.142822881403
129	79.7755127230415	62.641798493515	96.909226952568
130	100.761899324329	83.1574571094403	118.366341539218
131	111.074055154101	93.01114818718	129.136962121021
132	128.863230187763	110.353210455361	147.373249920165

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code