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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, 26 Dec 2010 15:20:25 +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/26/t1293376700c2p3fpmuxqii2wa.htm/, Retrieved Mon, 06 May 2024 13:57:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115660, Retrieved Mon, 06 May 2024 13:57:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

107

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

-       [Exponential Smoothing] [Retail sale of wi...] [2010-12-26 15:20:25] [87de14193c1d167d0627ce6c19969ca9] [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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115660&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115660&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0374406816921577
beta	0.180510709878271
gamma	0.605025766097544

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0374406816921577 \tabularnewline
beta & 0.180510709878271 \tabularnewline
gamma & 0.605025766097544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115660&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]0.0374406816921577[/C][/ROW]
[ROW][C]beta[/C][C]0.180510709878271[/C][/ROW]
[ROW][C]gamma[/C][C]0.605025766097544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115660&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	0.0374406816921577
beta	0.180510709878271
gamma	0.605025766097544

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	57.9	57.948705144157	-0.0487051441569477
14	63.7	63.6303585893703	0.0696414106296857
15	85	84.8545462246734	0.145453775326558
16	66.1	65.8779920277422	0.222007972257813
17	80.2	79.6525466332378	0.547453366762184
18	83.4	82.46783772939	0.932162270610036
19	85.7	83.1417637867953	2.55823621320472
20	81.8	79.7373757660508	2.06262423394917
21	69.4	69.232372482659	0.167627517340946
22	76.4	72.4089070088284	3.99109299117163
23	90.3	87.6567424581175	2.64325754188252
24	157.3	154.236840917238	3.06315908276193
25	65.3	59.8489963661493	5.45100363385067
26	68.4	66.1363154238624	2.26368457613756
27	72.7	88.5151219120917	-15.8151219120917
28	86.6	68.3761346092784	18.2238653907216
29	82.6	83.8688571282422	-1.26885712824222
30	84.8	87.190333725817	-2.39033372581697
31	93.4	88.9485453591528	4.45145464084719
32	82.2	85.3169164453911	-3.11691644539114
33	75.2	73.0406181827983	2.15938181720171
34	83.9	78.9614774890216	4.9385225109784
35	85.4	94.4595676702692	-9.05956767026915
36	166.3	164.636529290357	1.66347070964289
37	70.4	66.5391221657777	3.86087783422234
38	73.9	71.199106351561	2.70089364843899
39	82.4	83.7262544660784	-1.32625446607841
40	92.3	84.02053133728	8.27946866272
41	82.7	88.061233125874	-5.36123312587405
42	95.8	90.7759365885815	5.02406341141847
43	105.8	97.2490467691875	8.55095323081251
44	84.2	88.948820865085	-4.74882086508491
45	82.7	79.1865430283325	3.51345697166754
46	88.4	87.3722185013752	1.02778149862480
47	90.2	95.1061723789435	-4.90617237894347
48	176.6	177.141954535683	-0.541954535683431
49	69.5	73.6173444021006	-4.11734440210057
50	77.3	77.5777153804241	-0.277715380424141
51	98.6	88.3006424286072	10.2993575713928
52	86.4	95.1056862137858	-8.70568621378584
53	90.8	90.2617561817642	0.538243818235756
54	101.5	99.8349820018806	1.66501799811938
55	112.2	108.735304844972	3.46469515502804
56	93.6	91.4377308715287	2.16226912847132
57	93.8	86.4353103250508	7.36468967494922
58	90.8	93.7751873908708	-2.97518739087077
59	98.1	98.1667570034802	-0.0667570034802196
60	187.6	188.596943934841	-0.996943934841454
61	75	75.9700538521501	-0.970053852150102
62	83.7	82.7659105588678	0.934089441132244
63	99.7	100.909547260828	-1.20954726082755
64	104.9	95.8752860625806	9.0247139374194
65	98.9	97.2405902209396	1.65940977906040
66	117.3	108.384529069019	8.91547093098099
67	115.7	119.549984834011	-3.84998483401083
68	102.2	99.9270201497796	2.27297985022045
69	101.9	97.885708714722	4.01429128527796
70	96.6	99.2304817071666	-2.63048170716661
71	110	105.895448711970	4.10455128803022
72	203.7	203.405070427754	0.294929572246417
73	82.3	81.6826445750636	0.617355424936434
74	93.3	90.419722008517	2.88027799148301
75	121.9	108.980529036398	12.9194709636017
76	100.9	110.739123801432	-9.83912380143195
77	107.7	106.918078311387	0.781921688613053
78	130	123.691334570434	6.30866542956579
79	123.2	127.698680615347	-4.49868061534676
80	116.1	110.272436724977	5.82756327502264
81	105.3	109.358056609725	-4.05805660972473
82	107.7	106.320831923002	1.37916807699769
83	123.9	118.074712401493	5.82528759850682
84	205.2	222.200796333604	-17.0007963336039
85	90.3	89.2911670951508	1.00883290484919
86	106.9	100.254417100626	6.64558289937432
87	122.4	126.991486755384	-4.591486755384
88	111.3	113.733232389089	-2.43323238908924
89	122.6	116.579958935404	6.02004106459587
90	124.8	138.512650576417	-13.7126505764169
91	139.5	135.140282054159	4.35971794584052
92	118.8	123.056360645890	-4.25636064588959
93	111	115.337491648461	-4.33749164846083
94	121.2	115.357728816668	5.84227118333246
95	120.6	130.879044028428	-10.2790440284283
96	219.1	227.273459470361	-8.17345947036134
97	101.3	96.2495432639982	5.05045673600178
98	105	111.551212903444	-6.5512129034437
99	113.4	132.327383735175	-18.9273837351754
100	133.6	118.775939445074	14.8240605549257
101	123.9	127.485700584144	-3.58570058414379
102	136.2	137.851549927542	-1.65154992754162
103	151.7	145.698803343474	6.00119665652565
104	121.9	127.467128760491	-5.56712876049113
105	120.2	119.046232978534	1.15376702146578
106	132.2	125.404730830119	6.79526916988065
107	125.2	131.746027470783	-6.54602747078293
108	233.8	234.800218574158	-1.00021857415777

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 57.9 & 57.948705144157 & -0.0487051441569477 \tabularnewline
14 & 63.7 & 63.6303585893703 & 0.0696414106296857 \tabularnewline
15 & 85 & 84.8545462246734 & 0.145453775326558 \tabularnewline
16 & 66.1 & 65.8779920277422 & 0.222007972257813 \tabularnewline
17 & 80.2 & 79.6525466332378 & 0.547453366762184 \tabularnewline
18 & 83.4 & 82.46783772939 & 0.932162270610036 \tabularnewline
19 & 85.7 & 83.1417637867953 & 2.55823621320472 \tabularnewline
20 & 81.8 & 79.7373757660508 & 2.06262423394917 \tabularnewline
21 & 69.4 & 69.232372482659 & 0.167627517340946 \tabularnewline
22 & 76.4 & 72.4089070088284 & 3.99109299117163 \tabularnewline
23 & 90.3 & 87.6567424581175 & 2.64325754188252 \tabularnewline
24 & 157.3 & 154.236840917238 & 3.06315908276193 \tabularnewline
25 & 65.3 & 59.8489963661493 & 5.45100363385067 \tabularnewline
26 & 68.4 & 66.1363154238624 & 2.26368457613756 \tabularnewline
27 & 72.7 & 88.5151219120917 & -15.8151219120917 \tabularnewline
28 & 86.6 & 68.3761346092784 & 18.2238653907216 \tabularnewline
29 & 82.6 & 83.8688571282422 & -1.26885712824222 \tabularnewline
30 & 84.8 & 87.190333725817 & -2.39033372581697 \tabularnewline
31 & 93.4 & 88.9485453591528 & 4.45145464084719 \tabularnewline
32 & 82.2 & 85.3169164453911 & -3.11691644539114 \tabularnewline
33 & 75.2 & 73.0406181827983 & 2.15938181720171 \tabularnewline
34 & 83.9 & 78.9614774890216 & 4.9385225109784 \tabularnewline
35 & 85.4 & 94.4595676702692 & -9.05956767026915 \tabularnewline
36 & 166.3 & 164.636529290357 & 1.66347070964289 \tabularnewline
37 & 70.4 & 66.5391221657777 & 3.86087783422234 \tabularnewline
38 & 73.9 & 71.199106351561 & 2.70089364843899 \tabularnewline
39 & 82.4 & 83.7262544660784 & -1.32625446607841 \tabularnewline
40 & 92.3 & 84.02053133728 & 8.27946866272 \tabularnewline
41 & 82.7 & 88.061233125874 & -5.36123312587405 \tabularnewline
42 & 95.8 & 90.7759365885815 & 5.02406341141847 \tabularnewline
43 & 105.8 & 97.2490467691875 & 8.55095323081251 \tabularnewline
44 & 84.2 & 88.948820865085 & -4.74882086508491 \tabularnewline
45 & 82.7 & 79.1865430283325 & 3.51345697166754 \tabularnewline
46 & 88.4 & 87.3722185013752 & 1.02778149862480 \tabularnewline
47 & 90.2 & 95.1061723789435 & -4.90617237894347 \tabularnewline
48 & 176.6 & 177.141954535683 & -0.541954535683431 \tabularnewline
49 & 69.5 & 73.6173444021006 & -4.11734440210057 \tabularnewline
50 & 77.3 & 77.5777153804241 & -0.277715380424141 \tabularnewline
51 & 98.6 & 88.3006424286072 & 10.2993575713928 \tabularnewline
52 & 86.4 & 95.1056862137858 & -8.70568621378584 \tabularnewline
53 & 90.8 & 90.2617561817642 & 0.538243818235756 \tabularnewline
54 & 101.5 & 99.8349820018806 & 1.66501799811938 \tabularnewline
55 & 112.2 & 108.735304844972 & 3.46469515502804 \tabularnewline
56 & 93.6 & 91.4377308715287 & 2.16226912847132 \tabularnewline
57 & 93.8 & 86.4353103250508 & 7.36468967494922 \tabularnewline
58 & 90.8 & 93.7751873908708 & -2.97518739087077 \tabularnewline
59 & 98.1 & 98.1667570034802 & -0.0667570034802196 \tabularnewline
60 & 187.6 & 188.596943934841 & -0.996943934841454 \tabularnewline
61 & 75 & 75.9700538521501 & -0.970053852150102 \tabularnewline
62 & 83.7 & 82.7659105588678 & 0.934089441132244 \tabularnewline
63 & 99.7 & 100.909547260828 & -1.20954726082755 \tabularnewline
64 & 104.9 & 95.8752860625806 & 9.0247139374194 \tabularnewline
65 & 98.9 & 97.2405902209396 & 1.65940977906040 \tabularnewline
66 & 117.3 & 108.384529069019 & 8.91547093098099 \tabularnewline
67 & 115.7 & 119.549984834011 & -3.84998483401083 \tabularnewline
68 & 102.2 & 99.9270201497796 & 2.27297985022045 \tabularnewline
69 & 101.9 & 97.885708714722 & 4.01429128527796 \tabularnewline
70 & 96.6 & 99.2304817071666 & -2.63048170716661 \tabularnewline
71 & 110 & 105.895448711970 & 4.10455128803022 \tabularnewline
72 & 203.7 & 203.405070427754 & 0.294929572246417 \tabularnewline
73 & 82.3 & 81.6826445750636 & 0.617355424936434 \tabularnewline
74 & 93.3 & 90.419722008517 & 2.88027799148301 \tabularnewline
75 & 121.9 & 108.980529036398 & 12.9194709636017 \tabularnewline
76 & 100.9 & 110.739123801432 & -9.83912380143195 \tabularnewline
77 & 107.7 & 106.918078311387 & 0.781921688613053 \tabularnewline
78 & 130 & 123.691334570434 & 6.30866542956579 \tabularnewline
79 & 123.2 & 127.698680615347 & -4.49868061534676 \tabularnewline
80 & 116.1 & 110.272436724977 & 5.82756327502264 \tabularnewline
81 & 105.3 & 109.358056609725 & -4.05805660972473 \tabularnewline
82 & 107.7 & 106.320831923002 & 1.37916807699769 \tabularnewline
83 & 123.9 & 118.074712401493 & 5.82528759850682 \tabularnewline
84 & 205.2 & 222.200796333604 & -17.0007963336039 \tabularnewline
85 & 90.3 & 89.2911670951508 & 1.00883290484919 \tabularnewline
86 & 106.9 & 100.254417100626 & 6.64558289937432 \tabularnewline
87 & 122.4 & 126.991486755384 & -4.591486755384 \tabularnewline
88 & 111.3 & 113.733232389089 & -2.43323238908924 \tabularnewline
89 & 122.6 & 116.579958935404 & 6.02004106459587 \tabularnewline
90 & 124.8 & 138.512650576417 & -13.7126505764169 \tabularnewline
91 & 139.5 & 135.140282054159 & 4.35971794584052 \tabularnewline
92 & 118.8 & 123.056360645890 & -4.25636064588959 \tabularnewline
93 & 111 & 115.337491648461 & -4.33749164846083 \tabularnewline
94 & 121.2 & 115.357728816668 & 5.84227118333246 \tabularnewline
95 & 120.6 & 130.879044028428 & -10.2790440284283 \tabularnewline
96 & 219.1 & 227.273459470361 & -8.17345947036134 \tabularnewline
97 & 101.3 & 96.2495432639982 & 5.05045673600178 \tabularnewline
98 & 105 & 111.551212903444 & -6.5512129034437 \tabularnewline
99 & 113.4 & 132.327383735175 & -18.9273837351754 \tabularnewline
100 & 133.6 & 118.775939445074 & 14.8240605549257 \tabularnewline
101 & 123.9 & 127.485700584144 & -3.58570058414379 \tabularnewline
102 & 136.2 & 137.851549927542 & -1.65154992754162 \tabularnewline
103 & 151.7 & 145.698803343474 & 6.00119665652565 \tabularnewline
104 & 121.9 & 127.467128760491 & -5.56712876049113 \tabularnewline
105 & 120.2 & 119.046232978534 & 1.15376702146578 \tabularnewline
106 & 132.2 & 125.404730830119 & 6.79526916988065 \tabularnewline
107 & 125.2 & 131.746027470783 & -6.54602747078293 \tabularnewline
108 & 233.8 & 234.800218574158 & -1.00021857415777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115660&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]57.9[/C][C]57.948705144157[/C][C]-0.0487051441569477[/C][/ROW]
[ROW][C]14[/C][C]63.7[/C][C]63.6303585893703[/C][C]0.0696414106296857[/C][/ROW]
[ROW][C]15[/C][C]85[/C][C]84.8545462246734[/C][C]0.145453775326558[/C][/ROW]
[ROW][C]16[/C][C]66.1[/C][C]65.8779920277422[/C][C]0.222007972257813[/C][/ROW]
[ROW][C]17[/C][C]80.2[/C][C]79.6525466332378[/C][C]0.547453366762184[/C][/ROW]
[ROW][C]18[/C][C]83.4[/C][C]82.46783772939[/C][C]0.932162270610036[/C][/ROW]
[ROW][C]19[/C][C]85.7[/C][C]83.1417637867953[/C][C]2.55823621320472[/C][/ROW]
[ROW][C]20[/C][C]81.8[/C][C]79.7373757660508[/C][C]2.06262423394917[/C][/ROW]
[ROW][C]21[/C][C]69.4[/C][C]69.232372482659[/C][C]0.167627517340946[/C][/ROW]
[ROW][C]22[/C][C]76.4[/C][C]72.4089070088284[/C][C]3.99109299117163[/C][/ROW]
[ROW][C]23[/C][C]90.3[/C][C]87.6567424581175[/C][C]2.64325754188252[/C][/ROW]
[ROW][C]24[/C][C]157.3[/C][C]154.236840917238[/C][C]3.06315908276193[/C][/ROW]
[ROW][C]25[/C][C]65.3[/C][C]59.8489963661493[/C][C]5.45100363385067[/C][/ROW]
[ROW][C]26[/C][C]68.4[/C][C]66.1363154238624[/C][C]2.26368457613756[/C][/ROW]
[ROW][C]27[/C][C]72.7[/C][C]88.5151219120917[/C][C]-15.8151219120917[/C][/ROW]
[ROW][C]28[/C][C]86.6[/C][C]68.3761346092784[/C][C]18.2238653907216[/C][/ROW]
[ROW][C]29[/C][C]82.6[/C][C]83.8688571282422[/C][C]-1.26885712824222[/C][/ROW]
[ROW][C]30[/C][C]84.8[/C][C]87.190333725817[/C][C]-2.39033372581697[/C][/ROW]
[ROW][C]31[/C][C]93.4[/C][C]88.9485453591528[/C][C]4.45145464084719[/C][/ROW]
[ROW][C]32[/C][C]82.2[/C][C]85.3169164453911[/C][C]-3.11691644539114[/C][/ROW]
[ROW][C]33[/C][C]75.2[/C][C]73.0406181827983[/C][C]2.15938181720171[/C][/ROW]
[ROW][C]34[/C][C]83.9[/C][C]78.9614774890216[/C][C]4.9385225109784[/C][/ROW]
[ROW][C]35[/C][C]85.4[/C][C]94.4595676702692[/C][C]-9.05956767026915[/C][/ROW]
[ROW][C]36[/C][C]166.3[/C][C]164.636529290357[/C][C]1.66347070964289[/C][/ROW]
[ROW][C]37[/C][C]70.4[/C][C]66.5391221657777[/C][C]3.86087783422234[/C][/ROW]
[ROW][C]38[/C][C]73.9[/C][C]71.199106351561[/C][C]2.70089364843899[/C][/ROW]
[ROW][C]39[/C][C]82.4[/C][C]83.7262544660784[/C][C]-1.32625446607841[/C][/ROW]
[ROW][C]40[/C][C]92.3[/C][C]84.02053133728[/C][C]8.27946866272[/C][/ROW]
[ROW][C]41[/C][C]82.7[/C][C]88.061233125874[/C][C]-5.36123312587405[/C][/ROW]
[ROW][C]42[/C][C]95.8[/C][C]90.7759365885815[/C][C]5.02406341141847[/C][/ROW]
[ROW][C]43[/C][C]105.8[/C][C]97.2490467691875[/C][C]8.55095323081251[/C][/ROW]
[ROW][C]44[/C][C]84.2[/C][C]88.948820865085[/C][C]-4.74882086508491[/C][/ROW]
[ROW][C]45[/C][C]82.7[/C][C]79.1865430283325[/C][C]3.51345697166754[/C][/ROW]
[ROW][C]46[/C][C]88.4[/C][C]87.3722185013752[/C][C]1.02778149862480[/C][/ROW]
[ROW][C]47[/C][C]90.2[/C][C]95.1061723789435[/C][C]-4.90617237894347[/C][/ROW]
[ROW][C]48[/C][C]176.6[/C][C]177.141954535683[/C][C]-0.541954535683431[/C][/ROW]
[ROW][C]49[/C][C]69.5[/C][C]73.6173444021006[/C][C]-4.11734440210057[/C][/ROW]
[ROW][C]50[/C][C]77.3[/C][C]77.5777153804241[/C][C]-0.277715380424141[/C][/ROW]
[ROW][C]51[/C][C]98.6[/C][C]88.3006424286072[/C][C]10.2993575713928[/C][/ROW]
[ROW][C]52[/C][C]86.4[/C][C]95.1056862137858[/C][C]-8.70568621378584[/C][/ROW]
[ROW][C]53[/C][C]90.8[/C][C]90.2617561817642[/C][C]0.538243818235756[/C][/ROW]
[ROW][C]54[/C][C]101.5[/C][C]99.8349820018806[/C][C]1.66501799811938[/C][/ROW]
[ROW][C]55[/C][C]112.2[/C][C]108.735304844972[/C][C]3.46469515502804[/C][/ROW]
[ROW][C]56[/C][C]93.6[/C][C]91.4377308715287[/C][C]2.16226912847132[/C][/ROW]
[ROW][C]57[/C][C]93.8[/C][C]86.4353103250508[/C][C]7.36468967494922[/C][/ROW]
[ROW][C]58[/C][C]90.8[/C][C]93.7751873908708[/C][C]-2.97518739087077[/C][/ROW]
[ROW][C]59[/C][C]98.1[/C][C]98.1667570034802[/C][C]-0.0667570034802196[/C][/ROW]
[ROW][C]60[/C][C]187.6[/C][C]188.596943934841[/C][C]-0.996943934841454[/C][/ROW]
[ROW][C]61[/C][C]75[/C][C]75.9700538521501[/C][C]-0.970053852150102[/C][/ROW]
[ROW][C]62[/C][C]83.7[/C][C]82.7659105588678[/C][C]0.934089441132244[/C][/ROW]
[ROW][C]63[/C][C]99.7[/C][C]100.909547260828[/C][C]-1.20954726082755[/C][/ROW]
[ROW][C]64[/C][C]104.9[/C][C]95.8752860625806[/C][C]9.0247139374194[/C][/ROW]
[ROW][C]65[/C][C]98.9[/C][C]97.2405902209396[/C][C]1.65940977906040[/C][/ROW]
[ROW][C]66[/C][C]117.3[/C][C]108.384529069019[/C][C]8.91547093098099[/C][/ROW]
[ROW][C]67[/C][C]115.7[/C][C]119.549984834011[/C][C]-3.84998483401083[/C][/ROW]
[ROW][C]68[/C][C]102.2[/C][C]99.9270201497796[/C][C]2.27297985022045[/C][/ROW]
[ROW][C]69[/C][C]101.9[/C][C]97.885708714722[/C][C]4.01429128527796[/C][/ROW]
[ROW][C]70[/C][C]96.6[/C][C]99.2304817071666[/C][C]-2.63048170716661[/C][/ROW]
[ROW][C]71[/C][C]110[/C][C]105.895448711970[/C][C]4.10455128803022[/C][/ROW]
[ROW][C]72[/C][C]203.7[/C][C]203.405070427754[/C][C]0.294929572246417[/C][/ROW]
[ROW][C]73[/C][C]82.3[/C][C]81.6826445750636[/C][C]0.617355424936434[/C][/ROW]
[ROW][C]74[/C][C]93.3[/C][C]90.419722008517[/C][C]2.88027799148301[/C][/ROW]
[ROW][C]75[/C][C]121.9[/C][C]108.980529036398[/C][C]12.9194709636017[/C][/ROW]
[ROW][C]76[/C][C]100.9[/C][C]110.739123801432[/C][C]-9.83912380143195[/C][/ROW]
[ROW][C]77[/C][C]107.7[/C][C]106.918078311387[/C][C]0.781921688613053[/C][/ROW]
[ROW][C]78[/C][C]130[/C][C]123.691334570434[/C][C]6.30866542956579[/C][/ROW]
[ROW][C]79[/C][C]123.2[/C][C]127.698680615347[/C][C]-4.49868061534676[/C][/ROW]
[ROW][C]80[/C][C]116.1[/C][C]110.272436724977[/C][C]5.82756327502264[/C][/ROW]
[ROW][C]81[/C][C]105.3[/C][C]109.358056609725[/C][C]-4.05805660972473[/C][/ROW]
[ROW][C]82[/C][C]107.7[/C][C]106.320831923002[/C][C]1.37916807699769[/C][/ROW]
[ROW][C]83[/C][C]123.9[/C][C]118.074712401493[/C][C]5.82528759850682[/C][/ROW]
[ROW][C]84[/C][C]205.2[/C][C]222.200796333604[/C][C]-17.0007963336039[/C][/ROW]
[ROW][C]85[/C][C]90.3[/C][C]89.2911670951508[/C][C]1.00883290484919[/C][/ROW]
[ROW][C]86[/C][C]106.9[/C][C]100.254417100626[/C][C]6.64558289937432[/C][/ROW]
[ROW][C]87[/C][C]122.4[/C][C]126.991486755384[/C][C]-4.591486755384[/C][/ROW]
[ROW][C]88[/C][C]111.3[/C][C]113.733232389089[/C][C]-2.43323238908924[/C][/ROW]
[ROW][C]89[/C][C]122.6[/C][C]116.579958935404[/C][C]6.02004106459587[/C][/ROW]
[ROW][C]90[/C][C]124.8[/C][C]138.512650576417[/C][C]-13.7126505764169[/C][/ROW]
[ROW][C]91[/C][C]139.5[/C][C]135.140282054159[/C][C]4.35971794584052[/C][/ROW]
[ROW][C]92[/C][C]118.8[/C][C]123.056360645890[/C][C]-4.25636064588959[/C][/ROW]
[ROW][C]93[/C][C]111[/C][C]115.337491648461[/C][C]-4.33749164846083[/C][/ROW]
[ROW][C]94[/C][C]121.2[/C][C]115.357728816668[/C][C]5.84227118333246[/C][/ROW]
[ROW][C]95[/C][C]120.6[/C][C]130.879044028428[/C][C]-10.2790440284283[/C][/ROW]
[ROW][C]96[/C][C]219.1[/C][C]227.273459470361[/C][C]-8.17345947036134[/C][/ROW]
[ROW][C]97[/C][C]101.3[/C][C]96.2495432639982[/C][C]5.05045673600178[/C][/ROW]
[ROW][C]98[/C][C]105[/C][C]111.551212903444[/C][C]-6.5512129034437[/C][/ROW]
[ROW][C]99[/C][C]113.4[/C][C]132.327383735175[/C][C]-18.9273837351754[/C][/ROW]
[ROW][C]100[/C][C]133.6[/C][C]118.775939445074[/C][C]14.8240605549257[/C][/ROW]
[ROW][C]101[/C][C]123.9[/C][C]127.485700584144[/C][C]-3.58570058414379[/C][/ROW]
[ROW][C]102[/C][C]136.2[/C][C]137.851549927542[/C][C]-1.65154992754162[/C][/ROW]
[ROW][C]103[/C][C]151.7[/C][C]145.698803343474[/C][C]6.00119665652565[/C][/ROW]
[ROW][C]104[/C][C]121.9[/C][C]127.467128760491[/C][C]-5.56712876049113[/C][/ROW]
[ROW][C]105[/C][C]120.2[/C][C]119.046232978534[/C][C]1.15376702146578[/C][/ROW]
[ROW][C]106[/C][C]132.2[/C][C]125.404730830119[/C][C]6.79526916988065[/C][/ROW]
[ROW][C]107[/C][C]125.2[/C][C]131.746027470783[/C][C]-6.54602747078293[/C][/ROW]
[ROW][C]108[/C][C]233.8[/C][C]234.800218574158[/C][C]-1.00021857415777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115660&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	57.9	57.948705144157	-0.0487051441569477
14	63.7	63.6303585893703	0.0696414106296857
15	85	84.8545462246734	0.145453775326558
16	66.1	65.8779920277422	0.222007972257813
17	80.2	79.6525466332378	0.547453366762184
18	83.4	82.46783772939	0.932162270610036
19	85.7	83.1417637867953	2.55823621320472
20	81.8	79.7373757660508	2.06262423394917
21	69.4	69.232372482659	0.167627517340946
22	76.4	72.4089070088284	3.99109299117163
23	90.3	87.6567424581175	2.64325754188252
24	157.3	154.236840917238	3.06315908276193
25	65.3	59.8489963661493	5.45100363385067
26	68.4	66.1363154238624	2.26368457613756
27	72.7	88.5151219120917	-15.8151219120917
28	86.6	68.3761346092784	18.2238653907216
29	82.6	83.8688571282422	-1.26885712824222
30	84.8	87.190333725817	-2.39033372581697
31	93.4	88.9485453591528	4.45145464084719
32	82.2	85.3169164453911	-3.11691644539114
33	75.2	73.0406181827983	2.15938181720171
34	83.9	78.9614774890216	4.9385225109784
35	85.4	94.4595676702692	-9.05956767026915
36	166.3	164.636529290357	1.66347070964289
37	70.4	66.5391221657777	3.86087783422234
38	73.9	71.199106351561	2.70089364843899
39	82.4	83.7262544660784	-1.32625446607841
40	92.3	84.02053133728	8.27946866272
41	82.7	88.061233125874	-5.36123312587405
42	95.8	90.7759365885815	5.02406341141847
43	105.8	97.2490467691875	8.55095323081251
44	84.2	88.948820865085	-4.74882086508491
45	82.7	79.1865430283325	3.51345697166754
46	88.4	87.3722185013752	1.02778149862480
47	90.2	95.1061723789435	-4.90617237894347
48	176.6	177.141954535683	-0.541954535683431
49	69.5	73.6173444021006	-4.11734440210057
50	77.3	77.5777153804241	-0.277715380424141
51	98.6	88.3006424286072	10.2993575713928
52	86.4	95.1056862137858	-8.70568621378584
53	90.8	90.2617561817642	0.538243818235756
54	101.5	99.8349820018806	1.66501799811938
55	112.2	108.735304844972	3.46469515502804
56	93.6	91.4377308715287	2.16226912847132
57	93.8	86.4353103250508	7.36468967494922
58	90.8	93.7751873908708	-2.97518739087077
59	98.1	98.1667570034802	-0.0667570034802196
60	187.6	188.596943934841	-0.996943934841454
61	75	75.9700538521501	-0.970053852150102
62	83.7	82.7659105588678	0.934089441132244
63	99.7	100.909547260828	-1.20954726082755
64	104.9	95.8752860625806	9.0247139374194
65	98.9	97.2405902209396	1.65940977906040
66	117.3	108.384529069019	8.91547093098099
67	115.7	119.549984834011	-3.84998483401083
68	102.2	99.9270201497796	2.27297985022045
69	101.9	97.885708714722	4.01429128527796
70	96.6	99.2304817071666	-2.63048170716661
71	110	105.895448711970	4.10455128803022
72	203.7	203.405070427754	0.294929572246417
73	82.3	81.6826445750636	0.617355424936434
74	93.3	90.419722008517	2.88027799148301
75	121.9	108.980529036398	12.9194709636017
76	100.9	110.739123801432	-9.83912380143195
77	107.7	106.918078311387	0.781921688613053
78	130	123.691334570434	6.30866542956579
79	123.2	127.698680615347	-4.49868061534676
80	116.1	110.272436724977	5.82756327502264
81	105.3	109.358056609725	-4.05805660972473
82	107.7	106.320831923002	1.37916807699769
83	123.9	118.074712401493	5.82528759850682
84	205.2	222.200796333604	-17.0007963336039
85	90.3	89.2911670951508	1.00883290484919
86	106.9	100.254417100626	6.64558289937432
87	122.4	126.991486755384	-4.591486755384
88	111.3	113.733232389089	-2.43323238908924
89	122.6	116.579958935404	6.02004106459587
90	124.8	138.512650576417	-13.7126505764169
91	139.5	135.140282054159	4.35971794584052
92	118.8	123.056360645890	-4.25636064588959
93	111	115.337491648461	-4.33749164846083
94	121.2	115.357728816668	5.84227118333246
95	120.6	130.879044028428	-10.2790440284283
96	219.1	227.273459470361	-8.17345947036134
97	101.3	96.2495432639982	5.05045673600178
98	105	111.551212903444	-6.5512129034437
99	113.4	132.327383735175	-18.9273837351754
100	133.6	118.775939445074	14.8240605549257
101	123.9	127.485700584144	-3.58570058414379
102	136.2	137.851549927542	-1.65154992754162
103	151.7	145.698803343474	6.00119665652565
104	121.9	127.467128760491	-5.56712876049113
105	120.2	119.046232978534	1.15376702146578
106	132.2	125.404730830119	6.79526916988065
107	125.2	131.746027470783	-6.54602747078293
108	233.8	234.800218574158	-1.00021857415777

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	104.720886767167	97.1658108821946	112.275962652140
110	113.405032371249	105.827662374376	120.982402368121
111	127.840307448734	120.223906734607	135.456708162860
112	135.06758713278	127.40340878845	142.731765477110
113	132.294141308603	124.589058638876	139.999223978329
114	144.532266559535	136.733869779740	152.330663339330
115	157.557334633567	149.629342512148	165.485326754985
116	130.924831635917	123.045170184615	138.80449308722
117	126.364465653528	118.433023114808	134.295908192247
118	136.453592955893	128.364269614092	144.542916297694
119	134.595071071724	126.417053045136	142.773089098312
120	246.821782631884	223.808026154102	269.835539109665

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 104.720886767167 & 97.1658108821946 & 112.275962652140 \tabularnewline
110 & 113.405032371249 & 105.827662374376 & 120.982402368121 \tabularnewline
111 & 127.840307448734 & 120.223906734607 & 135.456708162860 \tabularnewline
112 & 135.06758713278 & 127.40340878845 & 142.731765477110 \tabularnewline
113 & 132.294141308603 & 124.589058638876 & 139.999223978329 \tabularnewline
114 & 144.532266559535 & 136.733869779740 & 152.330663339330 \tabularnewline
115 & 157.557334633567 & 149.629342512148 & 165.485326754985 \tabularnewline
116 & 130.924831635917 & 123.045170184615 & 138.80449308722 \tabularnewline
117 & 126.364465653528 & 118.433023114808 & 134.295908192247 \tabularnewline
118 & 136.453592955893 & 128.364269614092 & 144.542916297694 \tabularnewline
119 & 134.595071071724 & 126.417053045136 & 142.773089098312 \tabularnewline
120 & 246.821782631884 & 223.808026154102 & 269.835539109665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115660&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]104.720886767167[/C][C]97.1658108821946[/C][C]112.275962652140[/C][/ROW]
[ROW][C]110[/C][C]113.405032371249[/C][C]105.827662374376[/C][C]120.982402368121[/C][/ROW]
[ROW][C]111[/C][C]127.840307448734[/C][C]120.223906734607[/C][C]135.456708162860[/C][/ROW]
[ROW][C]112[/C][C]135.06758713278[/C][C]127.40340878845[/C][C]142.731765477110[/C][/ROW]
[ROW][C]113[/C][C]132.294141308603[/C][C]124.589058638876[/C][C]139.999223978329[/C][/ROW]
[ROW][C]114[/C][C]144.532266559535[/C][C]136.733869779740[/C][C]152.330663339330[/C][/ROW]
[ROW][C]115[/C][C]157.557334633567[/C][C]149.629342512148[/C][C]165.485326754985[/C][/ROW]
[ROW][C]116[/C][C]130.924831635917[/C][C]123.045170184615[/C][C]138.80449308722[/C][/ROW]
[ROW][C]117[/C][C]126.364465653528[/C][C]118.433023114808[/C][C]134.295908192247[/C][/ROW]
[ROW][C]118[/C][C]136.453592955893[/C][C]128.364269614092[/C][C]144.542916297694[/C][/ROW]
[ROW][C]119[/C][C]134.595071071724[/C][C]126.417053045136[/C][C]142.773089098312[/C][/ROW]
[ROW][C]120[/C][C]246.821782631884[/C][C]223.808026154102[/C][C]269.835539109665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115660&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	104.720886767167	97.1658108821946	112.275962652140
110	113.405032371249	105.827662374376	120.982402368121
111	127.840307448734	120.223906734607	135.456708162860
112	135.06758713278	127.40340878845	142.731765477110
113	132.294141308603	124.589058638876	139.999223978329
114	144.532266559535	136.733869779740	152.330663339330
115	157.557334633567	149.629342512148	165.485326754985
116	130.924831635917	123.045170184615	138.80449308722
117	126.364465653528	118.433023114808	134.295908192247
118	136.453592955893	128.364269614092	144.542916297694
119	134.595071071724	126.417053045136	142.773089098312
120	246.821782631884	223.808026154102	269.835539109665

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