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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 02 Apr 2015 21:19:11 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1428006041zogfz09d8drlwdh.htm/, Retrieved Thu, 09 May 2024 06:30:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278654, Retrieved Thu, 09 May 2024 06:30:13 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [omzetontwikkeling...] [2015-04-02 20:19:11] [48109ce6b54c2eacc50b3a62a110bb1c] [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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278654&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278654&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278654&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.507538951709474
beta	0
gamma	0.316699583294714

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.507538951709474 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.316699583294714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278654&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]0.507538951709474[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.316699583294714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278654&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278654&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	0.507538951709474
beta	0
gamma	0.316699583294714

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	108.3	104.712606837607	3.58739316239314
14	117.2	115.391157460426	1.80884253957353
15	128.7	127.854524364578	0.845475635422034
16	116.5	116.395611706751	0.104388293248519
17	131.7	131.706401689486	-0.00640168948643804
18	139.9	140.098461440524	-0.198461440524142
19	107.4	109.688876720188	-2.28887672018791
20	96.1	91.5599914868404	4.54000851315962
21	126.5	131.238698172837	-4.73869817283702
22	116.4	118.520599794203	-2.12059979420323
23	109.8	105.1604549888	4.63954501119981
24	148	153.993846991336	-5.9938469913356
25	111.4	111.556542791833	-0.156542791833047
26	117	120.057513401611	-3.05751340161088
27	141.7	129.900766282489	11.799233717511
28	120	123.885730900139	-3.88573090013902
29	132.1	137.154100919848	-5.05410091984791
30	146.7	142.954302631973	3.74569736802681
31	122.5	114.220506354416	8.27949364558442
32	99.6	102.520528762305	-2.9205287623046
33	122.7	136.96559459093	-14.2655945909298
34	139	119.820549597154	19.179450402846
35	117.8	118.325337055661	-0.525337055660643
36	125.5	162.878942924713	-37.3789429247132
37	134.5	105.422878892173	29.0771211078274
38	121.3	128.308630848297	-7.00863084829719
39	126.7	138.463628818224	-11.7636288182242
40	117.7	118.043261158769	-0.343261158768897
41	123	132.927350988526	-9.92735098852626
42	132.1	137.626624447194	-5.52662444719371
43	113.1	104.893864557244	8.20613544275611
44	89.2	91.4098745866224	-2.20987458662238
45	121.7	124.446223565186	-2.7462235651862
46	105.3	118.363871156228	-13.0638711562278
47	85.3	97.4307148153924	-12.1307148153925
48	105.3	130.346369649142	-25.0463696491416
49	72.2	89.5142014622703	-17.3142014622703
50	92.1	83.2265366120973	8.8734633879027
51	97.2	100.70071605547	-3.50071605547025
52	78.6	86.2552442429667	-7.65524424296666
53	78.1	95.9334620242341	-17.8334620242341
54	93	97.3064232073737	-4.30642320737367
55	81	67.3347545406728	13.6652454593272
56	65.9	54.9969716142461	10.9030283857539
57	88.6	94.6049794499028	-6.00497944990276
58	85.7	85.2595183876001	0.44048161239995
59	76.3	71.325884218525	4.97411578147496
60	96.8	110.908552786833	-14.1085527868327
61	76.8	76.83367873335	-0.0336787333500439
62	85.6	83.4008383268934	2.19916167310657
63	119.2	95.5576453166867	23.6423546833133
64	91.4	94.2403897805504	-2.84038978055037
65	95.7	104.774916421671	-9.07491642167062
66	112.3	112.702887510599	-0.402887510598873
67	95.2	87.5153164001653	7.68468359983467
68	82.8	71.7113639010069	11.0886360989931
69	111.3	108.77656463271	2.52343536729045
70	108.2	104.764854630367	3.43514536963312
71	97	93.058204564181	3.94179543581896
72	124.4	129.140755207049	-4.74075520704864
73	99.3	102.015551762753	-2.71555176275263
74	117.6	107.569795051985	10.0302049480151
75	131.5	127.045489281538	4.45451071846219
76	114.2	111.85934821271	2.34065178729038
77	116.8	124.051104714273	-7.2511047142726
78	116.5	134.257240068885	-17.7572400688854
79	105.4	101.523014507491	3.87698549250885
80	89.2	84.3173948528739	4.88260514712614
81	115.8	116.896945516208	-1.0969455162077
82	111.4	111.1899435012	0.210056498800185
83	106.4	97.9254534737437	8.47454652625633
84	128.4	134.954402077284	-6.55440207728441
85	107.7	107.224557404104	0.475442595895942
86	111	116.386210994251	-5.38621099425119
87	129.8	127.167876049812	2.63212395018779
88	130.5	110.727120603045	19.7728793969553
89	142.9	130.27046010149	12.6295398985096
90	159.9	148.92823690651	10.9717630934899
91	84.1	134.14922109766	-50.0492210976596
92	75	89.7307897431289	-14.7307897431289
93	100.7	111.423194595418	-10.7231945954184
94	106.8	101.034339134997	5.76566086500257
95	97.4	91.8784828428191	5.5215171571809
96	113	125.064705996125	-12.0647059961253
97	76.9	95.6345575510029	-18.7345575510029
98	87.3	94.132191363217	-6.83219136321699
99	103.7	105.430522286813	-1.73052228681313
100	92.1	89.4488640219172	2.65113597808282
101	92.9	99.188160807849	-6.28816080784898
102	112.2	107.985917095431	4.21408290456938
103	88.7	80.2601478909746	8.43985210902545
104	74.6	71.0355400030087	3.56445999699127
105	101.5	102.638530120805	-1.13853012080475
106	119.7	99.6859035382187	20.0140964617813
107	120.7	97.7236061203972	22.9763938796028
108	153.5	137.026072900488	16.4739270995119

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 108.3 & 104.712606837607 & 3.58739316239314 \tabularnewline
14 & 117.2 & 115.391157460426 & 1.80884253957353 \tabularnewline
15 & 128.7 & 127.854524364578 & 0.845475635422034 \tabularnewline
16 & 116.5 & 116.395611706751 & 0.104388293248519 \tabularnewline
17 & 131.7 & 131.706401689486 & -0.00640168948643804 \tabularnewline
18 & 139.9 & 140.098461440524 & -0.198461440524142 \tabularnewline
19 & 107.4 & 109.688876720188 & -2.28887672018791 \tabularnewline
20 & 96.1 & 91.5599914868404 & 4.54000851315962 \tabularnewline
21 & 126.5 & 131.238698172837 & -4.73869817283702 \tabularnewline
22 & 116.4 & 118.520599794203 & -2.12059979420323 \tabularnewline
23 & 109.8 & 105.1604549888 & 4.63954501119981 \tabularnewline
24 & 148 & 153.993846991336 & -5.9938469913356 \tabularnewline
25 & 111.4 & 111.556542791833 & -0.156542791833047 \tabularnewline
26 & 117 & 120.057513401611 & -3.05751340161088 \tabularnewline
27 & 141.7 & 129.900766282489 & 11.799233717511 \tabularnewline
28 & 120 & 123.885730900139 & -3.88573090013902 \tabularnewline
29 & 132.1 & 137.154100919848 & -5.05410091984791 \tabularnewline
30 & 146.7 & 142.954302631973 & 3.74569736802681 \tabularnewline
31 & 122.5 & 114.220506354416 & 8.27949364558442 \tabularnewline
32 & 99.6 & 102.520528762305 & -2.9205287623046 \tabularnewline
33 & 122.7 & 136.96559459093 & -14.2655945909298 \tabularnewline
34 & 139 & 119.820549597154 & 19.179450402846 \tabularnewline
35 & 117.8 & 118.325337055661 & -0.525337055660643 \tabularnewline
36 & 125.5 & 162.878942924713 & -37.3789429247132 \tabularnewline
37 & 134.5 & 105.422878892173 & 29.0771211078274 \tabularnewline
38 & 121.3 & 128.308630848297 & -7.00863084829719 \tabularnewline
39 & 126.7 & 138.463628818224 & -11.7636288182242 \tabularnewline
40 & 117.7 & 118.043261158769 & -0.343261158768897 \tabularnewline
41 & 123 & 132.927350988526 & -9.92735098852626 \tabularnewline
42 & 132.1 & 137.626624447194 & -5.52662444719371 \tabularnewline
43 & 113.1 & 104.893864557244 & 8.20613544275611 \tabularnewline
44 & 89.2 & 91.4098745866224 & -2.20987458662238 \tabularnewline
45 & 121.7 & 124.446223565186 & -2.7462235651862 \tabularnewline
46 & 105.3 & 118.363871156228 & -13.0638711562278 \tabularnewline
47 & 85.3 & 97.4307148153924 & -12.1307148153925 \tabularnewline
48 & 105.3 & 130.346369649142 & -25.0463696491416 \tabularnewline
49 & 72.2 & 89.5142014622703 & -17.3142014622703 \tabularnewline
50 & 92.1 & 83.2265366120973 & 8.8734633879027 \tabularnewline
51 & 97.2 & 100.70071605547 & -3.50071605547025 \tabularnewline
52 & 78.6 & 86.2552442429667 & -7.65524424296666 \tabularnewline
53 & 78.1 & 95.9334620242341 & -17.8334620242341 \tabularnewline
54 & 93 & 97.3064232073737 & -4.30642320737367 \tabularnewline
55 & 81 & 67.3347545406728 & 13.6652454593272 \tabularnewline
56 & 65.9 & 54.9969716142461 & 10.9030283857539 \tabularnewline
57 & 88.6 & 94.6049794499028 & -6.00497944990276 \tabularnewline
58 & 85.7 & 85.2595183876001 & 0.44048161239995 \tabularnewline
59 & 76.3 & 71.325884218525 & 4.97411578147496 \tabularnewline
60 & 96.8 & 110.908552786833 & -14.1085527868327 \tabularnewline
61 & 76.8 & 76.83367873335 & -0.0336787333500439 \tabularnewline
62 & 85.6 & 83.4008383268934 & 2.19916167310657 \tabularnewline
63 & 119.2 & 95.5576453166867 & 23.6423546833133 \tabularnewline
64 & 91.4 & 94.2403897805504 & -2.84038978055037 \tabularnewline
65 & 95.7 & 104.774916421671 & -9.07491642167062 \tabularnewline
66 & 112.3 & 112.702887510599 & -0.402887510598873 \tabularnewline
67 & 95.2 & 87.5153164001653 & 7.68468359983467 \tabularnewline
68 & 82.8 & 71.7113639010069 & 11.0886360989931 \tabularnewline
69 & 111.3 & 108.77656463271 & 2.52343536729045 \tabularnewline
70 & 108.2 & 104.764854630367 & 3.43514536963312 \tabularnewline
71 & 97 & 93.058204564181 & 3.94179543581896 \tabularnewline
72 & 124.4 & 129.140755207049 & -4.74075520704864 \tabularnewline
73 & 99.3 & 102.015551762753 & -2.71555176275263 \tabularnewline
74 & 117.6 & 107.569795051985 & 10.0302049480151 \tabularnewline
75 & 131.5 & 127.045489281538 & 4.45451071846219 \tabularnewline
76 & 114.2 & 111.85934821271 & 2.34065178729038 \tabularnewline
77 & 116.8 & 124.051104714273 & -7.2511047142726 \tabularnewline
78 & 116.5 & 134.257240068885 & -17.7572400688854 \tabularnewline
79 & 105.4 & 101.523014507491 & 3.87698549250885 \tabularnewline
80 & 89.2 & 84.3173948528739 & 4.88260514712614 \tabularnewline
81 & 115.8 & 116.896945516208 & -1.0969455162077 \tabularnewline
82 & 111.4 & 111.1899435012 & 0.210056498800185 \tabularnewline
83 & 106.4 & 97.9254534737437 & 8.47454652625633 \tabularnewline
84 & 128.4 & 134.954402077284 & -6.55440207728441 \tabularnewline
85 & 107.7 & 107.224557404104 & 0.475442595895942 \tabularnewline
86 & 111 & 116.386210994251 & -5.38621099425119 \tabularnewline
87 & 129.8 & 127.167876049812 & 2.63212395018779 \tabularnewline
88 & 130.5 & 110.727120603045 & 19.7728793969553 \tabularnewline
89 & 142.9 & 130.27046010149 & 12.6295398985096 \tabularnewline
90 & 159.9 & 148.92823690651 & 10.9717630934899 \tabularnewline
91 & 84.1 & 134.14922109766 & -50.0492210976596 \tabularnewline
92 & 75 & 89.7307897431289 & -14.7307897431289 \tabularnewline
93 & 100.7 & 111.423194595418 & -10.7231945954184 \tabularnewline
94 & 106.8 & 101.034339134997 & 5.76566086500257 \tabularnewline
95 & 97.4 & 91.8784828428191 & 5.5215171571809 \tabularnewline
96 & 113 & 125.064705996125 & -12.0647059961253 \tabularnewline
97 & 76.9 & 95.6345575510029 & -18.7345575510029 \tabularnewline
98 & 87.3 & 94.132191363217 & -6.83219136321699 \tabularnewline
99 & 103.7 & 105.430522286813 & -1.73052228681313 \tabularnewline
100 & 92.1 & 89.4488640219172 & 2.65113597808282 \tabularnewline
101 & 92.9 & 99.188160807849 & -6.28816080784898 \tabularnewline
102 & 112.2 & 107.985917095431 & 4.21408290456938 \tabularnewline
103 & 88.7 & 80.2601478909746 & 8.43985210902545 \tabularnewline
104 & 74.6 & 71.0355400030087 & 3.56445999699127 \tabularnewline
105 & 101.5 & 102.638530120805 & -1.13853012080475 \tabularnewline
106 & 119.7 & 99.6859035382187 & 20.0140964617813 \tabularnewline
107 & 120.7 & 97.7236061203972 & 22.9763938796028 \tabularnewline
108 & 153.5 & 137.026072900488 & 16.4739270995119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278654&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]108.3[/C][C]104.712606837607[/C][C]3.58739316239314[/C][/ROW]
[ROW][C]14[/C][C]117.2[/C][C]115.391157460426[/C][C]1.80884253957353[/C][/ROW]
[ROW][C]15[/C][C]128.7[/C][C]127.854524364578[/C][C]0.845475635422034[/C][/ROW]
[ROW][C]16[/C][C]116.5[/C][C]116.395611706751[/C][C]0.104388293248519[/C][/ROW]
[ROW][C]17[/C][C]131.7[/C][C]131.706401689486[/C][C]-0.00640168948643804[/C][/ROW]
[ROW][C]18[/C][C]139.9[/C][C]140.098461440524[/C][C]-0.198461440524142[/C][/ROW]
[ROW][C]19[/C][C]107.4[/C][C]109.688876720188[/C][C]-2.28887672018791[/C][/ROW]
[ROW][C]20[/C][C]96.1[/C][C]91.5599914868404[/C][C]4.54000851315962[/C][/ROW]
[ROW][C]21[/C][C]126.5[/C][C]131.238698172837[/C][C]-4.73869817283702[/C][/ROW]
[ROW][C]22[/C][C]116.4[/C][C]118.520599794203[/C][C]-2.12059979420323[/C][/ROW]
[ROW][C]23[/C][C]109.8[/C][C]105.1604549888[/C][C]4.63954501119981[/C][/ROW]
[ROW][C]24[/C][C]148[/C][C]153.993846991336[/C][C]-5.9938469913356[/C][/ROW]
[ROW][C]25[/C][C]111.4[/C][C]111.556542791833[/C][C]-0.156542791833047[/C][/ROW]
[ROW][C]26[/C][C]117[/C][C]120.057513401611[/C][C]-3.05751340161088[/C][/ROW]
[ROW][C]27[/C][C]141.7[/C][C]129.900766282489[/C][C]11.799233717511[/C][/ROW]
[ROW][C]28[/C][C]120[/C][C]123.885730900139[/C][C]-3.88573090013902[/C][/ROW]
[ROW][C]29[/C][C]132.1[/C][C]137.154100919848[/C][C]-5.05410091984791[/C][/ROW]
[ROW][C]30[/C][C]146.7[/C][C]142.954302631973[/C][C]3.74569736802681[/C][/ROW]
[ROW][C]31[/C][C]122.5[/C][C]114.220506354416[/C][C]8.27949364558442[/C][/ROW]
[ROW][C]32[/C][C]99.6[/C][C]102.520528762305[/C][C]-2.9205287623046[/C][/ROW]
[ROW][C]33[/C][C]122.7[/C][C]136.96559459093[/C][C]-14.2655945909298[/C][/ROW]
[ROW][C]34[/C][C]139[/C][C]119.820549597154[/C][C]19.179450402846[/C][/ROW]
[ROW][C]35[/C][C]117.8[/C][C]118.325337055661[/C][C]-0.525337055660643[/C][/ROW]
[ROW][C]36[/C][C]125.5[/C][C]162.878942924713[/C][C]-37.3789429247132[/C][/ROW]
[ROW][C]37[/C][C]134.5[/C][C]105.422878892173[/C][C]29.0771211078274[/C][/ROW]
[ROW][C]38[/C][C]121.3[/C][C]128.308630848297[/C][C]-7.00863084829719[/C][/ROW]
[ROW][C]39[/C][C]126.7[/C][C]138.463628818224[/C][C]-11.7636288182242[/C][/ROW]
[ROW][C]40[/C][C]117.7[/C][C]118.043261158769[/C][C]-0.343261158768897[/C][/ROW]
[ROW][C]41[/C][C]123[/C][C]132.927350988526[/C][C]-9.92735098852626[/C][/ROW]
[ROW][C]42[/C][C]132.1[/C][C]137.626624447194[/C][C]-5.52662444719371[/C][/ROW]
[ROW][C]43[/C][C]113.1[/C][C]104.893864557244[/C][C]8.20613544275611[/C][/ROW]
[ROW][C]44[/C][C]89.2[/C][C]91.4098745866224[/C][C]-2.20987458662238[/C][/ROW]
[ROW][C]45[/C][C]121.7[/C][C]124.446223565186[/C][C]-2.7462235651862[/C][/ROW]
[ROW][C]46[/C][C]105.3[/C][C]118.363871156228[/C][C]-13.0638711562278[/C][/ROW]
[ROW][C]47[/C][C]85.3[/C][C]97.4307148153924[/C][C]-12.1307148153925[/C][/ROW]
[ROW][C]48[/C][C]105.3[/C][C]130.346369649142[/C][C]-25.0463696491416[/C][/ROW]
[ROW][C]49[/C][C]72.2[/C][C]89.5142014622703[/C][C]-17.3142014622703[/C][/ROW]
[ROW][C]50[/C][C]92.1[/C][C]83.2265366120973[/C][C]8.8734633879027[/C][/ROW]
[ROW][C]51[/C][C]97.2[/C][C]100.70071605547[/C][C]-3.50071605547025[/C][/ROW]
[ROW][C]52[/C][C]78.6[/C][C]86.2552442429667[/C][C]-7.65524424296666[/C][/ROW]
[ROW][C]53[/C][C]78.1[/C][C]95.9334620242341[/C][C]-17.8334620242341[/C][/ROW]
[ROW][C]54[/C][C]93[/C][C]97.3064232073737[/C][C]-4.30642320737367[/C][/ROW]
[ROW][C]55[/C][C]81[/C][C]67.3347545406728[/C][C]13.6652454593272[/C][/ROW]
[ROW][C]56[/C][C]65.9[/C][C]54.9969716142461[/C][C]10.9030283857539[/C][/ROW]
[ROW][C]57[/C][C]88.6[/C][C]94.6049794499028[/C][C]-6.00497944990276[/C][/ROW]
[ROW][C]58[/C][C]85.7[/C][C]85.2595183876001[/C][C]0.44048161239995[/C][/ROW]
[ROW][C]59[/C][C]76.3[/C][C]71.325884218525[/C][C]4.97411578147496[/C][/ROW]
[ROW][C]60[/C][C]96.8[/C][C]110.908552786833[/C][C]-14.1085527868327[/C][/ROW]
[ROW][C]61[/C][C]76.8[/C][C]76.83367873335[/C][C]-0.0336787333500439[/C][/ROW]
[ROW][C]62[/C][C]85.6[/C][C]83.4008383268934[/C][C]2.19916167310657[/C][/ROW]
[ROW][C]63[/C][C]119.2[/C][C]95.5576453166867[/C][C]23.6423546833133[/C][/ROW]
[ROW][C]64[/C][C]91.4[/C][C]94.2403897805504[/C][C]-2.84038978055037[/C][/ROW]
[ROW][C]65[/C][C]95.7[/C][C]104.774916421671[/C][C]-9.07491642167062[/C][/ROW]
[ROW][C]66[/C][C]112.3[/C][C]112.702887510599[/C][C]-0.402887510598873[/C][/ROW]
[ROW][C]67[/C][C]95.2[/C][C]87.5153164001653[/C][C]7.68468359983467[/C][/ROW]
[ROW][C]68[/C][C]82.8[/C][C]71.7113639010069[/C][C]11.0886360989931[/C][/ROW]
[ROW][C]69[/C][C]111.3[/C][C]108.77656463271[/C][C]2.52343536729045[/C][/ROW]
[ROW][C]70[/C][C]108.2[/C][C]104.764854630367[/C][C]3.43514536963312[/C][/ROW]
[ROW][C]71[/C][C]97[/C][C]93.058204564181[/C][C]3.94179543581896[/C][/ROW]
[ROW][C]72[/C][C]124.4[/C][C]129.140755207049[/C][C]-4.74075520704864[/C][/ROW]
[ROW][C]73[/C][C]99.3[/C][C]102.015551762753[/C][C]-2.71555176275263[/C][/ROW]
[ROW][C]74[/C][C]117.6[/C][C]107.569795051985[/C][C]10.0302049480151[/C][/ROW]
[ROW][C]75[/C][C]131.5[/C][C]127.045489281538[/C][C]4.45451071846219[/C][/ROW]
[ROW][C]76[/C][C]114.2[/C][C]111.85934821271[/C][C]2.34065178729038[/C][/ROW]
[ROW][C]77[/C][C]116.8[/C][C]124.051104714273[/C][C]-7.2511047142726[/C][/ROW]
[ROW][C]78[/C][C]116.5[/C][C]134.257240068885[/C][C]-17.7572400688854[/C][/ROW]
[ROW][C]79[/C][C]105.4[/C][C]101.523014507491[/C][C]3.87698549250885[/C][/ROW]
[ROW][C]80[/C][C]89.2[/C][C]84.3173948528739[/C][C]4.88260514712614[/C][/ROW]
[ROW][C]81[/C][C]115.8[/C][C]116.896945516208[/C][C]-1.0969455162077[/C][/ROW]
[ROW][C]82[/C][C]111.4[/C][C]111.1899435012[/C][C]0.210056498800185[/C][/ROW]
[ROW][C]83[/C][C]106.4[/C][C]97.9254534737437[/C][C]8.47454652625633[/C][/ROW]
[ROW][C]84[/C][C]128.4[/C][C]134.954402077284[/C][C]-6.55440207728441[/C][/ROW]
[ROW][C]85[/C][C]107.7[/C][C]107.224557404104[/C][C]0.475442595895942[/C][/ROW]
[ROW][C]86[/C][C]111[/C][C]116.386210994251[/C][C]-5.38621099425119[/C][/ROW]
[ROW][C]87[/C][C]129.8[/C][C]127.167876049812[/C][C]2.63212395018779[/C][/ROW]
[ROW][C]88[/C][C]130.5[/C][C]110.727120603045[/C][C]19.7728793969553[/C][/ROW]
[ROW][C]89[/C][C]142.9[/C][C]130.27046010149[/C][C]12.6295398985096[/C][/ROW]
[ROW][C]90[/C][C]159.9[/C][C]148.92823690651[/C][C]10.9717630934899[/C][/ROW]
[ROW][C]91[/C][C]84.1[/C][C]134.14922109766[/C][C]-50.0492210976596[/C][/ROW]
[ROW][C]92[/C][C]75[/C][C]89.7307897431289[/C][C]-14.7307897431289[/C][/ROW]
[ROW][C]93[/C][C]100.7[/C][C]111.423194595418[/C][C]-10.7231945954184[/C][/ROW]
[ROW][C]94[/C][C]106.8[/C][C]101.034339134997[/C][C]5.76566086500257[/C][/ROW]
[ROW][C]95[/C][C]97.4[/C][C]91.8784828428191[/C][C]5.5215171571809[/C][/ROW]
[ROW][C]96[/C][C]113[/C][C]125.064705996125[/C][C]-12.0647059961253[/C][/ROW]
[ROW][C]97[/C][C]76.9[/C][C]95.6345575510029[/C][C]-18.7345575510029[/C][/ROW]
[ROW][C]98[/C][C]87.3[/C][C]94.132191363217[/C][C]-6.83219136321699[/C][/ROW]
[ROW][C]99[/C][C]103.7[/C][C]105.430522286813[/C][C]-1.73052228681313[/C][/ROW]
[ROW][C]100[/C][C]92.1[/C][C]89.4488640219172[/C][C]2.65113597808282[/C][/ROW]
[ROW][C]101[/C][C]92.9[/C][C]99.188160807849[/C][C]-6.28816080784898[/C][/ROW]
[ROW][C]102[/C][C]112.2[/C][C]107.985917095431[/C][C]4.21408290456938[/C][/ROW]
[ROW][C]103[/C][C]88.7[/C][C]80.2601478909746[/C][C]8.43985210902545[/C][/ROW]
[ROW][C]104[/C][C]74.6[/C][C]71.0355400030087[/C][C]3.56445999699127[/C][/ROW]
[ROW][C]105[/C][C]101.5[/C][C]102.638530120805[/C][C]-1.13853012080475[/C][/ROW]
[ROW][C]106[/C][C]119.7[/C][C]99.6859035382187[/C][C]20.0140964617813[/C][/ROW]
[ROW][C]107[/C][C]120.7[/C][C]97.7236061203972[/C][C]22.9763938796028[/C][/ROW]
[ROW][C]108[/C][C]153.5[/C][C]137.026072900488[/C][C]16.4739270995119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278654&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278654&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	108.3	104.712606837607	3.58739316239314
14	117.2	115.391157460426	1.80884253957353
15	128.7	127.854524364578	0.845475635422034
16	116.5	116.395611706751	0.104388293248519
17	131.7	131.706401689486	-0.00640168948643804
18	139.9	140.098461440524	-0.198461440524142
19	107.4	109.688876720188	-2.28887672018791
20	96.1	91.5599914868404	4.54000851315962
21	126.5	131.238698172837	-4.73869817283702
22	116.4	118.520599794203	-2.12059979420323
23	109.8	105.1604549888	4.63954501119981
24	148	153.993846991336	-5.9938469913356
25	111.4	111.556542791833	-0.156542791833047
26	117	120.057513401611	-3.05751340161088
27	141.7	129.900766282489	11.799233717511
28	120	123.885730900139	-3.88573090013902
29	132.1	137.154100919848	-5.05410091984791
30	146.7	142.954302631973	3.74569736802681
31	122.5	114.220506354416	8.27949364558442
32	99.6	102.520528762305	-2.9205287623046
33	122.7	136.96559459093	-14.2655945909298
34	139	119.820549597154	19.179450402846
35	117.8	118.325337055661	-0.525337055660643
36	125.5	162.878942924713	-37.3789429247132
37	134.5	105.422878892173	29.0771211078274
38	121.3	128.308630848297	-7.00863084829719
39	126.7	138.463628818224	-11.7636288182242
40	117.7	118.043261158769	-0.343261158768897
41	123	132.927350988526	-9.92735098852626
42	132.1	137.626624447194	-5.52662444719371
43	113.1	104.893864557244	8.20613544275611
44	89.2	91.4098745866224	-2.20987458662238
45	121.7	124.446223565186	-2.7462235651862
46	105.3	118.363871156228	-13.0638711562278
47	85.3	97.4307148153924	-12.1307148153925
48	105.3	130.346369649142	-25.0463696491416
49	72.2	89.5142014622703	-17.3142014622703
50	92.1	83.2265366120973	8.8734633879027
51	97.2	100.70071605547	-3.50071605547025
52	78.6	86.2552442429667	-7.65524424296666
53	78.1	95.9334620242341	-17.8334620242341
54	93	97.3064232073737	-4.30642320737367
55	81	67.3347545406728	13.6652454593272
56	65.9	54.9969716142461	10.9030283857539
57	88.6	94.6049794499028	-6.00497944990276
58	85.7	85.2595183876001	0.44048161239995
59	76.3	71.325884218525	4.97411578147496
60	96.8	110.908552786833	-14.1085527868327
61	76.8	76.83367873335	-0.0336787333500439
62	85.6	83.4008383268934	2.19916167310657
63	119.2	95.5576453166867	23.6423546833133
64	91.4	94.2403897805504	-2.84038978055037
65	95.7	104.774916421671	-9.07491642167062
66	112.3	112.702887510599	-0.402887510598873
67	95.2	87.5153164001653	7.68468359983467
68	82.8	71.7113639010069	11.0886360989931
69	111.3	108.77656463271	2.52343536729045
70	108.2	104.764854630367	3.43514536963312
71	97	93.058204564181	3.94179543581896
72	124.4	129.140755207049	-4.74075520704864
73	99.3	102.015551762753	-2.71555176275263
74	117.6	107.569795051985	10.0302049480151
75	131.5	127.045489281538	4.45451071846219
76	114.2	111.85934821271	2.34065178729038
77	116.8	124.051104714273	-7.2511047142726
78	116.5	134.257240068885	-17.7572400688854
79	105.4	101.523014507491	3.87698549250885
80	89.2	84.3173948528739	4.88260514712614
81	115.8	116.896945516208	-1.0969455162077
82	111.4	111.1899435012	0.210056498800185
83	106.4	97.9254534737437	8.47454652625633
84	128.4	134.954402077284	-6.55440207728441
85	107.7	107.224557404104	0.475442595895942
86	111	116.386210994251	-5.38621099425119
87	129.8	127.167876049812	2.63212395018779
88	130.5	110.727120603045	19.7728793969553
89	142.9	130.27046010149	12.6295398985096
90	159.9	148.92823690651	10.9717630934899
91	84.1	134.14922109766	-50.0492210976596
92	75	89.7307897431289	-14.7307897431289
93	100.7	111.423194595418	-10.7231945954184
94	106.8	101.034339134997	5.76566086500257
95	97.4	91.8784828428191	5.5215171571809
96	113	125.064705996125	-12.0647059961253
97	76.9	95.6345575510029	-18.7345575510029
98	87.3	94.132191363217	-6.83219136321699
99	103.7	105.430522286813	-1.73052228681313
100	92.1	89.4488640219172	2.65113597808282
101	92.9	99.188160807849	-6.28816080784898
102	112.2	107.985917095431	4.21408290456938
103	88.7	80.2601478909746	8.43985210902545
104	74.6	71.0355400030087	3.56445999699127
105	101.5	102.638530120805	-1.13853012080475
106	119.7	99.6859035382187	20.0140964617813
107	120.7	97.7236061203972	22.9763938796028
108	153.5	137.026072900488	16.4739270995119

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	121.040147599197	98.1790013535041	143.901293844889
110	130.902618431973	105.265539595728	156.539697268218
111	146.464220175568	118.323722403767	174.604717947369
112	132.044242479154	101.605526697544	162.482958260764
113	139.043792018234	106.468598664663	171.618985371806
114	152.670987976973	118.091065686553	187.250910267393
115	123.465467851647	86.9908351708323	159.940100532462
116	109.19692934921	70.9212630220346	147.472595676385
117	138.257328450069	98.2616482285979	178.25300867154
118	139.181560614857	97.5368461847272	180.826275044987
119	127.523336107765	84.2924438713563	170.754228344173
120	154.15024894258	109.389352535729	198.911145349432

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 121.040147599197 & 98.1790013535041 & 143.901293844889 \tabularnewline
110 & 130.902618431973 & 105.265539595728 & 156.539697268218 \tabularnewline
111 & 146.464220175568 & 118.323722403767 & 174.604717947369 \tabularnewline
112 & 132.044242479154 & 101.605526697544 & 162.482958260764 \tabularnewline
113 & 139.043792018234 & 106.468598664663 & 171.618985371806 \tabularnewline
114 & 152.670987976973 & 118.091065686553 & 187.250910267393 \tabularnewline
115 & 123.465467851647 & 86.9908351708323 & 159.940100532462 \tabularnewline
116 & 109.19692934921 & 70.9212630220346 & 147.472595676385 \tabularnewline
117 & 138.257328450069 & 98.2616482285979 & 178.25300867154 \tabularnewline
118 & 139.181560614857 & 97.5368461847272 & 180.826275044987 \tabularnewline
119 & 127.523336107765 & 84.2924438713563 & 170.754228344173 \tabularnewline
120 & 154.15024894258 & 109.389352535729 & 198.911145349432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278654&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]121.040147599197[/C][C]98.1790013535041[/C][C]143.901293844889[/C][/ROW]
[ROW][C]110[/C][C]130.902618431973[/C][C]105.265539595728[/C][C]156.539697268218[/C][/ROW]
[ROW][C]111[/C][C]146.464220175568[/C][C]118.323722403767[/C][C]174.604717947369[/C][/ROW]
[ROW][C]112[/C][C]132.044242479154[/C][C]101.605526697544[/C][C]162.482958260764[/C][/ROW]
[ROW][C]113[/C][C]139.043792018234[/C][C]106.468598664663[/C][C]171.618985371806[/C][/ROW]
[ROW][C]114[/C][C]152.670987976973[/C][C]118.091065686553[/C][C]187.250910267393[/C][/ROW]
[ROW][C]115[/C][C]123.465467851647[/C][C]86.9908351708323[/C][C]159.940100532462[/C][/ROW]
[ROW][C]116[/C][C]109.19692934921[/C][C]70.9212630220346[/C][C]147.472595676385[/C][/ROW]
[ROW][C]117[/C][C]138.257328450069[/C][C]98.2616482285979[/C][C]178.25300867154[/C][/ROW]
[ROW][C]118[/C][C]139.181560614857[/C][C]97.5368461847272[/C][C]180.826275044987[/C][/ROW]
[ROW][C]119[/C][C]127.523336107765[/C][C]84.2924438713563[/C][C]170.754228344173[/C][/ROW]
[ROW][C]120[/C][C]154.15024894258[/C][C]109.389352535729[/C][C]198.911145349432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278654&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278654&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	121.040147599197	98.1790013535041	143.901293844889
110	130.902618431973	105.265539595728	156.539697268218
111	146.464220175568	118.323722403767	174.604717947369
112	132.044242479154	101.605526697544	162.482958260764
113	139.043792018234	106.468598664663	171.618985371806
114	152.670987976973	118.091065686553	187.250910267393
115	123.465467851647	86.9908351708323	159.940100532462
116	109.19692934921	70.9212630220346	147.472595676385
117	138.257328450069	98.2616482285979	178.25300867154
118	139.181560614857	97.5368461847272	180.826275044987
119	127.523336107765	84.2924438713563	170.754228344173
120	154.15024894258	109.389352535729	198.911145349432

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