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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 16 Dec 2013 11:30:54 -0500

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/2013/Dec/16/t1387211466k3gqxze0ug5v22z.htm/, Retrieved Fri, 26 Apr 2024 19:44:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232393, Retrieved Fri, 26 Apr 2024 19:44:01 +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] [] [2013-12-16 16:30:54] [629d05b8910d8b56ad89862016f2bc6c] [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	6 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 6 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232393&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232393&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232393&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	6 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999958313321697
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999958313321697 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232393&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]0.999958313321697[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232393&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232393&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	0.999958313321697
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	119.9	120.6	-0.699999999999989
3	119.48	119.900029180675	-0.420029180674817
4	117.45	119.480017509621	-2.03001750962133
5	118.37	117.450084624687	0.919915375313124
6	117.07	118.369961651784	-1.29996165178369
7	114.98	117.070054191083	-2.09005419108317
8	112.59	114.980087127417	-2.39008712741671
9	111.7	112.590099634793	-0.890099634793202
10	112.04	111.700037105297	0.339962894702865
11	110.79	112.039985828076	-1.24998582807618
12	109.82	110.790052107757	-0.970052107757112
13	109.11	109.82004043825	-0.710040438250147
14	109.84	109.110029599227	0.729970400772672
15	109.31	109.839969569959	-0.529969569958737
16	108.29	109.310022092671	-1.02002209267097
17	107.42	108.290042521333	-0.870042521332849
18	106.71	107.420036269183	-0.710036269182709
19	105.11	106.710029599054	-1.60002959905353
20	104.43	105.110066699919	-0.680066699919166
21	105.55	104.430028349722	1.11997165027825
22	106.12	105.549953312102	0.5700466878979
23	105.78	106.119976236647	-0.339976236647104
24	105.33	105.78001417248	-0.45001417248001
25	104.63	105.330018759596	-0.700018759596048
26	104.62	104.630029181457	-0.0100291814568294
27	105.57	104.620000418083	0.949999581916728
28	107.5	105.569960397673	1.93003960232697
29	107.52	107.49991954306	0.0200804569400077
30	107.76	107.519999162912	0.240000837087564
31	106.74	107.759989995162	-1.01998999516232
32	106.21	106.740042519995	-0.530042519994808
33	105.77	106.210022095712	-0.44002209571201
34	105.27	105.77001834306	-0.500018343059551
35	104.35	105.270020844104	-0.920020844103817
36	103.52	104.350038352613	-0.830038352612959
37	102.28	103.520034601542	-1.24003460154178
38	100.93	102.280051692924	-1.35005169292351
39	101.04	100.930056279171	0.109943720829378
40	99.95	101.039995416811	-1.08999541681148
41	99.55	99.9500454382883	-0.400045438288302
42	99.56	99.5500166765655	0.00998332343451125
43	99.01	99.5599995838284	-0.549999583828409
44	98.64	99.0100229276557	-0.370022927655725
45	98.98	98.6400154250267	0.339984574973258
46	100.8	98.9799858271724	1.8200141728276
47	100.32	100.799924129655	-0.479924129654677
48	100.72	100.320020006443	0.39997999355721
49	280.8	100.719983326163	180.080016673837
50	280.4	280.792493062276	-0.39249306227623
51	280.4	280.400016361732	-1.63617320367848e-05
52	280.3	280.400000000682	-0.10000000068203
53	281	280.300004168668	0.699995831332103
54	280.9	280.999970819499	-0.0999708194989921
55	279.7	280.900004167451	-1.20000416745137
56	283.1	279.700050024188	3.39994997581232
57	290.6	283.099858267379	7.50014173262088
58	291.6	290.599687344004	1.00031265599563
59	291.7	291.599958300288	0.10004169971188
60	291.8	291.699995829594	0.10000417040618
61	291.7	291.799995831158	-0.0999958311583669
62	291.5	291.700004168494	-0.200004168494047
63	291.7	291.500008337509	0.199991662490561
64	293.4	291.699991663012	1.70000833698811
65	293.1	293.399929132299	-0.299929132299326
66	293.1	293.100012503049	-1.25030492768019e-05
67	292.6	293.100000000521	-0.500000000521197
68	292.1	292.600020843339	-0.5000208433392
69	292.2	292.100020844208	0.0999791557919139
70	292	292.199995832201	-0.199995832201068
71	292.1	292.000008337162	0.0999916628380788
72	293.4	292.09999583168	1.30000416832024
73	292.2	293.399945807144	-1.19994580714445
74	292.1	292.200050021755	-0.100050021754782
75	291.6	292.100004170753	-0.500004170753073
76	290.9	291.600020843513	-0.700020843513073
77	290.9	290.900029181544	-2.91815437094556e-05
78	290.8	290.900000001216	-0.100000001216472
79	290.5	290.800004168668	-0.300004168667897
80	290	290.500012506177	-0.500012506177256
81	290.2	290.000020843861	0.199979156139477
82	290.1	290.199991663533	-0.099991663533217
83	291	290.10000416832	0.899995831679689
84	291.8	290.999962482163	0.800037517836699

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 119.9 & 120.6 & -0.699999999999989 \tabularnewline
3 & 119.48 & 119.900029180675 & -0.420029180674817 \tabularnewline
4 & 117.45 & 119.480017509621 & -2.03001750962133 \tabularnewline
5 & 118.37 & 117.450084624687 & 0.919915375313124 \tabularnewline
6 & 117.07 & 118.369961651784 & -1.29996165178369 \tabularnewline
7 & 114.98 & 117.070054191083 & -2.09005419108317 \tabularnewline
8 & 112.59 & 114.980087127417 & -2.39008712741671 \tabularnewline
9 & 111.7 & 112.590099634793 & -0.890099634793202 \tabularnewline
10 & 112.04 & 111.700037105297 & 0.339962894702865 \tabularnewline
11 & 110.79 & 112.039985828076 & -1.24998582807618 \tabularnewline
12 & 109.82 & 110.790052107757 & -0.970052107757112 \tabularnewline
13 & 109.11 & 109.82004043825 & -0.710040438250147 \tabularnewline
14 & 109.84 & 109.110029599227 & 0.729970400772672 \tabularnewline
15 & 109.31 & 109.839969569959 & -0.529969569958737 \tabularnewline
16 & 108.29 & 109.310022092671 & -1.02002209267097 \tabularnewline
17 & 107.42 & 108.290042521333 & -0.870042521332849 \tabularnewline
18 & 106.71 & 107.420036269183 & -0.710036269182709 \tabularnewline
19 & 105.11 & 106.710029599054 & -1.60002959905353 \tabularnewline
20 & 104.43 & 105.110066699919 & -0.680066699919166 \tabularnewline
21 & 105.55 & 104.430028349722 & 1.11997165027825 \tabularnewline
22 & 106.12 & 105.549953312102 & 0.5700466878979 \tabularnewline
23 & 105.78 & 106.119976236647 & -0.339976236647104 \tabularnewline
24 & 105.33 & 105.78001417248 & -0.45001417248001 \tabularnewline
25 & 104.63 & 105.330018759596 & -0.700018759596048 \tabularnewline
26 & 104.62 & 104.630029181457 & -0.0100291814568294 \tabularnewline
27 & 105.57 & 104.620000418083 & 0.949999581916728 \tabularnewline
28 & 107.5 & 105.569960397673 & 1.93003960232697 \tabularnewline
29 & 107.52 & 107.49991954306 & 0.0200804569400077 \tabularnewline
30 & 107.76 & 107.519999162912 & 0.240000837087564 \tabularnewline
31 & 106.74 & 107.759989995162 & -1.01998999516232 \tabularnewline
32 & 106.21 & 106.740042519995 & -0.530042519994808 \tabularnewline
33 & 105.77 & 106.210022095712 & -0.44002209571201 \tabularnewline
34 & 105.27 & 105.77001834306 & -0.500018343059551 \tabularnewline
35 & 104.35 & 105.270020844104 & -0.920020844103817 \tabularnewline
36 & 103.52 & 104.350038352613 & -0.830038352612959 \tabularnewline
37 & 102.28 & 103.520034601542 & -1.24003460154178 \tabularnewline
38 & 100.93 & 102.280051692924 & -1.35005169292351 \tabularnewline
39 & 101.04 & 100.930056279171 & 0.109943720829378 \tabularnewline
40 & 99.95 & 101.039995416811 & -1.08999541681148 \tabularnewline
41 & 99.55 & 99.9500454382883 & -0.400045438288302 \tabularnewline
42 & 99.56 & 99.5500166765655 & 0.00998332343451125 \tabularnewline
43 & 99.01 & 99.5599995838284 & -0.549999583828409 \tabularnewline
44 & 98.64 & 99.0100229276557 & -0.370022927655725 \tabularnewline
45 & 98.98 & 98.6400154250267 & 0.339984574973258 \tabularnewline
46 & 100.8 & 98.9799858271724 & 1.8200141728276 \tabularnewline
47 & 100.32 & 100.799924129655 & -0.479924129654677 \tabularnewline
48 & 100.72 & 100.320020006443 & 0.39997999355721 \tabularnewline
49 & 280.8 & 100.719983326163 & 180.080016673837 \tabularnewline
50 & 280.4 & 280.792493062276 & -0.39249306227623 \tabularnewline
51 & 280.4 & 280.400016361732 & -1.63617320367848e-05 \tabularnewline
52 & 280.3 & 280.400000000682 & -0.10000000068203 \tabularnewline
53 & 281 & 280.300004168668 & 0.699995831332103 \tabularnewline
54 & 280.9 & 280.999970819499 & -0.0999708194989921 \tabularnewline
55 & 279.7 & 280.900004167451 & -1.20000416745137 \tabularnewline
56 & 283.1 & 279.700050024188 & 3.39994997581232 \tabularnewline
57 & 290.6 & 283.099858267379 & 7.50014173262088 \tabularnewline
58 & 291.6 & 290.599687344004 & 1.00031265599563 \tabularnewline
59 & 291.7 & 291.599958300288 & 0.10004169971188 \tabularnewline
60 & 291.8 & 291.699995829594 & 0.10000417040618 \tabularnewline
61 & 291.7 & 291.799995831158 & -0.0999958311583669 \tabularnewline
62 & 291.5 & 291.700004168494 & -0.200004168494047 \tabularnewline
63 & 291.7 & 291.500008337509 & 0.199991662490561 \tabularnewline
64 & 293.4 & 291.699991663012 & 1.70000833698811 \tabularnewline
65 & 293.1 & 293.399929132299 & -0.299929132299326 \tabularnewline
66 & 293.1 & 293.100012503049 & -1.25030492768019e-05 \tabularnewline
67 & 292.6 & 293.100000000521 & -0.500000000521197 \tabularnewline
68 & 292.1 & 292.600020843339 & -0.5000208433392 \tabularnewline
69 & 292.2 & 292.100020844208 & 0.0999791557919139 \tabularnewline
70 & 292 & 292.199995832201 & -0.199995832201068 \tabularnewline
71 & 292.1 & 292.000008337162 & 0.0999916628380788 \tabularnewline
72 & 293.4 & 292.09999583168 & 1.30000416832024 \tabularnewline
73 & 292.2 & 293.399945807144 & -1.19994580714445 \tabularnewline
74 & 292.1 & 292.200050021755 & -0.100050021754782 \tabularnewline
75 & 291.6 & 292.100004170753 & -0.500004170753073 \tabularnewline
76 & 290.9 & 291.600020843513 & -0.700020843513073 \tabularnewline
77 & 290.9 & 290.900029181544 & -2.91815437094556e-05 \tabularnewline
78 & 290.8 & 290.900000001216 & -0.100000001216472 \tabularnewline
79 & 290.5 & 290.800004168668 & -0.300004168667897 \tabularnewline
80 & 290 & 290.500012506177 & -0.500012506177256 \tabularnewline
81 & 290.2 & 290.000020843861 & 0.199979156139477 \tabularnewline
82 & 290.1 & 290.199991663533 & -0.099991663533217 \tabularnewline
83 & 291 & 290.10000416832 & 0.899995831679689 \tabularnewline
84 & 291.8 & 290.999962482163 & 0.800037517836699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232393&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]2[/C][C]119.9[/C][C]120.6[/C][C]-0.699999999999989[/C][/ROW]
[ROW][C]3[/C][C]119.48[/C][C]119.900029180675[/C][C]-0.420029180674817[/C][/ROW]
[ROW][C]4[/C][C]117.45[/C][C]119.480017509621[/C][C]-2.03001750962133[/C][/ROW]
[ROW][C]5[/C][C]118.37[/C][C]117.450084624687[/C][C]0.919915375313124[/C][/ROW]
[ROW][C]6[/C][C]117.07[/C][C]118.369961651784[/C][C]-1.29996165178369[/C][/ROW]
[ROW][C]7[/C][C]114.98[/C][C]117.070054191083[/C][C]-2.09005419108317[/C][/ROW]
[ROW][C]8[/C][C]112.59[/C][C]114.980087127417[/C][C]-2.39008712741671[/C][/ROW]
[ROW][C]9[/C][C]111.7[/C][C]112.590099634793[/C][C]-0.890099634793202[/C][/ROW]
[ROW][C]10[/C][C]112.04[/C][C]111.700037105297[/C][C]0.339962894702865[/C][/ROW]
[ROW][C]11[/C][C]110.79[/C][C]112.039985828076[/C][C]-1.24998582807618[/C][/ROW]
[ROW][C]12[/C][C]109.82[/C][C]110.790052107757[/C][C]-0.970052107757112[/C][/ROW]
[ROW][C]13[/C][C]109.11[/C][C]109.82004043825[/C][C]-0.710040438250147[/C][/ROW]
[ROW][C]14[/C][C]109.84[/C][C]109.110029599227[/C][C]0.729970400772672[/C][/ROW]
[ROW][C]15[/C][C]109.31[/C][C]109.839969569959[/C][C]-0.529969569958737[/C][/ROW]
[ROW][C]16[/C][C]108.29[/C][C]109.310022092671[/C][C]-1.02002209267097[/C][/ROW]
[ROW][C]17[/C][C]107.42[/C][C]108.290042521333[/C][C]-0.870042521332849[/C][/ROW]
[ROW][C]18[/C][C]106.71[/C][C]107.420036269183[/C][C]-0.710036269182709[/C][/ROW]
[ROW][C]19[/C][C]105.11[/C][C]106.710029599054[/C][C]-1.60002959905353[/C][/ROW]
[ROW][C]20[/C][C]104.43[/C][C]105.110066699919[/C][C]-0.680066699919166[/C][/ROW]
[ROW][C]21[/C][C]105.55[/C][C]104.430028349722[/C][C]1.11997165027825[/C][/ROW]
[ROW][C]22[/C][C]106.12[/C][C]105.549953312102[/C][C]0.5700466878979[/C][/ROW]
[ROW][C]23[/C][C]105.78[/C][C]106.119976236647[/C][C]-0.339976236647104[/C][/ROW]
[ROW][C]24[/C][C]105.33[/C][C]105.78001417248[/C][C]-0.45001417248001[/C][/ROW]
[ROW][C]25[/C][C]104.63[/C][C]105.330018759596[/C][C]-0.700018759596048[/C][/ROW]
[ROW][C]26[/C][C]104.62[/C][C]104.630029181457[/C][C]-0.0100291814568294[/C][/ROW]
[ROW][C]27[/C][C]105.57[/C][C]104.620000418083[/C][C]0.949999581916728[/C][/ROW]
[ROW][C]28[/C][C]107.5[/C][C]105.569960397673[/C][C]1.93003960232697[/C][/ROW]
[ROW][C]29[/C][C]107.52[/C][C]107.49991954306[/C][C]0.0200804569400077[/C][/ROW]
[ROW][C]30[/C][C]107.76[/C][C]107.519999162912[/C][C]0.240000837087564[/C][/ROW]
[ROW][C]31[/C][C]106.74[/C][C]107.759989995162[/C][C]-1.01998999516232[/C][/ROW]
[ROW][C]32[/C][C]106.21[/C][C]106.740042519995[/C][C]-0.530042519994808[/C][/ROW]
[ROW][C]33[/C][C]105.77[/C][C]106.210022095712[/C][C]-0.44002209571201[/C][/ROW]
[ROW][C]34[/C][C]105.27[/C][C]105.77001834306[/C][C]-0.500018343059551[/C][/ROW]
[ROW][C]35[/C][C]104.35[/C][C]105.270020844104[/C][C]-0.920020844103817[/C][/ROW]
[ROW][C]36[/C][C]103.52[/C][C]104.350038352613[/C][C]-0.830038352612959[/C][/ROW]
[ROW][C]37[/C][C]102.28[/C][C]103.520034601542[/C][C]-1.24003460154178[/C][/ROW]
[ROW][C]38[/C][C]100.93[/C][C]102.280051692924[/C][C]-1.35005169292351[/C][/ROW]
[ROW][C]39[/C][C]101.04[/C][C]100.930056279171[/C][C]0.109943720829378[/C][/ROW]
[ROW][C]40[/C][C]99.95[/C][C]101.039995416811[/C][C]-1.08999541681148[/C][/ROW]
[ROW][C]41[/C][C]99.55[/C][C]99.9500454382883[/C][C]-0.400045438288302[/C][/ROW]
[ROW][C]42[/C][C]99.56[/C][C]99.5500166765655[/C][C]0.00998332343451125[/C][/ROW]
[ROW][C]43[/C][C]99.01[/C][C]99.5599995838284[/C][C]-0.549999583828409[/C][/ROW]
[ROW][C]44[/C][C]98.64[/C][C]99.0100229276557[/C][C]-0.370022927655725[/C][/ROW]
[ROW][C]45[/C][C]98.98[/C][C]98.6400154250267[/C][C]0.339984574973258[/C][/ROW]
[ROW][C]46[/C][C]100.8[/C][C]98.9799858271724[/C][C]1.8200141728276[/C][/ROW]
[ROW][C]47[/C][C]100.32[/C][C]100.799924129655[/C][C]-0.479924129654677[/C][/ROW]
[ROW][C]48[/C][C]100.72[/C][C]100.320020006443[/C][C]0.39997999355721[/C][/ROW]
[ROW][C]49[/C][C]280.8[/C][C]100.719983326163[/C][C]180.080016673837[/C][/ROW]
[ROW][C]50[/C][C]280.4[/C][C]280.792493062276[/C][C]-0.39249306227623[/C][/ROW]
[ROW][C]51[/C][C]280.4[/C][C]280.400016361732[/C][C]-1.63617320367848e-05[/C][/ROW]
[ROW][C]52[/C][C]280.3[/C][C]280.400000000682[/C][C]-0.10000000068203[/C][/ROW]
[ROW][C]53[/C][C]281[/C][C]280.300004168668[/C][C]0.699995831332103[/C][/ROW]
[ROW][C]54[/C][C]280.9[/C][C]280.999970819499[/C][C]-0.0999708194989921[/C][/ROW]
[ROW][C]55[/C][C]279.7[/C][C]280.900004167451[/C][C]-1.20000416745137[/C][/ROW]
[ROW][C]56[/C][C]283.1[/C][C]279.700050024188[/C][C]3.39994997581232[/C][/ROW]
[ROW][C]57[/C][C]290.6[/C][C]283.099858267379[/C][C]7.50014173262088[/C][/ROW]
[ROW][C]58[/C][C]291.6[/C][C]290.599687344004[/C][C]1.00031265599563[/C][/ROW]
[ROW][C]59[/C][C]291.7[/C][C]291.599958300288[/C][C]0.10004169971188[/C][/ROW]
[ROW][C]60[/C][C]291.8[/C][C]291.699995829594[/C][C]0.10000417040618[/C][/ROW]
[ROW][C]61[/C][C]291.7[/C][C]291.799995831158[/C][C]-0.0999958311583669[/C][/ROW]
[ROW][C]62[/C][C]291.5[/C][C]291.700004168494[/C][C]-0.200004168494047[/C][/ROW]
[ROW][C]63[/C][C]291.7[/C][C]291.500008337509[/C][C]0.199991662490561[/C][/ROW]
[ROW][C]64[/C][C]293.4[/C][C]291.699991663012[/C][C]1.70000833698811[/C][/ROW]
[ROW][C]65[/C][C]293.1[/C][C]293.399929132299[/C][C]-0.299929132299326[/C][/ROW]
[ROW][C]66[/C][C]293.1[/C][C]293.100012503049[/C][C]-1.25030492768019e-05[/C][/ROW]
[ROW][C]67[/C][C]292.6[/C][C]293.100000000521[/C][C]-0.500000000521197[/C][/ROW]
[ROW][C]68[/C][C]292.1[/C][C]292.600020843339[/C][C]-0.5000208433392[/C][/ROW]
[ROW][C]69[/C][C]292.2[/C][C]292.100020844208[/C][C]0.0999791557919139[/C][/ROW]
[ROW][C]70[/C][C]292[/C][C]292.199995832201[/C][C]-0.199995832201068[/C][/ROW]
[ROW][C]71[/C][C]292.1[/C][C]292.000008337162[/C][C]0.0999916628380788[/C][/ROW]
[ROW][C]72[/C][C]293.4[/C][C]292.09999583168[/C][C]1.30000416832024[/C][/ROW]
[ROW][C]73[/C][C]292.2[/C][C]293.399945807144[/C][C]-1.19994580714445[/C][/ROW]
[ROW][C]74[/C][C]292.1[/C][C]292.200050021755[/C][C]-0.100050021754782[/C][/ROW]
[ROW][C]75[/C][C]291.6[/C][C]292.100004170753[/C][C]-0.500004170753073[/C][/ROW]
[ROW][C]76[/C][C]290.9[/C][C]291.600020843513[/C][C]-0.700020843513073[/C][/ROW]
[ROW][C]77[/C][C]290.9[/C][C]290.900029181544[/C][C]-2.91815437094556e-05[/C][/ROW]
[ROW][C]78[/C][C]290.8[/C][C]290.900000001216[/C][C]-0.100000001216472[/C][/ROW]
[ROW][C]79[/C][C]290.5[/C][C]290.800004168668[/C][C]-0.300004168667897[/C][/ROW]
[ROW][C]80[/C][C]290[/C][C]290.500012506177[/C][C]-0.500012506177256[/C][/ROW]
[ROW][C]81[/C][C]290.2[/C][C]290.000020843861[/C][C]0.199979156139477[/C][/ROW]
[ROW][C]82[/C][C]290.1[/C][C]290.199991663533[/C][C]-0.099991663533217[/C][/ROW]
[ROW][C]83[/C][C]291[/C][C]290.10000416832[/C][C]0.899995831679689[/C][/ROW]
[ROW][C]84[/C][C]291.8[/C][C]290.999962482163[/C][C]0.800037517836699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232393&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232393&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
2	119.9	120.6	-0.699999999999989
3	119.48	119.900029180675	-0.420029180674817
4	117.45	119.480017509621	-2.03001750962133
5	118.37	117.450084624687	0.919915375313124
6	117.07	118.369961651784	-1.29996165178369
7	114.98	117.070054191083	-2.09005419108317
8	112.59	114.980087127417	-2.39008712741671
9	111.7	112.590099634793	-0.890099634793202
10	112.04	111.700037105297	0.339962894702865
11	110.79	112.039985828076	-1.24998582807618
12	109.82	110.790052107757	-0.970052107757112
13	109.11	109.82004043825	-0.710040438250147
14	109.84	109.110029599227	0.729970400772672
15	109.31	109.839969569959	-0.529969569958737
16	108.29	109.310022092671	-1.02002209267097
17	107.42	108.290042521333	-0.870042521332849
18	106.71	107.420036269183	-0.710036269182709
19	105.11	106.710029599054	-1.60002959905353
20	104.43	105.110066699919	-0.680066699919166
21	105.55	104.430028349722	1.11997165027825
22	106.12	105.549953312102	0.5700466878979
23	105.78	106.119976236647	-0.339976236647104
24	105.33	105.78001417248	-0.45001417248001
25	104.63	105.330018759596	-0.700018759596048
26	104.62	104.630029181457	-0.0100291814568294
27	105.57	104.620000418083	0.949999581916728
28	107.5	105.569960397673	1.93003960232697
29	107.52	107.49991954306	0.0200804569400077
30	107.76	107.519999162912	0.240000837087564
31	106.74	107.759989995162	-1.01998999516232
32	106.21	106.740042519995	-0.530042519994808
33	105.77	106.210022095712	-0.44002209571201
34	105.27	105.77001834306	-0.500018343059551
35	104.35	105.270020844104	-0.920020844103817
36	103.52	104.350038352613	-0.830038352612959
37	102.28	103.520034601542	-1.24003460154178
38	100.93	102.280051692924	-1.35005169292351
39	101.04	100.930056279171	0.109943720829378
40	99.95	101.039995416811	-1.08999541681148
41	99.55	99.9500454382883	-0.400045438288302
42	99.56	99.5500166765655	0.00998332343451125
43	99.01	99.5599995838284	-0.549999583828409
44	98.64	99.0100229276557	-0.370022927655725
45	98.98	98.6400154250267	0.339984574973258
46	100.8	98.9799858271724	1.8200141728276
47	100.32	100.799924129655	-0.479924129654677
48	100.72	100.320020006443	0.39997999355721
49	280.8	100.719983326163	180.080016673837
50	280.4	280.792493062276	-0.39249306227623
51	280.4	280.400016361732	-1.63617320367848e-05
52	280.3	280.400000000682	-0.10000000068203
53	281	280.300004168668	0.699995831332103
54	280.9	280.999970819499	-0.0999708194989921
55	279.7	280.900004167451	-1.20000416745137
56	283.1	279.700050024188	3.39994997581232
57	290.6	283.099858267379	7.50014173262088
58	291.6	290.599687344004	1.00031265599563
59	291.7	291.599958300288	0.10004169971188
60	291.8	291.699995829594	0.10000417040618
61	291.7	291.799995831158	-0.0999958311583669
62	291.5	291.700004168494	-0.200004168494047
63	291.7	291.500008337509	0.199991662490561
64	293.4	291.699991663012	1.70000833698811
65	293.1	293.399929132299	-0.299929132299326
66	293.1	293.100012503049	-1.25030492768019e-05
67	292.6	293.100000000521	-0.500000000521197
68	292.1	292.600020843339	-0.5000208433392
69	292.2	292.100020844208	0.0999791557919139
70	292	292.199995832201	-0.199995832201068
71	292.1	292.000008337162	0.0999916628380788
72	293.4	292.09999583168	1.30000416832024
73	292.2	293.399945807144	-1.19994580714445
74	292.1	292.200050021755	-0.100050021754782
75	291.6	292.100004170753	-0.500004170753073
76	290.9	291.600020843513	-0.700020843513073
77	290.9	290.900029181544	-2.91815437094556e-05
78	290.8	290.900000001216	-0.100000001216472
79	290.5	290.800004168668	-0.300004168667897
80	290	290.500012506177	-0.500012506177256
81	290.2	290.000020843861	0.199979156139477
82	290.1	290.199991663533	-0.099991663533217
83	291	290.10000416832	0.899995831679689
84	291.8	290.999962482163	0.800037517836699

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	291.799966649093	252.959205230573	330.640728067614
86	291.799966649093	236.871979972711	346.727953325476
87	291.799966649093	224.527664079081	359.072269219105
88	291.799966649093	214.120872512887	369.4790607853
89	291.799966649093	204.952280217202	378.647653080985
90	291.799966649093	196.663225001492	386.936708296695
91	291.799966649093	189.04064306202	394.559290236167
92	291.799966649093	181.94571066953	401.654222628657
93	291.799966649093	175.282000096403	408.317933201783
94	291.799966649093	168.979302661618	414.620630636568
95	291.799966649093	162.984616340698	420.615316957489
96	291.799966649093	157.256763744506	426.343169553681

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 291.799966649093 & 252.959205230573 & 330.640728067614 \tabularnewline
86 & 291.799966649093 & 236.871979972711 & 346.727953325476 \tabularnewline
87 & 291.799966649093 & 224.527664079081 & 359.072269219105 \tabularnewline
88 & 291.799966649093 & 214.120872512887 & 369.4790607853 \tabularnewline
89 & 291.799966649093 & 204.952280217202 & 378.647653080985 \tabularnewline
90 & 291.799966649093 & 196.663225001492 & 386.936708296695 \tabularnewline
91 & 291.799966649093 & 189.04064306202 & 394.559290236167 \tabularnewline
92 & 291.799966649093 & 181.94571066953 & 401.654222628657 \tabularnewline
93 & 291.799966649093 & 175.282000096403 & 408.317933201783 \tabularnewline
94 & 291.799966649093 & 168.979302661618 & 414.620630636568 \tabularnewline
95 & 291.799966649093 & 162.984616340698 & 420.615316957489 \tabularnewline
96 & 291.799966649093 & 157.256763744506 & 426.343169553681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232393&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]85[/C][C]291.799966649093[/C][C]252.959205230573[/C][C]330.640728067614[/C][/ROW]
[ROW][C]86[/C][C]291.799966649093[/C][C]236.871979972711[/C][C]346.727953325476[/C][/ROW]
[ROW][C]87[/C][C]291.799966649093[/C][C]224.527664079081[/C][C]359.072269219105[/C][/ROW]
[ROW][C]88[/C][C]291.799966649093[/C][C]214.120872512887[/C][C]369.4790607853[/C][/ROW]
[ROW][C]89[/C][C]291.799966649093[/C][C]204.952280217202[/C][C]378.647653080985[/C][/ROW]
[ROW][C]90[/C][C]291.799966649093[/C][C]196.663225001492[/C][C]386.936708296695[/C][/ROW]
[ROW][C]91[/C][C]291.799966649093[/C][C]189.04064306202[/C][C]394.559290236167[/C][/ROW]
[ROW][C]92[/C][C]291.799966649093[/C][C]181.94571066953[/C][C]401.654222628657[/C][/ROW]
[ROW][C]93[/C][C]291.799966649093[/C][C]175.282000096403[/C][C]408.317933201783[/C][/ROW]
[ROW][C]94[/C][C]291.799966649093[/C][C]168.979302661618[/C][C]414.620630636568[/C][/ROW]
[ROW][C]95[/C][C]291.799966649093[/C][C]162.984616340698[/C][C]420.615316957489[/C][/ROW]
[ROW][C]96[/C][C]291.799966649093[/C][C]157.256763744506[/C][C]426.343169553681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232393&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232393&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
85	291.799966649093	252.959205230573	330.640728067614
86	291.799966649093	236.871979972711	346.727953325476
87	291.799966649093	224.527664079081	359.072269219105
88	291.799966649093	214.120872512887	369.4790607853
89	291.799966649093	204.952280217202	378.647653080985
90	291.799966649093	196.663225001492	386.936708296695
91	291.799966649093	189.04064306202	394.559290236167
92	291.799966649093	181.94571066953	401.654222628657
93	291.799966649093	175.282000096403	408.317933201783
94	291.799966649093	168.979302661618	414.620630636568
95	291.799966649093	162.984616340698	420.615316957489
96	291.799966649093	157.256763744506	426.343169553681

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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