Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 26 May 2013 07:55:24 -0400

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/May/26/t1369569404id3osmqbjrtoxnl.htm/, Retrieved Mon, 29 Apr 2024 12:55:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210591, Retrieved Mon, 29 Apr 2024 12:55:16 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

113

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

-       [Exponential Smoothing] [] [2013-05-26 11:55:24] [fc1511b4e6b29b74e67a180b347b8f2c] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210591&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210591&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210591&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	5 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.99995830862336
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99995830862336 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210591&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]0.99995830862336[/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=210591&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210591&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	0.99995830862336
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	119.9	120.6	-0.699999999999989
3	119.48	119.900029183964	-0.420029183963649
4	117.45	119.480017511595	-2.03001751159491
5	118.37	117.450084634225	0.919915365775339
6	117.07	118.369961647462	-1.29996164746201
7	114.98	117.070054197191	-2.09005419719065
8	112.59	114.980087137237	-2.39008713723673
9	111.7	112.590099646023	-0.890099646023046
10	112.04	111.70003710948	0.339962890520411
11	110.79	112.039985826479	-1.24998582647909
12	110.79	110.79005211363	-5.21136298914371e-05
13	109.82	110.790000002173	-0.970000002172696
14	109.11	109.820040440635	-0.710040440635424
15	109.84	109.110029602563	0.72997039743656
16	109.31	109.839969566529	-0.529969566529232
17	108.29	109.310022095161	-1.0200220951608
18	107.42	108.290042526125	-0.87004252612536
19	106.71	107.420036273271	-0.71003627327066
20	105.11	106.71002960239	-1.6000296023897
21	104.43	105.110066707437	-0.680066707436779
22	105.11	104.430028352917	0.679971647082752
23	104.43	105.109971651046	-0.679971651045946
24	105.55	104.430028348954	1.11997165104579
25	106.12	105.54995330684	0.570046693159938
26	105.78	106.119976233969	-0.339976233968613
27	105.33	105.780014174077	-0.450014174077225
28	104.63	105.33001876171	-0.700018761710425
29	104.62	104.630029184746	-0.0100291847458465
30	105.57	104.620000418131	0.949999581869477
31	107.5	105.56996039321	1.93003960679039
32	107.52	107.499919533992	0.0200804660081673
33	107.76	107.519999162818	0.240000837182279
34	106.74	107.759989994035	-1.01998999403472
35	106.21	106.740042524787	-0.530042524787007
36	105.77	106.210022098203	-0.440022098202533
37	105.27	105.770018345127	-0.500018345127032
38	104.35	105.270020846453	-0.920020846453156
39	103.52	104.350038356936	-0.830038356935631
40	102.28	103.520034605442	-1.24003460544176
41	100.93	102.28005169875	-1.35005169874978
42	101.04	100.930056285514	0.10994371448615
43	99.95	101.039995416295	-1.0899954162952
44	99.55	99.9500454434094	-0.400045443409439
45	99.56	99.5500166784452	0.00998332155475623
46	99.01	99.5599995837816	-0.549999583781585
47	98.64	99.0100229302398	-0.370022930239799
48	98.98	98.6400154267653	0.339984573234659
49	100.8	98.9799858255751	1.82001417442488
50	100.32	100.799924121104	-0.479924121103565
51	100.72	100.320020008697	0.399979991302715
52	280.8	100.719983324284	180.080016675716
53	280.4	280.792492216199	-0.3924922161994
54	280.4	280.400016363541	-1.6363540794373e-05
55	280.3	280.400000000682	-0.100000000682201
56	281	280.300004169138	0.699995830862292
57	280.9	280.99997081621	-0.0999708162102024
58	279.7	280.900004167921	-1.20000416792095
59	283.1	279.700050029826	3.3999499701743
60	290.6	283.099858251405	7.50014174859479
61	291.6	290.599687308766	1.00031269123451
62	291.7	291.599958295587	0.100041704413115
63	291.8	291.699995829124	0.100004170876389
64	291.7	291.799995830688	-0.0999958306884423
65	291.5	291.700004168964	-0.200004168963801
66	291.7	291.500008338449	0.199991661550825
67	293.4	291.699991662072	1.70000833792767
68	293.1	293.399929124312	-0.29992912431203
69	292.6	293.100012504458	-0.500012504458084
70	292.1	292.60002084621	-0.500020846209623
71	292.2	292.100020846557	0.0999791534425185
72	292	292.199995831731	-0.199995831731428
73	292.1	292.000008338102	0.0999916618984571
74	293.4	292.09999583121	1.30000416879
75	292.2	293.399945801037	-1.19994580103656
76	292.1	292.200050027392	-0.100050027392285
77	291.6	292.100004171223	-0.500004171223395
78	290.9	291.600020845862	-0.700020845862298
79	290.9	290.900029184833	-2.91848327265143e-05
80	290.8	290.900000001217	-0.100000001216699
81	290.5	290.800004169138	-0.300004169137708
82	290	290.500012507587	-0.500012507586803
83	290.2	290.00002084621	0.199979153790196
84	290.1	290.199991662594	-0.0999916625937658

\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 & 119.900029183964 & -0.420029183963649 \tabularnewline
4 & 117.45 & 119.480017511595 & -2.03001751159491 \tabularnewline
5 & 118.37 & 117.450084634225 & 0.919915365775339 \tabularnewline
6 & 117.07 & 118.369961647462 & -1.29996164746201 \tabularnewline
7 & 114.98 & 117.070054197191 & -2.09005419719065 \tabularnewline
8 & 112.59 & 114.980087137237 & -2.39008713723673 \tabularnewline
9 & 111.7 & 112.590099646023 & -0.890099646023046 \tabularnewline
10 & 112.04 & 111.70003710948 & 0.339962890520411 \tabularnewline
11 & 110.79 & 112.039985826479 & -1.24998582647909 \tabularnewline
12 & 110.79 & 110.79005211363 & -5.21136298914371e-05 \tabularnewline
13 & 109.82 & 110.790000002173 & -0.970000002172696 \tabularnewline
14 & 109.11 & 109.820040440635 & -0.710040440635424 \tabularnewline
15 & 109.84 & 109.110029602563 & 0.72997039743656 \tabularnewline
16 & 109.31 & 109.839969566529 & -0.529969566529232 \tabularnewline
17 & 108.29 & 109.310022095161 & -1.0200220951608 \tabularnewline
18 & 107.42 & 108.290042526125 & -0.87004252612536 \tabularnewline
19 & 106.71 & 107.420036273271 & -0.71003627327066 \tabularnewline
20 & 105.11 & 106.71002960239 & -1.6000296023897 \tabularnewline
21 & 104.43 & 105.110066707437 & -0.680066707436779 \tabularnewline
22 & 105.11 & 104.430028352917 & 0.679971647082752 \tabularnewline
23 & 104.43 & 105.109971651046 & -0.679971651045946 \tabularnewline
24 & 105.55 & 104.430028348954 & 1.11997165104579 \tabularnewline
25 & 106.12 & 105.54995330684 & 0.570046693159938 \tabularnewline
26 & 105.78 & 106.119976233969 & -0.339976233968613 \tabularnewline
27 & 105.33 & 105.780014174077 & -0.450014174077225 \tabularnewline
28 & 104.63 & 105.33001876171 & -0.700018761710425 \tabularnewline
29 & 104.62 & 104.630029184746 & -0.0100291847458465 \tabularnewline
30 & 105.57 & 104.620000418131 & 0.949999581869477 \tabularnewline
31 & 107.5 & 105.56996039321 & 1.93003960679039 \tabularnewline
32 & 107.52 & 107.499919533992 & 0.0200804660081673 \tabularnewline
33 & 107.76 & 107.519999162818 & 0.240000837182279 \tabularnewline
34 & 106.74 & 107.759989994035 & -1.01998999403472 \tabularnewline
35 & 106.21 & 106.740042524787 & -0.530042524787007 \tabularnewline
36 & 105.77 & 106.210022098203 & -0.440022098202533 \tabularnewline
37 & 105.27 & 105.770018345127 & -0.500018345127032 \tabularnewline
38 & 104.35 & 105.270020846453 & -0.920020846453156 \tabularnewline
39 & 103.52 & 104.350038356936 & -0.830038356935631 \tabularnewline
40 & 102.28 & 103.520034605442 & -1.24003460544176 \tabularnewline
41 & 100.93 & 102.28005169875 & -1.35005169874978 \tabularnewline
42 & 101.04 & 100.930056285514 & 0.10994371448615 \tabularnewline
43 & 99.95 & 101.039995416295 & -1.0899954162952 \tabularnewline
44 & 99.55 & 99.9500454434094 & -0.400045443409439 \tabularnewline
45 & 99.56 & 99.5500166784452 & 0.00998332155475623 \tabularnewline
46 & 99.01 & 99.5599995837816 & -0.549999583781585 \tabularnewline
47 & 98.64 & 99.0100229302398 & -0.370022930239799 \tabularnewline
48 & 98.98 & 98.6400154267653 & 0.339984573234659 \tabularnewline
49 & 100.8 & 98.9799858255751 & 1.82001417442488 \tabularnewline
50 & 100.32 & 100.799924121104 & -0.479924121103565 \tabularnewline
51 & 100.72 & 100.320020008697 & 0.399979991302715 \tabularnewline
52 & 280.8 & 100.719983324284 & 180.080016675716 \tabularnewline
53 & 280.4 & 280.792492216199 & -0.3924922161994 \tabularnewline
54 & 280.4 & 280.400016363541 & -1.6363540794373e-05 \tabularnewline
55 & 280.3 & 280.400000000682 & -0.100000000682201 \tabularnewline
56 & 281 & 280.300004169138 & 0.699995830862292 \tabularnewline
57 & 280.9 & 280.99997081621 & -0.0999708162102024 \tabularnewline
58 & 279.7 & 280.900004167921 & -1.20000416792095 \tabularnewline
59 & 283.1 & 279.700050029826 & 3.3999499701743 \tabularnewline
60 & 290.6 & 283.099858251405 & 7.50014174859479 \tabularnewline
61 & 291.6 & 290.599687308766 & 1.00031269123451 \tabularnewline
62 & 291.7 & 291.599958295587 & 0.100041704413115 \tabularnewline
63 & 291.8 & 291.699995829124 & 0.100004170876389 \tabularnewline
64 & 291.7 & 291.799995830688 & -0.0999958306884423 \tabularnewline
65 & 291.5 & 291.700004168964 & -0.200004168963801 \tabularnewline
66 & 291.7 & 291.500008338449 & 0.199991661550825 \tabularnewline
67 & 293.4 & 291.699991662072 & 1.70000833792767 \tabularnewline
68 & 293.1 & 293.399929124312 & -0.29992912431203 \tabularnewline
69 & 292.6 & 293.100012504458 & -0.500012504458084 \tabularnewline
70 & 292.1 & 292.60002084621 & -0.500020846209623 \tabularnewline
71 & 292.2 & 292.100020846557 & 0.0999791534425185 \tabularnewline
72 & 292 & 292.199995831731 & -0.199995831731428 \tabularnewline
73 & 292.1 & 292.000008338102 & 0.0999916618984571 \tabularnewline
74 & 293.4 & 292.09999583121 & 1.30000416879 \tabularnewline
75 & 292.2 & 293.399945801037 & -1.19994580103656 \tabularnewline
76 & 292.1 & 292.200050027392 & -0.100050027392285 \tabularnewline
77 & 291.6 & 292.100004171223 & -0.500004171223395 \tabularnewline
78 & 290.9 & 291.600020845862 & -0.700020845862298 \tabularnewline
79 & 290.9 & 290.900029184833 & -2.91848327265143e-05 \tabularnewline
80 & 290.8 & 290.900000001217 & -0.100000001216699 \tabularnewline
81 & 290.5 & 290.800004169138 & -0.300004169137708 \tabularnewline
82 & 290 & 290.500012507587 & -0.500012507586803 \tabularnewline
83 & 290.2 & 290.00002084621 & 0.199979153790196 \tabularnewline
84 & 290.1 & 290.199991662594 & -0.0999916625937658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210591&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]119.900029183964[/C][C]-0.420029183963649[/C][/ROW]
[ROW][C]4[/C][C]117.45[/C][C]119.480017511595[/C][C]-2.03001751159491[/C][/ROW]
[ROW][C]5[/C][C]118.37[/C][C]117.450084634225[/C][C]0.919915365775339[/C][/ROW]
[ROW][C]6[/C][C]117.07[/C][C]118.369961647462[/C][C]-1.29996164746201[/C][/ROW]
[ROW][C]7[/C][C]114.98[/C][C]117.070054197191[/C][C]-2.09005419719065[/C][/ROW]
[ROW][C]8[/C][C]112.59[/C][C]114.980087137237[/C][C]-2.39008713723673[/C][/ROW]
[ROW][C]9[/C][C]111.7[/C][C]112.590099646023[/C][C]-0.890099646023046[/C][/ROW]
[ROW][C]10[/C][C]112.04[/C][C]111.70003710948[/C][C]0.339962890520411[/C][/ROW]
[ROW][C]11[/C][C]110.79[/C][C]112.039985826479[/C][C]-1.24998582647909[/C][/ROW]
[ROW][C]12[/C][C]110.79[/C][C]110.79005211363[/C][C]-5.21136298914371e-05[/C][/ROW]
[ROW][C]13[/C][C]109.82[/C][C]110.790000002173[/C][C]-0.970000002172696[/C][/ROW]
[ROW][C]14[/C][C]109.11[/C][C]109.820040440635[/C][C]-0.710040440635424[/C][/ROW]
[ROW][C]15[/C][C]109.84[/C][C]109.110029602563[/C][C]0.72997039743656[/C][/ROW]
[ROW][C]16[/C][C]109.31[/C][C]109.839969566529[/C][C]-0.529969566529232[/C][/ROW]
[ROW][C]17[/C][C]108.29[/C][C]109.310022095161[/C][C]-1.0200220951608[/C][/ROW]
[ROW][C]18[/C][C]107.42[/C][C]108.290042526125[/C][C]-0.87004252612536[/C][/ROW]
[ROW][C]19[/C][C]106.71[/C][C]107.420036273271[/C][C]-0.71003627327066[/C][/ROW]
[ROW][C]20[/C][C]105.11[/C][C]106.71002960239[/C][C]-1.6000296023897[/C][/ROW]
[ROW][C]21[/C][C]104.43[/C][C]105.110066707437[/C][C]-0.680066707436779[/C][/ROW]
[ROW][C]22[/C][C]105.11[/C][C]104.430028352917[/C][C]0.679971647082752[/C][/ROW]
[ROW][C]23[/C][C]104.43[/C][C]105.109971651046[/C][C]-0.679971651045946[/C][/ROW]
[ROW][C]24[/C][C]105.55[/C][C]104.430028348954[/C][C]1.11997165104579[/C][/ROW]
[ROW][C]25[/C][C]106.12[/C][C]105.54995330684[/C][C]0.570046693159938[/C][/ROW]
[ROW][C]26[/C][C]105.78[/C][C]106.119976233969[/C][C]-0.339976233968613[/C][/ROW]
[ROW][C]27[/C][C]105.33[/C][C]105.780014174077[/C][C]-0.450014174077225[/C][/ROW]
[ROW][C]28[/C][C]104.63[/C][C]105.33001876171[/C][C]-0.700018761710425[/C][/ROW]
[ROW][C]29[/C][C]104.62[/C][C]104.630029184746[/C][C]-0.0100291847458465[/C][/ROW]
[ROW][C]30[/C][C]105.57[/C][C]104.620000418131[/C][C]0.949999581869477[/C][/ROW]
[ROW][C]31[/C][C]107.5[/C][C]105.56996039321[/C][C]1.93003960679039[/C][/ROW]
[ROW][C]32[/C][C]107.52[/C][C]107.499919533992[/C][C]0.0200804660081673[/C][/ROW]
[ROW][C]33[/C][C]107.76[/C][C]107.519999162818[/C][C]0.240000837182279[/C][/ROW]
[ROW][C]34[/C][C]106.74[/C][C]107.759989994035[/C][C]-1.01998999403472[/C][/ROW]
[ROW][C]35[/C][C]106.21[/C][C]106.740042524787[/C][C]-0.530042524787007[/C][/ROW]
[ROW][C]36[/C][C]105.77[/C][C]106.210022098203[/C][C]-0.440022098202533[/C][/ROW]
[ROW][C]37[/C][C]105.27[/C][C]105.770018345127[/C][C]-0.500018345127032[/C][/ROW]
[ROW][C]38[/C][C]104.35[/C][C]105.270020846453[/C][C]-0.920020846453156[/C][/ROW]
[ROW][C]39[/C][C]103.52[/C][C]104.350038356936[/C][C]-0.830038356935631[/C][/ROW]
[ROW][C]40[/C][C]102.28[/C][C]103.520034605442[/C][C]-1.24003460544176[/C][/ROW]
[ROW][C]41[/C][C]100.93[/C][C]102.28005169875[/C][C]-1.35005169874978[/C][/ROW]
[ROW][C]42[/C][C]101.04[/C][C]100.930056285514[/C][C]0.10994371448615[/C][/ROW]
[ROW][C]43[/C][C]99.95[/C][C]101.039995416295[/C][C]-1.0899954162952[/C][/ROW]
[ROW][C]44[/C][C]99.55[/C][C]99.9500454434094[/C][C]-0.400045443409439[/C][/ROW]
[ROW][C]45[/C][C]99.56[/C][C]99.5500166784452[/C][C]0.00998332155475623[/C][/ROW]
[ROW][C]46[/C][C]99.01[/C][C]99.5599995837816[/C][C]-0.549999583781585[/C][/ROW]
[ROW][C]47[/C][C]98.64[/C][C]99.0100229302398[/C][C]-0.370022930239799[/C][/ROW]
[ROW][C]48[/C][C]98.98[/C][C]98.6400154267653[/C][C]0.339984573234659[/C][/ROW]
[ROW][C]49[/C][C]100.8[/C][C]98.9799858255751[/C][C]1.82001417442488[/C][/ROW]
[ROW][C]50[/C][C]100.32[/C][C]100.799924121104[/C][C]-0.479924121103565[/C][/ROW]
[ROW][C]51[/C][C]100.72[/C][C]100.320020008697[/C][C]0.399979991302715[/C][/ROW]
[ROW][C]52[/C][C]280.8[/C][C]100.719983324284[/C][C]180.080016675716[/C][/ROW]
[ROW][C]53[/C][C]280.4[/C][C]280.792492216199[/C][C]-0.3924922161994[/C][/ROW]
[ROW][C]54[/C][C]280.4[/C][C]280.400016363541[/C][C]-1.6363540794373e-05[/C][/ROW]
[ROW][C]55[/C][C]280.3[/C][C]280.400000000682[/C][C]-0.100000000682201[/C][/ROW]
[ROW][C]56[/C][C]281[/C][C]280.300004169138[/C][C]0.699995830862292[/C][/ROW]
[ROW][C]57[/C][C]280.9[/C][C]280.99997081621[/C][C]-0.0999708162102024[/C][/ROW]
[ROW][C]58[/C][C]279.7[/C][C]280.900004167921[/C][C]-1.20000416792095[/C][/ROW]
[ROW][C]59[/C][C]283.1[/C][C]279.700050029826[/C][C]3.3999499701743[/C][/ROW]
[ROW][C]60[/C][C]290.6[/C][C]283.099858251405[/C][C]7.50014174859479[/C][/ROW]
[ROW][C]61[/C][C]291.6[/C][C]290.599687308766[/C][C]1.00031269123451[/C][/ROW]
[ROW][C]62[/C][C]291.7[/C][C]291.599958295587[/C][C]0.100041704413115[/C][/ROW]
[ROW][C]63[/C][C]291.8[/C][C]291.699995829124[/C][C]0.100004170876389[/C][/ROW]
[ROW][C]64[/C][C]291.7[/C][C]291.799995830688[/C][C]-0.0999958306884423[/C][/ROW]
[ROW][C]65[/C][C]291.5[/C][C]291.700004168964[/C][C]-0.200004168963801[/C][/ROW]
[ROW][C]66[/C][C]291.7[/C][C]291.500008338449[/C][C]0.199991661550825[/C][/ROW]
[ROW][C]67[/C][C]293.4[/C][C]291.699991662072[/C][C]1.70000833792767[/C][/ROW]
[ROW][C]68[/C][C]293.1[/C][C]293.399929124312[/C][C]-0.29992912431203[/C][/ROW]
[ROW][C]69[/C][C]292.6[/C][C]293.100012504458[/C][C]-0.500012504458084[/C][/ROW]
[ROW][C]70[/C][C]292.1[/C][C]292.60002084621[/C][C]-0.500020846209623[/C][/ROW]
[ROW][C]71[/C][C]292.2[/C][C]292.100020846557[/C][C]0.0999791534425185[/C][/ROW]
[ROW][C]72[/C][C]292[/C][C]292.199995831731[/C][C]-0.199995831731428[/C][/ROW]
[ROW][C]73[/C][C]292.1[/C][C]292.000008338102[/C][C]0.0999916618984571[/C][/ROW]
[ROW][C]74[/C][C]293.4[/C][C]292.09999583121[/C][C]1.30000416879[/C][/ROW]
[ROW][C]75[/C][C]292.2[/C][C]293.399945801037[/C][C]-1.19994580103656[/C][/ROW]
[ROW][C]76[/C][C]292.1[/C][C]292.200050027392[/C][C]-0.100050027392285[/C][/ROW]
[ROW][C]77[/C][C]291.6[/C][C]292.100004171223[/C][C]-0.500004171223395[/C][/ROW]
[ROW][C]78[/C][C]290.9[/C][C]291.600020845862[/C][C]-0.700020845862298[/C][/ROW]
[ROW][C]79[/C][C]290.9[/C][C]290.900029184833[/C][C]-2.91848327265143e-05[/C][/ROW]
[ROW][C]80[/C][C]290.8[/C][C]290.900000001217[/C][C]-0.100000001216699[/C][/ROW]
[ROW][C]81[/C][C]290.5[/C][C]290.800004169138[/C][C]-0.300004169137708[/C][/ROW]
[ROW][C]82[/C][C]290[/C][C]290.500012507587[/C][C]-0.500012507586803[/C][/ROW]
[ROW][C]83[/C][C]290.2[/C][C]290.00002084621[/C][C]0.199979153790196[/C][/ROW]
[ROW][C]84[/C][C]290.1[/C][C]290.199991662594[/C][C]-0.0999916625937658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210591&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210591&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	119.900029183964	-0.420029183963649
4	117.45	119.480017511595	-2.03001751159491
5	118.37	117.450084634225	0.919915365775339
6	117.07	118.369961647462	-1.29996164746201
7	114.98	117.070054197191	-2.09005419719065
8	112.59	114.980087137237	-2.39008713723673
9	111.7	112.590099646023	-0.890099646023046
10	112.04	111.70003710948	0.339962890520411
11	110.79	112.039985826479	-1.24998582647909
12	110.79	110.79005211363	-5.21136298914371e-05
13	109.82	110.790000002173	-0.970000002172696
14	109.11	109.820040440635	-0.710040440635424
15	109.84	109.110029602563	0.72997039743656
16	109.31	109.839969566529	-0.529969566529232
17	108.29	109.310022095161	-1.0200220951608
18	107.42	108.290042526125	-0.87004252612536
19	106.71	107.420036273271	-0.71003627327066
20	105.11	106.71002960239	-1.6000296023897
21	104.43	105.110066707437	-0.680066707436779
22	105.11	104.430028352917	0.679971647082752
23	104.43	105.109971651046	-0.679971651045946
24	105.55	104.430028348954	1.11997165104579
25	106.12	105.54995330684	0.570046693159938
26	105.78	106.119976233969	-0.339976233968613
27	105.33	105.780014174077	-0.450014174077225
28	104.63	105.33001876171	-0.700018761710425
29	104.62	104.630029184746	-0.0100291847458465
30	105.57	104.620000418131	0.949999581869477
31	107.5	105.56996039321	1.93003960679039
32	107.52	107.499919533992	0.0200804660081673
33	107.76	107.519999162818	0.240000837182279
34	106.74	107.759989994035	-1.01998999403472
35	106.21	106.740042524787	-0.530042524787007
36	105.77	106.210022098203	-0.440022098202533
37	105.27	105.770018345127	-0.500018345127032
38	104.35	105.270020846453	-0.920020846453156
39	103.52	104.350038356936	-0.830038356935631
40	102.28	103.520034605442	-1.24003460544176
41	100.93	102.28005169875	-1.35005169874978
42	101.04	100.930056285514	0.10994371448615
43	99.95	101.039995416295	-1.0899954162952
44	99.55	99.9500454434094	-0.400045443409439
45	99.56	99.5500166784452	0.00998332155475623
46	99.01	99.5599995837816	-0.549999583781585
47	98.64	99.0100229302398	-0.370022930239799
48	98.98	98.6400154267653	0.339984573234659
49	100.8	98.9799858255751	1.82001417442488
50	100.32	100.799924121104	-0.479924121103565
51	100.72	100.320020008697	0.399979991302715
52	280.8	100.719983324284	180.080016675716
53	280.4	280.792492216199	-0.3924922161994
54	280.4	280.400016363541	-1.6363540794373e-05
55	280.3	280.400000000682	-0.100000000682201
56	281	280.300004169138	0.699995830862292
57	280.9	280.99997081621	-0.0999708162102024
58	279.7	280.900004167921	-1.20000416792095
59	283.1	279.700050029826	3.3999499701743
60	290.6	283.099858251405	7.50014174859479
61	291.6	290.599687308766	1.00031269123451
62	291.7	291.599958295587	0.100041704413115
63	291.8	291.699995829124	0.100004170876389
64	291.7	291.799995830688	-0.0999958306884423
65	291.5	291.700004168964	-0.200004168963801
66	291.7	291.500008338449	0.199991661550825
67	293.4	291.699991662072	1.70000833792767
68	293.1	293.399929124312	-0.29992912431203
69	292.6	293.100012504458	-0.500012504458084
70	292.1	292.60002084621	-0.500020846209623
71	292.2	292.100020846557	0.0999791534425185
72	292	292.199995831731	-0.199995831731428
73	292.1	292.000008338102	0.0999916618984571
74	293.4	292.09999583121	1.30000416879
75	292.2	293.399945801037	-1.19994580103656
76	292.1	292.200050027392	-0.100050027392285
77	291.6	292.100004171223	-0.500004171223395
78	290.9	291.600020845862	-0.700020845862298
79	290.9	290.900029184833	-2.91848327265143e-05
80	290.8	290.900000001217	-0.100000001216699
81	290.5	290.800004169138	-0.300004169137708
82	290	290.500012507587	-0.500012507586803
83	290.2	290.00002084621	0.199979153790196
84	290.1	290.199991662594	-0.0999916625937658

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	290.10000416879	251.255351242534	328.944657095046
86	290.10000416879	235.166514313146	345.033494024434
87	290.10000416879	222.820961707716	357.379046629864
88	290.10000416879	212.413127534201	367.786880803379
89	290.10000416879	203.243616677733	376.956391659847
90	290.10000416879	194.953731016577	385.246277321003
91	290.10000416879	187.330385401791	392.86962293579
92	290.10000416879	180.234742196348	399.965266141232
93	290.10000416879	173.570364012167	406.629644325413
94	290.10000416879	167.267035134451	412.932973203129
95	290.10000416879	161.27174822876	418.92826010882
96	290.10000416879	155.543321780628	424.656686556952

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 290.10000416879 & 251.255351242534 & 328.944657095046 \tabularnewline
86 & 290.10000416879 & 235.166514313146 & 345.033494024434 \tabularnewline
87 & 290.10000416879 & 222.820961707716 & 357.379046629864 \tabularnewline
88 & 290.10000416879 & 212.413127534201 & 367.786880803379 \tabularnewline
89 & 290.10000416879 & 203.243616677733 & 376.956391659847 \tabularnewline
90 & 290.10000416879 & 194.953731016577 & 385.246277321003 \tabularnewline
91 & 290.10000416879 & 187.330385401791 & 392.86962293579 \tabularnewline
92 & 290.10000416879 & 180.234742196348 & 399.965266141232 \tabularnewline
93 & 290.10000416879 & 173.570364012167 & 406.629644325413 \tabularnewline
94 & 290.10000416879 & 167.267035134451 & 412.932973203129 \tabularnewline
95 & 290.10000416879 & 161.27174822876 & 418.92826010882 \tabularnewline
96 & 290.10000416879 & 155.543321780628 & 424.656686556952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210591&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]290.10000416879[/C][C]251.255351242534[/C][C]328.944657095046[/C][/ROW]
[ROW][C]86[/C][C]290.10000416879[/C][C]235.166514313146[/C][C]345.033494024434[/C][/ROW]
[ROW][C]87[/C][C]290.10000416879[/C][C]222.820961707716[/C][C]357.379046629864[/C][/ROW]
[ROW][C]88[/C][C]290.10000416879[/C][C]212.413127534201[/C][C]367.786880803379[/C][/ROW]
[ROW][C]89[/C][C]290.10000416879[/C][C]203.243616677733[/C][C]376.956391659847[/C][/ROW]
[ROW][C]90[/C][C]290.10000416879[/C][C]194.953731016577[/C][C]385.246277321003[/C][/ROW]
[ROW][C]91[/C][C]290.10000416879[/C][C]187.330385401791[/C][C]392.86962293579[/C][/ROW]
[ROW][C]92[/C][C]290.10000416879[/C][C]180.234742196348[/C][C]399.965266141232[/C][/ROW]
[ROW][C]93[/C][C]290.10000416879[/C][C]173.570364012167[/C][C]406.629644325413[/C][/ROW]
[ROW][C]94[/C][C]290.10000416879[/C][C]167.267035134451[/C][C]412.932973203129[/C][/ROW]
[ROW][C]95[/C][C]290.10000416879[/C][C]161.27174822876[/C][C]418.92826010882[/C][/ROW]
[ROW][C]96[/C][C]290.10000416879[/C][C]155.543321780628[/C][C]424.656686556952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210591&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210591&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	290.10000416879	251.255351242534	328.944657095046
86	290.10000416879	235.166514313146	345.033494024434
87	290.10000416879	222.820961707716	357.379046629864
88	290.10000416879	212.413127534201	367.786880803379
89	290.10000416879	203.243616677733	376.956391659847
90	290.10000416879	194.953731016577	385.246277321003
91	290.10000416879	187.330385401791	392.86962293579
92	290.10000416879	180.234742196348	399.965266141232
93	290.10000416879	173.570364012167	406.629644325413
94	290.10000416879	167.267035134451	412.932973203129
95	290.10000416879	161.27174822876	418.92826010882
96	290.10000416879	155.543321780628	424.656686556952

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