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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 19:24:32 +0100

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/2015/Apr/02/t14279990837v4suyrio44hfl2.htm/, Retrieved Thu, 09 May 2024 11:19:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278621, Retrieved Thu, 09 May 2024 11:19:15 +0000

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No (this computation is public)

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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] [] [2015-04-02 18:24:32] [f6ba6fe2e657f2a4c34c9d874eedca96] [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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278621&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278621&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278621&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999933893038648
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278621&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]0.999933893038648[/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=278621&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278621&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	0.999933893038648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	103.9	101.97	1.93000000000001
3	106.85	103.899872413565	2.9501275864354
4	106.93	106.84980497603	0.0801950239703615
5	107.13	106.929994698551	0.200005301449337
6	107.07	107.129986778257	-0.0599867782572687
7	107.2	107.070003965544	0.129996034456369
8	107.78	107.199991406357	0.58000859364283
9	108	107.779961657394	0.22003834260569
10	108.11	107.999985453934	0.110014546066211
11	107.26	108.109992727273	-0.84999272727265
12	105.3	107.260056190436	-1.96005619043638
13	105.55	105.300129573359	0.249870426641181
14	105.38	105.549983481825	-0.169983481825355
15	106.12	105.380011237091	0.739988762908553
16	106.85	106.119951081591	0.730048918408542
17	107.92	106.849951738684	1.07004826131565
18	107.97	107.919929262361	0.0500707376390466
19	107.76	107.969996689976	-0.209996689975668
20	107.99	107.760013882243	0.229986117756923
21	108.41	107.989984796317	0.420015203683406
22	107.61	108.409972234071	-0.799972234071149
23	106.54	107.610052883734	-1.07005288373355
24	106.24	106.540070737945	-0.300070737944637
25	106.19	106.240019836765	-0.050019836764676
26	106.71	106.190003306659	0.519996693340588
27	106.36	106.709965624599	-0.349965624598681
28	107.53	106.360023135164	1.16997686483597
29	107.89	107.529922656385	0.360077343615387
30	108	107.889976196381	0.110023803619043
31	108.05	107.999992726661	0.0500072733393324
32	108.86	108.049996694171	0.810003305828886
33	109.27	108.859946453143	0.410053546857228
34	108.87	109.269972892606	-0.399972892606016
35	108.88	108.870026440993	0.00997355900743457
36	108.19	108.879999340678	-0.689999340678312
37	108.19	108.19004561376	-4.56137597524275e-05
38	108.91	108.190000003015	0.719999996984612
39	110.39	108.909952402988	1.48004759701197
40	111.21	110.389902158551	0.820097841449282
41	111.44	111.209945785824	0.230054214176306
42	111.87	111.439984791815	0.430015208185054
43	111.88	111.869971573001	0.0100284269987441
44	111.93	111.879999337051	0.0500006629488468
45	111.76	111.929996694608	-0.169996694608102
46	111.66	111.760011237965	-0.100011237964921
47	110.25	111.660006611439	-1.41000661143903
48	109.05	110.250093211253	-1.20009321125256
49	109.47	109.050079334516	0.419920665484469
50	109.68	109.469972240321	0.210027759679207
51	110.93	109.679986115703	1.25001388429699
52	111.86	110.92991736538	0.930082634619538
53	112.66	111.859938515063	0.800061484936776
54	112.96	112.659947110366	0.300052889633662
55	113.14	112.959980164415	0.180019835584787
56	113.53	113.139988099436	0.390011900564318
57	113.62	113.529974217498	0.0900257825016411
58	112.51	113.619994048669	-1.10999404866908
59	111	112.510073378334	-1.51007337833367
60	108.49	111.000099826362	-2.51009982636246
61	108.52	108.490165935072	0.0298340649277975
62	110.66	108.519998027761	2.14000197223938
63	111.15	110.659858530972	0.490141469027677
64	112.14	111.149967598237	0.990032401763145
65	113.38	112.139934551966	1.2400654480337
66	113.75	113.379918023041	0.370081976958659
67	113.89	113.749975535005	0.140024464994951
68	113.92	113.889990743408	0.0300092565918959
69	116.4	113.919998016179	2.48000198382077
70	115.86	116.399836054605	-0.539836054604706
71	115.16	115.860035686921	-0.700035686921197
72	114.45	115.160046277232	-0.710046277232095
73	114.65	114.450046939002	0.199953060998197
74	114.85	114.649986781711	0.200013218289257
75	116.51	114.849986777734	1.6600132222661
76	118.18	116.50989026157	1.67010973842993
77	118.75	118.17988959412	0.57011040587993
78	119.06	118.749962311733	0.310037688266561
79	119.28	119.059979504351	0.220020495649464
80	119.68	119.279985455114	0.400014544886403
81	119.28	119.679973556254	-0.39997355625394
82	117.3	119.280026441036	-1.98002644103643
83	114.23	117.300130893531	-3.07013089353141
84	112.56	114.230202957024	-1.67020295702432
85	112.83	112.560110412042	0.269889587957664
86	112.35	112.829982158419	-0.479982158419446
87	112.8	112.350031730162	0.449968269837996
88	113.84	112.799970253965	1.04002974603503
89	115.02	113.839931246794	1.18006875320621
90	115.46	115.019921989241	0.44007801075945
91	115	115.45997090778	-0.459970907779947
92	115.3	115.000030407279	0.29996959272097
93	116.09	115.299980169922	0.790019830078279
94	115.49	116.08994777419	-0.59994777418963
95	112.89	115.490039660724	-2.60003966072431
96	110.66	112.890171880721	-2.23017188072137

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 103.9 & 101.97 & 1.93000000000001 \tabularnewline
3 & 106.85 & 103.899872413565 & 2.9501275864354 \tabularnewline
4 & 106.93 & 106.84980497603 & 0.0801950239703615 \tabularnewline
5 & 107.13 & 106.929994698551 & 0.200005301449337 \tabularnewline
6 & 107.07 & 107.129986778257 & -0.0599867782572687 \tabularnewline
7 & 107.2 & 107.070003965544 & 0.129996034456369 \tabularnewline
8 & 107.78 & 107.199991406357 & 0.58000859364283 \tabularnewline
9 & 108 & 107.779961657394 & 0.22003834260569 \tabularnewline
10 & 108.11 & 107.999985453934 & 0.110014546066211 \tabularnewline
11 & 107.26 & 108.109992727273 & -0.84999272727265 \tabularnewline
12 & 105.3 & 107.260056190436 & -1.96005619043638 \tabularnewline
13 & 105.55 & 105.300129573359 & 0.249870426641181 \tabularnewline
14 & 105.38 & 105.549983481825 & -0.169983481825355 \tabularnewline
15 & 106.12 & 105.380011237091 & 0.739988762908553 \tabularnewline
16 & 106.85 & 106.119951081591 & 0.730048918408542 \tabularnewline
17 & 107.92 & 106.849951738684 & 1.07004826131565 \tabularnewline
18 & 107.97 & 107.919929262361 & 0.0500707376390466 \tabularnewline
19 & 107.76 & 107.969996689976 & -0.209996689975668 \tabularnewline
20 & 107.99 & 107.760013882243 & 0.229986117756923 \tabularnewline
21 & 108.41 & 107.989984796317 & 0.420015203683406 \tabularnewline
22 & 107.61 & 108.409972234071 & -0.799972234071149 \tabularnewline
23 & 106.54 & 107.610052883734 & -1.07005288373355 \tabularnewline
24 & 106.24 & 106.540070737945 & -0.300070737944637 \tabularnewline
25 & 106.19 & 106.240019836765 & -0.050019836764676 \tabularnewline
26 & 106.71 & 106.190003306659 & 0.519996693340588 \tabularnewline
27 & 106.36 & 106.709965624599 & -0.349965624598681 \tabularnewline
28 & 107.53 & 106.360023135164 & 1.16997686483597 \tabularnewline
29 & 107.89 & 107.529922656385 & 0.360077343615387 \tabularnewline
30 & 108 & 107.889976196381 & 0.110023803619043 \tabularnewline
31 & 108.05 & 107.999992726661 & 0.0500072733393324 \tabularnewline
32 & 108.86 & 108.049996694171 & 0.810003305828886 \tabularnewline
33 & 109.27 & 108.859946453143 & 0.410053546857228 \tabularnewline
34 & 108.87 & 109.269972892606 & -0.399972892606016 \tabularnewline
35 & 108.88 & 108.870026440993 & 0.00997355900743457 \tabularnewline
36 & 108.19 & 108.879999340678 & -0.689999340678312 \tabularnewline
37 & 108.19 & 108.19004561376 & -4.56137597524275e-05 \tabularnewline
38 & 108.91 & 108.190000003015 & 0.719999996984612 \tabularnewline
39 & 110.39 & 108.909952402988 & 1.48004759701197 \tabularnewline
40 & 111.21 & 110.389902158551 & 0.820097841449282 \tabularnewline
41 & 111.44 & 111.209945785824 & 0.230054214176306 \tabularnewline
42 & 111.87 & 111.439984791815 & 0.430015208185054 \tabularnewline
43 & 111.88 & 111.869971573001 & 0.0100284269987441 \tabularnewline
44 & 111.93 & 111.879999337051 & 0.0500006629488468 \tabularnewline
45 & 111.76 & 111.929996694608 & -0.169996694608102 \tabularnewline
46 & 111.66 & 111.760011237965 & -0.100011237964921 \tabularnewline
47 & 110.25 & 111.660006611439 & -1.41000661143903 \tabularnewline
48 & 109.05 & 110.250093211253 & -1.20009321125256 \tabularnewline
49 & 109.47 & 109.050079334516 & 0.419920665484469 \tabularnewline
50 & 109.68 & 109.469972240321 & 0.210027759679207 \tabularnewline
51 & 110.93 & 109.679986115703 & 1.25001388429699 \tabularnewline
52 & 111.86 & 110.92991736538 & 0.930082634619538 \tabularnewline
53 & 112.66 & 111.859938515063 & 0.800061484936776 \tabularnewline
54 & 112.96 & 112.659947110366 & 0.300052889633662 \tabularnewline
55 & 113.14 & 112.959980164415 & 0.180019835584787 \tabularnewline
56 & 113.53 & 113.139988099436 & 0.390011900564318 \tabularnewline
57 & 113.62 & 113.529974217498 & 0.0900257825016411 \tabularnewline
58 & 112.51 & 113.619994048669 & -1.10999404866908 \tabularnewline
59 & 111 & 112.510073378334 & -1.51007337833367 \tabularnewline
60 & 108.49 & 111.000099826362 & -2.51009982636246 \tabularnewline
61 & 108.52 & 108.490165935072 & 0.0298340649277975 \tabularnewline
62 & 110.66 & 108.519998027761 & 2.14000197223938 \tabularnewline
63 & 111.15 & 110.659858530972 & 0.490141469027677 \tabularnewline
64 & 112.14 & 111.149967598237 & 0.990032401763145 \tabularnewline
65 & 113.38 & 112.139934551966 & 1.2400654480337 \tabularnewline
66 & 113.75 & 113.379918023041 & 0.370081976958659 \tabularnewline
67 & 113.89 & 113.749975535005 & 0.140024464994951 \tabularnewline
68 & 113.92 & 113.889990743408 & 0.0300092565918959 \tabularnewline
69 & 116.4 & 113.919998016179 & 2.48000198382077 \tabularnewline
70 & 115.86 & 116.399836054605 & -0.539836054604706 \tabularnewline
71 & 115.16 & 115.860035686921 & -0.700035686921197 \tabularnewline
72 & 114.45 & 115.160046277232 & -0.710046277232095 \tabularnewline
73 & 114.65 & 114.450046939002 & 0.199953060998197 \tabularnewline
74 & 114.85 & 114.649986781711 & 0.200013218289257 \tabularnewline
75 & 116.51 & 114.849986777734 & 1.6600132222661 \tabularnewline
76 & 118.18 & 116.50989026157 & 1.67010973842993 \tabularnewline
77 & 118.75 & 118.17988959412 & 0.57011040587993 \tabularnewline
78 & 119.06 & 118.749962311733 & 0.310037688266561 \tabularnewline
79 & 119.28 & 119.059979504351 & 0.220020495649464 \tabularnewline
80 & 119.68 & 119.279985455114 & 0.400014544886403 \tabularnewline
81 & 119.28 & 119.679973556254 & -0.39997355625394 \tabularnewline
82 & 117.3 & 119.280026441036 & -1.98002644103643 \tabularnewline
83 & 114.23 & 117.300130893531 & -3.07013089353141 \tabularnewline
84 & 112.56 & 114.230202957024 & -1.67020295702432 \tabularnewline
85 & 112.83 & 112.560110412042 & 0.269889587957664 \tabularnewline
86 & 112.35 & 112.829982158419 & -0.479982158419446 \tabularnewline
87 & 112.8 & 112.350031730162 & 0.449968269837996 \tabularnewline
88 & 113.84 & 112.799970253965 & 1.04002974603503 \tabularnewline
89 & 115.02 & 113.839931246794 & 1.18006875320621 \tabularnewline
90 & 115.46 & 115.019921989241 & 0.44007801075945 \tabularnewline
91 & 115 & 115.45997090778 & -0.459970907779947 \tabularnewline
92 & 115.3 & 115.000030407279 & 0.29996959272097 \tabularnewline
93 & 116.09 & 115.299980169922 & 0.790019830078279 \tabularnewline
94 & 115.49 & 116.08994777419 & -0.59994777418963 \tabularnewline
95 & 112.89 & 115.490039660724 & -2.60003966072431 \tabularnewline
96 & 110.66 & 112.890171880721 & -2.23017188072137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278621&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]103.9[/C][C]101.97[/C][C]1.93000000000001[/C][/ROW]
[ROW][C]3[/C][C]106.85[/C][C]103.899872413565[/C][C]2.9501275864354[/C][/ROW]
[ROW][C]4[/C][C]106.93[/C][C]106.84980497603[/C][C]0.0801950239703615[/C][/ROW]
[ROW][C]5[/C][C]107.13[/C][C]106.929994698551[/C][C]0.200005301449337[/C][/ROW]
[ROW][C]6[/C][C]107.07[/C][C]107.129986778257[/C][C]-0.0599867782572687[/C][/ROW]
[ROW][C]7[/C][C]107.2[/C][C]107.070003965544[/C][C]0.129996034456369[/C][/ROW]
[ROW][C]8[/C][C]107.78[/C][C]107.199991406357[/C][C]0.58000859364283[/C][/ROW]
[ROW][C]9[/C][C]108[/C][C]107.779961657394[/C][C]0.22003834260569[/C][/ROW]
[ROW][C]10[/C][C]108.11[/C][C]107.999985453934[/C][C]0.110014546066211[/C][/ROW]
[ROW][C]11[/C][C]107.26[/C][C]108.109992727273[/C][C]-0.84999272727265[/C][/ROW]
[ROW][C]12[/C][C]105.3[/C][C]107.260056190436[/C][C]-1.96005619043638[/C][/ROW]
[ROW][C]13[/C][C]105.55[/C][C]105.300129573359[/C][C]0.249870426641181[/C][/ROW]
[ROW][C]14[/C][C]105.38[/C][C]105.549983481825[/C][C]-0.169983481825355[/C][/ROW]
[ROW][C]15[/C][C]106.12[/C][C]105.380011237091[/C][C]0.739988762908553[/C][/ROW]
[ROW][C]16[/C][C]106.85[/C][C]106.119951081591[/C][C]0.730048918408542[/C][/ROW]
[ROW][C]17[/C][C]107.92[/C][C]106.849951738684[/C][C]1.07004826131565[/C][/ROW]
[ROW][C]18[/C][C]107.97[/C][C]107.919929262361[/C][C]0.0500707376390466[/C][/ROW]
[ROW][C]19[/C][C]107.76[/C][C]107.969996689976[/C][C]-0.209996689975668[/C][/ROW]
[ROW][C]20[/C][C]107.99[/C][C]107.760013882243[/C][C]0.229986117756923[/C][/ROW]
[ROW][C]21[/C][C]108.41[/C][C]107.989984796317[/C][C]0.420015203683406[/C][/ROW]
[ROW][C]22[/C][C]107.61[/C][C]108.409972234071[/C][C]-0.799972234071149[/C][/ROW]
[ROW][C]23[/C][C]106.54[/C][C]107.610052883734[/C][C]-1.07005288373355[/C][/ROW]
[ROW][C]24[/C][C]106.24[/C][C]106.540070737945[/C][C]-0.300070737944637[/C][/ROW]
[ROW][C]25[/C][C]106.19[/C][C]106.240019836765[/C][C]-0.050019836764676[/C][/ROW]
[ROW][C]26[/C][C]106.71[/C][C]106.190003306659[/C][C]0.519996693340588[/C][/ROW]
[ROW][C]27[/C][C]106.36[/C][C]106.709965624599[/C][C]-0.349965624598681[/C][/ROW]
[ROW][C]28[/C][C]107.53[/C][C]106.360023135164[/C][C]1.16997686483597[/C][/ROW]
[ROW][C]29[/C][C]107.89[/C][C]107.529922656385[/C][C]0.360077343615387[/C][/ROW]
[ROW][C]30[/C][C]108[/C][C]107.889976196381[/C][C]0.110023803619043[/C][/ROW]
[ROW][C]31[/C][C]108.05[/C][C]107.999992726661[/C][C]0.0500072733393324[/C][/ROW]
[ROW][C]32[/C][C]108.86[/C][C]108.049996694171[/C][C]0.810003305828886[/C][/ROW]
[ROW][C]33[/C][C]109.27[/C][C]108.859946453143[/C][C]0.410053546857228[/C][/ROW]
[ROW][C]34[/C][C]108.87[/C][C]109.269972892606[/C][C]-0.399972892606016[/C][/ROW]
[ROW][C]35[/C][C]108.88[/C][C]108.870026440993[/C][C]0.00997355900743457[/C][/ROW]
[ROW][C]36[/C][C]108.19[/C][C]108.879999340678[/C][C]-0.689999340678312[/C][/ROW]
[ROW][C]37[/C][C]108.19[/C][C]108.19004561376[/C][C]-4.56137597524275e-05[/C][/ROW]
[ROW][C]38[/C][C]108.91[/C][C]108.190000003015[/C][C]0.719999996984612[/C][/ROW]
[ROW][C]39[/C][C]110.39[/C][C]108.909952402988[/C][C]1.48004759701197[/C][/ROW]
[ROW][C]40[/C][C]111.21[/C][C]110.389902158551[/C][C]0.820097841449282[/C][/ROW]
[ROW][C]41[/C][C]111.44[/C][C]111.209945785824[/C][C]0.230054214176306[/C][/ROW]
[ROW][C]42[/C][C]111.87[/C][C]111.439984791815[/C][C]0.430015208185054[/C][/ROW]
[ROW][C]43[/C][C]111.88[/C][C]111.869971573001[/C][C]0.0100284269987441[/C][/ROW]
[ROW][C]44[/C][C]111.93[/C][C]111.879999337051[/C][C]0.0500006629488468[/C][/ROW]
[ROW][C]45[/C][C]111.76[/C][C]111.929996694608[/C][C]-0.169996694608102[/C][/ROW]
[ROW][C]46[/C][C]111.66[/C][C]111.760011237965[/C][C]-0.100011237964921[/C][/ROW]
[ROW][C]47[/C][C]110.25[/C][C]111.660006611439[/C][C]-1.41000661143903[/C][/ROW]
[ROW][C]48[/C][C]109.05[/C][C]110.250093211253[/C][C]-1.20009321125256[/C][/ROW]
[ROW][C]49[/C][C]109.47[/C][C]109.050079334516[/C][C]0.419920665484469[/C][/ROW]
[ROW][C]50[/C][C]109.68[/C][C]109.469972240321[/C][C]0.210027759679207[/C][/ROW]
[ROW][C]51[/C][C]110.93[/C][C]109.679986115703[/C][C]1.25001388429699[/C][/ROW]
[ROW][C]52[/C][C]111.86[/C][C]110.92991736538[/C][C]0.930082634619538[/C][/ROW]
[ROW][C]53[/C][C]112.66[/C][C]111.859938515063[/C][C]0.800061484936776[/C][/ROW]
[ROW][C]54[/C][C]112.96[/C][C]112.659947110366[/C][C]0.300052889633662[/C][/ROW]
[ROW][C]55[/C][C]113.14[/C][C]112.959980164415[/C][C]0.180019835584787[/C][/ROW]
[ROW][C]56[/C][C]113.53[/C][C]113.139988099436[/C][C]0.390011900564318[/C][/ROW]
[ROW][C]57[/C][C]113.62[/C][C]113.529974217498[/C][C]0.0900257825016411[/C][/ROW]
[ROW][C]58[/C][C]112.51[/C][C]113.619994048669[/C][C]-1.10999404866908[/C][/ROW]
[ROW][C]59[/C][C]111[/C][C]112.510073378334[/C][C]-1.51007337833367[/C][/ROW]
[ROW][C]60[/C][C]108.49[/C][C]111.000099826362[/C][C]-2.51009982636246[/C][/ROW]
[ROW][C]61[/C][C]108.52[/C][C]108.490165935072[/C][C]0.0298340649277975[/C][/ROW]
[ROW][C]62[/C][C]110.66[/C][C]108.519998027761[/C][C]2.14000197223938[/C][/ROW]
[ROW][C]63[/C][C]111.15[/C][C]110.659858530972[/C][C]0.490141469027677[/C][/ROW]
[ROW][C]64[/C][C]112.14[/C][C]111.149967598237[/C][C]0.990032401763145[/C][/ROW]
[ROW][C]65[/C][C]113.38[/C][C]112.139934551966[/C][C]1.2400654480337[/C][/ROW]
[ROW][C]66[/C][C]113.75[/C][C]113.379918023041[/C][C]0.370081976958659[/C][/ROW]
[ROW][C]67[/C][C]113.89[/C][C]113.749975535005[/C][C]0.140024464994951[/C][/ROW]
[ROW][C]68[/C][C]113.92[/C][C]113.889990743408[/C][C]0.0300092565918959[/C][/ROW]
[ROW][C]69[/C][C]116.4[/C][C]113.919998016179[/C][C]2.48000198382077[/C][/ROW]
[ROW][C]70[/C][C]115.86[/C][C]116.399836054605[/C][C]-0.539836054604706[/C][/ROW]
[ROW][C]71[/C][C]115.16[/C][C]115.860035686921[/C][C]-0.700035686921197[/C][/ROW]
[ROW][C]72[/C][C]114.45[/C][C]115.160046277232[/C][C]-0.710046277232095[/C][/ROW]
[ROW][C]73[/C][C]114.65[/C][C]114.450046939002[/C][C]0.199953060998197[/C][/ROW]
[ROW][C]74[/C][C]114.85[/C][C]114.649986781711[/C][C]0.200013218289257[/C][/ROW]
[ROW][C]75[/C][C]116.51[/C][C]114.849986777734[/C][C]1.6600132222661[/C][/ROW]
[ROW][C]76[/C][C]118.18[/C][C]116.50989026157[/C][C]1.67010973842993[/C][/ROW]
[ROW][C]77[/C][C]118.75[/C][C]118.17988959412[/C][C]0.57011040587993[/C][/ROW]
[ROW][C]78[/C][C]119.06[/C][C]118.749962311733[/C][C]0.310037688266561[/C][/ROW]
[ROW][C]79[/C][C]119.28[/C][C]119.059979504351[/C][C]0.220020495649464[/C][/ROW]
[ROW][C]80[/C][C]119.68[/C][C]119.279985455114[/C][C]0.400014544886403[/C][/ROW]
[ROW][C]81[/C][C]119.28[/C][C]119.679973556254[/C][C]-0.39997355625394[/C][/ROW]
[ROW][C]82[/C][C]117.3[/C][C]119.280026441036[/C][C]-1.98002644103643[/C][/ROW]
[ROW][C]83[/C][C]114.23[/C][C]117.300130893531[/C][C]-3.07013089353141[/C][/ROW]
[ROW][C]84[/C][C]112.56[/C][C]114.230202957024[/C][C]-1.67020295702432[/C][/ROW]
[ROW][C]85[/C][C]112.83[/C][C]112.560110412042[/C][C]0.269889587957664[/C][/ROW]
[ROW][C]86[/C][C]112.35[/C][C]112.829982158419[/C][C]-0.479982158419446[/C][/ROW]
[ROW][C]87[/C][C]112.8[/C][C]112.350031730162[/C][C]0.449968269837996[/C][/ROW]
[ROW][C]88[/C][C]113.84[/C][C]112.799970253965[/C][C]1.04002974603503[/C][/ROW]
[ROW][C]89[/C][C]115.02[/C][C]113.839931246794[/C][C]1.18006875320621[/C][/ROW]
[ROW][C]90[/C][C]115.46[/C][C]115.019921989241[/C][C]0.44007801075945[/C][/ROW]
[ROW][C]91[/C][C]115[/C][C]115.45997090778[/C][C]-0.459970907779947[/C][/ROW]
[ROW][C]92[/C][C]115.3[/C][C]115.000030407279[/C][C]0.29996959272097[/C][/ROW]
[ROW][C]93[/C][C]116.09[/C][C]115.299980169922[/C][C]0.790019830078279[/C][/ROW]
[ROW][C]94[/C][C]115.49[/C][C]116.08994777419[/C][C]-0.59994777418963[/C][/ROW]
[ROW][C]95[/C][C]112.89[/C][C]115.490039660724[/C][C]-2.60003966072431[/C][/ROW]
[ROW][C]96[/C][C]110.66[/C][C]112.890171880721[/C][C]-2.23017188072137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278621&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278621&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	103.9	101.97	1.93000000000001
3	106.85	103.899872413565	2.9501275864354
4	106.93	106.84980497603	0.0801950239703615
5	107.13	106.929994698551	0.200005301449337
6	107.07	107.129986778257	-0.0599867782572687
7	107.2	107.070003965544	0.129996034456369
8	107.78	107.199991406357	0.58000859364283
9	108	107.779961657394	0.22003834260569
10	108.11	107.999985453934	0.110014546066211
11	107.26	108.109992727273	-0.84999272727265
12	105.3	107.260056190436	-1.96005619043638
13	105.55	105.300129573359	0.249870426641181
14	105.38	105.549983481825	-0.169983481825355
15	106.12	105.380011237091	0.739988762908553
16	106.85	106.119951081591	0.730048918408542
17	107.92	106.849951738684	1.07004826131565
18	107.97	107.919929262361	0.0500707376390466
19	107.76	107.969996689976	-0.209996689975668
20	107.99	107.760013882243	0.229986117756923
21	108.41	107.989984796317	0.420015203683406
22	107.61	108.409972234071	-0.799972234071149
23	106.54	107.610052883734	-1.07005288373355
24	106.24	106.540070737945	-0.300070737944637
25	106.19	106.240019836765	-0.050019836764676
26	106.71	106.190003306659	0.519996693340588
27	106.36	106.709965624599	-0.349965624598681
28	107.53	106.360023135164	1.16997686483597
29	107.89	107.529922656385	0.360077343615387
30	108	107.889976196381	0.110023803619043
31	108.05	107.999992726661	0.0500072733393324
32	108.86	108.049996694171	0.810003305828886
33	109.27	108.859946453143	0.410053546857228
34	108.87	109.269972892606	-0.399972892606016
35	108.88	108.870026440993	0.00997355900743457
36	108.19	108.879999340678	-0.689999340678312
37	108.19	108.19004561376	-4.56137597524275e-05
38	108.91	108.190000003015	0.719999996984612
39	110.39	108.909952402988	1.48004759701197
40	111.21	110.389902158551	0.820097841449282
41	111.44	111.209945785824	0.230054214176306
42	111.87	111.439984791815	0.430015208185054
43	111.88	111.869971573001	0.0100284269987441
44	111.93	111.879999337051	0.0500006629488468
45	111.76	111.929996694608	-0.169996694608102
46	111.66	111.760011237965	-0.100011237964921
47	110.25	111.660006611439	-1.41000661143903
48	109.05	110.250093211253	-1.20009321125256
49	109.47	109.050079334516	0.419920665484469
50	109.68	109.469972240321	0.210027759679207
51	110.93	109.679986115703	1.25001388429699
52	111.86	110.92991736538	0.930082634619538
53	112.66	111.859938515063	0.800061484936776
54	112.96	112.659947110366	0.300052889633662
55	113.14	112.959980164415	0.180019835584787
56	113.53	113.139988099436	0.390011900564318
57	113.62	113.529974217498	0.0900257825016411
58	112.51	113.619994048669	-1.10999404866908
59	111	112.510073378334	-1.51007337833367
60	108.49	111.000099826362	-2.51009982636246
61	108.52	108.490165935072	0.0298340649277975
62	110.66	108.519998027761	2.14000197223938
63	111.15	110.659858530972	0.490141469027677
64	112.14	111.149967598237	0.990032401763145
65	113.38	112.139934551966	1.2400654480337
66	113.75	113.379918023041	0.370081976958659
67	113.89	113.749975535005	0.140024464994951
68	113.92	113.889990743408	0.0300092565918959
69	116.4	113.919998016179	2.48000198382077
70	115.86	116.399836054605	-0.539836054604706
71	115.16	115.860035686921	-0.700035686921197
72	114.45	115.160046277232	-0.710046277232095
73	114.65	114.450046939002	0.199953060998197
74	114.85	114.649986781711	0.200013218289257
75	116.51	114.849986777734	1.6600132222661
76	118.18	116.50989026157	1.67010973842993
77	118.75	118.17988959412	0.57011040587993
78	119.06	118.749962311733	0.310037688266561
79	119.28	119.059979504351	0.220020495649464
80	119.68	119.279985455114	0.400014544886403
81	119.28	119.679973556254	-0.39997355625394
82	117.3	119.280026441036	-1.98002644103643
83	114.23	117.300130893531	-3.07013089353141
84	112.56	114.230202957024	-1.67020295702432
85	112.83	112.560110412042	0.269889587957664
86	112.35	112.829982158419	-0.479982158419446
87	112.8	112.350031730162	0.449968269837996
88	113.84	112.799970253965	1.04002974603503
89	115.02	113.839931246794	1.18006875320621
90	115.46	115.019921989241	0.44007801075945
91	115	115.45997090778	-0.459970907779947
92	115.3	115.000030407279	0.29996959272097
93	116.09	115.299980169922	0.790019830078279
94	115.49	116.08994777419	-0.59994777418963
95	112.89	115.490039660724	-2.60003966072431
96	110.66	112.890171880721	-2.23017188072137

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	110.660147429886	108.652326615786	112.667968243986
98	110.660147429886	107.820753857163	113.49954100261
99	110.660147429886	107.182653030162	114.137641829611
100	110.660147429886	106.644704896441	114.675589963332
101	110.660147429886	106.170761037661	115.149533822111
102	110.660147429886	105.742281874792	115.578012984981
103	110.660147429886	105.34825388264	115.972040977133
104	110.660147429886	104.981501068598	116.338793791174
105	110.660147429886	104.637038935441	116.683255924332
106	110.660147429886	104.311238281446	117.009056578327
107	110.660147429886	104.001359340869	117.318935518904
108	110.660147429886	103.705273581014	117.615021278759

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 110.660147429886 & 108.652326615786 & 112.667968243986 \tabularnewline
98 & 110.660147429886 & 107.820753857163 & 113.49954100261 \tabularnewline
99 & 110.660147429886 & 107.182653030162 & 114.137641829611 \tabularnewline
100 & 110.660147429886 & 106.644704896441 & 114.675589963332 \tabularnewline
101 & 110.660147429886 & 106.170761037661 & 115.149533822111 \tabularnewline
102 & 110.660147429886 & 105.742281874792 & 115.578012984981 \tabularnewline
103 & 110.660147429886 & 105.34825388264 & 115.972040977133 \tabularnewline
104 & 110.660147429886 & 104.981501068598 & 116.338793791174 \tabularnewline
105 & 110.660147429886 & 104.637038935441 & 116.683255924332 \tabularnewline
106 & 110.660147429886 & 104.311238281446 & 117.009056578327 \tabularnewline
107 & 110.660147429886 & 104.001359340869 & 117.318935518904 \tabularnewline
108 & 110.660147429886 & 103.705273581014 & 117.615021278759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278621&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]97[/C][C]110.660147429886[/C][C]108.652326615786[/C][C]112.667968243986[/C][/ROW]
[ROW][C]98[/C][C]110.660147429886[/C][C]107.820753857163[/C][C]113.49954100261[/C][/ROW]
[ROW][C]99[/C][C]110.660147429886[/C][C]107.182653030162[/C][C]114.137641829611[/C][/ROW]
[ROW][C]100[/C][C]110.660147429886[/C][C]106.644704896441[/C][C]114.675589963332[/C][/ROW]
[ROW][C]101[/C][C]110.660147429886[/C][C]106.170761037661[/C][C]115.149533822111[/C][/ROW]
[ROW][C]102[/C][C]110.660147429886[/C][C]105.742281874792[/C][C]115.578012984981[/C][/ROW]
[ROW][C]103[/C][C]110.660147429886[/C][C]105.34825388264[/C][C]115.972040977133[/C][/ROW]
[ROW][C]104[/C][C]110.660147429886[/C][C]104.981501068598[/C][C]116.338793791174[/C][/ROW]
[ROW][C]105[/C][C]110.660147429886[/C][C]104.637038935441[/C][C]116.683255924332[/C][/ROW]
[ROW][C]106[/C][C]110.660147429886[/C][C]104.311238281446[/C][C]117.009056578327[/C][/ROW]
[ROW][C]107[/C][C]110.660147429886[/C][C]104.001359340869[/C][C]117.318935518904[/C][/ROW]
[ROW][C]108[/C][C]110.660147429886[/C][C]103.705273581014[/C][C]117.615021278759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278621&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278621&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
97	110.660147429886	108.652326615786	112.667968243986
98	110.660147429886	107.820753857163	113.49954100261
99	110.660147429886	107.182653030162	114.137641829611
100	110.660147429886	106.644704896441	114.675589963332
101	110.660147429886	106.170761037661	115.149533822111
102	110.660147429886	105.742281874792	115.578012984981
103	110.660147429886	105.34825388264	115.972040977133
104	110.660147429886	104.981501068598	116.338793791174
105	110.660147429886	104.637038935441	116.683255924332
106	110.660147429886	104.311238281446	117.009056578327
107	110.660147429886	104.001359340869	117.318935518904
108	110.660147429886	103.705273581014	117.615021278759

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