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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 01 Apr 2015 15:17:36 +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/01/t1427897882jtfttuack8810mh.htm/, Retrieved Thu, 09 May 2024 13:48:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278518, Retrieved Thu, 09 May 2024 13:48:30 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

148

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

-       [Exponential Smoothing] [consumentenprijze...] [2015-04-01 14:17:36] [0793dda36b6d92f80d1980fc1d00d6bd] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278518&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278518&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.03393249138588
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.03393249138588 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278518&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.03393249138588[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278518&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	1
beta	0.03393249138588
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	99.84	99.44	0.400000000000006
4	100.3	100.233572996554	0.0664270034456393
5	100.38	100.695827030277	-0.315827030276552
6	100.02	100.765110232292	-0.745110232292262
7	99.83	100.379826785753	-0.549826785753481
8	100.36	100.171169793082	0.188830206917828
9	100.74	100.707577272452	0.0324227275481803
10	100.49	101.088677456375	-0.598677456375043
11	100.33	100.818362838744	-0.488362838743669
12	99.96	100.641791470925	-0.681791470924821
13	100.08	100.248656587711	-0.1686565877107
14	100.54	100.362933649501	0.177066350498976
15	101.63	100.828941951914	0.80105804808592
16	102.12	101.94612384723	0.173876152769679
17	102.19	102.442023898286	-0.25202389828641
18	101.77	102.503472099529	-0.733472099528768
19	101.29	102.05858356383	-0.768583563829708
20	101.47	101.552503608671	-0.0825036086707485
21	102.07	101.72970405568	0.340295944319777
22	102.11	102.341251144879	-0.231251144879494
23	102.26	102.373404217398	-0.1134042173979
24	101.83	102.519556129768	-0.689556129767922
25	102.11	102.066157772334	0.0438422276655075
26	102.8	102.347645448347	0.452354551652903
27	103.82	103.052994965274	0.767005034725585
28	104.2	104.099021357008	0.100978642991848
29	104.57	104.482447813942	0.0875521860583461
30	104.38	104.855418677741	-0.475418677740876
31	104.54	104.649286537554	-0.109286537553743
32	104.74	104.80557817306	-0.0655781730596345
33	105.19	105.003352942267	0.186647057732827
34	104.95	105.459686341946	-0.509686341945894
35	104.57	105.202391414538	-0.632391414538318
36	103.81	104.800932798312	-0.990932798311974
37	104.08	104.007307979669	0.0726920203307202
38	104.81	104.279774601023	0.530225398977024
39	105.86	105.027766469806	0.832233530193662
40	106.1	106.106006226901	-0.00600622690068064
41	106.24	106.345802420658	-0.105802420658108
42	105.87	106.482212280931	-0.612212280930507
43	104.74	106.091438392982	-1.35143839298152
44	105.03	104.915580721353	0.114419278646892
45	105.59	105.20946325254	0.380536747459814
46	105.69	105.782375812445	-0.0923758124453826
47	105.58	105.879241270985	-0.299241270985306
48	104.96	105.759087269135	-0.799087269135299
49	104.93	105.111972247259	-0.181972247258784
50	105.68	105.075797475546	0.604202524453783
51	106.93	105.846299572503	1.08370042749742
52	107.29	107.133072227924	0.156927772076486
53	107.25	107.498397178198	-0.248397178197706
54	106.74	107.449968443088	-0.709968443088229
55	106.44	106.915877445009	-0.475877445008891
56	106.6	106.599729737705	0.000270262294606027
57	107.26	106.759738908378	0.500261091621638
58	107.35	107.436714013561	-0.086714013560524
59	107.22	107.523771591042	-0.303771591042334
60	106.99	107.383463864146	-0.393463864146028
61	106.87	107.140112654965	-0.270112654965217
62	107.68	107.010947059627	0.669052940372595
63	108.9	107.843649692763	1.0563503072367
64	109.48	109.099494290464	0.380505709535925
65	109.57	109.692405797175	-0.12240579717519
66	109.03	109.778252263517	-0.748252263516946
67	109.58	109.212862200031	0.367137799969299
68	109.76	109.775320100266	-0.0153201002655834
69	110.15	109.954800251095	0.195199748904699
70	110.2	110.351423864894	-0.15142386489353
71	109.86	110.396285675902	-0.53628567590242
72	109.58	110.038088166824	-0.458088166824481
73	109.52	109.74254409405	-0.222544094049738
74	110.35	109.674992618495	0.675007381504585
75	111.61	110.527897300654	1.08210269934628
76	112.06	111.824615741178	0.235384258822066
77	111.9	112.282602915513	-0.382602915512777
78	111.36	112.109620245378	-0.74962024537794
79	112.09	111.544183762859	0.54581623714104
80	112.24	112.292704667624	-0.0527046676240417
81	112.7	112.440916266944	0.25908373305613
82	113.36	112.909707623484	0.450292376515961
83	112.9	113.584987165671	-0.684987165671274
84	112.74	113.101743844573	-0.361743844572715
85	112.77	112.929468974683	-0.159468974682852
86	113.66	112.954057795073	0.705942204926899
87	114.87	113.868012172861	1.00198782713929
88	114.97	115.112012116174	-0.142012116173888
89	115	115.207193291265	-0.207193291265114
90	114.57	115.230162706694	-0.660162706694052
91	115.54	114.777761741336	0.762238258664141
92	115.39	115.773626384482	-0.383626384481985
93	115.46	115.610608985495	-0.150608985495154
94	115.13	115.675498447392	-0.545498447392205
95	114.56	115.326988326025	-0.766988326025043
96	114.62	114.730962501259	-0.110962501259138

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99.84 & 99.44 & 0.400000000000006 \tabularnewline
4 & 100.3 & 100.233572996554 & 0.0664270034456393 \tabularnewline
5 & 100.38 & 100.695827030277 & -0.315827030276552 \tabularnewline
6 & 100.02 & 100.765110232292 & -0.745110232292262 \tabularnewline
7 & 99.83 & 100.379826785753 & -0.549826785753481 \tabularnewline
8 & 100.36 & 100.171169793082 & 0.188830206917828 \tabularnewline
9 & 100.74 & 100.707577272452 & 0.0324227275481803 \tabularnewline
10 & 100.49 & 101.088677456375 & -0.598677456375043 \tabularnewline
11 & 100.33 & 100.818362838744 & -0.488362838743669 \tabularnewline
12 & 99.96 & 100.641791470925 & -0.681791470924821 \tabularnewline
13 & 100.08 & 100.248656587711 & -0.1686565877107 \tabularnewline
14 & 100.54 & 100.362933649501 & 0.177066350498976 \tabularnewline
15 & 101.63 & 100.828941951914 & 0.80105804808592 \tabularnewline
16 & 102.12 & 101.94612384723 & 0.173876152769679 \tabularnewline
17 & 102.19 & 102.442023898286 & -0.25202389828641 \tabularnewline
18 & 101.77 & 102.503472099529 & -0.733472099528768 \tabularnewline
19 & 101.29 & 102.05858356383 & -0.768583563829708 \tabularnewline
20 & 101.47 & 101.552503608671 & -0.0825036086707485 \tabularnewline
21 & 102.07 & 101.72970405568 & 0.340295944319777 \tabularnewline
22 & 102.11 & 102.341251144879 & -0.231251144879494 \tabularnewline
23 & 102.26 & 102.373404217398 & -0.1134042173979 \tabularnewline
24 & 101.83 & 102.519556129768 & -0.689556129767922 \tabularnewline
25 & 102.11 & 102.066157772334 & 0.0438422276655075 \tabularnewline
26 & 102.8 & 102.347645448347 & 0.452354551652903 \tabularnewline
27 & 103.82 & 103.052994965274 & 0.767005034725585 \tabularnewline
28 & 104.2 & 104.099021357008 & 0.100978642991848 \tabularnewline
29 & 104.57 & 104.482447813942 & 0.0875521860583461 \tabularnewline
30 & 104.38 & 104.855418677741 & -0.475418677740876 \tabularnewline
31 & 104.54 & 104.649286537554 & -0.109286537553743 \tabularnewline
32 & 104.74 & 104.80557817306 & -0.0655781730596345 \tabularnewline
33 & 105.19 & 105.003352942267 & 0.186647057732827 \tabularnewline
34 & 104.95 & 105.459686341946 & -0.509686341945894 \tabularnewline
35 & 104.57 & 105.202391414538 & -0.632391414538318 \tabularnewline
36 & 103.81 & 104.800932798312 & -0.990932798311974 \tabularnewline
37 & 104.08 & 104.007307979669 & 0.0726920203307202 \tabularnewline
38 & 104.81 & 104.279774601023 & 0.530225398977024 \tabularnewline
39 & 105.86 & 105.027766469806 & 0.832233530193662 \tabularnewline
40 & 106.1 & 106.106006226901 & -0.00600622690068064 \tabularnewline
41 & 106.24 & 106.345802420658 & -0.105802420658108 \tabularnewline
42 & 105.87 & 106.482212280931 & -0.612212280930507 \tabularnewline
43 & 104.74 & 106.091438392982 & -1.35143839298152 \tabularnewline
44 & 105.03 & 104.915580721353 & 0.114419278646892 \tabularnewline
45 & 105.59 & 105.20946325254 & 0.380536747459814 \tabularnewline
46 & 105.69 & 105.782375812445 & -0.0923758124453826 \tabularnewline
47 & 105.58 & 105.879241270985 & -0.299241270985306 \tabularnewline
48 & 104.96 & 105.759087269135 & -0.799087269135299 \tabularnewline
49 & 104.93 & 105.111972247259 & -0.181972247258784 \tabularnewline
50 & 105.68 & 105.075797475546 & 0.604202524453783 \tabularnewline
51 & 106.93 & 105.846299572503 & 1.08370042749742 \tabularnewline
52 & 107.29 & 107.133072227924 & 0.156927772076486 \tabularnewline
53 & 107.25 & 107.498397178198 & -0.248397178197706 \tabularnewline
54 & 106.74 & 107.449968443088 & -0.709968443088229 \tabularnewline
55 & 106.44 & 106.915877445009 & -0.475877445008891 \tabularnewline
56 & 106.6 & 106.599729737705 & 0.000270262294606027 \tabularnewline
57 & 107.26 & 106.759738908378 & 0.500261091621638 \tabularnewline
58 & 107.35 & 107.436714013561 & -0.086714013560524 \tabularnewline
59 & 107.22 & 107.523771591042 & -0.303771591042334 \tabularnewline
60 & 106.99 & 107.383463864146 & -0.393463864146028 \tabularnewline
61 & 106.87 & 107.140112654965 & -0.270112654965217 \tabularnewline
62 & 107.68 & 107.010947059627 & 0.669052940372595 \tabularnewline
63 & 108.9 & 107.843649692763 & 1.0563503072367 \tabularnewline
64 & 109.48 & 109.099494290464 & 0.380505709535925 \tabularnewline
65 & 109.57 & 109.692405797175 & -0.12240579717519 \tabularnewline
66 & 109.03 & 109.778252263517 & -0.748252263516946 \tabularnewline
67 & 109.58 & 109.212862200031 & 0.367137799969299 \tabularnewline
68 & 109.76 & 109.775320100266 & -0.0153201002655834 \tabularnewline
69 & 110.15 & 109.954800251095 & 0.195199748904699 \tabularnewline
70 & 110.2 & 110.351423864894 & -0.15142386489353 \tabularnewline
71 & 109.86 & 110.396285675902 & -0.53628567590242 \tabularnewline
72 & 109.58 & 110.038088166824 & -0.458088166824481 \tabularnewline
73 & 109.52 & 109.74254409405 & -0.222544094049738 \tabularnewline
74 & 110.35 & 109.674992618495 & 0.675007381504585 \tabularnewline
75 & 111.61 & 110.527897300654 & 1.08210269934628 \tabularnewline
76 & 112.06 & 111.824615741178 & 0.235384258822066 \tabularnewline
77 & 111.9 & 112.282602915513 & -0.382602915512777 \tabularnewline
78 & 111.36 & 112.109620245378 & -0.74962024537794 \tabularnewline
79 & 112.09 & 111.544183762859 & 0.54581623714104 \tabularnewline
80 & 112.24 & 112.292704667624 & -0.0527046676240417 \tabularnewline
81 & 112.7 & 112.440916266944 & 0.25908373305613 \tabularnewline
82 & 113.36 & 112.909707623484 & 0.450292376515961 \tabularnewline
83 & 112.9 & 113.584987165671 & -0.684987165671274 \tabularnewline
84 & 112.74 & 113.101743844573 & -0.361743844572715 \tabularnewline
85 & 112.77 & 112.929468974683 & -0.159468974682852 \tabularnewline
86 & 113.66 & 112.954057795073 & 0.705942204926899 \tabularnewline
87 & 114.87 & 113.868012172861 & 1.00198782713929 \tabularnewline
88 & 114.97 & 115.112012116174 & -0.142012116173888 \tabularnewline
89 & 115 & 115.207193291265 & -0.207193291265114 \tabularnewline
90 & 114.57 & 115.230162706694 & -0.660162706694052 \tabularnewline
91 & 115.54 & 114.777761741336 & 0.762238258664141 \tabularnewline
92 & 115.39 & 115.773626384482 & -0.383626384481985 \tabularnewline
93 & 115.46 & 115.610608985495 & -0.150608985495154 \tabularnewline
94 & 115.13 & 115.675498447392 & -0.545498447392205 \tabularnewline
95 & 114.56 & 115.326988326025 & -0.766988326025043 \tabularnewline
96 & 114.62 & 114.730962501259 & -0.110962501259138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278518&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]3[/C][C]99.84[/C][C]99.44[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]4[/C][C]100.3[/C][C]100.233572996554[/C][C]0.0664270034456393[/C][/ROW]
[ROW][C]5[/C][C]100.38[/C][C]100.695827030277[/C][C]-0.315827030276552[/C][/ROW]
[ROW][C]6[/C][C]100.02[/C][C]100.765110232292[/C][C]-0.745110232292262[/C][/ROW]
[ROW][C]7[/C][C]99.83[/C][C]100.379826785753[/C][C]-0.549826785753481[/C][/ROW]
[ROW][C]8[/C][C]100.36[/C][C]100.171169793082[/C][C]0.188830206917828[/C][/ROW]
[ROW][C]9[/C][C]100.74[/C][C]100.707577272452[/C][C]0.0324227275481803[/C][/ROW]
[ROW][C]10[/C][C]100.49[/C][C]101.088677456375[/C][C]-0.598677456375043[/C][/ROW]
[ROW][C]11[/C][C]100.33[/C][C]100.818362838744[/C][C]-0.488362838743669[/C][/ROW]
[ROW][C]12[/C][C]99.96[/C][C]100.641791470925[/C][C]-0.681791470924821[/C][/ROW]
[ROW][C]13[/C][C]100.08[/C][C]100.248656587711[/C][C]-0.1686565877107[/C][/ROW]
[ROW][C]14[/C][C]100.54[/C][C]100.362933649501[/C][C]0.177066350498976[/C][/ROW]
[ROW][C]15[/C][C]101.63[/C][C]100.828941951914[/C][C]0.80105804808592[/C][/ROW]
[ROW][C]16[/C][C]102.12[/C][C]101.94612384723[/C][C]0.173876152769679[/C][/ROW]
[ROW][C]17[/C][C]102.19[/C][C]102.442023898286[/C][C]-0.25202389828641[/C][/ROW]
[ROW][C]18[/C][C]101.77[/C][C]102.503472099529[/C][C]-0.733472099528768[/C][/ROW]
[ROW][C]19[/C][C]101.29[/C][C]102.05858356383[/C][C]-0.768583563829708[/C][/ROW]
[ROW][C]20[/C][C]101.47[/C][C]101.552503608671[/C][C]-0.0825036086707485[/C][/ROW]
[ROW][C]21[/C][C]102.07[/C][C]101.72970405568[/C][C]0.340295944319777[/C][/ROW]
[ROW][C]22[/C][C]102.11[/C][C]102.341251144879[/C][C]-0.231251144879494[/C][/ROW]
[ROW][C]23[/C][C]102.26[/C][C]102.373404217398[/C][C]-0.1134042173979[/C][/ROW]
[ROW][C]24[/C][C]101.83[/C][C]102.519556129768[/C][C]-0.689556129767922[/C][/ROW]
[ROW][C]25[/C][C]102.11[/C][C]102.066157772334[/C][C]0.0438422276655075[/C][/ROW]
[ROW][C]26[/C][C]102.8[/C][C]102.347645448347[/C][C]0.452354551652903[/C][/ROW]
[ROW][C]27[/C][C]103.82[/C][C]103.052994965274[/C][C]0.767005034725585[/C][/ROW]
[ROW][C]28[/C][C]104.2[/C][C]104.099021357008[/C][C]0.100978642991848[/C][/ROW]
[ROW][C]29[/C][C]104.57[/C][C]104.482447813942[/C][C]0.0875521860583461[/C][/ROW]
[ROW][C]30[/C][C]104.38[/C][C]104.855418677741[/C][C]-0.475418677740876[/C][/ROW]
[ROW][C]31[/C][C]104.54[/C][C]104.649286537554[/C][C]-0.109286537553743[/C][/ROW]
[ROW][C]32[/C][C]104.74[/C][C]104.80557817306[/C][C]-0.0655781730596345[/C][/ROW]
[ROW][C]33[/C][C]105.19[/C][C]105.003352942267[/C][C]0.186647057732827[/C][/ROW]
[ROW][C]34[/C][C]104.95[/C][C]105.459686341946[/C][C]-0.509686341945894[/C][/ROW]
[ROW][C]35[/C][C]104.57[/C][C]105.202391414538[/C][C]-0.632391414538318[/C][/ROW]
[ROW][C]36[/C][C]103.81[/C][C]104.800932798312[/C][C]-0.990932798311974[/C][/ROW]
[ROW][C]37[/C][C]104.08[/C][C]104.007307979669[/C][C]0.0726920203307202[/C][/ROW]
[ROW][C]38[/C][C]104.81[/C][C]104.279774601023[/C][C]0.530225398977024[/C][/ROW]
[ROW][C]39[/C][C]105.86[/C][C]105.027766469806[/C][C]0.832233530193662[/C][/ROW]
[ROW][C]40[/C][C]106.1[/C][C]106.106006226901[/C][C]-0.00600622690068064[/C][/ROW]
[ROW][C]41[/C][C]106.24[/C][C]106.345802420658[/C][C]-0.105802420658108[/C][/ROW]
[ROW][C]42[/C][C]105.87[/C][C]106.482212280931[/C][C]-0.612212280930507[/C][/ROW]
[ROW][C]43[/C][C]104.74[/C][C]106.091438392982[/C][C]-1.35143839298152[/C][/ROW]
[ROW][C]44[/C][C]105.03[/C][C]104.915580721353[/C][C]0.114419278646892[/C][/ROW]
[ROW][C]45[/C][C]105.59[/C][C]105.20946325254[/C][C]0.380536747459814[/C][/ROW]
[ROW][C]46[/C][C]105.69[/C][C]105.782375812445[/C][C]-0.0923758124453826[/C][/ROW]
[ROW][C]47[/C][C]105.58[/C][C]105.879241270985[/C][C]-0.299241270985306[/C][/ROW]
[ROW][C]48[/C][C]104.96[/C][C]105.759087269135[/C][C]-0.799087269135299[/C][/ROW]
[ROW][C]49[/C][C]104.93[/C][C]105.111972247259[/C][C]-0.181972247258784[/C][/ROW]
[ROW][C]50[/C][C]105.68[/C][C]105.075797475546[/C][C]0.604202524453783[/C][/ROW]
[ROW][C]51[/C][C]106.93[/C][C]105.846299572503[/C][C]1.08370042749742[/C][/ROW]
[ROW][C]52[/C][C]107.29[/C][C]107.133072227924[/C][C]0.156927772076486[/C][/ROW]
[ROW][C]53[/C][C]107.25[/C][C]107.498397178198[/C][C]-0.248397178197706[/C][/ROW]
[ROW][C]54[/C][C]106.74[/C][C]107.449968443088[/C][C]-0.709968443088229[/C][/ROW]
[ROW][C]55[/C][C]106.44[/C][C]106.915877445009[/C][C]-0.475877445008891[/C][/ROW]
[ROW][C]56[/C][C]106.6[/C][C]106.599729737705[/C][C]0.000270262294606027[/C][/ROW]
[ROW][C]57[/C][C]107.26[/C][C]106.759738908378[/C][C]0.500261091621638[/C][/ROW]
[ROW][C]58[/C][C]107.35[/C][C]107.436714013561[/C][C]-0.086714013560524[/C][/ROW]
[ROW][C]59[/C][C]107.22[/C][C]107.523771591042[/C][C]-0.303771591042334[/C][/ROW]
[ROW][C]60[/C][C]106.99[/C][C]107.383463864146[/C][C]-0.393463864146028[/C][/ROW]
[ROW][C]61[/C][C]106.87[/C][C]107.140112654965[/C][C]-0.270112654965217[/C][/ROW]
[ROW][C]62[/C][C]107.68[/C][C]107.010947059627[/C][C]0.669052940372595[/C][/ROW]
[ROW][C]63[/C][C]108.9[/C][C]107.843649692763[/C][C]1.0563503072367[/C][/ROW]
[ROW][C]64[/C][C]109.48[/C][C]109.099494290464[/C][C]0.380505709535925[/C][/ROW]
[ROW][C]65[/C][C]109.57[/C][C]109.692405797175[/C][C]-0.12240579717519[/C][/ROW]
[ROW][C]66[/C][C]109.03[/C][C]109.778252263517[/C][C]-0.748252263516946[/C][/ROW]
[ROW][C]67[/C][C]109.58[/C][C]109.212862200031[/C][C]0.367137799969299[/C][/ROW]
[ROW][C]68[/C][C]109.76[/C][C]109.775320100266[/C][C]-0.0153201002655834[/C][/ROW]
[ROW][C]69[/C][C]110.15[/C][C]109.954800251095[/C][C]0.195199748904699[/C][/ROW]
[ROW][C]70[/C][C]110.2[/C][C]110.351423864894[/C][C]-0.15142386489353[/C][/ROW]
[ROW][C]71[/C][C]109.86[/C][C]110.396285675902[/C][C]-0.53628567590242[/C][/ROW]
[ROW][C]72[/C][C]109.58[/C][C]110.038088166824[/C][C]-0.458088166824481[/C][/ROW]
[ROW][C]73[/C][C]109.52[/C][C]109.74254409405[/C][C]-0.222544094049738[/C][/ROW]
[ROW][C]74[/C][C]110.35[/C][C]109.674992618495[/C][C]0.675007381504585[/C][/ROW]
[ROW][C]75[/C][C]111.61[/C][C]110.527897300654[/C][C]1.08210269934628[/C][/ROW]
[ROW][C]76[/C][C]112.06[/C][C]111.824615741178[/C][C]0.235384258822066[/C][/ROW]
[ROW][C]77[/C][C]111.9[/C][C]112.282602915513[/C][C]-0.382602915512777[/C][/ROW]
[ROW][C]78[/C][C]111.36[/C][C]112.109620245378[/C][C]-0.74962024537794[/C][/ROW]
[ROW][C]79[/C][C]112.09[/C][C]111.544183762859[/C][C]0.54581623714104[/C][/ROW]
[ROW][C]80[/C][C]112.24[/C][C]112.292704667624[/C][C]-0.0527046676240417[/C][/ROW]
[ROW][C]81[/C][C]112.7[/C][C]112.440916266944[/C][C]0.25908373305613[/C][/ROW]
[ROW][C]82[/C][C]113.36[/C][C]112.909707623484[/C][C]0.450292376515961[/C][/ROW]
[ROW][C]83[/C][C]112.9[/C][C]113.584987165671[/C][C]-0.684987165671274[/C][/ROW]
[ROW][C]84[/C][C]112.74[/C][C]113.101743844573[/C][C]-0.361743844572715[/C][/ROW]
[ROW][C]85[/C][C]112.77[/C][C]112.929468974683[/C][C]-0.159468974682852[/C][/ROW]
[ROW][C]86[/C][C]113.66[/C][C]112.954057795073[/C][C]0.705942204926899[/C][/ROW]
[ROW][C]87[/C][C]114.87[/C][C]113.868012172861[/C][C]1.00198782713929[/C][/ROW]
[ROW][C]88[/C][C]114.97[/C][C]115.112012116174[/C][C]-0.142012116173888[/C][/ROW]
[ROW][C]89[/C][C]115[/C][C]115.207193291265[/C][C]-0.207193291265114[/C][/ROW]
[ROW][C]90[/C][C]114.57[/C][C]115.230162706694[/C][C]-0.660162706694052[/C][/ROW]
[ROW][C]91[/C][C]115.54[/C][C]114.777761741336[/C][C]0.762238258664141[/C][/ROW]
[ROW][C]92[/C][C]115.39[/C][C]115.773626384482[/C][C]-0.383626384481985[/C][/ROW]
[ROW][C]93[/C][C]115.46[/C][C]115.610608985495[/C][C]-0.150608985495154[/C][/ROW]
[ROW][C]94[/C][C]115.13[/C][C]115.675498447392[/C][C]-0.545498447392205[/C][/ROW]
[ROW][C]95[/C][C]114.56[/C][C]115.326988326025[/C][C]-0.766988326025043[/C][/ROW]
[ROW][C]96[/C][C]114.62[/C][C]114.730962501259[/C][C]-0.110962501259138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278518&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278518&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
3	99.84	99.44	0.400000000000006
4	100.3	100.233572996554	0.0664270034456393
5	100.38	100.695827030277	-0.315827030276552
6	100.02	100.765110232292	-0.745110232292262
7	99.83	100.379826785753	-0.549826785753481
8	100.36	100.171169793082	0.188830206917828
9	100.74	100.707577272452	0.0324227275481803
10	100.49	101.088677456375	-0.598677456375043
11	100.33	100.818362838744	-0.488362838743669
12	99.96	100.641791470925	-0.681791470924821
13	100.08	100.248656587711	-0.1686565877107
14	100.54	100.362933649501	0.177066350498976
15	101.63	100.828941951914	0.80105804808592
16	102.12	101.94612384723	0.173876152769679
17	102.19	102.442023898286	-0.25202389828641
18	101.77	102.503472099529	-0.733472099528768
19	101.29	102.05858356383	-0.768583563829708
20	101.47	101.552503608671	-0.0825036086707485
21	102.07	101.72970405568	0.340295944319777
22	102.11	102.341251144879	-0.231251144879494
23	102.26	102.373404217398	-0.1134042173979
24	101.83	102.519556129768	-0.689556129767922
25	102.11	102.066157772334	0.0438422276655075
26	102.8	102.347645448347	0.452354551652903
27	103.82	103.052994965274	0.767005034725585
28	104.2	104.099021357008	0.100978642991848
29	104.57	104.482447813942	0.0875521860583461
30	104.38	104.855418677741	-0.475418677740876
31	104.54	104.649286537554	-0.109286537553743
32	104.74	104.80557817306	-0.0655781730596345
33	105.19	105.003352942267	0.186647057732827
34	104.95	105.459686341946	-0.509686341945894
35	104.57	105.202391414538	-0.632391414538318
36	103.81	104.800932798312	-0.990932798311974
37	104.08	104.007307979669	0.0726920203307202
38	104.81	104.279774601023	0.530225398977024
39	105.86	105.027766469806	0.832233530193662
40	106.1	106.106006226901	-0.00600622690068064
41	106.24	106.345802420658	-0.105802420658108
42	105.87	106.482212280931	-0.612212280930507
43	104.74	106.091438392982	-1.35143839298152
44	105.03	104.915580721353	0.114419278646892
45	105.59	105.20946325254	0.380536747459814
46	105.69	105.782375812445	-0.0923758124453826
47	105.58	105.879241270985	-0.299241270985306
48	104.96	105.759087269135	-0.799087269135299
49	104.93	105.111972247259	-0.181972247258784
50	105.68	105.075797475546	0.604202524453783
51	106.93	105.846299572503	1.08370042749742
52	107.29	107.133072227924	0.156927772076486
53	107.25	107.498397178198	-0.248397178197706
54	106.74	107.449968443088	-0.709968443088229
55	106.44	106.915877445009	-0.475877445008891
56	106.6	106.599729737705	0.000270262294606027
57	107.26	106.759738908378	0.500261091621638
58	107.35	107.436714013561	-0.086714013560524
59	107.22	107.523771591042	-0.303771591042334
60	106.99	107.383463864146	-0.393463864146028
61	106.87	107.140112654965	-0.270112654965217
62	107.68	107.010947059627	0.669052940372595
63	108.9	107.843649692763	1.0563503072367
64	109.48	109.099494290464	0.380505709535925
65	109.57	109.692405797175	-0.12240579717519
66	109.03	109.778252263517	-0.748252263516946
67	109.58	109.212862200031	0.367137799969299
68	109.76	109.775320100266	-0.0153201002655834
69	110.15	109.954800251095	0.195199748904699
70	110.2	110.351423864894	-0.15142386489353
71	109.86	110.396285675902	-0.53628567590242
72	109.58	110.038088166824	-0.458088166824481
73	109.52	109.74254409405	-0.222544094049738
74	110.35	109.674992618495	0.675007381504585
75	111.61	110.527897300654	1.08210269934628
76	112.06	111.824615741178	0.235384258822066
77	111.9	112.282602915513	-0.382602915512777
78	111.36	112.109620245378	-0.74962024537794
79	112.09	111.544183762859	0.54581623714104
80	112.24	112.292704667624	-0.0527046676240417
81	112.7	112.440916266944	0.25908373305613
82	113.36	112.909707623484	0.450292376515961
83	112.9	113.584987165671	-0.684987165671274
84	112.74	113.101743844573	-0.361743844572715
85	112.77	112.929468974683	-0.159468974682852
86	113.66	112.954057795073	0.705942204926899
87	114.87	113.868012172861	1.00198782713929
88	114.97	115.112012116174	-0.142012116173888
89	115	115.207193291265	-0.207193291265114
90	114.57	115.230162706694	-0.660162706694052
91	115.54	114.777761741336	0.762238258664141
92	115.39	115.773626384482	-0.383626384481985
93	115.46	115.610608985495	-0.150608985495154
94	115.13	115.675498447392	-0.545498447392205
95	114.56	115.326988326025	-0.766988326025043
96	114.62	114.730962501259	-0.110962501259138

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	114.787197267141	113.782498408098	115.791896126184
98	114.954394534282	113.509228069151	116.399560999413
99	115.121591801423	113.321707509629	116.921476093217
100	115.288789068564	113.175739998334	117.401838138794
101	115.455986335705	113.054526496332	117.857446175078
102	115.623183602846	112.949607917604	118.296759288088
103	115.790380869987	112.856050682856	118.724711057118
104	115.957578137128	112.770699729123	119.144456545133
105	116.124775404269	112.691404977744	119.558145830795
106	116.29197267141	112.616631372672	119.967313970148
107	116.459169938551	112.545243261039	120.373096616063
108	116.626367205692	112.476376587625	120.776357823759

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 114.787197267141 & 113.782498408098 & 115.791896126184 \tabularnewline
98 & 114.954394534282 & 113.509228069151 & 116.399560999413 \tabularnewline
99 & 115.121591801423 & 113.321707509629 & 116.921476093217 \tabularnewline
100 & 115.288789068564 & 113.175739998334 & 117.401838138794 \tabularnewline
101 & 115.455986335705 & 113.054526496332 & 117.857446175078 \tabularnewline
102 & 115.623183602846 & 112.949607917604 & 118.296759288088 \tabularnewline
103 & 115.790380869987 & 112.856050682856 & 118.724711057118 \tabularnewline
104 & 115.957578137128 & 112.770699729123 & 119.144456545133 \tabularnewline
105 & 116.124775404269 & 112.691404977744 & 119.558145830795 \tabularnewline
106 & 116.29197267141 & 112.616631372672 & 119.967313970148 \tabularnewline
107 & 116.459169938551 & 112.545243261039 & 120.373096616063 \tabularnewline
108 & 116.626367205692 & 112.476376587625 & 120.776357823759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278518&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]114.787197267141[/C][C]113.782498408098[/C][C]115.791896126184[/C][/ROW]
[ROW][C]98[/C][C]114.954394534282[/C][C]113.509228069151[/C][C]116.399560999413[/C][/ROW]
[ROW][C]99[/C][C]115.121591801423[/C][C]113.321707509629[/C][C]116.921476093217[/C][/ROW]
[ROW][C]100[/C][C]115.288789068564[/C][C]113.175739998334[/C][C]117.401838138794[/C][/ROW]
[ROW][C]101[/C][C]115.455986335705[/C][C]113.054526496332[/C][C]117.857446175078[/C][/ROW]
[ROW][C]102[/C][C]115.623183602846[/C][C]112.949607917604[/C][C]118.296759288088[/C][/ROW]
[ROW][C]103[/C][C]115.790380869987[/C][C]112.856050682856[/C][C]118.724711057118[/C][/ROW]
[ROW][C]104[/C][C]115.957578137128[/C][C]112.770699729123[/C][C]119.144456545133[/C][/ROW]
[ROW][C]105[/C][C]116.124775404269[/C][C]112.691404977744[/C][C]119.558145830795[/C][/ROW]
[ROW][C]106[/C][C]116.29197267141[/C][C]112.616631372672[/C][C]119.967313970148[/C][/ROW]
[ROW][C]107[/C][C]116.459169938551[/C][C]112.545243261039[/C][C]120.373096616063[/C][/ROW]
[ROW][C]108[/C][C]116.626367205692[/C][C]112.476376587625[/C][C]120.776357823759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278518&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278518&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	114.787197267141	113.782498408098	115.791896126184
98	114.954394534282	113.509228069151	116.399560999413
99	115.121591801423	113.321707509629	116.921476093217
100	115.288789068564	113.175739998334	117.401838138794
101	115.455986335705	113.054526496332	117.857446175078
102	115.623183602846	112.949607917604	118.296759288088
103	115.790380869987	112.856050682856	118.724711057118
104	115.957578137128	112.770699729123	119.144456545133
105	116.124775404269	112.691404977744	119.558145830795
106	116.29197267141	112.616631372672	119.967313970148
107	116.459169938551	112.545243261039	120.373096616063
108	116.626367205692	112.476376587625	120.776357823759

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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