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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 01 Apr 2015 15:17:36 +0100
Cite this page as followsStatistical 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, 31 Oct 2024 23:12:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278518, Retrieved Thu, 31 Oct 2024 23:12:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186
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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Dataseries X:
98,68
99,06
99,84
100,3
100,38
100,02
99,83
100,36
100,74
100,49
100,33
99,96
100,08
100,54
101,63
102,12
102,19
101,77
101,29
101,47
102,07
102,11
102,26
101,83
102,11
102,8
103,82
104,2
104,57
104,38
104,54
104,74
105,19
104,95
104,57
103,81
104,08
104,81
105,86
106,1
106,24
105,87
104,74
105,03
105,59
105,69
105,58
104,96
104,93
105,68
106,93
107,29
107,25
106,74
106,44
106,6
107,26
107,35
107,22
106,99
106,87
107,68
108,9
109,48
109,57
109,03
109,58
109,76
110,15
110,2
109,86
109,58
109,52
110,35
111,61
112,06
111,9
111,36
112,09
112,24
112,7
113,36
112,9
112,74
112,77
113,66
114,87
114,97
115
114,57
115,54
115,39
115,46
115,13
114,56
114,62




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.03393249138588
gammaFALSE

\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
ParameterValue
alpha1
beta0.03393249138588
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
399.8499.440.400000000000006
4100.3100.2335729965540.0664270034456393
5100.38100.695827030277-0.315827030276552
6100.02100.765110232292-0.745110232292262
799.83100.379826785753-0.549826785753481
8100.36100.1711697930820.188830206917828
9100.74100.7075772724520.0324227275481803
10100.49101.088677456375-0.598677456375043
11100.33100.818362838744-0.488362838743669
1299.96100.641791470925-0.681791470924821
13100.08100.248656587711-0.1686565877107
14100.54100.3629336495010.177066350498976
15101.63100.8289419519140.80105804808592
16102.12101.946123847230.173876152769679
17102.19102.442023898286-0.25202389828641
18101.77102.503472099529-0.733472099528768
19101.29102.05858356383-0.768583563829708
20101.47101.552503608671-0.0825036086707485
21102.07101.729704055680.340295944319777
22102.11102.341251144879-0.231251144879494
23102.26102.373404217398-0.1134042173979
24101.83102.519556129768-0.689556129767922
25102.11102.0661577723340.0438422276655075
26102.8102.3476454483470.452354551652903
27103.82103.0529949652740.767005034725585
28104.2104.0990213570080.100978642991848
29104.57104.4824478139420.0875521860583461
30104.38104.855418677741-0.475418677740876
31104.54104.649286537554-0.109286537553743
32104.74104.80557817306-0.0655781730596345
33105.19105.0033529422670.186647057732827
34104.95105.459686341946-0.509686341945894
35104.57105.202391414538-0.632391414538318
36103.81104.800932798312-0.990932798311974
37104.08104.0073079796690.0726920203307202
38104.81104.2797746010230.530225398977024
39105.86105.0277664698060.832233530193662
40106.1106.106006226901-0.00600622690068064
41106.24106.345802420658-0.105802420658108
42105.87106.482212280931-0.612212280930507
43104.74106.091438392982-1.35143839298152
44105.03104.9155807213530.114419278646892
45105.59105.209463252540.380536747459814
46105.69105.782375812445-0.0923758124453826
47105.58105.879241270985-0.299241270985306
48104.96105.759087269135-0.799087269135299
49104.93105.111972247259-0.181972247258784
50105.68105.0757974755460.604202524453783
51106.93105.8462995725031.08370042749742
52107.29107.1330722279240.156927772076486
53107.25107.498397178198-0.248397178197706
54106.74107.449968443088-0.709968443088229
55106.44106.915877445009-0.475877445008891
56106.6106.5997297377050.000270262294606027
57107.26106.7597389083780.500261091621638
58107.35107.436714013561-0.086714013560524
59107.22107.523771591042-0.303771591042334
60106.99107.383463864146-0.393463864146028
61106.87107.140112654965-0.270112654965217
62107.68107.0109470596270.669052940372595
63108.9107.8436496927631.0563503072367
64109.48109.0994942904640.380505709535925
65109.57109.692405797175-0.12240579717519
66109.03109.778252263517-0.748252263516946
67109.58109.2128622000310.367137799969299
68109.76109.775320100266-0.0153201002655834
69110.15109.9548002510950.195199748904699
70110.2110.351423864894-0.15142386489353
71109.86110.396285675902-0.53628567590242
72109.58110.038088166824-0.458088166824481
73109.52109.74254409405-0.222544094049738
74110.35109.6749926184950.675007381504585
75111.61110.5278973006541.08210269934628
76112.06111.8246157411780.235384258822066
77111.9112.282602915513-0.382602915512777
78111.36112.109620245378-0.74962024537794
79112.09111.5441837628590.54581623714104
80112.24112.292704667624-0.0527046676240417
81112.7112.4409162669440.25908373305613
82113.36112.9097076234840.450292376515961
83112.9113.584987165671-0.684987165671274
84112.74113.101743844573-0.361743844572715
85112.77112.929468974683-0.159468974682852
86113.66112.9540577950730.705942204926899
87114.87113.8680121728611.00198782713929
88114.97115.112012116174-0.142012116173888
89115115.207193291265-0.207193291265114
90114.57115.230162706694-0.660162706694052
91115.54114.7777617413360.762238258664141
92115.39115.773626384482-0.383626384481985
93115.46115.610608985495-0.150608985495154
94115.13115.675498447392-0.545498447392205
95114.56115.326988326025-0.766988326025043
96114.62114.730962501259-0.110962501259138

\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
tObservedFittedResiduals
399.8499.440.400000000000006
4100.3100.2335729965540.0664270034456393
5100.38100.695827030277-0.315827030276552
6100.02100.765110232292-0.745110232292262
799.83100.379826785753-0.549826785753481
8100.36100.1711697930820.188830206917828
9100.74100.7075772724520.0324227275481803
10100.49101.088677456375-0.598677456375043
11100.33100.818362838744-0.488362838743669
1299.96100.641791470925-0.681791470924821
13100.08100.248656587711-0.1686565877107
14100.54100.3629336495010.177066350498976
15101.63100.8289419519140.80105804808592
16102.12101.946123847230.173876152769679
17102.19102.442023898286-0.25202389828641
18101.77102.503472099529-0.733472099528768
19101.29102.05858356383-0.768583563829708
20101.47101.552503608671-0.0825036086707485
21102.07101.729704055680.340295944319777
22102.11102.341251144879-0.231251144879494
23102.26102.373404217398-0.1134042173979
24101.83102.519556129768-0.689556129767922
25102.11102.0661577723340.0438422276655075
26102.8102.3476454483470.452354551652903
27103.82103.0529949652740.767005034725585
28104.2104.0990213570080.100978642991848
29104.57104.4824478139420.0875521860583461
30104.38104.855418677741-0.475418677740876
31104.54104.649286537554-0.109286537553743
32104.74104.80557817306-0.0655781730596345
33105.19105.0033529422670.186647057732827
34104.95105.459686341946-0.509686341945894
35104.57105.202391414538-0.632391414538318
36103.81104.800932798312-0.990932798311974
37104.08104.0073079796690.0726920203307202
38104.81104.2797746010230.530225398977024
39105.86105.0277664698060.832233530193662
40106.1106.106006226901-0.00600622690068064
41106.24106.345802420658-0.105802420658108
42105.87106.482212280931-0.612212280930507
43104.74106.091438392982-1.35143839298152
44105.03104.9155807213530.114419278646892
45105.59105.209463252540.380536747459814
46105.69105.782375812445-0.0923758124453826
47105.58105.879241270985-0.299241270985306
48104.96105.759087269135-0.799087269135299
49104.93105.111972247259-0.181972247258784
50105.68105.0757974755460.604202524453783
51106.93105.8462995725031.08370042749742
52107.29107.1330722279240.156927772076486
53107.25107.498397178198-0.248397178197706
54106.74107.449968443088-0.709968443088229
55106.44106.915877445009-0.475877445008891
56106.6106.5997297377050.000270262294606027
57107.26106.7597389083780.500261091621638
58107.35107.436714013561-0.086714013560524
59107.22107.523771591042-0.303771591042334
60106.99107.383463864146-0.393463864146028
61106.87107.140112654965-0.270112654965217
62107.68107.0109470596270.669052940372595
63108.9107.8436496927631.0563503072367
64109.48109.0994942904640.380505709535925
65109.57109.692405797175-0.12240579717519
66109.03109.778252263517-0.748252263516946
67109.58109.2128622000310.367137799969299
68109.76109.775320100266-0.0153201002655834
69110.15109.9548002510950.195199748904699
70110.2110.351423864894-0.15142386489353
71109.86110.396285675902-0.53628567590242
72109.58110.038088166824-0.458088166824481
73109.52109.74254409405-0.222544094049738
74110.35109.6749926184950.675007381504585
75111.61110.5278973006541.08210269934628
76112.06111.8246157411780.235384258822066
77111.9112.282602915513-0.382602915512777
78111.36112.109620245378-0.74962024537794
79112.09111.5441837628590.54581623714104
80112.24112.292704667624-0.0527046676240417
81112.7112.4409162669440.25908373305613
82113.36112.9097076234840.450292376515961
83112.9113.584987165671-0.684987165671274
84112.74113.101743844573-0.361743844572715
85112.77112.929468974683-0.159468974682852
86113.66112.9540577950730.705942204926899
87114.87113.8680121728611.00198782713929
88114.97115.112012116174-0.142012116173888
89115115.207193291265-0.207193291265114
90114.57115.230162706694-0.660162706694052
91115.54114.7777617413360.762238258664141
92115.39115.773626384482-0.383626384481985
93115.46115.610608985495-0.150608985495154
94115.13115.675498447392-0.545498447392205
95114.56115.326988326025-0.766988326025043
96114.62114.730962501259-0.110962501259138







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97114.787197267141113.782498408098115.791896126184
98114.954394534282113.509228069151116.399560999413
99115.121591801423113.321707509629116.921476093217
100115.288789068564113.175739998334117.401838138794
101115.455986335705113.054526496332117.857446175078
102115.623183602846112.949607917604118.296759288088
103115.790380869987112.856050682856118.724711057118
104115.957578137128112.770699729123119.144456545133
105116.124775404269112.691404977744119.558145830795
106116.29197267141112.616631372672119.967313970148
107116.459169938551112.545243261039120.373096616063
108116.626367205692112.476376587625120.776357823759

\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
tForecast95% Lower Bound95% Upper Bound
97114.787197267141113.782498408098115.791896126184
98114.954394534282113.509228069151116.399560999413
99115.121591801423113.321707509629116.921476093217
100115.288789068564113.175739998334117.401838138794
101115.455986335705113.054526496332117.857446175078
102115.623183602846112.949607917604118.296759288088
103115.790380869987112.856050682856118.724711057118
104115.957578137128112.770699729123119.144456545133
105116.124775404269112.691404977744119.558145830795
106116.29197267141112.616631372672119.967313970148
107116.459169938551112.545243261039120.373096616063
108116.626367205692112.476376587625120.776357823759



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')