Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 30 Mar 2015 15:17:47 +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/Mar/30/t1427725129fpen3m24u360mfh.htm/, Retrieved Sun, 19 May 2024 15:22:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278470, Retrieved Sun, 19 May 2024 15:22:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-03-30 14:17:47] [679411f6187277139d0a9a0a87b165a8] [Current]
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Dataseries X:
96.01
96.39
97.16
97.46
97.6
97.02
96.95
97.23
98
98.04
97.76
96.99
97.44
98
98.84
98.98
98.92
98.63
98.52
98.97
99.74
99.68
99.45
98.97
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
107
107.74
109.02
109.54
109.71
109.18
109.23
109.38
110.17
110.15
110.01
109.54
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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278470&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278470&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.698782679915408
beta0.00697335150702502
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.698782679915408 \tabularnewline
beta & 0.00697335150702502 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278470&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]0.698782679915408[/C][/ROW]
[ROW][C]beta[/C][C]0.00697335150702502[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278470&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
alpha0.698782679915408
beta0.00697335150702502
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397.4496.68123365119470.758766348805324
149897.77017211405280.229827885947216
1598.8498.76400352843290.0759964715670662
1698.9898.95538962456590.0246103754340936
1798.9298.91309559602290.0069044039771029
1898.6398.61430695420110.0156930457988977
1998.5298.5645884215023-0.0445884215022687
2098.9798.82838420238370.141615797616311
2199.7499.71113560962690.028864390373073
2299.6899.7763049732419-0.0963049732418568
2399.4599.44338597576480.00661402423524748
2498.9798.67990640778660.290093592213353
2598.6899.5808103686628-0.900810368662761
2699.0699.3536069949557-0.293606994955653
2799.8499.939252929405-0.0992529294050399
28100.399.98801144802560.311988551974395
29100.38100.1355634851840.244436514815874
30100.0299.99730131788910.022698682110871
3199.8399.9293652225701-0.0993652225700856
32100.36100.211643843280.148356156719913
33100.74101.071273600321-0.331273600320785
34100.49100.841693891438-0.35169389143752
35100.33100.352752131988-0.0227521319876587
3699.9699.64141387579560.31858612420443
37100.08100.198469798543-0.11846979854262
38100.54100.705895088176-0.165895088175887
39101.63101.4496395247970.180360475203344
40102.12101.8199801997850.300019800214685
41102.19101.9353855506140.254614449386139
42101.77101.7292449873680.0407550126317773
43101.29101.633410404347-0.343410404346528
44101.47101.82381527937-0.353815279370039
45102.07102.190663845468-0.120663845468471
46102.11102.098056012410.0119439875904277
47102.26101.9577142444580.302285755541575
48101.83101.5642676217660.265732378234034
49102.11101.9551350012140.154864998786152
50102.8102.650508584710.149491415290015
51103.82103.7412481067680.0787518932321944
52104.2104.0831417361560.116858263843753
53104.57104.0545615021030.515438497897321
54104.38103.9574708769590.422529123040519
55104.54104.0090501287790.530949871220969
56104.74104.826022062776-0.086022062776081
57105.19105.479500832865-0.289500832865329
58104.95105.316258094717-0.3662580947165
59104.57105.002021794171-0.432021794170922
60103.81104.0715424506-0.261542450600004
61104.08104.0638217708970.0161782291025645
62104.81104.6711605533080.138839446691705
63105.86105.750825746640.109174253359569
64106.1106.130524399041-0.0305243990407718
65106.24106.1173922001930.122607799807454
66105.87105.7070501792270.162949820773235
67104.74105.602565527091-0.862565527090666
68105.03105.251750828327-0.221750828326918
69105.59105.741276195827-0.151276195826895
70105.69105.6419965778130.048003422187449
71105.58105.588866222545-0.00886622254461145
72104.96104.993780712405-0.0337807124055018
73104.93105.226748293927-0.296748293927479
74105.68105.6517717004460.0282282995544136
75106.93106.646432671980.283567328019572
76107.29107.1022733219660.187726678034437
77107.25107.2831307237-0.0331307236996992
78106.74106.765640182886-0.0256401828864199
79106.44106.2081206047270.231879395273438
80106.6106.819814928972-0.219814928972127
81107.26107.34013889323-0.0801388932296163
82107.35107.3498454679150.000154532085346659
83107.22107.242520982755-0.0225209827548696
84106.99106.6190500658420.370949934157522
85107107.05826602095-0.0582660209500858
86107.74107.76290441393-0.0229044139298935
87109.02108.8195064545220.200493545477528
88109.54109.1926951875060.347304812493675
89109.71109.4188111562870.291188843713215
90109.18109.121213024180.0587869758201407
91109.23108.6918812471040.538118752895627
92109.38109.392570706782-0.0125707067815881
93110.17110.1227490525230.047250947477238
94110.15110.252871984483-0.102871984482974
95110.01110.068069030861-0.0580690308614749
96109.54109.5293800091850.010619990815087
97109.52109.591426143704-0.0714261437040307
98110.35110.3181503489970.0318496510032276
99111.61111.5106558689440.0993441310558296
100112.06111.8661551765720.193844823428108
101111.9111.969060552351-0.0690605523508623
102111.36111.3385952487580.021404751242045
103112.09111.0206967193331.06930328066694
104112.24111.9326658091230.307334190877427
105112.7112.927122876758-0.227122876757605
106113.36112.8239732086740.536026791326435
107112.9113.101352582668-0.201352582668022
108112.74112.4748258607790.265174139221088
109112.77112.6962749550830.0737250449165998
110113.66113.5853497110370.0746502889630989
111114.87114.8697697293110.000230270689414169
112114.97115.199411509447-0.229411509447004
113115114.9284879857680.0715120142324821
114114.57114.4128700100810.1571299899189
115115.54114.5079135742661.03208642573392
116115.39115.1672250150810.222774984918757
117115.46115.963009001065-0.503009001065337
118115.13115.9072187929-0.777218792900086
119114.56115.037327515317-0.477327515317342
120114.62114.3500095473350.269990452664743

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 97.44 & 96.6812336511947 & 0.758766348805324 \tabularnewline
14 & 98 & 97.7701721140528 & 0.229827885947216 \tabularnewline
15 & 98.84 & 98.7640035284329 & 0.0759964715670662 \tabularnewline
16 & 98.98 & 98.9553896245659 & 0.0246103754340936 \tabularnewline
17 & 98.92 & 98.9130955960229 & 0.0069044039771029 \tabularnewline
18 & 98.63 & 98.6143069542011 & 0.0156930457988977 \tabularnewline
19 & 98.52 & 98.5645884215023 & -0.0445884215022687 \tabularnewline
20 & 98.97 & 98.8283842023837 & 0.141615797616311 \tabularnewline
21 & 99.74 & 99.7111356096269 & 0.028864390373073 \tabularnewline
22 & 99.68 & 99.7763049732419 & -0.0963049732418568 \tabularnewline
23 & 99.45 & 99.4433859757648 & 0.00661402423524748 \tabularnewline
24 & 98.97 & 98.6799064077866 & 0.290093592213353 \tabularnewline
25 & 98.68 & 99.5808103686628 & -0.900810368662761 \tabularnewline
26 & 99.06 & 99.3536069949557 & -0.293606994955653 \tabularnewline
27 & 99.84 & 99.939252929405 & -0.0992529294050399 \tabularnewline
28 & 100.3 & 99.9880114480256 & 0.311988551974395 \tabularnewline
29 & 100.38 & 100.135563485184 & 0.244436514815874 \tabularnewline
30 & 100.02 & 99.9973013178891 & 0.022698682110871 \tabularnewline
31 & 99.83 & 99.9293652225701 & -0.0993652225700856 \tabularnewline
32 & 100.36 & 100.21164384328 & 0.148356156719913 \tabularnewline
33 & 100.74 & 101.071273600321 & -0.331273600320785 \tabularnewline
34 & 100.49 & 100.841693891438 & -0.35169389143752 \tabularnewline
35 & 100.33 & 100.352752131988 & -0.0227521319876587 \tabularnewline
36 & 99.96 & 99.6414138757956 & 0.31858612420443 \tabularnewline
37 & 100.08 & 100.198469798543 & -0.11846979854262 \tabularnewline
38 & 100.54 & 100.705895088176 & -0.165895088175887 \tabularnewline
39 & 101.63 & 101.449639524797 & 0.180360475203344 \tabularnewline
40 & 102.12 & 101.819980199785 & 0.300019800214685 \tabularnewline
41 & 102.19 & 101.935385550614 & 0.254614449386139 \tabularnewline
42 & 101.77 & 101.729244987368 & 0.0407550126317773 \tabularnewline
43 & 101.29 & 101.633410404347 & -0.343410404346528 \tabularnewline
44 & 101.47 & 101.82381527937 & -0.353815279370039 \tabularnewline
45 & 102.07 & 102.190663845468 & -0.120663845468471 \tabularnewline
46 & 102.11 & 102.09805601241 & 0.0119439875904277 \tabularnewline
47 & 102.26 & 101.957714244458 & 0.302285755541575 \tabularnewline
48 & 101.83 & 101.564267621766 & 0.265732378234034 \tabularnewline
49 & 102.11 & 101.955135001214 & 0.154864998786152 \tabularnewline
50 & 102.8 & 102.65050858471 & 0.149491415290015 \tabularnewline
51 & 103.82 & 103.741248106768 & 0.0787518932321944 \tabularnewline
52 & 104.2 & 104.083141736156 & 0.116858263843753 \tabularnewline
53 & 104.57 & 104.054561502103 & 0.515438497897321 \tabularnewline
54 & 104.38 & 103.957470876959 & 0.422529123040519 \tabularnewline
55 & 104.54 & 104.009050128779 & 0.530949871220969 \tabularnewline
56 & 104.74 & 104.826022062776 & -0.086022062776081 \tabularnewline
57 & 105.19 & 105.479500832865 & -0.289500832865329 \tabularnewline
58 & 104.95 & 105.316258094717 & -0.3662580947165 \tabularnewline
59 & 104.57 & 105.002021794171 & -0.432021794170922 \tabularnewline
60 & 103.81 & 104.0715424506 & -0.261542450600004 \tabularnewline
61 & 104.08 & 104.063821770897 & 0.0161782291025645 \tabularnewline
62 & 104.81 & 104.671160553308 & 0.138839446691705 \tabularnewline
63 & 105.86 & 105.75082574664 & 0.109174253359569 \tabularnewline
64 & 106.1 & 106.130524399041 & -0.0305243990407718 \tabularnewline
65 & 106.24 & 106.117392200193 & 0.122607799807454 \tabularnewline
66 & 105.87 & 105.707050179227 & 0.162949820773235 \tabularnewline
67 & 104.74 & 105.602565527091 & -0.862565527090666 \tabularnewline
68 & 105.03 & 105.251750828327 & -0.221750828326918 \tabularnewline
69 & 105.59 & 105.741276195827 & -0.151276195826895 \tabularnewline
70 & 105.69 & 105.641996577813 & 0.048003422187449 \tabularnewline
71 & 105.58 & 105.588866222545 & -0.00886622254461145 \tabularnewline
72 & 104.96 & 104.993780712405 & -0.0337807124055018 \tabularnewline
73 & 104.93 & 105.226748293927 & -0.296748293927479 \tabularnewline
74 & 105.68 & 105.651771700446 & 0.0282282995544136 \tabularnewline
75 & 106.93 & 106.64643267198 & 0.283567328019572 \tabularnewline
76 & 107.29 & 107.102273321966 & 0.187726678034437 \tabularnewline
77 & 107.25 & 107.2831307237 & -0.0331307236996992 \tabularnewline
78 & 106.74 & 106.765640182886 & -0.0256401828864199 \tabularnewline
79 & 106.44 & 106.208120604727 & 0.231879395273438 \tabularnewline
80 & 106.6 & 106.819814928972 & -0.219814928972127 \tabularnewline
81 & 107.26 & 107.34013889323 & -0.0801388932296163 \tabularnewline
82 & 107.35 & 107.349845467915 & 0.000154532085346659 \tabularnewline
83 & 107.22 & 107.242520982755 & -0.0225209827548696 \tabularnewline
84 & 106.99 & 106.619050065842 & 0.370949934157522 \tabularnewline
85 & 107 & 107.05826602095 & -0.0582660209500858 \tabularnewline
86 & 107.74 & 107.76290441393 & -0.0229044139298935 \tabularnewline
87 & 109.02 & 108.819506454522 & 0.200493545477528 \tabularnewline
88 & 109.54 & 109.192695187506 & 0.347304812493675 \tabularnewline
89 & 109.71 & 109.418811156287 & 0.291188843713215 \tabularnewline
90 & 109.18 & 109.12121302418 & 0.0587869758201407 \tabularnewline
91 & 109.23 & 108.691881247104 & 0.538118752895627 \tabularnewline
92 & 109.38 & 109.392570706782 & -0.0125707067815881 \tabularnewline
93 & 110.17 & 110.122749052523 & 0.047250947477238 \tabularnewline
94 & 110.15 & 110.252871984483 & -0.102871984482974 \tabularnewline
95 & 110.01 & 110.068069030861 & -0.0580690308614749 \tabularnewline
96 & 109.54 & 109.529380009185 & 0.010619990815087 \tabularnewline
97 & 109.52 & 109.591426143704 & -0.0714261437040307 \tabularnewline
98 & 110.35 & 110.318150348997 & 0.0318496510032276 \tabularnewline
99 & 111.61 & 111.510655868944 & 0.0993441310558296 \tabularnewline
100 & 112.06 & 111.866155176572 & 0.193844823428108 \tabularnewline
101 & 111.9 & 111.969060552351 & -0.0690605523508623 \tabularnewline
102 & 111.36 & 111.338595248758 & 0.021404751242045 \tabularnewline
103 & 112.09 & 111.020696719333 & 1.06930328066694 \tabularnewline
104 & 112.24 & 111.932665809123 & 0.307334190877427 \tabularnewline
105 & 112.7 & 112.927122876758 & -0.227122876757605 \tabularnewline
106 & 113.36 & 112.823973208674 & 0.536026791326435 \tabularnewline
107 & 112.9 & 113.101352582668 & -0.201352582668022 \tabularnewline
108 & 112.74 & 112.474825860779 & 0.265174139221088 \tabularnewline
109 & 112.77 & 112.696274955083 & 0.0737250449165998 \tabularnewline
110 & 113.66 & 113.585349711037 & 0.0746502889630989 \tabularnewline
111 & 114.87 & 114.869769729311 & 0.000230270689414169 \tabularnewline
112 & 114.97 & 115.199411509447 & -0.229411509447004 \tabularnewline
113 & 115 & 114.928487985768 & 0.0715120142324821 \tabularnewline
114 & 114.57 & 114.412870010081 & 0.1571299899189 \tabularnewline
115 & 115.54 & 114.507913574266 & 1.03208642573392 \tabularnewline
116 & 115.39 & 115.167225015081 & 0.222774984918757 \tabularnewline
117 & 115.46 & 115.963009001065 & -0.503009001065337 \tabularnewline
118 & 115.13 & 115.9072187929 & -0.777218792900086 \tabularnewline
119 & 114.56 & 115.037327515317 & -0.477327515317342 \tabularnewline
120 & 114.62 & 114.350009547335 & 0.269990452664743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278470&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]13[/C][C]97.44[/C][C]96.6812336511947[/C][C]0.758766348805324[/C][/ROW]
[ROW][C]14[/C][C]98[/C][C]97.7701721140528[/C][C]0.229827885947216[/C][/ROW]
[ROW][C]15[/C][C]98.84[/C][C]98.7640035284329[/C][C]0.0759964715670662[/C][/ROW]
[ROW][C]16[/C][C]98.98[/C][C]98.9553896245659[/C][C]0.0246103754340936[/C][/ROW]
[ROW][C]17[/C][C]98.92[/C][C]98.9130955960229[/C][C]0.0069044039771029[/C][/ROW]
[ROW][C]18[/C][C]98.63[/C][C]98.6143069542011[/C][C]0.0156930457988977[/C][/ROW]
[ROW][C]19[/C][C]98.52[/C][C]98.5645884215023[/C][C]-0.0445884215022687[/C][/ROW]
[ROW][C]20[/C][C]98.97[/C][C]98.8283842023837[/C][C]0.141615797616311[/C][/ROW]
[ROW][C]21[/C][C]99.74[/C][C]99.7111356096269[/C][C]0.028864390373073[/C][/ROW]
[ROW][C]22[/C][C]99.68[/C][C]99.7763049732419[/C][C]-0.0963049732418568[/C][/ROW]
[ROW][C]23[/C][C]99.45[/C][C]99.4433859757648[/C][C]0.00661402423524748[/C][/ROW]
[ROW][C]24[/C][C]98.97[/C][C]98.6799064077866[/C][C]0.290093592213353[/C][/ROW]
[ROW][C]25[/C][C]98.68[/C][C]99.5808103686628[/C][C]-0.900810368662761[/C][/ROW]
[ROW][C]26[/C][C]99.06[/C][C]99.3536069949557[/C][C]-0.293606994955653[/C][/ROW]
[ROW][C]27[/C][C]99.84[/C][C]99.939252929405[/C][C]-0.0992529294050399[/C][/ROW]
[ROW][C]28[/C][C]100.3[/C][C]99.9880114480256[/C][C]0.311988551974395[/C][/ROW]
[ROW][C]29[/C][C]100.38[/C][C]100.135563485184[/C][C]0.244436514815874[/C][/ROW]
[ROW][C]30[/C][C]100.02[/C][C]99.9973013178891[/C][C]0.022698682110871[/C][/ROW]
[ROW][C]31[/C][C]99.83[/C][C]99.9293652225701[/C][C]-0.0993652225700856[/C][/ROW]
[ROW][C]32[/C][C]100.36[/C][C]100.21164384328[/C][C]0.148356156719913[/C][/ROW]
[ROW][C]33[/C][C]100.74[/C][C]101.071273600321[/C][C]-0.331273600320785[/C][/ROW]
[ROW][C]34[/C][C]100.49[/C][C]100.841693891438[/C][C]-0.35169389143752[/C][/ROW]
[ROW][C]35[/C][C]100.33[/C][C]100.352752131988[/C][C]-0.0227521319876587[/C][/ROW]
[ROW][C]36[/C][C]99.96[/C][C]99.6414138757956[/C][C]0.31858612420443[/C][/ROW]
[ROW][C]37[/C][C]100.08[/C][C]100.198469798543[/C][C]-0.11846979854262[/C][/ROW]
[ROW][C]38[/C][C]100.54[/C][C]100.705895088176[/C][C]-0.165895088175887[/C][/ROW]
[ROW][C]39[/C][C]101.63[/C][C]101.449639524797[/C][C]0.180360475203344[/C][/ROW]
[ROW][C]40[/C][C]102.12[/C][C]101.819980199785[/C][C]0.300019800214685[/C][/ROW]
[ROW][C]41[/C][C]102.19[/C][C]101.935385550614[/C][C]0.254614449386139[/C][/ROW]
[ROW][C]42[/C][C]101.77[/C][C]101.729244987368[/C][C]0.0407550126317773[/C][/ROW]
[ROW][C]43[/C][C]101.29[/C][C]101.633410404347[/C][C]-0.343410404346528[/C][/ROW]
[ROW][C]44[/C][C]101.47[/C][C]101.82381527937[/C][C]-0.353815279370039[/C][/ROW]
[ROW][C]45[/C][C]102.07[/C][C]102.190663845468[/C][C]-0.120663845468471[/C][/ROW]
[ROW][C]46[/C][C]102.11[/C][C]102.09805601241[/C][C]0.0119439875904277[/C][/ROW]
[ROW][C]47[/C][C]102.26[/C][C]101.957714244458[/C][C]0.302285755541575[/C][/ROW]
[ROW][C]48[/C][C]101.83[/C][C]101.564267621766[/C][C]0.265732378234034[/C][/ROW]
[ROW][C]49[/C][C]102.11[/C][C]101.955135001214[/C][C]0.154864998786152[/C][/ROW]
[ROW][C]50[/C][C]102.8[/C][C]102.65050858471[/C][C]0.149491415290015[/C][/ROW]
[ROW][C]51[/C][C]103.82[/C][C]103.741248106768[/C][C]0.0787518932321944[/C][/ROW]
[ROW][C]52[/C][C]104.2[/C][C]104.083141736156[/C][C]0.116858263843753[/C][/ROW]
[ROW][C]53[/C][C]104.57[/C][C]104.054561502103[/C][C]0.515438497897321[/C][/ROW]
[ROW][C]54[/C][C]104.38[/C][C]103.957470876959[/C][C]0.422529123040519[/C][/ROW]
[ROW][C]55[/C][C]104.54[/C][C]104.009050128779[/C][C]0.530949871220969[/C][/ROW]
[ROW][C]56[/C][C]104.74[/C][C]104.826022062776[/C][C]-0.086022062776081[/C][/ROW]
[ROW][C]57[/C][C]105.19[/C][C]105.479500832865[/C][C]-0.289500832865329[/C][/ROW]
[ROW][C]58[/C][C]104.95[/C][C]105.316258094717[/C][C]-0.3662580947165[/C][/ROW]
[ROW][C]59[/C][C]104.57[/C][C]105.002021794171[/C][C]-0.432021794170922[/C][/ROW]
[ROW][C]60[/C][C]103.81[/C][C]104.0715424506[/C][C]-0.261542450600004[/C][/ROW]
[ROW][C]61[/C][C]104.08[/C][C]104.063821770897[/C][C]0.0161782291025645[/C][/ROW]
[ROW][C]62[/C][C]104.81[/C][C]104.671160553308[/C][C]0.138839446691705[/C][/ROW]
[ROW][C]63[/C][C]105.86[/C][C]105.75082574664[/C][C]0.109174253359569[/C][/ROW]
[ROW][C]64[/C][C]106.1[/C][C]106.130524399041[/C][C]-0.0305243990407718[/C][/ROW]
[ROW][C]65[/C][C]106.24[/C][C]106.117392200193[/C][C]0.122607799807454[/C][/ROW]
[ROW][C]66[/C][C]105.87[/C][C]105.707050179227[/C][C]0.162949820773235[/C][/ROW]
[ROW][C]67[/C][C]104.74[/C][C]105.602565527091[/C][C]-0.862565527090666[/C][/ROW]
[ROW][C]68[/C][C]105.03[/C][C]105.251750828327[/C][C]-0.221750828326918[/C][/ROW]
[ROW][C]69[/C][C]105.59[/C][C]105.741276195827[/C][C]-0.151276195826895[/C][/ROW]
[ROW][C]70[/C][C]105.69[/C][C]105.641996577813[/C][C]0.048003422187449[/C][/ROW]
[ROW][C]71[/C][C]105.58[/C][C]105.588866222545[/C][C]-0.00886622254461145[/C][/ROW]
[ROW][C]72[/C][C]104.96[/C][C]104.993780712405[/C][C]-0.0337807124055018[/C][/ROW]
[ROW][C]73[/C][C]104.93[/C][C]105.226748293927[/C][C]-0.296748293927479[/C][/ROW]
[ROW][C]74[/C][C]105.68[/C][C]105.651771700446[/C][C]0.0282282995544136[/C][/ROW]
[ROW][C]75[/C][C]106.93[/C][C]106.64643267198[/C][C]0.283567328019572[/C][/ROW]
[ROW][C]76[/C][C]107.29[/C][C]107.102273321966[/C][C]0.187726678034437[/C][/ROW]
[ROW][C]77[/C][C]107.25[/C][C]107.2831307237[/C][C]-0.0331307236996992[/C][/ROW]
[ROW][C]78[/C][C]106.74[/C][C]106.765640182886[/C][C]-0.0256401828864199[/C][/ROW]
[ROW][C]79[/C][C]106.44[/C][C]106.208120604727[/C][C]0.231879395273438[/C][/ROW]
[ROW][C]80[/C][C]106.6[/C][C]106.819814928972[/C][C]-0.219814928972127[/C][/ROW]
[ROW][C]81[/C][C]107.26[/C][C]107.34013889323[/C][C]-0.0801388932296163[/C][/ROW]
[ROW][C]82[/C][C]107.35[/C][C]107.349845467915[/C][C]0.000154532085346659[/C][/ROW]
[ROW][C]83[/C][C]107.22[/C][C]107.242520982755[/C][C]-0.0225209827548696[/C][/ROW]
[ROW][C]84[/C][C]106.99[/C][C]106.619050065842[/C][C]0.370949934157522[/C][/ROW]
[ROW][C]85[/C][C]107[/C][C]107.05826602095[/C][C]-0.0582660209500858[/C][/ROW]
[ROW][C]86[/C][C]107.74[/C][C]107.76290441393[/C][C]-0.0229044139298935[/C][/ROW]
[ROW][C]87[/C][C]109.02[/C][C]108.819506454522[/C][C]0.200493545477528[/C][/ROW]
[ROW][C]88[/C][C]109.54[/C][C]109.192695187506[/C][C]0.347304812493675[/C][/ROW]
[ROW][C]89[/C][C]109.71[/C][C]109.418811156287[/C][C]0.291188843713215[/C][/ROW]
[ROW][C]90[/C][C]109.18[/C][C]109.12121302418[/C][C]0.0587869758201407[/C][/ROW]
[ROW][C]91[/C][C]109.23[/C][C]108.691881247104[/C][C]0.538118752895627[/C][/ROW]
[ROW][C]92[/C][C]109.38[/C][C]109.392570706782[/C][C]-0.0125707067815881[/C][/ROW]
[ROW][C]93[/C][C]110.17[/C][C]110.122749052523[/C][C]0.047250947477238[/C][/ROW]
[ROW][C]94[/C][C]110.15[/C][C]110.252871984483[/C][C]-0.102871984482974[/C][/ROW]
[ROW][C]95[/C][C]110.01[/C][C]110.068069030861[/C][C]-0.0580690308614749[/C][/ROW]
[ROW][C]96[/C][C]109.54[/C][C]109.529380009185[/C][C]0.010619990815087[/C][/ROW]
[ROW][C]97[/C][C]109.52[/C][C]109.591426143704[/C][C]-0.0714261437040307[/C][/ROW]
[ROW][C]98[/C][C]110.35[/C][C]110.318150348997[/C][C]0.0318496510032276[/C][/ROW]
[ROW][C]99[/C][C]111.61[/C][C]111.510655868944[/C][C]0.0993441310558296[/C][/ROW]
[ROW][C]100[/C][C]112.06[/C][C]111.866155176572[/C][C]0.193844823428108[/C][/ROW]
[ROW][C]101[/C][C]111.9[/C][C]111.969060552351[/C][C]-0.0690605523508623[/C][/ROW]
[ROW][C]102[/C][C]111.36[/C][C]111.338595248758[/C][C]0.021404751242045[/C][/ROW]
[ROW][C]103[/C][C]112.09[/C][C]111.020696719333[/C][C]1.06930328066694[/C][/ROW]
[ROW][C]104[/C][C]112.24[/C][C]111.932665809123[/C][C]0.307334190877427[/C][/ROW]
[ROW][C]105[/C][C]112.7[/C][C]112.927122876758[/C][C]-0.227122876757605[/C][/ROW]
[ROW][C]106[/C][C]113.36[/C][C]112.823973208674[/C][C]0.536026791326435[/C][/ROW]
[ROW][C]107[/C][C]112.9[/C][C]113.101352582668[/C][C]-0.201352582668022[/C][/ROW]
[ROW][C]108[/C][C]112.74[/C][C]112.474825860779[/C][C]0.265174139221088[/C][/ROW]
[ROW][C]109[/C][C]112.77[/C][C]112.696274955083[/C][C]0.0737250449165998[/C][/ROW]
[ROW][C]110[/C][C]113.66[/C][C]113.585349711037[/C][C]0.0746502889630989[/C][/ROW]
[ROW][C]111[/C][C]114.87[/C][C]114.869769729311[/C][C]0.000230270689414169[/C][/ROW]
[ROW][C]112[/C][C]114.97[/C][C]115.199411509447[/C][C]-0.229411509447004[/C][/ROW]
[ROW][C]113[/C][C]115[/C][C]114.928487985768[/C][C]0.0715120142324821[/C][/ROW]
[ROW][C]114[/C][C]114.57[/C][C]114.412870010081[/C][C]0.1571299899189[/C][/ROW]
[ROW][C]115[/C][C]115.54[/C][C]114.507913574266[/C][C]1.03208642573392[/C][/ROW]
[ROW][C]116[/C][C]115.39[/C][C]115.167225015081[/C][C]0.222774984918757[/C][/ROW]
[ROW][C]117[/C][C]115.46[/C][C]115.963009001065[/C][C]-0.503009001065337[/C][/ROW]
[ROW][C]118[/C][C]115.13[/C][C]115.9072187929[/C][C]-0.777218792900086[/C][/ROW]
[ROW][C]119[/C][C]114.56[/C][C]115.037327515317[/C][C]-0.477327515317342[/C][/ROW]
[ROW][C]120[/C][C]114.62[/C][C]114.350009547335[/C][C]0.269990452664743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278470&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278470&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
1397.4496.68123365119470.758766348805324
149897.77017211405280.229827885947216
1598.8498.76400352843290.0759964715670662
1698.9898.95538962456590.0246103754340936
1798.9298.91309559602290.0069044039771029
1898.6398.61430695420110.0156930457988977
1998.5298.5645884215023-0.0445884215022687
2098.9798.82838420238370.141615797616311
2199.7499.71113560962690.028864390373073
2299.6899.7763049732419-0.0963049732418568
2399.4599.44338597576480.00661402423524748
2498.9798.67990640778660.290093592213353
2598.6899.5808103686628-0.900810368662761
2699.0699.3536069949557-0.293606994955653
2799.8499.939252929405-0.0992529294050399
28100.399.98801144802560.311988551974395
29100.38100.1355634851840.244436514815874
30100.0299.99730131788910.022698682110871
3199.8399.9293652225701-0.0993652225700856
32100.36100.211643843280.148356156719913
33100.74101.071273600321-0.331273600320785
34100.49100.841693891438-0.35169389143752
35100.33100.352752131988-0.0227521319876587
3699.9699.64141387579560.31858612420443
37100.08100.198469798543-0.11846979854262
38100.54100.705895088176-0.165895088175887
39101.63101.4496395247970.180360475203344
40102.12101.8199801997850.300019800214685
41102.19101.9353855506140.254614449386139
42101.77101.7292449873680.0407550126317773
43101.29101.633410404347-0.343410404346528
44101.47101.82381527937-0.353815279370039
45102.07102.190663845468-0.120663845468471
46102.11102.098056012410.0119439875904277
47102.26101.9577142444580.302285755541575
48101.83101.5642676217660.265732378234034
49102.11101.9551350012140.154864998786152
50102.8102.650508584710.149491415290015
51103.82103.7412481067680.0787518932321944
52104.2104.0831417361560.116858263843753
53104.57104.0545615021030.515438497897321
54104.38103.9574708769590.422529123040519
55104.54104.0090501287790.530949871220969
56104.74104.826022062776-0.086022062776081
57105.19105.479500832865-0.289500832865329
58104.95105.316258094717-0.3662580947165
59104.57105.002021794171-0.432021794170922
60103.81104.0715424506-0.261542450600004
61104.08104.0638217708970.0161782291025645
62104.81104.6711605533080.138839446691705
63105.86105.750825746640.109174253359569
64106.1106.130524399041-0.0305243990407718
65106.24106.1173922001930.122607799807454
66105.87105.7070501792270.162949820773235
67104.74105.602565527091-0.862565527090666
68105.03105.251750828327-0.221750828326918
69105.59105.741276195827-0.151276195826895
70105.69105.6419965778130.048003422187449
71105.58105.588866222545-0.00886622254461145
72104.96104.993780712405-0.0337807124055018
73104.93105.226748293927-0.296748293927479
74105.68105.6517717004460.0282282995544136
75106.93106.646432671980.283567328019572
76107.29107.1022733219660.187726678034437
77107.25107.2831307237-0.0331307236996992
78106.74106.765640182886-0.0256401828864199
79106.44106.2081206047270.231879395273438
80106.6106.819814928972-0.219814928972127
81107.26107.34013889323-0.0801388932296163
82107.35107.3498454679150.000154532085346659
83107.22107.242520982755-0.0225209827548696
84106.99106.6190500658420.370949934157522
85107107.05826602095-0.0582660209500858
86107.74107.76290441393-0.0229044139298935
87109.02108.8195064545220.200493545477528
88109.54109.1926951875060.347304812493675
89109.71109.4188111562870.291188843713215
90109.18109.121213024180.0587869758201407
91109.23108.6918812471040.538118752895627
92109.38109.392570706782-0.0125707067815881
93110.17110.1227490525230.047250947477238
94110.15110.252871984483-0.102871984482974
95110.01110.068069030861-0.0580690308614749
96109.54109.5293800091850.010619990815087
97109.52109.591426143704-0.0714261437040307
98110.35110.3181503489970.0318496510032276
99111.61111.5106558689440.0993441310558296
100112.06111.8661551765720.193844823428108
101111.9111.969060552351-0.0690605523508623
102111.36111.3385952487580.021404751242045
103112.09111.0206967193331.06930328066694
104112.24111.9326658091230.307334190877427
105112.7112.927122876758-0.227122876757605
106113.36112.8239732086740.536026791326435
107112.9113.101352582668-0.201352582668022
108112.74112.4748258607790.265174139221088
109112.77112.6962749550830.0737250449165998
110113.66113.5853497110370.0746502889630989
111114.87114.8697697293110.000230270689414169
112114.97115.199411509447-0.229411509447004
113115114.9284879857680.0715120142324821
114114.57114.4128700100810.1571299899189
115115.54114.5079135742661.03208642573392
116115.39115.1672250150810.222774984918757
117115.46115.963009001065-0.503009001065337
118115.13115.9072187929-0.777218792900086
119114.56115.037327515317-0.477327515317342
120114.62114.3500095473350.269990452664743







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121114.513992079475113.915494023906115.112490135044
122115.361654681601114.62836516772116.094944195483
123116.586162116499115.735126924502117.437197308496
124116.846818123818115.894093896578117.799542351059
125116.82399066138115.779770879336117.868210443425
126116.272797117729115.147293681648117.39830055381
127116.519903515781115.312289883021117.72751714854
128116.204068603555114.923315080494117.484822126617
129116.619706850015115.262574242761117.976839457268
130116.827464926438115.398880513243118.256049339633
131116.583828926992115.091115569165118.07654228482
132116.451398625416112.311910307691120.590886943141

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 114.513992079475 & 113.915494023906 & 115.112490135044 \tabularnewline
122 & 115.361654681601 & 114.62836516772 & 116.094944195483 \tabularnewline
123 & 116.586162116499 & 115.735126924502 & 117.437197308496 \tabularnewline
124 & 116.846818123818 & 115.894093896578 & 117.799542351059 \tabularnewline
125 & 116.82399066138 & 115.779770879336 & 117.868210443425 \tabularnewline
126 & 116.272797117729 & 115.147293681648 & 117.39830055381 \tabularnewline
127 & 116.519903515781 & 115.312289883021 & 117.72751714854 \tabularnewline
128 & 116.204068603555 & 114.923315080494 & 117.484822126617 \tabularnewline
129 & 116.619706850015 & 115.262574242761 & 117.976839457268 \tabularnewline
130 & 116.827464926438 & 115.398880513243 & 118.256049339633 \tabularnewline
131 & 116.583828926992 & 115.091115569165 & 118.07654228482 \tabularnewline
132 & 116.451398625416 & 112.311910307691 & 120.590886943141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278470&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]121[/C][C]114.513992079475[/C][C]113.915494023906[/C][C]115.112490135044[/C][/ROW]
[ROW][C]122[/C][C]115.361654681601[/C][C]114.62836516772[/C][C]116.094944195483[/C][/ROW]
[ROW][C]123[/C][C]116.586162116499[/C][C]115.735126924502[/C][C]117.437197308496[/C][/ROW]
[ROW][C]124[/C][C]116.846818123818[/C][C]115.894093896578[/C][C]117.799542351059[/C][/ROW]
[ROW][C]125[/C][C]116.82399066138[/C][C]115.779770879336[/C][C]117.868210443425[/C][/ROW]
[ROW][C]126[/C][C]116.272797117729[/C][C]115.147293681648[/C][C]117.39830055381[/C][/ROW]
[ROW][C]127[/C][C]116.519903515781[/C][C]115.312289883021[/C][C]117.72751714854[/C][/ROW]
[ROW][C]128[/C][C]116.204068603555[/C][C]114.923315080494[/C][C]117.484822126617[/C][/ROW]
[ROW][C]129[/C][C]116.619706850015[/C][C]115.262574242761[/C][C]117.976839457268[/C][/ROW]
[ROW][C]130[/C][C]116.827464926438[/C][C]115.398880513243[/C][C]118.256049339633[/C][/ROW]
[ROW][C]131[/C][C]116.583828926992[/C][C]115.091115569165[/C][C]118.07654228482[/C][/ROW]
[ROW][C]132[/C][C]116.451398625416[/C][C]112.311910307691[/C][C]120.590886943141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278470&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278470&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
121114.513992079475113.915494023906115.112490135044
122115.361654681601114.62836516772116.094944195483
123116.586162116499115.735126924502117.437197308496
124116.846818123818115.894093896578117.799542351059
125116.82399066138115.779770879336117.868210443425
126116.272797117729115.147293681648117.39830055381
127116.519903515781115.312289883021117.72751714854
128116.204068603555114.923315080494117.484822126617
129116.619706850015115.262574242761117.976839457268
130116.827464926438115.398880513243118.256049339633
131116.583828926992115.091115569165118.07654228482
132116.451398625416112.311910307691120.590886943141



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')