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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 10 Apr 2015 13:09:40 +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/10/t14286679525i2i8oy1utu0ocf.htm/, Retrieved Thu, 09 May 2024 10:28:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278705, Retrieved Thu, 09 May 2024 10:28:46 +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] [exponential smoot...] [2015-04-10 12:09:40] [b81b5adcb18a6dd731e9cb79a54989dd] [Current]
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Dataseries X:
101.94
102.62
102.71
103.39
104.51
104.09
104.29
104.57
105.39
105.15
106.13
105.46
106.47
106.62
106.52
108.04
107.15
107.32
107.76
107.26
107.89
109.08
110.4
111.03
112.05
112.28
112.8
114.17
114.92
114.65
115.49
114.67
114.71
115.15
115.03
115.07
116.46
116.37
116.2
116.5
116.38
115.44
114.96
114.48
114.3
114.66
114.97
114.79
116.16
116.52
117.14
117.27
117.58
117.21
117.08
117.06
117.55
117.61
117.74
117.87
118.59
119.09
118.93
119.62
120.09
120.38
120.49
120.02
120.17
120.58
121.54
121.51
121.81
122.85
122.97
122.96
123.4
123.23
123.24
123.72
123.99
125.1
125.4
125.35
126.37
127.17
127.66
128.48
129.21
129.48
128.63
128.16
128.1
128.08
128.14
128.19




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=278705&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=278705&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278705&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
alpha0.999952363504392
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999952363504392 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278705&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]0.999952363504392[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278705&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278705&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
alpha0.999952363504392
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2102.62101.940.680000000000007
3102.71102.6199676071830.0900323928170081
4103.39102.7099957111720.680004288827689
5104.51103.3899676069791.12003239302132
6104.09104.509946645582-0.419946645581831
7104.29104.0900200047870.199979995213468
8104.57104.2899904736540.280009526346149
9105.39104.5699866613270.820013338672581
10105.15105.389960937438-0.239960937438184
11106.13105.1500114308980.979988569101849
12105.46106.129953316779-0.66995331677883
13106.47105.4600319142281.00996808577177
14106.62106.469951888660.150048111340297
15106.52106.619992852234-0.0999928522338109
16108.04106.5200047633091.51999523669095
17107.15108.039927592754-0.88992759275358
18107.32107.1500423930320.169957606968126
19107.76107.3199919038150.440008096184812
20107.26107.759979039556-0.499979039556251
21107.89107.2600238172490.629976182750667
22109.08107.8899699901421.19003000985765
23110.4109.0799433111411.32005668885934
24111.03110.3999371171250.630062882874654
25112.05111.0299699860121.02003001398775
26112.28112.0499514093450.230048590655286
27112.8112.2799890412910.520010958708667
28114.17112.79997522851.37002477149974
29114.92114.1699347368210.75006526317901
30114.65114.919964269519-0.269964269519377
31115.49114.6500128601520.839987139848247
32114.67115.489959985956-0.819959985956288
33114.71114.670039060020.0399609399797214
34115.15114.7099980964010.440001903599153
35115.03115.149979039851-0.119979039851259
36115.07115.0300057153810.0399942846189845
37116.46115.0699980948121.39000190518756
38116.37116.45993378518-0.0899337851803494
39116.2116.37000428413-0.170004284130357
40116.5116.2000080984080.299991901591653
41116.38116.499985709437-0.119985709437103
42115.44116.380005715699-0.940005715698732
43114.96115.440044778578-0.480044778578147
44114.48114.960022867651-0.480022867650973
45114.3114.480022866607-0.180022866607231
46114.66114.3000085756580.359991424341501
47114.97114.659982851270.310017148729912
48114.79114.969985231869-0.179985231869438
49116.16114.7900085738661.36999142613428
50116.52116.1599347384090.360065261590549
51117.14116.5199828477530.620017152247257
52117.27117.1399704645560.130029535444351
53117.58117.2699938058490.310006194151384
54117.21117.579985232391-0.369985232391301
55117.08117.2100176248-0.130017624799891
56117.06117.080006193584-0.0200061935839955
57117.55117.0600009530250.489999046975043
58117.61117.5499766581630.0600233418374501
59117.74117.6099971406980.130002859301655
60117.87117.7399938071190.130006192880657
61118.59117.8699938069610.720006193039438
62119.09118.5899657014280.500034298571862
63118.93119.089976180118-0.159976180118335
64119.62118.9300076207050.68999237929539
65120.09119.6199671311810.470032868818947
66120.38120.0899776092810.290022390718676
67120.49120.379986184350.110013815650333
68120.02120.489994759327-0.469994759327349
69120.17120.0200223889030.149977611096716
70120.58120.1699928555920.410007144407814
71121.54120.5799804686960.960019531303544
72121.51121.539954268034-0.0299542680338192
73121.81121.5100014269160.299998573083641
74122.85121.8099857091191.04001429088071
75122.97122.8499504573640.120049542636195
76122.96122.96999428126-0.0099942812604894
77123.4122.9600004760930.439999523907474
78123.23123.399979039965-0.169979039964616
79123.24123.2300080972060.00999190279419793
80123.72123.2399995240210.480000475979239
81123.99123.7199771344590.270022865540568
82125.1123.9899871370571.11001286294305
83125.4125.0999471228770.30005287712288
84125.35125.399985706532-0.0499857065324534
85126.37125.3500023811441.01999761885612
86127.17126.3699514108880.80004858911208
87127.66127.1699618884890.490038111511083
88128.48127.6599766563020.820023343698338
89129.21128.4799609369620.730039063038447
90129.48129.2099652234970.270034776502598
91128.63129.47998713649-0.849987136489545
92128.16128.630040490409-0.470040490408508
93128.1128.160022391082-0.060022391081759
94128.08128.100002859256-0.0200028592563513
95128.14128.0800009528660.0599990471338572
96128.19128.1399971418560.050002858144353

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 102.62 & 101.94 & 0.680000000000007 \tabularnewline
3 & 102.71 & 102.619967607183 & 0.0900323928170081 \tabularnewline
4 & 103.39 & 102.709995711172 & 0.680004288827689 \tabularnewline
5 & 104.51 & 103.389967606979 & 1.12003239302132 \tabularnewline
6 & 104.09 & 104.509946645582 & -0.419946645581831 \tabularnewline
7 & 104.29 & 104.090020004787 & 0.199979995213468 \tabularnewline
8 & 104.57 & 104.289990473654 & 0.280009526346149 \tabularnewline
9 & 105.39 & 104.569986661327 & 0.820013338672581 \tabularnewline
10 & 105.15 & 105.389960937438 & -0.239960937438184 \tabularnewline
11 & 106.13 & 105.150011430898 & 0.979988569101849 \tabularnewline
12 & 105.46 & 106.129953316779 & -0.66995331677883 \tabularnewline
13 & 106.47 & 105.460031914228 & 1.00996808577177 \tabularnewline
14 & 106.62 & 106.46995188866 & 0.150048111340297 \tabularnewline
15 & 106.52 & 106.619992852234 & -0.0999928522338109 \tabularnewline
16 & 108.04 & 106.520004763309 & 1.51999523669095 \tabularnewline
17 & 107.15 & 108.039927592754 & -0.88992759275358 \tabularnewline
18 & 107.32 & 107.150042393032 & 0.169957606968126 \tabularnewline
19 & 107.76 & 107.319991903815 & 0.440008096184812 \tabularnewline
20 & 107.26 & 107.759979039556 & -0.499979039556251 \tabularnewline
21 & 107.89 & 107.260023817249 & 0.629976182750667 \tabularnewline
22 & 109.08 & 107.889969990142 & 1.19003000985765 \tabularnewline
23 & 110.4 & 109.079943311141 & 1.32005668885934 \tabularnewline
24 & 111.03 & 110.399937117125 & 0.630062882874654 \tabularnewline
25 & 112.05 & 111.029969986012 & 1.02003001398775 \tabularnewline
26 & 112.28 & 112.049951409345 & 0.230048590655286 \tabularnewline
27 & 112.8 & 112.279989041291 & 0.520010958708667 \tabularnewline
28 & 114.17 & 112.7999752285 & 1.37002477149974 \tabularnewline
29 & 114.92 & 114.169934736821 & 0.75006526317901 \tabularnewline
30 & 114.65 & 114.919964269519 & -0.269964269519377 \tabularnewline
31 & 115.49 & 114.650012860152 & 0.839987139848247 \tabularnewline
32 & 114.67 & 115.489959985956 & -0.819959985956288 \tabularnewline
33 & 114.71 & 114.67003906002 & 0.0399609399797214 \tabularnewline
34 & 115.15 & 114.709998096401 & 0.440001903599153 \tabularnewline
35 & 115.03 & 115.149979039851 & -0.119979039851259 \tabularnewline
36 & 115.07 & 115.030005715381 & 0.0399942846189845 \tabularnewline
37 & 116.46 & 115.069998094812 & 1.39000190518756 \tabularnewline
38 & 116.37 & 116.45993378518 & -0.0899337851803494 \tabularnewline
39 & 116.2 & 116.37000428413 & -0.170004284130357 \tabularnewline
40 & 116.5 & 116.200008098408 & 0.299991901591653 \tabularnewline
41 & 116.38 & 116.499985709437 & -0.119985709437103 \tabularnewline
42 & 115.44 & 116.380005715699 & -0.940005715698732 \tabularnewline
43 & 114.96 & 115.440044778578 & -0.480044778578147 \tabularnewline
44 & 114.48 & 114.960022867651 & -0.480022867650973 \tabularnewline
45 & 114.3 & 114.480022866607 & -0.180022866607231 \tabularnewline
46 & 114.66 & 114.300008575658 & 0.359991424341501 \tabularnewline
47 & 114.97 & 114.65998285127 & 0.310017148729912 \tabularnewline
48 & 114.79 & 114.969985231869 & -0.179985231869438 \tabularnewline
49 & 116.16 & 114.790008573866 & 1.36999142613428 \tabularnewline
50 & 116.52 & 116.159934738409 & 0.360065261590549 \tabularnewline
51 & 117.14 & 116.519982847753 & 0.620017152247257 \tabularnewline
52 & 117.27 & 117.139970464556 & 0.130029535444351 \tabularnewline
53 & 117.58 & 117.269993805849 & 0.310006194151384 \tabularnewline
54 & 117.21 & 117.579985232391 & -0.369985232391301 \tabularnewline
55 & 117.08 & 117.2100176248 & -0.130017624799891 \tabularnewline
56 & 117.06 & 117.080006193584 & -0.0200061935839955 \tabularnewline
57 & 117.55 & 117.060000953025 & 0.489999046975043 \tabularnewline
58 & 117.61 & 117.549976658163 & 0.0600233418374501 \tabularnewline
59 & 117.74 & 117.609997140698 & 0.130002859301655 \tabularnewline
60 & 117.87 & 117.739993807119 & 0.130006192880657 \tabularnewline
61 & 118.59 & 117.869993806961 & 0.720006193039438 \tabularnewline
62 & 119.09 & 118.589965701428 & 0.500034298571862 \tabularnewline
63 & 118.93 & 119.089976180118 & -0.159976180118335 \tabularnewline
64 & 119.62 & 118.930007620705 & 0.68999237929539 \tabularnewline
65 & 120.09 & 119.619967131181 & 0.470032868818947 \tabularnewline
66 & 120.38 & 120.089977609281 & 0.290022390718676 \tabularnewline
67 & 120.49 & 120.37998618435 & 0.110013815650333 \tabularnewline
68 & 120.02 & 120.489994759327 & -0.469994759327349 \tabularnewline
69 & 120.17 & 120.020022388903 & 0.149977611096716 \tabularnewline
70 & 120.58 & 120.169992855592 & 0.410007144407814 \tabularnewline
71 & 121.54 & 120.579980468696 & 0.960019531303544 \tabularnewline
72 & 121.51 & 121.539954268034 & -0.0299542680338192 \tabularnewline
73 & 121.81 & 121.510001426916 & 0.299998573083641 \tabularnewline
74 & 122.85 & 121.809985709119 & 1.04001429088071 \tabularnewline
75 & 122.97 & 122.849950457364 & 0.120049542636195 \tabularnewline
76 & 122.96 & 122.96999428126 & -0.0099942812604894 \tabularnewline
77 & 123.4 & 122.960000476093 & 0.439999523907474 \tabularnewline
78 & 123.23 & 123.399979039965 & -0.169979039964616 \tabularnewline
79 & 123.24 & 123.230008097206 & 0.00999190279419793 \tabularnewline
80 & 123.72 & 123.239999524021 & 0.480000475979239 \tabularnewline
81 & 123.99 & 123.719977134459 & 0.270022865540568 \tabularnewline
82 & 125.1 & 123.989987137057 & 1.11001286294305 \tabularnewline
83 & 125.4 & 125.099947122877 & 0.30005287712288 \tabularnewline
84 & 125.35 & 125.399985706532 & -0.0499857065324534 \tabularnewline
85 & 126.37 & 125.350002381144 & 1.01999761885612 \tabularnewline
86 & 127.17 & 126.369951410888 & 0.80004858911208 \tabularnewline
87 & 127.66 & 127.169961888489 & 0.490038111511083 \tabularnewline
88 & 128.48 & 127.659976656302 & 0.820023343698338 \tabularnewline
89 & 129.21 & 128.479960936962 & 0.730039063038447 \tabularnewline
90 & 129.48 & 129.209965223497 & 0.270034776502598 \tabularnewline
91 & 128.63 & 129.47998713649 & -0.849987136489545 \tabularnewline
92 & 128.16 & 128.630040490409 & -0.470040490408508 \tabularnewline
93 & 128.1 & 128.160022391082 & -0.060022391081759 \tabularnewline
94 & 128.08 & 128.100002859256 & -0.0200028592563513 \tabularnewline
95 & 128.14 & 128.080000952866 & 0.0599990471338572 \tabularnewline
96 & 128.19 & 128.139997141856 & 0.050002858144353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278705&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]102.62[/C][C]101.94[/C][C]0.680000000000007[/C][/ROW]
[ROW][C]3[/C][C]102.71[/C][C]102.619967607183[/C][C]0.0900323928170081[/C][/ROW]
[ROW][C]4[/C][C]103.39[/C][C]102.709995711172[/C][C]0.680004288827689[/C][/ROW]
[ROW][C]5[/C][C]104.51[/C][C]103.389967606979[/C][C]1.12003239302132[/C][/ROW]
[ROW][C]6[/C][C]104.09[/C][C]104.509946645582[/C][C]-0.419946645581831[/C][/ROW]
[ROW][C]7[/C][C]104.29[/C][C]104.090020004787[/C][C]0.199979995213468[/C][/ROW]
[ROW][C]8[/C][C]104.57[/C][C]104.289990473654[/C][C]0.280009526346149[/C][/ROW]
[ROW][C]9[/C][C]105.39[/C][C]104.569986661327[/C][C]0.820013338672581[/C][/ROW]
[ROW][C]10[/C][C]105.15[/C][C]105.389960937438[/C][C]-0.239960937438184[/C][/ROW]
[ROW][C]11[/C][C]106.13[/C][C]105.150011430898[/C][C]0.979988569101849[/C][/ROW]
[ROW][C]12[/C][C]105.46[/C][C]106.129953316779[/C][C]-0.66995331677883[/C][/ROW]
[ROW][C]13[/C][C]106.47[/C][C]105.460031914228[/C][C]1.00996808577177[/C][/ROW]
[ROW][C]14[/C][C]106.62[/C][C]106.46995188866[/C][C]0.150048111340297[/C][/ROW]
[ROW][C]15[/C][C]106.52[/C][C]106.619992852234[/C][C]-0.0999928522338109[/C][/ROW]
[ROW][C]16[/C][C]108.04[/C][C]106.520004763309[/C][C]1.51999523669095[/C][/ROW]
[ROW][C]17[/C][C]107.15[/C][C]108.039927592754[/C][C]-0.88992759275358[/C][/ROW]
[ROW][C]18[/C][C]107.32[/C][C]107.150042393032[/C][C]0.169957606968126[/C][/ROW]
[ROW][C]19[/C][C]107.76[/C][C]107.319991903815[/C][C]0.440008096184812[/C][/ROW]
[ROW][C]20[/C][C]107.26[/C][C]107.759979039556[/C][C]-0.499979039556251[/C][/ROW]
[ROW][C]21[/C][C]107.89[/C][C]107.260023817249[/C][C]0.629976182750667[/C][/ROW]
[ROW][C]22[/C][C]109.08[/C][C]107.889969990142[/C][C]1.19003000985765[/C][/ROW]
[ROW][C]23[/C][C]110.4[/C][C]109.079943311141[/C][C]1.32005668885934[/C][/ROW]
[ROW][C]24[/C][C]111.03[/C][C]110.399937117125[/C][C]0.630062882874654[/C][/ROW]
[ROW][C]25[/C][C]112.05[/C][C]111.029969986012[/C][C]1.02003001398775[/C][/ROW]
[ROW][C]26[/C][C]112.28[/C][C]112.049951409345[/C][C]0.230048590655286[/C][/ROW]
[ROW][C]27[/C][C]112.8[/C][C]112.279989041291[/C][C]0.520010958708667[/C][/ROW]
[ROW][C]28[/C][C]114.17[/C][C]112.7999752285[/C][C]1.37002477149974[/C][/ROW]
[ROW][C]29[/C][C]114.92[/C][C]114.169934736821[/C][C]0.75006526317901[/C][/ROW]
[ROW][C]30[/C][C]114.65[/C][C]114.919964269519[/C][C]-0.269964269519377[/C][/ROW]
[ROW][C]31[/C][C]115.49[/C][C]114.650012860152[/C][C]0.839987139848247[/C][/ROW]
[ROW][C]32[/C][C]114.67[/C][C]115.489959985956[/C][C]-0.819959985956288[/C][/ROW]
[ROW][C]33[/C][C]114.71[/C][C]114.67003906002[/C][C]0.0399609399797214[/C][/ROW]
[ROW][C]34[/C][C]115.15[/C][C]114.709998096401[/C][C]0.440001903599153[/C][/ROW]
[ROW][C]35[/C][C]115.03[/C][C]115.149979039851[/C][C]-0.119979039851259[/C][/ROW]
[ROW][C]36[/C][C]115.07[/C][C]115.030005715381[/C][C]0.0399942846189845[/C][/ROW]
[ROW][C]37[/C][C]116.46[/C][C]115.069998094812[/C][C]1.39000190518756[/C][/ROW]
[ROW][C]38[/C][C]116.37[/C][C]116.45993378518[/C][C]-0.0899337851803494[/C][/ROW]
[ROW][C]39[/C][C]116.2[/C][C]116.37000428413[/C][C]-0.170004284130357[/C][/ROW]
[ROW][C]40[/C][C]116.5[/C][C]116.200008098408[/C][C]0.299991901591653[/C][/ROW]
[ROW][C]41[/C][C]116.38[/C][C]116.499985709437[/C][C]-0.119985709437103[/C][/ROW]
[ROW][C]42[/C][C]115.44[/C][C]116.380005715699[/C][C]-0.940005715698732[/C][/ROW]
[ROW][C]43[/C][C]114.96[/C][C]115.440044778578[/C][C]-0.480044778578147[/C][/ROW]
[ROW][C]44[/C][C]114.48[/C][C]114.960022867651[/C][C]-0.480022867650973[/C][/ROW]
[ROW][C]45[/C][C]114.3[/C][C]114.480022866607[/C][C]-0.180022866607231[/C][/ROW]
[ROW][C]46[/C][C]114.66[/C][C]114.300008575658[/C][C]0.359991424341501[/C][/ROW]
[ROW][C]47[/C][C]114.97[/C][C]114.65998285127[/C][C]0.310017148729912[/C][/ROW]
[ROW][C]48[/C][C]114.79[/C][C]114.969985231869[/C][C]-0.179985231869438[/C][/ROW]
[ROW][C]49[/C][C]116.16[/C][C]114.790008573866[/C][C]1.36999142613428[/C][/ROW]
[ROW][C]50[/C][C]116.52[/C][C]116.159934738409[/C][C]0.360065261590549[/C][/ROW]
[ROW][C]51[/C][C]117.14[/C][C]116.519982847753[/C][C]0.620017152247257[/C][/ROW]
[ROW][C]52[/C][C]117.27[/C][C]117.139970464556[/C][C]0.130029535444351[/C][/ROW]
[ROW][C]53[/C][C]117.58[/C][C]117.269993805849[/C][C]0.310006194151384[/C][/ROW]
[ROW][C]54[/C][C]117.21[/C][C]117.579985232391[/C][C]-0.369985232391301[/C][/ROW]
[ROW][C]55[/C][C]117.08[/C][C]117.2100176248[/C][C]-0.130017624799891[/C][/ROW]
[ROW][C]56[/C][C]117.06[/C][C]117.080006193584[/C][C]-0.0200061935839955[/C][/ROW]
[ROW][C]57[/C][C]117.55[/C][C]117.060000953025[/C][C]0.489999046975043[/C][/ROW]
[ROW][C]58[/C][C]117.61[/C][C]117.549976658163[/C][C]0.0600233418374501[/C][/ROW]
[ROW][C]59[/C][C]117.74[/C][C]117.609997140698[/C][C]0.130002859301655[/C][/ROW]
[ROW][C]60[/C][C]117.87[/C][C]117.739993807119[/C][C]0.130006192880657[/C][/ROW]
[ROW][C]61[/C][C]118.59[/C][C]117.869993806961[/C][C]0.720006193039438[/C][/ROW]
[ROW][C]62[/C][C]119.09[/C][C]118.589965701428[/C][C]0.500034298571862[/C][/ROW]
[ROW][C]63[/C][C]118.93[/C][C]119.089976180118[/C][C]-0.159976180118335[/C][/ROW]
[ROW][C]64[/C][C]119.62[/C][C]118.930007620705[/C][C]0.68999237929539[/C][/ROW]
[ROW][C]65[/C][C]120.09[/C][C]119.619967131181[/C][C]0.470032868818947[/C][/ROW]
[ROW][C]66[/C][C]120.38[/C][C]120.089977609281[/C][C]0.290022390718676[/C][/ROW]
[ROW][C]67[/C][C]120.49[/C][C]120.37998618435[/C][C]0.110013815650333[/C][/ROW]
[ROW][C]68[/C][C]120.02[/C][C]120.489994759327[/C][C]-0.469994759327349[/C][/ROW]
[ROW][C]69[/C][C]120.17[/C][C]120.020022388903[/C][C]0.149977611096716[/C][/ROW]
[ROW][C]70[/C][C]120.58[/C][C]120.169992855592[/C][C]0.410007144407814[/C][/ROW]
[ROW][C]71[/C][C]121.54[/C][C]120.579980468696[/C][C]0.960019531303544[/C][/ROW]
[ROW][C]72[/C][C]121.51[/C][C]121.539954268034[/C][C]-0.0299542680338192[/C][/ROW]
[ROW][C]73[/C][C]121.81[/C][C]121.510001426916[/C][C]0.299998573083641[/C][/ROW]
[ROW][C]74[/C][C]122.85[/C][C]121.809985709119[/C][C]1.04001429088071[/C][/ROW]
[ROW][C]75[/C][C]122.97[/C][C]122.849950457364[/C][C]0.120049542636195[/C][/ROW]
[ROW][C]76[/C][C]122.96[/C][C]122.96999428126[/C][C]-0.0099942812604894[/C][/ROW]
[ROW][C]77[/C][C]123.4[/C][C]122.960000476093[/C][C]0.439999523907474[/C][/ROW]
[ROW][C]78[/C][C]123.23[/C][C]123.399979039965[/C][C]-0.169979039964616[/C][/ROW]
[ROW][C]79[/C][C]123.24[/C][C]123.230008097206[/C][C]0.00999190279419793[/C][/ROW]
[ROW][C]80[/C][C]123.72[/C][C]123.239999524021[/C][C]0.480000475979239[/C][/ROW]
[ROW][C]81[/C][C]123.99[/C][C]123.719977134459[/C][C]0.270022865540568[/C][/ROW]
[ROW][C]82[/C][C]125.1[/C][C]123.989987137057[/C][C]1.11001286294305[/C][/ROW]
[ROW][C]83[/C][C]125.4[/C][C]125.099947122877[/C][C]0.30005287712288[/C][/ROW]
[ROW][C]84[/C][C]125.35[/C][C]125.399985706532[/C][C]-0.0499857065324534[/C][/ROW]
[ROW][C]85[/C][C]126.37[/C][C]125.350002381144[/C][C]1.01999761885612[/C][/ROW]
[ROW][C]86[/C][C]127.17[/C][C]126.369951410888[/C][C]0.80004858911208[/C][/ROW]
[ROW][C]87[/C][C]127.66[/C][C]127.169961888489[/C][C]0.490038111511083[/C][/ROW]
[ROW][C]88[/C][C]128.48[/C][C]127.659976656302[/C][C]0.820023343698338[/C][/ROW]
[ROW][C]89[/C][C]129.21[/C][C]128.479960936962[/C][C]0.730039063038447[/C][/ROW]
[ROW][C]90[/C][C]129.48[/C][C]129.209965223497[/C][C]0.270034776502598[/C][/ROW]
[ROW][C]91[/C][C]128.63[/C][C]129.47998713649[/C][C]-0.849987136489545[/C][/ROW]
[ROW][C]92[/C][C]128.16[/C][C]128.630040490409[/C][C]-0.470040490408508[/C][/ROW]
[ROW][C]93[/C][C]128.1[/C][C]128.160022391082[/C][C]-0.060022391081759[/C][/ROW]
[ROW][C]94[/C][C]128.08[/C][C]128.100002859256[/C][C]-0.0200028592563513[/C][/ROW]
[ROW][C]95[/C][C]128.14[/C][C]128.080000952866[/C][C]0.0599990471338572[/C][/ROW]
[ROW][C]96[/C][C]128.19[/C][C]128.139997141856[/C][C]0.050002858144353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278705&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278705&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
2102.62101.940.680000000000007
3102.71102.6199676071830.0900323928170081
4103.39102.7099957111720.680004288827689
5104.51103.3899676069791.12003239302132
6104.09104.509946645582-0.419946645581831
7104.29104.0900200047870.199979995213468
8104.57104.2899904736540.280009526346149
9105.39104.5699866613270.820013338672581
10105.15105.389960937438-0.239960937438184
11106.13105.1500114308980.979988569101849
12105.46106.129953316779-0.66995331677883
13106.47105.4600319142281.00996808577177
14106.62106.469951888660.150048111340297
15106.52106.619992852234-0.0999928522338109
16108.04106.5200047633091.51999523669095
17107.15108.039927592754-0.88992759275358
18107.32107.1500423930320.169957606968126
19107.76107.3199919038150.440008096184812
20107.26107.759979039556-0.499979039556251
21107.89107.2600238172490.629976182750667
22109.08107.8899699901421.19003000985765
23110.4109.0799433111411.32005668885934
24111.03110.3999371171250.630062882874654
25112.05111.0299699860121.02003001398775
26112.28112.0499514093450.230048590655286
27112.8112.2799890412910.520010958708667
28114.17112.79997522851.37002477149974
29114.92114.1699347368210.75006526317901
30114.65114.919964269519-0.269964269519377
31115.49114.6500128601520.839987139848247
32114.67115.489959985956-0.819959985956288
33114.71114.670039060020.0399609399797214
34115.15114.7099980964010.440001903599153
35115.03115.149979039851-0.119979039851259
36115.07115.0300057153810.0399942846189845
37116.46115.0699980948121.39000190518756
38116.37116.45993378518-0.0899337851803494
39116.2116.37000428413-0.170004284130357
40116.5116.2000080984080.299991901591653
41116.38116.499985709437-0.119985709437103
42115.44116.380005715699-0.940005715698732
43114.96115.440044778578-0.480044778578147
44114.48114.960022867651-0.480022867650973
45114.3114.480022866607-0.180022866607231
46114.66114.3000085756580.359991424341501
47114.97114.659982851270.310017148729912
48114.79114.969985231869-0.179985231869438
49116.16114.7900085738661.36999142613428
50116.52116.1599347384090.360065261590549
51117.14116.5199828477530.620017152247257
52117.27117.1399704645560.130029535444351
53117.58117.2699938058490.310006194151384
54117.21117.579985232391-0.369985232391301
55117.08117.2100176248-0.130017624799891
56117.06117.080006193584-0.0200061935839955
57117.55117.0600009530250.489999046975043
58117.61117.5499766581630.0600233418374501
59117.74117.6099971406980.130002859301655
60117.87117.7399938071190.130006192880657
61118.59117.8699938069610.720006193039438
62119.09118.5899657014280.500034298571862
63118.93119.089976180118-0.159976180118335
64119.62118.9300076207050.68999237929539
65120.09119.6199671311810.470032868818947
66120.38120.0899776092810.290022390718676
67120.49120.379986184350.110013815650333
68120.02120.489994759327-0.469994759327349
69120.17120.0200223889030.149977611096716
70120.58120.1699928555920.410007144407814
71121.54120.5799804686960.960019531303544
72121.51121.539954268034-0.0299542680338192
73121.81121.5100014269160.299998573083641
74122.85121.8099857091191.04001429088071
75122.97122.8499504573640.120049542636195
76122.96122.96999428126-0.0099942812604894
77123.4122.9600004760930.439999523907474
78123.23123.399979039965-0.169979039964616
79123.24123.2300080972060.00999190279419793
80123.72123.2399995240210.480000475979239
81123.99123.7199771344590.270022865540568
82125.1123.9899871370571.11001286294305
83125.4125.0999471228770.30005287712288
84125.35125.399985706532-0.0499857065324534
85126.37125.3500023811441.01999761885612
86127.17126.3699514108880.80004858911208
87127.66127.1699618884890.490038111511083
88128.48127.6599766563020.820023343698338
89129.21128.4799609369620.730039063038447
90129.48129.2099652234970.270034776502598
91128.63129.47998713649-0.849987136489545
92128.16128.630040490409-0.470040490408508
93128.1128.160022391082-0.060022391081759
94128.08128.100002859256-0.0200028592563513
95128.14128.0800009528660.0599990471338572
96128.19128.1399971418560.050002858144353







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97128.189997618039127.117104802934129.262890433144
98128.189997618039126.672734186931129.707261049147
99128.189997618039126.331751766154130.048243469925
100128.189997618039126.044288650653130.335706585425
101128.189997618039125.791027776754130.588967459324
102128.189997618039125.56206199743130.817933238648
103128.189997618039125.351505949434131.028489286644
104128.189997618039125.155524965433131.224470270645
105128.189997618039124.971455462639131.408539773439
106128.189997618039124.797358095078131.582637141
107128.189997618039124.631768808725131.748226427353
108128.189997618039124.473550176449131.906445059629

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 128.189997618039 & 127.117104802934 & 129.262890433144 \tabularnewline
98 & 128.189997618039 & 126.672734186931 & 129.707261049147 \tabularnewline
99 & 128.189997618039 & 126.331751766154 & 130.048243469925 \tabularnewline
100 & 128.189997618039 & 126.044288650653 & 130.335706585425 \tabularnewline
101 & 128.189997618039 & 125.791027776754 & 130.588967459324 \tabularnewline
102 & 128.189997618039 & 125.56206199743 & 130.817933238648 \tabularnewline
103 & 128.189997618039 & 125.351505949434 & 131.028489286644 \tabularnewline
104 & 128.189997618039 & 125.155524965433 & 131.224470270645 \tabularnewline
105 & 128.189997618039 & 124.971455462639 & 131.408539773439 \tabularnewline
106 & 128.189997618039 & 124.797358095078 & 131.582637141 \tabularnewline
107 & 128.189997618039 & 124.631768808725 & 131.748226427353 \tabularnewline
108 & 128.189997618039 & 124.473550176449 & 131.906445059629 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278705&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]128.189997618039[/C][C]127.117104802934[/C][C]129.262890433144[/C][/ROW]
[ROW][C]98[/C][C]128.189997618039[/C][C]126.672734186931[/C][C]129.707261049147[/C][/ROW]
[ROW][C]99[/C][C]128.189997618039[/C][C]126.331751766154[/C][C]130.048243469925[/C][/ROW]
[ROW][C]100[/C][C]128.189997618039[/C][C]126.044288650653[/C][C]130.335706585425[/C][/ROW]
[ROW][C]101[/C][C]128.189997618039[/C][C]125.791027776754[/C][C]130.588967459324[/C][/ROW]
[ROW][C]102[/C][C]128.189997618039[/C][C]125.56206199743[/C][C]130.817933238648[/C][/ROW]
[ROW][C]103[/C][C]128.189997618039[/C][C]125.351505949434[/C][C]131.028489286644[/C][/ROW]
[ROW][C]104[/C][C]128.189997618039[/C][C]125.155524965433[/C][C]131.224470270645[/C][/ROW]
[ROW][C]105[/C][C]128.189997618039[/C][C]124.971455462639[/C][C]131.408539773439[/C][/ROW]
[ROW][C]106[/C][C]128.189997618039[/C][C]124.797358095078[/C][C]131.582637141[/C][/ROW]
[ROW][C]107[/C][C]128.189997618039[/C][C]124.631768808725[/C][C]131.748226427353[/C][/ROW]
[ROW][C]108[/C][C]128.189997618039[/C][C]124.473550176449[/C][C]131.906445059629[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278705&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278705&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
97128.189997618039127.117104802934129.262890433144
98128.189997618039126.672734186931129.707261049147
99128.189997618039126.331751766154130.048243469925
100128.189997618039126.044288650653130.335706585425
101128.189997618039125.791027776754130.588967459324
102128.189997618039125.56206199743130.817933238648
103128.189997618039125.351505949434131.028489286644
104128.189997618039125.155524965433131.224470270645
105128.189997618039124.971455462639131.408539773439
106128.189997618039124.797358095078131.582637141
107128.189997618039124.631768808725131.748226427353
108128.189997618039124.473550176449131.906445059629



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')