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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 computationMon, 26 May 2008 08:58:41 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t12118139862lmupso6qc5svd5.htm/, Retrieved Sun, 19 May 2024 09:02:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13262, Retrieved Sun, 19 May 2024 09:02:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Mathieu Demoor - ...] [2008-05-26 14:58:41] [8c69c5b6690db7c1e43065ff98235337] [Current]
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Dataseries X:
113
110
107
103
98
98
137
148
147
139
130
128
127
123
118
114
108
111
151
159
158
148
138
137
136
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13262&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13262&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.937593174294072
beta0.0731471036939834
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.937593174294072 \tabularnewline
beta & 0.0731471036939834 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13262&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]0.937593174294072[/C][/ROW]
[ROW][C]beta[/C][C]0.0731471036939834[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13262&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
alpha0.937593174294072
beta0.0731471036939834
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13127122.5545833333334.44541666666665
14123122.6694449772030.330555022796545
15118118.073910629612-0.0739106296119871
16114114.177416424979-0.177416424978730
17108108.296708279908-0.29670827990779
18111111.283803991852-0.283803991852068
19151151.221868100264-0.221868100264260
20159159.161120003202-0.161120003201972
21158158.187945605629-0.187945605628727
22148148.343396645151-0.343396645150591
23138138.412880278382-0.412880278382204
24137137.430566949828-0.430566949828261
25136136.179565822465-0.179565822465264
26133131.5340334853401.46596651465961
27126127.888434317083-1.88843431708335
28120122.070374080312-2.07037408031229
29114114.063752344231-0.0637523442314603
30116116.942403115319-0.94240311531891
31153155.893998058285-2.89399805828549
32162160.7755732841911.22442671580916
33161160.6387308458920.361269154108214
34149150.876013973298-1.87601397329829
35139138.9756727850710.0243272149286042
36135137.90364608892-2.90364608892006
37130133.681425394496-3.68142539449602
38127124.9469589231012.05304107689935
39122120.7744152769961.22558472300449
40117117.210206036495-0.210206036494895
41112110.5459888006181.45401119938174
42113114.370038852264-1.37003885226360
43149152.346752738744-3.34675273874350
44157156.5776552972630.422344702736893
45157155.0967199591521.90328004084841
46147146.2077154126510.792284587348945
47137136.6783000380010.32169996199903
48132135.473309999590-3.47330999958976
49125130.400316274253-5.40031627425279
50123120.026092635862.97390736414009
51117116.3424564093120.657543590687624
52114111.7942434105882.20575658941212
53111107.3029577236673.69704227633292
54112113.011533432335-1.01153343233503
55144151.183321242829-7.18332124282941
56150151.771482489708-1.77148248970838
57149147.8947743968731.10522560312731
58134137.702177581065-3.70217758106509
59123123.135169070005-0.135169070004679
60116120.439405733113-4.43940573311335
61117113.4485104151853.55148958481513
62111111.712143845337-0.712143845337124
63105103.8972329429211.10276705707878
6410299.36291059061582.63708940938416
659594.89852088659020.101479113409752
669396.2248969991282-3.22489699912825
67124131.067314299266-7.06731429926583
68130131.240960305020-1.24096030502017
69124127.216558566435-3.21655856643456
70115111.5508402194423.44915978055781
71106103.2809056927452.71909430725508
72105102.5578414109242.44215858907555

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 127 & 122.554583333333 & 4.44541666666665 \tabularnewline
14 & 123 & 122.669444977203 & 0.330555022796545 \tabularnewline
15 & 118 & 118.073910629612 & -0.0739106296119871 \tabularnewline
16 & 114 & 114.177416424979 & -0.177416424978730 \tabularnewline
17 & 108 & 108.296708279908 & -0.29670827990779 \tabularnewline
18 & 111 & 111.283803991852 & -0.283803991852068 \tabularnewline
19 & 151 & 151.221868100264 & -0.221868100264260 \tabularnewline
20 & 159 & 159.161120003202 & -0.161120003201972 \tabularnewline
21 & 158 & 158.187945605629 & -0.187945605628727 \tabularnewline
22 & 148 & 148.343396645151 & -0.343396645150591 \tabularnewline
23 & 138 & 138.412880278382 & -0.412880278382204 \tabularnewline
24 & 137 & 137.430566949828 & -0.430566949828261 \tabularnewline
25 & 136 & 136.179565822465 & -0.179565822465264 \tabularnewline
26 & 133 & 131.534033485340 & 1.46596651465961 \tabularnewline
27 & 126 & 127.888434317083 & -1.88843431708335 \tabularnewline
28 & 120 & 122.070374080312 & -2.07037408031229 \tabularnewline
29 & 114 & 114.063752344231 & -0.0637523442314603 \tabularnewline
30 & 116 & 116.942403115319 & -0.94240311531891 \tabularnewline
31 & 153 & 155.893998058285 & -2.89399805828549 \tabularnewline
32 & 162 & 160.775573284191 & 1.22442671580916 \tabularnewline
33 & 161 & 160.638730845892 & 0.361269154108214 \tabularnewline
34 & 149 & 150.876013973298 & -1.87601397329829 \tabularnewline
35 & 139 & 138.975672785071 & 0.0243272149286042 \tabularnewline
36 & 135 & 137.90364608892 & -2.90364608892006 \tabularnewline
37 & 130 & 133.681425394496 & -3.68142539449602 \tabularnewline
38 & 127 & 124.946958923101 & 2.05304107689935 \tabularnewline
39 & 122 & 120.774415276996 & 1.22558472300449 \tabularnewline
40 & 117 & 117.210206036495 & -0.210206036494895 \tabularnewline
41 & 112 & 110.545988800618 & 1.45401119938174 \tabularnewline
42 & 113 & 114.370038852264 & -1.37003885226360 \tabularnewline
43 & 149 & 152.346752738744 & -3.34675273874350 \tabularnewline
44 & 157 & 156.577655297263 & 0.422344702736893 \tabularnewline
45 & 157 & 155.096719959152 & 1.90328004084841 \tabularnewline
46 & 147 & 146.207715412651 & 0.792284587348945 \tabularnewline
47 & 137 & 136.678300038001 & 0.32169996199903 \tabularnewline
48 & 132 & 135.473309999590 & -3.47330999958976 \tabularnewline
49 & 125 & 130.400316274253 & -5.40031627425279 \tabularnewline
50 & 123 & 120.02609263586 & 2.97390736414009 \tabularnewline
51 & 117 & 116.342456409312 & 0.657543590687624 \tabularnewline
52 & 114 & 111.794243410588 & 2.20575658941212 \tabularnewline
53 & 111 & 107.302957723667 & 3.69704227633292 \tabularnewline
54 & 112 & 113.011533432335 & -1.01153343233503 \tabularnewline
55 & 144 & 151.183321242829 & -7.18332124282941 \tabularnewline
56 & 150 & 151.771482489708 & -1.77148248970838 \tabularnewline
57 & 149 & 147.894774396873 & 1.10522560312731 \tabularnewline
58 & 134 & 137.702177581065 & -3.70217758106509 \tabularnewline
59 & 123 & 123.135169070005 & -0.135169070004679 \tabularnewline
60 & 116 & 120.439405733113 & -4.43940573311335 \tabularnewline
61 & 117 & 113.448510415185 & 3.55148958481513 \tabularnewline
62 & 111 & 111.712143845337 & -0.712143845337124 \tabularnewline
63 & 105 & 103.897232942921 & 1.10276705707878 \tabularnewline
64 & 102 & 99.3629105906158 & 2.63708940938416 \tabularnewline
65 & 95 & 94.8985208865902 & 0.101479113409752 \tabularnewline
66 & 93 & 96.2248969991282 & -3.22489699912825 \tabularnewline
67 & 124 & 131.067314299266 & -7.06731429926583 \tabularnewline
68 & 130 & 131.240960305020 & -1.24096030502017 \tabularnewline
69 & 124 & 127.216558566435 & -3.21655856643456 \tabularnewline
70 & 115 & 111.550840219442 & 3.44915978055781 \tabularnewline
71 & 106 & 103.280905692745 & 2.71909430725508 \tabularnewline
72 & 105 & 102.557841410924 & 2.44215858907555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13262&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]127[/C][C]122.554583333333[/C][C]4.44541666666665[/C][/ROW]
[ROW][C]14[/C][C]123[/C][C]122.669444977203[/C][C]0.330555022796545[/C][/ROW]
[ROW][C]15[/C][C]118[/C][C]118.073910629612[/C][C]-0.0739106296119871[/C][/ROW]
[ROW][C]16[/C][C]114[/C][C]114.177416424979[/C][C]-0.177416424978730[/C][/ROW]
[ROW][C]17[/C][C]108[/C][C]108.296708279908[/C][C]-0.29670827990779[/C][/ROW]
[ROW][C]18[/C][C]111[/C][C]111.283803991852[/C][C]-0.283803991852068[/C][/ROW]
[ROW][C]19[/C][C]151[/C][C]151.221868100264[/C][C]-0.221868100264260[/C][/ROW]
[ROW][C]20[/C][C]159[/C][C]159.161120003202[/C][C]-0.161120003201972[/C][/ROW]
[ROW][C]21[/C][C]158[/C][C]158.187945605629[/C][C]-0.187945605628727[/C][/ROW]
[ROW][C]22[/C][C]148[/C][C]148.343396645151[/C][C]-0.343396645150591[/C][/ROW]
[ROW][C]23[/C][C]138[/C][C]138.412880278382[/C][C]-0.412880278382204[/C][/ROW]
[ROW][C]24[/C][C]137[/C][C]137.430566949828[/C][C]-0.430566949828261[/C][/ROW]
[ROW][C]25[/C][C]136[/C][C]136.179565822465[/C][C]-0.179565822465264[/C][/ROW]
[ROW][C]26[/C][C]133[/C][C]131.534033485340[/C][C]1.46596651465961[/C][/ROW]
[ROW][C]27[/C][C]126[/C][C]127.888434317083[/C][C]-1.88843431708335[/C][/ROW]
[ROW][C]28[/C][C]120[/C][C]122.070374080312[/C][C]-2.07037408031229[/C][/ROW]
[ROW][C]29[/C][C]114[/C][C]114.063752344231[/C][C]-0.0637523442314603[/C][/ROW]
[ROW][C]30[/C][C]116[/C][C]116.942403115319[/C][C]-0.94240311531891[/C][/ROW]
[ROW][C]31[/C][C]153[/C][C]155.893998058285[/C][C]-2.89399805828549[/C][/ROW]
[ROW][C]32[/C][C]162[/C][C]160.775573284191[/C][C]1.22442671580916[/C][/ROW]
[ROW][C]33[/C][C]161[/C][C]160.638730845892[/C][C]0.361269154108214[/C][/ROW]
[ROW][C]34[/C][C]149[/C][C]150.876013973298[/C][C]-1.87601397329829[/C][/ROW]
[ROW][C]35[/C][C]139[/C][C]138.975672785071[/C][C]0.0243272149286042[/C][/ROW]
[ROW][C]36[/C][C]135[/C][C]137.90364608892[/C][C]-2.90364608892006[/C][/ROW]
[ROW][C]37[/C][C]130[/C][C]133.681425394496[/C][C]-3.68142539449602[/C][/ROW]
[ROW][C]38[/C][C]127[/C][C]124.946958923101[/C][C]2.05304107689935[/C][/ROW]
[ROW][C]39[/C][C]122[/C][C]120.774415276996[/C][C]1.22558472300449[/C][/ROW]
[ROW][C]40[/C][C]117[/C][C]117.210206036495[/C][C]-0.210206036494895[/C][/ROW]
[ROW][C]41[/C][C]112[/C][C]110.545988800618[/C][C]1.45401119938174[/C][/ROW]
[ROW][C]42[/C][C]113[/C][C]114.370038852264[/C][C]-1.37003885226360[/C][/ROW]
[ROW][C]43[/C][C]149[/C][C]152.346752738744[/C][C]-3.34675273874350[/C][/ROW]
[ROW][C]44[/C][C]157[/C][C]156.577655297263[/C][C]0.422344702736893[/C][/ROW]
[ROW][C]45[/C][C]157[/C][C]155.096719959152[/C][C]1.90328004084841[/C][/ROW]
[ROW][C]46[/C][C]147[/C][C]146.207715412651[/C][C]0.792284587348945[/C][/ROW]
[ROW][C]47[/C][C]137[/C][C]136.678300038001[/C][C]0.32169996199903[/C][/ROW]
[ROW][C]48[/C][C]132[/C][C]135.473309999590[/C][C]-3.47330999958976[/C][/ROW]
[ROW][C]49[/C][C]125[/C][C]130.400316274253[/C][C]-5.40031627425279[/C][/ROW]
[ROW][C]50[/C][C]123[/C][C]120.02609263586[/C][C]2.97390736414009[/C][/ROW]
[ROW][C]51[/C][C]117[/C][C]116.342456409312[/C][C]0.657543590687624[/C][/ROW]
[ROW][C]52[/C][C]114[/C][C]111.794243410588[/C][C]2.20575658941212[/C][/ROW]
[ROW][C]53[/C][C]111[/C][C]107.302957723667[/C][C]3.69704227633292[/C][/ROW]
[ROW][C]54[/C][C]112[/C][C]113.011533432335[/C][C]-1.01153343233503[/C][/ROW]
[ROW][C]55[/C][C]144[/C][C]151.183321242829[/C][C]-7.18332124282941[/C][/ROW]
[ROW][C]56[/C][C]150[/C][C]151.771482489708[/C][C]-1.77148248970838[/C][/ROW]
[ROW][C]57[/C][C]149[/C][C]147.894774396873[/C][C]1.10522560312731[/C][/ROW]
[ROW][C]58[/C][C]134[/C][C]137.702177581065[/C][C]-3.70217758106509[/C][/ROW]
[ROW][C]59[/C][C]123[/C][C]123.135169070005[/C][C]-0.135169070004679[/C][/ROW]
[ROW][C]60[/C][C]116[/C][C]120.439405733113[/C][C]-4.43940573311335[/C][/ROW]
[ROW][C]61[/C][C]117[/C][C]113.448510415185[/C][C]3.55148958481513[/C][/ROW]
[ROW][C]62[/C][C]111[/C][C]111.712143845337[/C][C]-0.712143845337124[/C][/ROW]
[ROW][C]63[/C][C]105[/C][C]103.897232942921[/C][C]1.10276705707878[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]99.3629105906158[/C][C]2.63708940938416[/C][/ROW]
[ROW][C]65[/C][C]95[/C][C]94.8985208865902[/C][C]0.101479113409752[/C][/ROW]
[ROW][C]66[/C][C]93[/C][C]96.2248969991282[/C][C]-3.22489699912825[/C][/ROW]
[ROW][C]67[/C][C]124[/C][C]131.067314299266[/C][C]-7.06731429926583[/C][/ROW]
[ROW][C]68[/C][C]130[/C][C]131.240960305020[/C][C]-1.24096030502017[/C][/ROW]
[ROW][C]69[/C][C]124[/C][C]127.216558566435[/C][C]-3.21655856643456[/C][/ROW]
[ROW][C]70[/C][C]115[/C][C]111.550840219442[/C][C]3.44915978055781[/C][/ROW]
[ROW][C]71[/C][C]106[/C][C]103.280905692745[/C][C]2.71909430725508[/C][/ROW]
[ROW][C]72[/C][C]105[/C][C]102.557841410924[/C][C]2.44215858907555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13262&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13262&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
13127122.5545833333334.44541666666665
14123122.6694449772030.330555022796545
15118118.073910629612-0.0739106296119871
16114114.177416424979-0.177416424978730
17108108.296708279908-0.29670827990779
18111111.283803991852-0.283803991852068
19151151.221868100264-0.221868100264260
20159159.161120003202-0.161120003201972
21158158.187945605629-0.187945605628727
22148148.343396645151-0.343396645150591
23138138.412880278382-0.412880278382204
24137137.430566949828-0.430566949828261
25136136.179565822465-0.179565822465264
26133131.5340334853401.46596651465961
27126127.888434317083-1.88843431708335
28120122.070374080312-2.07037408031229
29114114.063752344231-0.0637523442314603
30116116.942403115319-0.94240311531891
31153155.893998058285-2.89399805828549
32162160.7755732841911.22442671580916
33161160.6387308458920.361269154108214
34149150.876013973298-1.87601397329829
35139138.9756727850710.0243272149286042
36135137.90364608892-2.90364608892006
37130133.681425394496-3.68142539449602
38127124.9469589231012.05304107689935
39122120.7744152769961.22558472300449
40117117.210206036495-0.210206036494895
41112110.5459888006181.45401119938174
42113114.370038852264-1.37003885226360
43149152.346752738744-3.34675273874350
44157156.5776552972630.422344702736893
45157155.0967199591521.90328004084841
46147146.2077154126510.792284587348945
47137136.6783000380010.32169996199903
48132135.473309999590-3.47330999958976
49125130.400316274253-5.40031627425279
50123120.026092635862.97390736414009
51117116.3424564093120.657543590687624
52114111.7942434105882.20575658941212
53111107.3029577236673.69704227633292
54112113.011533432335-1.01153343233503
55144151.183321242829-7.18332124282941
56150151.771482489708-1.77148248970838
57149147.8947743968731.10522560312731
58134137.702177581065-3.70217758106509
59123123.135169070005-0.135169070004679
60116120.439405733113-4.43940573311335
61117113.4485104151853.55148958481513
62111111.712143845337-0.712143845337124
63105103.8972329429211.10276705707878
6410299.36291059061582.63708940938416
659594.89852088659020.101479113409752
669396.2248969991282-3.22489699912825
67124131.067314299266-7.06731429926583
68130131.240960305020-1.24096030502017
69124127.216558566435-3.21655856643456
70115111.5508402194423.44915978055781
71106103.2809056927452.71909430725508
72105102.5578414109242.44215858907555







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.55486817711297.7048423823639107.404893971860
7497.016128263142990.1359449640257103.896311562260
7589.824580684651981.19277068042898.4563906888758
7684.118832722883873.85931543910894.3783500066596
7776.609598207694964.785603341392788.433593073997
7877.212191567353263.85640995101190.5679731836954
79114.63857977246799.7661516459297129.511007899004
80122.086910381982105.702015462796138.471805301168
81119.472656255579101.572232475334137.373080035825
82107.82926884905888.405274205693127.253263492423
8396.633834794469175.6747019350271117.592967653911
8493.511572240998871.0031849601905116.019959521807

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.554868177112 & 97.7048423823639 & 107.404893971860 \tabularnewline
74 & 97.0161282631429 & 90.1359449640257 & 103.896311562260 \tabularnewline
75 & 89.8245806846519 & 81.192770680428 & 98.4563906888758 \tabularnewline
76 & 84.1188327228838 & 73.859315439108 & 94.3783500066596 \tabularnewline
77 & 76.6095982076949 & 64.7856033413927 & 88.433593073997 \tabularnewline
78 & 77.2121915673532 & 63.856409951011 & 90.5679731836954 \tabularnewline
79 & 114.638579772467 & 99.7661516459297 & 129.511007899004 \tabularnewline
80 & 122.086910381982 & 105.702015462796 & 138.471805301168 \tabularnewline
81 & 119.472656255579 & 101.572232475334 & 137.373080035825 \tabularnewline
82 & 107.829268849058 & 88.405274205693 & 127.253263492423 \tabularnewline
83 & 96.6338347944691 & 75.6747019350271 & 117.592967653911 \tabularnewline
84 & 93.5115722409988 & 71.0031849601905 & 116.019959521807 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13262&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]73[/C][C]102.554868177112[/C][C]97.7048423823639[/C][C]107.404893971860[/C][/ROW]
[ROW][C]74[/C][C]97.0161282631429[/C][C]90.1359449640257[/C][C]103.896311562260[/C][/ROW]
[ROW][C]75[/C][C]89.8245806846519[/C][C]81.192770680428[/C][C]98.4563906888758[/C][/ROW]
[ROW][C]76[/C][C]84.1188327228838[/C][C]73.859315439108[/C][C]94.3783500066596[/C][/ROW]
[ROW][C]77[/C][C]76.6095982076949[/C][C]64.7856033413927[/C][C]88.433593073997[/C][/ROW]
[ROW][C]78[/C][C]77.2121915673532[/C][C]63.856409951011[/C][C]90.5679731836954[/C][/ROW]
[ROW][C]79[/C][C]114.638579772467[/C][C]99.7661516459297[/C][C]129.511007899004[/C][/ROW]
[ROW][C]80[/C][C]122.086910381982[/C][C]105.702015462796[/C][C]138.471805301168[/C][/ROW]
[ROW][C]81[/C][C]119.472656255579[/C][C]101.572232475334[/C][C]137.373080035825[/C][/ROW]
[ROW][C]82[/C][C]107.829268849058[/C][C]88.405274205693[/C][C]127.253263492423[/C][/ROW]
[ROW][C]83[/C][C]96.6338347944691[/C][C]75.6747019350271[/C][C]117.592967653911[/C][/ROW]
[ROW][C]84[/C][C]93.5115722409988[/C][C]71.0031849601905[/C][C]116.019959521807[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13262&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13262&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
73102.55486817711297.7048423823639107.404893971860
7497.016128263142990.1359449640257103.896311562260
7589.824580684651981.19277068042898.4563906888758
7684.118832722883873.85931543910894.3783500066596
7776.609598207694964.785603341392788.433593073997
7877.212191567353263.85640995101190.5679731836954
79114.63857977246799.7661516459297129.511007899004
80122.086910381982105.702015462796138.471805301168
81119.472656255579101.572232475334137.373080035825
82107.82926884905888.405274205693127.253263492423
8396.633834794469175.6747019350271117.592967653911
8493.511572240998871.0031849601905116.019959521807



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')