Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 15:17:53 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/19/t12822310458fkkprli1bx53s5.htm/, Retrieved Fri, 03 May 2024 09:55:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79314, Retrieved Fri, 03 May 2024 09:55:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSebastien Delforge
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-08-19 15:17:53] [923770d86edf74ed976a539eae527e37] [Current]
Feedback Forum

Post a new message
Dataseries X:
152
151
150
148
146
145
146
148
149
149
150
152
154
164
167
162
164
172
169
174
181
181
172
181
183
200
199
190
197
194
190
195
204
197
185
193
192
211
210
197
191
182
170
166
175
163
153
171
165
184
179
163
163
148
132
127
130
118
113
137
133
155
151
132
134
118
102
98
91
77
74
102
98
113
114
96
102
90
72
67
62
48
43
75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79314&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79314&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79314&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.68474816558974
beta0.0484142369247786
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.68474816558974 \tabularnewline
beta & 0.0484142369247786 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79314&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]0.68474816558974[/C][/ROW]
[ROW][C]beta[/C][C]0.0484142369247786[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79314&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79314&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
alpha0.68474816558974
beta0.0484142369247786
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13154144.8359672674619.16403273253883
14164161.1343271508742.86567284912621
15167165.9741541614451.0258458385552
16162161.3634381485730.63656185142682
17164163.9029574861570.0970425138432347
18172172.206012609827-0.20601260982744
19169167.9355587614241.06444123857591
20174172.6233734332261.37662656677364
21181175.6951058788695.30489412113099
22181180.3633709042790.63662909572102
23172183.005512855122-11.0055128551225
24181177.8744547272013.12554527279937
25183185.769098014831-2.76909801483075
26200193.0815774670396.91842253296088
27199200.299674096934-1.29967409693418
28190192.590318968473-2.59031896847293
29197192.6935893624584.30641063754163
30194205.047316652563-11.0473166525628
31190192.661589180187-2.66158918018743
32195194.7893312342930.210668765707368
33204198.0129618475785.98703815242203
34197200.989829140711-3.98982914071127
35185195.771548158604-10.7715481586036
36193195.193438722546-2.19343872254629
37192197.012799544763-5.0127995447634
38211205.5703871010345.42961289896593
39210208.2222960835061.77770391649355
40197201.007652023794-4.00765202379412
41191201.621407359169-10.6214073591685
42182197.49976665005-15.4997666500497
43170183.481191098833-13.4811910988334
44166177.111132856874-11.1111328568743
45175171.8340635445593.16593645544128
46163168.481072611454-5.48107261145361
47153158.914898331573-5.91489833157252
48171161.0016977332869.99830226671415
49165168.459043447272-3.45904344727165
50184177.7367992565416.26320074345924
51179178.6456720622480.354327937751975
52163168.737820776871-5.73782077687088
53163164.31916293143-1.31916293143036
54148163.330836659677-15.3308366596767
55132149.048683472034-17.0486834720345
56127138.675541179729-11.6755411797294
57130134.398375136249-4.39837513624875
58118123.375456794781-5.3754567947815
59113113.519716842537-0.519716842537136
60137119.55280426332917.4471957366711
61133127.2896501964545.71034980354649
62155141.63468846599613.3653115340036
63151145.5667098398365.43329016016389
64132138.481315791507-6.48131579150703
65134134.017262240619-0.0172622406192886
66118129.320401850065-11.3204018500655
67102116.977404334652-14.9774043346518
6898108.210193541373-10.2101935413729
6991105.132757856971-14.1327578569713
707788.0546121733445-11.0546121733445
717475.7623205168778-1.76232051687779
7210280.335634883940721.6643651160593
739888.23900674836249.76099325163764
74113102.60076199288410.3992380071156
75114102.98852448910211.011475510898
769698.9267959768588-2.92679597685881
7710297.54815847209424.45184152790577
789093.5835723365682-3.58357233656815
797285.8936956684969-13.8936956684969
806777.8467294371392-10.8467294371392
816271.2022309296126-9.20223092961255
824859.3055385324514-11.3055385324514
834349.3224024174947-6.32240241749469
847550.676745404642824.3232545953572

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 154 & 144.835967267461 & 9.16403273253883 \tabularnewline
14 & 164 & 161.134327150874 & 2.86567284912621 \tabularnewline
15 & 167 & 165.974154161445 & 1.0258458385552 \tabularnewline
16 & 162 & 161.363438148573 & 0.63656185142682 \tabularnewline
17 & 164 & 163.902957486157 & 0.0970425138432347 \tabularnewline
18 & 172 & 172.206012609827 & -0.20601260982744 \tabularnewline
19 & 169 & 167.935558761424 & 1.06444123857591 \tabularnewline
20 & 174 & 172.623373433226 & 1.37662656677364 \tabularnewline
21 & 181 & 175.695105878869 & 5.30489412113099 \tabularnewline
22 & 181 & 180.363370904279 & 0.63662909572102 \tabularnewline
23 & 172 & 183.005512855122 & -11.0055128551225 \tabularnewline
24 & 181 & 177.874454727201 & 3.12554527279937 \tabularnewline
25 & 183 & 185.769098014831 & -2.76909801483075 \tabularnewline
26 & 200 & 193.081577467039 & 6.91842253296088 \tabularnewline
27 & 199 & 200.299674096934 & -1.29967409693418 \tabularnewline
28 & 190 & 192.590318968473 & -2.59031896847293 \tabularnewline
29 & 197 & 192.693589362458 & 4.30641063754163 \tabularnewline
30 & 194 & 205.047316652563 & -11.0473166525628 \tabularnewline
31 & 190 & 192.661589180187 & -2.66158918018743 \tabularnewline
32 & 195 & 194.789331234293 & 0.210668765707368 \tabularnewline
33 & 204 & 198.012961847578 & 5.98703815242203 \tabularnewline
34 & 197 & 200.989829140711 & -3.98982914071127 \tabularnewline
35 & 185 & 195.771548158604 & -10.7715481586036 \tabularnewline
36 & 193 & 195.193438722546 & -2.19343872254629 \tabularnewline
37 & 192 & 197.012799544763 & -5.0127995447634 \tabularnewline
38 & 211 & 205.570387101034 & 5.42961289896593 \tabularnewline
39 & 210 & 208.222296083506 & 1.77770391649355 \tabularnewline
40 & 197 & 201.007652023794 & -4.00765202379412 \tabularnewline
41 & 191 & 201.621407359169 & -10.6214073591685 \tabularnewline
42 & 182 & 197.49976665005 & -15.4997666500497 \tabularnewline
43 & 170 & 183.481191098833 & -13.4811910988334 \tabularnewline
44 & 166 & 177.111132856874 & -11.1111328568743 \tabularnewline
45 & 175 & 171.834063544559 & 3.16593645544128 \tabularnewline
46 & 163 & 168.481072611454 & -5.48107261145361 \tabularnewline
47 & 153 & 158.914898331573 & -5.91489833157252 \tabularnewline
48 & 171 & 161.001697733286 & 9.99830226671415 \tabularnewline
49 & 165 & 168.459043447272 & -3.45904344727165 \tabularnewline
50 & 184 & 177.736799256541 & 6.26320074345924 \tabularnewline
51 & 179 & 178.645672062248 & 0.354327937751975 \tabularnewline
52 & 163 & 168.737820776871 & -5.73782077687088 \tabularnewline
53 & 163 & 164.31916293143 & -1.31916293143036 \tabularnewline
54 & 148 & 163.330836659677 & -15.3308366596767 \tabularnewline
55 & 132 & 149.048683472034 & -17.0486834720345 \tabularnewline
56 & 127 & 138.675541179729 & -11.6755411797294 \tabularnewline
57 & 130 & 134.398375136249 & -4.39837513624875 \tabularnewline
58 & 118 & 123.375456794781 & -5.3754567947815 \tabularnewline
59 & 113 & 113.519716842537 & -0.519716842537136 \tabularnewline
60 & 137 & 119.552804263329 & 17.4471957366711 \tabularnewline
61 & 133 & 127.289650196454 & 5.71034980354649 \tabularnewline
62 & 155 & 141.634688465996 & 13.3653115340036 \tabularnewline
63 & 151 & 145.566709839836 & 5.43329016016389 \tabularnewline
64 & 132 & 138.481315791507 & -6.48131579150703 \tabularnewline
65 & 134 & 134.017262240619 & -0.0172622406192886 \tabularnewline
66 & 118 & 129.320401850065 & -11.3204018500655 \tabularnewline
67 & 102 & 116.977404334652 & -14.9774043346518 \tabularnewline
68 & 98 & 108.210193541373 & -10.2101935413729 \tabularnewline
69 & 91 & 105.132757856971 & -14.1327578569713 \tabularnewline
70 & 77 & 88.0546121733445 & -11.0546121733445 \tabularnewline
71 & 74 & 75.7623205168778 & -1.76232051687779 \tabularnewline
72 & 102 & 80.3356348839407 & 21.6643651160593 \tabularnewline
73 & 98 & 88.2390067483624 & 9.76099325163764 \tabularnewline
74 & 113 & 102.600761992884 & 10.3992380071156 \tabularnewline
75 & 114 & 102.988524489102 & 11.011475510898 \tabularnewline
76 & 96 & 98.9267959768588 & -2.92679597685881 \tabularnewline
77 & 102 & 97.5481584720942 & 4.45184152790577 \tabularnewline
78 & 90 & 93.5835723365682 & -3.58357233656815 \tabularnewline
79 & 72 & 85.8936956684969 & -13.8936956684969 \tabularnewline
80 & 67 & 77.8467294371392 & -10.8467294371392 \tabularnewline
81 & 62 & 71.2022309296126 & -9.20223092961255 \tabularnewline
82 & 48 & 59.3055385324514 & -11.3055385324514 \tabularnewline
83 & 43 & 49.3224024174947 & -6.32240241749469 \tabularnewline
84 & 75 & 50.6767454046428 & 24.3232545953572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79314&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]154[/C][C]144.835967267461[/C][C]9.16403273253883[/C][/ROW]
[ROW][C]14[/C][C]164[/C][C]161.134327150874[/C][C]2.86567284912621[/C][/ROW]
[ROW][C]15[/C][C]167[/C][C]165.974154161445[/C][C]1.0258458385552[/C][/ROW]
[ROW][C]16[/C][C]162[/C][C]161.363438148573[/C][C]0.63656185142682[/C][/ROW]
[ROW][C]17[/C][C]164[/C][C]163.902957486157[/C][C]0.0970425138432347[/C][/ROW]
[ROW][C]18[/C][C]172[/C][C]172.206012609827[/C][C]-0.20601260982744[/C][/ROW]
[ROW][C]19[/C][C]169[/C][C]167.935558761424[/C][C]1.06444123857591[/C][/ROW]
[ROW][C]20[/C][C]174[/C][C]172.623373433226[/C][C]1.37662656677364[/C][/ROW]
[ROW][C]21[/C][C]181[/C][C]175.695105878869[/C][C]5.30489412113099[/C][/ROW]
[ROW][C]22[/C][C]181[/C][C]180.363370904279[/C][C]0.63662909572102[/C][/ROW]
[ROW][C]23[/C][C]172[/C][C]183.005512855122[/C][C]-11.0055128551225[/C][/ROW]
[ROW][C]24[/C][C]181[/C][C]177.874454727201[/C][C]3.12554527279937[/C][/ROW]
[ROW][C]25[/C][C]183[/C][C]185.769098014831[/C][C]-2.76909801483075[/C][/ROW]
[ROW][C]26[/C][C]200[/C][C]193.081577467039[/C][C]6.91842253296088[/C][/ROW]
[ROW][C]27[/C][C]199[/C][C]200.299674096934[/C][C]-1.29967409693418[/C][/ROW]
[ROW][C]28[/C][C]190[/C][C]192.590318968473[/C][C]-2.59031896847293[/C][/ROW]
[ROW][C]29[/C][C]197[/C][C]192.693589362458[/C][C]4.30641063754163[/C][/ROW]
[ROW][C]30[/C][C]194[/C][C]205.047316652563[/C][C]-11.0473166525628[/C][/ROW]
[ROW][C]31[/C][C]190[/C][C]192.661589180187[/C][C]-2.66158918018743[/C][/ROW]
[ROW][C]32[/C][C]195[/C][C]194.789331234293[/C][C]0.210668765707368[/C][/ROW]
[ROW][C]33[/C][C]204[/C][C]198.012961847578[/C][C]5.98703815242203[/C][/ROW]
[ROW][C]34[/C][C]197[/C][C]200.989829140711[/C][C]-3.98982914071127[/C][/ROW]
[ROW][C]35[/C][C]185[/C][C]195.771548158604[/C][C]-10.7715481586036[/C][/ROW]
[ROW][C]36[/C][C]193[/C][C]195.193438722546[/C][C]-2.19343872254629[/C][/ROW]
[ROW][C]37[/C][C]192[/C][C]197.012799544763[/C][C]-5.0127995447634[/C][/ROW]
[ROW][C]38[/C][C]211[/C][C]205.570387101034[/C][C]5.42961289896593[/C][/ROW]
[ROW][C]39[/C][C]210[/C][C]208.222296083506[/C][C]1.77770391649355[/C][/ROW]
[ROW][C]40[/C][C]197[/C][C]201.007652023794[/C][C]-4.00765202379412[/C][/ROW]
[ROW][C]41[/C][C]191[/C][C]201.621407359169[/C][C]-10.6214073591685[/C][/ROW]
[ROW][C]42[/C][C]182[/C][C]197.49976665005[/C][C]-15.4997666500497[/C][/ROW]
[ROW][C]43[/C][C]170[/C][C]183.481191098833[/C][C]-13.4811910988334[/C][/ROW]
[ROW][C]44[/C][C]166[/C][C]177.111132856874[/C][C]-11.1111328568743[/C][/ROW]
[ROW][C]45[/C][C]175[/C][C]171.834063544559[/C][C]3.16593645544128[/C][/ROW]
[ROW][C]46[/C][C]163[/C][C]168.481072611454[/C][C]-5.48107261145361[/C][/ROW]
[ROW][C]47[/C][C]153[/C][C]158.914898331573[/C][C]-5.91489833157252[/C][/ROW]
[ROW][C]48[/C][C]171[/C][C]161.001697733286[/C][C]9.99830226671415[/C][/ROW]
[ROW][C]49[/C][C]165[/C][C]168.459043447272[/C][C]-3.45904344727165[/C][/ROW]
[ROW][C]50[/C][C]184[/C][C]177.736799256541[/C][C]6.26320074345924[/C][/ROW]
[ROW][C]51[/C][C]179[/C][C]178.645672062248[/C][C]0.354327937751975[/C][/ROW]
[ROW][C]52[/C][C]163[/C][C]168.737820776871[/C][C]-5.73782077687088[/C][/ROW]
[ROW][C]53[/C][C]163[/C][C]164.31916293143[/C][C]-1.31916293143036[/C][/ROW]
[ROW][C]54[/C][C]148[/C][C]163.330836659677[/C][C]-15.3308366596767[/C][/ROW]
[ROW][C]55[/C][C]132[/C][C]149.048683472034[/C][C]-17.0486834720345[/C][/ROW]
[ROW][C]56[/C][C]127[/C][C]138.675541179729[/C][C]-11.6755411797294[/C][/ROW]
[ROW][C]57[/C][C]130[/C][C]134.398375136249[/C][C]-4.39837513624875[/C][/ROW]
[ROW][C]58[/C][C]118[/C][C]123.375456794781[/C][C]-5.3754567947815[/C][/ROW]
[ROW][C]59[/C][C]113[/C][C]113.519716842537[/C][C]-0.519716842537136[/C][/ROW]
[ROW][C]60[/C][C]137[/C][C]119.552804263329[/C][C]17.4471957366711[/C][/ROW]
[ROW][C]61[/C][C]133[/C][C]127.289650196454[/C][C]5.71034980354649[/C][/ROW]
[ROW][C]62[/C][C]155[/C][C]141.634688465996[/C][C]13.3653115340036[/C][/ROW]
[ROW][C]63[/C][C]151[/C][C]145.566709839836[/C][C]5.43329016016389[/C][/ROW]
[ROW][C]64[/C][C]132[/C][C]138.481315791507[/C][C]-6.48131579150703[/C][/ROW]
[ROW][C]65[/C][C]134[/C][C]134.017262240619[/C][C]-0.0172622406192886[/C][/ROW]
[ROW][C]66[/C][C]118[/C][C]129.320401850065[/C][C]-11.3204018500655[/C][/ROW]
[ROW][C]67[/C][C]102[/C][C]116.977404334652[/C][C]-14.9774043346518[/C][/ROW]
[ROW][C]68[/C][C]98[/C][C]108.210193541373[/C][C]-10.2101935413729[/C][/ROW]
[ROW][C]69[/C][C]91[/C][C]105.132757856971[/C][C]-14.1327578569713[/C][/ROW]
[ROW][C]70[/C][C]77[/C][C]88.0546121733445[/C][C]-11.0546121733445[/C][/ROW]
[ROW][C]71[/C][C]74[/C][C]75.7623205168778[/C][C]-1.76232051687779[/C][/ROW]
[ROW][C]72[/C][C]102[/C][C]80.3356348839407[/C][C]21.6643651160593[/C][/ROW]
[ROW][C]73[/C][C]98[/C][C]88.2390067483624[/C][C]9.76099325163764[/C][/ROW]
[ROW][C]74[/C][C]113[/C][C]102.600761992884[/C][C]10.3992380071156[/C][/ROW]
[ROW][C]75[/C][C]114[/C][C]102.988524489102[/C][C]11.011475510898[/C][/ROW]
[ROW][C]76[/C][C]96[/C][C]98.9267959768588[/C][C]-2.92679597685881[/C][/ROW]
[ROW][C]77[/C][C]102[/C][C]97.5481584720942[/C][C]4.45184152790577[/C][/ROW]
[ROW][C]78[/C][C]90[/C][C]93.5835723365682[/C][C]-3.58357233656815[/C][/ROW]
[ROW][C]79[/C][C]72[/C][C]85.8936956684969[/C][C]-13.8936956684969[/C][/ROW]
[ROW][C]80[/C][C]67[/C][C]77.8467294371392[/C][C]-10.8467294371392[/C][/ROW]
[ROW][C]81[/C][C]62[/C][C]71.2022309296126[/C][C]-9.20223092961255[/C][/ROW]
[ROW][C]82[/C][C]48[/C][C]59.3055385324514[/C][C]-11.3055385324514[/C][/ROW]
[ROW][C]83[/C][C]43[/C][C]49.3224024174947[/C][C]-6.32240241749469[/C][/ROW]
[ROW][C]84[/C][C]75[/C][C]50.6767454046428[/C][C]24.3232545953572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79314&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79314&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
13154144.8359672674619.16403273253883
14164161.1343271508742.86567284912621
15167165.9741541614451.0258458385552
16162161.3634381485730.63656185142682
17164163.9029574861570.0970425138432347
18172172.206012609827-0.20601260982744
19169167.9355587614241.06444123857591
20174172.6233734332261.37662656677364
21181175.6951058788695.30489412113099
22181180.3633709042790.63662909572102
23172183.005512855122-11.0055128551225
24181177.8744547272013.12554527279937
25183185.769098014831-2.76909801483075
26200193.0815774670396.91842253296088
27199200.299674096934-1.29967409693418
28190192.590318968473-2.59031896847293
29197192.6935893624584.30641063754163
30194205.047316652563-11.0473166525628
31190192.661589180187-2.66158918018743
32195194.7893312342930.210668765707368
33204198.0129618475785.98703815242203
34197200.989829140711-3.98982914071127
35185195.771548158604-10.7715481586036
36193195.193438722546-2.19343872254629
37192197.012799544763-5.0127995447634
38211205.5703871010345.42961289896593
39210208.2222960835061.77770391649355
40197201.007652023794-4.00765202379412
41191201.621407359169-10.6214073591685
42182197.49976665005-15.4997666500497
43170183.481191098833-13.4811910988334
44166177.111132856874-11.1111328568743
45175171.8340635445593.16593645544128
46163168.481072611454-5.48107261145361
47153158.914898331573-5.91489833157252
48171161.0016977332869.99830226671415
49165168.459043447272-3.45904344727165
50184177.7367992565416.26320074345924
51179178.6456720622480.354327937751975
52163168.737820776871-5.73782077687088
53163164.31916293143-1.31916293143036
54148163.330836659677-15.3308366596767
55132149.048683472034-17.0486834720345
56127138.675541179729-11.6755411797294
57130134.398375136249-4.39837513624875
58118123.375456794781-5.3754567947815
59113113.519716842537-0.519716842537136
60137119.55280426332917.4471957366711
61133127.2896501964545.71034980354649
62155141.63468846599613.3653115340036
63151145.5667098398365.43329016016389
64132138.481315791507-6.48131579150703
65134134.017262240619-0.0172622406192886
66118129.320401850065-11.3204018500655
67102116.977404334652-14.9774043346518
6898108.210193541373-10.2101935413729
6991105.132757856971-14.1327578569713
707788.0546121733445-11.0546121733445
717475.7623205168778-1.76232051687779
7210280.335634883940721.6643651160593
739888.23900674836249.76099325163764
74113102.60076199288410.3992380071156
75114102.98852448910211.011475510898
769698.9267959768588-2.92679597685881
7710297.54815847209424.45184152790577
789093.5835723365682-3.58357233656815
797285.8936956684969-13.8936956684969
806777.8467294371392-10.8467294371392
816271.2022309296126-9.20223092961255
824859.3055385324514-11.3055385324514
834349.3224024174947-6.32240241749469
847550.676745404642824.3232545953572







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8559.040604957536241.781782292473376.2994276225991
8662.071246441517340.061169047448684.081323835586
8756.521413362116831.510145694935881.5326810292978
8846.736206792240620.541269586936972.9311439975443
8946.258661349603415.778613253823476.7387094453834
9040.06745475834058.3377079293527771.7972015873281
9134.39630699599111.7036509617652167.088963030217
9233.9067363299783-3.4596697004516171.2731423604082
9333.1087477135537-9.0170487350971375.2345441622046
9428.4635178206857-14.033265944999370.9603015863707
9527.2522466805133-19.929781309474174.4342746705008
9635.127576383553-32.0373669776888102.292519744795

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 59.0406049575362 & 41.7817822924733 & 76.2994276225991 \tabularnewline
86 & 62.0712464415173 & 40.0611690474486 & 84.081323835586 \tabularnewline
87 & 56.5214133621168 & 31.5101456949358 & 81.5326810292978 \tabularnewline
88 & 46.7362067922406 & 20.5412695869369 & 72.9311439975443 \tabularnewline
89 & 46.2586613496034 & 15.7786132538234 & 76.7387094453834 \tabularnewline
90 & 40.0674547583405 & 8.33770792935277 & 71.7972015873281 \tabularnewline
91 & 34.3963069959911 & 1.70365096176521 & 67.088963030217 \tabularnewline
92 & 33.9067363299783 & -3.45966970045161 & 71.2731423604082 \tabularnewline
93 & 33.1087477135537 & -9.01704873509713 & 75.2345441622046 \tabularnewline
94 & 28.4635178206857 & -14.0332659449993 & 70.9603015863707 \tabularnewline
95 & 27.2522466805133 & -19.9297813094741 & 74.4342746705008 \tabularnewline
96 & 35.127576383553 & -32.0373669776888 & 102.292519744795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79314&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]85[/C][C]59.0406049575362[/C][C]41.7817822924733[/C][C]76.2994276225991[/C][/ROW]
[ROW][C]86[/C][C]62.0712464415173[/C][C]40.0611690474486[/C][C]84.081323835586[/C][/ROW]
[ROW][C]87[/C][C]56.5214133621168[/C][C]31.5101456949358[/C][C]81.5326810292978[/C][/ROW]
[ROW][C]88[/C][C]46.7362067922406[/C][C]20.5412695869369[/C][C]72.9311439975443[/C][/ROW]
[ROW][C]89[/C][C]46.2586613496034[/C][C]15.7786132538234[/C][C]76.7387094453834[/C][/ROW]
[ROW][C]90[/C][C]40.0674547583405[/C][C]8.33770792935277[/C][C]71.7972015873281[/C][/ROW]
[ROW][C]91[/C][C]34.3963069959911[/C][C]1.70365096176521[/C][C]67.088963030217[/C][/ROW]
[ROW][C]92[/C][C]33.9067363299783[/C][C]-3.45966970045161[/C][C]71.2731423604082[/C][/ROW]
[ROW][C]93[/C][C]33.1087477135537[/C][C]-9.01704873509713[/C][C]75.2345441622046[/C][/ROW]
[ROW][C]94[/C][C]28.4635178206857[/C][C]-14.0332659449993[/C][C]70.9603015863707[/C][/ROW]
[ROW][C]95[/C][C]27.2522466805133[/C][C]-19.9297813094741[/C][C]74.4342746705008[/C][/ROW]
[ROW][C]96[/C][C]35.127576383553[/C][C]-32.0373669776888[/C][C]102.292519744795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79314&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79314&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
8559.040604957536241.781782292473376.2994276225991
8662.071246441517340.061169047448684.081323835586
8756.521413362116831.510145694935881.5326810292978
8846.736206792240620.541269586936972.9311439975443
8946.258661349603415.778613253823476.7387094453834
9040.06745475834058.3377079293527771.7972015873281
9134.39630699599111.7036509617652167.088963030217
9233.9067363299783-3.4596697004516171.2731423604082
9333.1087477135537-9.0170487350971375.2345441622046
9428.4635178206857-14.033265944999370.9603015863707
9527.2522466805133-19.929781309474174.4342746705008
9635.127576383553-32.0373669776888102.292519744795



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')