Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 11 Aug 2010 13:42:05 +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/11/t1281534099ljrobcmcg3dd1aq.htm/, Retrieved Mon, 06 May 2024 05:53:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78633, Retrieved Mon, 06 May 2024 05:53:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMarianne Nykjaer
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 stap 32] [2010-08-11 13:42:05] [aec95ccba2c38285ca49e8d90cbfedc9] [Current]
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Dataseries X:
268
267
266
264
284
283
268
258
259
259
260
262
255
259
258
258
288
289
271
268
274
284
284
279
273
280
276
271
298
297
278
270
280
289
288
293
285
283
275
268
295
290
267
252
268
278
280
278
261
263
259
265
294
285
255
231
246
258
265
260
238
241
239
233
265
255
224
194
210
222
230
225
206
204
207
195
230
221
195
162
182
203
211
206
187
181
189
174
213
201
177
140
165
192
197
196
176
164
177
165
208
195
164
123
147
173
176
170
157
145
148
135
175
168
140
109
129
150
150
152




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78633&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78633&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78633&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.131066859076249
beta0.192073350226661
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.131066859076249 \tabularnewline
beta & 0.192073350226661 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78633&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]0.131066859076249[/C][/ROW]
[ROW][C]beta[/C][C]0.192073350226661[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78633&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78633&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
alpha0.131066859076249
beta0.192073350226661
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32662660
4264265-1
5284263.84375869019720.1562413098027
6283265.96782178241417.0321782175861
7268268.111199468881-0.111199468880557
8258268.004849102474-10.0048491024741
9259266.349902573036-7.34990257303565
10259264.857901786057-5.85790178605691
11260263.413983396093-3.41398339609327
12262262.204436556555-0.204436556554924
13255261.410408362313-6.41040836231332
14259259.641604426522-0.64160442652161
15258258.612747464200-0.612747464199515
16258257.5722471124460.427752887553822
17288256.67889031765631.3211096823442
18289260.62312049667728.3768795033234
19271264.8958320285636.10416797143716
20268266.4029982926761.59700170732361
21274267.3596280720096.64037192799077
22284269.1444442612314.8555557387699
23284272.37997924522411.6200207547762
24279275.4839704613663.51602953863431
25273277.614311115199-4.61431111519943
26280278.5628708085091.43712919149090
27276280.340752713723-4.34075271372285
28271281.252069720199-10.2520697201994
29298281.13051874961816.8694812503824
30297284.98838420254512.0116157974549
31278288.511930318781-10.5119303187805
32270288.818753918452-18.8187539184518
33280287.563076446760-7.56307644676025
34289287.5922489727091.40775102729083
35288288.832639037869-0.832639037868546
36293289.758426983653.24157301634989
37285291.299813926765-6.29981392676501
38283291.432046896729-8.43204689672945
39275291.072542639377-16.0725426393769
40268289.307005170526-21.3070051705262
41295286.3190109869728.68098901302847
42290287.4799881412182.52001185878237
43267287.896905285385-20.8969052853852
44252284.718572537776-32.7185725377756
45268279.167138902158-11.1671389021582
46278276.1592573937031.84074260629654
47280274.902617741845.09738225815977
48278274.2011394187823.79886058121815
49261273.425102166603-12.4251021666029
50263270.209845953033-7.20984595303258
51259267.496633078963-8.49663307896282
52265264.4008669872100.599133012789537
53294262.51233723250531.4876627674946
54285265.46495466906419.5350453309355
55255267.342764116597-12.3427641165966
56231264.731726898528-33.7317268985279
57246258.468127813007-12.4681278130072
58258254.6776036030033.32239639699739
59265253.04033330876111.9596666912393
60260252.8362009428017.16379905719879
61238252.183833975882-14.1838339758823
62241248.376429569067-7.37642956906689
63239245.275552713591-6.27555271359094
64233242.160980737222-9.16098073722236
65265238.43760211453126.5623978854694
66255240.06506830025114.9349316997490
67224240.544537716172-16.5445377161721
68194236.481592300834-42.4815923008337
69210227.949707855236-17.9497078552356
70222222.181266415188-0.181266415187537
71230218.73711550292911.2628844970706
72225217.0764504363457.92354956365526
73206215.177580236703-9.17758023670271
74204210.806278126015-6.80627812601548
75207206.5744308215830.425569178417078
76195203.301152498974-8.30115249897415
77230198.67511322151931.3248867784812
78221200.03132126850920.9686787314915
79195200.558048624364-5.55804862436398
80162197.468080322886-35.4680803228862
81182189.565008671361-7.56500867136131
82203185.12866004173917.8713399582611
83211184.47607490056526.5239250994354
84206185.62528216222220.3747178377780
85187186.4814544725580.518545527442285
86181184.748194743731-3.74819474373098
87189182.3613480251786.63865197482184
88174181.502997098763-7.50299709876276
89213178.60226081535134.3977391846495
90201182.05926661979318.9407333802070
91177183.967193781927-6.96719378192682
92140182.304055029179-42.3040550291788
93165174.944443514279-9.94444351427862
94192171.57575873831220.4242412616883
95197172.70157114547524.2984288545247
96196174.94686075183321.0531392481673
97176177.296801659332-1.29680165933232
98164176.684759742071-12.6847597420713
99177174.260802068512.73919793148994
100165173.927371885104-8.92737188510375
101208171.84009935600436.1599006439956
102195176.57257965864518.4274203413551
103164179.444819649786-15.4448196497861
104123177.488716684159-54.4887166841589
105147169.043529254827-22.0435292548266
106173164.2958968929348.70410310706595
107176163.79738114353312.2026188564671
108170164.0645990919705.93540090802958
109157163.659812926461-6.65981292646097
110145161.436554511906-16.4365545119065
111148157.518108054075-9.51810805407467
112135154.266827500942-19.2668275009417
113175149.25278111031525.7472188896854
114168150.78675648770117.2132435122986
115140151.635544467583-11.6355444675829
116109148.41029397791-39.4102939779101
117129140.552561804427-11.5525618044268
118150136.05522568999913.9447743100006
119150135.25079736866014.7492026313398
120152134.92310601564817.0768939843519

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 266 & 266 & 0 \tabularnewline
4 & 264 & 265 & -1 \tabularnewline
5 & 284 & 263.843758690197 & 20.1562413098027 \tabularnewline
6 & 283 & 265.967821782414 & 17.0321782175861 \tabularnewline
7 & 268 & 268.111199468881 & -0.111199468880557 \tabularnewline
8 & 258 & 268.004849102474 & -10.0048491024741 \tabularnewline
9 & 259 & 266.349902573036 & -7.34990257303565 \tabularnewline
10 & 259 & 264.857901786057 & -5.85790178605691 \tabularnewline
11 & 260 & 263.413983396093 & -3.41398339609327 \tabularnewline
12 & 262 & 262.204436556555 & -0.204436556554924 \tabularnewline
13 & 255 & 261.410408362313 & -6.41040836231332 \tabularnewline
14 & 259 & 259.641604426522 & -0.64160442652161 \tabularnewline
15 & 258 & 258.612747464200 & -0.612747464199515 \tabularnewline
16 & 258 & 257.572247112446 & 0.427752887553822 \tabularnewline
17 & 288 & 256.678890317656 & 31.3211096823442 \tabularnewline
18 & 289 & 260.623120496677 & 28.3768795033234 \tabularnewline
19 & 271 & 264.895832028563 & 6.10416797143716 \tabularnewline
20 & 268 & 266.402998292676 & 1.59700170732361 \tabularnewline
21 & 274 & 267.359628072009 & 6.64037192799077 \tabularnewline
22 & 284 & 269.14444426123 & 14.8555557387699 \tabularnewline
23 & 284 & 272.379979245224 & 11.6200207547762 \tabularnewline
24 & 279 & 275.483970461366 & 3.51602953863431 \tabularnewline
25 & 273 & 277.614311115199 & -4.61431111519943 \tabularnewline
26 & 280 & 278.562870808509 & 1.43712919149090 \tabularnewline
27 & 276 & 280.340752713723 & -4.34075271372285 \tabularnewline
28 & 271 & 281.252069720199 & -10.2520697201994 \tabularnewline
29 & 298 & 281.130518749618 & 16.8694812503824 \tabularnewline
30 & 297 & 284.988384202545 & 12.0116157974549 \tabularnewline
31 & 278 & 288.511930318781 & -10.5119303187805 \tabularnewline
32 & 270 & 288.818753918452 & -18.8187539184518 \tabularnewline
33 & 280 & 287.563076446760 & -7.56307644676025 \tabularnewline
34 & 289 & 287.592248972709 & 1.40775102729083 \tabularnewline
35 & 288 & 288.832639037869 & -0.832639037868546 \tabularnewline
36 & 293 & 289.75842698365 & 3.24157301634989 \tabularnewline
37 & 285 & 291.299813926765 & -6.29981392676501 \tabularnewline
38 & 283 & 291.432046896729 & -8.43204689672945 \tabularnewline
39 & 275 & 291.072542639377 & -16.0725426393769 \tabularnewline
40 & 268 & 289.307005170526 & -21.3070051705262 \tabularnewline
41 & 295 & 286.319010986972 & 8.68098901302847 \tabularnewline
42 & 290 & 287.479988141218 & 2.52001185878237 \tabularnewline
43 & 267 & 287.896905285385 & -20.8969052853852 \tabularnewline
44 & 252 & 284.718572537776 & -32.7185725377756 \tabularnewline
45 & 268 & 279.167138902158 & -11.1671389021582 \tabularnewline
46 & 278 & 276.159257393703 & 1.84074260629654 \tabularnewline
47 & 280 & 274.90261774184 & 5.09738225815977 \tabularnewline
48 & 278 & 274.201139418782 & 3.79886058121815 \tabularnewline
49 & 261 & 273.425102166603 & -12.4251021666029 \tabularnewline
50 & 263 & 270.209845953033 & -7.20984595303258 \tabularnewline
51 & 259 & 267.496633078963 & -8.49663307896282 \tabularnewline
52 & 265 & 264.400866987210 & 0.599133012789537 \tabularnewline
53 & 294 & 262.512337232505 & 31.4876627674946 \tabularnewline
54 & 285 & 265.464954669064 & 19.5350453309355 \tabularnewline
55 & 255 & 267.342764116597 & -12.3427641165966 \tabularnewline
56 & 231 & 264.731726898528 & -33.7317268985279 \tabularnewline
57 & 246 & 258.468127813007 & -12.4681278130072 \tabularnewline
58 & 258 & 254.677603603003 & 3.32239639699739 \tabularnewline
59 & 265 & 253.040333308761 & 11.9596666912393 \tabularnewline
60 & 260 & 252.836200942801 & 7.16379905719879 \tabularnewline
61 & 238 & 252.183833975882 & -14.1838339758823 \tabularnewline
62 & 241 & 248.376429569067 & -7.37642956906689 \tabularnewline
63 & 239 & 245.275552713591 & -6.27555271359094 \tabularnewline
64 & 233 & 242.160980737222 & -9.16098073722236 \tabularnewline
65 & 265 & 238.437602114531 & 26.5623978854694 \tabularnewline
66 & 255 & 240.065068300251 & 14.9349316997490 \tabularnewline
67 & 224 & 240.544537716172 & -16.5445377161721 \tabularnewline
68 & 194 & 236.481592300834 & -42.4815923008337 \tabularnewline
69 & 210 & 227.949707855236 & -17.9497078552356 \tabularnewline
70 & 222 & 222.181266415188 & -0.181266415187537 \tabularnewline
71 & 230 & 218.737115502929 & 11.2628844970706 \tabularnewline
72 & 225 & 217.076450436345 & 7.92354956365526 \tabularnewline
73 & 206 & 215.177580236703 & -9.17758023670271 \tabularnewline
74 & 204 & 210.806278126015 & -6.80627812601548 \tabularnewline
75 & 207 & 206.574430821583 & 0.425569178417078 \tabularnewline
76 & 195 & 203.301152498974 & -8.30115249897415 \tabularnewline
77 & 230 & 198.675113221519 & 31.3248867784812 \tabularnewline
78 & 221 & 200.031321268509 & 20.9686787314915 \tabularnewline
79 & 195 & 200.558048624364 & -5.55804862436398 \tabularnewline
80 & 162 & 197.468080322886 & -35.4680803228862 \tabularnewline
81 & 182 & 189.565008671361 & -7.56500867136131 \tabularnewline
82 & 203 & 185.128660041739 & 17.8713399582611 \tabularnewline
83 & 211 & 184.476074900565 & 26.5239250994354 \tabularnewline
84 & 206 & 185.625282162222 & 20.3747178377780 \tabularnewline
85 & 187 & 186.481454472558 & 0.518545527442285 \tabularnewline
86 & 181 & 184.748194743731 & -3.74819474373098 \tabularnewline
87 & 189 & 182.361348025178 & 6.63865197482184 \tabularnewline
88 & 174 & 181.502997098763 & -7.50299709876276 \tabularnewline
89 & 213 & 178.602260815351 & 34.3977391846495 \tabularnewline
90 & 201 & 182.059266619793 & 18.9407333802070 \tabularnewline
91 & 177 & 183.967193781927 & -6.96719378192682 \tabularnewline
92 & 140 & 182.304055029179 & -42.3040550291788 \tabularnewline
93 & 165 & 174.944443514279 & -9.94444351427862 \tabularnewline
94 & 192 & 171.575758738312 & 20.4242412616883 \tabularnewline
95 & 197 & 172.701571145475 & 24.2984288545247 \tabularnewline
96 & 196 & 174.946860751833 & 21.0531392481673 \tabularnewline
97 & 176 & 177.296801659332 & -1.29680165933232 \tabularnewline
98 & 164 & 176.684759742071 & -12.6847597420713 \tabularnewline
99 & 177 & 174.26080206851 & 2.73919793148994 \tabularnewline
100 & 165 & 173.927371885104 & -8.92737188510375 \tabularnewline
101 & 208 & 171.840099356004 & 36.1599006439956 \tabularnewline
102 & 195 & 176.572579658645 & 18.4274203413551 \tabularnewline
103 & 164 & 179.444819649786 & -15.4448196497861 \tabularnewline
104 & 123 & 177.488716684159 & -54.4887166841589 \tabularnewline
105 & 147 & 169.043529254827 & -22.0435292548266 \tabularnewline
106 & 173 & 164.295896892934 & 8.70410310706595 \tabularnewline
107 & 176 & 163.797381143533 & 12.2026188564671 \tabularnewline
108 & 170 & 164.064599091970 & 5.93540090802958 \tabularnewline
109 & 157 & 163.659812926461 & -6.65981292646097 \tabularnewline
110 & 145 & 161.436554511906 & -16.4365545119065 \tabularnewline
111 & 148 & 157.518108054075 & -9.51810805407467 \tabularnewline
112 & 135 & 154.266827500942 & -19.2668275009417 \tabularnewline
113 & 175 & 149.252781110315 & 25.7472188896854 \tabularnewline
114 & 168 & 150.786756487701 & 17.2132435122986 \tabularnewline
115 & 140 & 151.635544467583 & -11.6355444675829 \tabularnewline
116 & 109 & 148.41029397791 & -39.4102939779101 \tabularnewline
117 & 129 & 140.552561804427 & -11.5525618044268 \tabularnewline
118 & 150 & 136.055225689999 & 13.9447743100006 \tabularnewline
119 & 150 & 135.250797368660 & 14.7492026313398 \tabularnewline
120 & 152 & 134.923106015648 & 17.0768939843519 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78633&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]266[/C][C]266[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]264[/C][C]265[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]284[/C][C]263.843758690197[/C][C]20.1562413098027[/C][/ROW]
[ROW][C]6[/C][C]283[/C][C]265.967821782414[/C][C]17.0321782175861[/C][/ROW]
[ROW][C]7[/C][C]268[/C][C]268.111199468881[/C][C]-0.111199468880557[/C][/ROW]
[ROW][C]8[/C][C]258[/C][C]268.004849102474[/C][C]-10.0048491024741[/C][/ROW]
[ROW][C]9[/C][C]259[/C][C]266.349902573036[/C][C]-7.34990257303565[/C][/ROW]
[ROW][C]10[/C][C]259[/C][C]264.857901786057[/C][C]-5.85790178605691[/C][/ROW]
[ROW][C]11[/C][C]260[/C][C]263.413983396093[/C][C]-3.41398339609327[/C][/ROW]
[ROW][C]12[/C][C]262[/C][C]262.204436556555[/C][C]-0.204436556554924[/C][/ROW]
[ROW][C]13[/C][C]255[/C][C]261.410408362313[/C][C]-6.41040836231332[/C][/ROW]
[ROW][C]14[/C][C]259[/C][C]259.641604426522[/C][C]-0.64160442652161[/C][/ROW]
[ROW][C]15[/C][C]258[/C][C]258.612747464200[/C][C]-0.612747464199515[/C][/ROW]
[ROW][C]16[/C][C]258[/C][C]257.572247112446[/C][C]0.427752887553822[/C][/ROW]
[ROW][C]17[/C][C]288[/C][C]256.678890317656[/C][C]31.3211096823442[/C][/ROW]
[ROW][C]18[/C][C]289[/C][C]260.623120496677[/C][C]28.3768795033234[/C][/ROW]
[ROW][C]19[/C][C]271[/C][C]264.895832028563[/C][C]6.10416797143716[/C][/ROW]
[ROW][C]20[/C][C]268[/C][C]266.402998292676[/C][C]1.59700170732361[/C][/ROW]
[ROW][C]21[/C][C]274[/C][C]267.359628072009[/C][C]6.64037192799077[/C][/ROW]
[ROW][C]22[/C][C]284[/C][C]269.14444426123[/C][C]14.8555557387699[/C][/ROW]
[ROW][C]23[/C][C]284[/C][C]272.379979245224[/C][C]11.6200207547762[/C][/ROW]
[ROW][C]24[/C][C]279[/C][C]275.483970461366[/C][C]3.51602953863431[/C][/ROW]
[ROW][C]25[/C][C]273[/C][C]277.614311115199[/C][C]-4.61431111519943[/C][/ROW]
[ROW][C]26[/C][C]280[/C][C]278.562870808509[/C][C]1.43712919149090[/C][/ROW]
[ROW][C]27[/C][C]276[/C][C]280.340752713723[/C][C]-4.34075271372285[/C][/ROW]
[ROW][C]28[/C][C]271[/C][C]281.252069720199[/C][C]-10.2520697201994[/C][/ROW]
[ROW][C]29[/C][C]298[/C][C]281.130518749618[/C][C]16.8694812503824[/C][/ROW]
[ROW][C]30[/C][C]297[/C][C]284.988384202545[/C][C]12.0116157974549[/C][/ROW]
[ROW][C]31[/C][C]278[/C][C]288.511930318781[/C][C]-10.5119303187805[/C][/ROW]
[ROW][C]32[/C][C]270[/C][C]288.818753918452[/C][C]-18.8187539184518[/C][/ROW]
[ROW][C]33[/C][C]280[/C][C]287.563076446760[/C][C]-7.56307644676025[/C][/ROW]
[ROW][C]34[/C][C]289[/C][C]287.592248972709[/C][C]1.40775102729083[/C][/ROW]
[ROW][C]35[/C][C]288[/C][C]288.832639037869[/C][C]-0.832639037868546[/C][/ROW]
[ROW][C]36[/C][C]293[/C][C]289.75842698365[/C][C]3.24157301634989[/C][/ROW]
[ROW][C]37[/C][C]285[/C][C]291.299813926765[/C][C]-6.29981392676501[/C][/ROW]
[ROW][C]38[/C][C]283[/C][C]291.432046896729[/C][C]-8.43204689672945[/C][/ROW]
[ROW][C]39[/C][C]275[/C][C]291.072542639377[/C][C]-16.0725426393769[/C][/ROW]
[ROW][C]40[/C][C]268[/C][C]289.307005170526[/C][C]-21.3070051705262[/C][/ROW]
[ROW][C]41[/C][C]295[/C][C]286.319010986972[/C][C]8.68098901302847[/C][/ROW]
[ROW][C]42[/C][C]290[/C][C]287.479988141218[/C][C]2.52001185878237[/C][/ROW]
[ROW][C]43[/C][C]267[/C][C]287.896905285385[/C][C]-20.8969052853852[/C][/ROW]
[ROW][C]44[/C][C]252[/C][C]284.718572537776[/C][C]-32.7185725377756[/C][/ROW]
[ROW][C]45[/C][C]268[/C][C]279.167138902158[/C][C]-11.1671389021582[/C][/ROW]
[ROW][C]46[/C][C]278[/C][C]276.159257393703[/C][C]1.84074260629654[/C][/ROW]
[ROW][C]47[/C][C]280[/C][C]274.90261774184[/C][C]5.09738225815977[/C][/ROW]
[ROW][C]48[/C][C]278[/C][C]274.201139418782[/C][C]3.79886058121815[/C][/ROW]
[ROW][C]49[/C][C]261[/C][C]273.425102166603[/C][C]-12.4251021666029[/C][/ROW]
[ROW][C]50[/C][C]263[/C][C]270.209845953033[/C][C]-7.20984595303258[/C][/ROW]
[ROW][C]51[/C][C]259[/C][C]267.496633078963[/C][C]-8.49663307896282[/C][/ROW]
[ROW][C]52[/C][C]265[/C][C]264.400866987210[/C][C]0.599133012789537[/C][/ROW]
[ROW][C]53[/C][C]294[/C][C]262.512337232505[/C][C]31.4876627674946[/C][/ROW]
[ROW][C]54[/C][C]285[/C][C]265.464954669064[/C][C]19.5350453309355[/C][/ROW]
[ROW][C]55[/C][C]255[/C][C]267.342764116597[/C][C]-12.3427641165966[/C][/ROW]
[ROW][C]56[/C][C]231[/C][C]264.731726898528[/C][C]-33.7317268985279[/C][/ROW]
[ROW][C]57[/C][C]246[/C][C]258.468127813007[/C][C]-12.4681278130072[/C][/ROW]
[ROW][C]58[/C][C]258[/C][C]254.677603603003[/C][C]3.32239639699739[/C][/ROW]
[ROW][C]59[/C][C]265[/C][C]253.040333308761[/C][C]11.9596666912393[/C][/ROW]
[ROW][C]60[/C][C]260[/C][C]252.836200942801[/C][C]7.16379905719879[/C][/ROW]
[ROW][C]61[/C][C]238[/C][C]252.183833975882[/C][C]-14.1838339758823[/C][/ROW]
[ROW][C]62[/C][C]241[/C][C]248.376429569067[/C][C]-7.37642956906689[/C][/ROW]
[ROW][C]63[/C][C]239[/C][C]245.275552713591[/C][C]-6.27555271359094[/C][/ROW]
[ROW][C]64[/C][C]233[/C][C]242.160980737222[/C][C]-9.16098073722236[/C][/ROW]
[ROW][C]65[/C][C]265[/C][C]238.437602114531[/C][C]26.5623978854694[/C][/ROW]
[ROW][C]66[/C][C]255[/C][C]240.065068300251[/C][C]14.9349316997490[/C][/ROW]
[ROW][C]67[/C][C]224[/C][C]240.544537716172[/C][C]-16.5445377161721[/C][/ROW]
[ROW][C]68[/C][C]194[/C][C]236.481592300834[/C][C]-42.4815923008337[/C][/ROW]
[ROW][C]69[/C][C]210[/C][C]227.949707855236[/C][C]-17.9497078552356[/C][/ROW]
[ROW][C]70[/C][C]222[/C][C]222.181266415188[/C][C]-0.181266415187537[/C][/ROW]
[ROW][C]71[/C][C]230[/C][C]218.737115502929[/C][C]11.2628844970706[/C][/ROW]
[ROW][C]72[/C][C]225[/C][C]217.076450436345[/C][C]7.92354956365526[/C][/ROW]
[ROW][C]73[/C][C]206[/C][C]215.177580236703[/C][C]-9.17758023670271[/C][/ROW]
[ROW][C]74[/C][C]204[/C][C]210.806278126015[/C][C]-6.80627812601548[/C][/ROW]
[ROW][C]75[/C][C]207[/C][C]206.574430821583[/C][C]0.425569178417078[/C][/ROW]
[ROW][C]76[/C][C]195[/C][C]203.301152498974[/C][C]-8.30115249897415[/C][/ROW]
[ROW][C]77[/C][C]230[/C][C]198.675113221519[/C][C]31.3248867784812[/C][/ROW]
[ROW][C]78[/C][C]221[/C][C]200.031321268509[/C][C]20.9686787314915[/C][/ROW]
[ROW][C]79[/C][C]195[/C][C]200.558048624364[/C][C]-5.55804862436398[/C][/ROW]
[ROW][C]80[/C][C]162[/C][C]197.468080322886[/C][C]-35.4680803228862[/C][/ROW]
[ROW][C]81[/C][C]182[/C][C]189.565008671361[/C][C]-7.56500867136131[/C][/ROW]
[ROW][C]82[/C][C]203[/C][C]185.128660041739[/C][C]17.8713399582611[/C][/ROW]
[ROW][C]83[/C][C]211[/C][C]184.476074900565[/C][C]26.5239250994354[/C][/ROW]
[ROW][C]84[/C][C]206[/C][C]185.625282162222[/C][C]20.3747178377780[/C][/ROW]
[ROW][C]85[/C][C]187[/C][C]186.481454472558[/C][C]0.518545527442285[/C][/ROW]
[ROW][C]86[/C][C]181[/C][C]184.748194743731[/C][C]-3.74819474373098[/C][/ROW]
[ROW][C]87[/C][C]189[/C][C]182.361348025178[/C][C]6.63865197482184[/C][/ROW]
[ROW][C]88[/C][C]174[/C][C]181.502997098763[/C][C]-7.50299709876276[/C][/ROW]
[ROW][C]89[/C][C]213[/C][C]178.602260815351[/C][C]34.3977391846495[/C][/ROW]
[ROW][C]90[/C][C]201[/C][C]182.059266619793[/C][C]18.9407333802070[/C][/ROW]
[ROW][C]91[/C][C]177[/C][C]183.967193781927[/C][C]-6.96719378192682[/C][/ROW]
[ROW][C]92[/C][C]140[/C][C]182.304055029179[/C][C]-42.3040550291788[/C][/ROW]
[ROW][C]93[/C][C]165[/C][C]174.944443514279[/C][C]-9.94444351427862[/C][/ROW]
[ROW][C]94[/C][C]192[/C][C]171.575758738312[/C][C]20.4242412616883[/C][/ROW]
[ROW][C]95[/C][C]197[/C][C]172.701571145475[/C][C]24.2984288545247[/C][/ROW]
[ROW][C]96[/C][C]196[/C][C]174.946860751833[/C][C]21.0531392481673[/C][/ROW]
[ROW][C]97[/C][C]176[/C][C]177.296801659332[/C][C]-1.29680165933232[/C][/ROW]
[ROW][C]98[/C][C]164[/C][C]176.684759742071[/C][C]-12.6847597420713[/C][/ROW]
[ROW][C]99[/C][C]177[/C][C]174.26080206851[/C][C]2.73919793148994[/C][/ROW]
[ROW][C]100[/C][C]165[/C][C]173.927371885104[/C][C]-8.92737188510375[/C][/ROW]
[ROW][C]101[/C][C]208[/C][C]171.840099356004[/C][C]36.1599006439956[/C][/ROW]
[ROW][C]102[/C][C]195[/C][C]176.572579658645[/C][C]18.4274203413551[/C][/ROW]
[ROW][C]103[/C][C]164[/C][C]179.444819649786[/C][C]-15.4448196497861[/C][/ROW]
[ROW][C]104[/C][C]123[/C][C]177.488716684159[/C][C]-54.4887166841589[/C][/ROW]
[ROW][C]105[/C][C]147[/C][C]169.043529254827[/C][C]-22.0435292548266[/C][/ROW]
[ROW][C]106[/C][C]173[/C][C]164.295896892934[/C][C]8.70410310706595[/C][/ROW]
[ROW][C]107[/C][C]176[/C][C]163.797381143533[/C][C]12.2026188564671[/C][/ROW]
[ROW][C]108[/C][C]170[/C][C]164.064599091970[/C][C]5.93540090802958[/C][/ROW]
[ROW][C]109[/C][C]157[/C][C]163.659812926461[/C][C]-6.65981292646097[/C][/ROW]
[ROW][C]110[/C][C]145[/C][C]161.436554511906[/C][C]-16.4365545119065[/C][/ROW]
[ROW][C]111[/C][C]148[/C][C]157.518108054075[/C][C]-9.51810805407467[/C][/ROW]
[ROW][C]112[/C][C]135[/C][C]154.266827500942[/C][C]-19.2668275009417[/C][/ROW]
[ROW][C]113[/C][C]175[/C][C]149.252781110315[/C][C]25.7472188896854[/C][/ROW]
[ROW][C]114[/C][C]168[/C][C]150.786756487701[/C][C]17.2132435122986[/C][/ROW]
[ROW][C]115[/C][C]140[/C][C]151.635544467583[/C][C]-11.6355444675829[/C][/ROW]
[ROW][C]116[/C][C]109[/C][C]148.41029397791[/C][C]-39.4102939779101[/C][/ROW]
[ROW][C]117[/C][C]129[/C][C]140.552561804427[/C][C]-11.5525618044268[/C][/ROW]
[ROW][C]118[/C][C]150[/C][C]136.055225689999[/C][C]13.9447743100006[/C][/ROW]
[ROW][C]119[/C][C]150[/C][C]135.250797368660[/C][C]14.7492026313398[/C][/ROW]
[ROW][C]120[/C][C]152[/C][C]134.923106015648[/C][C]17.0768939843519[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78633&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78633&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
32662660
4264265-1
5284263.84375869019720.1562413098027
6283265.96782178241417.0321782175861
7268268.111199468881-0.111199468880557
8258268.004849102474-10.0048491024741
9259266.349902573036-7.34990257303565
10259264.857901786057-5.85790178605691
11260263.413983396093-3.41398339609327
12262262.204436556555-0.204436556554924
13255261.410408362313-6.41040836231332
14259259.641604426522-0.64160442652161
15258258.612747464200-0.612747464199515
16258257.5722471124460.427752887553822
17288256.67889031765631.3211096823442
18289260.62312049667728.3768795033234
19271264.8958320285636.10416797143716
20268266.4029982926761.59700170732361
21274267.3596280720096.64037192799077
22284269.1444442612314.8555557387699
23284272.37997924522411.6200207547762
24279275.4839704613663.51602953863431
25273277.614311115199-4.61431111519943
26280278.5628708085091.43712919149090
27276280.340752713723-4.34075271372285
28271281.252069720199-10.2520697201994
29298281.13051874961816.8694812503824
30297284.98838420254512.0116157974549
31278288.511930318781-10.5119303187805
32270288.818753918452-18.8187539184518
33280287.563076446760-7.56307644676025
34289287.5922489727091.40775102729083
35288288.832639037869-0.832639037868546
36293289.758426983653.24157301634989
37285291.299813926765-6.29981392676501
38283291.432046896729-8.43204689672945
39275291.072542639377-16.0725426393769
40268289.307005170526-21.3070051705262
41295286.3190109869728.68098901302847
42290287.4799881412182.52001185878237
43267287.896905285385-20.8969052853852
44252284.718572537776-32.7185725377756
45268279.167138902158-11.1671389021582
46278276.1592573937031.84074260629654
47280274.902617741845.09738225815977
48278274.2011394187823.79886058121815
49261273.425102166603-12.4251021666029
50263270.209845953033-7.20984595303258
51259267.496633078963-8.49663307896282
52265264.4008669872100.599133012789537
53294262.51233723250531.4876627674946
54285265.46495466906419.5350453309355
55255267.342764116597-12.3427641165966
56231264.731726898528-33.7317268985279
57246258.468127813007-12.4681278130072
58258254.6776036030033.32239639699739
59265253.04033330876111.9596666912393
60260252.8362009428017.16379905719879
61238252.183833975882-14.1838339758823
62241248.376429569067-7.37642956906689
63239245.275552713591-6.27555271359094
64233242.160980737222-9.16098073722236
65265238.43760211453126.5623978854694
66255240.06506830025114.9349316997490
67224240.544537716172-16.5445377161721
68194236.481592300834-42.4815923008337
69210227.949707855236-17.9497078552356
70222222.181266415188-0.181266415187537
71230218.73711550292911.2628844970706
72225217.0764504363457.92354956365526
73206215.177580236703-9.17758023670271
74204210.806278126015-6.80627812601548
75207206.5744308215830.425569178417078
76195203.301152498974-8.30115249897415
77230198.67511322151931.3248867784812
78221200.03132126850920.9686787314915
79195200.558048624364-5.55804862436398
80162197.468080322886-35.4680803228862
81182189.565008671361-7.56500867136131
82203185.12866004173917.8713399582611
83211184.47607490056526.5239250994354
84206185.62528216222220.3747178377780
85187186.4814544725580.518545527442285
86181184.748194743731-3.74819474373098
87189182.3613480251786.63865197482184
88174181.502997098763-7.50299709876276
89213178.60226081535134.3977391846495
90201182.05926661979318.9407333802070
91177183.967193781927-6.96719378192682
92140182.304055029179-42.3040550291788
93165174.944443514279-9.94444351427862
94192171.57575873831220.4242412616883
95197172.70157114547524.2984288545247
96196174.94686075183321.0531392481673
97176177.296801659332-1.29680165933232
98164176.684759742071-12.6847597420713
99177174.260802068512.73919793148994
100165173.927371885104-8.92737188510375
101208171.84009935600436.1599006439956
102195176.57257965864518.4274203413551
103164179.444819649786-15.4448196497861
104123177.488716684159-54.4887166841589
105147169.043529254827-22.0435292548266
106173164.2958968929348.70410310706595
107176163.79738114353312.2026188564671
108170164.0645990919705.93540090802958
109157163.659812926461-6.65981292646097
110145161.436554511906-16.4365545119065
111148157.518108054075-9.51810805407467
112135154.266827500942-19.2668275009417
113175149.25278111031525.7472188896854
114168150.78675648770117.2132435122986
115140151.635544467583-11.6355444675829
116109148.41029397791-39.4102939779101
117129140.552561804427-11.5525618044268
118150136.05522568999913.9447743100006
119150135.25079736866014.7492026313398
120152134.92310601564817.0768939843519







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121135.330399283344102.105376737128168.555421829561
122133.49947769373399.8713665238017167.127588863665
123131.66855610412397.5045233757499165.832588832495
124129.83763451451294.9908966482832164.68437238074
125128.00671292490192.3193049731988163.694120876603
126126.1757913352989.4815387343311162.870043936249
127124.34486974567986.4723783395158162.217361151842
128122.51394815606883.2894330805575161.738463231579
129120.68302656645779.9328325885497161.433220544365
130118.85210497684676.4048201780365161.299389775656
131117.02118338723672.7093021580612161.33306461641
132115.19026179762568.8514011559819161.529122439267

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 135.330399283344 & 102.105376737128 & 168.555421829561 \tabularnewline
122 & 133.499477693733 & 99.8713665238017 & 167.127588863665 \tabularnewline
123 & 131.668556104123 & 97.5045233757499 & 165.832588832495 \tabularnewline
124 & 129.837634514512 & 94.9908966482832 & 164.68437238074 \tabularnewline
125 & 128.006712924901 & 92.3193049731988 & 163.694120876603 \tabularnewline
126 & 126.17579133529 & 89.4815387343311 & 162.870043936249 \tabularnewline
127 & 124.344869745679 & 86.4723783395158 & 162.217361151842 \tabularnewline
128 & 122.513948156068 & 83.2894330805575 & 161.738463231579 \tabularnewline
129 & 120.683026566457 & 79.9328325885497 & 161.433220544365 \tabularnewline
130 & 118.852104976846 & 76.4048201780365 & 161.299389775656 \tabularnewline
131 & 117.021183387236 & 72.7093021580612 & 161.33306461641 \tabularnewline
132 & 115.190261797625 & 68.8514011559819 & 161.529122439267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78633&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]135.330399283344[/C][C]102.105376737128[/C][C]168.555421829561[/C][/ROW]
[ROW][C]122[/C][C]133.499477693733[/C][C]99.8713665238017[/C][C]167.127588863665[/C][/ROW]
[ROW][C]123[/C][C]131.668556104123[/C][C]97.5045233757499[/C][C]165.832588832495[/C][/ROW]
[ROW][C]124[/C][C]129.837634514512[/C][C]94.9908966482832[/C][C]164.68437238074[/C][/ROW]
[ROW][C]125[/C][C]128.006712924901[/C][C]92.3193049731988[/C][C]163.694120876603[/C][/ROW]
[ROW][C]126[/C][C]126.17579133529[/C][C]89.4815387343311[/C][C]162.870043936249[/C][/ROW]
[ROW][C]127[/C][C]124.344869745679[/C][C]86.4723783395158[/C][C]162.217361151842[/C][/ROW]
[ROW][C]128[/C][C]122.513948156068[/C][C]83.2894330805575[/C][C]161.738463231579[/C][/ROW]
[ROW][C]129[/C][C]120.683026566457[/C][C]79.9328325885497[/C][C]161.433220544365[/C][/ROW]
[ROW][C]130[/C][C]118.852104976846[/C][C]76.4048201780365[/C][C]161.299389775656[/C][/ROW]
[ROW][C]131[/C][C]117.021183387236[/C][C]72.7093021580612[/C][C]161.33306461641[/C][/ROW]
[ROW][C]132[/C][C]115.190261797625[/C][C]68.8514011559819[/C][C]161.529122439267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78633&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78633&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
121135.330399283344102.105376737128168.555421829561
122133.49947769373399.8713665238017167.127588863665
123131.66855610412397.5045233757499165.832588832495
124129.83763451451294.9908966482832164.68437238074
125128.00671292490192.3193049731988163.694120876603
126126.1757913352989.4815387343311162.870043936249
127124.34486974567986.4723783395158162.217361151842
128122.51394815606883.2894330805575161.738463231579
129120.68302656645779.9328325885497161.433220544365
130118.85210497684676.4048201780365161.299389775656
131117.02118338723672.7093021580612161.33306461641
132115.19026179762568.8514011559819161.529122439267



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