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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 computationThu, 10 Aug 2017 12:10:47 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/10/t1502359885sdn09317d0iaiyt.htm/, Retrieved Sat, 18 May 2024 23:30:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307076, Retrieved Sat, 18 May 2024 23:30:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-10 10:10:47] [ad161bcd2bdcbffd0567a2be7a0bbb46] [Current]
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Dataseries X:
209704
208923
208131
206492
222706
221848
209704
201630
202411
202411
203280
204842
207273
207273
205711
201630
222706
225918
221067
209704
214566
207273
210562
212135
213774
209704
210562
204842
222706
228349
223498
214566
224279
213774
223498
222706
225137
216205
225918
225137
239712
236423
223498
216986
225918
213774
222706
224279
227568
220286
224279
226710
235642
228349
218636
208131
217855
191125
204061
211343
218636
208131
208131
208131
213774
205711
195129
186274
192698
167618
182985
191917
193556
184624
185405
182985
191125
185405
174130
165979
179762
149831
169268
178123
178123
167618
157905
157124
165979
157905
142549
131967
143330
116611
140899
153824
157905
148973
137687
145761
148973
146542
122243
110968
119031
94743
119823
128755
136037
123893
112530
119031
122243
115819
91531
80949
90662
63943
93093
110968




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307076&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307076&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.379244790290636
beta0.0506954647934185
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.379244790290636 \tabularnewline
beta & 0.0506954647934185 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307076&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]0.379244790290636[/C][/ROW]
[ROW][C]beta[/C][C]0.0506954647934185[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307076&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
alpha0.379244790290636
beta0.0506954647934185
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13207273207288.777052553-15.7770525533997
14207273206829.902781575443.097218425042
15205711204967.575548738743.424451262166
16201630200860.578014649769.421985351248
17222706222059.00268356646.997316440014
18225918225294.20840314623.79159686013
19221067213219.2904395177847.70956048279
20209704208587.8887447641116.11125523614
21214566210562.4811982964003.5188017037
22207273213039.144462173-5766.14446217282
23210562212504.887988126-1942.88798812611
24212135213727.772814232-1592.77281423163
25213774215457.559407834-1683.55940783376
26209704214728.578432259-5024.57843225871
27210562210911.162313749-349.162313748617
28204842206259.859534995-1417.8595349949
29222706226888.664965203-4182.66496520303
30228349228134.238561025214.761438974587
31223498220062.7084438363435.29155616375
32214566209313.5033853455252.49661465475
33224279214481.9392941659797.0607058352
34213774212897.911055206876.088944794144
35223498217420.5579181176077.44208188323
36222706222196.693328369509.306671631464
37225137225017.95516129119.044838710484
38216205223029.377023731-6824.37702373115
39225918221726.9985409284191.00145907246
40225137218138.3504801986998.64951980172
41239712242260.94486429-2548.94486428975
42236423247891.831082428-11468.8310824282
43223498237307.132658469-13809.132658469
44216986220708.405919404-3722.40591940362
45225918225158.374865658759.625134342088
46213774214233.808115773-459.80811577331
47222706221096.4254611961609.57453880375
48224279220299.0139880043979.98601199585
49227568223815.4656607383752.53433926179
50220286218549.0075840091736.99241599123
51224279227281.642436784-3002.64243678385
52226710222381.954266974328.04573303033
53235642239141.738568626-3499.73856862634
54228349238383.800421263-10034.8004212626
55218636226433.059978999-7797.05997899896
56208131218142.862268436-10011.862268436
57217855222533.923294133-4678.92329413292
58191125208635.820164761-17510.8201647609
59204061209080.383965536-5019.38396553585
60211343206324.8208566945018.17914330596
61218636209070.5557039229565.44429607806
62208131204538.7421962873592.25780371347
63208131209977.374038732-1846.37403873159
64208131209301.604060577-1170.60406057735
65213774217474.967240868-3700.96724086767
66205711211964.58090559-6253.58090559026
67195129202592.079216556-7463.07921655552
68186274192806.507496188-6532.50749618848
69192698200104.467409181-7406.46740918065
70167618178070.425012804-10452.4250128042
71182985186930.733516517-3945.73351651744
72191917189618.6516709522298.34832904837
73193556192962.17615649593.823843509628
74184624181830.4212224052793.57877759513
75185405182630.6380530652774.36194693536
76182985183284.762212761-299.762212761067
77191125188556.7869251012568.21307489931
78185405183774.3973383691630.60266163116
79174130176873.98508671-2743.98508670978
80165979169616.104800004-3637.10480000425
81179762176115.755887153646.24411285034
82149831157743.574243938-7912.574243938
83169268170137.211494148-869.211494148039
84178123177179.225747702943.774252297997
85178123178713.942535509-590.942535509297
86167618169117.807551057-1499.80755105682
87157905168053.277087645-10148.2770876448
88157124161652.995241583-4528.99524158271
89165979165561.170288369417.829711631348
90157905159566.277660807-1661.27766080672
91142549149466.998056761-6917.9980567607
92131967140354.209254903-8387.20925490322
93143330146451.553321436-3121.55332143634
94116611122493.770384992-5882.77038499244
95140899135062.9684137665836.03158623385
96153824143183.64846263510640.3515373645
97157905146623.82720845911281.1727915407
98148973141980.282896356992.71710365021
99137687139130.749581575-1443.74958157507
100145761139217.1731693316543.8268306689
101148973149622.092208008-649.092208007845
102146542142728.791264223813.20873578009
103122243132645.025010741-10402.0250107407
104110968121973.308597338-11005.3085973383
105119031128958.486979795-9927.4869797952
10694743103575.684108378-8832.68410837839
107119823118826.165631058996.834368941651
108128755126110.3412889292644.65871107073
109136037126151.1506774219885.84932257942
110123893119707.3528782524185.64712174823
111112530111945.566005107584.433994893057
112119031116067.6015132962963.398486704
113122243119289.5697803232953.43021967671
114115819116658.069219592-839.069219591547
1159153199422.3214903636-7891.32149036363
1168094990058.59693823-9109.59693822995
1179066295009.4114319615-4347.41143196149
1186394376280.0396211326-12337.0396211326
1199309389405.12823175913687.87176824093
12011096895932.143899228115035.8561007719

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 207273 & 207288.777052553 & -15.7770525533997 \tabularnewline
14 & 207273 & 206829.902781575 & 443.097218425042 \tabularnewline
15 & 205711 & 204967.575548738 & 743.424451262166 \tabularnewline
16 & 201630 & 200860.578014649 & 769.421985351248 \tabularnewline
17 & 222706 & 222059.00268356 & 646.997316440014 \tabularnewline
18 & 225918 & 225294.20840314 & 623.79159686013 \tabularnewline
19 & 221067 & 213219.290439517 & 7847.70956048279 \tabularnewline
20 & 209704 & 208587.888744764 & 1116.11125523614 \tabularnewline
21 & 214566 & 210562.481198296 & 4003.5188017037 \tabularnewline
22 & 207273 & 213039.144462173 & -5766.14446217282 \tabularnewline
23 & 210562 & 212504.887988126 & -1942.88798812611 \tabularnewline
24 & 212135 & 213727.772814232 & -1592.77281423163 \tabularnewline
25 & 213774 & 215457.559407834 & -1683.55940783376 \tabularnewline
26 & 209704 & 214728.578432259 & -5024.57843225871 \tabularnewline
27 & 210562 & 210911.162313749 & -349.162313748617 \tabularnewline
28 & 204842 & 206259.859534995 & -1417.8595349949 \tabularnewline
29 & 222706 & 226888.664965203 & -4182.66496520303 \tabularnewline
30 & 228349 & 228134.238561025 & 214.761438974587 \tabularnewline
31 & 223498 & 220062.708443836 & 3435.29155616375 \tabularnewline
32 & 214566 & 209313.503385345 & 5252.49661465475 \tabularnewline
33 & 224279 & 214481.939294165 & 9797.0607058352 \tabularnewline
34 & 213774 & 212897.911055206 & 876.088944794144 \tabularnewline
35 & 223498 & 217420.557918117 & 6077.44208188323 \tabularnewline
36 & 222706 & 222196.693328369 & 509.306671631464 \tabularnewline
37 & 225137 & 225017.95516129 & 119.044838710484 \tabularnewline
38 & 216205 & 223029.377023731 & -6824.37702373115 \tabularnewline
39 & 225918 & 221726.998540928 & 4191.00145907246 \tabularnewline
40 & 225137 & 218138.350480198 & 6998.64951980172 \tabularnewline
41 & 239712 & 242260.94486429 & -2548.94486428975 \tabularnewline
42 & 236423 & 247891.831082428 & -11468.8310824282 \tabularnewline
43 & 223498 & 237307.132658469 & -13809.132658469 \tabularnewline
44 & 216986 & 220708.405919404 & -3722.40591940362 \tabularnewline
45 & 225918 & 225158.374865658 & 759.625134342088 \tabularnewline
46 & 213774 & 214233.808115773 & -459.80811577331 \tabularnewline
47 & 222706 & 221096.425461196 & 1609.57453880375 \tabularnewline
48 & 224279 & 220299.013988004 & 3979.98601199585 \tabularnewline
49 & 227568 & 223815.465660738 & 3752.53433926179 \tabularnewline
50 & 220286 & 218549.007584009 & 1736.99241599123 \tabularnewline
51 & 224279 & 227281.642436784 & -3002.64243678385 \tabularnewline
52 & 226710 & 222381.95426697 & 4328.04573303033 \tabularnewline
53 & 235642 & 239141.738568626 & -3499.73856862634 \tabularnewline
54 & 228349 & 238383.800421263 & -10034.8004212626 \tabularnewline
55 & 218636 & 226433.059978999 & -7797.05997899896 \tabularnewline
56 & 208131 & 218142.862268436 & -10011.862268436 \tabularnewline
57 & 217855 & 222533.923294133 & -4678.92329413292 \tabularnewline
58 & 191125 & 208635.820164761 & -17510.8201647609 \tabularnewline
59 & 204061 & 209080.383965536 & -5019.38396553585 \tabularnewline
60 & 211343 & 206324.820856694 & 5018.17914330596 \tabularnewline
61 & 218636 & 209070.555703922 & 9565.44429607806 \tabularnewline
62 & 208131 & 204538.742196287 & 3592.25780371347 \tabularnewline
63 & 208131 & 209977.374038732 & -1846.37403873159 \tabularnewline
64 & 208131 & 209301.604060577 & -1170.60406057735 \tabularnewline
65 & 213774 & 217474.967240868 & -3700.96724086767 \tabularnewline
66 & 205711 & 211964.58090559 & -6253.58090559026 \tabularnewline
67 & 195129 & 202592.079216556 & -7463.07921655552 \tabularnewline
68 & 186274 & 192806.507496188 & -6532.50749618848 \tabularnewline
69 & 192698 & 200104.467409181 & -7406.46740918065 \tabularnewline
70 & 167618 & 178070.425012804 & -10452.4250128042 \tabularnewline
71 & 182985 & 186930.733516517 & -3945.73351651744 \tabularnewline
72 & 191917 & 189618.651670952 & 2298.34832904837 \tabularnewline
73 & 193556 & 192962.17615649 & 593.823843509628 \tabularnewline
74 & 184624 & 181830.421222405 & 2793.57877759513 \tabularnewline
75 & 185405 & 182630.638053065 & 2774.36194693536 \tabularnewline
76 & 182985 & 183284.762212761 & -299.762212761067 \tabularnewline
77 & 191125 & 188556.786925101 & 2568.21307489931 \tabularnewline
78 & 185405 & 183774.397338369 & 1630.60266163116 \tabularnewline
79 & 174130 & 176873.98508671 & -2743.98508670978 \tabularnewline
80 & 165979 & 169616.104800004 & -3637.10480000425 \tabularnewline
81 & 179762 & 176115.75588715 & 3646.24411285034 \tabularnewline
82 & 149831 & 157743.574243938 & -7912.574243938 \tabularnewline
83 & 169268 & 170137.211494148 & -869.211494148039 \tabularnewline
84 & 178123 & 177179.225747702 & 943.774252297997 \tabularnewline
85 & 178123 & 178713.942535509 & -590.942535509297 \tabularnewline
86 & 167618 & 169117.807551057 & -1499.80755105682 \tabularnewline
87 & 157905 & 168053.277087645 & -10148.2770876448 \tabularnewline
88 & 157124 & 161652.995241583 & -4528.99524158271 \tabularnewline
89 & 165979 & 165561.170288369 & 417.829711631348 \tabularnewline
90 & 157905 & 159566.277660807 & -1661.27766080672 \tabularnewline
91 & 142549 & 149466.998056761 & -6917.9980567607 \tabularnewline
92 & 131967 & 140354.209254903 & -8387.20925490322 \tabularnewline
93 & 143330 & 146451.553321436 & -3121.55332143634 \tabularnewline
94 & 116611 & 122493.770384992 & -5882.77038499244 \tabularnewline
95 & 140899 & 135062.968413766 & 5836.03158623385 \tabularnewline
96 & 153824 & 143183.648462635 & 10640.3515373645 \tabularnewline
97 & 157905 & 146623.827208459 & 11281.1727915407 \tabularnewline
98 & 148973 & 141980.28289635 & 6992.71710365021 \tabularnewline
99 & 137687 & 139130.749581575 & -1443.74958157507 \tabularnewline
100 & 145761 & 139217.173169331 & 6543.8268306689 \tabularnewline
101 & 148973 & 149622.092208008 & -649.092208007845 \tabularnewline
102 & 146542 & 142728.79126422 & 3813.20873578009 \tabularnewline
103 & 122243 & 132645.025010741 & -10402.0250107407 \tabularnewline
104 & 110968 & 121973.308597338 & -11005.3085973383 \tabularnewline
105 & 119031 & 128958.486979795 & -9927.4869797952 \tabularnewline
106 & 94743 & 103575.684108378 & -8832.68410837839 \tabularnewline
107 & 119823 & 118826.165631058 & 996.834368941651 \tabularnewline
108 & 128755 & 126110.341288929 & 2644.65871107073 \tabularnewline
109 & 136037 & 126151.150677421 & 9885.84932257942 \tabularnewline
110 & 123893 & 119707.352878252 & 4185.64712174823 \tabularnewline
111 & 112530 & 111945.566005107 & 584.433994893057 \tabularnewline
112 & 119031 & 116067.601513296 & 2963.398486704 \tabularnewline
113 & 122243 & 119289.569780323 & 2953.43021967671 \tabularnewline
114 & 115819 & 116658.069219592 & -839.069219591547 \tabularnewline
115 & 91531 & 99422.3214903636 & -7891.32149036363 \tabularnewline
116 & 80949 & 90058.59693823 & -9109.59693822995 \tabularnewline
117 & 90662 & 95009.4114319615 & -4347.41143196149 \tabularnewline
118 & 63943 & 76280.0396211326 & -12337.0396211326 \tabularnewline
119 & 93093 & 89405.1282317591 & 3687.87176824093 \tabularnewline
120 & 110968 & 95932.1438992281 & 15035.8561007719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307076&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]207273[/C][C]207288.777052553[/C][C]-15.7770525533997[/C][/ROW]
[ROW][C]14[/C][C]207273[/C][C]206829.902781575[/C][C]443.097218425042[/C][/ROW]
[ROW][C]15[/C][C]205711[/C][C]204967.575548738[/C][C]743.424451262166[/C][/ROW]
[ROW][C]16[/C][C]201630[/C][C]200860.578014649[/C][C]769.421985351248[/C][/ROW]
[ROW][C]17[/C][C]222706[/C][C]222059.00268356[/C][C]646.997316440014[/C][/ROW]
[ROW][C]18[/C][C]225918[/C][C]225294.20840314[/C][C]623.79159686013[/C][/ROW]
[ROW][C]19[/C][C]221067[/C][C]213219.290439517[/C][C]7847.70956048279[/C][/ROW]
[ROW][C]20[/C][C]209704[/C][C]208587.888744764[/C][C]1116.11125523614[/C][/ROW]
[ROW][C]21[/C][C]214566[/C][C]210562.481198296[/C][C]4003.5188017037[/C][/ROW]
[ROW][C]22[/C][C]207273[/C][C]213039.144462173[/C][C]-5766.14446217282[/C][/ROW]
[ROW][C]23[/C][C]210562[/C][C]212504.887988126[/C][C]-1942.88798812611[/C][/ROW]
[ROW][C]24[/C][C]212135[/C][C]213727.772814232[/C][C]-1592.77281423163[/C][/ROW]
[ROW][C]25[/C][C]213774[/C][C]215457.559407834[/C][C]-1683.55940783376[/C][/ROW]
[ROW][C]26[/C][C]209704[/C][C]214728.578432259[/C][C]-5024.57843225871[/C][/ROW]
[ROW][C]27[/C][C]210562[/C][C]210911.162313749[/C][C]-349.162313748617[/C][/ROW]
[ROW][C]28[/C][C]204842[/C][C]206259.859534995[/C][C]-1417.8595349949[/C][/ROW]
[ROW][C]29[/C][C]222706[/C][C]226888.664965203[/C][C]-4182.66496520303[/C][/ROW]
[ROW][C]30[/C][C]228349[/C][C]228134.238561025[/C][C]214.761438974587[/C][/ROW]
[ROW][C]31[/C][C]223498[/C][C]220062.708443836[/C][C]3435.29155616375[/C][/ROW]
[ROW][C]32[/C][C]214566[/C][C]209313.503385345[/C][C]5252.49661465475[/C][/ROW]
[ROW][C]33[/C][C]224279[/C][C]214481.939294165[/C][C]9797.0607058352[/C][/ROW]
[ROW][C]34[/C][C]213774[/C][C]212897.911055206[/C][C]876.088944794144[/C][/ROW]
[ROW][C]35[/C][C]223498[/C][C]217420.557918117[/C][C]6077.44208188323[/C][/ROW]
[ROW][C]36[/C][C]222706[/C][C]222196.693328369[/C][C]509.306671631464[/C][/ROW]
[ROW][C]37[/C][C]225137[/C][C]225017.95516129[/C][C]119.044838710484[/C][/ROW]
[ROW][C]38[/C][C]216205[/C][C]223029.377023731[/C][C]-6824.37702373115[/C][/ROW]
[ROW][C]39[/C][C]225918[/C][C]221726.998540928[/C][C]4191.00145907246[/C][/ROW]
[ROW][C]40[/C][C]225137[/C][C]218138.350480198[/C][C]6998.64951980172[/C][/ROW]
[ROW][C]41[/C][C]239712[/C][C]242260.94486429[/C][C]-2548.94486428975[/C][/ROW]
[ROW][C]42[/C][C]236423[/C][C]247891.831082428[/C][C]-11468.8310824282[/C][/ROW]
[ROW][C]43[/C][C]223498[/C][C]237307.132658469[/C][C]-13809.132658469[/C][/ROW]
[ROW][C]44[/C][C]216986[/C][C]220708.405919404[/C][C]-3722.40591940362[/C][/ROW]
[ROW][C]45[/C][C]225918[/C][C]225158.374865658[/C][C]759.625134342088[/C][/ROW]
[ROW][C]46[/C][C]213774[/C][C]214233.808115773[/C][C]-459.80811577331[/C][/ROW]
[ROW][C]47[/C][C]222706[/C][C]221096.425461196[/C][C]1609.57453880375[/C][/ROW]
[ROW][C]48[/C][C]224279[/C][C]220299.013988004[/C][C]3979.98601199585[/C][/ROW]
[ROW][C]49[/C][C]227568[/C][C]223815.465660738[/C][C]3752.53433926179[/C][/ROW]
[ROW][C]50[/C][C]220286[/C][C]218549.007584009[/C][C]1736.99241599123[/C][/ROW]
[ROW][C]51[/C][C]224279[/C][C]227281.642436784[/C][C]-3002.64243678385[/C][/ROW]
[ROW][C]52[/C][C]226710[/C][C]222381.95426697[/C][C]4328.04573303033[/C][/ROW]
[ROW][C]53[/C][C]235642[/C][C]239141.738568626[/C][C]-3499.73856862634[/C][/ROW]
[ROW][C]54[/C][C]228349[/C][C]238383.800421263[/C][C]-10034.8004212626[/C][/ROW]
[ROW][C]55[/C][C]218636[/C][C]226433.059978999[/C][C]-7797.05997899896[/C][/ROW]
[ROW][C]56[/C][C]208131[/C][C]218142.862268436[/C][C]-10011.862268436[/C][/ROW]
[ROW][C]57[/C][C]217855[/C][C]222533.923294133[/C][C]-4678.92329413292[/C][/ROW]
[ROW][C]58[/C][C]191125[/C][C]208635.820164761[/C][C]-17510.8201647609[/C][/ROW]
[ROW][C]59[/C][C]204061[/C][C]209080.383965536[/C][C]-5019.38396553585[/C][/ROW]
[ROW][C]60[/C][C]211343[/C][C]206324.820856694[/C][C]5018.17914330596[/C][/ROW]
[ROW][C]61[/C][C]218636[/C][C]209070.555703922[/C][C]9565.44429607806[/C][/ROW]
[ROW][C]62[/C][C]208131[/C][C]204538.742196287[/C][C]3592.25780371347[/C][/ROW]
[ROW][C]63[/C][C]208131[/C][C]209977.374038732[/C][C]-1846.37403873159[/C][/ROW]
[ROW][C]64[/C][C]208131[/C][C]209301.604060577[/C][C]-1170.60406057735[/C][/ROW]
[ROW][C]65[/C][C]213774[/C][C]217474.967240868[/C][C]-3700.96724086767[/C][/ROW]
[ROW][C]66[/C][C]205711[/C][C]211964.58090559[/C][C]-6253.58090559026[/C][/ROW]
[ROW][C]67[/C][C]195129[/C][C]202592.079216556[/C][C]-7463.07921655552[/C][/ROW]
[ROW][C]68[/C][C]186274[/C][C]192806.507496188[/C][C]-6532.50749618848[/C][/ROW]
[ROW][C]69[/C][C]192698[/C][C]200104.467409181[/C][C]-7406.46740918065[/C][/ROW]
[ROW][C]70[/C][C]167618[/C][C]178070.425012804[/C][C]-10452.4250128042[/C][/ROW]
[ROW][C]71[/C][C]182985[/C][C]186930.733516517[/C][C]-3945.73351651744[/C][/ROW]
[ROW][C]72[/C][C]191917[/C][C]189618.651670952[/C][C]2298.34832904837[/C][/ROW]
[ROW][C]73[/C][C]193556[/C][C]192962.17615649[/C][C]593.823843509628[/C][/ROW]
[ROW][C]74[/C][C]184624[/C][C]181830.421222405[/C][C]2793.57877759513[/C][/ROW]
[ROW][C]75[/C][C]185405[/C][C]182630.638053065[/C][C]2774.36194693536[/C][/ROW]
[ROW][C]76[/C][C]182985[/C][C]183284.762212761[/C][C]-299.762212761067[/C][/ROW]
[ROW][C]77[/C][C]191125[/C][C]188556.786925101[/C][C]2568.21307489931[/C][/ROW]
[ROW][C]78[/C][C]185405[/C][C]183774.397338369[/C][C]1630.60266163116[/C][/ROW]
[ROW][C]79[/C][C]174130[/C][C]176873.98508671[/C][C]-2743.98508670978[/C][/ROW]
[ROW][C]80[/C][C]165979[/C][C]169616.104800004[/C][C]-3637.10480000425[/C][/ROW]
[ROW][C]81[/C][C]179762[/C][C]176115.75588715[/C][C]3646.24411285034[/C][/ROW]
[ROW][C]82[/C][C]149831[/C][C]157743.574243938[/C][C]-7912.574243938[/C][/ROW]
[ROW][C]83[/C][C]169268[/C][C]170137.211494148[/C][C]-869.211494148039[/C][/ROW]
[ROW][C]84[/C][C]178123[/C][C]177179.225747702[/C][C]943.774252297997[/C][/ROW]
[ROW][C]85[/C][C]178123[/C][C]178713.942535509[/C][C]-590.942535509297[/C][/ROW]
[ROW][C]86[/C][C]167618[/C][C]169117.807551057[/C][C]-1499.80755105682[/C][/ROW]
[ROW][C]87[/C][C]157905[/C][C]168053.277087645[/C][C]-10148.2770876448[/C][/ROW]
[ROW][C]88[/C][C]157124[/C][C]161652.995241583[/C][C]-4528.99524158271[/C][/ROW]
[ROW][C]89[/C][C]165979[/C][C]165561.170288369[/C][C]417.829711631348[/C][/ROW]
[ROW][C]90[/C][C]157905[/C][C]159566.277660807[/C][C]-1661.27766080672[/C][/ROW]
[ROW][C]91[/C][C]142549[/C][C]149466.998056761[/C][C]-6917.9980567607[/C][/ROW]
[ROW][C]92[/C][C]131967[/C][C]140354.209254903[/C][C]-8387.20925490322[/C][/ROW]
[ROW][C]93[/C][C]143330[/C][C]146451.553321436[/C][C]-3121.55332143634[/C][/ROW]
[ROW][C]94[/C][C]116611[/C][C]122493.770384992[/C][C]-5882.77038499244[/C][/ROW]
[ROW][C]95[/C][C]140899[/C][C]135062.968413766[/C][C]5836.03158623385[/C][/ROW]
[ROW][C]96[/C][C]153824[/C][C]143183.648462635[/C][C]10640.3515373645[/C][/ROW]
[ROW][C]97[/C][C]157905[/C][C]146623.827208459[/C][C]11281.1727915407[/C][/ROW]
[ROW][C]98[/C][C]148973[/C][C]141980.28289635[/C][C]6992.71710365021[/C][/ROW]
[ROW][C]99[/C][C]137687[/C][C]139130.749581575[/C][C]-1443.74958157507[/C][/ROW]
[ROW][C]100[/C][C]145761[/C][C]139217.173169331[/C][C]6543.8268306689[/C][/ROW]
[ROW][C]101[/C][C]148973[/C][C]149622.092208008[/C][C]-649.092208007845[/C][/ROW]
[ROW][C]102[/C][C]146542[/C][C]142728.79126422[/C][C]3813.20873578009[/C][/ROW]
[ROW][C]103[/C][C]122243[/C][C]132645.025010741[/C][C]-10402.0250107407[/C][/ROW]
[ROW][C]104[/C][C]110968[/C][C]121973.308597338[/C][C]-11005.3085973383[/C][/ROW]
[ROW][C]105[/C][C]119031[/C][C]128958.486979795[/C][C]-9927.4869797952[/C][/ROW]
[ROW][C]106[/C][C]94743[/C][C]103575.684108378[/C][C]-8832.68410837839[/C][/ROW]
[ROW][C]107[/C][C]119823[/C][C]118826.165631058[/C][C]996.834368941651[/C][/ROW]
[ROW][C]108[/C][C]128755[/C][C]126110.341288929[/C][C]2644.65871107073[/C][/ROW]
[ROW][C]109[/C][C]136037[/C][C]126151.150677421[/C][C]9885.84932257942[/C][/ROW]
[ROW][C]110[/C][C]123893[/C][C]119707.352878252[/C][C]4185.64712174823[/C][/ROW]
[ROW][C]111[/C][C]112530[/C][C]111945.566005107[/C][C]584.433994893057[/C][/ROW]
[ROW][C]112[/C][C]119031[/C][C]116067.601513296[/C][C]2963.398486704[/C][/ROW]
[ROW][C]113[/C][C]122243[/C][C]119289.569780323[/C][C]2953.43021967671[/C][/ROW]
[ROW][C]114[/C][C]115819[/C][C]116658.069219592[/C][C]-839.069219591547[/C][/ROW]
[ROW][C]115[/C][C]91531[/C][C]99422.3214903636[/C][C]-7891.32149036363[/C][/ROW]
[ROW][C]116[/C][C]80949[/C][C]90058.59693823[/C][C]-9109.59693822995[/C][/ROW]
[ROW][C]117[/C][C]90662[/C][C]95009.4114319615[/C][C]-4347.41143196149[/C][/ROW]
[ROW][C]118[/C][C]63943[/C][C]76280.0396211326[/C][C]-12337.0396211326[/C][/ROW]
[ROW][C]119[/C][C]93093[/C][C]89405.1282317591[/C][C]3687.87176824093[/C][/ROW]
[ROW][C]120[/C][C]110968[/C][C]95932.1438992281[/C][C]15035.8561007719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307076&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307076&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
13207273207288.777052553-15.7770525533997
14207273206829.902781575443.097218425042
15205711204967.575548738743.424451262166
16201630200860.578014649769.421985351248
17222706222059.00268356646.997316440014
18225918225294.20840314623.79159686013
19221067213219.2904395177847.70956048279
20209704208587.8887447641116.11125523614
21214566210562.4811982964003.5188017037
22207273213039.144462173-5766.14446217282
23210562212504.887988126-1942.88798812611
24212135213727.772814232-1592.77281423163
25213774215457.559407834-1683.55940783376
26209704214728.578432259-5024.57843225871
27210562210911.162313749-349.162313748617
28204842206259.859534995-1417.8595349949
29222706226888.664965203-4182.66496520303
30228349228134.238561025214.761438974587
31223498220062.7084438363435.29155616375
32214566209313.5033853455252.49661465475
33224279214481.9392941659797.0607058352
34213774212897.911055206876.088944794144
35223498217420.5579181176077.44208188323
36222706222196.693328369509.306671631464
37225137225017.95516129119.044838710484
38216205223029.377023731-6824.37702373115
39225918221726.9985409284191.00145907246
40225137218138.3504801986998.64951980172
41239712242260.94486429-2548.94486428975
42236423247891.831082428-11468.8310824282
43223498237307.132658469-13809.132658469
44216986220708.405919404-3722.40591940362
45225918225158.374865658759.625134342088
46213774214233.808115773-459.80811577331
47222706221096.4254611961609.57453880375
48224279220299.0139880043979.98601199585
49227568223815.4656607383752.53433926179
50220286218549.0075840091736.99241599123
51224279227281.642436784-3002.64243678385
52226710222381.954266974328.04573303033
53235642239141.738568626-3499.73856862634
54228349238383.800421263-10034.8004212626
55218636226433.059978999-7797.05997899896
56208131218142.862268436-10011.862268436
57217855222533.923294133-4678.92329413292
58191125208635.820164761-17510.8201647609
59204061209080.383965536-5019.38396553585
60211343206324.8208566945018.17914330596
61218636209070.5557039229565.44429607806
62208131204538.7421962873592.25780371347
63208131209977.374038732-1846.37403873159
64208131209301.604060577-1170.60406057735
65213774217474.967240868-3700.96724086767
66205711211964.58090559-6253.58090559026
67195129202592.079216556-7463.07921655552
68186274192806.507496188-6532.50749618848
69192698200104.467409181-7406.46740918065
70167618178070.425012804-10452.4250128042
71182985186930.733516517-3945.73351651744
72191917189618.6516709522298.34832904837
73193556192962.17615649593.823843509628
74184624181830.4212224052793.57877759513
75185405182630.6380530652774.36194693536
76182985183284.762212761-299.762212761067
77191125188556.7869251012568.21307489931
78185405183774.3973383691630.60266163116
79174130176873.98508671-2743.98508670978
80165979169616.104800004-3637.10480000425
81179762176115.755887153646.24411285034
82149831157743.574243938-7912.574243938
83169268170137.211494148-869.211494148039
84178123177179.225747702943.774252297997
85178123178713.942535509-590.942535509297
86167618169117.807551057-1499.80755105682
87157905168053.277087645-10148.2770876448
88157124161652.995241583-4528.99524158271
89165979165561.170288369417.829711631348
90157905159566.277660807-1661.27766080672
91142549149466.998056761-6917.9980567607
92131967140354.209254903-8387.20925490322
93143330146451.553321436-3121.55332143634
94116611122493.770384992-5882.77038499244
95140899135062.9684137665836.03158623385
96153824143183.64846263510640.3515373645
97157905146623.82720845911281.1727915407
98148973141980.282896356992.71710365021
99137687139130.749581575-1443.74958157507
100145761139217.1731693316543.8268306689
101148973149622.092208008-649.092208007845
102146542142728.791264223813.20873578009
103122243132645.025010741-10402.0250107407
104110968121973.308597338-11005.3085973383
105119031128958.486979795-9927.4869797952
10694743103575.684108378-8832.68410837839
107119823118826.165631058996.834368941651
108128755126110.3412889292644.65871107073
109136037126151.1506774219885.84932257942
110123893119707.3528782524185.64712174823
111112530111945.566005107584.433994893057
112119031116067.6015132962963.398486704
113122243119289.5697803232953.43021967671
114115819116658.069219592-839.069219591547
1159153199422.3214903636-7891.32149036363
1168094990058.59693823-9109.59693822995
1179066295009.4114319615-4347.41143196149
1186394376280.0396211326-12337.0396211326
1199309389405.12823175913687.87176824093
12011096895932.143899228115035.8561007719







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121103708.65126935492113.7197452149115303.582793492
12292494.111118293380155.637957705104832.584278882
12383097.326925267470094.24326851296100.4105820228
12486236.305532372872038.9378376746100433.673227071
12586824.865062186971477.7324478477102171.997676526
12681541.443738379465515.424203716297567.4632730427
12765660.336180696750160.142499480181160.5298619134
12859768.960580276143836.187632129875701.7335284224
12967581.373799811249176.118709014885986.6288906075
13050419.975778208333753.443637838967086.5079185778
13172086.890597210649336.79503976194836.9861546602
13280784.217604354456656.8950377666104911.540170942

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 103708.651269354 & 92113.7197452149 & 115303.582793492 \tabularnewline
122 & 92494.1111182933 & 80155.637957705 & 104832.584278882 \tabularnewline
123 & 83097.3269252674 & 70094.243268512 & 96100.4105820228 \tabularnewline
124 & 86236.3055323728 & 72038.9378376746 & 100433.673227071 \tabularnewline
125 & 86824.8650621869 & 71477.7324478477 & 102171.997676526 \tabularnewline
126 & 81541.4437383794 & 65515.4242037162 & 97567.4632730427 \tabularnewline
127 & 65660.3361806967 & 50160.1424994801 & 81160.5298619134 \tabularnewline
128 & 59768.9605802761 & 43836.1876321298 & 75701.7335284224 \tabularnewline
129 & 67581.3737998112 & 49176.1187090148 & 85986.6288906075 \tabularnewline
130 & 50419.9757782083 & 33753.4436378389 & 67086.5079185778 \tabularnewline
131 & 72086.8905972106 & 49336.795039761 & 94836.9861546602 \tabularnewline
132 & 80784.2176043544 & 56656.8950377666 & 104911.540170942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307076&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]103708.651269354[/C][C]92113.7197452149[/C][C]115303.582793492[/C][/ROW]
[ROW][C]122[/C][C]92494.1111182933[/C][C]80155.637957705[/C][C]104832.584278882[/C][/ROW]
[ROW][C]123[/C][C]83097.3269252674[/C][C]70094.243268512[/C][C]96100.4105820228[/C][/ROW]
[ROW][C]124[/C][C]86236.3055323728[/C][C]72038.9378376746[/C][C]100433.673227071[/C][/ROW]
[ROW][C]125[/C][C]86824.8650621869[/C][C]71477.7324478477[/C][C]102171.997676526[/C][/ROW]
[ROW][C]126[/C][C]81541.4437383794[/C][C]65515.4242037162[/C][C]97567.4632730427[/C][/ROW]
[ROW][C]127[/C][C]65660.3361806967[/C][C]50160.1424994801[/C][C]81160.5298619134[/C][/ROW]
[ROW][C]128[/C][C]59768.9605802761[/C][C]43836.1876321298[/C][C]75701.7335284224[/C][/ROW]
[ROW][C]129[/C][C]67581.3737998112[/C][C]49176.1187090148[/C][C]85986.6288906075[/C][/ROW]
[ROW][C]130[/C][C]50419.9757782083[/C][C]33753.4436378389[/C][C]67086.5079185778[/C][/ROW]
[ROW][C]131[/C][C]72086.8905972106[/C][C]49336.795039761[/C][C]94836.9861546602[/C][/ROW]
[ROW][C]132[/C][C]80784.2176043544[/C][C]56656.8950377666[/C][C]104911.540170942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307076&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307076&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
121103708.65126935492113.7197452149115303.582793492
12292494.111118293380155.637957705104832.584278882
12383097.326925267470094.24326851296100.4105820228
12486236.305532372872038.9378376746100433.673227071
12586824.865062186971477.7324478477102171.997676526
12681541.443738379465515.424203716297567.4632730427
12765660.336180696750160.142499480181160.5298619134
12859768.960580276143836.187632129875701.7335284224
12967581.373799811249176.118709014885986.6288906075
13050419.975778208333753.443637838967086.5079185778
13172086.890597210649336.79503976194836.9861546602
13280784.217604354456656.8950377666104911.540170942



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')