FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 03 Dec 2014 18:33:16 +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/2014/Dec/03/t1417631606uglh1sbjjgalbqo.htm/, Retrieved Thu, 16 May 2024 10:10:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263019, Retrieved Thu, 16 May 2024 10:10:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-03 18:33:16] [bc3b0a9d08b571f2c6b79bb1a1231eac] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
250,8
247,6
237,8
226,4
217,2
211,4
207,6
204,3
197,5
193,6
192,3
192
196,1
191,9
185,6
179,4
173,9
169,2
166,8
165,2
161,4
160,8
163,7
170,8
182,7
190,9
197,8
205,1
210,7
220,2
229,7
237,1
241,6
250,4
258,6
269,9
283,2
289,6
281,8
274,7
267,6
261,4
260,5
260,7
254,2
250,5
253,4
263,7
276,2
273,8
265,9
258,4
253,5
250,7
252,8
255,3
251,2
252,5
257,8
269,9
291,6
298,9
295,6
292,1
290,9
290,6
298
304
304,3
309,8
322,3
340,2
369,3
376,7
379,7
379,5
377,8
381,6
394,6
399,3
400,4
408,2
419,1
437,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263019&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263019&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263019&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]1[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263019&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3237.8244.4-6.59999999999997
4226.4228-1.60000000000002
5217.22152.19999999999999
6211.42083.40000000000003
7207.6205.61.99999999999997
8204.3203.80.500000000000028
9197.5201-3.50000000000003
10193.6190.72.90000000000001
11192.3189.72.60000000000002
121921910.999999999999972
13196.1191.74.40000000000001
14191.9200.2-8.29999999999998
15185.6187.7-2.10000000000002
16179.4179.30.100000000000023
17173.9173.20.699999999999989
18169.2168.40.799999999999983
19166.8164.52.30000000000004
20165.2164.40.799999999999955
21161.4163.6-2.19999999999996
22160.8157.63.19999999999999
23163.7160.23.49999999999997
24170.8166.64.20000000000005
25182.7177.94.79999999999995
26190.9194.6-3.69999999999996
27197.8199.1-1.30000000000001
28205.1204.70.399999999999977
29210.7212.4-1.69999999999999
30220.2216.33.90000000000001
31229.7229.70
32237.1239.2-2.09999999999999
33241.6244.5-2.90000000000001
34250.4246.14.30000000000001
35258.6259.2-0.600000000000023
36269.9266.83.09999999999991
37283.2281.22.00000000000006
38289.6296.5-6.89999999999998
39281.8296-14.2
40274.72740.699999999999989
41267.6267.65.6843418860808e-14
42261.4260.50.89999999999992
43260.5255.25.30000000000007
44260.7259.61.09999999999997
45254.2260.9-6.69999999999999
46250.5247.72.80000000000001
47253.4246.86.59999999999999
48263.7256.37.39999999999998
49276.22742.19999999999999
50273.8288.7-14.9
51265.9271.4-5.50000000000006
52258.42580.400000000000034
53253.5250.92.60000000000002
54250.7248.62.09999999999997
55252.8247.94.90000000000003
56255.3254.90.399999999999977
57251.2257.8-6.60000000000002
58252.5247.15.40000000000003
59257.8253.84
60269.9263.16.79999999999995
61291.62829.60000000000008
62298.9313.3-14.4000000000001
63295.6306.2-10.5999999999999
64292.1292.3-0.200000000000045
65290.9288.62.29999999999995
66290.6289.70.900000000000091
67298290.37.69999999999993
68304305.4-1.39999999999998
69304.3310-5.69999999999999
70309.8304.65.19999999999999
71322.3315.37
72340.2334.85.39999999999998
73369.3358.111.2
74376.7398.4-21.7
75379.7384.1-4.39999999999998
76379.5382.7-3.19999999999999
77377.8379.3-1.5
78381.6376.15.5
79394.6385.49.19999999999999
80399.3407.6-8.30000000000001
81400.4404-3.60000000000002
82408.2401.56.70000000000005
83419.14163.10000000000002
84437.74307.69999999999993

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 237.8 & 244.4 & -6.59999999999997 \tabularnewline
4 & 226.4 & 228 & -1.60000000000002 \tabularnewline
5 & 217.2 & 215 & 2.19999999999999 \tabularnewline
6 & 211.4 & 208 & 3.40000000000003 \tabularnewline
7 & 207.6 & 205.6 & 1.99999999999997 \tabularnewline
8 & 204.3 & 203.8 & 0.500000000000028 \tabularnewline
9 & 197.5 & 201 & -3.50000000000003 \tabularnewline
10 & 193.6 & 190.7 & 2.90000000000001 \tabularnewline
11 & 192.3 & 189.7 & 2.60000000000002 \tabularnewline
12 & 192 & 191 & 0.999999999999972 \tabularnewline
13 & 196.1 & 191.7 & 4.40000000000001 \tabularnewline
14 & 191.9 & 200.2 & -8.29999999999998 \tabularnewline
15 & 185.6 & 187.7 & -2.10000000000002 \tabularnewline
16 & 179.4 & 179.3 & 0.100000000000023 \tabularnewline
17 & 173.9 & 173.2 & 0.699999999999989 \tabularnewline
18 & 169.2 & 168.4 & 0.799999999999983 \tabularnewline
19 & 166.8 & 164.5 & 2.30000000000004 \tabularnewline
20 & 165.2 & 164.4 & 0.799999999999955 \tabularnewline
21 & 161.4 & 163.6 & -2.19999999999996 \tabularnewline
22 & 160.8 & 157.6 & 3.19999999999999 \tabularnewline
23 & 163.7 & 160.2 & 3.49999999999997 \tabularnewline
24 & 170.8 & 166.6 & 4.20000000000005 \tabularnewline
25 & 182.7 & 177.9 & 4.79999999999995 \tabularnewline
26 & 190.9 & 194.6 & -3.69999999999996 \tabularnewline
27 & 197.8 & 199.1 & -1.30000000000001 \tabularnewline
28 & 205.1 & 204.7 & 0.399999999999977 \tabularnewline
29 & 210.7 & 212.4 & -1.69999999999999 \tabularnewline
30 & 220.2 & 216.3 & 3.90000000000001 \tabularnewline
31 & 229.7 & 229.7 & 0 \tabularnewline
32 & 237.1 & 239.2 & -2.09999999999999 \tabularnewline
33 & 241.6 & 244.5 & -2.90000000000001 \tabularnewline
34 & 250.4 & 246.1 & 4.30000000000001 \tabularnewline
35 & 258.6 & 259.2 & -0.600000000000023 \tabularnewline
36 & 269.9 & 266.8 & 3.09999999999991 \tabularnewline
37 & 283.2 & 281.2 & 2.00000000000006 \tabularnewline
38 & 289.6 & 296.5 & -6.89999999999998 \tabularnewline
39 & 281.8 & 296 & -14.2 \tabularnewline
40 & 274.7 & 274 & 0.699999999999989 \tabularnewline
41 & 267.6 & 267.6 & 5.6843418860808e-14 \tabularnewline
42 & 261.4 & 260.5 & 0.89999999999992 \tabularnewline
43 & 260.5 & 255.2 & 5.30000000000007 \tabularnewline
44 & 260.7 & 259.6 & 1.09999999999997 \tabularnewline
45 & 254.2 & 260.9 & -6.69999999999999 \tabularnewline
46 & 250.5 & 247.7 & 2.80000000000001 \tabularnewline
47 & 253.4 & 246.8 & 6.59999999999999 \tabularnewline
48 & 263.7 & 256.3 & 7.39999999999998 \tabularnewline
49 & 276.2 & 274 & 2.19999999999999 \tabularnewline
50 & 273.8 & 288.7 & -14.9 \tabularnewline
51 & 265.9 & 271.4 & -5.50000000000006 \tabularnewline
52 & 258.4 & 258 & 0.400000000000034 \tabularnewline
53 & 253.5 & 250.9 & 2.60000000000002 \tabularnewline
54 & 250.7 & 248.6 & 2.09999999999997 \tabularnewline
55 & 252.8 & 247.9 & 4.90000000000003 \tabularnewline
56 & 255.3 & 254.9 & 0.399999999999977 \tabularnewline
57 & 251.2 & 257.8 & -6.60000000000002 \tabularnewline
58 & 252.5 & 247.1 & 5.40000000000003 \tabularnewline
59 & 257.8 & 253.8 & 4 \tabularnewline
60 & 269.9 & 263.1 & 6.79999999999995 \tabularnewline
61 & 291.6 & 282 & 9.60000000000008 \tabularnewline
62 & 298.9 & 313.3 & -14.4000000000001 \tabularnewline
63 & 295.6 & 306.2 & -10.5999999999999 \tabularnewline
64 & 292.1 & 292.3 & -0.200000000000045 \tabularnewline
65 & 290.9 & 288.6 & 2.29999999999995 \tabularnewline
66 & 290.6 & 289.7 & 0.900000000000091 \tabularnewline
67 & 298 & 290.3 & 7.69999999999993 \tabularnewline
68 & 304 & 305.4 & -1.39999999999998 \tabularnewline
69 & 304.3 & 310 & -5.69999999999999 \tabularnewline
70 & 309.8 & 304.6 & 5.19999999999999 \tabularnewline
71 & 322.3 & 315.3 & 7 \tabularnewline
72 & 340.2 & 334.8 & 5.39999999999998 \tabularnewline
73 & 369.3 & 358.1 & 11.2 \tabularnewline
74 & 376.7 & 398.4 & -21.7 \tabularnewline
75 & 379.7 & 384.1 & -4.39999999999998 \tabularnewline
76 & 379.5 & 382.7 & -3.19999999999999 \tabularnewline
77 & 377.8 & 379.3 & -1.5 \tabularnewline
78 & 381.6 & 376.1 & 5.5 \tabularnewline
79 & 394.6 & 385.4 & 9.19999999999999 \tabularnewline
80 & 399.3 & 407.6 & -8.30000000000001 \tabularnewline
81 & 400.4 & 404 & -3.60000000000002 \tabularnewline
82 & 408.2 & 401.5 & 6.70000000000005 \tabularnewline
83 & 419.1 & 416 & 3.10000000000002 \tabularnewline
84 & 437.7 & 430 & 7.69999999999993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263019&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]237.8[/C][C]244.4[/C][C]-6.59999999999997[/C][/ROW]
[ROW][C]4[/C][C]226.4[/C][C]228[/C][C]-1.60000000000002[/C][/ROW]
[ROW][C]5[/C][C]217.2[/C][C]215[/C][C]2.19999999999999[/C][/ROW]
[ROW][C]6[/C][C]211.4[/C][C]208[/C][C]3.40000000000003[/C][/ROW]
[ROW][C]7[/C][C]207.6[/C][C]205.6[/C][C]1.99999999999997[/C][/ROW]
[ROW][C]8[/C][C]204.3[/C][C]203.8[/C][C]0.500000000000028[/C][/ROW]
[ROW][C]9[/C][C]197.5[/C][C]201[/C][C]-3.50000000000003[/C][/ROW]
[ROW][C]10[/C][C]193.6[/C][C]190.7[/C][C]2.90000000000001[/C][/ROW]
[ROW][C]11[/C][C]192.3[/C][C]189.7[/C][C]2.60000000000002[/C][/ROW]
[ROW][C]12[/C][C]192[/C][C]191[/C][C]0.999999999999972[/C][/ROW]
[ROW][C]13[/C][C]196.1[/C][C]191.7[/C][C]4.40000000000001[/C][/ROW]
[ROW][C]14[/C][C]191.9[/C][C]200.2[/C][C]-8.29999999999998[/C][/ROW]
[ROW][C]15[/C][C]185.6[/C][C]187.7[/C][C]-2.10000000000002[/C][/ROW]
[ROW][C]16[/C][C]179.4[/C][C]179.3[/C][C]0.100000000000023[/C][/ROW]
[ROW][C]17[/C][C]173.9[/C][C]173.2[/C][C]0.699999999999989[/C][/ROW]
[ROW][C]18[/C][C]169.2[/C][C]168.4[/C][C]0.799999999999983[/C][/ROW]
[ROW][C]19[/C][C]166.8[/C][C]164.5[/C][C]2.30000000000004[/C][/ROW]
[ROW][C]20[/C][C]165.2[/C][C]164.4[/C][C]0.799999999999955[/C][/ROW]
[ROW][C]21[/C][C]161.4[/C][C]163.6[/C][C]-2.19999999999996[/C][/ROW]
[ROW][C]22[/C][C]160.8[/C][C]157.6[/C][C]3.19999999999999[/C][/ROW]
[ROW][C]23[/C][C]163.7[/C][C]160.2[/C][C]3.49999999999997[/C][/ROW]
[ROW][C]24[/C][C]170.8[/C][C]166.6[/C][C]4.20000000000005[/C][/ROW]
[ROW][C]25[/C][C]182.7[/C][C]177.9[/C][C]4.79999999999995[/C][/ROW]
[ROW][C]26[/C][C]190.9[/C][C]194.6[/C][C]-3.69999999999996[/C][/ROW]
[ROW][C]27[/C][C]197.8[/C][C]199.1[/C][C]-1.30000000000001[/C][/ROW]
[ROW][C]28[/C][C]205.1[/C][C]204.7[/C][C]0.399999999999977[/C][/ROW]
[ROW][C]29[/C][C]210.7[/C][C]212.4[/C][C]-1.69999999999999[/C][/ROW]
[ROW][C]30[/C][C]220.2[/C][C]216.3[/C][C]3.90000000000001[/C][/ROW]
[ROW][C]31[/C][C]229.7[/C][C]229.7[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]237.1[/C][C]239.2[/C][C]-2.09999999999999[/C][/ROW]
[ROW][C]33[/C][C]241.6[/C][C]244.5[/C][C]-2.90000000000001[/C][/ROW]
[ROW][C]34[/C][C]250.4[/C][C]246.1[/C][C]4.30000000000001[/C][/ROW]
[ROW][C]35[/C][C]258.6[/C][C]259.2[/C][C]-0.600000000000023[/C][/ROW]
[ROW][C]36[/C][C]269.9[/C][C]266.8[/C][C]3.09999999999991[/C][/ROW]
[ROW][C]37[/C][C]283.2[/C][C]281.2[/C][C]2.00000000000006[/C][/ROW]
[ROW][C]38[/C][C]289.6[/C][C]296.5[/C][C]-6.89999999999998[/C][/ROW]
[ROW][C]39[/C][C]281.8[/C][C]296[/C][C]-14.2[/C][/ROW]
[ROW][C]40[/C][C]274.7[/C][C]274[/C][C]0.699999999999989[/C][/ROW]
[ROW][C]41[/C][C]267.6[/C][C]267.6[/C][C]5.6843418860808e-14[/C][/ROW]
[ROW][C]42[/C][C]261.4[/C][C]260.5[/C][C]0.89999999999992[/C][/ROW]
[ROW][C]43[/C][C]260.5[/C][C]255.2[/C][C]5.30000000000007[/C][/ROW]
[ROW][C]44[/C][C]260.7[/C][C]259.6[/C][C]1.09999999999997[/C][/ROW]
[ROW][C]45[/C][C]254.2[/C][C]260.9[/C][C]-6.69999999999999[/C][/ROW]
[ROW][C]46[/C][C]250.5[/C][C]247.7[/C][C]2.80000000000001[/C][/ROW]
[ROW][C]47[/C][C]253.4[/C][C]246.8[/C][C]6.59999999999999[/C][/ROW]
[ROW][C]48[/C][C]263.7[/C][C]256.3[/C][C]7.39999999999998[/C][/ROW]
[ROW][C]49[/C][C]276.2[/C][C]274[/C][C]2.19999999999999[/C][/ROW]
[ROW][C]50[/C][C]273.8[/C][C]288.7[/C][C]-14.9[/C][/ROW]
[ROW][C]51[/C][C]265.9[/C][C]271.4[/C][C]-5.50000000000006[/C][/ROW]
[ROW][C]52[/C][C]258.4[/C][C]258[/C][C]0.400000000000034[/C][/ROW]
[ROW][C]53[/C][C]253.5[/C][C]250.9[/C][C]2.60000000000002[/C][/ROW]
[ROW][C]54[/C][C]250.7[/C][C]248.6[/C][C]2.09999999999997[/C][/ROW]
[ROW][C]55[/C][C]252.8[/C][C]247.9[/C][C]4.90000000000003[/C][/ROW]
[ROW][C]56[/C][C]255.3[/C][C]254.9[/C][C]0.399999999999977[/C][/ROW]
[ROW][C]57[/C][C]251.2[/C][C]257.8[/C][C]-6.60000000000002[/C][/ROW]
[ROW][C]58[/C][C]252.5[/C][C]247.1[/C][C]5.40000000000003[/C][/ROW]
[ROW][C]59[/C][C]257.8[/C][C]253.8[/C][C]4[/C][/ROW]
[ROW][C]60[/C][C]269.9[/C][C]263.1[/C][C]6.79999999999995[/C][/ROW]
[ROW][C]61[/C][C]291.6[/C][C]282[/C][C]9.60000000000008[/C][/ROW]
[ROW][C]62[/C][C]298.9[/C][C]313.3[/C][C]-14.4000000000001[/C][/ROW]
[ROW][C]63[/C][C]295.6[/C][C]306.2[/C][C]-10.5999999999999[/C][/ROW]
[ROW][C]64[/C][C]292.1[/C][C]292.3[/C][C]-0.200000000000045[/C][/ROW]
[ROW][C]65[/C][C]290.9[/C][C]288.6[/C][C]2.29999999999995[/C][/ROW]
[ROW][C]66[/C][C]290.6[/C][C]289.7[/C][C]0.900000000000091[/C][/ROW]
[ROW][C]67[/C][C]298[/C][C]290.3[/C][C]7.69999999999993[/C][/ROW]
[ROW][C]68[/C][C]304[/C][C]305.4[/C][C]-1.39999999999998[/C][/ROW]
[ROW][C]69[/C][C]304.3[/C][C]310[/C][C]-5.69999999999999[/C][/ROW]
[ROW][C]70[/C][C]309.8[/C][C]304.6[/C][C]5.19999999999999[/C][/ROW]
[ROW][C]71[/C][C]322.3[/C][C]315.3[/C][C]7[/C][/ROW]
[ROW][C]72[/C][C]340.2[/C][C]334.8[/C][C]5.39999999999998[/C][/ROW]
[ROW][C]73[/C][C]369.3[/C][C]358.1[/C][C]11.2[/C][/ROW]
[ROW][C]74[/C][C]376.7[/C][C]398.4[/C][C]-21.7[/C][/ROW]
[ROW][C]75[/C][C]379.7[/C][C]384.1[/C][C]-4.39999999999998[/C][/ROW]
[ROW][C]76[/C][C]379.5[/C][C]382.7[/C][C]-3.19999999999999[/C][/ROW]
[ROW][C]77[/C][C]377.8[/C][C]379.3[/C][C]-1.5[/C][/ROW]
[ROW][C]78[/C][C]381.6[/C][C]376.1[/C][C]5.5[/C][/ROW]
[ROW][C]79[/C][C]394.6[/C][C]385.4[/C][C]9.19999999999999[/C][/ROW]
[ROW][C]80[/C][C]399.3[/C][C]407.6[/C][C]-8.30000000000001[/C][/ROW]
[ROW][C]81[/C][C]400.4[/C][C]404[/C][C]-3.60000000000002[/C][/ROW]
[ROW][C]82[/C][C]408.2[/C][C]401.5[/C][C]6.70000000000005[/C][/ROW]
[ROW][C]83[/C][C]419.1[/C][C]416[/C][C]3.10000000000002[/C][/ROW]
[ROW][C]84[/C][C]437.7[/C][C]430[/C][C]7.69999999999993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263019&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3237.8244.4-6.59999999999997
4226.4228-1.60000000000002
5217.22152.19999999999999
6211.42083.40000000000003
7207.6205.61.99999999999997
8204.3203.80.500000000000028
9197.5201-3.50000000000003
10193.6190.72.90000000000001
11192.3189.72.60000000000002
121921910.999999999999972
13196.1191.74.40000000000001
14191.9200.2-8.29999999999998
15185.6187.7-2.10000000000002
16179.4179.30.100000000000023
17173.9173.20.699999999999989
18169.2168.40.799999999999983
19166.8164.52.30000000000004
20165.2164.40.799999999999955
21161.4163.6-2.19999999999996
22160.8157.63.19999999999999
23163.7160.23.49999999999997
24170.8166.64.20000000000005
25182.7177.94.79999999999995
26190.9194.6-3.69999999999996
27197.8199.1-1.30000000000001
28205.1204.70.399999999999977
29210.7212.4-1.69999999999999
30220.2216.33.90000000000001
31229.7229.70
32237.1239.2-2.09999999999999
33241.6244.5-2.90000000000001
34250.4246.14.30000000000001
35258.6259.2-0.600000000000023
36269.9266.83.09999999999991
37283.2281.22.00000000000006
38289.6296.5-6.89999999999998
39281.8296-14.2
40274.72740.699999999999989
41267.6267.65.6843418860808e-14
42261.4260.50.89999999999992
43260.5255.25.30000000000007
44260.7259.61.09999999999997
45254.2260.9-6.69999999999999
46250.5247.72.80000000000001
47253.4246.86.59999999999999
48263.7256.37.39999999999998
49276.22742.19999999999999
50273.8288.7-14.9
51265.9271.4-5.50000000000006
52258.42580.400000000000034
53253.5250.92.60000000000002
54250.7248.62.09999999999997
55252.8247.94.90000000000003
56255.3254.90.399999999999977
57251.2257.8-6.60000000000002
58252.5247.15.40000000000003
59257.8253.84
60269.9263.16.79999999999995
61291.62829.60000000000008
62298.9313.3-14.4000000000001
63295.6306.2-10.5999999999999
64292.1292.3-0.200000000000045
65290.9288.62.29999999999995
66290.6289.70.900000000000091
67298290.37.69999999999993
68304305.4-1.39999999999998
69304.3310-5.69999999999999
70309.8304.65.19999999999999
71322.3315.37
72340.2334.85.39999999999998
73369.3358.111.2
74376.7398.4-21.7
75379.7384.1-4.39999999999998
76379.5382.7-3.19999999999999
77377.8379.3-1.5
78381.6376.15.5
79394.6385.49.19999999999999
80399.3407.6-8.30000000000001
81400.4404-3.60000000000002
82408.2401.56.70000000000005
83419.14163.10000000000002
84437.74307.69999999999993






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85456.3444.879463978527467.720536021472
86474.9449.362905116503500.437094883497
87493.5450.76826703434536.23173296566
88512.1449.547148022392574.652851977608
89530.7446.003038035734615.396961964265
90549.3440.355029879231658.244970120769
91567.9432.770395462412703.029604537588
92586.5423.382118774118749.617881225882
93605.1412.299161671794797.900838328205
94623.7399.612901839856847.787098160143
95642.3385.401394774161899.198605225838
96660.9369.732319854113952.067680145886

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 456.3 & 444.879463978527 & 467.720536021472 \tabularnewline
86 & 474.9 & 449.362905116503 & 500.437094883497 \tabularnewline
87 & 493.5 & 450.76826703434 & 536.23173296566 \tabularnewline
88 & 512.1 & 449.547148022392 & 574.652851977608 \tabularnewline
89 & 530.7 & 446.003038035734 & 615.396961964265 \tabularnewline
90 & 549.3 & 440.355029879231 & 658.244970120769 \tabularnewline
91 & 567.9 & 432.770395462412 & 703.029604537588 \tabularnewline
92 & 586.5 & 423.382118774118 & 749.617881225882 \tabularnewline
93 & 605.1 & 412.299161671794 & 797.900838328205 \tabularnewline
94 & 623.7 & 399.612901839856 & 847.787098160143 \tabularnewline
95 & 642.3 & 385.401394774161 & 899.198605225838 \tabularnewline
96 & 660.9 & 369.732319854113 & 952.067680145886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263019&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]456.3[/C][C]444.879463978527[/C][C]467.720536021472[/C][/ROW]
[ROW][C]86[/C][C]474.9[/C][C]449.362905116503[/C][C]500.437094883497[/C][/ROW]
[ROW][C]87[/C][C]493.5[/C][C]450.76826703434[/C][C]536.23173296566[/C][/ROW]
[ROW][C]88[/C][C]512.1[/C][C]449.547148022392[/C][C]574.652851977608[/C][/ROW]
[ROW][C]89[/C][C]530.7[/C][C]446.003038035734[/C][C]615.396961964265[/C][/ROW]
[ROW][C]90[/C][C]549.3[/C][C]440.355029879231[/C][C]658.244970120769[/C][/ROW]
[ROW][C]91[/C][C]567.9[/C][C]432.770395462412[/C][C]703.029604537588[/C][/ROW]
[ROW][C]92[/C][C]586.5[/C][C]423.382118774118[/C][C]749.617881225882[/C][/ROW]
[ROW][C]93[/C][C]605.1[/C][C]412.299161671794[/C][C]797.900838328205[/C][/ROW]
[ROW][C]94[/C][C]623.7[/C][C]399.612901839856[/C][C]847.787098160143[/C][/ROW]
[ROW][C]95[/C][C]642.3[/C][C]385.401394774161[/C][C]899.198605225838[/C][/ROW]
[ROW][C]96[/C][C]660.9[/C][C]369.732319854113[/C][C]952.067680145886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263019&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263019&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85456.3444.879463978527467.720536021472
86474.9449.362905116503500.437094883497
87493.5450.76826703434536.23173296566
88512.1449.547148022392574.652851977608
89530.7446.003038035734615.396961964265
90549.3440.355029879231658.244970120769
91567.9432.770395462412703.029604537588
92586.5423.382118774118749.617881225882
93605.1412.299161671794797.900838328205
94623.7399.612901839856847.787098160143
95642.3385.401394774161899.198605225838
96660.9369.732319854113952.067680145886


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')