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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 04:02:10 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/06/t12442826183co41senuus5o6c.htm/, Retrieved Sun, 28 Apr 2024 23:39:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41942, Retrieved Sun, 28 Apr 2024 23:39:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2009-06-06 10:02:10] [24cccc75656fef950c2da981339c973f] [Current]
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Dataseries X:
88.6
95
96.3
83.3
96.9
103.4
99.3
103.8
113.4
111.5
114.2
90.6
90.8
96.4
90
92.1
97.2
95.1
88.5
91
90.5
75
66.3
66
68.4
70.6
83.9
90.1
90.6
87.1
90.8
94.1
99.8
96.8
87
96.3
107.1
115.2
106.1
89.5
91.3
97.6
100.7
104.6
94.7
101.8
102.5
105.3
110.3
109.8
117.3
118.8
131.3
125.9
133.1
147
145.8
164.4
149.8
137.7
151.7
156.8
180
180.4
170.4
191.6
199.5
218.2
217.5
205
194
199.3
219.3
211.1
215.2
240.2
242.2
240.7
255.4
253
218.2
203.7
205.6
215.6
188.5
202.9
214
230.3
230
241
259.6
247.8
270.3
289.7
322.7
315
320.2
329.5
360.6
382.2
435.4
464
468.8
403
351.6
252
188
146.5
152.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41942&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41942&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41942&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]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41942&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
alpha1
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
396.3951.30000000000000
483.396.3-13
596.983.313.6
6103.496.96.5
799.3103.4-4.10000000000001
8103.899.34.5
9113.4103.89.6
10111.5113.4-1.90000000000001
11114.2111.52.70000000000000
1290.6114.2-23.6
1390.890.60.200000000000003
1496.490.85.60000000000001
159096.4-6.4
1692.1902.09999999999999
1797.292.15.10000000000001
1895.197.2-2.10000000000001
1988.595.1-6.6
209188.52.5
2190.591-0.5
227590.5-15.5
2366.375-8.7
246666.3-0.299999999999997
2568.4662.40000000000001
2670.668.42.19999999999999
2783.970.613.3
2890.183.96.19999999999999
2990.690.10.5
3087.190.6-3.5
3190.887.13.7
3294.190.83.3
3399.894.15.7
3496.899.8-3
358796.8-9.8
3696.3879.3
37107.196.310.8
38115.2107.18.10000000000001
39106.1115.2-9.1
4089.5106.1-16.6
4191.389.51.80000000000000
4297.691.36.3
43100.797.63.10000000000001
44104.6100.73.89999999999999
4594.7104.6-9.9
46101.894.77.1
47102.5101.80.700000000000003
48105.3102.52.80000000000000
49110.3105.35
50109.8110.3-0.5
51117.3109.87.5
52118.8117.31.5
53131.3118.812.5000000000000
54125.9131.3-5.40000000000001
55133.1125.97.19999999999999
56147133.113.9
57145.8147-1.19999999999999
58164.4145.818.6
59149.8164.4-14.6
60137.7149.8-12.1000000000000
61151.7137.714
62156.8151.75.10000000000002
63180156.823.2
64180.41800.400000000000006
65170.4180.4-10
66191.6170.421.2
67199.5191.67.9
68218.2199.518.7
69217.5218.2-0.699999999999989
70205217.5-12.5
71194205-11
72199.31945.30000000000001
73219.3199.320
74211.1219.3-8.20000000000002
75215.2211.14.09999999999999
76240.2215.225
77242.2240.22
78240.7242.2-1.5
79255.4240.714.7000000000000
80253255.4-2.40000000000001
81218.2253-34.8
82203.7218.2-14.5
83205.6203.71.90000000000001
84215.6205.610
85188.5215.6-27.1
86202.9188.514.4
87214202.911.1
88230.321416.3
89230230.3-0.300000000000011
9024123011
91259.624118.6000000000000
92247.8259.6-11.8
93270.3247.822.5
94289.7270.319.4000000000000
95322.7289.733
96315322.7-7.69999999999999
97320.23155.19999999999999
98329.5320.29.30000000000001
99360.6329.531.1
100382.2360.621.6000000000000
101435.4382.253.2
102464435.428.6
103468.84644.80000000000001
104403468.8-65.8
105351.6403-51.4
106252351.6-99.6
107188252-64
108146.5188-41.5
109152.9146.56.4

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 96.3 & 95 & 1.30000000000000 \tabularnewline
4 & 83.3 & 96.3 & -13 \tabularnewline
5 & 96.9 & 83.3 & 13.6 \tabularnewline
6 & 103.4 & 96.9 & 6.5 \tabularnewline
7 & 99.3 & 103.4 & -4.10000000000001 \tabularnewline
8 & 103.8 & 99.3 & 4.5 \tabularnewline
9 & 113.4 & 103.8 & 9.6 \tabularnewline
10 & 111.5 & 113.4 & -1.90000000000001 \tabularnewline
11 & 114.2 & 111.5 & 2.70000000000000 \tabularnewline
12 & 90.6 & 114.2 & -23.6 \tabularnewline
13 & 90.8 & 90.6 & 0.200000000000003 \tabularnewline
14 & 96.4 & 90.8 & 5.60000000000001 \tabularnewline
15 & 90 & 96.4 & -6.4 \tabularnewline
16 & 92.1 & 90 & 2.09999999999999 \tabularnewline
17 & 97.2 & 92.1 & 5.10000000000001 \tabularnewline
18 & 95.1 & 97.2 & -2.10000000000001 \tabularnewline
19 & 88.5 & 95.1 & -6.6 \tabularnewline
20 & 91 & 88.5 & 2.5 \tabularnewline
21 & 90.5 & 91 & -0.5 \tabularnewline
22 & 75 & 90.5 & -15.5 \tabularnewline
23 & 66.3 & 75 & -8.7 \tabularnewline
24 & 66 & 66.3 & -0.299999999999997 \tabularnewline
25 & 68.4 & 66 & 2.40000000000001 \tabularnewline
26 & 70.6 & 68.4 & 2.19999999999999 \tabularnewline
27 & 83.9 & 70.6 & 13.3 \tabularnewline
28 & 90.1 & 83.9 & 6.19999999999999 \tabularnewline
29 & 90.6 & 90.1 & 0.5 \tabularnewline
30 & 87.1 & 90.6 & -3.5 \tabularnewline
31 & 90.8 & 87.1 & 3.7 \tabularnewline
32 & 94.1 & 90.8 & 3.3 \tabularnewline
33 & 99.8 & 94.1 & 5.7 \tabularnewline
34 & 96.8 & 99.8 & -3 \tabularnewline
35 & 87 & 96.8 & -9.8 \tabularnewline
36 & 96.3 & 87 & 9.3 \tabularnewline
37 & 107.1 & 96.3 & 10.8 \tabularnewline
38 & 115.2 & 107.1 & 8.10000000000001 \tabularnewline
39 & 106.1 & 115.2 & -9.1 \tabularnewline
40 & 89.5 & 106.1 & -16.6 \tabularnewline
41 & 91.3 & 89.5 & 1.80000000000000 \tabularnewline
42 & 97.6 & 91.3 & 6.3 \tabularnewline
43 & 100.7 & 97.6 & 3.10000000000001 \tabularnewline
44 & 104.6 & 100.7 & 3.89999999999999 \tabularnewline
45 & 94.7 & 104.6 & -9.9 \tabularnewline
46 & 101.8 & 94.7 & 7.1 \tabularnewline
47 & 102.5 & 101.8 & 0.700000000000003 \tabularnewline
48 & 105.3 & 102.5 & 2.80000000000000 \tabularnewline
49 & 110.3 & 105.3 & 5 \tabularnewline
50 & 109.8 & 110.3 & -0.5 \tabularnewline
51 & 117.3 & 109.8 & 7.5 \tabularnewline
52 & 118.8 & 117.3 & 1.5 \tabularnewline
53 & 131.3 & 118.8 & 12.5000000000000 \tabularnewline
54 & 125.9 & 131.3 & -5.40000000000001 \tabularnewline
55 & 133.1 & 125.9 & 7.19999999999999 \tabularnewline
56 & 147 & 133.1 & 13.9 \tabularnewline
57 & 145.8 & 147 & -1.19999999999999 \tabularnewline
58 & 164.4 & 145.8 & 18.6 \tabularnewline
59 & 149.8 & 164.4 & -14.6 \tabularnewline
60 & 137.7 & 149.8 & -12.1000000000000 \tabularnewline
61 & 151.7 & 137.7 & 14 \tabularnewline
62 & 156.8 & 151.7 & 5.10000000000002 \tabularnewline
63 & 180 & 156.8 & 23.2 \tabularnewline
64 & 180.4 & 180 & 0.400000000000006 \tabularnewline
65 & 170.4 & 180.4 & -10 \tabularnewline
66 & 191.6 & 170.4 & 21.2 \tabularnewline
67 & 199.5 & 191.6 & 7.9 \tabularnewline
68 & 218.2 & 199.5 & 18.7 \tabularnewline
69 & 217.5 & 218.2 & -0.699999999999989 \tabularnewline
70 & 205 & 217.5 & -12.5 \tabularnewline
71 & 194 & 205 & -11 \tabularnewline
72 & 199.3 & 194 & 5.30000000000001 \tabularnewline
73 & 219.3 & 199.3 & 20 \tabularnewline
74 & 211.1 & 219.3 & -8.20000000000002 \tabularnewline
75 & 215.2 & 211.1 & 4.09999999999999 \tabularnewline
76 & 240.2 & 215.2 & 25 \tabularnewline
77 & 242.2 & 240.2 & 2 \tabularnewline
78 & 240.7 & 242.2 & -1.5 \tabularnewline
79 & 255.4 & 240.7 & 14.7000000000000 \tabularnewline
80 & 253 & 255.4 & -2.40000000000001 \tabularnewline
81 & 218.2 & 253 & -34.8 \tabularnewline
82 & 203.7 & 218.2 & -14.5 \tabularnewline
83 & 205.6 & 203.7 & 1.90000000000001 \tabularnewline
84 & 215.6 & 205.6 & 10 \tabularnewline
85 & 188.5 & 215.6 & -27.1 \tabularnewline
86 & 202.9 & 188.5 & 14.4 \tabularnewline
87 & 214 & 202.9 & 11.1 \tabularnewline
88 & 230.3 & 214 & 16.3 \tabularnewline
89 & 230 & 230.3 & -0.300000000000011 \tabularnewline
90 & 241 & 230 & 11 \tabularnewline
91 & 259.6 & 241 & 18.6000000000000 \tabularnewline
92 & 247.8 & 259.6 & -11.8 \tabularnewline
93 & 270.3 & 247.8 & 22.5 \tabularnewline
94 & 289.7 & 270.3 & 19.4000000000000 \tabularnewline
95 & 322.7 & 289.7 & 33 \tabularnewline
96 & 315 & 322.7 & -7.69999999999999 \tabularnewline
97 & 320.2 & 315 & 5.19999999999999 \tabularnewline
98 & 329.5 & 320.2 & 9.30000000000001 \tabularnewline
99 & 360.6 & 329.5 & 31.1 \tabularnewline
100 & 382.2 & 360.6 & 21.6000000000000 \tabularnewline
101 & 435.4 & 382.2 & 53.2 \tabularnewline
102 & 464 & 435.4 & 28.6 \tabularnewline
103 & 468.8 & 464 & 4.80000000000001 \tabularnewline
104 & 403 & 468.8 & -65.8 \tabularnewline
105 & 351.6 & 403 & -51.4 \tabularnewline
106 & 252 & 351.6 & -99.6 \tabularnewline
107 & 188 & 252 & -64 \tabularnewline
108 & 146.5 & 188 & -41.5 \tabularnewline
109 & 152.9 & 146.5 & 6.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41942&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]96.3[/C][C]95[/C][C]1.30000000000000[/C][/ROW]
[ROW][C]4[/C][C]83.3[/C][C]96.3[/C][C]-13[/C][/ROW]
[ROW][C]5[/C][C]96.9[/C][C]83.3[/C][C]13.6[/C][/ROW]
[ROW][C]6[/C][C]103.4[/C][C]96.9[/C][C]6.5[/C][/ROW]
[ROW][C]7[/C][C]99.3[/C][C]103.4[/C][C]-4.10000000000001[/C][/ROW]
[ROW][C]8[/C][C]103.8[/C][C]99.3[/C][C]4.5[/C][/ROW]
[ROW][C]9[/C][C]113.4[/C][C]103.8[/C][C]9.6[/C][/ROW]
[ROW][C]10[/C][C]111.5[/C][C]113.4[/C][C]-1.90000000000001[/C][/ROW]
[ROW][C]11[/C][C]114.2[/C][C]111.5[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]12[/C][C]90.6[/C][C]114.2[/C][C]-23.6[/C][/ROW]
[ROW][C]13[/C][C]90.8[/C][C]90.6[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]14[/C][C]96.4[/C][C]90.8[/C][C]5.60000000000001[/C][/ROW]
[ROW][C]15[/C][C]90[/C][C]96.4[/C][C]-6.4[/C][/ROW]
[ROW][C]16[/C][C]92.1[/C][C]90[/C][C]2.09999999999999[/C][/ROW]
[ROW][C]17[/C][C]97.2[/C][C]92.1[/C][C]5.10000000000001[/C][/ROW]
[ROW][C]18[/C][C]95.1[/C][C]97.2[/C][C]-2.10000000000001[/C][/ROW]
[ROW][C]19[/C][C]88.5[/C][C]95.1[/C][C]-6.6[/C][/ROW]
[ROW][C]20[/C][C]91[/C][C]88.5[/C][C]2.5[/C][/ROW]
[ROW][C]21[/C][C]90.5[/C][C]91[/C][C]-0.5[/C][/ROW]
[ROW][C]22[/C][C]75[/C][C]90.5[/C][C]-15.5[/C][/ROW]
[ROW][C]23[/C][C]66.3[/C][C]75[/C][C]-8.7[/C][/ROW]
[ROW][C]24[/C][C]66[/C][C]66.3[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]25[/C][C]68.4[/C][C]66[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]26[/C][C]70.6[/C][C]68.4[/C][C]2.19999999999999[/C][/ROW]
[ROW][C]27[/C][C]83.9[/C][C]70.6[/C][C]13.3[/C][/ROW]
[ROW][C]28[/C][C]90.1[/C][C]83.9[/C][C]6.19999999999999[/C][/ROW]
[ROW][C]29[/C][C]90.6[/C][C]90.1[/C][C]0.5[/C][/ROW]
[ROW][C]30[/C][C]87.1[/C][C]90.6[/C][C]-3.5[/C][/ROW]
[ROW][C]31[/C][C]90.8[/C][C]87.1[/C][C]3.7[/C][/ROW]
[ROW][C]32[/C][C]94.1[/C][C]90.8[/C][C]3.3[/C][/ROW]
[ROW][C]33[/C][C]99.8[/C][C]94.1[/C][C]5.7[/C][/ROW]
[ROW][C]34[/C][C]96.8[/C][C]99.8[/C][C]-3[/C][/ROW]
[ROW][C]35[/C][C]87[/C][C]96.8[/C][C]-9.8[/C][/ROW]
[ROW][C]36[/C][C]96.3[/C][C]87[/C][C]9.3[/C][/ROW]
[ROW][C]37[/C][C]107.1[/C][C]96.3[/C][C]10.8[/C][/ROW]
[ROW][C]38[/C][C]115.2[/C][C]107.1[/C][C]8.10000000000001[/C][/ROW]
[ROW][C]39[/C][C]106.1[/C][C]115.2[/C][C]-9.1[/C][/ROW]
[ROW][C]40[/C][C]89.5[/C][C]106.1[/C][C]-16.6[/C][/ROW]
[ROW][C]41[/C][C]91.3[/C][C]89.5[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]42[/C][C]97.6[/C][C]91.3[/C][C]6.3[/C][/ROW]
[ROW][C]43[/C][C]100.7[/C][C]97.6[/C][C]3.10000000000001[/C][/ROW]
[ROW][C]44[/C][C]104.6[/C][C]100.7[/C][C]3.89999999999999[/C][/ROW]
[ROW][C]45[/C][C]94.7[/C][C]104.6[/C][C]-9.9[/C][/ROW]
[ROW][C]46[/C][C]101.8[/C][C]94.7[/C][C]7.1[/C][/ROW]
[ROW][C]47[/C][C]102.5[/C][C]101.8[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]48[/C][C]105.3[/C][C]102.5[/C][C]2.80000000000000[/C][/ROW]
[ROW][C]49[/C][C]110.3[/C][C]105.3[/C][C]5[/C][/ROW]
[ROW][C]50[/C][C]109.8[/C][C]110.3[/C][C]-0.5[/C][/ROW]
[ROW][C]51[/C][C]117.3[/C][C]109.8[/C][C]7.5[/C][/ROW]
[ROW][C]52[/C][C]118.8[/C][C]117.3[/C][C]1.5[/C][/ROW]
[ROW][C]53[/C][C]131.3[/C][C]118.8[/C][C]12.5000000000000[/C][/ROW]
[ROW][C]54[/C][C]125.9[/C][C]131.3[/C][C]-5.40000000000001[/C][/ROW]
[ROW][C]55[/C][C]133.1[/C][C]125.9[/C][C]7.19999999999999[/C][/ROW]
[ROW][C]56[/C][C]147[/C][C]133.1[/C][C]13.9[/C][/ROW]
[ROW][C]57[/C][C]145.8[/C][C]147[/C][C]-1.19999999999999[/C][/ROW]
[ROW][C]58[/C][C]164.4[/C][C]145.8[/C][C]18.6[/C][/ROW]
[ROW][C]59[/C][C]149.8[/C][C]164.4[/C][C]-14.6[/C][/ROW]
[ROW][C]60[/C][C]137.7[/C][C]149.8[/C][C]-12.1000000000000[/C][/ROW]
[ROW][C]61[/C][C]151.7[/C][C]137.7[/C][C]14[/C][/ROW]
[ROW][C]62[/C][C]156.8[/C][C]151.7[/C][C]5.10000000000002[/C][/ROW]
[ROW][C]63[/C][C]180[/C][C]156.8[/C][C]23.2[/C][/ROW]
[ROW][C]64[/C][C]180.4[/C][C]180[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]65[/C][C]170.4[/C][C]180.4[/C][C]-10[/C][/ROW]
[ROW][C]66[/C][C]191.6[/C][C]170.4[/C][C]21.2[/C][/ROW]
[ROW][C]67[/C][C]199.5[/C][C]191.6[/C][C]7.9[/C][/ROW]
[ROW][C]68[/C][C]218.2[/C][C]199.5[/C][C]18.7[/C][/ROW]
[ROW][C]69[/C][C]217.5[/C][C]218.2[/C][C]-0.699999999999989[/C][/ROW]
[ROW][C]70[/C][C]205[/C][C]217.5[/C][C]-12.5[/C][/ROW]
[ROW][C]71[/C][C]194[/C][C]205[/C][C]-11[/C][/ROW]
[ROW][C]72[/C][C]199.3[/C][C]194[/C][C]5.30000000000001[/C][/ROW]
[ROW][C]73[/C][C]219.3[/C][C]199.3[/C][C]20[/C][/ROW]
[ROW][C]74[/C][C]211.1[/C][C]219.3[/C][C]-8.20000000000002[/C][/ROW]
[ROW][C]75[/C][C]215.2[/C][C]211.1[/C][C]4.09999999999999[/C][/ROW]
[ROW][C]76[/C][C]240.2[/C][C]215.2[/C][C]25[/C][/ROW]
[ROW][C]77[/C][C]242.2[/C][C]240.2[/C][C]2[/C][/ROW]
[ROW][C]78[/C][C]240.7[/C][C]242.2[/C][C]-1.5[/C][/ROW]
[ROW][C]79[/C][C]255.4[/C][C]240.7[/C][C]14.7000000000000[/C][/ROW]
[ROW][C]80[/C][C]253[/C][C]255.4[/C][C]-2.40000000000001[/C][/ROW]
[ROW][C]81[/C][C]218.2[/C][C]253[/C][C]-34.8[/C][/ROW]
[ROW][C]82[/C][C]203.7[/C][C]218.2[/C][C]-14.5[/C][/ROW]
[ROW][C]83[/C][C]205.6[/C][C]203.7[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]84[/C][C]215.6[/C][C]205.6[/C][C]10[/C][/ROW]
[ROW][C]85[/C][C]188.5[/C][C]215.6[/C][C]-27.1[/C][/ROW]
[ROW][C]86[/C][C]202.9[/C][C]188.5[/C][C]14.4[/C][/ROW]
[ROW][C]87[/C][C]214[/C][C]202.9[/C][C]11.1[/C][/ROW]
[ROW][C]88[/C][C]230.3[/C][C]214[/C][C]16.3[/C][/ROW]
[ROW][C]89[/C][C]230[/C][C]230.3[/C][C]-0.300000000000011[/C][/ROW]
[ROW][C]90[/C][C]241[/C][C]230[/C][C]11[/C][/ROW]
[ROW][C]91[/C][C]259.6[/C][C]241[/C][C]18.6000000000000[/C][/ROW]
[ROW][C]92[/C][C]247.8[/C][C]259.6[/C][C]-11.8[/C][/ROW]
[ROW][C]93[/C][C]270.3[/C][C]247.8[/C][C]22.5[/C][/ROW]
[ROW][C]94[/C][C]289.7[/C][C]270.3[/C][C]19.4000000000000[/C][/ROW]
[ROW][C]95[/C][C]322.7[/C][C]289.7[/C][C]33[/C][/ROW]
[ROW][C]96[/C][C]315[/C][C]322.7[/C][C]-7.69999999999999[/C][/ROW]
[ROW][C]97[/C][C]320.2[/C][C]315[/C][C]5.19999999999999[/C][/ROW]
[ROW][C]98[/C][C]329.5[/C][C]320.2[/C][C]9.30000000000001[/C][/ROW]
[ROW][C]99[/C][C]360.6[/C][C]329.5[/C][C]31.1[/C][/ROW]
[ROW][C]100[/C][C]382.2[/C][C]360.6[/C][C]21.6000000000000[/C][/ROW]
[ROW][C]101[/C][C]435.4[/C][C]382.2[/C][C]53.2[/C][/ROW]
[ROW][C]102[/C][C]464[/C][C]435.4[/C][C]28.6[/C][/ROW]
[ROW][C]103[/C][C]468.8[/C][C]464[/C][C]4.80000000000001[/C][/ROW]
[ROW][C]104[/C][C]403[/C][C]468.8[/C][C]-65.8[/C][/ROW]
[ROW][C]105[/C][C]351.6[/C][C]403[/C][C]-51.4[/C][/ROW]
[ROW][C]106[/C][C]252[/C][C]351.6[/C][C]-99.6[/C][/ROW]
[ROW][C]107[/C][C]188[/C][C]252[/C][C]-64[/C][/ROW]
[ROW][C]108[/C][C]146.5[/C][C]188[/C][C]-41.5[/C][/ROW]
[ROW][C]109[/C][C]152.9[/C][C]146.5[/C][C]6.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41942&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41942&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
396.3951.30000000000000
483.396.3-13
596.983.313.6
6103.496.96.5
799.3103.4-4.10000000000001
8103.899.34.5
9113.4103.89.6
10111.5113.4-1.90000000000001
11114.2111.52.70000000000000
1290.6114.2-23.6
1390.890.60.200000000000003
1496.490.85.60000000000001
159096.4-6.4
1692.1902.09999999999999
1797.292.15.10000000000001
1895.197.2-2.10000000000001
1988.595.1-6.6
209188.52.5
2190.591-0.5
227590.5-15.5
2366.375-8.7
246666.3-0.299999999999997
2568.4662.40000000000001
2670.668.42.19999999999999
2783.970.613.3
2890.183.96.19999999999999
2990.690.10.5
3087.190.6-3.5
3190.887.13.7
3294.190.83.3
3399.894.15.7
3496.899.8-3
358796.8-9.8
3696.3879.3
37107.196.310.8
38115.2107.18.10000000000001
39106.1115.2-9.1
4089.5106.1-16.6
4191.389.51.80000000000000
4297.691.36.3
43100.797.63.10000000000001
44104.6100.73.89999999999999
4594.7104.6-9.9
46101.894.77.1
47102.5101.80.700000000000003
48105.3102.52.80000000000000
49110.3105.35
50109.8110.3-0.5
51117.3109.87.5
52118.8117.31.5
53131.3118.812.5000000000000
54125.9131.3-5.40000000000001
55133.1125.97.19999999999999
56147133.113.9
57145.8147-1.19999999999999
58164.4145.818.6
59149.8164.4-14.6
60137.7149.8-12.1000000000000
61151.7137.714
62156.8151.75.10000000000002
63180156.823.2
64180.41800.400000000000006
65170.4180.4-10
66191.6170.421.2
67199.5191.67.9
68218.2199.518.7
69217.5218.2-0.699999999999989
70205217.5-12.5
71194205-11
72199.31945.30000000000001
73219.3199.320
74211.1219.3-8.20000000000002
75215.2211.14.09999999999999
76240.2215.225
77242.2240.22
78240.7242.2-1.5
79255.4240.714.7000000000000
80253255.4-2.40000000000001
81218.2253-34.8
82203.7218.2-14.5
83205.6203.71.90000000000001
84215.6205.610
85188.5215.6-27.1
86202.9188.514.4
87214202.911.1
88230.321416.3
89230230.3-0.300000000000011
9024123011
91259.624118.6000000000000
92247.8259.6-11.8
93270.3247.822.5
94289.7270.319.4000000000000
95322.7289.733
96315322.7-7.69999999999999
97320.23155.19999999999999
98329.5320.29.30000000000001
99360.6329.531.1
100382.2360.621.6000000000000
101435.4382.253.2
102464435.428.6
103468.84644.80000000000001
104403468.8-65.8
105351.6403-51.4
106252351.6-99.6
107188252-64
108146.5188-41.5
109152.9146.56.4







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
110152.9114.429793770068191.370206229933
111152.998.4949126023395207.305087397660
112152.986.2676482321042219.532351767896
113152.975.959587540135229.840412459865
114152.966.878003761435238.921996238565
115152.958.6676244370268247.132375562973
116152.951.1174014302309254.682598569769
117152.944.089825204679261.710174795321
118152.937.4893813102025268.310618689798
119152.931.246526257014274.553473742986
120152.925.3087603277211280.491239672279
121152.919.6352964642083286.164703535792

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
110 & 152.9 & 114.429793770068 & 191.370206229933 \tabularnewline
111 & 152.9 & 98.4949126023395 & 207.305087397660 \tabularnewline
112 & 152.9 & 86.2676482321042 & 219.532351767896 \tabularnewline
113 & 152.9 & 75.959587540135 & 229.840412459865 \tabularnewline
114 & 152.9 & 66.878003761435 & 238.921996238565 \tabularnewline
115 & 152.9 & 58.6676244370268 & 247.132375562973 \tabularnewline
116 & 152.9 & 51.1174014302309 & 254.682598569769 \tabularnewline
117 & 152.9 & 44.089825204679 & 261.710174795321 \tabularnewline
118 & 152.9 & 37.4893813102025 & 268.310618689798 \tabularnewline
119 & 152.9 & 31.246526257014 & 274.553473742986 \tabularnewline
120 & 152.9 & 25.3087603277211 & 280.491239672279 \tabularnewline
121 & 152.9 & 19.6352964642083 & 286.164703535792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41942&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]110[/C][C]152.9[/C][C]114.429793770068[/C][C]191.370206229933[/C][/ROW]
[ROW][C]111[/C][C]152.9[/C][C]98.4949126023395[/C][C]207.305087397660[/C][/ROW]
[ROW][C]112[/C][C]152.9[/C][C]86.2676482321042[/C][C]219.532351767896[/C][/ROW]
[ROW][C]113[/C][C]152.9[/C][C]75.959587540135[/C][C]229.840412459865[/C][/ROW]
[ROW][C]114[/C][C]152.9[/C][C]66.878003761435[/C][C]238.921996238565[/C][/ROW]
[ROW][C]115[/C][C]152.9[/C][C]58.6676244370268[/C][C]247.132375562973[/C][/ROW]
[ROW][C]116[/C][C]152.9[/C][C]51.1174014302309[/C][C]254.682598569769[/C][/ROW]
[ROW][C]117[/C][C]152.9[/C][C]44.089825204679[/C][C]261.710174795321[/C][/ROW]
[ROW][C]118[/C][C]152.9[/C][C]37.4893813102025[/C][C]268.310618689798[/C][/ROW]
[ROW][C]119[/C][C]152.9[/C][C]31.246526257014[/C][C]274.553473742986[/C][/ROW]
[ROW][C]120[/C][C]152.9[/C][C]25.3087603277211[/C][C]280.491239672279[/C][/ROW]
[ROW][C]121[/C][C]152.9[/C][C]19.6352964642083[/C][C]286.164703535792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41942&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41942&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
110152.9114.429793770068191.370206229933
111152.998.4949126023395207.305087397660
112152.986.2676482321042219.532351767896
113152.975.959587540135229.840412459865
114152.966.878003761435238.921996238565
115152.958.6676244370268247.132375562973
116152.951.1174014302309254.682598569769
117152.944.089825204679261.710174795321
118152.937.4893813102025268.310618689798
119152.931.246526257014274.553473742986
120152.925.3087603277211280.491239672279
121152.919.6352964642083286.164703535792



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')