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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:18:16 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356081625vv5kbko2b3wmprr.htm/, Retrieved Thu, 28 Mar 2024 23:10:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203355, Retrieved Thu, 28 Mar 2024 23:10:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Classical Deompos...] [2012-12-21 09:18:16] [79b2fff90bae55fa563973a9f648a974] [Current]
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Dataseries X:
104.42
104.42
104.42
104.42
104.42
104.42
104.42
104.44
104.44
104.44
105.19
105.19
105.19
106.38
106.38
106.38
106.38
106.38
106.38
106.72
106.73
106.72
108.6
108.6
109.65
109.65
109.65
109.65
109.65
109.65
109.65
109.65
112.27
112.27
112.27
112.27
112.27
114.98
114.98
114.98
114.98
114.98
114.98
116.04
116.59
116.59
116.59
116.59
118.75
118.75
118.75
118.75
118.75
118.75
118.75
119.31
119.31
119.31
119.31
119.31
121.19
121.19
121.19
121.19
121.19
122.91
122.91
122.91
122.91
122.91
122.91
122.91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203355&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203355&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999958402777615
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999958402777615 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203355&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]0.999958402777615[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203355&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
alpha0.999958402777615
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2104.42104.420
3104.42104.420
4104.42104.420
5104.42104.420
6104.42104.420
7104.42104.420
8104.44104.420.019999999999996
9104.44104.4399991680568.31944447554633e-07
10104.44104.4399999999653.46034312315169e-11
11105.19104.440.75
12105.19105.1899688020833.11979167832988e-05
13105.19105.1899999987021.29774946344696e-09
14106.38105.191.19000000000005
15106.38106.3799504993054.95006946437115e-05
16106.38106.3799999979412.05909600481391e-09
17106.38106.388.5265128291212e-14
18106.38106.380
19106.38106.380
20106.72106.380.340000000000003
21106.73106.7199858569440.0100141430556135
22106.72106.729999583439-0.00999958343946616
23108.6106.7200004159551.87999958404509
24108.6108.5999217972397.82027607755253e-05
25109.65108.5999999967471.05000000325303
26109.65109.6499563229164.36770836387268e-05
27109.65109.6499999981831.81684356448386e-09
28109.65109.657.105427357601e-14
29109.65109.650
30109.65109.650
31109.65109.650
32109.65109.650
33112.27109.652.61999999999999
34112.27112.2698910152770.000108984722643868
35112.27112.2699999954674.53346160611545e-09
36112.27112.271.84741111297626e-13
37112.27112.270
38114.98112.272.71000000000001
39114.98114.9798872715270.000112728472657864
40114.98114.9799999953114.68919836293935e-09
41114.98114.981.98951966012828e-13
42114.98114.980
43114.98114.980
44116.04114.981.06
45116.59116.0399559069440.550044093055732
46116.59116.5899771196942.28803064601379e-05
47116.59116.5899999990489.51757783695939e-10
48116.59116.594.2632564145606e-14
49118.75116.592.16
50118.75118.749910158.98500003501113e-05
51118.75118.7499999962623.73751163351699e-09
52118.75118.751.56319401867222e-13
53118.75118.750
54118.75118.750
55118.75118.750
56119.31118.750.560000000000002
57119.31119.3099767055552.32944445315297e-05
58119.31119.3099999990319.68981339610764e-10
59119.31119.314.2632564145606e-14
60119.31119.310
61121.19119.311.88
62121.19121.1899217972227.82027780843464e-05
63121.19121.1899999967473.25302096371161e-09
64121.19121.191.4210854715202e-13
65121.19121.190
66122.91121.191.72
67122.91122.9099284527777.15472225039093e-05
68122.91122.9099999970242.97616509215004e-09
69122.91122.911.27897692436818e-13
70122.91122.910
71122.91122.910
72122.91122.910

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 104.42 & 104.42 & 0 \tabularnewline
3 & 104.42 & 104.42 & 0 \tabularnewline
4 & 104.42 & 104.42 & 0 \tabularnewline
5 & 104.42 & 104.42 & 0 \tabularnewline
6 & 104.42 & 104.42 & 0 \tabularnewline
7 & 104.42 & 104.42 & 0 \tabularnewline
8 & 104.44 & 104.42 & 0.019999999999996 \tabularnewline
9 & 104.44 & 104.439999168056 & 8.31944447554633e-07 \tabularnewline
10 & 104.44 & 104.439999999965 & 3.46034312315169e-11 \tabularnewline
11 & 105.19 & 104.44 & 0.75 \tabularnewline
12 & 105.19 & 105.189968802083 & 3.11979167832988e-05 \tabularnewline
13 & 105.19 & 105.189999998702 & 1.29774946344696e-09 \tabularnewline
14 & 106.38 & 105.19 & 1.19000000000005 \tabularnewline
15 & 106.38 & 106.379950499305 & 4.95006946437115e-05 \tabularnewline
16 & 106.38 & 106.379999997941 & 2.05909600481391e-09 \tabularnewline
17 & 106.38 & 106.38 & 8.5265128291212e-14 \tabularnewline
18 & 106.38 & 106.38 & 0 \tabularnewline
19 & 106.38 & 106.38 & 0 \tabularnewline
20 & 106.72 & 106.38 & 0.340000000000003 \tabularnewline
21 & 106.73 & 106.719985856944 & 0.0100141430556135 \tabularnewline
22 & 106.72 & 106.729999583439 & -0.00999958343946616 \tabularnewline
23 & 108.6 & 106.720000415955 & 1.87999958404509 \tabularnewline
24 & 108.6 & 108.599921797239 & 7.82027607755253e-05 \tabularnewline
25 & 109.65 & 108.599999996747 & 1.05000000325303 \tabularnewline
26 & 109.65 & 109.649956322916 & 4.36770836387268e-05 \tabularnewline
27 & 109.65 & 109.649999998183 & 1.81684356448386e-09 \tabularnewline
28 & 109.65 & 109.65 & 7.105427357601e-14 \tabularnewline
29 & 109.65 & 109.65 & 0 \tabularnewline
30 & 109.65 & 109.65 & 0 \tabularnewline
31 & 109.65 & 109.65 & 0 \tabularnewline
32 & 109.65 & 109.65 & 0 \tabularnewline
33 & 112.27 & 109.65 & 2.61999999999999 \tabularnewline
34 & 112.27 & 112.269891015277 & 0.000108984722643868 \tabularnewline
35 & 112.27 & 112.269999995467 & 4.53346160611545e-09 \tabularnewline
36 & 112.27 & 112.27 & 1.84741111297626e-13 \tabularnewline
37 & 112.27 & 112.27 & 0 \tabularnewline
38 & 114.98 & 112.27 & 2.71000000000001 \tabularnewline
39 & 114.98 & 114.979887271527 & 0.000112728472657864 \tabularnewline
40 & 114.98 & 114.979999995311 & 4.68919836293935e-09 \tabularnewline
41 & 114.98 & 114.98 & 1.98951966012828e-13 \tabularnewline
42 & 114.98 & 114.98 & 0 \tabularnewline
43 & 114.98 & 114.98 & 0 \tabularnewline
44 & 116.04 & 114.98 & 1.06 \tabularnewline
45 & 116.59 & 116.039955906944 & 0.550044093055732 \tabularnewline
46 & 116.59 & 116.589977119694 & 2.28803064601379e-05 \tabularnewline
47 & 116.59 & 116.589999999048 & 9.51757783695939e-10 \tabularnewline
48 & 116.59 & 116.59 & 4.2632564145606e-14 \tabularnewline
49 & 118.75 & 116.59 & 2.16 \tabularnewline
50 & 118.75 & 118.74991015 & 8.98500003501113e-05 \tabularnewline
51 & 118.75 & 118.749999996262 & 3.73751163351699e-09 \tabularnewline
52 & 118.75 & 118.75 & 1.56319401867222e-13 \tabularnewline
53 & 118.75 & 118.75 & 0 \tabularnewline
54 & 118.75 & 118.75 & 0 \tabularnewline
55 & 118.75 & 118.75 & 0 \tabularnewline
56 & 119.31 & 118.75 & 0.560000000000002 \tabularnewline
57 & 119.31 & 119.309976705555 & 2.32944445315297e-05 \tabularnewline
58 & 119.31 & 119.309999999031 & 9.68981339610764e-10 \tabularnewline
59 & 119.31 & 119.31 & 4.2632564145606e-14 \tabularnewline
60 & 119.31 & 119.31 & 0 \tabularnewline
61 & 121.19 & 119.31 & 1.88 \tabularnewline
62 & 121.19 & 121.189921797222 & 7.82027780843464e-05 \tabularnewline
63 & 121.19 & 121.189999996747 & 3.25302096371161e-09 \tabularnewline
64 & 121.19 & 121.19 & 1.4210854715202e-13 \tabularnewline
65 & 121.19 & 121.19 & 0 \tabularnewline
66 & 122.91 & 121.19 & 1.72 \tabularnewline
67 & 122.91 & 122.909928452777 & 7.15472225039093e-05 \tabularnewline
68 & 122.91 & 122.909999997024 & 2.97616509215004e-09 \tabularnewline
69 & 122.91 & 122.91 & 1.27897692436818e-13 \tabularnewline
70 & 122.91 & 122.91 & 0 \tabularnewline
71 & 122.91 & 122.91 & 0 \tabularnewline
72 & 122.91 & 122.91 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203355&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]2[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]104.44[/C][C]104.42[/C][C]0.019999999999996[/C][/ROW]
[ROW][C]9[/C][C]104.44[/C][C]104.439999168056[/C][C]8.31944447554633e-07[/C][/ROW]
[ROW][C]10[/C][C]104.44[/C][C]104.439999999965[/C][C]3.46034312315169e-11[/C][/ROW]
[ROW][C]11[/C][C]105.19[/C][C]104.44[/C][C]0.75[/C][/ROW]
[ROW][C]12[/C][C]105.19[/C][C]105.189968802083[/C][C]3.11979167832988e-05[/C][/ROW]
[ROW][C]13[/C][C]105.19[/C][C]105.189999998702[/C][C]1.29774946344696e-09[/C][/ROW]
[ROW][C]14[/C][C]106.38[/C][C]105.19[/C][C]1.19000000000005[/C][/ROW]
[ROW][C]15[/C][C]106.38[/C][C]106.379950499305[/C][C]4.95006946437115e-05[/C][/ROW]
[ROW][C]16[/C][C]106.38[/C][C]106.379999997941[/C][C]2.05909600481391e-09[/C][/ROW]
[ROW][C]17[/C][C]106.38[/C][C]106.38[/C][C]8.5265128291212e-14[/C][/ROW]
[ROW][C]18[/C][C]106.38[/C][C]106.38[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]106.38[/C][C]106.38[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]106.72[/C][C]106.38[/C][C]0.340000000000003[/C][/ROW]
[ROW][C]21[/C][C]106.73[/C][C]106.719985856944[/C][C]0.0100141430556135[/C][/ROW]
[ROW][C]22[/C][C]106.72[/C][C]106.729999583439[/C][C]-0.00999958343946616[/C][/ROW]
[ROW][C]23[/C][C]108.6[/C][C]106.720000415955[/C][C]1.87999958404509[/C][/ROW]
[ROW][C]24[/C][C]108.6[/C][C]108.599921797239[/C][C]7.82027607755253e-05[/C][/ROW]
[ROW][C]25[/C][C]109.65[/C][C]108.599999996747[/C][C]1.05000000325303[/C][/ROW]
[ROW][C]26[/C][C]109.65[/C][C]109.649956322916[/C][C]4.36770836387268e-05[/C][/ROW]
[ROW][C]27[/C][C]109.65[/C][C]109.649999998183[/C][C]1.81684356448386e-09[/C][/ROW]
[ROW][C]28[/C][C]109.65[/C][C]109.65[/C][C]7.105427357601e-14[/C][/ROW]
[ROW][C]29[/C][C]109.65[/C][C]109.65[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]109.65[/C][C]109.65[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]109.65[/C][C]109.65[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]109.65[/C][C]109.65[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]112.27[/C][C]109.65[/C][C]2.61999999999999[/C][/ROW]
[ROW][C]34[/C][C]112.27[/C][C]112.269891015277[/C][C]0.000108984722643868[/C][/ROW]
[ROW][C]35[/C][C]112.27[/C][C]112.269999995467[/C][C]4.53346160611545e-09[/C][/ROW]
[ROW][C]36[/C][C]112.27[/C][C]112.27[/C][C]1.84741111297626e-13[/C][/ROW]
[ROW][C]37[/C][C]112.27[/C][C]112.27[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]114.98[/C][C]112.27[/C][C]2.71000000000001[/C][/ROW]
[ROW][C]39[/C][C]114.98[/C][C]114.979887271527[/C][C]0.000112728472657864[/C][/ROW]
[ROW][C]40[/C][C]114.98[/C][C]114.979999995311[/C][C]4.68919836293935e-09[/C][/ROW]
[ROW][C]41[/C][C]114.98[/C][C]114.98[/C][C]1.98951966012828e-13[/C][/ROW]
[ROW][C]42[/C][C]114.98[/C][C]114.98[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]114.98[/C][C]114.98[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]116.04[/C][C]114.98[/C][C]1.06[/C][/ROW]
[ROW][C]45[/C][C]116.59[/C][C]116.039955906944[/C][C]0.550044093055732[/C][/ROW]
[ROW][C]46[/C][C]116.59[/C][C]116.589977119694[/C][C]2.28803064601379e-05[/C][/ROW]
[ROW][C]47[/C][C]116.59[/C][C]116.589999999048[/C][C]9.51757783695939e-10[/C][/ROW]
[ROW][C]48[/C][C]116.59[/C][C]116.59[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]49[/C][C]118.75[/C][C]116.59[/C][C]2.16[/C][/ROW]
[ROW][C]50[/C][C]118.75[/C][C]118.74991015[/C][C]8.98500003501113e-05[/C][/ROW]
[ROW][C]51[/C][C]118.75[/C][C]118.749999996262[/C][C]3.73751163351699e-09[/C][/ROW]
[ROW][C]52[/C][C]118.75[/C][C]118.75[/C][C]1.56319401867222e-13[/C][/ROW]
[ROW][C]53[/C][C]118.75[/C][C]118.75[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]118.75[/C][C]118.75[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]118.75[/C][C]118.75[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]119.31[/C][C]118.75[/C][C]0.560000000000002[/C][/ROW]
[ROW][C]57[/C][C]119.31[/C][C]119.309976705555[/C][C]2.32944445315297e-05[/C][/ROW]
[ROW][C]58[/C][C]119.31[/C][C]119.309999999031[/C][C]9.68981339610764e-10[/C][/ROW]
[ROW][C]59[/C][C]119.31[/C][C]119.31[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]60[/C][C]119.31[/C][C]119.31[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]121.19[/C][C]119.31[/C][C]1.88[/C][/ROW]
[ROW][C]62[/C][C]121.19[/C][C]121.189921797222[/C][C]7.82027780843464e-05[/C][/ROW]
[ROW][C]63[/C][C]121.19[/C][C]121.189999996747[/C][C]3.25302096371161e-09[/C][/ROW]
[ROW][C]64[/C][C]121.19[/C][C]121.19[/C][C]1.4210854715202e-13[/C][/ROW]
[ROW][C]65[/C][C]121.19[/C][C]121.19[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]122.91[/C][C]121.19[/C][C]1.72[/C][/ROW]
[ROW][C]67[/C][C]122.91[/C][C]122.909928452777[/C][C]7.15472225039093e-05[/C][/ROW]
[ROW][C]68[/C][C]122.91[/C][C]122.909999997024[/C][C]2.97616509215004e-09[/C][/ROW]
[ROW][C]69[/C][C]122.91[/C][C]122.91[/C][C]1.27897692436818e-13[/C][/ROW]
[ROW][C]70[/C][C]122.91[/C][C]122.91[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]122.91[/C][C]122.91[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]122.91[/C][C]122.91[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203355&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
2104.42104.420
3104.42104.420
4104.42104.420
5104.42104.420
6104.42104.420
7104.42104.420
8104.44104.420.019999999999996
9104.44104.4399991680568.31944447554633e-07
10104.44104.4399999999653.46034312315169e-11
11105.19104.440.75
12105.19105.1899688020833.11979167832988e-05
13105.19105.1899999987021.29774946344696e-09
14106.38105.191.19000000000005
15106.38106.3799504993054.95006946437115e-05
16106.38106.3799999979412.05909600481391e-09
17106.38106.388.5265128291212e-14
18106.38106.380
19106.38106.380
20106.72106.380.340000000000003
21106.73106.7199858569440.0100141430556135
22106.72106.729999583439-0.00999958343946616
23108.6106.7200004159551.87999958404509
24108.6108.5999217972397.82027607755253e-05
25109.65108.5999999967471.05000000325303
26109.65109.6499563229164.36770836387268e-05
27109.65109.6499999981831.81684356448386e-09
28109.65109.657.105427357601e-14
29109.65109.650
30109.65109.650
31109.65109.650
32109.65109.650
33112.27109.652.61999999999999
34112.27112.2698910152770.000108984722643868
35112.27112.2699999954674.53346160611545e-09
36112.27112.271.84741111297626e-13
37112.27112.270
38114.98112.272.71000000000001
39114.98114.9798872715270.000112728472657864
40114.98114.9799999953114.68919836293935e-09
41114.98114.981.98951966012828e-13
42114.98114.980
43114.98114.980
44116.04114.981.06
45116.59116.0399559069440.550044093055732
46116.59116.5899771196942.28803064601379e-05
47116.59116.5899999990489.51757783695939e-10
48116.59116.594.2632564145606e-14
49118.75116.592.16
50118.75118.749910158.98500003501113e-05
51118.75118.7499999962623.73751163351699e-09
52118.75118.751.56319401867222e-13
53118.75118.750
54118.75118.750
55118.75118.750
56119.31118.750.560000000000002
57119.31119.3099767055552.32944445315297e-05
58119.31119.3099999990319.68981339610764e-10
59119.31119.314.2632564145606e-14
60119.31119.310
61121.19119.311.88
62121.19121.1899217972227.82027780843464e-05
63121.19121.1899999967473.25302096371161e-09
64121.19121.191.4210854715202e-13
65121.19121.190
66122.91121.191.72
67122.91122.9099284527777.15472225039093e-05
68122.91122.9099999970242.97616509215004e-09
69122.91122.911.27897692436818e-13
70122.91122.910
71122.91122.910
72122.91122.910







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73122.91121.647974205371124.172025794629
74122.91121.125263125606124.694736874394
75122.91120.724167820866125.095832179133
76122.91120.386027155485125.433972844515
77122.91120.088118442535125.731881557465
78122.91119.818787919136126.001212080864
79122.91119.571112650389126.248887349611
80122.91119.340581932877126.479418067123
81122.91119.124062607171126.695937392829
82122.91118.919273431199126.900726568801
83122.91118.724492246878127.095507753122
84122.91118.538381105819127.281618894181

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 122.91 & 121.647974205371 & 124.172025794629 \tabularnewline
74 & 122.91 & 121.125263125606 & 124.694736874394 \tabularnewline
75 & 122.91 & 120.724167820866 & 125.095832179133 \tabularnewline
76 & 122.91 & 120.386027155485 & 125.433972844515 \tabularnewline
77 & 122.91 & 120.088118442535 & 125.731881557465 \tabularnewline
78 & 122.91 & 119.818787919136 & 126.001212080864 \tabularnewline
79 & 122.91 & 119.571112650389 & 126.248887349611 \tabularnewline
80 & 122.91 & 119.340581932877 & 126.479418067123 \tabularnewline
81 & 122.91 & 119.124062607171 & 126.695937392829 \tabularnewline
82 & 122.91 & 118.919273431199 & 126.900726568801 \tabularnewline
83 & 122.91 & 118.724492246878 & 127.095507753122 \tabularnewline
84 & 122.91 & 118.538381105819 & 127.281618894181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203355&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]73[/C][C]122.91[/C][C]121.647974205371[/C][C]124.172025794629[/C][/ROW]
[ROW][C]74[/C][C]122.91[/C][C]121.125263125606[/C][C]124.694736874394[/C][/ROW]
[ROW][C]75[/C][C]122.91[/C][C]120.724167820866[/C][C]125.095832179133[/C][/ROW]
[ROW][C]76[/C][C]122.91[/C][C]120.386027155485[/C][C]125.433972844515[/C][/ROW]
[ROW][C]77[/C][C]122.91[/C][C]120.088118442535[/C][C]125.731881557465[/C][/ROW]
[ROW][C]78[/C][C]122.91[/C][C]119.818787919136[/C][C]126.001212080864[/C][/ROW]
[ROW][C]79[/C][C]122.91[/C][C]119.571112650389[/C][C]126.248887349611[/C][/ROW]
[ROW][C]80[/C][C]122.91[/C][C]119.340581932877[/C][C]126.479418067123[/C][/ROW]
[ROW][C]81[/C][C]122.91[/C][C]119.124062607171[/C][C]126.695937392829[/C][/ROW]
[ROW][C]82[/C][C]122.91[/C][C]118.919273431199[/C][C]126.900726568801[/C][/ROW]
[ROW][C]83[/C][C]122.91[/C][C]118.724492246878[/C][C]127.095507753122[/C][/ROW]
[ROW][C]84[/C][C]122.91[/C][C]118.538381105819[/C][C]127.281618894181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203355&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203355&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
73122.91121.647974205371124.172025794629
74122.91121.125263125606124.694736874394
75122.91120.724167820866125.095832179133
76122.91120.386027155485125.433972844515
77122.91120.088118442535125.731881557465
78122.91119.818787919136126.001212080864
79122.91119.571112650389126.248887349611
80122.91119.340581932877126.479418067123
81122.91119.124062607171126.695937392829
82122.91118.919273431199126.900726568801
83122.91118.724492246878127.095507753122
84122.91118.538381105819127.281618894181



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')