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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 17:32:16 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461601984iv9d0mr286owpk5.htm/, Retrieved Mon, 06 May 2024 10:09:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294740, Retrieved Mon, 06 May 2024 10:09:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 16:32:16] [e1772292a6a44abe5991636299c33e7e] [Current]
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Dataseries X:
92,8
92,9
93,06
93,28
93,41
93,49
93,49
93,5
93,56
94,12
94,3
94,36
94,36
94,5
94,85
95,16
95,73
95,76
95,76
95,81
96,09
96,48
96,71
96,69
96,69
96,66
96,73
96,84
97,87
98
97,98
98,03
98,11
98,18
98,32
98,34
98,28
98,52
98,56
99,6
100,16
100,46
100,46
100,68
100,83
100,64
100,9
100,92
100,75
100,96
101,05
101,33
101,38
101,44
101,51
101,4
101,26
100,83
100,75
100,81
100,82
100,85
100,79
100,84
101,04
101,11
101,15
101,11
101,28
101,62
102,07
102,14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294740&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294740&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919206385201
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999919206385201 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294740&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]0.999919206385201[/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=294740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294740&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
alpha0.999919206385201
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
292.992.80.100000000000009
393.0692.89999192063850.160008079361475
493.2893.05998707236890.220012927631132
593.4193.27998222436030.130017775639715
693.4993.40998949539390.0800105046060935
793.4993.48999353566216.46433788631384e-06
893.593.48999999947770.0100000005222824
993.5693.49999919206380.0600008079361913
1094.1293.55999515231780.560004847682166
1194.394.11995475518410.180045244815943
1294.3694.29998545349380.060014546506153
1394.3694.35999515120784.84879215889578e-06
1494.594.35999999960820.140000000391751
1594.8594.49998868889390.350011311106101
1695.1694.8499717213210.310028278679042
1795.7395.15997495169470.57002504830534
1895.7695.72995394561580.0300460543841865
1995.7695.75999757247072.42752933843349e-06
2095.8195.75999999980390.0500000001961212
2196.0995.80999596031920.280004039680762
2296.4896.08997737746150.390022622538524
2396.7196.47996848866250.230031511337515
2496.6996.7099814149227-0.0199814149226683
2596.6996.6900016143707-1.61437073131765e-06
2696.6696.6900000001304-0.0300000001304284
2796.7396.66000242380850.0699975761915539
2896.8496.72999434464280.110005655357213
2997.8796.83999111224551.03000888775455
309897.86991678185870.130083218141323
3197.9897.9999894901066-0.0199894901065818
3298.0397.98000161502320.0499983849768313
3398.1198.02999596044980.0800040395502464
3498.1898.10999353618440.0700064638155595
3598.3298.17999434392470.14000565607526
3698.3498.31998868843690.0200113115630671
3798.2898.3399983832138-0.0599983832137951
3898.5298.28000484748630.239995152513728
3998.5698.51998060992410.040019390075912
4099.698.55999676668881.04000323331118
41100.1699.59991597437940.560084025620625
42100.46100.1599547487870.300045251213021
43100.46100.459975758262.42417404479056e-05
44100.68100.4599999980410.220000001958596
45100.83100.6799822254050.150017774595398
46100.64100.829987879522-0.189987879521709
47100.9100.6400153498080.25998465019245
48100.92100.89997899490.0200210050996787
49100.75100.919998382431-0.169998382430634
50100.96100.7500137347840.209986265216159
51101.05100.9599830344510.0900169655494381
52101.33101.0499927272040.280007272796041
53101.38101.32997737720.0500226227997445
54101.44101.3799959584910.0600040415085203
55101.51101.4399951520570.070004847943423
56101.4101.509994344055-0.109994344055281
57101.26101.400008886841-0.140008886840675
58100.83101.260011311824-0.430011311824074
59100.75100.830034742168-0.0800347421682801
60100.81100.7500064662960.0599935337038744
61100.82100.8099951529060.01000484709445
62100.85100.8199991916720.0300008083277561
63100.79100.849997576126-0.0599975761262357
64100.84100.7900048474210.0499951525789442
65101.04100.8399959607110.200004039289098
66101.11101.0399838409510.0700161590493025
67101.15101.1099943431410.0400056568585825
68101.11101.149996767798-0.039996767798371
69101.28101.1100032314830.169996768516555
70101.62101.2799862653470.340013734653439
71102.07101.6199725290610.450027470938693
72102.14102.0699636406540.0700363593461475

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 92.9 & 92.8 & 0.100000000000009 \tabularnewline
3 & 93.06 & 92.8999919206385 & 0.160008079361475 \tabularnewline
4 & 93.28 & 93.0599870723689 & 0.220012927631132 \tabularnewline
5 & 93.41 & 93.2799822243603 & 0.130017775639715 \tabularnewline
6 & 93.49 & 93.4099894953939 & 0.0800105046060935 \tabularnewline
7 & 93.49 & 93.4899935356621 & 6.46433788631384e-06 \tabularnewline
8 & 93.5 & 93.4899999994777 & 0.0100000005222824 \tabularnewline
9 & 93.56 & 93.4999991920638 & 0.0600008079361913 \tabularnewline
10 & 94.12 & 93.5599951523178 & 0.560004847682166 \tabularnewline
11 & 94.3 & 94.1199547551841 & 0.180045244815943 \tabularnewline
12 & 94.36 & 94.2999854534938 & 0.060014546506153 \tabularnewline
13 & 94.36 & 94.3599951512078 & 4.84879215889578e-06 \tabularnewline
14 & 94.5 & 94.3599999996082 & 0.140000000391751 \tabularnewline
15 & 94.85 & 94.4999886888939 & 0.350011311106101 \tabularnewline
16 & 95.16 & 94.849971721321 & 0.310028278679042 \tabularnewline
17 & 95.73 & 95.1599749516947 & 0.57002504830534 \tabularnewline
18 & 95.76 & 95.7299539456158 & 0.0300460543841865 \tabularnewline
19 & 95.76 & 95.7599975724707 & 2.42752933843349e-06 \tabularnewline
20 & 95.81 & 95.7599999998039 & 0.0500000001961212 \tabularnewline
21 & 96.09 & 95.8099959603192 & 0.280004039680762 \tabularnewline
22 & 96.48 & 96.0899773774615 & 0.390022622538524 \tabularnewline
23 & 96.71 & 96.4799684886625 & 0.230031511337515 \tabularnewline
24 & 96.69 & 96.7099814149227 & -0.0199814149226683 \tabularnewline
25 & 96.69 & 96.6900016143707 & -1.61437073131765e-06 \tabularnewline
26 & 96.66 & 96.6900000001304 & -0.0300000001304284 \tabularnewline
27 & 96.73 & 96.6600024238085 & 0.0699975761915539 \tabularnewline
28 & 96.84 & 96.7299943446428 & 0.110005655357213 \tabularnewline
29 & 97.87 & 96.8399911122455 & 1.03000888775455 \tabularnewline
30 & 98 & 97.8699167818587 & 0.130083218141323 \tabularnewline
31 & 97.98 & 97.9999894901066 & -0.0199894901065818 \tabularnewline
32 & 98.03 & 97.9800016150232 & 0.0499983849768313 \tabularnewline
33 & 98.11 & 98.0299959604498 & 0.0800040395502464 \tabularnewline
34 & 98.18 & 98.1099935361844 & 0.0700064638155595 \tabularnewline
35 & 98.32 & 98.1799943439247 & 0.14000565607526 \tabularnewline
36 & 98.34 & 98.3199886884369 & 0.0200113115630671 \tabularnewline
37 & 98.28 & 98.3399983832138 & -0.0599983832137951 \tabularnewline
38 & 98.52 & 98.2800048474863 & 0.239995152513728 \tabularnewline
39 & 98.56 & 98.5199806099241 & 0.040019390075912 \tabularnewline
40 & 99.6 & 98.5599967666888 & 1.04000323331118 \tabularnewline
41 & 100.16 & 99.5999159743794 & 0.560084025620625 \tabularnewline
42 & 100.46 & 100.159954748787 & 0.300045251213021 \tabularnewline
43 & 100.46 & 100.45997575826 & 2.42417404479056e-05 \tabularnewline
44 & 100.68 & 100.459999998041 & 0.220000001958596 \tabularnewline
45 & 100.83 & 100.679982225405 & 0.150017774595398 \tabularnewline
46 & 100.64 & 100.829987879522 & -0.189987879521709 \tabularnewline
47 & 100.9 & 100.640015349808 & 0.25998465019245 \tabularnewline
48 & 100.92 & 100.8999789949 & 0.0200210050996787 \tabularnewline
49 & 100.75 & 100.919998382431 & -0.169998382430634 \tabularnewline
50 & 100.96 & 100.750013734784 & 0.209986265216159 \tabularnewline
51 & 101.05 & 100.959983034451 & 0.0900169655494381 \tabularnewline
52 & 101.33 & 101.049992727204 & 0.280007272796041 \tabularnewline
53 & 101.38 & 101.3299773772 & 0.0500226227997445 \tabularnewline
54 & 101.44 & 101.379995958491 & 0.0600040415085203 \tabularnewline
55 & 101.51 & 101.439995152057 & 0.070004847943423 \tabularnewline
56 & 101.4 & 101.509994344055 & -0.109994344055281 \tabularnewline
57 & 101.26 & 101.400008886841 & -0.140008886840675 \tabularnewline
58 & 100.83 & 101.260011311824 & -0.430011311824074 \tabularnewline
59 & 100.75 & 100.830034742168 & -0.0800347421682801 \tabularnewline
60 & 100.81 & 100.750006466296 & 0.0599935337038744 \tabularnewline
61 & 100.82 & 100.809995152906 & 0.01000484709445 \tabularnewline
62 & 100.85 & 100.819999191672 & 0.0300008083277561 \tabularnewline
63 & 100.79 & 100.849997576126 & -0.0599975761262357 \tabularnewline
64 & 100.84 & 100.790004847421 & 0.0499951525789442 \tabularnewline
65 & 101.04 & 100.839995960711 & 0.200004039289098 \tabularnewline
66 & 101.11 & 101.039983840951 & 0.0700161590493025 \tabularnewline
67 & 101.15 & 101.109994343141 & 0.0400056568585825 \tabularnewline
68 & 101.11 & 101.149996767798 & -0.039996767798371 \tabularnewline
69 & 101.28 & 101.110003231483 & 0.169996768516555 \tabularnewline
70 & 101.62 & 101.279986265347 & 0.340013734653439 \tabularnewline
71 & 102.07 & 101.619972529061 & 0.450027470938693 \tabularnewline
72 & 102.14 & 102.069963640654 & 0.0700363593461475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294740&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]92.9[/C][C]92.8[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]3[/C][C]93.06[/C][C]92.8999919206385[/C][C]0.160008079361475[/C][/ROW]
[ROW][C]4[/C][C]93.28[/C][C]93.0599870723689[/C][C]0.220012927631132[/C][/ROW]
[ROW][C]5[/C][C]93.41[/C][C]93.2799822243603[/C][C]0.130017775639715[/C][/ROW]
[ROW][C]6[/C][C]93.49[/C][C]93.4099894953939[/C][C]0.0800105046060935[/C][/ROW]
[ROW][C]7[/C][C]93.49[/C][C]93.4899935356621[/C][C]6.46433788631384e-06[/C][/ROW]
[ROW][C]8[/C][C]93.5[/C][C]93.4899999994777[/C][C]0.0100000005222824[/C][/ROW]
[ROW][C]9[/C][C]93.56[/C][C]93.4999991920638[/C][C]0.0600008079361913[/C][/ROW]
[ROW][C]10[/C][C]94.12[/C][C]93.5599951523178[/C][C]0.560004847682166[/C][/ROW]
[ROW][C]11[/C][C]94.3[/C][C]94.1199547551841[/C][C]0.180045244815943[/C][/ROW]
[ROW][C]12[/C][C]94.36[/C][C]94.2999854534938[/C][C]0.060014546506153[/C][/ROW]
[ROW][C]13[/C][C]94.36[/C][C]94.3599951512078[/C][C]4.84879215889578e-06[/C][/ROW]
[ROW][C]14[/C][C]94.5[/C][C]94.3599999996082[/C][C]0.140000000391751[/C][/ROW]
[ROW][C]15[/C][C]94.85[/C][C]94.4999886888939[/C][C]0.350011311106101[/C][/ROW]
[ROW][C]16[/C][C]95.16[/C][C]94.849971721321[/C][C]0.310028278679042[/C][/ROW]
[ROW][C]17[/C][C]95.73[/C][C]95.1599749516947[/C][C]0.57002504830534[/C][/ROW]
[ROW][C]18[/C][C]95.76[/C][C]95.7299539456158[/C][C]0.0300460543841865[/C][/ROW]
[ROW][C]19[/C][C]95.76[/C][C]95.7599975724707[/C][C]2.42752933843349e-06[/C][/ROW]
[ROW][C]20[/C][C]95.81[/C][C]95.7599999998039[/C][C]0.0500000001961212[/C][/ROW]
[ROW][C]21[/C][C]96.09[/C][C]95.8099959603192[/C][C]0.280004039680762[/C][/ROW]
[ROW][C]22[/C][C]96.48[/C][C]96.0899773774615[/C][C]0.390022622538524[/C][/ROW]
[ROW][C]23[/C][C]96.71[/C][C]96.4799684886625[/C][C]0.230031511337515[/C][/ROW]
[ROW][C]24[/C][C]96.69[/C][C]96.7099814149227[/C][C]-0.0199814149226683[/C][/ROW]
[ROW][C]25[/C][C]96.69[/C][C]96.6900016143707[/C][C]-1.61437073131765e-06[/C][/ROW]
[ROW][C]26[/C][C]96.66[/C][C]96.6900000001304[/C][C]-0.0300000001304284[/C][/ROW]
[ROW][C]27[/C][C]96.73[/C][C]96.6600024238085[/C][C]0.0699975761915539[/C][/ROW]
[ROW][C]28[/C][C]96.84[/C][C]96.7299943446428[/C][C]0.110005655357213[/C][/ROW]
[ROW][C]29[/C][C]97.87[/C][C]96.8399911122455[/C][C]1.03000888775455[/C][/ROW]
[ROW][C]30[/C][C]98[/C][C]97.8699167818587[/C][C]0.130083218141323[/C][/ROW]
[ROW][C]31[/C][C]97.98[/C][C]97.9999894901066[/C][C]-0.0199894901065818[/C][/ROW]
[ROW][C]32[/C][C]98.03[/C][C]97.9800016150232[/C][C]0.0499983849768313[/C][/ROW]
[ROW][C]33[/C][C]98.11[/C][C]98.0299959604498[/C][C]0.0800040395502464[/C][/ROW]
[ROW][C]34[/C][C]98.18[/C][C]98.1099935361844[/C][C]0.0700064638155595[/C][/ROW]
[ROW][C]35[/C][C]98.32[/C][C]98.1799943439247[/C][C]0.14000565607526[/C][/ROW]
[ROW][C]36[/C][C]98.34[/C][C]98.3199886884369[/C][C]0.0200113115630671[/C][/ROW]
[ROW][C]37[/C][C]98.28[/C][C]98.3399983832138[/C][C]-0.0599983832137951[/C][/ROW]
[ROW][C]38[/C][C]98.52[/C][C]98.2800048474863[/C][C]0.239995152513728[/C][/ROW]
[ROW][C]39[/C][C]98.56[/C][C]98.5199806099241[/C][C]0.040019390075912[/C][/ROW]
[ROW][C]40[/C][C]99.6[/C][C]98.5599967666888[/C][C]1.04000323331118[/C][/ROW]
[ROW][C]41[/C][C]100.16[/C][C]99.5999159743794[/C][C]0.560084025620625[/C][/ROW]
[ROW][C]42[/C][C]100.46[/C][C]100.159954748787[/C][C]0.300045251213021[/C][/ROW]
[ROW][C]43[/C][C]100.46[/C][C]100.45997575826[/C][C]2.42417404479056e-05[/C][/ROW]
[ROW][C]44[/C][C]100.68[/C][C]100.459999998041[/C][C]0.220000001958596[/C][/ROW]
[ROW][C]45[/C][C]100.83[/C][C]100.679982225405[/C][C]0.150017774595398[/C][/ROW]
[ROW][C]46[/C][C]100.64[/C][C]100.829987879522[/C][C]-0.189987879521709[/C][/ROW]
[ROW][C]47[/C][C]100.9[/C][C]100.640015349808[/C][C]0.25998465019245[/C][/ROW]
[ROW][C]48[/C][C]100.92[/C][C]100.8999789949[/C][C]0.0200210050996787[/C][/ROW]
[ROW][C]49[/C][C]100.75[/C][C]100.919998382431[/C][C]-0.169998382430634[/C][/ROW]
[ROW][C]50[/C][C]100.96[/C][C]100.750013734784[/C][C]0.209986265216159[/C][/ROW]
[ROW][C]51[/C][C]101.05[/C][C]100.959983034451[/C][C]0.0900169655494381[/C][/ROW]
[ROW][C]52[/C][C]101.33[/C][C]101.049992727204[/C][C]0.280007272796041[/C][/ROW]
[ROW][C]53[/C][C]101.38[/C][C]101.3299773772[/C][C]0.0500226227997445[/C][/ROW]
[ROW][C]54[/C][C]101.44[/C][C]101.379995958491[/C][C]0.0600040415085203[/C][/ROW]
[ROW][C]55[/C][C]101.51[/C][C]101.439995152057[/C][C]0.070004847943423[/C][/ROW]
[ROW][C]56[/C][C]101.4[/C][C]101.509994344055[/C][C]-0.109994344055281[/C][/ROW]
[ROW][C]57[/C][C]101.26[/C][C]101.400008886841[/C][C]-0.140008886840675[/C][/ROW]
[ROW][C]58[/C][C]100.83[/C][C]101.260011311824[/C][C]-0.430011311824074[/C][/ROW]
[ROW][C]59[/C][C]100.75[/C][C]100.830034742168[/C][C]-0.0800347421682801[/C][/ROW]
[ROW][C]60[/C][C]100.81[/C][C]100.750006466296[/C][C]0.0599935337038744[/C][/ROW]
[ROW][C]61[/C][C]100.82[/C][C]100.809995152906[/C][C]0.01000484709445[/C][/ROW]
[ROW][C]62[/C][C]100.85[/C][C]100.819999191672[/C][C]0.0300008083277561[/C][/ROW]
[ROW][C]63[/C][C]100.79[/C][C]100.849997576126[/C][C]-0.0599975761262357[/C][/ROW]
[ROW][C]64[/C][C]100.84[/C][C]100.790004847421[/C][C]0.0499951525789442[/C][/ROW]
[ROW][C]65[/C][C]101.04[/C][C]100.839995960711[/C][C]0.200004039289098[/C][/ROW]
[ROW][C]66[/C][C]101.11[/C][C]101.039983840951[/C][C]0.0700161590493025[/C][/ROW]
[ROW][C]67[/C][C]101.15[/C][C]101.109994343141[/C][C]0.0400056568585825[/C][/ROW]
[ROW][C]68[/C][C]101.11[/C][C]101.149996767798[/C][C]-0.039996767798371[/C][/ROW]
[ROW][C]69[/C][C]101.28[/C][C]101.110003231483[/C][C]0.169996768516555[/C][/ROW]
[ROW][C]70[/C][C]101.62[/C][C]101.279986265347[/C][C]0.340013734653439[/C][/ROW]
[ROW][C]71[/C][C]102.07[/C][C]101.619972529061[/C][C]0.450027470938693[/C][/ROW]
[ROW][C]72[/C][C]102.14[/C][C]102.069963640654[/C][C]0.0700363593461475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294740&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
292.992.80.100000000000009
393.0692.89999192063850.160008079361475
493.2893.05998707236890.220012927631132
593.4193.27998222436030.130017775639715
693.4993.40998949539390.0800105046060935
793.4993.48999353566216.46433788631384e-06
893.593.48999999947770.0100000005222824
993.5693.49999919206380.0600008079361913
1094.1293.55999515231780.560004847682166
1194.394.11995475518410.180045244815943
1294.3694.29998545349380.060014546506153
1394.3694.35999515120784.84879215889578e-06
1494.594.35999999960820.140000000391751
1594.8594.49998868889390.350011311106101
1695.1694.8499717213210.310028278679042
1795.7395.15997495169470.57002504830534
1895.7695.72995394561580.0300460543841865
1995.7695.75999757247072.42752933843349e-06
2095.8195.75999999980390.0500000001961212
2196.0995.80999596031920.280004039680762
2296.4896.08997737746150.390022622538524
2396.7196.47996848866250.230031511337515
2496.6996.7099814149227-0.0199814149226683
2596.6996.6900016143707-1.61437073131765e-06
2696.6696.6900000001304-0.0300000001304284
2796.7396.66000242380850.0699975761915539
2896.8496.72999434464280.110005655357213
2997.8796.83999111224551.03000888775455
309897.86991678185870.130083218141323
3197.9897.9999894901066-0.0199894901065818
3298.0397.98000161502320.0499983849768313
3398.1198.02999596044980.0800040395502464
3498.1898.10999353618440.0700064638155595
3598.3298.17999434392470.14000565607526
3698.3498.31998868843690.0200113115630671
3798.2898.3399983832138-0.0599983832137951
3898.5298.28000484748630.239995152513728
3998.5698.51998060992410.040019390075912
4099.698.55999676668881.04000323331118
41100.1699.59991597437940.560084025620625
42100.46100.1599547487870.300045251213021
43100.46100.459975758262.42417404479056e-05
44100.68100.4599999980410.220000001958596
45100.83100.6799822254050.150017774595398
46100.64100.829987879522-0.189987879521709
47100.9100.6400153498080.25998465019245
48100.92100.89997899490.0200210050996787
49100.75100.919998382431-0.169998382430634
50100.96100.7500137347840.209986265216159
51101.05100.9599830344510.0900169655494381
52101.33101.0499927272040.280007272796041
53101.38101.32997737720.0500226227997445
54101.44101.3799959584910.0600040415085203
55101.51101.4399951520570.070004847943423
56101.4101.509994344055-0.109994344055281
57101.26101.400008886841-0.140008886840675
58100.83101.260011311824-0.430011311824074
59100.75100.830034742168-0.0800347421682801
60100.81100.7500064662960.0599935337038744
61100.82100.8099951529060.01000484709445
62100.85100.8199991916720.0300008083277561
63100.79100.849997576126-0.0599975761262357
64100.84100.7900048474210.0499951525789442
65101.04100.8399959607110.200004039289098
66101.11101.0399838409510.0700161590493025
67101.15101.1099943431410.0400056568585825
68101.11101.149996767798-0.039996767798371
69101.28101.1100032314830.169996768516555
70101.62101.2799862653470.340013734653439
71102.07101.6199725290610.450027470938693
72102.14102.0699636406540.0700363593461475







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.139994341509101.686987159418102.593001523601
74102.139994341509101.499371320391102.780617362628
75102.139994341509101.355405147505102.924583535513
76102.139994341509101.234034876904103.045953806115
77102.139994341509101.127104959756103.152883723263
78102.139994341509101.030432604683103.249556078336
79102.139994341509100.941532996288103.338455686731
80102.139994341509100.858787120116103.421201562903
81102.139994341509100.781070395031103.498918287987
82102.139994341509100.707564014941103.572424668078
83102.139994341509100.637649844188103.642338838831
84102.139994341509100.570847650854103.709141032164

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.139994341509 & 101.686987159418 & 102.593001523601 \tabularnewline
74 & 102.139994341509 & 101.499371320391 & 102.780617362628 \tabularnewline
75 & 102.139994341509 & 101.355405147505 & 102.924583535513 \tabularnewline
76 & 102.139994341509 & 101.234034876904 & 103.045953806115 \tabularnewline
77 & 102.139994341509 & 101.127104959756 & 103.152883723263 \tabularnewline
78 & 102.139994341509 & 101.030432604683 & 103.249556078336 \tabularnewline
79 & 102.139994341509 & 100.941532996288 & 103.338455686731 \tabularnewline
80 & 102.139994341509 & 100.858787120116 & 103.421201562903 \tabularnewline
81 & 102.139994341509 & 100.781070395031 & 103.498918287987 \tabularnewline
82 & 102.139994341509 & 100.707564014941 & 103.572424668078 \tabularnewline
83 & 102.139994341509 & 100.637649844188 & 103.642338838831 \tabularnewline
84 & 102.139994341509 & 100.570847650854 & 103.709141032164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294740&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]102.139994341509[/C][C]101.686987159418[/C][C]102.593001523601[/C][/ROW]
[ROW][C]74[/C][C]102.139994341509[/C][C]101.499371320391[/C][C]102.780617362628[/C][/ROW]
[ROW][C]75[/C][C]102.139994341509[/C][C]101.355405147505[/C][C]102.924583535513[/C][/ROW]
[ROW][C]76[/C][C]102.139994341509[/C][C]101.234034876904[/C][C]103.045953806115[/C][/ROW]
[ROW][C]77[/C][C]102.139994341509[/C][C]101.127104959756[/C][C]103.152883723263[/C][/ROW]
[ROW][C]78[/C][C]102.139994341509[/C][C]101.030432604683[/C][C]103.249556078336[/C][/ROW]
[ROW][C]79[/C][C]102.139994341509[/C][C]100.941532996288[/C][C]103.338455686731[/C][/ROW]
[ROW][C]80[/C][C]102.139994341509[/C][C]100.858787120116[/C][C]103.421201562903[/C][/ROW]
[ROW][C]81[/C][C]102.139994341509[/C][C]100.781070395031[/C][C]103.498918287987[/C][/ROW]
[ROW][C]82[/C][C]102.139994341509[/C][C]100.707564014941[/C][C]103.572424668078[/C][/ROW]
[ROW][C]83[/C][C]102.139994341509[/C][C]100.637649844188[/C][C]103.642338838831[/C][/ROW]
[ROW][C]84[/C][C]102.139994341509[/C][C]100.570847650854[/C][C]103.709141032164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294740&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
73102.139994341509101.686987159418102.593001523601
74102.139994341509101.499371320391102.780617362628
75102.139994341509101.355405147505102.924583535513
76102.139994341509101.234034876904103.045953806115
77102.139994341509101.127104959756103.152883723263
78102.139994341509101.030432604683103.249556078336
79102.139994341509100.941532996288103.338455686731
80102.139994341509100.858787120116103.421201562903
81102.139994341509100.781070395031103.498918287987
82102.139994341509100.707564014941103.572424668078
83102.139994341509100.637649844188103.642338838831
84102.139994341509100.570847650854103.709141032164



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')