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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 11:07:54 -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/2008/May/27/t1211908131dfni1imvxw6txbw.htm/, Retrieved Sun, 19 May 2024 22:26:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13363, Retrieved Sun, 19 May 2024 22:26:04 +0000
QR Codes:

Original text written by user:Kara Van den Acker
IsPrivate?No (this computation is public)
User-defined keywordsInleiding tot kwantitatief onderzoek
Estimated Impact187

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave10(oefening2)] [2008-05-27 17:07:54] [90941d2aa133223de960c34c4b1bc975] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
107,5
107,5
113,3
107,8
104,5
105,1
104,2
106,6
103,8
107,7
106,4
110
113,2
113,9
112
113,9
113,1
111,7
110,7
113,5
114
112,7
112,2
115,8
118,4
118,8
123,9
118
120,2
118,7
119,8
124,8
121,3
120,2
118,3
129,6
130,2
127,19
133,1
129,12
123,28
123,36
124,13
126,96
127,14
123,7
123,67
130,19
134,01
124,96
129,96
128,32
132,38
126,25
128,91
131,42
129,44
126,86
126,71
131,63
132,78
126,61
132,84
123,14
128,13
125,49
126,48
130,86
127,32
126,56
126,64
129,26
126,47
135,38
135,5
132,22
122,62
125,16
128,5
133,86
128,87
125,07
125,25
132,16
130,24

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13363&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]6 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=13363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13363&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 time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.209409698147397
beta0.108381287029044
gamma0.300287584116774

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.209409698147397 \tabularnewline
beta & 0.108381287029044 \tabularnewline
gamma & 0.300287584116774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13363&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]0.209409698147397[/C][/ROW]
[ROW][C]beta[/C][C]0.108381287029044[/C][/ROW]
[ROW][C]gamma[/C][C]0.300287584116774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13363&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
alpha0.209409698147397
beta0.108381287029044
gamma0.300287584116774






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13113.2109.7759280644253.42407193557545
14113.9111.2832256949972.61677430500343
15112109.9726649292982.02733507070204
16113.9112.400221428091.49977857191004
17113.1112.2652287993860.834771200614057
18111.7111.3689099618900.331090038109721
19110.7110.787274521677-0.0872745216767044
20113.5113.958962582679-0.458962582679035
21114114.461425076549-0.461425076549176
22112.7113.178410302636-0.478410302635695
23112.2112.877345775629-0.677345775628766
24115.8116.524038337809-0.724038337808935
25118.4121.764793423966-3.36479342396572
26118.8121.673020616404-2.87302061640438
27123.9118.7645081897715.13549181022938
28118121.777885565704-3.77788556570430
29120.2120.1350474428620.0649525571383265
30118.7118.6642680234420.0357319765576989
31119.8117.6569390223472.14306097765316
32124.8121.2425021182453.55749788175487
33121.3122.544992746328-1.24499274632808
34120.2120.912761006353-0.71276100635258
35118.3120.397980217044-2.09798021704368
36129.6123.8514466439175.74855335608321
37130.2130.1870024698820.0129975301183265
38127.19131.061621092611-3.87162109261138
39133.1129.8680561585503.23194384145026
40129.12130.362799559793-1.24279955979347
41123.28130.244471314226-6.96447131422588
42123.36127.113206928932-3.75320692893187
43124.13125.623117572303-1.49311757230296
44126.96128.733258718716-1.77325871871643
45127.14127.398746033049-0.258746033049405
46123.7125.720577032665-2.02057703266482
47123.67124.228710615527-0.558710615527261
48130.19129.7559326753170.434067324682786
49134.01133.2695759014680.740424098532287
50124.96132.938970192895-7.9789701928952
51129.96132.072407311814-2.11240731181402
52128.32129.764534108095-1.44453410809507
53132.38127.6215551020424.75844489795772
54126.25127.341780942959-1.09178094295946
55128.91126.6544110684592.255588931541
56131.42130.3309250276201.08907497238025
57129.44129.799105801815-0.359105801815161
58126.86127.498202352423-0.638202352422951
59126.71126.5179630876750.192036912324724
60131.63132.463297611215-0.833297611214817
61132.78135.719117079147-2.93911707914731
62126.61132.290671591549-5.6806715915494
63132.84133.170367078481-0.330367078480549
64123.14131.254569897908-8.11456989790811
65128.13128.916188809941-0.786188809941109
66125.49125.729692385253-0.239692385253207
67126.48125.6527981448930.827201855107106
68130.86128.3144500993912.54554990060947
69127.32127.401647275270-0.0816472752695745
70126.56124.7874476827931.77255231720679
71126.64124.2310098147992.40899018520055
72129.26130.064637612067-0.804637612066955
73126.47132.521887934877-6.05188793487736
74135.38127.5454685447507.83453145524955
75135.5132.4968433748303.00315662517031
76132.22129.4623225335422.75767746645801
77122.62131.469291974559-8.84929197455872
78125.16126.821957640582-1.66195764058216
79128.5126.7911980463671.7088019536328
80133.86130.1808918162463.67910818375356
81128.87128.992825158372-0.122825158372166
82125.07126.913764603838-1.84376460383797
83125.25125.791821816828-0.54182181682782
84132.16130.2386483920601.92135160793961
85130.24132.060014233799-1.82001423379899

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 113.2 & 109.775928064425 & 3.42407193557545 \tabularnewline
14 & 113.9 & 111.283225694997 & 2.61677430500343 \tabularnewline
15 & 112 & 109.972664929298 & 2.02733507070204 \tabularnewline
16 & 113.9 & 112.40022142809 & 1.49977857191004 \tabularnewline
17 & 113.1 & 112.265228799386 & 0.834771200614057 \tabularnewline
18 & 111.7 & 111.368909961890 & 0.331090038109721 \tabularnewline
19 & 110.7 & 110.787274521677 & -0.0872745216767044 \tabularnewline
20 & 113.5 & 113.958962582679 & -0.458962582679035 \tabularnewline
21 & 114 & 114.461425076549 & -0.461425076549176 \tabularnewline
22 & 112.7 & 113.178410302636 & -0.478410302635695 \tabularnewline
23 & 112.2 & 112.877345775629 & -0.677345775628766 \tabularnewline
24 & 115.8 & 116.524038337809 & -0.724038337808935 \tabularnewline
25 & 118.4 & 121.764793423966 & -3.36479342396572 \tabularnewline
26 & 118.8 & 121.673020616404 & -2.87302061640438 \tabularnewline
27 & 123.9 & 118.764508189771 & 5.13549181022938 \tabularnewline
28 & 118 & 121.777885565704 & -3.77788556570430 \tabularnewline
29 & 120.2 & 120.135047442862 & 0.0649525571383265 \tabularnewline
30 & 118.7 & 118.664268023442 & 0.0357319765576989 \tabularnewline
31 & 119.8 & 117.656939022347 & 2.14306097765316 \tabularnewline
32 & 124.8 & 121.242502118245 & 3.55749788175487 \tabularnewline
33 & 121.3 & 122.544992746328 & -1.24499274632808 \tabularnewline
34 & 120.2 & 120.912761006353 & -0.71276100635258 \tabularnewline
35 & 118.3 & 120.397980217044 & -2.09798021704368 \tabularnewline
36 & 129.6 & 123.851446643917 & 5.74855335608321 \tabularnewline
37 & 130.2 & 130.187002469882 & 0.0129975301183265 \tabularnewline
38 & 127.19 & 131.061621092611 & -3.87162109261138 \tabularnewline
39 & 133.1 & 129.868056158550 & 3.23194384145026 \tabularnewline
40 & 129.12 & 130.362799559793 & -1.24279955979347 \tabularnewline
41 & 123.28 & 130.244471314226 & -6.96447131422588 \tabularnewline
42 & 123.36 & 127.113206928932 & -3.75320692893187 \tabularnewline
43 & 124.13 & 125.623117572303 & -1.49311757230296 \tabularnewline
44 & 126.96 & 128.733258718716 & -1.77325871871643 \tabularnewline
45 & 127.14 & 127.398746033049 & -0.258746033049405 \tabularnewline
46 & 123.7 & 125.720577032665 & -2.02057703266482 \tabularnewline
47 & 123.67 & 124.228710615527 & -0.558710615527261 \tabularnewline
48 & 130.19 & 129.755932675317 & 0.434067324682786 \tabularnewline
49 & 134.01 & 133.269575901468 & 0.740424098532287 \tabularnewline
50 & 124.96 & 132.938970192895 & -7.9789701928952 \tabularnewline
51 & 129.96 & 132.072407311814 & -2.11240731181402 \tabularnewline
52 & 128.32 & 129.764534108095 & -1.44453410809507 \tabularnewline
53 & 132.38 & 127.621555102042 & 4.75844489795772 \tabularnewline
54 & 126.25 & 127.341780942959 & -1.09178094295946 \tabularnewline
55 & 128.91 & 126.654411068459 & 2.255588931541 \tabularnewline
56 & 131.42 & 130.330925027620 & 1.08907497238025 \tabularnewline
57 & 129.44 & 129.799105801815 & -0.359105801815161 \tabularnewline
58 & 126.86 & 127.498202352423 & -0.638202352422951 \tabularnewline
59 & 126.71 & 126.517963087675 & 0.192036912324724 \tabularnewline
60 & 131.63 & 132.463297611215 & -0.833297611214817 \tabularnewline
61 & 132.78 & 135.719117079147 & -2.93911707914731 \tabularnewline
62 & 126.61 & 132.290671591549 & -5.6806715915494 \tabularnewline
63 & 132.84 & 133.170367078481 & -0.330367078480549 \tabularnewline
64 & 123.14 & 131.254569897908 & -8.11456989790811 \tabularnewline
65 & 128.13 & 128.916188809941 & -0.786188809941109 \tabularnewline
66 & 125.49 & 125.729692385253 & -0.239692385253207 \tabularnewline
67 & 126.48 & 125.652798144893 & 0.827201855107106 \tabularnewline
68 & 130.86 & 128.314450099391 & 2.54554990060947 \tabularnewline
69 & 127.32 & 127.401647275270 & -0.0816472752695745 \tabularnewline
70 & 126.56 & 124.787447682793 & 1.77255231720679 \tabularnewline
71 & 126.64 & 124.231009814799 & 2.40899018520055 \tabularnewline
72 & 129.26 & 130.064637612067 & -0.804637612066955 \tabularnewline
73 & 126.47 & 132.521887934877 & -6.05188793487736 \tabularnewline
74 & 135.38 & 127.545468544750 & 7.83453145524955 \tabularnewline
75 & 135.5 & 132.496843374830 & 3.00315662517031 \tabularnewline
76 & 132.22 & 129.462322533542 & 2.75767746645801 \tabularnewline
77 & 122.62 & 131.469291974559 & -8.84929197455872 \tabularnewline
78 & 125.16 & 126.821957640582 & -1.66195764058216 \tabularnewline
79 & 128.5 & 126.791198046367 & 1.7088019536328 \tabularnewline
80 & 133.86 & 130.180891816246 & 3.67910818375356 \tabularnewline
81 & 128.87 & 128.992825158372 & -0.122825158372166 \tabularnewline
82 & 125.07 & 126.913764603838 & -1.84376460383797 \tabularnewline
83 & 125.25 & 125.791821816828 & -0.54182181682782 \tabularnewline
84 & 132.16 & 130.238648392060 & 1.92135160793961 \tabularnewline
85 & 130.24 & 132.060014233799 & -1.82001423379899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13363&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]113.2[/C][C]109.775928064425[/C][C]3.42407193557545[/C][/ROW]
[ROW][C]14[/C][C]113.9[/C][C]111.283225694997[/C][C]2.61677430500343[/C][/ROW]
[ROW][C]15[/C][C]112[/C][C]109.972664929298[/C][C]2.02733507070204[/C][/ROW]
[ROW][C]16[/C][C]113.9[/C][C]112.40022142809[/C][C]1.49977857191004[/C][/ROW]
[ROW][C]17[/C][C]113.1[/C][C]112.265228799386[/C][C]0.834771200614057[/C][/ROW]
[ROW][C]18[/C][C]111.7[/C][C]111.368909961890[/C][C]0.331090038109721[/C][/ROW]
[ROW][C]19[/C][C]110.7[/C][C]110.787274521677[/C][C]-0.0872745216767044[/C][/ROW]
[ROW][C]20[/C][C]113.5[/C][C]113.958962582679[/C][C]-0.458962582679035[/C][/ROW]
[ROW][C]21[/C][C]114[/C][C]114.461425076549[/C][C]-0.461425076549176[/C][/ROW]
[ROW][C]22[/C][C]112.7[/C][C]113.178410302636[/C][C]-0.478410302635695[/C][/ROW]
[ROW][C]23[/C][C]112.2[/C][C]112.877345775629[/C][C]-0.677345775628766[/C][/ROW]
[ROW][C]24[/C][C]115.8[/C][C]116.524038337809[/C][C]-0.724038337808935[/C][/ROW]
[ROW][C]25[/C][C]118.4[/C][C]121.764793423966[/C][C]-3.36479342396572[/C][/ROW]
[ROW][C]26[/C][C]118.8[/C][C]121.673020616404[/C][C]-2.87302061640438[/C][/ROW]
[ROW][C]27[/C][C]123.9[/C][C]118.764508189771[/C][C]5.13549181022938[/C][/ROW]
[ROW][C]28[/C][C]118[/C][C]121.777885565704[/C][C]-3.77788556570430[/C][/ROW]
[ROW][C]29[/C][C]120.2[/C][C]120.135047442862[/C][C]0.0649525571383265[/C][/ROW]
[ROW][C]30[/C][C]118.7[/C][C]118.664268023442[/C][C]0.0357319765576989[/C][/ROW]
[ROW][C]31[/C][C]119.8[/C][C]117.656939022347[/C][C]2.14306097765316[/C][/ROW]
[ROW][C]32[/C][C]124.8[/C][C]121.242502118245[/C][C]3.55749788175487[/C][/ROW]
[ROW][C]33[/C][C]121.3[/C][C]122.544992746328[/C][C]-1.24499274632808[/C][/ROW]
[ROW][C]34[/C][C]120.2[/C][C]120.912761006353[/C][C]-0.71276100635258[/C][/ROW]
[ROW][C]35[/C][C]118.3[/C][C]120.397980217044[/C][C]-2.09798021704368[/C][/ROW]
[ROW][C]36[/C][C]129.6[/C][C]123.851446643917[/C][C]5.74855335608321[/C][/ROW]
[ROW][C]37[/C][C]130.2[/C][C]130.187002469882[/C][C]0.0129975301183265[/C][/ROW]
[ROW][C]38[/C][C]127.19[/C][C]131.061621092611[/C][C]-3.87162109261138[/C][/ROW]
[ROW][C]39[/C][C]133.1[/C][C]129.868056158550[/C][C]3.23194384145026[/C][/ROW]
[ROW][C]40[/C][C]129.12[/C][C]130.362799559793[/C][C]-1.24279955979347[/C][/ROW]
[ROW][C]41[/C][C]123.28[/C][C]130.244471314226[/C][C]-6.96447131422588[/C][/ROW]
[ROW][C]42[/C][C]123.36[/C][C]127.113206928932[/C][C]-3.75320692893187[/C][/ROW]
[ROW][C]43[/C][C]124.13[/C][C]125.623117572303[/C][C]-1.49311757230296[/C][/ROW]
[ROW][C]44[/C][C]126.96[/C][C]128.733258718716[/C][C]-1.77325871871643[/C][/ROW]
[ROW][C]45[/C][C]127.14[/C][C]127.398746033049[/C][C]-0.258746033049405[/C][/ROW]
[ROW][C]46[/C][C]123.7[/C][C]125.720577032665[/C][C]-2.02057703266482[/C][/ROW]
[ROW][C]47[/C][C]123.67[/C][C]124.228710615527[/C][C]-0.558710615527261[/C][/ROW]
[ROW][C]48[/C][C]130.19[/C][C]129.755932675317[/C][C]0.434067324682786[/C][/ROW]
[ROW][C]49[/C][C]134.01[/C][C]133.269575901468[/C][C]0.740424098532287[/C][/ROW]
[ROW][C]50[/C][C]124.96[/C][C]132.938970192895[/C][C]-7.9789701928952[/C][/ROW]
[ROW][C]51[/C][C]129.96[/C][C]132.072407311814[/C][C]-2.11240731181402[/C][/ROW]
[ROW][C]52[/C][C]128.32[/C][C]129.764534108095[/C][C]-1.44453410809507[/C][/ROW]
[ROW][C]53[/C][C]132.38[/C][C]127.621555102042[/C][C]4.75844489795772[/C][/ROW]
[ROW][C]54[/C][C]126.25[/C][C]127.341780942959[/C][C]-1.09178094295946[/C][/ROW]
[ROW][C]55[/C][C]128.91[/C][C]126.654411068459[/C][C]2.255588931541[/C][/ROW]
[ROW][C]56[/C][C]131.42[/C][C]130.330925027620[/C][C]1.08907497238025[/C][/ROW]
[ROW][C]57[/C][C]129.44[/C][C]129.799105801815[/C][C]-0.359105801815161[/C][/ROW]
[ROW][C]58[/C][C]126.86[/C][C]127.498202352423[/C][C]-0.638202352422951[/C][/ROW]
[ROW][C]59[/C][C]126.71[/C][C]126.517963087675[/C][C]0.192036912324724[/C][/ROW]
[ROW][C]60[/C][C]131.63[/C][C]132.463297611215[/C][C]-0.833297611214817[/C][/ROW]
[ROW][C]61[/C][C]132.78[/C][C]135.719117079147[/C][C]-2.93911707914731[/C][/ROW]
[ROW][C]62[/C][C]126.61[/C][C]132.290671591549[/C][C]-5.6806715915494[/C][/ROW]
[ROW][C]63[/C][C]132.84[/C][C]133.170367078481[/C][C]-0.330367078480549[/C][/ROW]
[ROW][C]64[/C][C]123.14[/C][C]131.254569897908[/C][C]-8.11456989790811[/C][/ROW]
[ROW][C]65[/C][C]128.13[/C][C]128.916188809941[/C][C]-0.786188809941109[/C][/ROW]
[ROW][C]66[/C][C]125.49[/C][C]125.729692385253[/C][C]-0.239692385253207[/C][/ROW]
[ROW][C]67[/C][C]126.48[/C][C]125.652798144893[/C][C]0.827201855107106[/C][/ROW]
[ROW][C]68[/C][C]130.86[/C][C]128.314450099391[/C][C]2.54554990060947[/C][/ROW]
[ROW][C]69[/C][C]127.32[/C][C]127.401647275270[/C][C]-0.0816472752695745[/C][/ROW]
[ROW][C]70[/C][C]126.56[/C][C]124.787447682793[/C][C]1.77255231720679[/C][/ROW]
[ROW][C]71[/C][C]126.64[/C][C]124.231009814799[/C][C]2.40899018520055[/C][/ROW]
[ROW][C]72[/C][C]129.26[/C][C]130.064637612067[/C][C]-0.804637612066955[/C][/ROW]
[ROW][C]73[/C][C]126.47[/C][C]132.521887934877[/C][C]-6.05188793487736[/C][/ROW]
[ROW][C]74[/C][C]135.38[/C][C]127.545468544750[/C][C]7.83453145524955[/C][/ROW]
[ROW][C]75[/C][C]135.5[/C][C]132.496843374830[/C][C]3.00315662517031[/C][/ROW]
[ROW][C]76[/C][C]132.22[/C][C]129.462322533542[/C][C]2.75767746645801[/C][/ROW]
[ROW][C]77[/C][C]122.62[/C][C]131.469291974559[/C][C]-8.84929197455872[/C][/ROW]
[ROW][C]78[/C][C]125.16[/C][C]126.821957640582[/C][C]-1.66195764058216[/C][/ROW]
[ROW][C]79[/C][C]128.5[/C][C]126.791198046367[/C][C]1.7088019536328[/C][/ROW]
[ROW][C]80[/C][C]133.86[/C][C]130.180891816246[/C][C]3.67910818375356[/C][/ROW]
[ROW][C]81[/C][C]128.87[/C][C]128.992825158372[/C][C]-0.122825158372166[/C][/ROW]
[ROW][C]82[/C][C]125.07[/C][C]126.913764603838[/C][C]-1.84376460383797[/C][/ROW]
[ROW][C]83[/C][C]125.25[/C][C]125.791821816828[/C][C]-0.54182181682782[/C][/ROW]
[ROW][C]84[/C][C]132.16[/C][C]130.238648392060[/C][C]1.92135160793961[/C][/ROW]
[ROW][C]85[/C][C]130.24[/C][C]132.060014233799[/C][C]-1.82001423379899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13363&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13363&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
13113.2109.7759280644253.42407193557545
14113.9111.2832256949972.61677430500343
15112109.9726649292982.02733507070204
16113.9112.400221428091.49977857191004
17113.1112.2652287993860.834771200614057
18111.7111.3689099618900.331090038109721
19110.7110.787274521677-0.0872745216767044
20113.5113.958962582679-0.458962582679035
21114114.461425076549-0.461425076549176
22112.7113.178410302636-0.478410302635695
23112.2112.877345775629-0.677345775628766
24115.8116.524038337809-0.724038337808935
25118.4121.764793423966-3.36479342396572
26118.8121.673020616404-2.87302061640438
27123.9118.7645081897715.13549181022938
28118121.777885565704-3.77788556570430
29120.2120.1350474428620.0649525571383265
30118.7118.6642680234420.0357319765576989
31119.8117.6569390223472.14306097765316
32124.8121.2425021182453.55749788175487
33121.3122.544992746328-1.24499274632808
34120.2120.912761006353-0.71276100635258
35118.3120.397980217044-2.09798021704368
36129.6123.8514466439175.74855335608321
37130.2130.1870024698820.0129975301183265
38127.19131.061621092611-3.87162109261138
39133.1129.8680561585503.23194384145026
40129.12130.362799559793-1.24279955979347
41123.28130.244471314226-6.96447131422588
42123.36127.113206928932-3.75320692893187
43124.13125.623117572303-1.49311757230296
44126.96128.733258718716-1.77325871871643
45127.14127.398746033049-0.258746033049405
46123.7125.720577032665-2.02057703266482
47123.67124.228710615527-0.558710615527261
48130.19129.7559326753170.434067324682786
49134.01133.2695759014680.740424098532287
50124.96132.938970192895-7.9789701928952
51129.96132.072407311814-2.11240731181402
52128.32129.764534108095-1.44453410809507
53132.38127.6215551020424.75844489795772
54126.25127.341780942959-1.09178094295946
55128.91126.6544110684592.255588931541
56131.42130.3309250276201.08907497238025
57129.44129.799105801815-0.359105801815161
58126.86127.498202352423-0.638202352422951
59126.71126.5179630876750.192036912324724
60131.63132.463297611215-0.833297611214817
61132.78135.719117079147-2.93911707914731
62126.61132.290671591549-5.6806715915494
63132.84133.170367078481-0.330367078480549
64123.14131.254569897908-8.11456989790811
65128.13128.916188809941-0.786188809941109
66125.49125.729692385253-0.239692385253207
67126.48125.6527981448930.827201855107106
68130.86128.3144500993912.54554990060947
69127.32127.401647275270-0.0816472752695745
70126.56124.7874476827931.77255231720679
71126.64124.2310098147992.40899018520055
72129.26130.064637612067-0.804637612066955
73126.47132.521887934877-6.05188793487736
74135.38127.5454685447507.83453145524955
75135.5132.4968433748303.00315662517031
76132.22129.4623225335422.75767746645801
77122.62131.469291974559-8.84929197455872
78125.16126.821957640582-1.66195764058216
79128.5126.7911980463671.7088019536328
80133.86130.1808918162463.67910818375356
81128.87128.992825158372-0.122825158372166
82125.07126.913764603838-1.84376460383797
83125.25125.791821816828-0.54182181682782
84132.16130.2386483920601.92135160793961
85130.24132.060014233799-1.82001423379899






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
86131.375554384317128.674459266286134.076649502349
87133.497534448056130.443377559773136.551691336338
88129.673844622614126.288270108523133.059419136705
89128.160094092738124.408137655013131.912050530463
90127.093142655933122.954097234358131.232188077509
91128.284521302000123.692535223561132.876507380438
92131.826550842537126.690006781396136.963094903677
93128.910182569821123.400144902906134.420220236735
94126.396098367387120.500339684379132.291857050395
95125.958437923751119.592311489528132.324564357975
96131.121477066829124.01415631411138.228797819549
97131.60993913128940.0240179663676223.19586029621

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 131.375554384317 & 128.674459266286 & 134.076649502349 \tabularnewline
87 & 133.497534448056 & 130.443377559773 & 136.551691336338 \tabularnewline
88 & 129.673844622614 & 126.288270108523 & 133.059419136705 \tabularnewline
89 & 128.160094092738 & 124.408137655013 & 131.912050530463 \tabularnewline
90 & 127.093142655933 & 122.954097234358 & 131.232188077509 \tabularnewline
91 & 128.284521302000 & 123.692535223561 & 132.876507380438 \tabularnewline
92 & 131.826550842537 & 126.690006781396 & 136.963094903677 \tabularnewline
93 & 128.910182569821 & 123.400144902906 & 134.420220236735 \tabularnewline
94 & 126.396098367387 & 120.500339684379 & 132.291857050395 \tabularnewline
95 & 125.958437923751 & 119.592311489528 & 132.324564357975 \tabularnewline
96 & 131.121477066829 & 124.01415631411 & 138.228797819549 \tabularnewline
97 & 131.609939131289 & 40.0240179663676 & 223.19586029621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13363&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]86[/C][C]131.375554384317[/C][C]128.674459266286[/C][C]134.076649502349[/C][/ROW]
[ROW][C]87[/C][C]133.497534448056[/C][C]130.443377559773[/C][C]136.551691336338[/C][/ROW]
[ROW][C]88[/C][C]129.673844622614[/C][C]126.288270108523[/C][C]133.059419136705[/C][/ROW]
[ROW][C]89[/C][C]128.160094092738[/C][C]124.408137655013[/C][C]131.912050530463[/C][/ROW]
[ROW][C]90[/C][C]127.093142655933[/C][C]122.954097234358[/C][C]131.232188077509[/C][/ROW]
[ROW][C]91[/C][C]128.284521302000[/C][C]123.692535223561[/C][C]132.876507380438[/C][/ROW]
[ROW][C]92[/C][C]131.826550842537[/C][C]126.690006781396[/C][C]136.963094903677[/C][/ROW]
[ROW][C]93[/C][C]128.910182569821[/C][C]123.400144902906[/C][C]134.420220236735[/C][/ROW]
[ROW][C]94[/C][C]126.396098367387[/C][C]120.500339684379[/C][C]132.291857050395[/C][/ROW]
[ROW][C]95[/C][C]125.958437923751[/C][C]119.592311489528[/C][C]132.324564357975[/C][/ROW]
[ROW][C]96[/C][C]131.121477066829[/C][C]124.01415631411[/C][C]138.228797819549[/C][/ROW]
[ROW][C]97[/C][C]131.609939131289[/C][C]40.0240179663676[/C][C]223.19586029621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13363&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13363&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
86131.375554384317128.674459266286134.076649502349
87133.497534448056130.443377559773136.551691336338
88129.673844622614126.288270108523133.059419136705
89128.160094092738124.408137655013131.912050530463
90127.093142655933122.954097234358131.232188077509
91128.284521302000123.692535223561132.876507380438
92131.826550842537126.690006781396136.963094903677
93128.910182569821123.400144902906134.420220236735
94126.396098367387120.500339684379132.291857050395
95125.958437923751119.592311489528132.324564357975
96131.121477066829124.01415631411138.228797819549
97131.60993913128940.0240179663676223.19586029621


Figures (Output of Computation)

Input Parameters & R Code

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