Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 26 Nov 2016 12:21:31 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/26/t14801631634ewm03llajcevwa.htm/, Retrieved Tue, 21 Apr 2026 20:39:40 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 21 Apr 2026 20:39:40 +0200

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0400322277620813
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0400322277620813 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.0400322277620813[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Parameter	Value
alpha	0.0400322277620813
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	95.2	103.1	-7.89999999999999
3	110.2	102.78374540068	7.41625459932045
4	105.3	103.080634593941	2.21936540605887
5	107.4	103.169480735364	4.23051926463624
6	108.1	103.338837846118	4.76116215388244
7	108	103.529437773874	4.47056222612602
8	98.8	103.708404339135	-4.90840433913482
9	104.2	103.511909978682	0.688090021317819
10	107.8	103.539455755136	4.26054424486361
11	103.5	103.710014832737	-0.210014832737187
12	129.6	103.70160747112	25.8983925288804
13	100.1	104.738377819508	-4.63837781950757
14	96	104.55269322219	-8.55269322219044
15	111.4	104.210309859141	7.1896901408595
16	108.3	104.498129172398	3.8018708276018
17	103.6	104.650326531291	-1.05032653129076
18	106.8	104.608279620366	2.19172037963443
19	102.5	104.696019069794	-2.19601906979389
20	101	104.608107534222	-3.60810753422203
21	105.5	104.463666951622	1.03633304837803
22	105.1	104.505153672252	0.594846327747987
23	103.9	104.528966695928	-0.628966695927843
24	126.4	104.503787757902	21.8962122420983
25	101	105.380341913504	-4.38034191350424
26	99.3	105.204987068347	-5.90498706834704
27	113.5	104.968597281095	8.53140271890517
28	99.1	105.310128337868	-6.2101283378681
29	108.2	105.061523065815	3.13847693418521
30	109.2	105.18716328927	4.01283671072987
31	100.1	105.347806082446	-5.2478060824461
32	105.5	105.137724714102	0.362275285897624
33	103	105.15222740086	-2.15222740086
34	105.8	105.066068943353	0.733931056647023
35	106.1	105.095449838574	1.00455016142567
36	122.2	105.135664219435	17.064335780565
37	101.9	105.818787596011	-3.91878759601117
38	94.5	105.661909798416	-11.1619097984164
39	112.1	105.215073683106	6.88492631689357
40	97.6	105.490692621549	-7.89069262154946
41	110	105.174810617323	4.82518938267698
42	104.6	105.367973697686	-0.76797369768552
43	102.1	105.337229999704	-3.23722999970448
44	106	105.207636471038	0.792363528961943
45	98.5	105.2393565483	-6.73935654829982
46	106.2	104.969565091988	1.2304349080116
47	106	105.018822142472	0.981177857527669
48	120.9	105.05810087794	15.84189912206
49	105.1	105.692287391778	-0.5922873917782
50	102.4	105.66857680801	-3.26857680800991
51	94.2	105.537728396774	-11.3377283967738
52	105.6	105.08385387129	0.516146128710446
53	102.9	105.104516350673	-2.20451635067261
54	111.4	105.016264650017	6.38373534998274
55	105.4	105.271819797521	0.128180202479385
56	104.6	105.276951136581	-0.676951136580868
57	103.6	105.249851274497	-1.64985127449746
58	102.1	105.183804052503	-3.08380405250323
59	109.3	105.0603525063	4.23964749370022
60	103.9	105.230075040399	-1.33007504039853
61	125.3	105.176829173441	20.1231708265594
62	105.9	105.982404531265	-0.0824045312647144
63	106.2	105.979105694301	0.220894305699503
64	96.2	105.987948585458	-9.78794858545761
65	105.5	105.596115198361	-0.0961151983610335
66	104.7	105.592267492849	-0.892267492848831
67	111	105.55654803735	5.44345196264959
68	109.2	105.774461546131	3.42553845386885
69	108.3	105.911593481724	2.38840651827581
70	106.7	106.007206715452	0.692793284547761
71	103.6	106.034940774011	-2.43494077401131
72	103.9	105.937464670359	-2.0374646703589
73	104.7	105.855900420618	-1.1559004206179
74	112.4	105.809627151709	6.59037284829057
75	103.2	106.073454458609	-2.87345445860923
76	129.1	105.958423675258	23.1415763247418
77	114.9	106.884832529464	8.01516747053614
78	107.6	107.205697539196	0.394302460804411
79	102.8	107.221482345114	-4.42148234511365
80	99.1	107.044480556828	-7.94448055682803
81	111.9	106.726445301726	5.17355469827436
82	104.6	106.933554221747	-2.33355422174657
83	103.7	106.840136847646	-3.14013684764643
84	108.5	106.714430174157	1.78556982584266
85	110.1	106.785910512111	3.31408948788942
86	107.5	106.918580897314	0.581419102686326
87	106.8	106.941856399258	-0.141856399257634

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 95.2 & 103.1 & -7.89999999999999 \tabularnewline
3 & 110.2 & 102.78374540068 & 7.41625459932045 \tabularnewline
4 & 105.3 & 103.080634593941 & 2.21936540605887 \tabularnewline
5 & 107.4 & 103.169480735364 & 4.23051926463624 \tabularnewline
6 & 108.1 & 103.338837846118 & 4.76116215388244 \tabularnewline
7 & 108 & 103.529437773874 & 4.47056222612602 \tabularnewline
8 & 98.8 & 103.708404339135 & -4.90840433913482 \tabularnewline
9 & 104.2 & 103.511909978682 & 0.688090021317819 \tabularnewline
10 & 107.8 & 103.539455755136 & 4.26054424486361 \tabularnewline
11 & 103.5 & 103.710014832737 & -0.210014832737187 \tabularnewline
12 & 129.6 & 103.70160747112 & 25.8983925288804 \tabularnewline
13 & 100.1 & 104.738377819508 & -4.63837781950757 \tabularnewline
14 & 96 & 104.55269322219 & -8.55269322219044 \tabularnewline
15 & 111.4 & 104.210309859141 & 7.1896901408595 \tabularnewline
16 & 108.3 & 104.498129172398 & 3.8018708276018 \tabularnewline
17 & 103.6 & 104.650326531291 & -1.05032653129076 \tabularnewline
18 & 106.8 & 104.608279620366 & 2.19172037963443 \tabularnewline
19 & 102.5 & 104.696019069794 & -2.19601906979389 \tabularnewline
20 & 101 & 104.608107534222 & -3.60810753422203 \tabularnewline
21 & 105.5 & 104.463666951622 & 1.03633304837803 \tabularnewline
22 & 105.1 & 104.505153672252 & 0.594846327747987 \tabularnewline
23 & 103.9 & 104.528966695928 & -0.628966695927843 \tabularnewline
24 & 126.4 & 104.503787757902 & 21.8962122420983 \tabularnewline
25 & 101 & 105.380341913504 & -4.38034191350424 \tabularnewline
26 & 99.3 & 105.204987068347 & -5.90498706834704 \tabularnewline
27 & 113.5 & 104.968597281095 & 8.53140271890517 \tabularnewline
28 & 99.1 & 105.310128337868 & -6.2101283378681 \tabularnewline
29 & 108.2 & 105.061523065815 & 3.13847693418521 \tabularnewline
30 & 109.2 & 105.18716328927 & 4.01283671072987 \tabularnewline
31 & 100.1 & 105.347806082446 & -5.2478060824461 \tabularnewline
32 & 105.5 & 105.137724714102 & 0.362275285897624 \tabularnewline
33 & 103 & 105.15222740086 & -2.15222740086 \tabularnewline
34 & 105.8 & 105.066068943353 & 0.733931056647023 \tabularnewline
35 & 106.1 & 105.095449838574 & 1.00455016142567 \tabularnewline
36 & 122.2 & 105.135664219435 & 17.064335780565 \tabularnewline
37 & 101.9 & 105.818787596011 & -3.91878759601117 \tabularnewline
38 & 94.5 & 105.661909798416 & -11.1619097984164 \tabularnewline
39 & 112.1 & 105.215073683106 & 6.88492631689357 \tabularnewline
40 & 97.6 & 105.490692621549 & -7.89069262154946 \tabularnewline
41 & 110 & 105.174810617323 & 4.82518938267698 \tabularnewline
42 & 104.6 & 105.367973697686 & -0.76797369768552 \tabularnewline
43 & 102.1 & 105.337229999704 & -3.23722999970448 \tabularnewline
44 & 106 & 105.207636471038 & 0.792363528961943 \tabularnewline
45 & 98.5 & 105.2393565483 & -6.73935654829982 \tabularnewline
46 & 106.2 & 104.969565091988 & 1.2304349080116 \tabularnewline
47 & 106 & 105.018822142472 & 0.981177857527669 \tabularnewline
48 & 120.9 & 105.05810087794 & 15.84189912206 \tabularnewline
49 & 105.1 & 105.692287391778 & -0.5922873917782 \tabularnewline
50 & 102.4 & 105.66857680801 & -3.26857680800991 \tabularnewline
51 & 94.2 & 105.537728396774 & -11.3377283967738 \tabularnewline
52 & 105.6 & 105.08385387129 & 0.516146128710446 \tabularnewline
53 & 102.9 & 105.104516350673 & -2.20451635067261 \tabularnewline
54 & 111.4 & 105.016264650017 & 6.38373534998274 \tabularnewline
55 & 105.4 & 105.271819797521 & 0.128180202479385 \tabularnewline
56 & 104.6 & 105.276951136581 & -0.676951136580868 \tabularnewline
57 & 103.6 & 105.249851274497 & -1.64985127449746 \tabularnewline
58 & 102.1 & 105.183804052503 & -3.08380405250323 \tabularnewline
59 & 109.3 & 105.0603525063 & 4.23964749370022 \tabularnewline
60 & 103.9 & 105.230075040399 & -1.33007504039853 \tabularnewline
61 & 125.3 & 105.176829173441 & 20.1231708265594 \tabularnewline
62 & 105.9 & 105.982404531265 & -0.0824045312647144 \tabularnewline
63 & 106.2 & 105.979105694301 & 0.220894305699503 \tabularnewline
64 & 96.2 & 105.987948585458 & -9.78794858545761 \tabularnewline
65 & 105.5 & 105.596115198361 & -0.0961151983610335 \tabularnewline
66 & 104.7 & 105.592267492849 & -0.892267492848831 \tabularnewline
67 & 111 & 105.55654803735 & 5.44345196264959 \tabularnewline
68 & 109.2 & 105.774461546131 & 3.42553845386885 \tabularnewline
69 & 108.3 & 105.911593481724 & 2.38840651827581 \tabularnewline
70 & 106.7 & 106.007206715452 & 0.692793284547761 \tabularnewline
71 & 103.6 & 106.034940774011 & -2.43494077401131 \tabularnewline
72 & 103.9 & 105.937464670359 & -2.0374646703589 \tabularnewline
73 & 104.7 & 105.855900420618 & -1.1559004206179 \tabularnewline
74 & 112.4 & 105.809627151709 & 6.59037284829057 \tabularnewline
75 & 103.2 & 106.073454458609 & -2.87345445860923 \tabularnewline
76 & 129.1 & 105.958423675258 & 23.1415763247418 \tabularnewline
77 & 114.9 & 106.884832529464 & 8.01516747053614 \tabularnewline
78 & 107.6 & 107.205697539196 & 0.394302460804411 \tabularnewline
79 & 102.8 & 107.221482345114 & -4.42148234511365 \tabularnewline
80 & 99.1 & 107.044480556828 & -7.94448055682803 \tabularnewline
81 & 111.9 & 106.726445301726 & 5.17355469827436 \tabularnewline
82 & 104.6 & 106.933554221747 & -2.33355422174657 \tabularnewline
83 & 103.7 & 106.840136847646 & -3.14013684764643 \tabularnewline
84 & 108.5 & 106.714430174157 & 1.78556982584266 \tabularnewline
85 & 110.1 & 106.785910512111 & 3.31408948788942 \tabularnewline
86 & 107.5 & 106.918580897314 & 0.581419102686326 \tabularnewline
87 & 106.8 & 106.941856399258 & -0.141856399257634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]95.2[/C][C]103.1[/C][C]-7.89999999999999[/C][/ROW]
[ROW][C]3[/C][C]110.2[/C][C]102.78374540068[/C][C]7.41625459932045[/C][/ROW]
[ROW][C]4[/C][C]105.3[/C][C]103.080634593941[/C][C]2.21936540605887[/C][/ROW]
[ROW][C]5[/C][C]107.4[/C][C]103.169480735364[/C][C]4.23051926463624[/C][/ROW]
[ROW][C]6[/C][C]108.1[/C][C]103.338837846118[/C][C]4.76116215388244[/C][/ROW]
[ROW][C]7[/C][C]108[/C][C]103.529437773874[/C][C]4.47056222612602[/C][/ROW]
[ROW][C]8[/C][C]98.8[/C][C]103.708404339135[/C][C]-4.90840433913482[/C][/ROW]
[ROW][C]9[/C][C]104.2[/C][C]103.511909978682[/C][C]0.688090021317819[/C][/ROW]
[ROW][C]10[/C][C]107.8[/C][C]103.539455755136[/C][C]4.26054424486361[/C][/ROW]
[ROW][C]11[/C][C]103.5[/C][C]103.710014832737[/C][C]-0.210014832737187[/C][/ROW]
[ROW][C]12[/C][C]129.6[/C][C]103.70160747112[/C][C]25.8983925288804[/C][/ROW]
[ROW][C]13[/C][C]100.1[/C][C]104.738377819508[/C][C]-4.63837781950757[/C][/ROW]
[ROW][C]14[/C][C]96[/C][C]104.55269322219[/C][C]-8.55269322219044[/C][/ROW]
[ROW][C]15[/C][C]111.4[/C][C]104.210309859141[/C][C]7.1896901408595[/C][/ROW]
[ROW][C]16[/C][C]108.3[/C][C]104.498129172398[/C][C]3.8018708276018[/C][/ROW]
[ROW][C]17[/C][C]103.6[/C][C]104.650326531291[/C][C]-1.05032653129076[/C][/ROW]
[ROW][C]18[/C][C]106.8[/C][C]104.608279620366[/C][C]2.19172037963443[/C][/ROW]
[ROW][C]19[/C][C]102.5[/C][C]104.696019069794[/C][C]-2.19601906979389[/C][/ROW]
[ROW][C]20[/C][C]101[/C][C]104.608107534222[/C][C]-3.60810753422203[/C][/ROW]
[ROW][C]21[/C][C]105.5[/C][C]104.463666951622[/C][C]1.03633304837803[/C][/ROW]
[ROW][C]22[/C][C]105.1[/C][C]104.505153672252[/C][C]0.594846327747987[/C][/ROW]
[ROW][C]23[/C][C]103.9[/C][C]104.528966695928[/C][C]-0.628966695927843[/C][/ROW]
[ROW][C]24[/C][C]126.4[/C][C]104.503787757902[/C][C]21.8962122420983[/C][/ROW]
[ROW][C]25[/C][C]101[/C][C]105.380341913504[/C][C]-4.38034191350424[/C][/ROW]
[ROW][C]26[/C][C]99.3[/C][C]105.204987068347[/C][C]-5.90498706834704[/C][/ROW]
[ROW][C]27[/C][C]113.5[/C][C]104.968597281095[/C][C]8.53140271890517[/C][/ROW]
[ROW][C]28[/C][C]99.1[/C][C]105.310128337868[/C][C]-6.2101283378681[/C][/ROW]
[ROW][C]29[/C][C]108.2[/C][C]105.061523065815[/C][C]3.13847693418521[/C][/ROW]
[ROW][C]30[/C][C]109.2[/C][C]105.18716328927[/C][C]4.01283671072987[/C][/ROW]
[ROW][C]31[/C][C]100.1[/C][C]105.347806082446[/C][C]-5.2478060824461[/C][/ROW]
[ROW][C]32[/C][C]105.5[/C][C]105.137724714102[/C][C]0.362275285897624[/C][/ROW]
[ROW][C]33[/C][C]103[/C][C]105.15222740086[/C][C]-2.15222740086[/C][/ROW]
[ROW][C]34[/C][C]105.8[/C][C]105.066068943353[/C][C]0.733931056647023[/C][/ROW]
[ROW][C]35[/C][C]106.1[/C][C]105.095449838574[/C][C]1.00455016142567[/C][/ROW]
[ROW][C]36[/C][C]122.2[/C][C]105.135664219435[/C][C]17.064335780565[/C][/ROW]
[ROW][C]37[/C][C]101.9[/C][C]105.818787596011[/C][C]-3.91878759601117[/C][/ROW]
[ROW][C]38[/C][C]94.5[/C][C]105.661909798416[/C][C]-11.1619097984164[/C][/ROW]
[ROW][C]39[/C][C]112.1[/C][C]105.215073683106[/C][C]6.88492631689357[/C][/ROW]
[ROW][C]40[/C][C]97.6[/C][C]105.490692621549[/C][C]-7.89069262154946[/C][/ROW]
[ROW][C]41[/C][C]110[/C][C]105.174810617323[/C][C]4.82518938267698[/C][/ROW]
[ROW][C]42[/C][C]104.6[/C][C]105.367973697686[/C][C]-0.76797369768552[/C][/ROW]
[ROW][C]43[/C][C]102.1[/C][C]105.337229999704[/C][C]-3.23722999970448[/C][/ROW]
[ROW][C]44[/C][C]106[/C][C]105.207636471038[/C][C]0.792363528961943[/C][/ROW]
[ROW][C]45[/C][C]98.5[/C][C]105.2393565483[/C][C]-6.73935654829982[/C][/ROW]
[ROW][C]46[/C][C]106.2[/C][C]104.969565091988[/C][C]1.2304349080116[/C][/ROW]
[ROW][C]47[/C][C]106[/C][C]105.018822142472[/C][C]0.981177857527669[/C][/ROW]
[ROW][C]48[/C][C]120.9[/C][C]105.05810087794[/C][C]15.84189912206[/C][/ROW]
[ROW][C]49[/C][C]105.1[/C][C]105.692287391778[/C][C]-0.5922873917782[/C][/ROW]
[ROW][C]50[/C][C]102.4[/C][C]105.66857680801[/C][C]-3.26857680800991[/C][/ROW]
[ROW][C]51[/C][C]94.2[/C][C]105.537728396774[/C][C]-11.3377283967738[/C][/ROW]
[ROW][C]52[/C][C]105.6[/C][C]105.08385387129[/C][C]0.516146128710446[/C][/ROW]
[ROW][C]53[/C][C]102.9[/C][C]105.104516350673[/C][C]-2.20451635067261[/C][/ROW]
[ROW][C]54[/C][C]111.4[/C][C]105.016264650017[/C][C]6.38373534998274[/C][/ROW]
[ROW][C]55[/C][C]105.4[/C][C]105.271819797521[/C][C]0.128180202479385[/C][/ROW]
[ROW][C]56[/C][C]104.6[/C][C]105.276951136581[/C][C]-0.676951136580868[/C][/ROW]
[ROW][C]57[/C][C]103.6[/C][C]105.249851274497[/C][C]-1.64985127449746[/C][/ROW]
[ROW][C]58[/C][C]102.1[/C][C]105.183804052503[/C][C]-3.08380405250323[/C][/ROW]
[ROW][C]59[/C][C]109.3[/C][C]105.0603525063[/C][C]4.23964749370022[/C][/ROW]
[ROW][C]60[/C][C]103.9[/C][C]105.230075040399[/C][C]-1.33007504039853[/C][/ROW]
[ROW][C]61[/C][C]125.3[/C][C]105.176829173441[/C][C]20.1231708265594[/C][/ROW]
[ROW][C]62[/C][C]105.9[/C][C]105.982404531265[/C][C]-0.0824045312647144[/C][/ROW]
[ROW][C]63[/C][C]106.2[/C][C]105.979105694301[/C][C]0.220894305699503[/C][/ROW]
[ROW][C]64[/C][C]96.2[/C][C]105.987948585458[/C][C]-9.78794858545761[/C][/ROW]
[ROW][C]65[/C][C]105.5[/C][C]105.596115198361[/C][C]-0.0961151983610335[/C][/ROW]
[ROW][C]66[/C][C]104.7[/C][C]105.592267492849[/C][C]-0.892267492848831[/C][/ROW]
[ROW][C]67[/C][C]111[/C][C]105.55654803735[/C][C]5.44345196264959[/C][/ROW]
[ROW][C]68[/C][C]109.2[/C][C]105.774461546131[/C][C]3.42553845386885[/C][/ROW]
[ROW][C]69[/C][C]108.3[/C][C]105.911593481724[/C][C]2.38840651827581[/C][/ROW]
[ROW][C]70[/C][C]106.7[/C][C]106.007206715452[/C][C]0.692793284547761[/C][/ROW]
[ROW][C]71[/C][C]103.6[/C][C]106.034940774011[/C][C]-2.43494077401131[/C][/ROW]
[ROW][C]72[/C][C]103.9[/C][C]105.937464670359[/C][C]-2.0374646703589[/C][/ROW]
[ROW][C]73[/C][C]104.7[/C][C]105.855900420618[/C][C]-1.1559004206179[/C][/ROW]
[ROW][C]74[/C][C]112.4[/C][C]105.809627151709[/C][C]6.59037284829057[/C][/ROW]
[ROW][C]75[/C][C]103.2[/C][C]106.073454458609[/C][C]-2.87345445860923[/C][/ROW]
[ROW][C]76[/C][C]129.1[/C][C]105.958423675258[/C][C]23.1415763247418[/C][/ROW]
[ROW][C]77[/C][C]114.9[/C][C]106.884832529464[/C][C]8.01516747053614[/C][/ROW]
[ROW][C]78[/C][C]107.6[/C][C]107.205697539196[/C][C]0.394302460804411[/C][/ROW]
[ROW][C]79[/C][C]102.8[/C][C]107.221482345114[/C][C]-4.42148234511365[/C][/ROW]
[ROW][C]80[/C][C]99.1[/C][C]107.044480556828[/C][C]-7.94448055682803[/C][/ROW]
[ROW][C]81[/C][C]111.9[/C][C]106.726445301726[/C][C]5.17355469827436[/C][/ROW]
[ROW][C]82[/C][C]104.6[/C][C]106.933554221747[/C][C]-2.33355422174657[/C][/ROW]
[ROW][C]83[/C][C]103.7[/C][C]106.840136847646[/C][C]-3.14013684764643[/C][/ROW]
[ROW][C]84[/C][C]108.5[/C][C]106.714430174157[/C][C]1.78556982584266[/C][/ROW]
[ROW][C]85[/C][C]110.1[/C][C]106.785910512111[/C][C]3.31408948788942[/C][/ROW]
[ROW][C]86[/C][C]107.5[/C][C]106.918580897314[/C][C]0.581419102686326[/C][/ROW]
[ROW][C]87[/C][C]106.8[/C][C]106.941856399258[/C][C]-0.141856399257634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Observed	Fitted	Residuals
2	95.2	103.1	-7.89999999999999
3	110.2	102.78374540068	7.41625459932045
4	105.3	103.080634593941	2.21936540605887
5	107.4	103.169480735364	4.23051926463624
6	108.1	103.338837846118	4.76116215388244
7	108	103.529437773874	4.47056222612602
8	98.8	103.708404339135	-4.90840433913482
9	104.2	103.511909978682	0.688090021317819
10	107.8	103.539455755136	4.26054424486361
11	103.5	103.710014832737	-0.210014832737187
12	129.6	103.70160747112	25.8983925288804
13	100.1	104.738377819508	-4.63837781950757
14	96	104.55269322219	-8.55269322219044
15	111.4	104.210309859141	7.1896901408595
16	108.3	104.498129172398	3.8018708276018
17	103.6	104.650326531291	-1.05032653129076
18	106.8	104.608279620366	2.19172037963443
19	102.5	104.696019069794	-2.19601906979389
20	101	104.608107534222	-3.60810753422203
21	105.5	104.463666951622	1.03633304837803
22	105.1	104.505153672252	0.594846327747987
23	103.9	104.528966695928	-0.628966695927843
24	126.4	104.503787757902	21.8962122420983
25	101	105.380341913504	-4.38034191350424
26	99.3	105.204987068347	-5.90498706834704
27	113.5	104.968597281095	8.53140271890517
28	99.1	105.310128337868	-6.2101283378681
29	108.2	105.061523065815	3.13847693418521
30	109.2	105.18716328927	4.01283671072987
31	100.1	105.347806082446	-5.2478060824461
32	105.5	105.137724714102	0.362275285897624
33	103	105.15222740086	-2.15222740086
34	105.8	105.066068943353	0.733931056647023
35	106.1	105.095449838574	1.00455016142567
36	122.2	105.135664219435	17.064335780565
37	101.9	105.818787596011	-3.91878759601117
38	94.5	105.661909798416	-11.1619097984164
39	112.1	105.215073683106	6.88492631689357
40	97.6	105.490692621549	-7.89069262154946
41	110	105.174810617323	4.82518938267698
42	104.6	105.367973697686	-0.76797369768552
43	102.1	105.337229999704	-3.23722999970448
44	106	105.207636471038	0.792363528961943
45	98.5	105.2393565483	-6.73935654829982
46	106.2	104.969565091988	1.2304349080116
47	106	105.018822142472	0.981177857527669
48	120.9	105.05810087794	15.84189912206
49	105.1	105.692287391778	-0.5922873917782
50	102.4	105.66857680801	-3.26857680800991
51	94.2	105.537728396774	-11.3377283967738
52	105.6	105.08385387129	0.516146128710446
53	102.9	105.104516350673	-2.20451635067261
54	111.4	105.016264650017	6.38373534998274
55	105.4	105.271819797521	0.128180202479385
56	104.6	105.276951136581	-0.676951136580868
57	103.6	105.249851274497	-1.64985127449746
58	102.1	105.183804052503	-3.08380405250323
59	109.3	105.0603525063	4.23964749370022
60	103.9	105.230075040399	-1.33007504039853
61	125.3	105.176829173441	20.1231708265594
62	105.9	105.982404531265	-0.0824045312647144
63	106.2	105.979105694301	0.220894305699503
64	96.2	105.987948585458	-9.78794858545761
65	105.5	105.596115198361	-0.0961151983610335
66	104.7	105.592267492849	-0.892267492848831
67	111	105.55654803735	5.44345196264959
68	109.2	105.774461546131	3.42553845386885
69	108.3	105.911593481724	2.38840651827581
70	106.7	106.007206715452	0.692793284547761
71	103.6	106.034940774011	-2.43494077401131
72	103.9	105.937464670359	-2.0374646703589
73	104.7	105.855900420618	-1.1559004206179
74	112.4	105.809627151709	6.59037284829057
75	103.2	106.073454458609	-2.87345445860923
76	129.1	105.958423675258	23.1415763247418
77	114.9	106.884832529464	8.01516747053614
78	107.6	107.205697539196	0.394302460804411
79	102.8	107.221482345114	-4.42148234511365
80	99.1	107.044480556828	-7.94448055682803
81	111.9	106.726445301726	5.17355469827436
82	104.6	106.933554221747	-2.33355422174657
83	103.7	106.840136847646	-3.14013684764643
84	108.5	106.714430174157	1.78556982584266
85	110.1	106.785910512111	3.31408948788942
86	107.5	106.918580897314	0.581419102686326
87	106.8	106.941856399258	-0.141856399257634

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
88	106.936177571573	93.2830591484555	120.589295994691
89	106.936177571573	93.2721234258353	120.600231717311
90	106.936177571573	93.2611964483819	120.611158694764
91	106.936177571573	93.2502781951485	120.622076947998
92	106.936177571573	93.239368645272	120.632986497874
93	106.936177571573	93.2284677779722	120.643887365174
94	106.936177571573	93.2175755725513	120.654779570595
95	106.936177571573	93.2066920083939	120.665663134752
96	106.936177571573	93.195817064966	120.67653807818
97	106.936177571573	93.1849507218149	120.687404421331
98	106.936177571573	93.1740929585687	120.698262184577
99	106.936177571573	93.1632437549357	120.70911138821

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
88 & 106.936177571573 & 93.2830591484555 & 120.589295994691 \tabularnewline
89 & 106.936177571573 & 93.2721234258353 & 120.600231717311 \tabularnewline
90 & 106.936177571573 & 93.2611964483819 & 120.611158694764 \tabularnewline
91 & 106.936177571573 & 93.2502781951485 & 120.622076947998 \tabularnewline
92 & 106.936177571573 & 93.239368645272 & 120.632986497874 \tabularnewline
93 & 106.936177571573 & 93.2284677779722 & 120.643887365174 \tabularnewline
94 & 106.936177571573 & 93.2175755725513 & 120.654779570595 \tabularnewline
95 & 106.936177571573 & 93.2066920083939 & 120.665663134752 \tabularnewline
96 & 106.936177571573 & 93.195817064966 & 120.67653807818 \tabularnewline
97 & 106.936177571573 & 93.1849507218149 & 120.687404421331 \tabularnewline
98 & 106.936177571573 & 93.1740929585687 & 120.698262184577 \tabularnewline
99 & 106.936177571573 & 93.1632437549357 & 120.70911138821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]88[/C][C]106.936177571573[/C][C]93.2830591484555[/C][C]120.589295994691[/C][/ROW]
[ROW][C]89[/C][C]106.936177571573[/C][C]93.2721234258353[/C][C]120.600231717311[/C][/ROW]
[ROW][C]90[/C][C]106.936177571573[/C][C]93.2611964483819[/C][C]120.611158694764[/C][/ROW]
[ROW][C]91[/C][C]106.936177571573[/C][C]93.2502781951485[/C][C]120.622076947998[/C][/ROW]
[ROW][C]92[/C][C]106.936177571573[/C][C]93.239368645272[/C][C]120.632986497874[/C][/ROW]
[ROW][C]93[/C][C]106.936177571573[/C][C]93.2284677779722[/C][C]120.643887365174[/C][/ROW]
[ROW][C]94[/C][C]106.936177571573[/C][C]93.2175755725513[/C][C]120.654779570595[/C][/ROW]
[ROW][C]95[/C][C]106.936177571573[/C][C]93.2066920083939[/C][C]120.665663134752[/C][/ROW]
[ROW][C]96[/C][C]106.936177571573[/C][C]93.195817064966[/C][C]120.67653807818[/C][/ROW]
[ROW][C]97[/C][C]106.936177571573[/C][C]93.1849507218149[/C][C]120.687404421331[/C][/ROW]
[ROW][C]98[/C][C]106.936177571573[/C][C]93.1740929585687[/C][C]120.698262184577[/C][/ROW]
[ROW][C]99[/C][C]106.936177571573[/C][C]93.1632437549357[/C][C]120.70911138821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Forecast	95% Lower Bound	95% Upper Bound
88	106.936177571573	93.2830591484555	120.589295994691
89	106.936177571573	93.2721234258353	120.600231717311
90	106.936177571573	93.2611964483819	120.611158694764
91	106.936177571573	93.2502781951485	120.622076947998
92	106.936177571573	93.239368645272	120.632986497874
93	106.936177571573	93.2284677779722	120.643887365174
94	106.936177571573	93.2175755725513	120.654779570595
95	106.936177571573	93.2066920083939	120.665663134752
96	106.936177571573	93.195817064966	120.67653807818
97	106.936177571573	93.1849507218149	120.687404421331
98	106.936177571573	93.1740929585687	120.698262184577
99	106.936177571573	93.1632437549357	120.70911138821

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code