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

Sun, 29 Nov 2015 17:14:07 +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/2015/Nov/29/t1448817292p4dcj5l8argi7y6.htm/, Retrieved Wed, 15 May 2024 12:19:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284499, Retrieved Wed, 15 May 2024 12:19:11 +0000

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

131

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2015-11-29 17:14:07] [bdd544630eb102d4e9b9d691f462dd0a] [Current]

Feedback Forum

Post a new message

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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284499&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284499&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284499&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999920456737714
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999920456737714 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284499&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]0.999920456737714[/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=284499&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284499&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	0.999920456737714
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	86.48	86.48	0
3	86.7	86.48	0.219999999999999
4	87.86	86.6999825004823	1.16001749951771
5	88.24	87.8599077284238	0.380092271576217
6	88.23	88.2399697662208	-0.00996976622074897
7	88.73	88.2300007930277	0.499999206972262
8	88.82	88.7299602284319	0.0900397715680583
9	87.16	88.8199928379428	-1.65999283794282
10	86.29	87.1601320412457	-0.870132041245697
11	86.37	86.2900692131412	0.0799307868588102
12	86.59	86.3699936420445	0.22000635795554
13	85.46	86.5899824999766	-1.12998249997656
14	85.85	85.4600898824944	0.389910117505622
15	86.93	85.8499689852773	1.08003101472275
16	87.66	86.9299140908097	0.730085909190265
17	87.84	87.659941926585	0.180058073414969
18	88.09	87.8399856775934	0.250014322406557
19	88.58	88.0899801130452	0.490019886954812
20	88.06	88.5799610222196	-0.519961022219604
21	88.26	88.060041359396	0.199958640604038
22	89	88.2599840946374	0.740015905362597
23	90.78	88.9999411367208	1.78005886327925
24	90	90.779858408311	-0.779858408310957
25	89.84	90.0000620324819	-0.160062032481918
26	89.82	89.8400127318562	-0.0200127318562409
27	91.12	89.820001591878	1.29999840812202
28	91.5	91.1198965938857	0.380103406114344
29	93.03	91.4999697653351	1.53003023466492
30	94.23	93.0298782964037	1.20012170359627
31	94.76	94.2299045384046	0.530095461595451
32	92.83	94.7599578344777	-1.92995783447768
33	92.49	92.8301535151422	-0.340153515142234
34	90.85	92.4900270569203	-1.64002705692027
35	88.19	90.8501304531023	-2.66013045310234
36	86.31	88.1902115954543	-1.88021159545434
37	85.74	86.3101495581641	-0.57014955816409
38	86.62	85.7400453515558	0.879954648444155
39	86.66	86.6199300055366	0.0400699944633942
40	87.39	86.6599968127019	0.730003187298081
41	87.59	87.389941933165	0.200058066834998
42	88.8	87.5899840867287	1.21001591327128
43	88.64	88.7999037513868	-0.159903751386835
44	89.55	88.640012719266	0.909987280733958
45	89.04	89.549927616643	-0.50992761664304
46	88.49	89.0400405613062	-0.550040561306176
47	89.5	88.4900437520206	1.00995624797937
48	89.46	89.4999196647853	-0.0399196647852733
49	90.33	89.4600031753403	0.869996824659651
50	90.27	90.3299307976144	-0.0599307976143848
51	91.5	90.2700047670912	1.22999523290885
52	92.53	91.4999021621666	1.03009783783342
53	93.14	92.5299180626575	0.610081937342486
54	93.01	93.1399514720924	-0.129951472092444
55	92.84	93.010010336764	-0.170010336764037
56	92.88	92.8400135231768	0.0399864768231737
57	93.05	92.8799968193452	0.170003180654803
58	93.17	93.0499864773924	0.120013522607593
59	93.67	93.1699904537329	0.500009546267108
60	94.9	93.6699602276095	1.2300397723905
61	95.72	94.8999021586238	0.820097841376239
62	96.08	95.7199347667423	0.3600652332577
63	97.52	96.0799713592367	1.44002864076329
64	98.26	97.5198854554241	0.740114544575889
65	98.48	98.2599411288747	0.220058871125332
66	98.09	98.4799824957995	-0.389982495799487
67	98.03	98.09003102048	-0.0600310204799541
68	98.14	98.0300047750632	0.109995224936796
69	98.71	98.139991250621	0.570008749379014
70	98.69	98.7099546596445	-0.0199546596445401
71	98.72	98.6900015872587	0.0299984127412642
72	98.47	98.7199976138284	-0.249997613828384
73	99.49	98.4700198856258	1.01998011437423
74	99.84	99.4899188674542	0.350081132545768
75	100.9	99.8399721534047	1.06002784659535
76	101.31	100.899915681927	0.410084318073032
77	100.09	101.309967380556	-1.21996738055553
78	99.28	100.090097040185	-0.81009704018534
79	99.57	99.2800644377614	0.289935562238639
80	101.04	99.5699769375795	1.47002306242048
81	101.87	101.03988306957	0.830116930430009
82	101.39	101.869933969791	-0.47993396979129
83	100.3	101.390038175514	-1.09003817551366
84	99.95	100.300086705192	-0.350086705192481
85	99.87	99.9500278470386	-0.0800278470386075
86	100.51	99.870006365676	0.639993634323972
87	100.27	100.509949092818	-0.239949092818492
88	100.04	100.270019086334	-0.230019086333613
89	99.23	100.040018296469	-0.810018296468527
90	99.32	99.2300644314978	0.0899355685021845
91	99.95	99.3199928462315	0.630007153768517
92	100.23	99.9499498871757	0.280050112824284
93	101.02	100.2299777239	0.790022276099577
94	99.83	101.019937159051	-1.18993715905087
95	99.61	99.8300946514835	-0.220094651483535
96	100.12	99.6100175070466	0.509982492953412
97	99.83	100.119959434329	-0.289959434328807
98	100.03	99.8300230643193	0.199976935680667
99	100.07	100.029984093182	0.0400159068178425
100	100.46	100.069996817004	0.390003182995784
101	100.43	100.459968977875	-0.0299689778745034
102	100.68	100.43000238383	0.249997616169736
103	101.8	100.679980114374	1.12001988562594
104	101.21	101.799910909964	-0.589910909964473
105	100.63	101.210046923438	-0.580046923438232
106	100.55	100.630046138825	-0.0800461388245566
107	99.76	100.550006367131	-0.790006367130999
108	98.8	99.7600628396837	-0.960062839683687

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 86.48 & 86.48 & 0 \tabularnewline
3 & 86.7 & 86.48 & 0.219999999999999 \tabularnewline
4 & 87.86 & 86.6999825004823 & 1.16001749951771 \tabularnewline
5 & 88.24 & 87.8599077284238 & 0.380092271576217 \tabularnewline
6 & 88.23 & 88.2399697662208 & -0.00996976622074897 \tabularnewline
7 & 88.73 & 88.2300007930277 & 0.499999206972262 \tabularnewline
8 & 88.82 & 88.7299602284319 & 0.0900397715680583 \tabularnewline
9 & 87.16 & 88.8199928379428 & -1.65999283794282 \tabularnewline
10 & 86.29 & 87.1601320412457 & -0.870132041245697 \tabularnewline
11 & 86.37 & 86.2900692131412 & 0.0799307868588102 \tabularnewline
12 & 86.59 & 86.3699936420445 & 0.22000635795554 \tabularnewline
13 & 85.46 & 86.5899824999766 & -1.12998249997656 \tabularnewline
14 & 85.85 & 85.4600898824944 & 0.389910117505622 \tabularnewline
15 & 86.93 & 85.8499689852773 & 1.08003101472275 \tabularnewline
16 & 87.66 & 86.9299140908097 & 0.730085909190265 \tabularnewline
17 & 87.84 & 87.659941926585 & 0.180058073414969 \tabularnewline
18 & 88.09 & 87.8399856775934 & 0.250014322406557 \tabularnewline
19 & 88.58 & 88.0899801130452 & 0.490019886954812 \tabularnewline
20 & 88.06 & 88.5799610222196 & -0.519961022219604 \tabularnewline
21 & 88.26 & 88.060041359396 & 0.199958640604038 \tabularnewline
22 & 89 & 88.2599840946374 & 0.740015905362597 \tabularnewline
23 & 90.78 & 88.9999411367208 & 1.78005886327925 \tabularnewline
24 & 90 & 90.779858408311 & -0.779858408310957 \tabularnewline
25 & 89.84 & 90.0000620324819 & -0.160062032481918 \tabularnewline
26 & 89.82 & 89.8400127318562 & -0.0200127318562409 \tabularnewline
27 & 91.12 & 89.820001591878 & 1.29999840812202 \tabularnewline
28 & 91.5 & 91.1198965938857 & 0.380103406114344 \tabularnewline
29 & 93.03 & 91.4999697653351 & 1.53003023466492 \tabularnewline
30 & 94.23 & 93.0298782964037 & 1.20012170359627 \tabularnewline
31 & 94.76 & 94.2299045384046 & 0.530095461595451 \tabularnewline
32 & 92.83 & 94.7599578344777 & -1.92995783447768 \tabularnewline
33 & 92.49 & 92.8301535151422 & -0.340153515142234 \tabularnewline
34 & 90.85 & 92.4900270569203 & -1.64002705692027 \tabularnewline
35 & 88.19 & 90.8501304531023 & -2.66013045310234 \tabularnewline
36 & 86.31 & 88.1902115954543 & -1.88021159545434 \tabularnewline
37 & 85.74 & 86.3101495581641 & -0.57014955816409 \tabularnewline
38 & 86.62 & 85.7400453515558 & 0.879954648444155 \tabularnewline
39 & 86.66 & 86.6199300055366 & 0.0400699944633942 \tabularnewline
40 & 87.39 & 86.6599968127019 & 0.730003187298081 \tabularnewline
41 & 87.59 & 87.389941933165 & 0.200058066834998 \tabularnewline
42 & 88.8 & 87.5899840867287 & 1.21001591327128 \tabularnewline
43 & 88.64 & 88.7999037513868 & -0.159903751386835 \tabularnewline
44 & 89.55 & 88.640012719266 & 0.909987280733958 \tabularnewline
45 & 89.04 & 89.549927616643 & -0.50992761664304 \tabularnewline
46 & 88.49 & 89.0400405613062 & -0.550040561306176 \tabularnewline
47 & 89.5 & 88.4900437520206 & 1.00995624797937 \tabularnewline
48 & 89.46 & 89.4999196647853 & -0.0399196647852733 \tabularnewline
49 & 90.33 & 89.4600031753403 & 0.869996824659651 \tabularnewline
50 & 90.27 & 90.3299307976144 & -0.0599307976143848 \tabularnewline
51 & 91.5 & 90.2700047670912 & 1.22999523290885 \tabularnewline
52 & 92.53 & 91.4999021621666 & 1.03009783783342 \tabularnewline
53 & 93.14 & 92.5299180626575 & 0.610081937342486 \tabularnewline
54 & 93.01 & 93.1399514720924 & -0.129951472092444 \tabularnewline
55 & 92.84 & 93.010010336764 & -0.170010336764037 \tabularnewline
56 & 92.88 & 92.8400135231768 & 0.0399864768231737 \tabularnewline
57 & 93.05 & 92.8799968193452 & 0.170003180654803 \tabularnewline
58 & 93.17 & 93.0499864773924 & 0.120013522607593 \tabularnewline
59 & 93.67 & 93.1699904537329 & 0.500009546267108 \tabularnewline
60 & 94.9 & 93.6699602276095 & 1.2300397723905 \tabularnewline
61 & 95.72 & 94.8999021586238 & 0.820097841376239 \tabularnewline
62 & 96.08 & 95.7199347667423 & 0.3600652332577 \tabularnewline
63 & 97.52 & 96.0799713592367 & 1.44002864076329 \tabularnewline
64 & 98.26 & 97.5198854554241 & 0.740114544575889 \tabularnewline
65 & 98.48 & 98.2599411288747 & 0.220058871125332 \tabularnewline
66 & 98.09 & 98.4799824957995 & -0.389982495799487 \tabularnewline
67 & 98.03 & 98.09003102048 & -0.0600310204799541 \tabularnewline
68 & 98.14 & 98.0300047750632 & 0.109995224936796 \tabularnewline
69 & 98.71 & 98.139991250621 & 0.570008749379014 \tabularnewline
70 & 98.69 & 98.7099546596445 & -0.0199546596445401 \tabularnewline
71 & 98.72 & 98.6900015872587 & 0.0299984127412642 \tabularnewline
72 & 98.47 & 98.7199976138284 & -0.249997613828384 \tabularnewline
73 & 99.49 & 98.4700198856258 & 1.01998011437423 \tabularnewline
74 & 99.84 & 99.4899188674542 & 0.350081132545768 \tabularnewline
75 & 100.9 & 99.8399721534047 & 1.06002784659535 \tabularnewline
76 & 101.31 & 100.899915681927 & 0.410084318073032 \tabularnewline
77 & 100.09 & 101.309967380556 & -1.21996738055553 \tabularnewline
78 & 99.28 & 100.090097040185 & -0.81009704018534 \tabularnewline
79 & 99.57 & 99.2800644377614 & 0.289935562238639 \tabularnewline
80 & 101.04 & 99.5699769375795 & 1.47002306242048 \tabularnewline
81 & 101.87 & 101.03988306957 & 0.830116930430009 \tabularnewline
82 & 101.39 & 101.869933969791 & -0.47993396979129 \tabularnewline
83 & 100.3 & 101.390038175514 & -1.09003817551366 \tabularnewline
84 & 99.95 & 100.300086705192 & -0.350086705192481 \tabularnewline
85 & 99.87 & 99.9500278470386 & -0.0800278470386075 \tabularnewline
86 & 100.51 & 99.870006365676 & 0.639993634323972 \tabularnewline
87 & 100.27 & 100.509949092818 & -0.239949092818492 \tabularnewline
88 & 100.04 & 100.270019086334 & -0.230019086333613 \tabularnewline
89 & 99.23 & 100.040018296469 & -0.810018296468527 \tabularnewline
90 & 99.32 & 99.2300644314978 & 0.0899355685021845 \tabularnewline
91 & 99.95 & 99.3199928462315 & 0.630007153768517 \tabularnewline
92 & 100.23 & 99.9499498871757 & 0.280050112824284 \tabularnewline
93 & 101.02 & 100.2299777239 & 0.790022276099577 \tabularnewline
94 & 99.83 & 101.019937159051 & -1.18993715905087 \tabularnewline
95 & 99.61 & 99.8300946514835 & -0.220094651483535 \tabularnewline
96 & 100.12 & 99.6100175070466 & 0.509982492953412 \tabularnewline
97 & 99.83 & 100.119959434329 & -0.289959434328807 \tabularnewline
98 & 100.03 & 99.8300230643193 & 0.199976935680667 \tabularnewline
99 & 100.07 & 100.029984093182 & 0.0400159068178425 \tabularnewline
100 & 100.46 & 100.069996817004 & 0.390003182995784 \tabularnewline
101 & 100.43 & 100.459968977875 & -0.0299689778745034 \tabularnewline
102 & 100.68 & 100.43000238383 & 0.249997616169736 \tabularnewline
103 & 101.8 & 100.679980114374 & 1.12001988562594 \tabularnewline
104 & 101.21 & 101.799910909964 & -0.589910909964473 \tabularnewline
105 & 100.63 & 101.210046923438 & -0.580046923438232 \tabularnewline
106 & 100.55 & 100.630046138825 & -0.0800461388245566 \tabularnewline
107 & 99.76 & 100.550006367131 & -0.790006367130999 \tabularnewline
108 & 98.8 & 99.7600628396837 & -0.960062839683687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284499&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]86.48[/C][C]86.48[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]86.7[/C][C]86.48[/C][C]0.219999999999999[/C][/ROW]
[ROW][C]4[/C][C]87.86[/C][C]86.6999825004823[/C][C]1.16001749951771[/C][/ROW]
[ROW][C]5[/C][C]88.24[/C][C]87.8599077284238[/C][C]0.380092271576217[/C][/ROW]
[ROW][C]6[/C][C]88.23[/C][C]88.2399697662208[/C][C]-0.00996976622074897[/C][/ROW]
[ROW][C]7[/C][C]88.73[/C][C]88.2300007930277[/C][C]0.499999206972262[/C][/ROW]
[ROW][C]8[/C][C]88.82[/C][C]88.7299602284319[/C][C]0.0900397715680583[/C][/ROW]
[ROW][C]9[/C][C]87.16[/C][C]88.8199928379428[/C][C]-1.65999283794282[/C][/ROW]
[ROW][C]10[/C][C]86.29[/C][C]87.1601320412457[/C][C]-0.870132041245697[/C][/ROW]
[ROW][C]11[/C][C]86.37[/C][C]86.2900692131412[/C][C]0.0799307868588102[/C][/ROW]
[ROW][C]12[/C][C]86.59[/C][C]86.3699936420445[/C][C]0.22000635795554[/C][/ROW]
[ROW][C]13[/C][C]85.46[/C][C]86.5899824999766[/C][C]-1.12998249997656[/C][/ROW]
[ROW][C]14[/C][C]85.85[/C][C]85.4600898824944[/C][C]0.389910117505622[/C][/ROW]
[ROW][C]15[/C][C]86.93[/C][C]85.8499689852773[/C][C]1.08003101472275[/C][/ROW]
[ROW][C]16[/C][C]87.66[/C][C]86.9299140908097[/C][C]0.730085909190265[/C][/ROW]
[ROW][C]17[/C][C]87.84[/C][C]87.659941926585[/C][C]0.180058073414969[/C][/ROW]
[ROW][C]18[/C][C]88.09[/C][C]87.8399856775934[/C][C]0.250014322406557[/C][/ROW]
[ROW][C]19[/C][C]88.58[/C][C]88.0899801130452[/C][C]0.490019886954812[/C][/ROW]
[ROW][C]20[/C][C]88.06[/C][C]88.5799610222196[/C][C]-0.519961022219604[/C][/ROW]
[ROW][C]21[/C][C]88.26[/C][C]88.060041359396[/C][C]0.199958640604038[/C][/ROW]
[ROW][C]22[/C][C]89[/C][C]88.2599840946374[/C][C]0.740015905362597[/C][/ROW]
[ROW][C]23[/C][C]90.78[/C][C]88.9999411367208[/C][C]1.78005886327925[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]90.779858408311[/C][C]-0.779858408310957[/C][/ROW]
[ROW][C]25[/C][C]89.84[/C][C]90.0000620324819[/C][C]-0.160062032481918[/C][/ROW]
[ROW][C]26[/C][C]89.82[/C][C]89.8400127318562[/C][C]-0.0200127318562409[/C][/ROW]
[ROW][C]27[/C][C]91.12[/C][C]89.820001591878[/C][C]1.29999840812202[/C][/ROW]
[ROW][C]28[/C][C]91.5[/C][C]91.1198965938857[/C][C]0.380103406114344[/C][/ROW]
[ROW][C]29[/C][C]93.03[/C][C]91.4999697653351[/C][C]1.53003023466492[/C][/ROW]
[ROW][C]30[/C][C]94.23[/C][C]93.0298782964037[/C][C]1.20012170359627[/C][/ROW]
[ROW][C]31[/C][C]94.76[/C][C]94.2299045384046[/C][C]0.530095461595451[/C][/ROW]
[ROW][C]32[/C][C]92.83[/C][C]94.7599578344777[/C][C]-1.92995783447768[/C][/ROW]
[ROW][C]33[/C][C]92.49[/C][C]92.8301535151422[/C][C]-0.340153515142234[/C][/ROW]
[ROW][C]34[/C][C]90.85[/C][C]92.4900270569203[/C][C]-1.64002705692027[/C][/ROW]
[ROW][C]35[/C][C]88.19[/C][C]90.8501304531023[/C][C]-2.66013045310234[/C][/ROW]
[ROW][C]36[/C][C]86.31[/C][C]88.1902115954543[/C][C]-1.88021159545434[/C][/ROW]
[ROW][C]37[/C][C]85.74[/C][C]86.3101495581641[/C][C]-0.57014955816409[/C][/ROW]
[ROW][C]38[/C][C]86.62[/C][C]85.7400453515558[/C][C]0.879954648444155[/C][/ROW]
[ROW][C]39[/C][C]86.66[/C][C]86.6199300055366[/C][C]0.0400699944633942[/C][/ROW]
[ROW][C]40[/C][C]87.39[/C][C]86.6599968127019[/C][C]0.730003187298081[/C][/ROW]
[ROW][C]41[/C][C]87.59[/C][C]87.389941933165[/C][C]0.200058066834998[/C][/ROW]
[ROW][C]42[/C][C]88.8[/C][C]87.5899840867287[/C][C]1.21001591327128[/C][/ROW]
[ROW][C]43[/C][C]88.64[/C][C]88.7999037513868[/C][C]-0.159903751386835[/C][/ROW]
[ROW][C]44[/C][C]89.55[/C][C]88.640012719266[/C][C]0.909987280733958[/C][/ROW]
[ROW][C]45[/C][C]89.04[/C][C]89.549927616643[/C][C]-0.50992761664304[/C][/ROW]
[ROW][C]46[/C][C]88.49[/C][C]89.0400405613062[/C][C]-0.550040561306176[/C][/ROW]
[ROW][C]47[/C][C]89.5[/C][C]88.4900437520206[/C][C]1.00995624797937[/C][/ROW]
[ROW][C]48[/C][C]89.46[/C][C]89.4999196647853[/C][C]-0.0399196647852733[/C][/ROW]
[ROW][C]49[/C][C]90.33[/C][C]89.4600031753403[/C][C]0.869996824659651[/C][/ROW]
[ROW][C]50[/C][C]90.27[/C][C]90.3299307976144[/C][C]-0.0599307976143848[/C][/ROW]
[ROW][C]51[/C][C]91.5[/C][C]90.2700047670912[/C][C]1.22999523290885[/C][/ROW]
[ROW][C]52[/C][C]92.53[/C][C]91.4999021621666[/C][C]1.03009783783342[/C][/ROW]
[ROW][C]53[/C][C]93.14[/C][C]92.5299180626575[/C][C]0.610081937342486[/C][/ROW]
[ROW][C]54[/C][C]93.01[/C][C]93.1399514720924[/C][C]-0.129951472092444[/C][/ROW]
[ROW][C]55[/C][C]92.84[/C][C]93.010010336764[/C][C]-0.170010336764037[/C][/ROW]
[ROW][C]56[/C][C]92.88[/C][C]92.8400135231768[/C][C]0.0399864768231737[/C][/ROW]
[ROW][C]57[/C][C]93.05[/C][C]92.8799968193452[/C][C]0.170003180654803[/C][/ROW]
[ROW][C]58[/C][C]93.17[/C][C]93.0499864773924[/C][C]0.120013522607593[/C][/ROW]
[ROW][C]59[/C][C]93.67[/C][C]93.1699904537329[/C][C]0.500009546267108[/C][/ROW]
[ROW][C]60[/C][C]94.9[/C][C]93.6699602276095[/C][C]1.2300397723905[/C][/ROW]
[ROW][C]61[/C][C]95.72[/C][C]94.8999021586238[/C][C]0.820097841376239[/C][/ROW]
[ROW][C]62[/C][C]96.08[/C][C]95.7199347667423[/C][C]0.3600652332577[/C][/ROW]
[ROW][C]63[/C][C]97.52[/C][C]96.0799713592367[/C][C]1.44002864076329[/C][/ROW]
[ROW][C]64[/C][C]98.26[/C][C]97.5198854554241[/C][C]0.740114544575889[/C][/ROW]
[ROW][C]65[/C][C]98.48[/C][C]98.2599411288747[/C][C]0.220058871125332[/C][/ROW]
[ROW][C]66[/C][C]98.09[/C][C]98.4799824957995[/C][C]-0.389982495799487[/C][/ROW]
[ROW][C]67[/C][C]98.03[/C][C]98.09003102048[/C][C]-0.0600310204799541[/C][/ROW]
[ROW][C]68[/C][C]98.14[/C][C]98.0300047750632[/C][C]0.109995224936796[/C][/ROW]
[ROW][C]69[/C][C]98.71[/C][C]98.139991250621[/C][C]0.570008749379014[/C][/ROW]
[ROW][C]70[/C][C]98.69[/C][C]98.7099546596445[/C][C]-0.0199546596445401[/C][/ROW]
[ROW][C]71[/C][C]98.72[/C][C]98.6900015872587[/C][C]0.0299984127412642[/C][/ROW]
[ROW][C]72[/C][C]98.47[/C][C]98.7199976138284[/C][C]-0.249997613828384[/C][/ROW]
[ROW][C]73[/C][C]99.49[/C][C]98.4700198856258[/C][C]1.01998011437423[/C][/ROW]
[ROW][C]74[/C][C]99.84[/C][C]99.4899188674542[/C][C]0.350081132545768[/C][/ROW]
[ROW][C]75[/C][C]100.9[/C][C]99.8399721534047[/C][C]1.06002784659535[/C][/ROW]
[ROW][C]76[/C][C]101.31[/C][C]100.899915681927[/C][C]0.410084318073032[/C][/ROW]
[ROW][C]77[/C][C]100.09[/C][C]101.309967380556[/C][C]-1.21996738055553[/C][/ROW]
[ROW][C]78[/C][C]99.28[/C][C]100.090097040185[/C][C]-0.81009704018534[/C][/ROW]
[ROW][C]79[/C][C]99.57[/C][C]99.2800644377614[/C][C]0.289935562238639[/C][/ROW]
[ROW][C]80[/C][C]101.04[/C][C]99.5699769375795[/C][C]1.47002306242048[/C][/ROW]
[ROW][C]81[/C][C]101.87[/C][C]101.03988306957[/C][C]0.830116930430009[/C][/ROW]
[ROW][C]82[/C][C]101.39[/C][C]101.869933969791[/C][C]-0.47993396979129[/C][/ROW]
[ROW][C]83[/C][C]100.3[/C][C]101.390038175514[/C][C]-1.09003817551366[/C][/ROW]
[ROW][C]84[/C][C]99.95[/C][C]100.300086705192[/C][C]-0.350086705192481[/C][/ROW]
[ROW][C]85[/C][C]99.87[/C][C]99.9500278470386[/C][C]-0.0800278470386075[/C][/ROW]
[ROW][C]86[/C][C]100.51[/C][C]99.870006365676[/C][C]0.639993634323972[/C][/ROW]
[ROW][C]87[/C][C]100.27[/C][C]100.509949092818[/C][C]-0.239949092818492[/C][/ROW]
[ROW][C]88[/C][C]100.04[/C][C]100.270019086334[/C][C]-0.230019086333613[/C][/ROW]
[ROW][C]89[/C][C]99.23[/C][C]100.040018296469[/C][C]-0.810018296468527[/C][/ROW]
[ROW][C]90[/C][C]99.32[/C][C]99.2300644314978[/C][C]0.0899355685021845[/C][/ROW]
[ROW][C]91[/C][C]99.95[/C][C]99.3199928462315[/C][C]0.630007153768517[/C][/ROW]
[ROW][C]92[/C][C]100.23[/C][C]99.9499498871757[/C][C]0.280050112824284[/C][/ROW]
[ROW][C]93[/C][C]101.02[/C][C]100.2299777239[/C][C]0.790022276099577[/C][/ROW]
[ROW][C]94[/C][C]99.83[/C][C]101.019937159051[/C][C]-1.18993715905087[/C][/ROW]
[ROW][C]95[/C][C]99.61[/C][C]99.8300946514835[/C][C]-0.220094651483535[/C][/ROW]
[ROW][C]96[/C][C]100.12[/C][C]99.6100175070466[/C][C]0.509982492953412[/C][/ROW]
[ROW][C]97[/C][C]99.83[/C][C]100.119959434329[/C][C]-0.289959434328807[/C][/ROW]
[ROW][C]98[/C][C]100.03[/C][C]99.8300230643193[/C][C]0.199976935680667[/C][/ROW]
[ROW][C]99[/C][C]100.07[/C][C]100.029984093182[/C][C]0.0400159068178425[/C][/ROW]
[ROW][C]100[/C][C]100.46[/C][C]100.069996817004[/C][C]0.390003182995784[/C][/ROW]
[ROW][C]101[/C][C]100.43[/C][C]100.459968977875[/C][C]-0.0299689778745034[/C][/ROW]
[ROW][C]102[/C][C]100.68[/C][C]100.43000238383[/C][C]0.249997616169736[/C][/ROW]
[ROW][C]103[/C][C]101.8[/C][C]100.679980114374[/C][C]1.12001988562594[/C][/ROW]
[ROW][C]104[/C][C]101.21[/C][C]101.799910909964[/C][C]-0.589910909964473[/C][/ROW]
[ROW][C]105[/C][C]100.63[/C][C]101.210046923438[/C][C]-0.580046923438232[/C][/ROW]
[ROW][C]106[/C][C]100.55[/C][C]100.630046138825[/C][C]-0.0800461388245566[/C][/ROW]
[ROW][C]107[/C][C]99.76[/C][C]100.550006367131[/C][C]-0.790006367130999[/C][/ROW]
[ROW][C]108[/C][C]98.8[/C][C]99.7600628396837[/C][C]-0.960062839683687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284499&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284499&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	86.48	86.48	0
3	86.7	86.48	0.219999999999999
4	87.86	86.6999825004823	1.16001749951771
5	88.24	87.8599077284238	0.380092271576217
6	88.23	88.2399697662208	-0.00996976622074897
7	88.73	88.2300007930277	0.499999206972262
8	88.82	88.7299602284319	0.0900397715680583
9	87.16	88.8199928379428	-1.65999283794282
10	86.29	87.1601320412457	-0.870132041245697
11	86.37	86.2900692131412	0.0799307868588102
12	86.59	86.3699936420445	0.22000635795554
13	85.46	86.5899824999766	-1.12998249997656
14	85.85	85.4600898824944	0.389910117505622
15	86.93	85.8499689852773	1.08003101472275
16	87.66	86.9299140908097	0.730085909190265
17	87.84	87.659941926585	0.180058073414969
18	88.09	87.8399856775934	0.250014322406557
19	88.58	88.0899801130452	0.490019886954812
20	88.06	88.5799610222196	-0.519961022219604
21	88.26	88.060041359396	0.199958640604038
22	89	88.2599840946374	0.740015905362597
23	90.78	88.9999411367208	1.78005886327925
24	90	90.779858408311	-0.779858408310957
25	89.84	90.0000620324819	-0.160062032481918
26	89.82	89.8400127318562	-0.0200127318562409
27	91.12	89.820001591878	1.29999840812202
28	91.5	91.1198965938857	0.380103406114344
29	93.03	91.4999697653351	1.53003023466492
30	94.23	93.0298782964037	1.20012170359627
31	94.76	94.2299045384046	0.530095461595451
32	92.83	94.7599578344777	-1.92995783447768
33	92.49	92.8301535151422	-0.340153515142234
34	90.85	92.4900270569203	-1.64002705692027
35	88.19	90.8501304531023	-2.66013045310234
36	86.31	88.1902115954543	-1.88021159545434
37	85.74	86.3101495581641	-0.57014955816409
38	86.62	85.7400453515558	0.879954648444155
39	86.66	86.6199300055366	0.0400699944633942
40	87.39	86.6599968127019	0.730003187298081
41	87.59	87.389941933165	0.200058066834998
42	88.8	87.5899840867287	1.21001591327128
43	88.64	88.7999037513868	-0.159903751386835
44	89.55	88.640012719266	0.909987280733958
45	89.04	89.549927616643	-0.50992761664304
46	88.49	89.0400405613062	-0.550040561306176
47	89.5	88.4900437520206	1.00995624797937
48	89.46	89.4999196647853	-0.0399196647852733
49	90.33	89.4600031753403	0.869996824659651
50	90.27	90.3299307976144	-0.0599307976143848
51	91.5	90.2700047670912	1.22999523290885
52	92.53	91.4999021621666	1.03009783783342
53	93.14	92.5299180626575	0.610081937342486
54	93.01	93.1399514720924	-0.129951472092444
55	92.84	93.010010336764	-0.170010336764037
56	92.88	92.8400135231768	0.0399864768231737
57	93.05	92.8799968193452	0.170003180654803
58	93.17	93.0499864773924	0.120013522607593
59	93.67	93.1699904537329	0.500009546267108
60	94.9	93.6699602276095	1.2300397723905
61	95.72	94.8999021586238	0.820097841376239
62	96.08	95.7199347667423	0.3600652332577
63	97.52	96.0799713592367	1.44002864076329
64	98.26	97.5198854554241	0.740114544575889
65	98.48	98.2599411288747	0.220058871125332
66	98.09	98.4799824957995	-0.389982495799487
67	98.03	98.09003102048	-0.0600310204799541
68	98.14	98.0300047750632	0.109995224936796
69	98.71	98.139991250621	0.570008749379014
70	98.69	98.7099546596445	-0.0199546596445401
71	98.72	98.6900015872587	0.0299984127412642
72	98.47	98.7199976138284	-0.249997613828384
73	99.49	98.4700198856258	1.01998011437423
74	99.84	99.4899188674542	0.350081132545768
75	100.9	99.8399721534047	1.06002784659535
76	101.31	100.899915681927	0.410084318073032
77	100.09	101.309967380556	-1.21996738055553
78	99.28	100.090097040185	-0.81009704018534
79	99.57	99.2800644377614	0.289935562238639
80	101.04	99.5699769375795	1.47002306242048
81	101.87	101.03988306957	0.830116930430009
82	101.39	101.869933969791	-0.47993396979129
83	100.3	101.390038175514	-1.09003817551366
84	99.95	100.300086705192	-0.350086705192481
85	99.87	99.9500278470386	-0.0800278470386075
86	100.51	99.870006365676	0.639993634323972
87	100.27	100.509949092818	-0.239949092818492
88	100.04	100.270019086334	-0.230019086333613
89	99.23	100.040018296469	-0.810018296468527
90	99.32	99.2300644314978	0.0899355685021845
91	99.95	99.3199928462315	0.630007153768517
92	100.23	99.9499498871757	0.280050112824284
93	101.02	100.2299777239	0.790022276099577
94	99.83	101.019937159051	-1.18993715905087
95	99.61	99.8300946514835	-0.220094651483535
96	100.12	99.6100175070466	0.509982492953412
97	99.83	100.119959434329	-0.289959434328807
98	100.03	99.8300230643193	0.199976935680667
99	100.07	100.029984093182	0.0400159068178425
100	100.46	100.069996817004	0.390003182995784
101	100.43	100.459968977875	-0.0299689778745034
102	100.68	100.43000238383	0.249997616169736
103	101.8	100.679980114374	1.12001988562594
104	101.21	101.799910909964	-0.589910909964473
105	100.63	101.210046923438	-0.580046923438232
106	100.55	100.630046138825	-0.0800461388245566
107	99.76	100.550006367131	-0.790006367130999
108	98.8	99.7600628396837	-0.960062839683687

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	98.8000763665303	97.2395844492272	100.360568283833
110	98.8000763665303	96.5932953021344	101.006857430926
111	98.8000763665303	96.097368408133	101.502784324928
112	98.8000763665303	95.6792787199995	101.920874013061
113	98.8000763665303	95.3109324037796	102.289220329281
114	98.8000763665303	94.9779207921184	102.622231940942
115	98.8000763665303	94.6716843215307	102.92846841153
116	98.8000763665303	94.386645895862	103.213506837199
117	98.8000763665303	94.1189316174725	103.481221115588
118	98.8000763665303	93.865720906712	103.734431826349
119	98.8000763665303	93.6248844429349	103.975268290126
120	98.8000763665303	93.3947679490341	104.205384784026

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 98.8000763665303 & 97.2395844492272 & 100.360568283833 \tabularnewline
110 & 98.8000763665303 & 96.5932953021344 & 101.006857430926 \tabularnewline
111 & 98.8000763665303 & 96.097368408133 & 101.502784324928 \tabularnewline
112 & 98.8000763665303 & 95.6792787199995 & 101.920874013061 \tabularnewline
113 & 98.8000763665303 & 95.3109324037796 & 102.289220329281 \tabularnewline
114 & 98.8000763665303 & 94.9779207921184 & 102.622231940942 \tabularnewline
115 & 98.8000763665303 & 94.6716843215307 & 102.92846841153 \tabularnewline
116 & 98.8000763665303 & 94.386645895862 & 103.213506837199 \tabularnewline
117 & 98.8000763665303 & 94.1189316174725 & 103.481221115588 \tabularnewline
118 & 98.8000763665303 & 93.865720906712 & 103.734431826349 \tabularnewline
119 & 98.8000763665303 & 93.6248844429349 & 103.975268290126 \tabularnewline
120 & 98.8000763665303 & 93.3947679490341 & 104.205384784026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284499&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]109[/C][C]98.8000763665303[/C][C]97.2395844492272[/C][C]100.360568283833[/C][/ROW]
[ROW][C]110[/C][C]98.8000763665303[/C][C]96.5932953021344[/C][C]101.006857430926[/C][/ROW]
[ROW][C]111[/C][C]98.8000763665303[/C][C]96.097368408133[/C][C]101.502784324928[/C][/ROW]
[ROW][C]112[/C][C]98.8000763665303[/C][C]95.6792787199995[/C][C]101.920874013061[/C][/ROW]
[ROW][C]113[/C][C]98.8000763665303[/C][C]95.3109324037796[/C][C]102.289220329281[/C][/ROW]
[ROW][C]114[/C][C]98.8000763665303[/C][C]94.9779207921184[/C][C]102.622231940942[/C][/ROW]
[ROW][C]115[/C][C]98.8000763665303[/C][C]94.6716843215307[/C][C]102.92846841153[/C][/ROW]
[ROW][C]116[/C][C]98.8000763665303[/C][C]94.386645895862[/C][C]103.213506837199[/C][/ROW]
[ROW][C]117[/C][C]98.8000763665303[/C][C]94.1189316174725[/C][C]103.481221115588[/C][/ROW]
[ROW][C]118[/C][C]98.8000763665303[/C][C]93.865720906712[/C][C]103.734431826349[/C][/ROW]
[ROW][C]119[/C][C]98.8000763665303[/C][C]93.6248844429349[/C][C]103.975268290126[/C][/ROW]
[ROW][C]120[/C][C]98.8000763665303[/C][C]93.3947679490341[/C][C]104.205384784026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284499&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284499&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
109	98.8000763665303	97.2395844492272	100.360568283833
110	98.8000763665303	96.5932953021344	101.006857430926
111	98.8000763665303	96.097368408133	101.502784324928
112	98.8000763665303	95.6792787199995	101.920874013061
113	98.8000763665303	95.3109324037796	102.289220329281
114	98.8000763665303	94.9779207921184	102.622231940942
115	98.8000763665303	94.6716843215307	102.92846841153
116	98.8000763665303	94.386645895862	103.213506837199
117	98.8000763665303	94.1189316174725	103.481221115588
118	98.8000763665303	93.865720906712	103.734431826349
119	98.8000763665303	93.6248844429349	103.975268290126
120	98.8000763665303	93.3947679490341	104.205384784026

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=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