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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 26 Nov 2015 16:33:05 +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/26/t1448555600x80j5k3k4c2yv2q.htm/, Retrieved Tue, 14 May 2024 10:09:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284256, Retrieved Tue, 14 May 2024 10:09:53 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-11-26 16:33:05] [51347023fbb3308e181ecc8c43b3ca65] [Current]

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Dataseries X:

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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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284256&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284256&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284256&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284256&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	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	260.85	252.43	8.42000000000004
4	265.47	261.71	3.75999999999999
5	262.37	266.33	-3.96000000000004
6	272.39	263.23	9.15999999999997
7	277.49	273.25	4.24000000000001
8	274.41	278.35	-3.94
9	274.42	275.27	-0.849999999999966
10	267.1	275.28	-8.17999999999995
11	258.84	267.96	-9.12000000000006
12	253.97	259.7	-5.72999999999993
13	253.88	254.83	-0.949999999999989
14	253.3	254.74	-1.43999999999997
15	249.86	254.16	-4.29999999999998
16	246	250.72	-4.72
17	248.42	246.86	1.56
18	250.29	249.28	1.01000000000002
19	246.9	251.15	-4.24999999999997
20	255.2	247.76	7.44
21	253.33	256.06	-2.72999999999993
22	251.02	254.19	-3.16999999999999
23	254.5	251.88	2.62
24	253.18	255.36	-2.17999999999998
25	256.03	254.04	1.98999999999998
26	262.15	256.89	5.25999999999999
27	259.94	263.01	-3.06999999999999
28	253.75	260.8	-7.04999999999995
29	247.69	254.61	-6.91999999999999
30	242.42	248.55	-6.13
31	231.82	243.28	-11.46
32	235.88	232.68	3.20000000000002
33	240.68	236.74	3.94000000000003
34	260.15	241.54	18.61
35	265.32	261.01	4.31
36	265.02	266.18	-1.15999999999997
37	279.86	265.88	13.98
38	298.3	280.72	17.58
39	304.14	299.16	4.98000000000002
40	295.26	305	-9.74000000000001
41	281.93	296.12	-14.19
42	280.46	282.79	-2.32999999999998
43	272.06	281.32	-9.25999999999993
44	270.05	272.92	-2.86999999999995
45	271.84	270.91	0.930000000000007
46	268.49	272.7	-4.20999999999992
47	270.92	269.35	1.56999999999999
48	273.22	271.78	1.44000000000005
49	269.43	274.08	-4.65000000000003
50	271.21	270.29	0.920000000000016
51	265.4	272.07	-6.66999999999996
52	265.53	266.26	-0.730000000000018
53	276.78	266.39	10.39
54	281.49	277.64	3.85000000000002
55	283.75	282.35	1.39999999999998
56	281.45	284.61	-3.16000000000003
57	282.1	282.31	-0.209999999999923
58	274.01	282.96	-8.95000000000005
59	275.51	274.87	0.639999999999986
60	277.62	276.37	1.25
61	275.33	278.48	-3.15000000000003
62	271.15	276.19	-5.03999999999996
63	270.89	272.01	-1.12
64	265.29	271.75	-6.45999999999998
65	266.96	266.15	0.810000000000002
66	266.87	267.82	-0.949999999999932
67	267.68	267.73	-0.0500000000000114
68	272.37	268.54	3.83000000000004
69	285.05	273.23	11.82
70	296.79	285.91	10.8800000000001
71	309.15	297.65	11.5
72	304.19	310.01	-5.81999999999999
73	307.33	305.05	2.28000000000003
74	290.68	308.19	-17.5099999999999
75	292.26	291.54	0.720000000000027
76	294.81	293.12	1.69
77	293.67	295.67	-1.99999999999994
78	293.57	294.53	-0.95999999999998
79	286.28	294.43	-8.14999999999998
80	278.93	287.14	-8.20999999999998
81	284.22	279.79	4.43000000000006
82	282.09	285.08	-2.99000000000007
83	282.26	282.95	-0.689999999999941
84	285.79	283.12	2.67000000000002
85	294.01	286.65	7.36000000000001
86	292.73	294.87	-2.13999999999999
87	303.01	293.59	9.41999999999996
88	298.67	303.87	-5.19999999999999
89	292.38	299.53	-7.14999999999998
90	295.7	293.24	2.45999999999998
91	294.9	296.56	-1.65999999999997
92	299.46	295.76	3.69999999999999
93	299.75	300.32	-0.569999999999936
94	294.76	300.61	-5.85000000000002
95	297.68	295.62	2.06
96	300.24	298.54	1.70000000000005
97	302.48	301.1	1.38
98	310.2	303.34	6.85999999999996
99	311.49	311.06	0.430000000000064
100	307.37	312.35	-4.98000000000002
101	304.58	308.23	-3.65000000000003
102	305.87	305.44	0.430000000000064
103	309.81	306.73	3.07999999999998
104	313.91	310.67	3.24000000000007
105	313.2	314.77	-1.56999999999999
106	307.85	314.06	-6.20999999999992
107	306.89	308.71	-1.82000000000005
108	310.83	307.75	3.07999999999998

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 260.85 & 252.43 & 8.42000000000004 \tabularnewline
4 & 265.47 & 261.71 & 3.75999999999999 \tabularnewline
5 & 262.37 & 266.33 & -3.96000000000004 \tabularnewline
6 & 272.39 & 263.23 & 9.15999999999997 \tabularnewline
7 & 277.49 & 273.25 & 4.24000000000001 \tabularnewline
8 & 274.41 & 278.35 & -3.94 \tabularnewline
9 & 274.42 & 275.27 & -0.849999999999966 \tabularnewline
10 & 267.1 & 275.28 & -8.17999999999995 \tabularnewline
11 & 258.84 & 267.96 & -9.12000000000006 \tabularnewline
12 & 253.97 & 259.7 & -5.72999999999993 \tabularnewline
13 & 253.88 & 254.83 & -0.949999999999989 \tabularnewline
14 & 253.3 & 254.74 & -1.43999999999997 \tabularnewline
15 & 249.86 & 254.16 & -4.29999999999998 \tabularnewline
16 & 246 & 250.72 & -4.72 \tabularnewline
17 & 248.42 & 246.86 & 1.56 \tabularnewline
18 & 250.29 & 249.28 & 1.01000000000002 \tabularnewline
19 & 246.9 & 251.15 & -4.24999999999997 \tabularnewline
20 & 255.2 & 247.76 & 7.44 \tabularnewline
21 & 253.33 & 256.06 & -2.72999999999993 \tabularnewline
22 & 251.02 & 254.19 & -3.16999999999999 \tabularnewline
23 & 254.5 & 251.88 & 2.62 \tabularnewline
24 & 253.18 & 255.36 & -2.17999999999998 \tabularnewline
25 & 256.03 & 254.04 & 1.98999999999998 \tabularnewline
26 & 262.15 & 256.89 & 5.25999999999999 \tabularnewline
27 & 259.94 & 263.01 & -3.06999999999999 \tabularnewline
28 & 253.75 & 260.8 & -7.04999999999995 \tabularnewline
29 & 247.69 & 254.61 & -6.91999999999999 \tabularnewline
30 & 242.42 & 248.55 & -6.13 \tabularnewline
31 & 231.82 & 243.28 & -11.46 \tabularnewline
32 & 235.88 & 232.68 & 3.20000000000002 \tabularnewline
33 & 240.68 & 236.74 & 3.94000000000003 \tabularnewline
34 & 260.15 & 241.54 & 18.61 \tabularnewline
35 & 265.32 & 261.01 & 4.31 \tabularnewline
36 & 265.02 & 266.18 & -1.15999999999997 \tabularnewline
37 & 279.86 & 265.88 & 13.98 \tabularnewline
38 & 298.3 & 280.72 & 17.58 \tabularnewline
39 & 304.14 & 299.16 & 4.98000000000002 \tabularnewline
40 & 295.26 & 305 & -9.74000000000001 \tabularnewline
41 & 281.93 & 296.12 & -14.19 \tabularnewline
42 & 280.46 & 282.79 & -2.32999999999998 \tabularnewline
43 & 272.06 & 281.32 & -9.25999999999993 \tabularnewline
44 & 270.05 & 272.92 & -2.86999999999995 \tabularnewline
45 & 271.84 & 270.91 & 0.930000000000007 \tabularnewline
46 & 268.49 & 272.7 & -4.20999999999992 \tabularnewline
47 & 270.92 & 269.35 & 1.56999999999999 \tabularnewline
48 & 273.22 & 271.78 & 1.44000000000005 \tabularnewline
49 & 269.43 & 274.08 & -4.65000000000003 \tabularnewline
50 & 271.21 & 270.29 & 0.920000000000016 \tabularnewline
51 & 265.4 & 272.07 & -6.66999999999996 \tabularnewline
52 & 265.53 & 266.26 & -0.730000000000018 \tabularnewline
53 & 276.78 & 266.39 & 10.39 \tabularnewline
54 & 281.49 & 277.64 & 3.85000000000002 \tabularnewline
55 & 283.75 & 282.35 & 1.39999999999998 \tabularnewline
56 & 281.45 & 284.61 & -3.16000000000003 \tabularnewline
57 & 282.1 & 282.31 & -0.209999999999923 \tabularnewline
58 & 274.01 & 282.96 & -8.95000000000005 \tabularnewline
59 & 275.51 & 274.87 & 0.639999999999986 \tabularnewline
60 & 277.62 & 276.37 & 1.25 \tabularnewline
61 & 275.33 & 278.48 & -3.15000000000003 \tabularnewline
62 & 271.15 & 276.19 & -5.03999999999996 \tabularnewline
63 & 270.89 & 272.01 & -1.12 \tabularnewline
64 & 265.29 & 271.75 & -6.45999999999998 \tabularnewline
65 & 266.96 & 266.15 & 0.810000000000002 \tabularnewline
66 & 266.87 & 267.82 & -0.949999999999932 \tabularnewline
67 & 267.68 & 267.73 & -0.0500000000000114 \tabularnewline
68 & 272.37 & 268.54 & 3.83000000000004 \tabularnewline
69 & 285.05 & 273.23 & 11.82 \tabularnewline
70 & 296.79 & 285.91 & 10.8800000000001 \tabularnewline
71 & 309.15 & 297.65 & 11.5 \tabularnewline
72 & 304.19 & 310.01 & -5.81999999999999 \tabularnewline
73 & 307.33 & 305.05 & 2.28000000000003 \tabularnewline
74 & 290.68 & 308.19 & -17.5099999999999 \tabularnewline
75 & 292.26 & 291.54 & 0.720000000000027 \tabularnewline
76 & 294.81 & 293.12 & 1.69 \tabularnewline
77 & 293.67 & 295.67 & -1.99999999999994 \tabularnewline
78 & 293.57 & 294.53 & -0.95999999999998 \tabularnewline
79 & 286.28 & 294.43 & -8.14999999999998 \tabularnewline
80 & 278.93 & 287.14 & -8.20999999999998 \tabularnewline
81 & 284.22 & 279.79 & 4.43000000000006 \tabularnewline
82 & 282.09 & 285.08 & -2.99000000000007 \tabularnewline
83 & 282.26 & 282.95 & -0.689999999999941 \tabularnewline
84 & 285.79 & 283.12 & 2.67000000000002 \tabularnewline
85 & 294.01 & 286.65 & 7.36000000000001 \tabularnewline
86 & 292.73 & 294.87 & -2.13999999999999 \tabularnewline
87 & 303.01 & 293.59 & 9.41999999999996 \tabularnewline
88 & 298.67 & 303.87 & -5.19999999999999 \tabularnewline
89 & 292.38 & 299.53 & -7.14999999999998 \tabularnewline
90 & 295.7 & 293.24 & 2.45999999999998 \tabularnewline
91 & 294.9 & 296.56 & -1.65999999999997 \tabularnewline
92 & 299.46 & 295.76 & 3.69999999999999 \tabularnewline
93 & 299.75 & 300.32 & -0.569999999999936 \tabularnewline
94 & 294.76 & 300.61 & -5.85000000000002 \tabularnewline
95 & 297.68 & 295.62 & 2.06 \tabularnewline
96 & 300.24 & 298.54 & 1.70000000000005 \tabularnewline
97 & 302.48 & 301.1 & 1.38 \tabularnewline
98 & 310.2 & 303.34 & 6.85999999999996 \tabularnewline
99 & 311.49 & 311.06 & 0.430000000000064 \tabularnewline
100 & 307.37 & 312.35 & -4.98000000000002 \tabularnewline
101 & 304.58 & 308.23 & -3.65000000000003 \tabularnewline
102 & 305.87 & 305.44 & 0.430000000000064 \tabularnewline
103 & 309.81 & 306.73 & 3.07999999999998 \tabularnewline
104 & 313.91 & 310.67 & 3.24000000000007 \tabularnewline
105 & 313.2 & 314.77 & -1.56999999999999 \tabularnewline
106 & 307.85 & 314.06 & -6.20999999999992 \tabularnewline
107 & 306.89 & 308.71 & -1.82000000000005 \tabularnewline
108 & 310.83 & 307.75 & 3.07999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284256&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]3[/C][C]260.85[/C][C]252.43[/C][C]8.42000000000004[/C][/ROW]
[ROW][C]4[/C][C]265.47[/C][C]261.71[/C][C]3.75999999999999[/C][/ROW]
[ROW][C]5[/C][C]262.37[/C][C]266.33[/C][C]-3.96000000000004[/C][/ROW]
[ROW][C]6[/C][C]272.39[/C][C]263.23[/C][C]9.15999999999997[/C][/ROW]
[ROW][C]7[/C][C]277.49[/C][C]273.25[/C][C]4.24000000000001[/C][/ROW]
[ROW][C]8[/C][C]274.41[/C][C]278.35[/C][C]-3.94[/C][/ROW]
[ROW][C]9[/C][C]274.42[/C][C]275.27[/C][C]-0.849999999999966[/C][/ROW]
[ROW][C]10[/C][C]267.1[/C][C]275.28[/C][C]-8.17999999999995[/C][/ROW]
[ROW][C]11[/C][C]258.84[/C][C]267.96[/C][C]-9.12000000000006[/C][/ROW]
[ROW][C]12[/C][C]253.97[/C][C]259.7[/C][C]-5.72999999999993[/C][/ROW]
[ROW][C]13[/C][C]253.88[/C][C]254.83[/C][C]-0.949999999999989[/C][/ROW]
[ROW][C]14[/C][C]253.3[/C][C]254.74[/C][C]-1.43999999999997[/C][/ROW]
[ROW][C]15[/C][C]249.86[/C][C]254.16[/C][C]-4.29999999999998[/C][/ROW]
[ROW][C]16[/C][C]246[/C][C]250.72[/C][C]-4.72[/C][/ROW]
[ROW][C]17[/C][C]248.42[/C][C]246.86[/C][C]1.56[/C][/ROW]
[ROW][C]18[/C][C]250.29[/C][C]249.28[/C][C]1.01000000000002[/C][/ROW]
[ROW][C]19[/C][C]246.9[/C][C]251.15[/C][C]-4.24999999999997[/C][/ROW]
[ROW][C]20[/C][C]255.2[/C][C]247.76[/C][C]7.44[/C][/ROW]
[ROW][C]21[/C][C]253.33[/C][C]256.06[/C][C]-2.72999999999993[/C][/ROW]
[ROW][C]22[/C][C]251.02[/C][C]254.19[/C][C]-3.16999999999999[/C][/ROW]
[ROW][C]23[/C][C]254.5[/C][C]251.88[/C][C]2.62[/C][/ROW]
[ROW][C]24[/C][C]253.18[/C][C]255.36[/C][C]-2.17999999999998[/C][/ROW]
[ROW][C]25[/C][C]256.03[/C][C]254.04[/C][C]1.98999999999998[/C][/ROW]
[ROW][C]26[/C][C]262.15[/C][C]256.89[/C][C]5.25999999999999[/C][/ROW]
[ROW][C]27[/C][C]259.94[/C][C]263.01[/C][C]-3.06999999999999[/C][/ROW]
[ROW][C]28[/C][C]253.75[/C][C]260.8[/C][C]-7.04999999999995[/C][/ROW]
[ROW][C]29[/C][C]247.69[/C][C]254.61[/C][C]-6.91999999999999[/C][/ROW]
[ROW][C]30[/C][C]242.42[/C][C]248.55[/C][C]-6.13[/C][/ROW]
[ROW][C]31[/C][C]231.82[/C][C]243.28[/C][C]-11.46[/C][/ROW]
[ROW][C]32[/C][C]235.88[/C][C]232.68[/C][C]3.20000000000002[/C][/ROW]
[ROW][C]33[/C][C]240.68[/C][C]236.74[/C][C]3.94000000000003[/C][/ROW]
[ROW][C]34[/C][C]260.15[/C][C]241.54[/C][C]18.61[/C][/ROW]
[ROW][C]35[/C][C]265.32[/C][C]261.01[/C][C]4.31[/C][/ROW]
[ROW][C]36[/C][C]265.02[/C][C]266.18[/C][C]-1.15999999999997[/C][/ROW]
[ROW][C]37[/C][C]279.86[/C][C]265.88[/C][C]13.98[/C][/ROW]
[ROW][C]38[/C][C]298.3[/C][C]280.72[/C][C]17.58[/C][/ROW]
[ROW][C]39[/C][C]304.14[/C][C]299.16[/C][C]4.98000000000002[/C][/ROW]
[ROW][C]40[/C][C]295.26[/C][C]305[/C][C]-9.74000000000001[/C][/ROW]
[ROW][C]41[/C][C]281.93[/C][C]296.12[/C][C]-14.19[/C][/ROW]
[ROW][C]42[/C][C]280.46[/C][C]282.79[/C][C]-2.32999999999998[/C][/ROW]
[ROW][C]43[/C][C]272.06[/C][C]281.32[/C][C]-9.25999999999993[/C][/ROW]
[ROW][C]44[/C][C]270.05[/C][C]272.92[/C][C]-2.86999999999995[/C][/ROW]
[ROW][C]45[/C][C]271.84[/C][C]270.91[/C][C]0.930000000000007[/C][/ROW]
[ROW][C]46[/C][C]268.49[/C][C]272.7[/C][C]-4.20999999999992[/C][/ROW]
[ROW][C]47[/C][C]270.92[/C][C]269.35[/C][C]1.56999999999999[/C][/ROW]
[ROW][C]48[/C][C]273.22[/C][C]271.78[/C][C]1.44000000000005[/C][/ROW]
[ROW][C]49[/C][C]269.43[/C][C]274.08[/C][C]-4.65000000000003[/C][/ROW]
[ROW][C]50[/C][C]271.21[/C][C]270.29[/C][C]0.920000000000016[/C][/ROW]
[ROW][C]51[/C][C]265.4[/C][C]272.07[/C][C]-6.66999999999996[/C][/ROW]
[ROW][C]52[/C][C]265.53[/C][C]266.26[/C][C]-0.730000000000018[/C][/ROW]
[ROW][C]53[/C][C]276.78[/C][C]266.39[/C][C]10.39[/C][/ROW]
[ROW][C]54[/C][C]281.49[/C][C]277.64[/C][C]3.85000000000002[/C][/ROW]
[ROW][C]55[/C][C]283.75[/C][C]282.35[/C][C]1.39999999999998[/C][/ROW]
[ROW][C]56[/C][C]281.45[/C][C]284.61[/C][C]-3.16000000000003[/C][/ROW]
[ROW][C]57[/C][C]282.1[/C][C]282.31[/C][C]-0.209999999999923[/C][/ROW]
[ROW][C]58[/C][C]274.01[/C][C]282.96[/C][C]-8.95000000000005[/C][/ROW]
[ROW][C]59[/C][C]275.51[/C][C]274.87[/C][C]0.639999999999986[/C][/ROW]
[ROW][C]60[/C][C]277.62[/C][C]276.37[/C][C]1.25[/C][/ROW]
[ROW][C]61[/C][C]275.33[/C][C]278.48[/C][C]-3.15000000000003[/C][/ROW]
[ROW][C]62[/C][C]271.15[/C][C]276.19[/C][C]-5.03999999999996[/C][/ROW]
[ROW][C]63[/C][C]270.89[/C][C]272.01[/C][C]-1.12[/C][/ROW]
[ROW][C]64[/C][C]265.29[/C][C]271.75[/C][C]-6.45999999999998[/C][/ROW]
[ROW][C]65[/C][C]266.96[/C][C]266.15[/C][C]0.810000000000002[/C][/ROW]
[ROW][C]66[/C][C]266.87[/C][C]267.82[/C][C]-0.949999999999932[/C][/ROW]
[ROW][C]67[/C][C]267.68[/C][C]267.73[/C][C]-0.0500000000000114[/C][/ROW]
[ROW][C]68[/C][C]272.37[/C][C]268.54[/C][C]3.83000000000004[/C][/ROW]
[ROW][C]69[/C][C]285.05[/C][C]273.23[/C][C]11.82[/C][/ROW]
[ROW][C]70[/C][C]296.79[/C][C]285.91[/C][C]10.8800000000001[/C][/ROW]
[ROW][C]71[/C][C]309.15[/C][C]297.65[/C][C]11.5[/C][/ROW]
[ROW][C]72[/C][C]304.19[/C][C]310.01[/C][C]-5.81999999999999[/C][/ROW]
[ROW][C]73[/C][C]307.33[/C][C]305.05[/C][C]2.28000000000003[/C][/ROW]
[ROW][C]74[/C][C]290.68[/C][C]308.19[/C][C]-17.5099999999999[/C][/ROW]
[ROW][C]75[/C][C]292.26[/C][C]291.54[/C][C]0.720000000000027[/C][/ROW]
[ROW][C]76[/C][C]294.81[/C][C]293.12[/C][C]1.69[/C][/ROW]
[ROW][C]77[/C][C]293.67[/C][C]295.67[/C][C]-1.99999999999994[/C][/ROW]
[ROW][C]78[/C][C]293.57[/C][C]294.53[/C][C]-0.95999999999998[/C][/ROW]
[ROW][C]79[/C][C]286.28[/C][C]294.43[/C][C]-8.14999999999998[/C][/ROW]
[ROW][C]80[/C][C]278.93[/C][C]287.14[/C][C]-8.20999999999998[/C][/ROW]
[ROW][C]81[/C][C]284.22[/C][C]279.79[/C][C]4.43000000000006[/C][/ROW]
[ROW][C]82[/C][C]282.09[/C][C]285.08[/C][C]-2.99000000000007[/C][/ROW]
[ROW][C]83[/C][C]282.26[/C][C]282.95[/C][C]-0.689999999999941[/C][/ROW]
[ROW][C]84[/C][C]285.79[/C][C]283.12[/C][C]2.67000000000002[/C][/ROW]
[ROW][C]85[/C][C]294.01[/C][C]286.65[/C][C]7.36000000000001[/C][/ROW]
[ROW][C]86[/C][C]292.73[/C][C]294.87[/C][C]-2.13999999999999[/C][/ROW]
[ROW][C]87[/C][C]303.01[/C][C]293.59[/C][C]9.41999999999996[/C][/ROW]
[ROW][C]88[/C][C]298.67[/C][C]303.87[/C][C]-5.19999999999999[/C][/ROW]
[ROW][C]89[/C][C]292.38[/C][C]299.53[/C][C]-7.14999999999998[/C][/ROW]
[ROW][C]90[/C][C]295.7[/C][C]293.24[/C][C]2.45999999999998[/C][/ROW]
[ROW][C]91[/C][C]294.9[/C][C]296.56[/C][C]-1.65999999999997[/C][/ROW]
[ROW][C]92[/C][C]299.46[/C][C]295.76[/C][C]3.69999999999999[/C][/ROW]
[ROW][C]93[/C][C]299.75[/C][C]300.32[/C][C]-0.569999999999936[/C][/ROW]
[ROW][C]94[/C][C]294.76[/C][C]300.61[/C][C]-5.85000000000002[/C][/ROW]
[ROW][C]95[/C][C]297.68[/C][C]295.62[/C][C]2.06[/C][/ROW]
[ROW][C]96[/C][C]300.24[/C][C]298.54[/C][C]1.70000000000005[/C][/ROW]
[ROW][C]97[/C][C]302.48[/C][C]301.1[/C][C]1.38[/C][/ROW]
[ROW][C]98[/C][C]310.2[/C][C]303.34[/C][C]6.85999999999996[/C][/ROW]
[ROW][C]99[/C][C]311.49[/C][C]311.06[/C][C]0.430000000000064[/C][/ROW]
[ROW][C]100[/C][C]307.37[/C][C]312.35[/C][C]-4.98000000000002[/C][/ROW]
[ROW][C]101[/C][C]304.58[/C][C]308.23[/C][C]-3.65000000000003[/C][/ROW]
[ROW][C]102[/C][C]305.87[/C][C]305.44[/C][C]0.430000000000064[/C][/ROW]
[ROW][C]103[/C][C]309.81[/C][C]306.73[/C][C]3.07999999999998[/C][/ROW]
[ROW][C]104[/C][C]313.91[/C][C]310.67[/C][C]3.24000000000007[/C][/ROW]
[ROW][C]105[/C][C]313.2[/C][C]314.77[/C][C]-1.56999999999999[/C][/ROW]
[ROW][C]106[/C][C]307.85[/C][C]314.06[/C][C]-6.20999999999992[/C][/ROW]
[ROW][C]107[/C][C]306.89[/C][C]308.71[/C][C]-1.82000000000005[/C][/ROW]
[ROW][C]108[/C][C]310.83[/C][C]307.75[/C][C]3.07999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284256&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284256&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
3	260.85	252.43	8.42000000000004
4	265.47	261.71	3.75999999999999
5	262.37	266.33	-3.96000000000004
6	272.39	263.23	9.15999999999997
7	277.49	273.25	4.24000000000001
8	274.41	278.35	-3.94
9	274.42	275.27	-0.849999999999966
10	267.1	275.28	-8.17999999999995
11	258.84	267.96	-9.12000000000006
12	253.97	259.7	-5.72999999999993
13	253.88	254.83	-0.949999999999989
14	253.3	254.74	-1.43999999999997
15	249.86	254.16	-4.29999999999998
16	246	250.72	-4.72
17	248.42	246.86	1.56
18	250.29	249.28	1.01000000000002
19	246.9	251.15	-4.24999999999997
20	255.2	247.76	7.44
21	253.33	256.06	-2.72999999999993
22	251.02	254.19	-3.16999999999999
23	254.5	251.88	2.62
24	253.18	255.36	-2.17999999999998
25	256.03	254.04	1.98999999999998
26	262.15	256.89	5.25999999999999
27	259.94	263.01	-3.06999999999999
28	253.75	260.8	-7.04999999999995
29	247.69	254.61	-6.91999999999999
30	242.42	248.55	-6.13
31	231.82	243.28	-11.46
32	235.88	232.68	3.20000000000002
33	240.68	236.74	3.94000000000003
34	260.15	241.54	18.61
35	265.32	261.01	4.31
36	265.02	266.18	-1.15999999999997
37	279.86	265.88	13.98
38	298.3	280.72	17.58
39	304.14	299.16	4.98000000000002
40	295.26	305	-9.74000000000001
41	281.93	296.12	-14.19
42	280.46	282.79	-2.32999999999998
43	272.06	281.32	-9.25999999999993
44	270.05	272.92	-2.86999999999995
45	271.84	270.91	0.930000000000007
46	268.49	272.7	-4.20999999999992
47	270.92	269.35	1.56999999999999
48	273.22	271.78	1.44000000000005
49	269.43	274.08	-4.65000000000003
50	271.21	270.29	0.920000000000016
51	265.4	272.07	-6.66999999999996
52	265.53	266.26	-0.730000000000018
53	276.78	266.39	10.39
54	281.49	277.64	3.85000000000002
55	283.75	282.35	1.39999999999998
56	281.45	284.61	-3.16000000000003
57	282.1	282.31	-0.209999999999923
58	274.01	282.96	-8.95000000000005
59	275.51	274.87	0.639999999999986
60	277.62	276.37	1.25
61	275.33	278.48	-3.15000000000003
62	271.15	276.19	-5.03999999999996
63	270.89	272.01	-1.12
64	265.29	271.75	-6.45999999999998
65	266.96	266.15	0.810000000000002
66	266.87	267.82	-0.949999999999932
67	267.68	267.73	-0.0500000000000114
68	272.37	268.54	3.83000000000004
69	285.05	273.23	11.82
70	296.79	285.91	10.8800000000001
71	309.15	297.65	11.5
72	304.19	310.01	-5.81999999999999
73	307.33	305.05	2.28000000000003
74	290.68	308.19	-17.5099999999999
75	292.26	291.54	0.720000000000027
76	294.81	293.12	1.69
77	293.67	295.67	-1.99999999999994
78	293.57	294.53	-0.95999999999998
79	286.28	294.43	-8.14999999999998
80	278.93	287.14	-8.20999999999998
81	284.22	279.79	4.43000000000006
82	282.09	285.08	-2.99000000000007
83	282.26	282.95	-0.689999999999941
84	285.79	283.12	2.67000000000002
85	294.01	286.65	7.36000000000001
86	292.73	294.87	-2.13999999999999
87	303.01	293.59	9.41999999999996
88	298.67	303.87	-5.19999999999999
89	292.38	299.53	-7.14999999999998
90	295.7	293.24	2.45999999999998
91	294.9	296.56	-1.65999999999997
92	299.46	295.76	3.69999999999999
93	299.75	300.32	-0.569999999999936
94	294.76	300.61	-5.85000000000002
95	297.68	295.62	2.06
96	300.24	298.54	1.70000000000005
97	302.48	301.1	1.38
98	310.2	303.34	6.85999999999996
99	311.49	311.06	0.430000000000064
100	307.37	312.35	-4.98000000000002
101	304.58	308.23	-3.65000000000003
102	305.87	305.44	0.430000000000064
103	309.81	306.73	3.07999999999998
104	313.91	310.67	3.24000000000007
105	313.2	314.77	-1.56999999999999
106	307.85	314.06	-6.20999999999992
107	306.89	308.71	-1.82000000000005
108	310.83	307.75	3.07999999999998

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	311.69	299.693374252895	323.686625747105
110	312.55	295.58420916573	329.51579083427
111	313.41	292.631234686625	334.188765313375
112	314.27	290.27674850579	338.26325149421
113	315.13	288.304729328849	341.955270671151
114	315.99	286.604388284458	345.375611715542
115	316.85	285.109911701246	348.590088298754
116	317.71	283.77841833146	351.64158166854
117	318.57	282.580122758685	354.559877241315
118	319.43	281.493338402529	357.366661597471
119	320.29	280.501693646536	360.078306353464
120	321.15	279.59246937325	362.707530626749

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 311.69 & 299.693374252895 & 323.686625747105 \tabularnewline
110 & 312.55 & 295.58420916573 & 329.51579083427 \tabularnewline
111 & 313.41 & 292.631234686625 & 334.188765313375 \tabularnewline
112 & 314.27 & 290.27674850579 & 338.26325149421 \tabularnewline
113 & 315.13 & 288.304729328849 & 341.955270671151 \tabularnewline
114 & 315.99 & 286.604388284458 & 345.375611715542 \tabularnewline
115 & 316.85 & 285.109911701246 & 348.590088298754 \tabularnewline
116 & 317.71 & 283.77841833146 & 351.64158166854 \tabularnewline
117 & 318.57 & 282.580122758685 & 354.559877241315 \tabularnewline
118 & 319.43 & 281.493338402529 & 357.366661597471 \tabularnewline
119 & 320.29 & 280.501693646536 & 360.078306353464 \tabularnewline
120 & 321.15 & 279.59246937325 & 362.707530626749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284256&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]311.69[/C][C]299.693374252895[/C][C]323.686625747105[/C][/ROW]
[ROW][C]110[/C][C]312.55[/C][C]295.58420916573[/C][C]329.51579083427[/C][/ROW]
[ROW][C]111[/C][C]313.41[/C][C]292.631234686625[/C][C]334.188765313375[/C][/ROW]
[ROW][C]112[/C][C]314.27[/C][C]290.27674850579[/C][C]338.26325149421[/C][/ROW]
[ROW][C]113[/C][C]315.13[/C][C]288.304729328849[/C][C]341.955270671151[/C][/ROW]
[ROW][C]114[/C][C]315.99[/C][C]286.604388284458[/C][C]345.375611715542[/C][/ROW]
[ROW][C]115[/C][C]316.85[/C][C]285.109911701246[/C][C]348.590088298754[/C][/ROW]
[ROW][C]116[/C][C]317.71[/C][C]283.77841833146[/C][C]351.64158166854[/C][/ROW]
[ROW][C]117[/C][C]318.57[/C][C]282.580122758685[/C][C]354.559877241315[/C][/ROW]
[ROW][C]118[/C][C]319.43[/C][C]281.493338402529[/C][C]357.366661597471[/C][/ROW]
[ROW][C]119[/C][C]320.29[/C][C]280.501693646536[/C][C]360.078306353464[/C][/ROW]
[ROW][C]120[/C][C]321.15[/C][C]279.59246937325[/C][C]362.707530626749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284256&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284256&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	311.69	299.693374252895	323.686625747105
110	312.55	295.58420916573	329.51579083427
111	313.41	292.631234686625	334.188765313375
112	314.27	290.27674850579	338.26325149421
113	315.13	288.304729328849	341.955270671151
114	315.99	286.604388284458	345.375611715542
115	316.85	285.109911701246	348.590088298754
116	317.71	283.77841833146	351.64158166854
117	318.57	282.580122758685	354.559877241315
118	319.43	281.493338402529	357.366661597471
119	320.29	280.501693646536	360.078306353464
120	321.15	279.59246937325	362.707530626749

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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