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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 20 Nov 2012 15:57:25 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/20/t13534451195oymf38k0jq9b9y.htm/, Retrieved Mon, 29 Apr 2024 21:33:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191291, Retrieved Mon, 29 Apr 2024 21:33:25 +0000

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

-       [Multiple Regression] [WS7 blog 1] [2012-11-20 20:57:25] [8dfbd7005bbb2cc4a26b500e2e7611ce] [Current]

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2,45	2,44	2,46	2,45	2,45	2,43	2,42	2,43	2,46	2,47	2,48	2,49
0,55	0,55	0,55	0,55	0,56	0,55	0,55	0,56	0,55	0,56	0,56	0,56
1,41	1,37	1,4	1,38	1,44	1,43	1,45	1,47	1,47	1,44	1,45	1,45
1,1	1,1	1,1	1,09	1,09	1,08	1,08	1,08	1,08	1,08	1,08	1,06
1,65	1,65	1,64	1,64	1,64	1,63	1,63	1,63	1,63	1,63	1,62	1,61
1,65	1,65	1,65	1,65	1,64	1,64	1,64	1,64	1,64	1,63	1,63	1,62
4,15	4,14	4,13	4,13	4,12	4,11	4,11	4,1	4,1	4,1	4,08	4,06
5,64	5,64	5,63	5,61	5,59	5,58	5,58	5,57	5,56	5,55	5,51	5,44
6,64	6,61	6,63	6,62	6,59	6,57	6,52	6,51	6,51	6,48	6,49	6,47
1,6	1,6	1,6	1,59	1,58	1,58	1,58	1,57	1,58	1,57	1,57	1,56
0,98	0,98	0,98	0,98	0,97	0,97	0,97	0,97	0,97	0,97	0,97	0,96
1,03	1,03	1,02	1,02	1,02	1,02	1,02	1,03	1,03	1,02	1,02	1,02
4,72	4,6	4,62	4,63	4,65	4,61	4,65	4,59	4,65	4,65	4,63	4,48
3,17	3,16	3,16	3,15	3,19	3,2	3,2	3,2	3,22	3,21	3,2	3,15
7,3	7,29	7,27	7,26	7,2	7,19	7,18	7,15	7,14	7,12	7,11	7,08
3,25	3,23	3,23	3,25	3,25	3,27	3,27	3,29	3,27	3,28	3,29	3,24
0,65	0,65	0,65	0,65	0,65	0,65	0,66	0,65	0,66	0,65	0,65	0,65
4,1	4,1	4,11	4,12	4,15	4,13	4,12	4,12	4,18	4,19	4,2	4,19
6,58	6,57	6,56	6,43	6,45	6,41	6,33	6,39	6,39	6,39	6,39	6,4
15,21	15,19	15,17	15,19	15,18	15,15	15,2	15,06	14,97	15,13	15,05	15,16
10,99	11	10,9	10,99	11,04	11,03	10,99	11	10,87	10,88	10,91	10,92
8,19	8,3	8,18	8,24	8,3	8,34	8,3	8,27	8,22	8,22	8,22	8,12
5,89	5,88	5,89	5,91	5,89	5,87	5,87	5,84	5,83	5,83	5,83	5,8
15	15,18	15,18	15,18	15,05	15	15,13	15,08	14,98	15,1	14,95	15,12

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191291&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]7 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=191291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191291&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	7 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Multiple Linear Regression - Estimated Regression Equation
2005/12[t] = + 0.00472891862713576 + 0.129933274148402`2005/11`[t] + 1.38134444423706`2005/10`[t] -0.689395298957021`2005/09`[t] + 1.06575281674565`2005/08`[t] -1.11502202842671`2005/07`[t] + 0.980661518292317`2005/06`[t] -0.107463644420801`2005/05`[t] -0.961060792363887`2005/04`[t] -1.19812820806339`2005/03`[t] + 2.09852327243365`2005/02`[t] -0.586487789996359`2005/01`[t] -0.000641674979176878t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
2005/12[t] =  +  0.00472891862713576 +  0.129933274148402`2005/11`[t] +  1.38134444423706`2005/10`[t] -0.689395298957021`2005/09`[t] +  1.06575281674565`2005/08`[t] -1.11502202842671`2005/07`[t] +  0.980661518292317`2005/06`[t] -0.107463644420801`2005/05`[t] -0.961060792363887`2005/04`[t] -1.19812820806339`2005/03`[t] +  2.09852327243365`2005/02`[t] -0.586487789996359`2005/01`[t] -0.000641674979176878t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191291&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]2005/12[t] =  +  0.00472891862713576 +  0.129933274148402`2005/11`[t] +  1.38134444423706`2005/10`[t] -0.689395298957021`2005/09`[t] +  1.06575281674565`2005/08`[t] -1.11502202842671`2005/07`[t] +  0.980661518292317`2005/06`[t] -0.107463644420801`2005/05`[t] -0.961060792363887`2005/04`[t] -1.19812820806339`2005/03`[t] +  2.09852327243365`2005/02`[t] -0.586487789996359`2005/01`[t] -0.000641674979176878t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191291&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
2005/12[t] = + 0.00472891862713576 + 0.129933274148402`2005/11`[t] + 1.38134444423706`2005/10`[t] -0.689395298957021`2005/09`[t] + 1.06575281674565`2005/08`[t] -1.11502202842671`2005/07`[t] + 0.980661518292317`2005/06`[t] -0.107463644420801`2005/05`[t] -0.961060792363887`2005/04`[t] -1.19812820806339`2005/03`[t] + 2.09852327243365`2005/02`[t] -0.586487789996359`2005/01`[t] -0.000641674979176878t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	0.00472891862713576	0.012293	0.3847	0.707801	0.353901
`2005/11`	0.129933274148402	0.430036	0.3021	0.768178	0.384089
`2005/10`	1.38134444423706	0.382726	3.6092	0.004103	0.002052
`2005/09`	-0.689395298957021	0.363395	-1.8971	0.084364	0.042182
`2005/08`	1.06575281674565	0.580856	1.8348	0.093699	0.04685
`2005/07`	-1.11502202842671	0.634499	-1.7573	0.106621	0.05331
`2005/06`	0.980661518292317	0.626425	1.5655	0.145764	0.072882
`2005/05`	-0.107463644420801	0.375197	-0.2864	0.77988	0.38994
`2005/04`	-0.961060792363887	0.470669	-2.0419	0.065888	0.032944
`2005/03`	-1.19812820806339	0.737364	-1.6249	0.13247	0.066235
`2005/02`	2.09852327243365	0.819942	2.5594	0.026549	0.013275
`2005/01`	-0.586487789996359	0.194042	-3.0225	0.011604	0.005802
t	-0.000641674979176878	0.001173	-0.547	0.595313	0.297656

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 0.00472891862713576 & 0.012293 & 0.3847 & 0.707801 & 0.353901 \tabularnewline
`2005/11` & 0.129933274148402 & 0.430036 & 0.3021 & 0.768178 & 0.384089 \tabularnewline
`2005/10` & 1.38134444423706 & 0.382726 & 3.6092 & 0.004103 & 0.002052 \tabularnewline
`2005/09` & -0.689395298957021 & 0.363395 & -1.8971 & 0.084364 & 0.042182 \tabularnewline
`2005/08` & 1.06575281674565 & 0.580856 & 1.8348 & 0.093699 & 0.04685 \tabularnewline
`2005/07` & -1.11502202842671 & 0.634499 & -1.7573 & 0.106621 & 0.05331 \tabularnewline
`2005/06` & 0.980661518292317 & 0.626425 & 1.5655 & 0.145764 & 0.072882 \tabularnewline
`2005/05` & -0.107463644420801 & 0.375197 & -0.2864 & 0.77988 & 0.38994 \tabularnewline
`2005/04` & -0.961060792363887 & 0.470669 & -2.0419 & 0.065888 & 0.032944 \tabularnewline
`2005/03` & -1.19812820806339 & 0.737364 & -1.6249 & 0.13247 & 0.066235 \tabularnewline
`2005/02` & 2.09852327243365 & 0.819942 & 2.5594 & 0.026549 & 0.013275 \tabularnewline
`2005/01` & -0.586487789996359 & 0.194042 & -3.0225 & 0.011604 & 0.005802 \tabularnewline
t & -0.000641674979176878 & 0.001173 & -0.547 & 0.595313 & 0.297656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191291&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]0.00472891862713576[/C][C]0.012293[/C][C]0.3847[/C][C]0.707801[/C][C]0.353901[/C][/ROW]
[ROW][C]`2005/11`[/C][C]0.129933274148402[/C][C]0.430036[/C][C]0.3021[/C][C]0.768178[/C][C]0.384089[/C][/ROW]
[ROW][C]`2005/10`[/C][C]1.38134444423706[/C][C]0.382726[/C][C]3.6092[/C][C]0.004103[/C][C]0.002052[/C][/ROW]
[ROW][C]`2005/09`[/C][C]-0.689395298957021[/C][C]0.363395[/C][C]-1.8971[/C][C]0.084364[/C][C]0.042182[/C][/ROW]
[ROW][C]`2005/08`[/C][C]1.06575281674565[/C][C]0.580856[/C][C]1.8348[/C][C]0.093699[/C][C]0.04685[/C][/ROW]
[ROW][C]`2005/07`[/C][C]-1.11502202842671[/C][C]0.634499[/C][C]-1.7573[/C][C]0.106621[/C][C]0.05331[/C][/ROW]
[ROW][C]`2005/06`[/C][C]0.980661518292317[/C][C]0.626425[/C][C]1.5655[/C][C]0.145764[/C][C]0.072882[/C][/ROW]
[ROW][C]`2005/05`[/C][C]-0.107463644420801[/C][C]0.375197[/C][C]-0.2864[/C][C]0.77988[/C][C]0.38994[/C][/ROW]
[ROW][C]`2005/04`[/C][C]-0.961060792363887[/C][C]0.470669[/C][C]-2.0419[/C][C]0.065888[/C][C]0.032944[/C][/ROW]
[ROW][C]`2005/03`[/C][C]-1.19812820806339[/C][C]0.737364[/C][C]-1.6249[/C][C]0.13247[/C][C]0.066235[/C][/ROW]
[ROW][C]`2005/02`[/C][C]2.09852327243365[/C][C]0.819942[/C][C]2.5594[/C][C]0.026549[/C][C]0.013275[/C][/ROW]
[ROW][C]`2005/01`[/C][C]-0.586487789996359[/C][C]0.194042[/C][C]-3.0225[/C][C]0.011604[/C][C]0.005802[/C][/ROW]
[ROW][C]t[/C][C]-0.000641674979176878[/C][C]0.001173[/C][C]-0.547[/C][C]0.595313[/C][C]0.297656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191291&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191291&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	0.00472891862713576	0.012293	0.3847	0.707801	0.353901
`2005/11`	0.129933274148402	0.430036	0.3021	0.768178	0.384089
`2005/10`	1.38134444423706	0.382726	3.6092	0.004103	0.002052
`2005/09`	-0.689395298957021	0.363395	-1.8971	0.084364	0.042182
`2005/08`	1.06575281674565	0.580856	1.8348	0.093699	0.04685
`2005/07`	-1.11502202842671	0.634499	-1.7573	0.106621	0.05331
`2005/06`	0.980661518292317	0.626425	1.5655	0.145764	0.072882
`2005/05`	-0.107463644420801	0.375197	-0.2864	0.77988	0.38994
`2005/04`	-0.961060792363887	0.470669	-2.0419	0.065888	0.032944
`2005/03`	-1.19812820806339	0.737364	-1.6249	0.13247	0.066235
`2005/02`	2.09852327243365	0.819942	2.5594	0.026549	0.013275
`2005/01`	-0.586487789996359	0.194042	-3.0225	0.011604	0.005802
t	-0.000641674979176878	0.001173	-0.547	0.595313	0.297656

Multiple Linear Regression - Regression Statistics
Multiple R	0.99999205700978
R-squared	0.999984114082651
Adjusted R-squared	0.999966783990997
F-TEST (value)	57702.1826573012
F-TEST (DF numerator)	12
F-TEST (DF denominator)	11
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0242650456291831
Sum Squared Residuals	0.0064767168332497

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99999205700978 \tabularnewline
R-squared & 0.999984114082651 \tabularnewline
Adjusted R-squared & 0.999966783990997 \tabularnewline
F-TEST (value) & 57702.1826573012 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 11 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0242650456291831 \tabularnewline
Sum Squared Residuals & 0.0064767168332497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191291&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99999205700978[/C][/ROW]
[ROW][C]R-squared[/C][C]0.999984114082651[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.999966783990997[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]57702.1826573012[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]11[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0242650456291831[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0064767168332497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191291&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191291&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R	0.99999205700978
R-squared	0.999984114082651
Adjusted R-squared	0.999966783990997
F-TEST (value)	57702.1826573012
F-TEST (DF numerator)	12
F-TEST (DF denominator)	11
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0242650456291831
Sum Squared Residuals	0.0064767168332497

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	2.45	2.46426526863613	-0.0142652686361256
2	0.55	0.56542919313168	-0.01542919313168
3	1.41	1.42190685348082	-0.0119068534808228
4	1.1	1.12643127277518	-0.0264312727751839
5	1.65	1.64025258062521	0.00974741937479462
6	1.65	1.64962190245401	0.000378097545989533
7	4.15	4.12214950736056	0.0278504926394451
8	5.64	5.63039497176511	0.00960502823488586
9	6.64	6.64873417208688	-0.00873417208687876
10	1.6	1.60332316234763	-0.00332316234763146
11	0.98	0.98045203267049	-0.000452032670489602
12	1.03	1.00627362215215	0.0237263778478514
13	4.72	4.71477688236994	0.00522311763005661
14	3.17	3.15293269214808	0.0170673078519161
15	7.3	7.28439815650713	0.0156018434928701
16	3.25	3.23752863711519	0.0124713628848054
17	0.65	0.64314386759921	0.00685613240078949
18	4.1	4.09735327983454	0.00264672016545869
19	6.58	6.581539817959	-0.00153981795900251
20	15.21	15.1987196059724	0.0112803940275865
21	10.99	10.9713845058381	0.0186154941619101
22	8.19	8.22411632046864	-0.0341163204686408
23	5.89	5.92146044236279	-0.0314604423627941
24	15	15.0134112523391	-0.0134112523391101

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.45 & 2.46426526863613 & -0.0142652686361256 \tabularnewline
2 & 0.55 & 0.56542919313168 & -0.01542919313168 \tabularnewline
3 & 1.41 & 1.42190685348082 & -0.0119068534808228 \tabularnewline
4 & 1.1 & 1.12643127277518 & -0.0264312727751839 \tabularnewline
5 & 1.65 & 1.64025258062521 & 0.00974741937479462 \tabularnewline
6 & 1.65 & 1.64962190245401 & 0.000378097545989533 \tabularnewline
7 & 4.15 & 4.12214950736056 & 0.0278504926394451 \tabularnewline
8 & 5.64 & 5.63039497176511 & 0.00960502823488586 \tabularnewline
9 & 6.64 & 6.64873417208688 & -0.00873417208687876 \tabularnewline
10 & 1.6 & 1.60332316234763 & -0.00332316234763146 \tabularnewline
11 & 0.98 & 0.98045203267049 & -0.000452032670489602 \tabularnewline
12 & 1.03 & 1.00627362215215 & 0.0237263778478514 \tabularnewline
13 & 4.72 & 4.71477688236994 & 0.00522311763005661 \tabularnewline
14 & 3.17 & 3.15293269214808 & 0.0170673078519161 \tabularnewline
15 & 7.3 & 7.28439815650713 & 0.0156018434928701 \tabularnewline
16 & 3.25 & 3.23752863711519 & 0.0124713628848054 \tabularnewline
17 & 0.65 & 0.64314386759921 & 0.00685613240078949 \tabularnewline
18 & 4.1 & 4.09735327983454 & 0.00264672016545869 \tabularnewline
19 & 6.58 & 6.581539817959 & -0.00153981795900251 \tabularnewline
20 & 15.21 & 15.1987196059724 & 0.0112803940275865 \tabularnewline
21 & 10.99 & 10.9713845058381 & 0.0186154941619101 \tabularnewline
22 & 8.19 & 8.22411632046864 & -0.0341163204686408 \tabularnewline
23 & 5.89 & 5.92146044236279 & -0.0314604423627941 \tabularnewline
24 & 15 & 15.0134112523391 & -0.0134112523391101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191291&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]2.45[/C][C]2.46426526863613[/C][C]-0.0142652686361256[/C][/ROW]
[ROW][C]2[/C][C]0.55[/C][C]0.56542919313168[/C][C]-0.01542919313168[/C][/ROW]
[ROW][C]3[/C][C]1.41[/C][C]1.42190685348082[/C][C]-0.0119068534808228[/C][/ROW]
[ROW][C]4[/C][C]1.1[/C][C]1.12643127277518[/C][C]-0.0264312727751839[/C][/ROW]
[ROW][C]5[/C][C]1.65[/C][C]1.64025258062521[/C][C]0.00974741937479462[/C][/ROW]
[ROW][C]6[/C][C]1.65[/C][C]1.64962190245401[/C][C]0.000378097545989533[/C][/ROW]
[ROW][C]7[/C][C]4.15[/C][C]4.12214950736056[/C][C]0.0278504926394451[/C][/ROW]
[ROW][C]8[/C][C]5.64[/C][C]5.63039497176511[/C][C]0.00960502823488586[/C][/ROW]
[ROW][C]9[/C][C]6.64[/C][C]6.64873417208688[/C][C]-0.00873417208687876[/C][/ROW]
[ROW][C]10[/C][C]1.6[/C][C]1.60332316234763[/C][C]-0.00332316234763146[/C][/ROW]
[ROW][C]11[/C][C]0.98[/C][C]0.98045203267049[/C][C]-0.000452032670489602[/C][/ROW]
[ROW][C]12[/C][C]1.03[/C][C]1.00627362215215[/C][C]0.0237263778478514[/C][/ROW]
[ROW][C]13[/C][C]4.72[/C][C]4.71477688236994[/C][C]0.00522311763005661[/C][/ROW]
[ROW][C]14[/C][C]3.17[/C][C]3.15293269214808[/C][C]0.0170673078519161[/C][/ROW]
[ROW][C]15[/C][C]7.3[/C][C]7.28439815650713[/C][C]0.0156018434928701[/C][/ROW]
[ROW][C]16[/C][C]3.25[/C][C]3.23752863711519[/C][C]0.0124713628848054[/C][/ROW]
[ROW][C]17[/C][C]0.65[/C][C]0.64314386759921[/C][C]0.00685613240078949[/C][/ROW]
[ROW][C]18[/C][C]4.1[/C][C]4.09735327983454[/C][C]0.00264672016545869[/C][/ROW]
[ROW][C]19[/C][C]6.58[/C][C]6.581539817959[/C][C]-0.00153981795900251[/C][/ROW]
[ROW][C]20[/C][C]15.21[/C][C]15.1987196059724[/C][C]0.0112803940275865[/C][/ROW]
[ROW][C]21[/C][C]10.99[/C][C]10.9713845058381[/C][C]0.0186154941619101[/C][/ROW]
[ROW][C]22[/C][C]8.19[/C][C]8.22411632046864[/C][C]-0.0341163204686408[/C][/ROW]
[ROW][C]23[/C][C]5.89[/C][C]5.92146044236279[/C][C]-0.0314604423627941[/C][/ROW]
[ROW][C]24[/C][C]15[/C][C]15.0134112523391[/C][C]-0.0134112523391101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191291&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191291&T=4

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	2.45	2.46426526863613	-0.0142652686361256
2	0.55	0.56542919313168	-0.01542919313168
3	1.41	1.42190685348082	-0.0119068534808228
4	1.1	1.12643127277518	-0.0264312727751839
5	1.65	1.64025258062521	0.00974741937479462
6	1.65	1.64962190245401	0.000378097545989533
7	4.15	4.12214950736056	0.0278504926394451
8	5.64	5.63039497176511	0.00960502823488586
9	6.64	6.64873417208688	-0.00873417208687876
10	1.6	1.60332316234763	-0.00332316234763146
11	0.98	0.98045203267049	-0.000452032670489602
12	1.03	1.00627362215215	0.0237263778478514
13	4.72	4.71477688236994	0.00522311763005661
14	3.17	3.15293269214808	0.0170673078519161
15	7.3	7.28439815650713	0.0156018434928701
16	3.25	3.23752863711519	0.0124713628848054
17	0.65	0.64314386759921	0.00685613240078949
18	4.1	4.09735327983454	0.00264672016545869
19	6.58	6.581539817959	-0.00153981795900251
20	15.21	15.1987196059724	0.0112803940275865
21	10.99	10.9713845058381	0.0186154941619101
22	8.19	8.22411632046864	-0.0341163204686408
23	5.89	5.92146044236279	-0.0314604423627941
24	15	15.0134112523391	-0.0134112523391101

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code