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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSun, 22 Nov 2009 06:34:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/22/t1258896962m2idvh34mqhgeru.htm/, Retrieved Fri, 28 Nov 2025 19:01:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58628, Retrieved Fri, 28 Nov 2025 19:01:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscvm
Estimated Impact544

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [model 1] [2009-11-17 14:36:29] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D      [Multiple Regression] [multiple regression] [2009-11-19 21:38:11] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P         [Multiple Regression] [monthly dummies] [2009-11-19 22:00:07] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P           [Multiple Regression] [model3] [2009-11-20 08:47:44] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D            [Multiple Regression] [model 4] [2009-11-20 08:59:37] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D                [Multiple Regression] [W7: Model 4] [2009-11-22 13:34:45] [a5ada8bd39e806b5b90f09589c89554a] [Current]
-    D                  [Multiple Regression] [review 7] [2009-11-24 21:51:11] [309ee52d0058ff0a6f7eec15e07b2d9f]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,5	1,9	6,3	6,1	6,2	6,3
6,6	2	6,5	6,3	6,1	6,2
6,5	2,3	6,6	6,5	6,3	6,1
6,2	2,8	6,5	6,6	6,5	6,3
6,2	2,4	6,2	6,5	6,6	6,5
5,9	2,3	6,2	6,2	6,5	6,6
6,1	2,7	5,9	6,2	6,2	6,5
6,1	2,7	6,1	5,9	6,2	6,2
6,1	2,9	6,1	6,1	5,9	6,2
6,1	3	6,1	6,1	6,1	5,9
6,1	2,2	6,1	6,1	6,1	6,1
6,4	2,3	6,1	6,1	6,1	6,1
6,7	2,8	6,4	6,1	6,1	6,1
6,9	2,8	6,7	6,4	6,1	6,1
7	2,8	6,9	6,7	6,4	6,1
7	2,2	7	6,9	6,7	6,4
6,8	2,6	7	7	6,9	6,7
6,4	2,8	6,8	7	7	6,9
5,9	2,5	6,4	6,8	7	7
5,5	2,4	5,9	6,4	6,8	7
5,5	2,3	5,5	5,9	6,4	6,8
5,6	1,9	5,5	5,5	5,9	6,4
5,8	1,7	5,6	5,5	5,5	5,9
5,9	2	5,8	5,6	5,5	5,5
6,1	2,1	5,9	5,8	5,6	5,5
6,1	1,7	6,1	5,9	5,8	5,6
6	1,8	6,1	6,1	5,9	5,8
6	1,8	6	6,1	6,1	5,9
5,9	1,8	6	6	6,1	6,1
5,5	1,3	5,9	6	6	6,1
5,6	1,3	5,5	5,9	6	6
5,4	1,3	5,6	5,5	5,9	6
5,2	1,2	5,4	5,6	5,5	5,9
5,2	1,4	5,2	5,4	5,6	5,5
5,2	2,2	5,2	5,2	5,4	5,6
5,5	2,9	5,2	5,2	5,2	5,4
5,8	3,1	5,5	5,2	5,2	5,2
5,8	3,5	5,8	5,5	5,2	5,2
5,5	3,6	5,8	5,8	5,5	5,2
5,3	4,4	5,5	5,8	5,8	5,5
5,1	4,1	5,3	5,5	5,8	5,8
5,2	5,1	5,1	5,3	5,5	5,8
5,8	5,8	5,2	5,1	5,3	5,5
5,8	5,9	5,8	5,2	5,1	5,3
5,5	5,4	5,8	5,8	5,2	5,1
5	5,5	5,5	5,8	5,8	5,2
4,9	4,8	5	5,5	5,8	5,8
5,3	3,2	4,9	5	5,5	5,8
6,1	2,7	5,3	4,9	5	5,5
6,5	2,1	6,1	5,3	4,9	5
6,8	1,9	6,5	6,1	5,3	4,9
6,6	0,6	6,8	6,5	6,1	5,3
6,4	0,7	6,6	6,8	6,5	6,1
6,4	-0,2	6,4	6,6	6,8	6,5
6,6	-1	6,4	6,4	6,6	6,8
6,7	-1,7	6,6	6,4	6,4	6,6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58628&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58628&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
WMan>25[t] = + 0.205529147155612 -0.006701733132186Infl[t] + 1.46424310835333`Yt-1`[t] -0.572214153777315`Yt-2`[t] -0.306648555087636`Yt-3`[t] + 0.404540471386374`Yt-4`[t] + 0.00841686847188313M1[t] -0.192488288817357M2[t] -0.133691692405834M3[t] -0.162225291504273M4[t] -0.213984572812024M5[t] -0.354608452344717M6[t] -0.0590469925769761M7[t] -0.43876956278108M8[t] -0.336609775414806M9[t] -0.209948728671440M10[t] -0.200347599504354M11[t] + 0.00233719208955934t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WMan>25[t] =  +  0.205529147155612 -0.006701733132186Infl[t] +  1.46424310835333`Yt-1`[t] -0.572214153777315`Yt-2`[t] -0.306648555087636`Yt-3`[t] +  0.404540471386374`Yt-4`[t] +  0.00841686847188313M1[t] -0.192488288817357M2[t] -0.133691692405834M3[t] -0.162225291504273M4[t] -0.213984572812024M5[t] -0.354608452344717M6[t] -0.0590469925769761M7[t] -0.43876956278108M8[t] -0.336609775414806M9[t] -0.209948728671440M10[t] -0.200347599504354M11[t] +  0.00233719208955934t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58628&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WMan>25[t] =  +  0.205529147155612 -0.006701733132186Infl[t] +  1.46424310835333`Yt-1`[t] -0.572214153777315`Yt-2`[t] -0.306648555087636`Yt-3`[t] +  0.404540471386374`Yt-4`[t] +  0.00841686847188313M1[t] -0.192488288817357M2[t] -0.133691692405834M3[t] -0.162225291504273M4[t] -0.213984572812024M5[t] -0.354608452344717M6[t] -0.0590469925769761M7[t] -0.43876956278108M8[t] -0.336609775414806M9[t] -0.209948728671440M10[t] -0.200347599504354M11[t] +  0.00233719208955934t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58628&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
WMan>25[t] = + 0.205529147155612 -0.006701733132186Infl[t] + 1.46424310835333`Yt-1`[t] -0.572214153777315`Yt-2`[t] -0.306648555087636`Yt-3`[t] + 0.404540471386374`Yt-4`[t] + 0.00841686847188313M1[t] -0.192488288817357M2[t] -0.133691692405834M3[t] -0.162225291504273M4[t] -0.213984572812024M5[t] -0.354608452344717M6[t] -0.0590469925769761M7[t] -0.43876956278108M8[t] -0.336609775414806M9[t] -0.209948728671440M10[t] -0.200347599504354M11[t] + 0.00233719208955934t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.2055291471556120.6274580.32760.7450440.372522
Infl-0.0067017331321860.020618-0.3250.7469320.373466
`Yt-1`1.464243108353330.1571529.317400
`Yt-2`-0.5722141537773150.2819-2.02980.0494170.024708
`Yt-3`-0.3066485550876360.283438-1.08190.286120.14306
`Yt-4`0.4045404713863740.1709192.36690.0231380.011569
M10.008416868471883130.1204620.06990.9446620.472331
M2-0.1924882888173570.127934-1.50460.1406950.070348
M3-0.1336916924058340.132805-1.00670.3204590.160229
M4-0.1622252915042730.133475-1.21540.2317130.115856
M5-0.2139845728120240.130341-1.64170.1088980.054449
M6-0.3546084523447170.129565-2.73690.009380.00469
M7-0.05904699257697610.129365-0.45640.6506740.325337
M8-0.438769562781080.127628-3.43790.0014360.000718
M9-0.3366097754148060.140883-2.38930.021950.010975
M10-0.2099487286714400.127155-1.65110.1069540.053477
M11-0.2003475995043540.123495-1.62230.1130040.056502
t0.002337192089559340.0021091.10850.2746290.137315

\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) & 0.205529147155612 & 0.627458 & 0.3276 & 0.745044 & 0.372522 \tabularnewline
Infl & -0.006701733132186 & 0.020618 & -0.325 & 0.746932 & 0.373466 \tabularnewline
`Yt-1` & 1.46424310835333 & 0.157152 & 9.3174 & 0 & 0 \tabularnewline
`Yt-2` & -0.572214153777315 & 0.2819 & -2.0298 & 0.049417 & 0.024708 \tabularnewline
`Yt-3` & -0.306648555087636 & 0.283438 & -1.0819 & 0.28612 & 0.14306 \tabularnewline
`Yt-4` & 0.404540471386374 & 0.170919 & 2.3669 & 0.023138 & 0.011569 \tabularnewline
M1 & 0.00841686847188313 & 0.120462 & 0.0699 & 0.944662 & 0.472331 \tabularnewline
M2 & -0.192488288817357 & 0.127934 & -1.5046 & 0.140695 & 0.070348 \tabularnewline
M3 & -0.133691692405834 & 0.132805 & -1.0067 & 0.320459 & 0.160229 \tabularnewline
M4 & -0.162225291504273 & 0.133475 & -1.2154 & 0.231713 & 0.115856 \tabularnewline
M5 & -0.213984572812024 & 0.130341 & -1.6417 & 0.108898 & 0.054449 \tabularnewline
M6 & -0.354608452344717 & 0.129565 & -2.7369 & 0.00938 & 0.00469 \tabularnewline
M7 & -0.0590469925769761 & 0.129365 & -0.4564 & 0.650674 & 0.325337 \tabularnewline
M8 & -0.43876956278108 & 0.127628 & -3.4379 & 0.001436 & 0.000718 \tabularnewline
M9 & -0.336609775414806 & 0.140883 & -2.3893 & 0.02195 & 0.010975 \tabularnewline
M10 & -0.209948728671440 & 0.127155 & -1.6511 & 0.106954 & 0.053477 \tabularnewline
M11 & -0.200347599504354 & 0.123495 & -1.6223 & 0.113004 & 0.056502 \tabularnewline
t & 0.00233719208955934 & 0.002109 & 1.1085 & 0.274629 & 0.137315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58628&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]0.205529147155612[/C][C]0.627458[/C][C]0.3276[/C][C]0.745044[/C][C]0.372522[/C][/ROW]
[ROW][C]Infl[/C][C]-0.006701733132186[/C][C]0.020618[/C][C]-0.325[/C][C]0.746932[/C][C]0.373466[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]1.46424310835333[/C][C]0.157152[/C][C]9.3174[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]-0.572214153777315[/C][C]0.2819[/C][C]-2.0298[/C][C]0.049417[/C][C]0.024708[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]-0.306648555087636[/C][C]0.283438[/C][C]-1.0819[/C][C]0.28612[/C][C]0.14306[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]0.404540471386374[/C][C]0.170919[/C][C]2.3669[/C][C]0.023138[/C][C]0.011569[/C][/ROW]
[ROW][C]M1[/C][C]0.00841686847188313[/C][C]0.120462[/C][C]0.0699[/C][C]0.944662[/C][C]0.472331[/C][/ROW]
[ROW][C]M2[/C][C]-0.192488288817357[/C][C]0.127934[/C][C]-1.5046[/C][C]0.140695[/C][C]0.070348[/C][/ROW]
[ROW][C]M3[/C][C]-0.133691692405834[/C][C]0.132805[/C][C]-1.0067[/C][C]0.320459[/C][C]0.160229[/C][/ROW]
[ROW][C]M4[/C][C]-0.162225291504273[/C][C]0.133475[/C][C]-1.2154[/C][C]0.231713[/C][C]0.115856[/C][/ROW]
[ROW][C]M5[/C][C]-0.213984572812024[/C][C]0.130341[/C][C]-1.6417[/C][C]0.108898[/C][C]0.054449[/C][/ROW]
[ROW][C]M6[/C][C]-0.354608452344717[/C][C]0.129565[/C][C]-2.7369[/C][C]0.00938[/C][C]0.00469[/C][/ROW]
[ROW][C]M7[/C][C]-0.0590469925769761[/C][C]0.129365[/C][C]-0.4564[/C][C]0.650674[/C][C]0.325337[/C][/ROW]
[ROW][C]M8[/C][C]-0.43876956278108[/C][C]0.127628[/C][C]-3.4379[/C][C]0.001436[/C][C]0.000718[/C][/ROW]
[ROW][C]M9[/C][C]-0.336609775414806[/C][C]0.140883[/C][C]-2.3893[/C][C]0.02195[/C][C]0.010975[/C][/ROW]
[ROW][C]M10[/C][C]-0.209948728671440[/C][C]0.127155[/C][C]-1.6511[/C][C]0.106954[/C][C]0.053477[/C][/ROW]
[ROW][C]M11[/C][C]-0.200347599504354[/C][C]0.123495[/C][C]-1.6223[/C][C]0.113004[/C][C]0.056502[/C][/ROW]
[ROW][C]t[/C][C]0.00233719208955934[/C][C]0.002109[/C][C]1.1085[/C][C]0.274629[/C][C]0.137315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58628&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58628&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.2055291471556120.6274580.32760.7450440.372522
Infl-0.0067017331321860.020618-0.3250.7469320.373466
`Yt-1`1.464243108353330.1571529.317400
`Yt-2`-0.5722141537773150.2819-2.02980.0494170.024708
`Yt-3`-0.3066485550876360.283438-1.08190.286120.14306
`Yt-4`0.4045404713863740.1709192.36690.0231380.011569
M10.008416868471883130.1204620.06990.9446620.472331
M2-0.1924882888173570.127934-1.50460.1406950.070348
M3-0.1336916924058340.132805-1.00670.3204590.160229
M4-0.1622252915042730.133475-1.21540.2317130.115856
M5-0.2139845728120240.130341-1.64170.1088980.054449
M6-0.3546084523447170.129565-2.73690.009380.00469
M7-0.05904699257697610.129365-0.45640.6506740.325337
M8-0.438769562781080.127628-3.43790.0014360.000718
M9-0.3366097754148060.140883-2.38930.021950.010975
M10-0.2099487286714400.127155-1.65110.1069540.053477
M11-0.2003475995043540.123495-1.62230.1130040.056502
t0.002337192089559340.0021091.10850.2746290.137315






Multiple Linear Regression - Regression Statistics
Multiple R0.965451375198482
R-squared0.932096357872639
Adjusted R-squared0.901718412710399
F-TEST (value)30.6833247902241
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.172463277800623
Sum Squared Residuals1.13025612320992

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.965451375198482 \tabularnewline
R-squared & 0.932096357872639 \tabularnewline
Adjusted R-squared & 0.901718412710399 \tabularnewline
F-TEST (value) & 30.6833247902241 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.172463277800623 \tabularnewline
Sum Squared Residuals & 1.13025612320992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58628&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.965451375198482[/C][/ROW]
[ROW][C]R-squared[/C][C]0.932096357872639[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.901718412710399[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]30.6833247902241[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/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]0.172463277800623[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.13025612320992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58628&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58628&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.965451375198482
R-squared0.932096357872639
Adjusted R-squared0.901718412710399
F-TEST (value)30.6833247902241
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.172463277800623
Sum Squared Residuals1.13025612320992






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.56.58515908754108-0.08515908754108
26.66.554537548313520.0454624516864788
36.56.54385853879865-0.0438585387986542
46.26.33024392227036-0.130243922270363
56.25.951694247945290.248305752054712
65.96.05686088259597-0.156860882595968
76.15.964346428082050.135653571917952
86.15.930111776355450.169888223644548
96.16.010820144955670.0891798550443245
106.15.956456358041940.143543641958056
116.16.054664160081610.0453358399183878
126.46.25667877836230.143321221637694
136.76.70335490486366-0.00335490486365748
146.96.772395626036780.127604373963219
1576.862719223549050.137280776450954
1676.901892911388970.0981070886110306
176.86.85260114393856-0.0526011439385567
186.46.47036872696683-0.0703687269668295
195.96.33947753331655-0.439477533316553
205.55.52085614686701-0.0208561468670132
215.55.368184460941170.131815539058832
225.65.72025714352716-0.120257143527163
235.85.80034930858745-0.000349308587445725
245.96.07483459798009-0.174834597980089
256.16.086235109799420.0137648902005789
266.16.10509938026666-0.00509938026665854
2766.10136340346757-0.101363403467571
2865.907867021744470.0921329782555311
295.95.99657444218128-0.0965744421812821
305.55.74587916597767-0.245879165977672
315.65.474847942732730.125152057267267
325.45.50343739247321-0.103437392473210
335.25.34073988309028-0.140739883090282
345.25.097510940318250.102489059681746
355.25.32031446398078-0.120314463980777
365.55.498729659122410.00127034087758668
375.85.86650821128614-0.0665082112861441
385.85.93286823920639-0.132868239206394
395.55.72967304173477-0.229673041734773
405.35.288209890603770.0117901093962337
415.15.24097608720367-0.140976087203669
425.25.009576442239440.190423557760564
435.85.503618592096620.296381407903381
445.85.92730910704338-0.127309107043377
455.55.58025551101287-0.0802555110128746
4655.12577555811264-0.125775558112639
474.94.824672067350170.075327932649835
485.35.269756964535190.0302430354648085
496.15.95874268650970.141257313490303
506.56.53509920617665-0.0350992061766451
516.86.562385792449960.237614207550044
526.66.67178625399243-0.0717862539924327
536.46.35815407873120.0418459212687959
546.46.117314782220090.282685217779906
556.66.71770950377205-0.117709503772046
566.76.618285577260950.0817144227390516

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.5 & 6.58515908754108 & -0.08515908754108 \tabularnewline
2 & 6.6 & 6.55453754831352 & 0.0454624516864788 \tabularnewline
3 & 6.5 & 6.54385853879865 & -0.0438585387986542 \tabularnewline
4 & 6.2 & 6.33024392227036 & -0.130243922270363 \tabularnewline
5 & 6.2 & 5.95169424794529 & 0.248305752054712 \tabularnewline
6 & 5.9 & 6.05686088259597 & -0.156860882595968 \tabularnewline
7 & 6.1 & 5.96434642808205 & 0.135653571917952 \tabularnewline
8 & 6.1 & 5.93011177635545 & 0.169888223644548 \tabularnewline
9 & 6.1 & 6.01082014495567 & 0.0891798550443245 \tabularnewline
10 & 6.1 & 5.95645635804194 & 0.143543641958056 \tabularnewline
11 & 6.1 & 6.05466416008161 & 0.0453358399183878 \tabularnewline
12 & 6.4 & 6.2566787783623 & 0.143321221637694 \tabularnewline
13 & 6.7 & 6.70335490486366 & -0.00335490486365748 \tabularnewline
14 & 6.9 & 6.77239562603678 & 0.127604373963219 \tabularnewline
15 & 7 & 6.86271922354905 & 0.137280776450954 \tabularnewline
16 & 7 & 6.90189291138897 & 0.0981070886110306 \tabularnewline
17 & 6.8 & 6.85260114393856 & -0.0526011439385567 \tabularnewline
18 & 6.4 & 6.47036872696683 & -0.0703687269668295 \tabularnewline
19 & 5.9 & 6.33947753331655 & -0.439477533316553 \tabularnewline
20 & 5.5 & 5.52085614686701 & -0.0208561468670132 \tabularnewline
21 & 5.5 & 5.36818446094117 & 0.131815539058832 \tabularnewline
22 & 5.6 & 5.72025714352716 & -0.120257143527163 \tabularnewline
23 & 5.8 & 5.80034930858745 & -0.000349308587445725 \tabularnewline
24 & 5.9 & 6.07483459798009 & -0.174834597980089 \tabularnewline
25 & 6.1 & 6.08623510979942 & 0.0137648902005789 \tabularnewline
26 & 6.1 & 6.10509938026666 & -0.00509938026665854 \tabularnewline
27 & 6 & 6.10136340346757 & -0.101363403467571 \tabularnewline
28 & 6 & 5.90786702174447 & 0.0921329782555311 \tabularnewline
29 & 5.9 & 5.99657444218128 & -0.0965744421812821 \tabularnewline
30 & 5.5 & 5.74587916597767 & -0.245879165977672 \tabularnewline
31 & 5.6 & 5.47484794273273 & 0.125152057267267 \tabularnewline
32 & 5.4 & 5.50343739247321 & -0.103437392473210 \tabularnewline
33 & 5.2 & 5.34073988309028 & -0.140739883090282 \tabularnewline
34 & 5.2 & 5.09751094031825 & 0.102489059681746 \tabularnewline
35 & 5.2 & 5.32031446398078 & -0.120314463980777 \tabularnewline
36 & 5.5 & 5.49872965912241 & 0.00127034087758668 \tabularnewline
37 & 5.8 & 5.86650821128614 & -0.0665082112861441 \tabularnewline
38 & 5.8 & 5.93286823920639 & -0.132868239206394 \tabularnewline
39 & 5.5 & 5.72967304173477 & -0.229673041734773 \tabularnewline
40 & 5.3 & 5.28820989060377 & 0.0117901093962337 \tabularnewline
41 & 5.1 & 5.24097608720367 & -0.140976087203669 \tabularnewline
42 & 5.2 & 5.00957644223944 & 0.190423557760564 \tabularnewline
43 & 5.8 & 5.50361859209662 & 0.296381407903381 \tabularnewline
44 & 5.8 & 5.92730910704338 & -0.127309107043377 \tabularnewline
45 & 5.5 & 5.58025551101287 & -0.0802555110128746 \tabularnewline
46 & 5 & 5.12577555811264 & -0.125775558112639 \tabularnewline
47 & 4.9 & 4.82467206735017 & 0.075327932649835 \tabularnewline
48 & 5.3 & 5.26975696453519 & 0.0302430354648085 \tabularnewline
49 & 6.1 & 5.9587426865097 & 0.141257313490303 \tabularnewline
50 & 6.5 & 6.53509920617665 & -0.0350992061766451 \tabularnewline
51 & 6.8 & 6.56238579244996 & 0.237614207550044 \tabularnewline
52 & 6.6 & 6.67178625399243 & -0.0717862539924327 \tabularnewline
53 & 6.4 & 6.3581540787312 & 0.0418459212687959 \tabularnewline
54 & 6.4 & 6.11731478222009 & 0.282685217779906 \tabularnewline
55 & 6.6 & 6.71770950377205 & -0.117709503772046 \tabularnewline
56 & 6.7 & 6.61828557726095 & 0.0817144227390516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58628&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]6.5[/C][C]6.58515908754108[/C][C]-0.08515908754108[/C][/ROW]
[ROW][C]2[/C][C]6.6[/C][C]6.55453754831352[/C][C]0.0454624516864788[/C][/ROW]
[ROW][C]3[/C][C]6.5[/C][C]6.54385853879865[/C][C]-0.0438585387986542[/C][/ROW]
[ROW][C]4[/C][C]6.2[/C][C]6.33024392227036[/C][C]-0.130243922270363[/C][/ROW]
[ROW][C]5[/C][C]6.2[/C][C]5.95169424794529[/C][C]0.248305752054712[/C][/ROW]
[ROW][C]6[/C][C]5.9[/C][C]6.05686088259597[/C][C]-0.156860882595968[/C][/ROW]
[ROW][C]7[/C][C]6.1[/C][C]5.96434642808205[/C][C]0.135653571917952[/C][/ROW]
[ROW][C]8[/C][C]6.1[/C][C]5.93011177635545[/C][C]0.169888223644548[/C][/ROW]
[ROW][C]9[/C][C]6.1[/C][C]6.01082014495567[/C][C]0.0891798550443245[/C][/ROW]
[ROW][C]10[/C][C]6.1[/C][C]5.95645635804194[/C][C]0.143543641958056[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.05466416008161[/C][C]0.0453358399183878[/C][/ROW]
[ROW][C]12[/C][C]6.4[/C][C]6.2566787783623[/C][C]0.143321221637694[/C][/ROW]
[ROW][C]13[/C][C]6.7[/C][C]6.70335490486366[/C][C]-0.00335490486365748[/C][/ROW]
[ROW][C]14[/C][C]6.9[/C][C]6.77239562603678[/C][C]0.127604373963219[/C][/ROW]
[ROW][C]15[/C][C]7[/C][C]6.86271922354905[/C][C]0.137280776450954[/C][/ROW]
[ROW][C]16[/C][C]7[/C][C]6.90189291138897[/C][C]0.0981070886110306[/C][/ROW]
[ROW][C]17[/C][C]6.8[/C][C]6.85260114393856[/C][C]-0.0526011439385567[/C][/ROW]
[ROW][C]18[/C][C]6.4[/C][C]6.47036872696683[/C][C]-0.0703687269668295[/C][/ROW]
[ROW][C]19[/C][C]5.9[/C][C]6.33947753331655[/C][C]-0.439477533316553[/C][/ROW]
[ROW][C]20[/C][C]5.5[/C][C]5.52085614686701[/C][C]-0.0208561468670132[/C][/ROW]
[ROW][C]21[/C][C]5.5[/C][C]5.36818446094117[/C][C]0.131815539058832[/C][/ROW]
[ROW][C]22[/C][C]5.6[/C][C]5.72025714352716[/C][C]-0.120257143527163[/C][/ROW]
[ROW][C]23[/C][C]5.8[/C][C]5.80034930858745[/C][C]-0.000349308587445725[/C][/ROW]
[ROW][C]24[/C][C]5.9[/C][C]6.07483459798009[/C][C]-0.174834597980089[/C][/ROW]
[ROW][C]25[/C][C]6.1[/C][C]6.08623510979942[/C][C]0.0137648902005789[/C][/ROW]
[ROW][C]26[/C][C]6.1[/C][C]6.10509938026666[/C][C]-0.00509938026665854[/C][/ROW]
[ROW][C]27[/C][C]6[/C][C]6.10136340346757[/C][C]-0.101363403467571[/C][/ROW]
[ROW][C]28[/C][C]6[/C][C]5.90786702174447[/C][C]0.0921329782555311[/C][/ROW]
[ROW][C]29[/C][C]5.9[/C][C]5.99657444218128[/C][C]-0.0965744421812821[/C][/ROW]
[ROW][C]30[/C][C]5.5[/C][C]5.74587916597767[/C][C]-0.245879165977672[/C][/ROW]
[ROW][C]31[/C][C]5.6[/C][C]5.47484794273273[/C][C]0.125152057267267[/C][/ROW]
[ROW][C]32[/C][C]5.4[/C][C]5.50343739247321[/C][C]-0.103437392473210[/C][/ROW]
[ROW][C]33[/C][C]5.2[/C][C]5.34073988309028[/C][C]-0.140739883090282[/C][/ROW]
[ROW][C]34[/C][C]5.2[/C][C]5.09751094031825[/C][C]0.102489059681746[/C][/ROW]
[ROW][C]35[/C][C]5.2[/C][C]5.32031446398078[/C][C]-0.120314463980777[/C][/ROW]
[ROW][C]36[/C][C]5.5[/C][C]5.49872965912241[/C][C]0.00127034087758668[/C][/ROW]
[ROW][C]37[/C][C]5.8[/C][C]5.86650821128614[/C][C]-0.0665082112861441[/C][/ROW]
[ROW][C]38[/C][C]5.8[/C][C]5.93286823920639[/C][C]-0.132868239206394[/C][/ROW]
[ROW][C]39[/C][C]5.5[/C][C]5.72967304173477[/C][C]-0.229673041734773[/C][/ROW]
[ROW][C]40[/C][C]5.3[/C][C]5.28820989060377[/C][C]0.0117901093962337[/C][/ROW]
[ROW][C]41[/C][C]5.1[/C][C]5.24097608720367[/C][C]-0.140976087203669[/C][/ROW]
[ROW][C]42[/C][C]5.2[/C][C]5.00957644223944[/C][C]0.190423557760564[/C][/ROW]
[ROW][C]43[/C][C]5.8[/C][C]5.50361859209662[/C][C]0.296381407903381[/C][/ROW]
[ROW][C]44[/C][C]5.8[/C][C]5.92730910704338[/C][C]-0.127309107043377[/C][/ROW]
[ROW][C]45[/C][C]5.5[/C][C]5.58025551101287[/C][C]-0.0802555110128746[/C][/ROW]
[ROW][C]46[/C][C]5[/C][C]5.12577555811264[/C][C]-0.125775558112639[/C][/ROW]
[ROW][C]47[/C][C]4.9[/C][C]4.82467206735017[/C][C]0.075327932649835[/C][/ROW]
[ROW][C]48[/C][C]5.3[/C][C]5.26975696453519[/C][C]0.0302430354648085[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]5.9587426865097[/C][C]0.141257313490303[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.53509920617665[/C][C]-0.0350992061766451[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]6.56238579244996[/C][C]0.237614207550044[/C][/ROW]
[ROW][C]52[/C][C]6.6[/C][C]6.67178625399243[/C][C]-0.0717862539924327[/C][/ROW]
[ROW][C]53[/C][C]6.4[/C][C]6.3581540787312[/C][C]0.0418459212687959[/C][/ROW]
[ROW][C]54[/C][C]6.4[/C][C]6.11731478222009[/C][C]0.282685217779906[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.71770950377205[/C][C]-0.117709503772046[/C][/ROW]
[ROW][C]56[/C][C]6.7[/C][C]6.61828557726095[/C][C]0.0817144227390516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58628&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58628&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.56.58515908754108-0.08515908754108
26.66.554537548313520.0454624516864788
36.56.54385853879865-0.0438585387986542
46.26.33024392227036-0.130243922270363
56.25.951694247945290.248305752054712
65.96.05686088259597-0.156860882595968
76.15.964346428082050.135653571917952
86.15.930111776355450.169888223644548
96.16.010820144955670.0891798550443245
106.15.956456358041940.143543641958056
116.16.054664160081610.0453358399183878
126.46.25667877836230.143321221637694
136.76.70335490486366-0.00335490486365748
146.96.772395626036780.127604373963219
1576.862719223549050.137280776450954
1676.901892911388970.0981070886110306
176.86.85260114393856-0.0526011439385567
186.46.47036872696683-0.0703687269668295
195.96.33947753331655-0.439477533316553
205.55.52085614686701-0.0208561468670132
215.55.368184460941170.131815539058832
225.65.72025714352716-0.120257143527163
235.85.80034930858745-0.000349308587445725
245.96.07483459798009-0.174834597980089
256.16.086235109799420.0137648902005789
266.16.10509938026666-0.00509938026665854
2766.10136340346757-0.101363403467571
2865.907867021744470.0921329782555311
295.95.99657444218128-0.0965744421812821
305.55.74587916597767-0.245879165977672
315.65.474847942732730.125152057267267
325.45.50343739247321-0.103437392473210
335.25.34073988309028-0.140739883090282
345.25.097510940318250.102489059681746
355.25.32031446398078-0.120314463980777
365.55.498729659122410.00127034087758668
375.85.86650821128614-0.0665082112861441
385.85.93286823920639-0.132868239206394
395.55.72967304173477-0.229673041734773
405.35.288209890603770.0117901093962337
415.15.24097608720367-0.140976087203669
425.25.009576442239440.190423557760564
435.85.503618592096620.296381407903381
445.85.92730910704338-0.127309107043377
455.55.58025551101287-0.0802555110128746
4655.12577555811264-0.125775558112639
474.94.824672067350170.075327932649835
485.35.269756964535190.0302430354648085
496.15.95874268650970.141257313490303
506.56.53509920617665-0.0350992061766451
516.86.562385792449960.237614207550044
526.66.67178625399243-0.0717862539924327
536.46.35815407873120.0418459212687959
546.46.117314782220090.282685217779906
556.66.71770950377205-0.117709503772046
566.76.618285577260950.0817144227390516






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.5314189457374520.9371621085250970.468581054262548
220.4207357702889820.8414715405779640.579264229711018
230.6633056545764850.673388690847030.336694345423515
240.756798327149740.4864033457005190.243201672850260
250.6470193309162260.7059613381675470.352980669083774
260.581546231939910.836907536120180.41845376806009
270.471138962364840.942277924729680.52886103763516
280.5772035367397510.8455929265204970.422796463260249
290.856574810848530.286850378302940.14342518915147
300.7918553799519650.416289240096070.208144620048035
310.8833155727854020.2333688544291970.116684427214598
320.8312029431630460.3375941136739090.168797056836954
330.7349408411803390.5301183176393230.265059158819661
340.6645585354935570.6708829290128850.335441464506443
350.6781850206861930.6436299586276150.321814979313807

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.531418945737452 & 0.937162108525097 & 0.468581054262548 \tabularnewline
22 & 0.420735770288982 & 0.841471540577964 & 0.579264229711018 \tabularnewline
23 & 0.663305654576485 & 0.67338869084703 & 0.336694345423515 \tabularnewline
24 & 0.75679832714974 & 0.486403345700519 & 0.243201672850260 \tabularnewline
25 & 0.647019330916226 & 0.705961338167547 & 0.352980669083774 \tabularnewline
26 & 0.58154623193991 & 0.83690753612018 & 0.41845376806009 \tabularnewline
27 & 0.47113896236484 & 0.94227792472968 & 0.52886103763516 \tabularnewline
28 & 0.577203536739751 & 0.845592926520497 & 0.422796463260249 \tabularnewline
29 & 0.85657481084853 & 0.28685037830294 & 0.14342518915147 \tabularnewline
30 & 0.791855379951965 & 0.41628924009607 & 0.208144620048035 \tabularnewline
31 & 0.883315572785402 & 0.233368854429197 & 0.116684427214598 \tabularnewline
32 & 0.831202943163046 & 0.337594113673909 & 0.168797056836954 \tabularnewline
33 & 0.734940841180339 & 0.530118317639323 & 0.265059158819661 \tabularnewline
34 & 0.664558535493557 & 0.670882929012885 & 0.335441464506443 \tabularnewline
35 & 0.678185020686193 & 0.643629958627615 & 0.321814979313807 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58628&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]21[/C][C]0.531418945737452[/C][C]0.937162108525097[/C][C]0.468581054262548[/C][/ROW]
[ROW][C]22[/C][C]0.420735770288982[/C][C]0.841471540577964[/C][C]0.579264229711018[/C][/ROW]
[ROW][C]23[/C][C]0.663305654576485[/C][C]0.67338869084703[/C][C]0.336694345423515[/C][/ROW]
[ROW][C]24[/C][C]0.75679832714974[/C][C]0.486403345700519[/C][C]0.243201672850260[/C][/ROW]
[ROW][C]25[/C][C]0.647019330916226[/C][C]0.705961338167547[/C][C]0.352980669083774[/C][/ROW]
[ROW][C]26[/C][C]0.58154623193991[/C][C]0.83690753612018[/C][C]0.41845376806009[/C][/ROW]
[ROW][C]27[/C][C]0.47113896236484[/C][C]0.94227792472968[/C][C]0.52886103763516[/C][/ROW]
[ROW][C]28[/C][C]0.577203536739751[/C][C]0.845592926520497[/C][C]0.422796463260249[/C][/ROW]
[ROW][C]29[/C][C]0.85657481084853[/C][C]0.28685037830294[/C][C]0.14342518915147[/C][/ROW]
[ROW][C]30[/C][C]0.791855379951965[/C][C]0.41628924009607[/C][C]0.208144620048035[/C][/ROW]
[ROW][C]31[/C][C]0.883315572785402[/C][C]0.233368854429197[/C][C]0.116684427214598[/C][/ROW]
[ROW][C]32[/C][C]0.831202943163046[/C][C]0.337594113673909[/C][C]0.168797056836954[/C][/ROW]
[ROW][C]33[/C][C]0.734940841180339[/C][C]0.530118317639323[/C][C]0.265059158819661[/C][/ROW]
[ROW][C]34[/C][C]0.664558535493557[/C][C]0.670882929012885[/C][C]0.335441464506443[/C][/ROW]
[ROW][C]35[/C][C]0.678185020686193[/C][C]0.643629958627615[/C][C]0.321814979313807[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58628&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58628&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.5314189457374520.9371621085250970.468581054262548
220.4207357702889820.8414715405779640.579264229711018
230.6633056545764850.673388690847030.336694345423515
240.756798327149740.4864033457005190.243201672850260
250.6470193309162260.7059613381675470.352980669083774
260.581546231939910.836907536120180.41845376806009
270.471138962364840.942277924729680.52886103763516
280.5772035367397510.8455929265204970.422796463260249
290.856574810848530.286850378302940.14342518915147
300.7918553799519650.416289240096070.208144620048035
310.8833155727854020.2333688544291970.116684427214598
320.8312029431630460.3375941136739090.168797056836954
330.7349408411803390.5301183176393230.265059158819661
340.6645585354935570.6708829290128850.335441464506443
350.6781850206861930.6436299586276150.321814979313807






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58628&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58628&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58628&T=6

As an alternative you can also use a QR Code:  
QR Code


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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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')
}