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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, 06 Dec 2009 05:47:31 -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/Dec/06/t12601046403u8h0qqvmkmqzjk.htm/, Retrieved Thu, 20 Feb 2025 19:23:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64376, Retrieved Thu, 20 Feb 2025 19:23:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact235

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]
-   PD          [Multiple Regression] [multiple regressi...] [2009-12-06 12:47:31] [87085ce7f5378f281469a8b1f0969170] [Current]
-   PD            [Multiple Regression] [multiple regressi...] [2009-12-08 20:02:18] [ed603017d2bee8fbd82b6d5ec04e12c3]
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Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time11 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 & 11 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64376&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]11 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=64376&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64376&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 time11 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 1.42982007691866 -0.161193787467765Infl[t] + 0.929871660400964`M1(t)`[t] + 0.274012559640936`M2(t)`[t] -0.624835761341823`M3(t)`[t] + 0.251487269084980`M4(t)`[t] + 0.0239056796988475M1[t] -0.225226304943252M2[t] -0.22089214657853M3[t] -0.230237762317641M4[t] -0.000204885143931201M5[t] -0.149127441415511M6[t] -0.104503412749335M7[t] + 0.113480030247102M8[t] + 0.120527017026366M9[t] -0.150903024914468M10[t] -0.313224104489284M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkl[t] =  +  1.42982007691866 -0.161193787467765Infl[t] +  0.929871660400964`M1(t)`[t] +  0.274012559640936`M2(t)`[t] -0.624835761341823`M3(t)`[t] +  0.251487269084980`M4(t)`[t] +  0.0239056796988475M1[t] -0.225226304943252M2[t] -0.22089214657853M3[t] -0.230237762317641M4[t] -0.000204885143931201M5[t] -0.149127441415511M6[t] -0.104503412749335M7[t] +  0.113480030247102M8[t] +  0.120527017026366M9[t] -0.150903024914468M10[t] -0.313224104489284M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64376&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkl[t] =  +  1.42982007691866 -0.161193787467765Infl[t] +  0.929871660400964`M1(t)`[t] +  0.274012559640936`M2(t)`[t] -0.624835761341823`M3(t)`[t] +  0.251487269084980`M4(t)`[t] +  0.0239056796988475M1[t] -0.225226304943252M2[t] -0.22089214657853M3[t] -0.230237762317641M4[t] -0.000204885143931201M5[t] -0.149127441415511M6[t] -0.104503412749335M7[t] +  0.113480030247102M8[t] +  0.120527017026366M9[t] -0.150903024914468M10[t] -0.313224104489284M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64376&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64376&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
Werkl[t] = + 1.42982007691866 -0.161193787467765Infl[t] + 0.929871660400964`M1(t)`[t] + 0.274012559640936`M2(t)`[t] -0.624835761341823`M3(t)`[t] + 0.251487269084980`M4(t)`[t] + 0.0239056796988475M1[t] -0.225226304943252M2[t] -0.22089214657853M3[t] -0.230237762317641M4[t] -0.000204885143931201M5[t] -0.149127441415511M6[t] -0.104503412749335M7[t] + 0.113480030247102M8[t] + 0.120527017026366M9[t] -0.150903024914468M10[t] -0.313224104489284M11[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.429820076918660.3777073.78550.0005170.000259
Infl-0.1611937874677650.050531-3.190.0028070.001403
`M1(t)`0.9298716604009640.1550555.99711e-060
`M2(t)`0.2740125596409360.1986561.37930.1756510.087825
`M3(t)`-0.6248357613418230.199402-3.13360.0032730.001637
`M4(t)`0.2514872690849800.1320881.90390.0643160.032158
M10.02390567969884750.1018030.23480.8155740.407787
M2-0.2252263049432520.117582-1.91550.0627840.031392
M3-0.220892146578530.093864-2.35330.0237430.011872
M4-0.2302377623176410.087698-2.62540.01230.00615
M5-0.0002048851439312010.094075-0.00220.9982730.499137
M6-0.1491274414155110.111541-1.3370.1889790.09449
M7-0.1045034127493350.108288-0.9650.3404670.170234
M80.1134800302471020.0966371.17430.2473980.123699
M90.1205270170263660.1181671.020.3140290.157015
M10-0.1509030249144680.120953-1.24760.2196120.109806
M11-0.3132241044892840.097684-3.20650.0026830.001341

\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) & 1.42982007691866 & 0.377707 & 3.7855 & 0.000517 & 0.000259 \tabularnewline
Infl & -0.161193787467765 & 0.050531 & -3.19 & 0.002807 & 0.001403 \tabularnewline
`M1(t)` & 0.929871660400964 & 0.155055 & 5.9971 & 1e-06 & 0 \tabularnewline
`M2(t)` & 0.274012559640936 & 0.198656 & 1.3793 & 0.175651 & 0.087825 \tabularnewline
`M3(t)` & -0.624835761341823 & 0.199402 & -3.1336 & 0.003273 & 0.001637 \tabularnewline
`M4(t)` & 0.251487269084980 & 0.132088 & 1.9039 & 0.064316 & 0.032158 \tabularnewline
M1 & 0.0239056796988475 & 0.101803 & 0.2348 & 0.815574 & 0.407787 \tabularnewline
M2 & -0.225226304943252 & 0.117582 & -1.9155 & 0.062784 & 0.031392 \tabularnewline
M3 & -0.22089214657853 & 0.093864 & -2.3533 & 0.023743 & 0.011872 \tabularnewline
M4 & -0.230237762317641 & 0.087698 & -2.6254 & 0.0123 & 0.00615 \tabularnewline
M5 & -0.000204885143931201 & 0.094075 & -0.0022 & 0.998273 & 0.499137 \tabularnewline
M6 & -0.149127441415511 & 0.111541 & -1.337 & 0.188979 & 0.09449 \tabularnewline
M7 & -0.104503412749335 & 0.108288 & -0.965 & 0.340467 & 0.170234 \tabularnewline
M8 & 0.113480030247102 & 0.096637 & 1.1743 & 0.247398 & 0.123699 \tabularnewline
M9 & 0.120527017026366 & 0.118167 & 1.02 & 0.314029 & 0.157015 \tabularnewline
M10 & -0.150903024914468 & 0.120953 & -1.2476 & 0.219612 & 0.109806 \tabularnewline
M11 & -0.313224104489284 & 0.097684 & -3.2065 & 0.002683 & 0.001341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64376&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]1.42982007691866[/C][C]0.377707[/C][C]3.7855[/C][C]0.000517[/C][C]0.000259[/C][/ROW]
[ROW][C]Infl[/C][C]-0.161193787467765[/C][C]0.050531[/C][C]-3.19[/C][C]0.002807[/C][C]0.001403[/C][/ROW]
[ROW][C]`M1(t)`[/C][C]0.929871660400964[/C][C]0.155055[/C][C]5.9971[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]`M2(t)`[/C][C]0.274012559640936[/C][C]0.198656[/C][C]1.3793[/C][C]0.175651[/C][C]0.087825[/C][/ROW]
[ROW][C]`M3(t)`[/C][C]-0.624835761341823[/C][C]0.199402[/C][C]-3.1336[/C][C]0.003273[/C][C]0.001637[/C][/ROW]
[ROW][C]`M4(t)`[/C][C]0.251487269084980[/C][C]0.132088[/C][C]1.9039[/C][C]0.064316[/C][C]0.032158[/C][/ROW]
[ROW][C]M1[/C][C]0.0239056796988475[/C][C]0.101803[/C][C]0.2348[/C][C]0.815574[/C][C]0.407787[/C][/ROW]
[ROW][C]M2[/C][C]-0.225226304943252[/C][C]0.117582[/C][C]-1.9155[/C][C]0.062784[/C][C]0.031392[/C][/ROW]
[ROW][C]M3[/C][C]-0.22089214657853[/C][C]0.093864[/C][C]-2.3533[/C][C]0.023743[/C][C]0.011872[/C][/ROW]
[ROW][C]M4[/C][C]-0.230237762317641[/C][C]0.087698[/C][C]-2.6254[/C][C]0.0123[/C][C]0.00615[/C][/ROW]
[ROW][C]M5[/C][C]-0.000204885143931201[/C][C]0.094075[/C][C]-0.0022[/C][C]0.998273[/C][C]0.499137[/C][/ROW]
[ROW][C]M6[/C][C]-0.149127441415511[/C][C]0.111541[/C][C]-1.337[/C][C]0.188979[/C][C]0.09449[/C][/ROW]
[ROW][C]M7[/C][C]-0.104503412749335[/C][C]0.108288[/C][C]-0.965[/C][C]0.340467[/C][C]0.170234[/C][/ROW]
[ROW][C]M8[/C][C]0.113480030247102[/C][C]0.096637[/C][C]1.1743[/C][C]0.247398[/C][C]0.123699[/C][/ROW]
[ROW][C]M9[/C][C]0.120527017026366[/C][C]0.118167[/C][C]1.02[/C][C]0.314029[/C][C]0.157015[/C][/ROW]
[ROW][C]M10[/C][C]-0.150903024914468[/C][C]0.120953[/C][C]-1.2476[/C][C]0.219612[/C][C]0.109806[/C][/ROW]
[ROW][C]M11[/C][C]-0.313224104489284[/C][C]0.097684[/C][C]-3.2065[/C][C]0.002683[/C][C]0.001341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64376&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64376&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)1.429820076918660.3777073.78550.0005170.000259
Infl-0.1611937874677650.050531-3.190.0028070.001403
`M1(t)`0.9298716604009640.1550555.99711e-060
`M2(t)`0.2740125596409360.1986561.37930.1756510.087825
`M3(t)`-0.6248357613418230.199402-3.13360.0032730.001637
`M4(t)`0.2514872690849800.1320881.90390.0643160.032158
M10.02390567969884750.1018030.23480.8155740.407787
M2-0.2252263049432520.117582-1.91550.0627840.031392
M3-0.220892146578530.093864-2.35330.0237430.011872
M4-0.2302377623176410.087698-2.62540.01230.00615
M5-0.0002048851439312010.094075-0.00220.9982730.499137
M6-0.1491274414155110.111541-1.3370.1889790.09449
M7-0.1045034127493350.108288-0.9650.3404670.170234
M80.1134800302471020.0966371.17430.2473980.123699
M90.1205270170263660.1181671.020.3140290.157015
M10-0.1509030249144680.120953-1.24760.2196120.109806
M11-0.3132241044892840.097684-3.20650.0026830.001341






Multiple Linear Regression - Regression Statistics
Multiple R0.996807176456464
R-squared0.993624547035107
Adjusted R-squared0.991008976587972
F-TEST (value)379.888275662138
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.116875093448220
Sum Squared Residuals0.532731711272674

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996807176456464 \tabularnewline
R-squared & 0.993624547035107 \tabularnewline
Adjusted R-squared & 0.991008976587972 \tabularnewline
F-TEST (value) & 379.888275662138 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.116875093448220 \tabularnewline
Sum Squared Residuals & 0.532731711272674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64376&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996807176456464[/C][/ROW]
[ROW][C]R-squared[/C][C]0.993624547035107[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.991008976587972[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]379.888275662138[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/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]0.116875093448220[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.532731711272674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64376&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64376&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 R0.996807176456464
R-squared0.993624547035107
Adjusted R-squared0.991008976587972
F-TEST (value)379.888275662138
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.116875093448220
Sum Squared Residuals0.532731711272674






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13.43.275098566724490.124901433275512
23.43.361021720862650.0389782791373494
33.53.391076407817470.108923592182528
43.23.30848270019482-0.108482700194818
53.33.33725278902933-0.0372527890293275
63.33.201107569758490.0988924302415132
73.43.50185168844658-0.101851688446578
83.73.642653783129880.0573462168701186
93.94.04568976588913-0.145689765889134
1044.01219300528014-0.0121930052801432
113.73.86759835967312-0.167598359673116
123.93.879741250463330.0202587495366665
134.24.043589508273240.156410491726764
144.44.324701610243880.0752983897561186
154.34.39680053558722-0.0968005355872196
164.24.22823636989742-0.0282363698974241
174.34.288359853524070.0116401464759263
184.34.33392361602645-0.0339236160264512
194.34.45940312862918-0.159403128629182
204.54.58975426858294-0.089754268582938
2154.920759965578330.0792400344216706
225.25.169068265766160.0309317342338359
235.25.20476064582365-0.00476064582364498
245.45.359024971627530.0409750283724701
255.55.58580084442747-0.085800844427473
265.45.53475599157065-0.134755991570653
275.55.332417708844230.167582291155769
285.45.376471880863940.0235281191360633
295.75.64467052975110.0553294702488997
305.75.659675912593040.0403240874069642
316.15.874136012194170.225863987805826
326.56.299826800280280.20017319971972
336.96.9283511707889-0.0283511707889048
346.86.90465989107488-0.104659891074879
356.76.625736651160380.07426334883962
366.66.6208748005024-0.0208748005024079
376.56.67135116321846-0.171351163218463
386.46.355284984544630.0447150154553664
396.16.32492370637118-0.224923706371181
406.26.046550185773370.153449814226630
416.36.34082068906736-0.0408206890673564
426.46.41011104130691-0.0101110413069089
436.56.453313113864380.0466868861356242
446.76.7704695083861-0.0704695083860944
4576.905199097743630.0948009022563681
4676.914078837878810.0859211621211865
476.86.701904343342860.0980956566571407
486.76.74035897740673-0.0403589774067283
496.76.72415991735634-0.0241599173563395
506.56.52423569277818-0.0242356927781820
516.46.35478164137990.0452183586201034
526.16.14025886327045-0.040258863270452
536.26.188896138628140.0111038613718579
5466.09518186031512-0.0951818603151173
556.16.11129605686569-0.0112960568656909
566.16.1972956396208-0.0972956396208063

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3.4 & 3.27509856672449 & 0.124901433275512 \tabularnewline
2 & 3.4 & 3.36102172086265 & 0.0389782791373494 \tabularnewline
3 & 3.5 & 3.39107640781747 & 0.108923592182528 \tabularnewline
4 & 3.2 & 3.30848270019482 & -0.108482700194818 \tabularnewline
5 & 3.3 & 3.33725278902933 & -0.0372527890293275 \tabularnewline
6 & 3.3 & 3.20110756975849 & 0.0988924302415132 \tabularnewline
7 & 3.4 & 3.50185168844658 & -0.101851688446578 \tabularnewline
8 & 3.7 & 3.64265378312988 & 0.0573462168701186 \tabularnewline
9 & 3.9 & 4.04568976588913 & -0.145689765889134 \tabularnewline
10 & 4 & 4.01219300528014 & -0.0121930052801432 \tabularnewline
11 & 3.7 & 3.86759835967312 & -0.167598359673116 \tabularnewline
12 & 3.9 & 3.87974125046333 & 0.0202587495366665 \tabularnewline
13 & 4.2 & 4.04358950827324 & 0.156410491726764 \tabularnewline
14 & 4.4 & 4.32470161024388 & 0.0752983897561186 \tabularnewline
15 & 4.3 & 4.39680053558722 & -0.0968005355872196 \tabularnewline
16 & 4.2 & 4.22823636989742 & -0.0282363698974241 \tabularnewline
17 & 4.3 & 4.28835985352407 & 0.0116401464759263 \tabularnewline
18 & 4.3 & 4.33392361602645 & -0.0339236160264512 \tabularnewline
19 & 4.3 & 4.45940312862918 & -0.159403128629182 \tabularnewline
20 & 4.5 & 4.58975426858294 & -0.089754268582938 \tabularnewline
21 & 5 & 4.92075996557833 & 0.0792400344216706 \tabularnewline
22 & 5.2 & 5.16906826576616 & 0.0309317342338359 \tabularnewline
23 & 5.2 & 5.20476064582365 & -0.00476064582364498 \tabularnewline
24 & 5.4 & 5.35902497162753 & 0.0409750283724701 \tabularnewline
25 & 5.5 & 5.58580084442747 & -0.085800844427473 \tabularnewline
26 & 5.4 & 5.53475599157065 & -0.134755991570653 \tabularnewline
27 & 5.5 & 5.33241770884423 & 0.167582291155769 \tabularnewline
28 & 5.4 & 5.37647188086394 & 0.0235281191360633 \tabularnewline
29 & 5.7 & 5.6446705297511 & 0.0553294702488997 \tabularnewline
30 & 5.7 & 5.65967591259304 & 0.0403240874069642 \tabularnewline
31 & 6.1 & 5.87413601219417 & 0.225863987805826 \tabularnewline
32 & 6.5 & 6.29982680028028 & 0.20017319971972 \tabularnewline
33 & 6.9 & 6.9283511707889 & -0.0283511707889048 \tabularnewline
34 & 6.8 & 6.90465989107488 & -0.104659891074879 \tabularnewline
35 & 6.7 & 6.62573665116038 & 0.07426334883962 \tabularnewline
36 & 6.6 & 6.6208748005024 & -0.0208748005024079 \tabularnewline
37 & 6.5 & 6.67135116321846 & -0.171351163218463 \tabularnewline
38 & 6.4 & 6.35528498454463 & 0.0447150154553664 \tabularnewline
39 & 6.1 & 6.32492370637118 & -0.224923706371181 \tabularnewline
40 & 6.2 & 6.04655018577337 & 0.153449814226630 \tabularnewline
41 & 6.3 & 6.34082068906736 & -0.0408206890673564 \tabularnewline
42 & 6.4 & 6.41011104130691 & -0.0101110413069089 \tabularnewline
43 & 6.5 & 6.45331311386438 & 0.0466868861356242 \tabularnewline
44 & 6.7 & 6.7704695083861 & -0.0704695083860944 \tabularnewline
45 & 7 & 6.90519909774363 & 0.0948009022563681 \tabularnewline
46 & 7 & 6.91407883787881 & 0.0859211621211865 \tabularnewline
47 & 6.8 & 6.70190434334286 & 0.0980956566571407 \tabularnewline
48 & 6.7 & 6.74035897740673 & -0.0403589774067283 \tabularnewline
49 & 6.7 & 6.72415991735634 & -0.0241599173563395 \tabularnewline
50 & 6.5 & 6.52423569277818 & -0.0242356927781820 \tabularnewline
51 & 6.4 & 6.3547816413799 & 0.0452183586201034 \tabularnewline
52 & 6.1 & 6.14025886327045 & -0.040258863270452 \tabularnewline
53 & 6.2 & 6.18889613862814 & 0.0111038613718579 \tabularnewline
54 & 6 & 6.09518186031512 & -0.0951818603151173 \tabularnewline
55 & 6.1 & 6.11129605686569 & -0.0112960568656909 \tabularnewline
56 & 6.1 & 6.1972956396208 & -0.0972956396208063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64376&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]3.4[/C][C]3.27509856672449[/C][C]0.124901433275512[/C][/ROW]
[ROW][C]2[/C][C]3.4[/C][C]3.36102172086265[/C][C]0.0389782791373494[/C][/ROW]
[ROW][C]3[/C][C]3.5[/C][C]3.39107640781747[/C][C]0.108923592182528[/C][/ROW]
[ROW][C]4[/C][C]3.2[/C][C]3.30848270019482[/C][C]-0.108482700194818[/C][/ROW]
[ROW][C]5[/C][C]3.3[/C][C]3.33725278902933[/C][C]-0.0372527890293275[/C][/ROW]
[ROW][C]6[/C][C]3.3[/C][C]3.20110756975849[/C][C]0.0988924302415132[/C][/ROW]
[ROW][C]7[/C][C]3.4[/C][C]3.50185168844658[/C][C]-0.101851688446578[/C][/ROW]
[ROW][C]8[/C][C]3.7[/C][C]3.64265378312988[/C][C]0.0573462168701186[/C][/ROW]
[ROW][C]9[/C][C]3.9[/C][C]4.04568976588913[/C][C]-0.145689765889134[/C][/ROW]
[ROW][C]10[/C][C]4[/C][C]4.01219300528014[/C][C]-0.0121930052801432[/C][/ROW]
[ROW][C]11[/C][C]3.7[/C][C]3.86759835967312[/C][C]-0.167598359673116[/C][/ROW]
[ROW][C]12[/C][C]3.9[/C][C]3.87974125046333[/C][C]0.0202587495366665[/C][/ROW]
[ROW][C]13[/C][C]4.2[/C][C]4.04358950827324[/C][C]0.156410491726764[/C][/ROW]
[ROW][C]14[/C][C]4.4[/C][C]4.32470161024388[/C][C]0.0752983897561186[/C][/ROW]
[ROW][C]15[/C][C]4.3[/C][C]4.39680053558722[/C][C]-0.0968005355872196[/C][/ROW]
[ROW][C]16[/C][C]4.2[/C][C]4.22823636989742[/C][C]-0.0282363698974241[/C][/ROW]
[ROW][C]17[/C][C]4.3[/C][C]4.28835985352407[/C][C]0.0116401464759263[/C][/ROW]
[ROW][C]18[/C][C]4.3[/C][C]4.33392361602645[/C][C]-0.0339236160264512[/C][/ROW]
[ROW][C]19[/C][C]4.3[/C][C]4.45940312862918[/C][C]-0.159403128629182[/C][/ROW]
[ROW][C]20[/C][C]4.5[/C][C]4.58975426858294[/C][C]-0.089754268582938[/C][/ROW]
[ROW][C]21[/C][C]5[/C][C]4.92075996557833[/C][C]0.0792400344216706[/C][/ROW]
[ROW][C]22[/C][C]5.2[/C][C]5.16906826576616[/C][C]0.0309317342338359[/C][/ROW]
[ROW][C]23[/C][C]5.2[/C][C]5.20476064582365[/C][C]-0.00476064582364498[/C][/ROW]
[ROW][C]24[/C][C]5.4[/C][C]5.35902497162753[/C][C]0.0409750283724701[/C][/ROW]
[ROW][C]25[/C][C]5.5[/C][C]5.58580084442747[/C][C]-0.085800844427473[/C][/ROW]
[ROW][C]26[/C][C]5.4[/C][C]5.53475599157065[/C][C]-0.134755991570653[/C][/ROW]
[ROW][C]27[/C][C]5.5[/C][C]5.33241770884423[/C][C]0.167582291155769[/C][/ROW]
[ROW][C]28[/C][C]5.4[/C][C]5.37647188086394[/C][C]0.0235281191360633[/C][/ROW]
[ROW][C]29[/C][C]5.7[/C][C]5.6446705297511[/C][C]0.0553294702488997[/C][/ROW]
[ROW][C]30[/C][C]5.7[/C][C]5.65967591259304[/C][C]0.0403240874069642[/C][/ROW]
[ROW][C]31[/C][C]6.1[/C][C]5.87413601219417[/C][C]0.225863987805826[/C][/ROW]
[ROW][C]32[/C][C]6.5[/C][C]6.29982680028028[/C][C]0.20017319971972[/C][/ROW]
[ROW][C]33[/C][C]6.9[/C][C]6.9283511707889[/C][C]-0.0283511707889048[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]6.90465989107488[/C][C]-0.104659891074879[/C][/ROW]
[ROW][C]35[/C][C]6.7[/C][C]6.62573665116038[/C][C]0.07426334883962[/C][/ROW]
[ROW][C]36[/C][C]6.6[/C][C]6.6208748005024[/C][C]-0.0208748005024079[/C][/ROW]
[ROW][C]37[/C][C]6.5[/C][C]6.67135116321846[/C][C]-0.171351163218463[/C][/ROW]
[ROW][C]38[/C][C]6.4[/C][C]6.35528498454463[/C][C]0.0447150154553664[/C][/ROW]
[ROW][C]39[/C][C]6.1[/C][C]6.32492370637118[/C][C]-0.224923706371181[/C][/ROW]
[ROW][C]40[/C][C]6.2[/C][C]6.04655018577337[/C][C]0.153449814226630[/C][/ROW]
[ROW][C]41[/C][C]6.3[/C][C]6.34082068906736[/C][C]-0.0408206890673564[/C][/ROW]
[ROW][C]42[/C][C]6.4[/C][C]6.41011104130691[/C][C]-0.0101110413069089[/C][/ROW]
[ROW][C]43[/C][C]6.5[/C][C]6.45331311386438[/C][C]0.0466868861356242[/C][/ROW]
[ROW][C]44[/C][C]6.7[/C][C]6.7704695083861[/C][C]-0.0704695083860944[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]6.90519909774363[/C][C]0.0948009022563681[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]6.91407883787881[/C][C]0.0859211621211865[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.70190434334286[/C][C]0.0980956566571407[/C][/ROW]
[ROW][C]48[/C][C]6.7[/C][C]6.74035897740673[/C][C]-0.0403589774067283[/C][/ROW]
[ROW][C]49[/C][C]6.7[/C][C]6.72415991735634[/C][C]-0.0241599173563395[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.52423569277818[/C][C]-0.0242356927781820[/C][/ROW]
[ROW][C]51[/C][C]6.4[/C][C]6.3547816413799[/C][C]0.0452183586201034[/C][/ROW]
[ROW][C]52[/C][C]6.1[/C][C]6.14025886327045[/C][C]-0.040258863270452[/C][/ROW]
[ROW][C]53[/C][C]6.2[/C][C]6.18889613862814[/C][C]0.0111038613718579[/C][/ROW]
[ROW][C]54[/C][C]6[/C][C]6.09518186031512[/C][C]-0.0951818603151173[/C][/ROW]
[ROW][C]55[/C][C]6.1[/C][C]6.11129605686569[/C][C]-0.0112960568656909[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]6.1972956396208[/C][C]-0.0972956396208063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64376&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64376&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
13.43.275098566724490.124901433275512
23.43.361021720862650.0389782791373494
33.53.391076407817470.108923592182528
43.23.30848270019482-0.108482700194818
53.33.33725278902933-0.0372527890293275
63.33.201107569758490.0988924302415132
73.43.50185168844658-0.101851688446578
83.73.642653783129880.0573462168701186
93.94.04568976588913-0.145689765889134
1044.01219300528014-0.0121930052801432
113.73.86759835967312-0.167598359673116
123.93.879741250463330.0202587495366665
134.24.043589508273240.156410491726764
144.44.324701610243880.0752983897561186
154.34.39680053558722-0.0968005355872196
164.24.22823636989742-0.0282363698974241
174.34.288359853524070.0116401464759263
184.34.33392361602645-0.0339236160264512
194.34.45940312862918-0.159403128629182
204.54.58975426858294-0.089754268582938
2154.920759965578330.0792400344216706
225.25.169068265766160.0309317342338359
235.25.20476064582365-0.00476064582364498
245.45.359024971627530.0409750283724701
255.55.58580084442747-0.085800844427473
265.45.53475599157065-0.134755991570653
275.55.332417708844230.167582291155769
285.45.376471880863940.0235281191360633
295.75.64467052975110.0553294702488997
305.75.659675912593040.0403240874069642
316.15.874136012194170.225863987805826
326.56.299826800280280.20017319971972
336.96.9283511707889-0.0283511707889048
346.86.90465989107488-0.104659891074879
356.76.625736651160380.07426334883962
366.66.6208748005024-0.0208748005024079
376.56.67135116321846-0.171351163218463
386.46.355284984544630.0447150154553664
396.16.32492370637118-0.224923706371181
406.26.046550185773370.153449814226630
416.36.34082068906736-0.0408206890673564
426.46.41011104130691-0.0101110413069089
436.56.453313113864380.0466868861356242
446.76.7704695083861-0.0704695083860944
4576.905199097743630.0948009022563681
4676.914078837878810.0859211621211865
476.86.701904343342860.0980956566571407
486.76.74035897740673-0.0403589774067283
496.76.72415991735634-0.0241599173563395
506.56.52423569277818-0.0242356927781820
516.46.35478164137990.0452183586201034
526.16.14025886327045-0.040258863270452
536.26.188896138628140.0111038613718579
5466.09518186031512-0.0951818603151173
556.16.11129605686569-0.0112960568656909
566.16.1972956396208-0.0972956396208063






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.4446094821692240.8892189643384480.555390517830776
210.3313636615414340.6627273230828690.668636338458566
220.2198023440459400.4396046880918790.78019765595406
230.3961475618967780.7922951237935560.603852438103222
240.3378925654779660.6757851309559320.662107434522034
250.2868418580822240.5736837161644470.713158141917776
260.2785149845708460.5570299691416910.721485015429155
270.3036921153916160.6073842307832330.696307884608384
280.2323246283769280.4646492567538550.767675371623072
290.1576372514587950.3152745029175890.842362748541205
300.1131047157055830.2262094314111650.886895284294417
310.348288308919740.696576617839480.65171169108026
320.7082704930120580.5834590139758840.291729506987942
330.5947402162379340.8105195675241330.405259783762066
340.547827667820520.904344664358960.45217233217948
350.4983669104913890.9967338209827780.501633089508611
360.3693627866868580.7387255733737160.630637213313142

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.444609482169224 & 0.889218964338448 & 0.555390517830776 \tabularnewline
21 & 0.331363661541434 & 0.662727323082869 & 0.668636338458566 \tabularnewline
22 & 0.219802344045940 & 0.439604688091879 & 0.78019765595406 \tabularnewline
23 & 0.396147561896778 & 0.792295123793556 & 0.603852438103222 \tabularnewline
24 & 0.337892565477966 & 0.675785130955932 & 0.662107434522034 \tabularnewline
25 & 0.286841858082224 & 0.573683716164447 & 0.713158141917776 \tabularnewline
26 & 0.278514984570846 & 0.557029969141691 & 0.721485015429155 \tabularnewline
27 & 0.303692115391616 & 0.607384230783233 & 0.696307884608384 \tabularnewline
28 & 0.232324628376928 & 0.464649256753855 & 0.767675371623072 \tabularnewline
29 & 0.157637251458795 & 0.315274502917589 & 0.842362748541205 \tabularnewline
30 & 0.113104715705583 & 0.226209431411165 & 0.886895284294417 \tabularnewline
31 & 0.34828830891974 & 0.69657661783948 & 0.65171169108026 \tabularnewline
32 & 0.708270493012058 & 0.583459013975884 & 0.291729506987942 \tabularnewline
33 & 0.594740216237934 & 0.810519567524133 & 0.405259783762066 \tabularnewline
34 & 0.54782766782052 & 0.90434466435896 & 0.45217233217948 \tabularnewline
35 & 0.498366910491389 & 0.996733820982778 & 0.501633089508611 \tabularnewline
36 & 0.369362786686858 & 0.738725573373716 & 0.630637213313142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64376&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]20[/C][C]0.444609482169224[/C][C]0.889218964338448[/C][C]0.555390517830776[/C][/ROW]
[ROW][C]21[/C][C]0.331363661541434[/C][C]0.662727323082869[/C][C]0.668636338458566[/C][/ROW]
[ROW][C]22[/C][C]0.219802344045940[/C][C]0.439604688091879[/C][C]0.78019765595406[/C][/ROW]
[ROW][C]23[/C][C]0.396147561896778[/C][C]0.792295123793556[/C][C]0.603852438103222[/C][/ROW]
[ROW][C]24[/C][C]0.337892565477966[/C][C]0.675785130955932[/C][C]0.662107434522034[/C][/ROW]
[ROW][C]25[/C][C]0.286841858082224[/C][C]0.573683716164447[/C][C]0.713158141917776[/C][/ROW]
[ROW][C]26[/C][C]0.278514984570846[/C][C]0.557029969141691[/C][C]0.721485015429155[/C][/ROW]
[ROW][C]27[/C][C]0.303692115391616[/C][C]0.607384230783233[/C][C]0.696307884608384[/C][/ROW]
[ROW][C]28[/C][C]0.232324628376928[/C][C]0.464649256753855[/C][C]0.767675371623072[/C][/ROW]
[ROW][C]29[/C][C]0.157637251458795[/C][C]0.315274502917589[/C][C]0.842362748541205[/C][/ROW]
[ROW][C]30[/C][C]0.113104715705583[/C][C]0.226209431411165[/C][C]0.886895284294417[/C][/ROW]
[ROW][C]31[/C][C]0.34828830891974[/C][C]0.69657661783948[/C][C]0.65171169108026[/C][/ROW]
[ROW][C]32[/C][C]0.708270493012058[/C][C]0.583459013975884[/C][C]0.291729506987942[/C][/ROW]
[ROW][C]33[/C][C]0.594740216237934[/C][C]0.810519567524133[/C][C]0.405259783762066[/C][/ROW]
[ROW][C]34[/C][C]0.54782766782052[/C][C]0.90434466435896[/C][C]0.45217233217948[/C][/ROW]
[ROW][C]35[/C][C]0.498366910491389[/C][C]0.996733820982778[/C][C]0.501633089508611[/C][/ROW]
[ROW][C]36[/C][C]0.369362786686858[/C][C]0.738725573373716[/C][C]0.630637213313142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64376&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64376&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
200.4446094821692240.8892189643384480.555390517830776
210.3313636615414340.6627273230828690.668636338458566
220.2198023440459400.4396046880918790.78019765595406
230.3961475618967780.7922951237935560.603852438103222
240.3378925654779660.6757851309559320.662107434522034
250.2868418580822240.5736837161644470.713158141917776
260.2785149845708460.5570299691416910.721485015429155
270.3036921153916160.6073842307832330.696307884608384
280.2323246283769280.4646492567538550.767675371623072
290.1576372514587950.3152745029175890.842362748541205
300.1131047157055830.2262094314111650.886895284294417
310.348288308919740.696576617839480.65171169108026
320.7082704930120580.5834590139758840.291729506987942
330.5947402162379340.8105195675241330.405259783762066
340.547827667820520.904344664358960.45217233217948
350.4983669104913890.9967338209827780.501633089508611
360.3693627866868580.7387255733737160.630637213313142






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=64376&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=64376&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64376&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 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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')
}