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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 computationTue, 08 Dec 2009 13:02:18 -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/08/t1260302576k5levdxqldmym82.htm/, Retrieved Sun, 28 Apr 2024 10:15:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64827, Retrieved Sun, 28 Apr 2024 10:15:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact221

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] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   PD            [Multiple Regression] [multiple regressi...] [2009-12-08 20:02:18] [87085ce7f5378f281469a8b1f0969170] [Current]
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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 time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64827&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]4 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=64827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64827&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 1.3149507910685 -0.159167600444823Infl[t] + 0.93632565514663`M1(t)`[t] + 0.263924400008708`M2(t)`[t] -0.615614209427212`M3(t)`[t] + 0.282631398300656`M4(t)`[t] + 0.00902777251121043M1[t] -0.235331015871518M2[t] -0.221374298920867M3[t] -0.229468739745328M4[t] + 0.00109145062266700M5[t] -0.145332830885047M6[t] -0.0930736443421092M7[t] + 0.129767183891330M8[t] + 0.127508000172792M9[t] -0.142573675824709M10[t] -0.305949943876932M11[t] -0.00289354687189115t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkl[t] =  +  1.3149507910685 -0.159167600444823Infl[t] +  0.93632565514663`M1(t)`[t] +  0.263924400008708`M2(t)`[t] -0.615614209427212`M3(t)`[t] +  0.282631398300656`M4(t)`[t] +  0.00902777251121043M1[t] -0.235331015871518M2[t] -0.221374298920867M3[t] -0.229468739745328M4[t] +  0.00109145062266700M5[t] -0.145332830885047M6[t] -0.0930736443421092M7[t] +  0.129767183891330M8[t] +  0.127508000172792M9[t] -0.142573675824709M10[t] -0.305949943876932M11[t] -0.00289354687189115t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64827&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkl[t] =  +  1.3149507910685 -0.159167600444823Infl[t] +  0.93632565514663`M1(t)`[t] +  0.263924400008708`M2(t)`[t] -0.615614209427212`M3(t)`[t] +  0.282631398300656`M4(t)`[t] +  0.00902777251121043M1[t] -0.235331015871518M2[t] -0.221374298920867M3[t] -0.229468739745328M4[t] +  0.00109145062266700M5[t] -0.145332830885047M6[t] -0.0930736443421092M7[t] +  0.129767183891330M8[t] +  0.127508000172792M9[t] -0.142573675824709M10[t] -0.305949943876932M11[t] -0.00289354687189115t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64827&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] = + 1.3149507910685 -0.159167600444823Infl[t] + 0.93632565514663`M1(t)`[t] + 0.263924400008708`M2(t)`[t] -0.615614209427212`M3(t)`[t] + 0.282631398300656`M4(t)`[t] + 0.00902777251121043M1[t] -0.235331015871518M2[t] -0.221374298920867M3[t] -0.229468739745328M4[t] + 0.00109145062266700M5[t] -0.145332830885047M6[t] -0.0930736443421092M7[t] + 0.129767183891330M8[t] + 0.127508000172792M9[t] -0.142573675824709M10[t] -0.305949943876932M11[t] -0.00289354687189115t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.31495079106850.4073213.22830.0025670.001284
Infl-0.1591676004448230.050855-3.12980.0033550.001678
`M1(t)`0.936325655146630.1560655.99961e-060
`M2(t)`0.2639244000087080.2000891.3190.195050.097525
`M3(t)`-0.6156142094272120.200768-3.06630.0039790.00199
`M4(t)`0.2826313983006560.1386632.03830.0485270.024264
M10.009027772511210430.1040920.08670.9313430.465671
M2-0.2353310158715180.118892-1.97940.0550540.027527
M3-0.2213742989208670.094345-2.34640.024270.012135
M4-0.2294687397453280.08815-2.60320.0131020.006551
M50.001091450622667000.0945690.01150.9908520.495426
M6-0.1453328308850470.112216-1.29510.2030920.101546
M7-0.09307364434210920.109827-0.84750.4020450.201023
M80.1297671838913300.0993591.3060.1993870.099694
M90.1275080001727920.1191081.07050.2911360.145568
M10-0.1425736758247090.12204-1.16830.2499820.124991
M11-0.3059499438769320.098625-3.10210.0036150.001807
t-0.002893546871891150.003718-0.77820.4412840.220642

\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) & 1.3149507910685 & 0.407321 & 3.2283 & 0.002567 & 0.001284 \tabularnewline
Infl & -0.159167600444823 & 0.050855 & -3.1298 & 0.003355 & 0.001678 \tabularnewline
`M1(t)` & 0.93632565514663 & 0.156065 & 5.9996 & 1e-06 & 0 \tabularnewline
`M2(t)` & 0.263924400008708 & 0.200089 & 1.319 & 0.19505 & 0.097525 \tabularnewline
`M3(t)` & -0.615614209427212 & 0.200768 & -3.0663 & 0.003979 & 0.00199 \tabularnewline
`M4(t)` & 0.282631398300656 & 0.138663 & 2.0383 & 0.048527 & 0.024264 \tabularnewline
M1 & 0.00902777251121043 & 0.104092 & 0.0867 & 0.931343 & 0.465671 \tabularnewline
M2 & -0.235331015871518 & 0.118892 & -1.9794 & 0.055054 & 0.027527 \tabularnewline
M3 & -0.221374298920867 & 0.094345 & -2.3464 & 0.02427 & 0.012135 \tabularnewline
M4 & -0.229468739745328 & 0.08815 & -2.6032 & 0.013102 & 0.006551 \tabularnewline
M5 & 0.00109145062266700 & 0.094569 & 0.0115 & 0.990852 & 0.495426 \tabularnewline
M6 & -0.145332830885047 & 0.112216 & -1.2951 & 0.203092 & 0.101546 \tabularnewline
M7 & -0.0930736443421092 & 0.109827 & -0.8475 & 0.402045 & 0.201023 \tabularnewline
M8 & 0.129767183891330 & 0.099359 & 1.306 & 0.199387 & 0.099694 \tabularnewline
M9 & 0.127508000172792 & 0.119108 & 1.0705 & 0.291136 & 0.145568 \tabularnewline
M10 & -0.142573675824709 & 0.12204 & -1.1683 & 0.249982 & 0.124991 \tabularnewline
M11 & -0.305949943876932 & 0.098625 & -3.1021 & 0.003615 & 0.001807 \tabularnewline
t & -0.00289354687189115 & 0.003718 & -0.7782 & 0.441284 & 0.220642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64827&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]1.3149507910685[/C][C]0.407321[/C][C]3.2283[/C][C]0.002567[/C][C]0.001284[/C][/ROW]
[ROW][C]Infl[/C][C]-0.159167600444823[/C][C]0.050855[/C][C]-3.1298[/C][C]0.003355[/C][C]0.001678[/C][/ROW]
[ROW][C]`M1(t)`[/C][C]0.93632565514663[/C][C]0.156065[/C][C]5.9996[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]`M2(t)`[/C][C]0.263924400008708[/C][C]0.200089[/C][C]1.319[/C][C]0.19505[/C][C]0.097525[/C][/ROW]
[ROW][C]`M3(t)`[/C][C]-0.615614209427212[/C][C]0.200768[/C][C]-3.0663[/C][C]0.003979[/C][C]0.00199[/C][/ROW]
[ROW][C]`M4(t)`[/C][C]0.282631398300656[/C][C]0.138663[/C][C]2.0383[/C][C]0.048527[/C][C]0.024264[/C][/ROW]
[ROW][C]M1[/C][C]0.00902777251121043[/C][C]0.104092[/C][C]0.0867[/C][C]0.931343[/C][C]0.465671[/C][/ROW]
[ROW][C]M2[/C][C]-0.235331015871518[/C][C]0.118892[/C][C]-1.9794[/C][C]0.055054[/C][C]0.027527[/C][/ROW]
[ROW][C]M3[/C][C]-0.221374298920867[/C][C]0.094345[/C][C]-2.3464[/C][C]0.02427[/C][C]0.012135[/C][/ROW]
[ROW][C]M4[/C][C]-0.229468739745328[/C][C]0.08815[/C][C]-2.6032[/C][C]0.013102[/C][C]0.006551[/C][/ROW]
[ROW][C]M5[/C][C]0.00109145062266700[/C][C]0.094569[/C][C]0.0115[/C][C]0.990852[/C][C]0.495426[/C][/ROW]
[ROW][C]M6[/C][C]-0.145332830885047[/C][C]0.112216[/C][C]-1.2951[/C][C]0.203092[/C][C]0.101546[/C][/ROW]
[ROW][C]M7[/C][C]-0.0930736443421092[/C][C]0.109827[/C][C]-0.8475[/C][C]0.402045[/C][C]0.201023[/C][/ROW]
[ROW][C]M8[/C][C]0.129767183891330[/C][C]0.099359[/C][C]1.306[/C][C]0.199387[/C][C]0.099694[/C][/ROW]
[ROW][C]M9[/C][C]0.127508000172792[/C][C]0.119108[/C][C]1.0705[/C][C]0.291136[/C][C]0.145568[/C][/ROW]
[ROW][C]M10[/C][C]-0.142573675824709[/C][C]0.12204[/C][C]-1.1683[/C][C]0.249982[/C][C]0.124991[/C][/ROW]
[ROW][C]M11[/C][C]-0.305949943876932[/C][C]0.098625[/C][C]-3.1021[/C][C]0.003615[/C][C]0.001807[/C][/ROW]
[ROW][C]t[/C][C]-0.00289354687189115[/C][C]0.003718[/C][C]-0.7782[/C][C]0.441284[/C][C]0.220642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64827&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64827&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)1.31495079106850.4073213.22830.0025670.001284
Infl-0.1591676004448230.050855-3.12980.0033550.001678
`M1(t)`0.936325655146630.1560655.99961e-060
`M2(t)`0.2639244000087080.2000891.3190.195050.097525
`M3(t)`-0.6156142094272120.200768-3.06630.0039790.00199
`M4(t)`0.2826313983006560.1386632.03830.0485270.024264
M10.009027772511210430.1040920.08670.9313430.465671
M2-0.2353310158715180.118892-1.97940.0550540.027527
M3-0.2213742989208670.094345-2.34640.024270.012135
M4-0.2294687397453280.08815-2.60320.0131020.006551
M50.001091450622667000.0945690.01150.9908520.495426
M6-0.1453328308850470.112216-1.29510.2030920.101546
M7-0.09307364434210920.109827-0.84750.4020450.201023
M80.1297671838913300.0993591.3060.1993870.099694
M90.1275080001727920.1191081.07050.2911360.145568
M10-0.1425736758247090.12204-1.16830.2499820.124991
M11-0.3059499438769320.098625-3.10210.0036150.001807
t-0.002893546871891150.003718-0.77820.4412840.220642






Multiple Linear Regression - Regression Statistics
Multiple R0.996857337303617
R-squared0.993724550936056
Adjusted R-squared0.990917113196924
F-TEST (value)353.961385175043
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.117470646184170
Sum Squared Residuals0.524375403167206

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996857337303617 \tabularnewline
R-squared & 0.993724550936056 \tabularnewline
Adjusted R-squared & 0.990917113196924 \tabularnewline
F-TEST (value) & 353.961385175043 \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 & 0.117470646184170 \tabularnewline
Sum Squared Residuals & 0.524375403167206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64827&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996857337303617[/C][/ROW]
[ROW][C]R-squared[/C][C]0.993724550936056[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.990917113196924[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]353.961385175043[/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]0.117470646184170[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.524375403167206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64827&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64827&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 R0.996857337303617
R-squared0.993724550936056
Adjusted R-squared0.990917113196924
F-TEST (value)353.961385175043
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.117470646184170
Sum Squared Residuals0.524375403167206






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13.43.294407690460730.105592309539265
23.43.371589929750470.0284100702495298
33.53.396293221239010.103706778760986
43.23.31163505729733-0.111635057297334
53.33.34132272391045-0.0413227239104506
63.33.208565760278100.0914342397218962
73.43.51318800265273-0.113188002652732
83.73.648583489007060.0514165109929393
93.94.04265107496949-0.142651074969486
1044.00639040227828-0.00639040227827651
113.73.86195042996143-0.161950429961433
123.93.872168148028110.0278318519718896
134.24.0291053235450.170894676455
144.44.312566207449860.0874337925501418
154.34.38215956718492-0.0821595671849184
164.24.21808267085209-0.0180826708520933
174.34.287390886437420.0126091135625819
184.34.33931764421894-0.0393176442189398
194.34.46429076504799-0.164290765047995
204.54.59441348563676-0.0944134856367557
2154.91620634621710.0837936537829061
225.25.164178830922760.0358211690772407
235.25.194013505146880.00598649485311761
245.45.346324237233640.0536757627663631
255.55.57383321121165-0.0738332112116506
265.45.52952460113357-0.129524601133567
275.55.334308043768610.165691956231390
285.45.385525040303460.0144749596965406
295.75.651692879103040.04830712089696
305.75.667055746493770.0329442535062332
316.15.885423266940210.214576733059787
326.56.314703687835630.185296312164370
336.96.93810743897546-0.0381074389754614
346.86.9149033144418-0.114903314441804
356.76.643294329600370.0567056703996318
366.66.6453823165058-0.0453823165058071
376.56.69018875684809-0.190188756848094
386.46.372126457235080.0278735427649223
396.16.3442131830444-0.244213183044407
406.26.059233339915850.140766660084151
416.36.35057027008114-0.050570270081142
426.46.41403153003724-0.0140315300372397
436.56.452988094835380.0470119051646153
446.76.77557886064429-0.0755788606442928
4576.903035139837960.0969648601620419
4676.914527452357160.08547254764284
476.86.700741735291320.0992582647086835
486.76.73612529823245-0.0361252982324452
496.76.71246501793452-0.0124650179345213
506.56.51419280443103-0.0141928044310276
516.46.343025984763050.0569740152369497
526.16.12552389163126-0.0255238916312643
536.26.169023240467950.0309767595320506
5466.07102931897195-0.0710293189719499
556.16.084109870523680.0158901294763247
566.16.16672047687626-0.0667204768762612

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3.4 & 3.29440769046073 & 0.105592309539265 \tabularnewline
2 & 3.4 & 3.37158992975047 & 0.0284100702495298 \tabularnewline
3 & 3.5 & 3.39629322123901 & 0.103706778760986 \tabularnewline
4 & 3.2 & 3.31163505729733 & -0.111635057297334 \tabularnewline
5 & 3.3 & 3.34132272391045 & -0.0413227239104506 \tabularnewline
6 & 3.3 & 3.20856576027810 & 0.0914342397218962 \tabularnewline
7 & 3.4 & 3.51318800265273 & -0.113188002652732 \tabularnewline
8 & 3.7 & 3.64858348900706 & 0.0514165109929393 \tabularnewline
9 & 3.9 & 4.04265107496949 & -0.142651074969486 \tabularnewline
10 & 4 & 4.00639040227828 & -0.00639040227827651 \tabularnewline
11 & 3.7 & 3.86195042996143 & -0.161950429961433 \tabularnewline
12 & 3.9 & 3.87216814802811 & 0.0278318519718896 \tabularnewline
13 & 4.2 & 4.029105323545 & 0.170894676455 \tabularnewline
14 & 4.4 & 4.31256620744986 & 0.0874337925501418 \tabularnewline
15 & 4.3 & 4.38215956718492 & -0.0821595671849184 \tabularnewline
16 & 4.2 & 4.21808267085209 & -0.0180826708520933 \tabularnewline
17 & 4.3 & 4.28739088643742 & 0.0126091135625819 \tabularnewline
18 & 4.3 & 4.33931764421894 & -0.0393176442189398 \tabularnewline
19 & 4.3 & 4.46429076504799 & -0.164290765047995 \tabularnewline
20 & 4.5 & 4.59441348563676 & -0.0944134856367557 \tabularnewline
21 & 5 & 4.9162063462171 & 0.0837936537829061 \tabularnewline
22 & 5.2 & 5.16417883092276 & 0.0358211690772407 \tabularnewline
23 & 5.2 & 5.19401350514688 & 0.00598649485311761 \tabularnewline
24 & 5.4 & 5.34632423723364 & 0.0536757627663631 \tabularnewline
25 & 5.5 & 5.57383321121165 & -0.0738332112116506 \tabularnewline
26 & 5.4 & 5.52952460113357 & -0.129524601133567 \tabularnewline
27 & 5.5 & 5.33430804376861 & 0.165691956231390 \tabularnewline
28 & 5.4 & 5.38552504030346 & 0.0144749596965406 \tabularnewline
29 & 5.7 & 5.65169287910304 & 0.04830712089696 \tabularnewline
30 & 5.7 & 5.66705574649377 & 0.0329442535062332 \tabularnewline
31 & 6.1 & 5.88542326694021 & 0.214576733059787 \tabularnewline
32 & 6.5 & 6.31470368783563 & 0.185296312164370 \tabularnewline
33 & 6.9 & 6.93810743897546 & -0.0381074389754614 \tabularnewline
34 & 6.8 & 6.9149033144418 & -0.114903314441804 \tabularnewline
35 & 6.7 & 6.64329432960037 & 0.0567056703996318 \tabularnewline
36 & 6.6 & 6.6453823165058 & -0.0453823165058071 \tabularnewline
37 & 6.5 & 6.69018875684809 & -0.190188756848094 \tabularnewline
38 & 6.4 & 6.37212645723508 & 0.0278735427649223 \tabularnewline
39 & 6.1 & 6.3442131830444 & -0.244213183044407 \tabularnewline
40 & 6.2 & 6.05923333991585 & 0.140766660084151 \tabularnewline
41 & 6.3 & 6.35057027008114 & -0.050570270081142 \tabularnewline
42 & 6.4 & 6.41403153003724 & -0.0140315300372397 \tabularnewline
43 & 6.5 & 6.45298809483538 & 0.0470119051646153 \tabularnewline
44 & 6.7 & 6.77557886064429 & -0.0755788606442928 \tabularnewline
45 & 7 & 6.90303513983796 & 0.0969648601620419 \tabularnewline
46 & 7 & 6.91452745235716 & 0.08547254764284 \tabularnewline
47 & 6.8 & 6.70074173529132 & 0.0992582647086835 \tabularnewline
48 & 6.7 & 6.73612529823245 & -0.0361252982324452 \tabularnewline
49 & 6.7 & 6.71246501793452 & -0.0124650179345213 \tabularnewline
50 & 6.5 & 6.51419280443103 & -0.0141928044310276 \tabularnewline
51 & 6.4 & 6.34302598476305 & 0.0569740152369497 \tabularnewline
52 & 6.1 & 6.12552389163126 & -0.0255238916312643 \tabularnewline
53 & 6.2 & 6.16902324046795 & 0.0309767595320506 \tabularnewline
54 & 6 & 6.07102931897195 & -0.0710293189719499 \tabularnewline
55 & 6.1 & 6.08410987052368 & 0.0158901294763247 \tabularnewline
56 & 6.1 & 6.16672047687626 & -0.0667204768762612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64827&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]3.29440769046073[/C][C]0.105592309539265[/C][/ROW]
[ROW][C]2[/C][C]3.4[/C][C]3.37158992975047[/C][C]0.0284100702495298[/C][/ROW]
[ROW][C]3[/C][C]3.5[/C][C]3.39629322123901[/C][C]0.103706778760986[/C][/ROW]
[ROW][C]4[/C][C]3.2[/C][C]3.31163505729733[/C][C]-0.111635057297334[/C][/ROW]
[ROW][C]5[/C][C]3.3[/C][C]3.34132272391045[/C][C]-0.0413227239104506[/C][/ROW]
[ROW][C]6[/C][C]3.3[/C][C]3.20856576027810[/C][C]0.0914342397218962[/C][/ROW]
[ROW][C]7[/C][C]3.4[/C][C]3.51318800265273[/C][C]-0.113188002652732[/C][/ROW]
[ROW][C]8[/C][C]3.7[/C][C]3.64858348900706[/C][C]0.0514165109929393[/C][/ROW]
[ROW][C]9[/C][C]3.9[/C][C]4.04265107496949[/C][C]-0.142651074969486[/C][/ROW]
[ROW][C]10[/C][C]4[/C][C]4.00639040227828[/C][C]-0.00639040227827651[/C][/ROW]
[ROW][C]11[/C][C]3.7[/C][C]3.86195042996143[/C][C]-0.161950429961433[/C][/ROW]
[ROW][C]12[/C][C]3.9[/C][C]3.87216814802811[/C][C]0.0278318519718896[/C][/ROW]
[ROW][C]13[/C][C]4.2[/C][C]4.029105323545[/C][C]0.170894676455[/C][/ROW]
[ROW][C]14[/C][C]4.4[/C][C]4.31256620744986[/C][C]0.0874337925501418[/C][/ROW]
[ROW][C]15[/C][C]4.3[/C][C]4.38215956718492[/C][C]-0.0821595671849184[/C][/ROW]
[ROW][C]16[/C][C]4.2[/C][C]4.21808267085209[/C][C]-0.0180826708520933[/C][/ROW]
[ROW][C]17[/C][C]4.3[/C][C]4.28739088643742[/C][C]0.0126091135625819[/C][/ROW]
[ROW][C]18[/C][C]4.3[/C][C]4.33931764421894[/C][C]-0.0393176442189398[/C][/ROW]
[ROW][C]19[/C][C]4.3[/C][C]4.46429076504799[/C][C]-0.164290765047995[/C][/ROW]
[ROW][C]20[/C][C]4.5[/C][C]4.59441348563676[/C][C]-0.0944134856367557[/C][/ROW]
[ROW][C]21[/C][C]5[/C][C]4.9162063462171[/C][C]0.0837936537829061[/C][/ROW]
[ROW][C]22[/C][C]5.2[/C][C]5.16417883092276[/C][C]0.0358211690772407[/C][/ROW]
[ROW][C]23[/C][C]5.2[/C][C]5.19401350514688[/C][C]0.00598649485311761[/C][/ROW]
[ROW][C]24[/C][C]5.4[/C][C]5.34632423723364[/C][C]0.0536757627663631[/C][/ROW]
[ROW][C]25[/C][C]5.5[/C][C]5.57383321121165[/C][C]-0.0738332112116506[/C][/ROW]
[ROW][C]26[/C][C]5.4[/C][C]5.52952460113357[/C][C]-0.129524601133567[/C][/ROW]
[ROW][C]27[/C][C]5.5[/C][C]5.33430804376861[/C][C]0.165691956231390[/C][/ROW]
[ROW][C]28[/C][C]5.4[/C][C]5.38552504030346[/C][C]0.0144749596965406[/C][/ROW]
[ROW][C]29[/C][C]5.7[/C][C]5.65169287910304[/C][C]0.04830712089696[/C][/ROW]
[ROW][C]30[/C][C]5.7[/C][C]5.66705574649377[/C][C]0.0329442535062332[/C][/ROW]
[ROW][C]31[/C][C]6.1[/C][C]5.88542326694021[/C][C]0.214576733059787[/C][/ROW]
[ROW][C]32[/C][C]6.5[/C][C]6.31470368783563[/C][C]0.185296312164370[/C][/ROW]
[ROW][C]33[/C][C]6.9[/C][C]6.93810743897546[/C][C]-0.0381074389754614[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]6.9149033144418[/C][C]-0.114903314441804[/C][/ROW]
[ROW][C]35[/C][C]6.7[/C][C]6.64329432960037[/C][C]0.0567056703996318[/C][/ROW]
[ROW][C]36[/C][C]6.6[/C][C]6.6453823165058[/C][C]-0.0453823165058071[/C][/ROW]
[ROW][C]37[/C][C]6.5[/C][C]6.69018875684809[/C][C]-0.190188756848094[/C][/ROW]
[ROW][C]38[/C][C]6.4[/C][C]6.37212645723508[/C][C]0.0278735427649223[/C][/ROW]
[ROW][C]39[/C][C]6.1[/C][C]6.3442131830444[/C][C]-0.244213183044407[/C][/ROW]
[ROW][C]40[/C][C]6.2[/C][C]6.05923333991585[/C][C]0.140766660084151[/C][/ROW]
[ROW][C]41[/C][C]6.3[/C][C]6.35057027008114[/C][C]-0.050570270081142[/C][/ROW]
[ROW][C]42[/C][C]6.4[/C][C]6.41403153003724[/C][C]-0.0140315300372397[/C][/ROW]
[ROW][C]43[/C][C]6.5[/C][C]6.45298809483538[/C][C]0.0470119051646153[/C][/ROW]
[ROW][C]44[/C][C]6.7[/C][C]6.77557886064429[/C][C]-0.0755788606442928[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]6.90303513983796[/C][C]0.0969648601620419[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]6.91452745235716[/C][C]0.08547254764284[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.70074173529132[/C][C]0.0992582647086835[/C][/ROW]
[ROW][C]48[/C][C]6.7[/C][C]6.73612529823245[/C][C]-0.0361252982324452[/C][/ROW]
[ROW][C]49[/C][C]6.7[/C][C]6.71246501793452[/C][C]-0.0124650179345213[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.51419280443103[/C][C]-0.0141928044310276[/C][/ROW]
[ROW][C]51[/C][C]6.4[/C][C]6.34302598476305[/C][C]0.0569740152369497[/C][/ROW]
[ROW][C]52[/C][C]6.1[/C][C]6.12552389163126[/C][C]-0.0255238916312643[/C][/ROW]
[ROW][C]53[/C][C]6.2[/C][C]6.16902324046795[/C][C]0.0309767595320506[/C][/ROW]
[ROW][C]54[/C][C]6[/C][C]6.07102931897195[/C][C]-0.0710293189719499[/C][/ROW]
[ROW][C]55[/C][C]6.1[/C][C]6.08410987052368[/C][C]0.0158901294763247[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]6.16672047687626[/C][C]-0.0667204768762612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64827&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64827&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
13.43.294407690460730.105592309539265
23.43.371589929750470.0284100702495298
33.53.396293221239010.103706778760986
43.23.31163505729733-0.111635057297334
53.33.34132272391045-0.0413227239104506
63.33.208565760278100.0914342397218962
73.43.51318800265273-0.113188002652732
83.73.648583489007060.0514165109929393
93.94.04265107496949-0.142651074969486
1044.00639040227828-0.00639040227827651
113.73.86195042996143-0.161950429961433
123.93.872168148028110.0278318519718896
134.24.0291053235450.170894676455
144.44.312566207449860.0874337925501418
154.34.38215956718492-0.0821595671849184
164.24.21808267085209-0.0180826708520933
174.34.287390886437420.0126091135625819
184.34.33931764421894-0.0393176442189398
194.34.46429076504799-0.164290765047995
204.54.59441348563676-0.0944134856367557
2154.91620634621710.0837936537829061
225.25.164178830922760.0358211690772407
235.25.194013505146880.00598649485311761
245.45.346324237233640.0536757627663631
255.55.57383321121165-0.0738332112116506
265.45.52952460113357-0.129524601133567
275.55.334308043768610.165691956231390
285.45.385525040303460.0144749596965406
295.75.651692879103040.04830712089696
305.75.667055746493770.0329442535062332
316.15.885423266940210.214576733059787
326.56.314703687835630.185296312164370
336.96.93810743897546-0.0381074389754614
346.86.9149033144418-0.114903314441804
356.76.643294329600370.0567056703996318
366.66.6453823165058-0.0453823165058071
376.56.69018875684809-0.190188756848094
386.46.372126457235080.0278735427649223
396.16.3442131830444-0.244213183044407
406.26.059233339915850.140766660084151
416.36.35057027008114-0.050570270081142
426.46.41403153003724-0.0140315300372397
436.56.452988094835380.0470119051646153
446.76.77557886064429-0.0755788606442928
4576.903035139837960.0969648601620419
4676.914527452357160.08547254764284
476.86.700741735291320.0992582647086835
486.76.73612529823245-0.0361252982324452
496.76.71246501793452-0.0124650179345213
506.56.51419280443103-0.0141928044310276
516.46.343025984763050.0569740152369497
526.16.12552389163126-0.0255238916312643
536.26.169023240467950.0309767595320506
5466.07102931897195-0.0710293189719499
556.16.084109870523680.0158901294763247
566.16.16672047687626-0.0667204768762612






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.5042316360932840.9915367278134310.495768363906716
220.3649751224519970.7299502449039940.635024877548003
230.3629609753276180.7259219506552350.637039024672382
240.2741321413322870.5482642826645730.725867858667713
250.3687984711873730.7375969423747460.631201528812627
260.2855922172696050.571184434539210.714407782730395
270.3612077356674810.7224154713349630.638792264332519
280.2647426798153730.5294853596307470.735257320184627
290.1751911295698960.3503822591397930.824808870430104
300.1293074657076380.2586149314152750.870692534292362
310.3445953685034010.6891907370068010.6554046314966
320.6464115837731640.7071768324536720.353588416226836
330.5166953286328280.9666093427343440.483304671367172
340.4779134873139890.9558269746279780.522086512686011
350.6747820051983450.650435989603310.325217994801655

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.504231636093284 & 0.991536727813431 & 0.495768363906716 \tabularnewline
22 & 0.364975122451997 & 0.729950244903994 & 0.635024877548003 \tabularnewline
23 & 0.362960975327618 & 0.725921950655235 & 0.637039024672382 \tabularnewline
24 & 0.274132141332287 & 0.548264282664573 & 0.725867858667713 \tabularnewline
25 & 0.368798471187373 & 0.737596942374746 & 0.631201528812627 \tabularnewline
26 & 0.285592217269605 & 0.57118443453921 & 0.714407782730395 \tabularnewline
27 & 0.361207735667481 & 0.722415471334963 & 0.638792264332519 \tabularnewline
28 & 0.264742679815373 & 0.529485359630747 & 0.735257320184627 \tabularnewline
29 & 0.175191129569896 & 0.350382259139793 & 0.824808870430104 \tabularnewline
30 & 0.129307465707638 & 0.258614931415275 & 0.870692534292362 \tabularnewline
31 & 0.344595368503401 & 0.689190737006801 & 0.6554046314966 \tabularnewline
32 & 0.646411583773164 & 0.707176832453672 & 0.353588416226836 \tabularnewline
33 & 0.516695328632828 & 0.966609342734344 & 0.483304671367172 \tabularnewline
34 & 0.477913487313989 & 0.955826974627978 & 0.522086512686011 \tabularnewline
35 & 0.674782005198345 & 0.65043598960331 & 0.325217994801655 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64827&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]0.504231636093284[/C][C]0.991536727813431[/C][C]0.495768363906716[/C][/ROW]
[ROW][C]22[/C][C]0.364975122451997[/C][C]0.729950244903994[/C][C]0.635024877548003[/C][/ROW]
[ROW][C]23[/C][C]0.362960975327618[/C][C]0.725921950655235[/C][C]0.637039024672382[/C][/ROW]
[ROW][C]24[/C][C]0.274132141332287[/C][C]0.548264282664573[/C][C]0.725867858667713[/C][/ROW]
[ROW][C]25[/C][C]0.368798471187373[/C][C]0.737596942374746[/C][C]0.631201528812627[/C][/ROW]
[ROW][C]26[/C][C]0.285592217269605[/C][C]0.57118443453921[/C][C]0.714407782730395[/C][/ROW]
[ROW][C]27[/C][C]0.361207735667481[/C][C]0.722415471334963[/C][C]0.638792264332519[/C][/ROW]
[ROW][C]28[/C][C]0.264742679815373[/C][C]0.529485359630747[/C][C]0.735257320184627[/C][/ROW]
[ROW][C]29[/C][C]0.175191129569896[/C][C]0.350382259139793[/C][C]0.824808870430104[/C][/ROW]
[ROW][C]30[/C][C]0.129307465707638[/C][C]0.258614931415275[/C][C]0.870692534292362[/C][/ROW]
[ROW][C]31[/C][C]0.344595368503401[/C][C]0.689190737006801[/C][C]0.6554046314966[/C][/ROW]
[ROW][C]32[/C][C]0.646411583773164[/C][C]0.707176832453672[/C][C]0.353588416226836[/C][/ROW]
[ROW][C]33[/C][C]0.516695328632828[/C][C]0.966609342734344[/C][C]0.483304671367172[/C][/ROW]
[ROW][C]34[/C][C]0.477913487313989[/C][C]0.955826974627978[/C][C]0.522086512686011[/C][/ROW]
[ROW][C]35[/C][C]0.674782005198345[/C][C]0.65043598960331[/C][C]0.325217994801655[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64827&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64827&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
210.5042316360932840.9915367278134310.495768363906716
220.3649751224519970.7299502449039940.635024877548003
230.3629609753276180.7259219506552350.637039024672382
240.2741321413322870.5482642826645730.725867858667713
250.3687984711873730.7375969423747460.631201528812627
260.2855922172696050.571184434539210.714407782730395
270.3612077356674810.7224154713349630.638792264332519
280.2647426798153730.5294853596307470.735257320184627
290.1751911295698960.3503822591397930.824808870430104
300.1293074657076380.2586149314152750.870692534292362
310.3445953685034010.6891907370068010.6554046314966
320.6464115837731640.7071768324536720.353588416226836
330.5166953286328280.9666093427343440.483304671367172
340.4779134873139890.9558269746279780.522086512686011
350.6747820051983450.650435989603310.325217994801655






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=64827&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=64827&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64827&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')
}