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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 computationFri, 20 Nov 2009 06:35:13 -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/20/t1258724199e7wrt13al51a1z5.htm/, Retrieved Wed, 19 Nov 2025 23:15:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58149, Retrieved Wed, 19 Nov 2025 23:15:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws72lags
Estimated Impact414

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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-18 16:49:45] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D      [Multiple Regression] [] [2009-11-20 13:30:42] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D          [Multiple Regression] [] [2009-11-20 13:35:13] [2b548c9d2e9bba6e1eaf65bd4d551f41] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,70	110,30	8,10	8,00
7,50	103,90	7,70	8,10
7,60	101,60	7,50	7,70
7,80	94,60	7,60	7,50
7,80	95,90	7,80	7,60
7,80	104,70	7,80	7,80
7,50	102,80	7,80	7,80
7,50	98,10	7,50	7,80
7,10	113,90	7,50	7,50
7,50	80,90	7,10	7,50
7,50	95,70	7,50	7,10
7,60	113,20	7,50	7,50
7,70	105,90	7,60	7,50
7,70	108,80	7,70	7,60
7,90	102,30	7,70	7,70
8,10	99,00	7,90	7,70
8,20	100,70	8,10	7,90
8,20	115,50	8,20	8,10
8,20	100,70	8,20	8,20
7,90	109,90	8,20	8,20
7,30	114,60	7,90	8,20
6,90	85,40	7,30	7,90
6,60	100,50	6,90	7,30
6,70	114,80	6,60	6,90
6,90	116,50	6,70	6,60
7,00	112,90	6,90	6,70
7,10	102,00	7,00	6,90
7,20	106,00	7,10	7,00
7,10	105,30	7,20	7,10
6,90	118,80	7,10	7,20
7,00	106,10	6,90	7,10
6,80	109,30	7,00	6,90
6,40	117,20	6,80	7,00
6,70	92,50	6,40	6,80
6,60	104,20	6,70	6,40
6,40	112,50	6,60	6,70
6,30	122,40	6,40	6,60
6,20	113,30	6,30	6,40
6,50	100,00	6,20	6,30
6,80	110,70	6,50	6,20
6,80	112,80	6,80	6,50
6,40	109,80	6,80	6,80
6,10	117,30	6,40	6,80
5,80	109,10	6,10	6,40
6,10	115,90	5,80	6,10
7,20	96,00	6,10	5,80
7,30	99,80	7,20	6,10
6,90	116,80	7,30	7,20
6,10	115,70	6,90	7,30
5,80	99,40	6,10	6,90
6,20	94,30	5,80	6,10
7,10	91,00	6,20	5,80
7,70	93,20	7,10	6,20
7,90	103,10	7,70	7,10
7,70	94,10	7,90	7,70
7,40	91,80	7,70	7,90
7,50	102,70	7,40	7,70
8,00	82,60	7,50	7,40

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=58149&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=58149&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58149&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
Y[t] = + 4.07580781441513 -0.0165836837962970X[t] + 1.37883885721972Y1[t] -0.67582544891961Y2[t] -0.0963430856947516M1[t] -0.0639092820674027M2[t] + 0.0374513471373744M3[t] + 0.0151821678867695M4[t] -0.1580414784M5[t] -0.0227755674317749M6[t] -0.0688470670504502M7[t] -0.154153022084673M8[t] + 0.0124870320512885M9[t] + 0.10368881377741M10[t] -0.481693411399994M11[t] -0.00500950379451003t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  4.07580781441513 -0.0165836837962970X[t] +  1.37883885721972Y1[t] -0.67582544891961Y2[t] -0.0963430856947516M1[t] -0.0639092820674027M2[t] +  0.0374513471373744M3[t] +  0.0151821678867695M4[t] -0.1580414784M5[t] -0.0227755674317749M6[t] -0.0688470670504502M7[t] -0.154153022084673M8[t] +  0.0124870320512885M9[t] +  0.10368881377741M10[t] -0.481693411399994M11[t] -0.00500950379451003t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58149&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  4.07580781441513 -0.0165836837962970X[t] +  1.37883885721972Y1[t] -0.67582544891961Y2[t] -0.0963430856947516M1[t] -0.0639092820674027M2[t] +  0.0374513471373744M3[t] +  0.0151821678867695M4[t] -0.1580414784M5[t] -0.0227755674317749M6[t] -0.0688470670504502M7[t] -0.154153022084673M8[t] +  0.0124870320512885M9[t] +  0.10368881377741M10[t] -0.481693411399994M11[t] -0.00500950379451003t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58149&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58149&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
Y[t] = + 4.07580781441513 -0.0165836837962970X[t] + 1.37883885721972Y1[t] -0.67582544891961Y2[t] -0.0963430856947516M1[t] -0.0639092820674027M2[t] + 0.0374513471373744M3[t] + 0.0151821678867695M4[t] -0.1580414784M5[t] -0.0227755674317749M6[t] -0.0688470670504502M7[t] -0.154153022084673M8[t] + 0.0124870320512885M9[t] + 0.10368881377741M10[t] -0.481693411399994M11[t] -0.00500950379451003t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)4.075807814415131.0043994.0580.0002110.000105
X-0.01658368379629700.005499-3.01570.0043380.002169
Y11.378838857219720.11287512.215600
Y2-0.675825448919610.120155-5.62461e-061e-06
M1-0.09634308569475160.145639-0.66150.5118910.255946
M2-0.06390928206740270.151328-0.42230.6749430.337471
M30.03745134713737440.169160.22140.8258570.412929
M40.01518216788676950.1704990.0890.9294690.464735
M5-0.15804147840.16587-0.95280.3461410.173071
M6-0.02277556743177490.149099-0.15280.8793230.439661
M7-0.06884706705045020.153843-0.44750.6568040.328402
M8-0.1541530220846730.154904-0.99520.3253610.162681
M90.01248703205128850.1472770.08480.9328340.466417
M100.103688813777410.2070270.50080.6190940.309547
M11-0.4816934113999940.1816-2.65250.0112270.005614
t-0.005009503794510030.002393-2.09340.0423920.021196

\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) & 4.07580781441513 & 1.004399 & 4.058 & 0.000211 & 0.000105 \tabularnewline
X & -0.0165836837962970 & 0.005499 & -3.0157 & 0.004338 & 0.002169 \tabularnewline
Y1 & 1.37883885721972 & 0.112875 & 12.2156 & 0 & 0 \tabularnewline
Y2 & -0.67582544891961 & 0.120155 & -5.6246 & 1e-06 & 1e-06 \tabularnewline
M1 & -0.0963430856947516 & 0.145639 & -0.6615 & 0.511891 & 0.255946 \tabularnewline
M2 & -0.0639092820674027 & 0.151328 & -0.4223 & 0.674943 & 0.337471 \tabularnewline
M3 & 0.0374513471373744 & 0.16916 & 0.2214 & 0.825857 & 0.412929 \tabularnewline
M4 & 0.0151821678867695 & 0.170499 & 0.089 & 0.929469 & 0.464735 \tabularnewline
M5 & -0.1580414784 & 0.16587 & -0.9528 & 0.346141 & 0.173071 \tabularnewline
M6 & -0.0227755674317749 & 0.149099 & -0.1528 & 0.879323 & 0.439661 \tabularnewline
M7 & -0.0688470670504502 & 0.153843 & -0.4475 & 0.656804 & 0.328402 \tabularnewline
M8 & -0.154153022084673 & 0.154904 & -0.9952 & 0.325361 & 0.162681 \tabularnewline
M9 & 0.0124870320512885 & 0.147277 & 0.0848 & 0.932834 & 0.466417 \tabularnewline
M10 & 0.10368881377741 & 0.207027 & 0.5008 & 0.619094 & 0.309547 \tabularnewline
M11 & -0.481693411399994 & 0.1816 & -2.6525 & 0.011227 & 0.005614 \tabularnewline
t & -0.00500950379451003 & 0.002393 & -2.0934 & 0.042392 & 0.021196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58149&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]4.07580781441513[/C][C]1.004399[/C][C]4.058[/C][C]0.000211[/C][C]0.000105[/C][/ROW]
[ROW][C]X[/C][C]-0.0165836837962970[/C][C]0.005499[/C][C]-3.0157[/C][C]0.004338[/C][C]0.002169[/C][/ROW]
[ROW][C]Y1[/C][C]1.37883885721972[/C][C]0.112875[/C][C]12.2156[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.67582544891961[/C][C]0.120155[/C][C]-5.6246[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M1[/C][C]-0.0963430856947516[/C][C]0.145639[/C][C]-0.6615[/C][C]0.511891[/C][C]0.255946[/C][/ROW]
[ROW][C]M2[/C][C]-0.0639092820674027[/C][C]0.151328[/C][C]-0.4223[/C][C]0.674943[/C][C]0.337471[/C][/ROW]
[ROW][C]M3[/C][C]0.0374513471373744[/C][C]0.16916[/C][C]0.2214[/C][C]0.825857[/C][C]0.412929[/C][/ROW]
[ROW][C]M4[/C][C]0.0151821678867695[/C][C]0.170499[/C][C]0.089[/C][C]0.929469[/C][C]0.464735[/C][/ROW]
[ROW][C]M5[/C][C]-0.1580414784[/C][C]0.16587[/C][C]-0.9528[/C][C]0.346141[/C][C]0.173071[/C][/ROW]
[ROW][C]M6[/C][C]-0.0227755674317749[/C][C]0.149099[/C][C]-0.1528[/C][C]0.879323[/C][C]0.439661[/C][/ROW]
[ROW][C]M7[/C][C]-0.0688470670504502[/C][C]0.153843[/C][C]-0.4475[/C][C]0.656804[/C][C]0.328402[/C][/ROW]
[ROW][C]M8[/C][C]-0.154153022084673[/C][C]0.154904[/C][C]-0.9952[/C][C]0.325361[/C][C]0.162681[/C][/ROW]
[ROW][C]M9[/C][C]0.0124870320512885[/C][C]0.147277[/C][C]0.0848[/C][C]0.932834[/C][C]0.466417[/C][/ROW]
[ROW][C]M10[/C][C]0.10368881377741[/C][C]0.207027[/C][C]0.5008[/C][C]0.619094[/C][C]0.309547[/C][/ROW]
[ROW][C]M11[/C][C]-0.481693411399994[/C][C]0.1816[/C][C]-2.6525[/C][C]0.011227[/C][C]0.005614[/C][/ROW]
[ROW][C]t[/C][C]-0.00500950379451003[/C][C]0.002393[/C][C]-2.0934[/C][C]0.042392[/C][C]0.021196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58149&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58149&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)4.075807814415131.0043994.0580.0002110.000105
X-0.01658368379629700.005499-3.01570.0043380.002169
Y11.378838857219720.11287512.215600
Y2-0.675825448919610.120155-5.62461e-061e-06
M1-0.09634308569475160.145639-0.66150.5118910.255946
M2-0.06390928206740270.151328-0.42230.6749430.337471
M30.03745134713737440.169160.22140.8258570.412929
M40.01518216788676950.1704990.0890.9294690.464735
M5-0.15804147840.16587-0.95280.3461410.173071
M6-0.02277556743177490.149099-0.15280.8793230.439661
M7-0.06884706705045020.153843-0.44750.6568040.328402
M8-0.1541530220846730.154904-0.99520.3253610.162681
M90.01248703205128850.1472770.08480.9328340.466417
M100.103688813777410.2070270.50080.6190940.309547
M11-0.4816934113999940.1816-2.65250.0112270.005614
t-0.005009503794510030.002393-2.09340.0423920.021196






Multiple Linear Regression - Regression Statistics
Multiple R0.957899251774148
R-squared0.917570976549472
Adjusted R-squared0.888132039602854
F-TEST (value)31.168617882274
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.216671744732013
Sum Squared Residuals1.97175908853902

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.957899251774148 \tabularnewline
R-squared & 0.917570976549472 \tabularnewline
Adjusted R-squared & 0.888132039602854 \tabularnewline
F-TEST (value) & 31.168617882274 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.216671744732013 \tabularnewline
Sum Squared Residuals & 1.97175908853902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58149&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.957899251774148[/C][/ROW]
[ROW][C]R-squared[/C][C]0.917570976549472[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.888132039602854[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]31.168617882274[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/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]0.216671744732013[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.97175908853902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58149&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58149&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 R0.957899251774148
R-squared0.917570976549472
Adjusted R-squared0.888132039602854
F-TEST (value)31.168617882274
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.216671744732013
Sum Squared Residuals1.97175908853902






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.77.9072660543172-0.2072660543172
27.57.421707842666480.0782921573335173
37.67.550763848932130.0492361510678705
47.87.91261992796699-0.112619927966989
57.87.92101321550251-0.121013215502508
67.87.770168115484890.0298318845151131
77.57.75059611128467-0.250596111284665
87.57.324572309132610.175427690867388
97.17.42692829016845-0.326928290168453
107.57.50884659048998-0.00884659048997798
117.57.49488206378860.00511793621139902
127.67.411021325391040.188978674608957
137.77.568613513336720.131386486663279
147.77.618246470990310.0817535290096892
157.97.754808996184550.145191003815453
168.18.058024241111160.041975758888842
178.27.99220151023620.207798489763805
188.27.879738193162760.320261806837236
198.28.006513165042810.193486834957186
207.97.763627815288150.136372184711853
217.37.43366339462109-0.133663394621088
226.97.37954355974862-0.479543559748621
236.66.39269793191650.2073020680835
246.76.488913683636860.211086316363139
256.96.700000352091750.199999647908249
2676.995311140143240.00468885985675709
277.17.2751432148712-0.175143214871198
287.27.25183113747091-0.0518311374709055
297.17.15550790687705-0.0555079068770469
306.96.856418152186820.0435818478131835
3176.807764706434620.192235293565378
326.86.93743043496363-0.137430434963631
336.46.62469956697843-0.224699566978430
346.76.70413838157461-0.00413838157461365
356.66.60369938891978-0.00369938891978386
366.46.60210720061815-0.202107200618146
376.36.128390914993560.171609085006438
386.26.30400794143465-0.104007941434652
396.56.55062072050566-0.05062072050566
406.86.82713082289804-0.0271308228980438
416.86.82497595933457-0.0249759593345744
426.46.8022357832213-0.402235783221297
436.16.0752416084480.0247583915520039
445.85.97759087915082-0.177590879150825
456.15.815548357187420.284451642812577
467.26.848155234507150.351844765492855
477.37.50872061537512-0.208720615375115
486.97.09795779035395-0.197957790353950
496.16.39572916526077-0.295729165260766
505.85.86072660476531-0.0607266047653117
516.26.168663219506470.0313367804935349
527.16.95039387055290.149606129447097
537.77.70630140804968-0.00630140804967544
547.97.891439755944240.0085602440557647
557.77.8598844087899-0.159884408789902
567.47.396778561464790.00322143853521490
577.57.09916039104460.400839608955395
5887.859316233679640.140683766320358

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.7 & 7.9072660543172 & -0.2072660543172 \tabularnewline
2 & 7.5 & 7.42170784266648 & 0.0782921573335173 \tabularnewline
3 & 7.6 & 7.55076384893213 & 0.0492361510678705 \tabularnewline
4 & 7.8 & 7.91261992796699 & -0.112619927966989 \tabularnewline
5 & 7.8 & 7.92101321550251 & -0.121013215502508 \tabularnewline
6 & 7.8 & 7.77016811548489 & 0.0298318845151131 \tabularnewline
7 & 7.5 & 7.75059611128467 & -0.250596111284665 \tabularnewline
8 & 7.5 & 7.32457230913261 & 0.175427690867388 \tabularnewline
9 & 7.1 & 7.42692829016845 & -0.326928290168453 \tabularnewline
10 & 7.5 & 7.50884659048998 & -0.00884659048997798 \tabularnewline
11 & 7.5 & 7.4948820637886 & 0.00511793621139902 \tabularnewline
12 & 7.6 & 7.41102132539104 & 0.188978674608957 \tabularnewline
13 & 7.7 & 7.56861351333672 & 0.131386486663279 \tabularnewline
14 & 7.7 & 7.61824647099031 & 0.0817535290096892 \tabularnewline
15 & 7.9 & 7.75480899618455 & 0.145191003815453 \tabularnewline
16 & 8.1 & 8.05802424111116 & 0.041975758888842 \tabularnewline
17 & 8.2 & 7.9922015102362 & 0.207798489763805 \tabularnewline
18 & 8.2 & 7.87973819316276 & 0.320261806837236 \tabularnewline
19 & 8.2 & 8.00651316504281 & 0.193486834957186 \tabularnewline
20 & 7.9 & 7.76362781528815 & 0.136372184711853 \tabularnewline
21 & 7.3 & 7.43366339462109 & -0.133663394621088 \tabularnewline
22 & 6.9 & 7.37954355974862 & -0.479543559748621 \tabularnewline
23 & 6.6 & 6.3926979319165 & 0.2073020680835 \tabularnewline
24 & 6.7 & 6.48891368363686 & 0.211086316363139 \tabularnewline
25 & 6.9 & 6.70000035209175 & 0.199999647908249 \tabularnewline
26 & 7 & 6.99531114014324 & 0.00468885985675709 \tabularnewline
27 & 7.1 & 7.2751432148712 & -0.175143214871198 \tabularnewline
28 & 7.2 & 7.25183113747091 & -0.0518311374709055 \tabularnewline
29 & 7.1 & 7.15550790687705 & -0.0555079068770469 \tabularnewline
30 & 6.9 & 6.85641815218682 & 0.0435818478131835 \tabularnewline
31 & 7 & 6.80776470643462 & 0.192235293565378 \tabularnewline
32 & 6.8 & 6.93743043496363 & -0.137430434963631 \tabularnewline
33 & 6.4 & 6.62469956697843 & -0.224699566978430 \tabularnewline
34 & 6.7 & 6.70413838157461 & -0.00413838157461365 \tabularnewline
35 & 6.6 & 6.60369938891978 & -0.00369938891978386 \tabularnewline
36 & 6.4 & 6.60210720061815 & -0.202107200618146 \tabularnewline
37 & 6.3 & 6.12839091499356 & 0.171609085006438 \tabularnewline
38 & 6.2 & 6.30400794143465 & -0.104007941434652 \tabularnewline
39 & 6.5 & 6.55062072050566 & -0.05062072050566 \tabularnewline
40 & 6.8 & 6.82713082289804 & -0.0271308228980438 \tabularnewline
41 & 6.8 & 6.82497595933457 & -0.0249759593345744 \tabularnewline
42 & 6.4 & 6.8022357832213 & -0.402235783221297 \tabularnewline
43 & 6.1 & 6.075241608448 & 0.0247583915520039 \tabularnewline
44 & 5.8 & 5.97759087915082 & -0.177590879150825 \tabularnewline
45 & 6.1 & 5.81554835718742 & 0.284451642812577 \tabularnewline
46 & 7.2 & 6.84815523450715 & 0.351844765492855 \tabularnewline
47 & 7.3 & 7.50872061537512 & -0.208720615375115 \tabularnewline
48 & 6.9 & 7.09795779035395 & -0.197957790353950 \tabularnewline
49 & 6.1 & 6.39572916526077 & -0.295729165260766 \tabularnewline
50 & 5.8 & 5.86072660476531 & -0.0607266047653117 \tabularnewline
51 & 6.2 & 6.16866321950647 & 0.0313367804935349 \tabularnewline
52 & 7.1 & 6.9503938705529 & 0.149606129447097 \tabularnewline
53 & 7.7 & 7.70630140804968 & -0.00630140804967544 \tabularnewline
54 & 7.9 & 7.89143975594424 & 0.0085602440557647 \tabularnewline
55 & 7.7 & 7.8598844087899 & -0.159884408789902 \tabularnewline
56 & 7.4 & 7.39677856146479 & 0.00322143853521490 \tabularnewline
57 & 7.5 & 7.0991603910446 & 0.400839608955395 \tabularnewline
58 & 8 & 7.85931623367964 & 0.140683766320358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58149&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]7.7[/C][C]7.9072660543172[/C][C]-0.2072660543172[/C][/ROW]
[ROW][C]2[/C][C]7.5[/C][C]7.42170784266648[/C][C]0.0782921573335173[/C][/ROW]
[ROW][C]3[/C][C]7.6[/C][C]7.55076384893213[/C][C]0.0492361510678705[/C][/ROW]
[ROW][C]4[/C][C]7.8[/C][C]7.91261992796699[/C][C]-0.112619927966989[/C][/ROW]
[ROW][C]5[/C][C]7.8[/C][C]7.92101321550251[/C][C]-0.121013215502508[/C][/ROW]
[ROW][C]6[/C][C]7.8[/C][C]7.77016811548489[/C][C]0.0298318845151131[/C][/ROW]
[ROW][C]7[/C][C]7.5[/C][C]7.75059611128467[/C][C]-0.250596111284665[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]7.32457230913261[/C][C]0.175427690867388[/C][/ROW]
[ROW][C]9[/C][C]7.1[/C][C]7.42692829016845[/C][C]-0.326928290168453[/C][/ROW]
[ROW][C]10[/C][C]7.5[/C][C]7.50884659048998[/C][C]-0.00884659048997798[/C][/ROW]
[ROW][C]11[/C][C]7.5[/C][C]7.4948820637886[/C][C]0.00511793621139902[/C][/ROW]
[ROW][C]12[/C][C]7.6[/C][C]7.41102132539104[/C][C]0.188978674608957[/C][/ROW]
[ROW][C]13[/C][C]7.7[/C][C]7.56861351333672[/C][C]0.131386486663279[/C][/ROW]
[ROW][C]14[/C][C]7.7[/C][C]7.61824647099031[/C][C]0.0817535290096892[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.75480899618455[/C][C]0.145191003815453[/C][/ROW]
[ROW][C]16[/C][C]8.1[/C][C]8.05802424111116[/C][C]0.041975758888842[/C][/ROW]
[ROW][C]17[/C][C]8.2[/C][C]7.9922015102362[/C][C]0.207798489763805[/C][/ROW]
[ROW][C]18[/C][C]8.2[/C][C]7.87973819316276[/C][C]0.320261806837236[/C][/ROW]
[ROW][C]19[/C][C]8.2[/C][C]8.00651316504281[/C][C]0.193486834957186[/C][/ROW]
[ROW][C]20[/C][C]7.9[/C][C]7.76362781528815[/C][C]0.136372184711853[/C][/ROW]
[ROW][C]21[/C][C]7.3[/C][C]7.43366339462109[/C][C]-0.133663394621088[/C][/ROW]
[ROW][C]22[/C][C]6.9[/C][C]7.37954355974862[/C][C]-0.479543559748621[/C][/ROW]
[ROW][C]23[/C][C]6.6[/C][C]6.3926979319165[/C][C]0.2073020680835[/C][/ROW]
[ROW][C]24[/C][C]6.7[/C][C]6.48891368363686[/C][C]0.211086316363139[/C][/ROW]
[ROW][C]25[/C][C]6.9[/C][C]6.70000035209175[/C][C]0.199999647908249[/C][/ROW]
[ROW][C]26[/C][C]7[/C][C]6.99531114014324[/C][C]0.00468885985675709[/C][/ROW]
[ROW][C]27[/C][C]7.1[/C][C]7.2751432148712[/C][C]-0.175143214871198[/C][/ROW]
[ROW][C]28[/C][C]7.2[/C][C]7.25183113747091[/C][C]-0.0518311374709055[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.15550790687705[/C][C]-0.0555079068770469[/C][/ROW]
[ROW][C]30[/C][C]6.9[/C][C]6.85641815218682[/C][C]0.0435818478131835[/C][/ROW]
[ROW][C]31[/C][C]7[/C][C]6.80776470643462[/C][C]0.192235293565378[/C][/ROW]
[ROW][C]32[/C][C]6.8[/C][C]6.93743043496363[/C][C]-0.137430434963631[/C][/ROW]
[ROW][C]33[/C][C]6.4[/C][C]6.62469956697843[/C][C]-0.224699566978430[/C][/ROW]
[ROW][C]34[/C][C]6.7[/C][C]6.70413838157461[/C][C]-0.00413838157461365[/C][/ROW]
[ROW][C]35[/C][C]6.6[/C][C]6.60369938891978[/C][C]-0.00369938891978386[/C][/ROW]
[ROW][C]36[/C][C]6.4[/C][C]6.60210720061815[/C][C]-0.202107200618146[/C][/ROW]
[ROW][C]37[/C][C]6.3[/C][C]6.12839091499356[/C][C]0.171609085006438[/C][/ROW]
[ROW][C]38[/C][C]6.2[/C][C]6.30400794143465[/C][C]-0.104007941434652[/C][/ROW]
[ROW][C]39[/C][C]6.5[/C][C]6.55062072050566[/C][C]-0.05062072050566[/C][/ROW]
[ROW][C]40[/C][C]6.8[/C][C]6.82713082289804[/C][C]-0.0271308228980438[/C][/ROW]
[ROW][C]41[/C][C]6.8[/C][C]6.82497595933457[/C][C]-0.0249759593345744[/C][/ROW]
[ROW][C]42[/C][C]6.4[/C][C]6.8022357832213[/C][C]-0.402235783221297[/C][/ROW]
[ROW][C]43[/C][C]6.1[/C][C]6.075241608448[/C][C]0.0247583915520039[/C][/ROW]
[ROW][C]44[/C][C]5.8[/C][C]5.97759087915082[/C][C]-0.177590879150825[/C][/ROW]
[ROW][C]45[/C][C]6.1[/C][C]5.81554835718742[/C][C]0.284451642812577[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]6.84815523450715[/C][C]0.351844765492855[/C][/ROW]
[ROW][C]47[/C][C]7.3[/C][C]7.50872061537512[/C][C]-0.208720615375115[/C][/ROW]
[ROW][C]48[/C][C]6.9[/C][C]7.09795779035395[/C][C]-0.197957790353950[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.39572916526077[/C][C]-0.295729165260766[/C][/ROW]
[ROW][C]50[/C][C]5.8[/C][C]5.86072660476531[/C][C]-0.0607266047653117[/C][/ROW]
[ROW][C]51[/C][C]6.2[/C][C]6.16866321950647[/C][C]0.0313367804935349[/C][/ROW]
[ROW][C]52[/C][C]7.1[/C][C]6.9503938705529[/C][C]0.149606129447097[/C][/ROW]
[ROW][C]53[/C][C]7.7[/C][C]7.70630140804968[/C][C]-0.00630140804967544[/C][/ROW]
[ROW][C]54[/C][C]7.9[/C][C]7.89143975594424[/C][C]0.0085602440557647[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.8598844087899[/C][C]-0.159884408789902[/C][/ROW]
[ROW][C]56[/C][C]7.4[/C][C]7.39677856146479[/C][C]0.00322143853521490[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]7.0991603910446[/C][C]0.400839608955395[/C][/ROW]
[ROW][C]58[/C][C]8[/C][C]7.85931623367964[/C][C]0.140683766320358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58149&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58149&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
17.77.9072660543172-0.2072660543172
27.57.421707842666480.0782921573335173
37.67.550763848932130.0492361510678705
47.87.91261992796699-0.112619927966989
57.87.92101321550251-0.121013215502508
67.87.770168115484890.0298318845151131
77.57.75059611128467-0.250596111284665
87.57.324572309132610.175427690867388
97.17.42692829016845-0.326928290168453
107.57.50884659048998-0.00884659048997798
117.57.49488206378860.00511793621139902
127.67.411021325391040.188978674608957
137.77.568613513336720.131386486663279
147.77.618246470990310.0817535290096892
157.97.754808996184550.145191003815453
168.18.058024241111160.041975758888842
178.27.99220151023620.207798489763805
188.27.879738193162760.320261806837236
198.28.006513165042810.193486834957186
207.97.763627815288150.136372184711853
217.37.43366339462109-0.133663394621088
226.97.37954355974862-0.479543559748621
236.66.39269793191650.2073020680835
246.76.488913683636860.211086316363139
256.96.700000352091750.199999647908249
2676.995311140143240.00468885985675709
277.17.2751432148712-0.175143214871198
287.27.25183113747091-0.0518311374709055
297.17.15550790687705-0.0555079068770469
306.96.856418152186820.0435818478131835
3176.807764706434620.192235293565378
326.86.93743043496363-0.137430434963631
336.46.62469956697843-0.224699566978430
346.76.70413838157461-0.00413838157461365
356.66.60369938891978-0.00369938891978386
366.46.60210720061815-0.202107200618146
376.36.128390914993560.171609085006438
386.26.30400794143465-0.104007941434652
396.56.55062072050566-0.05062072050566
406.86.82713082289804-0.0271308228980438
416.86.82497595933457-0.0249759593345744
426.46.8022357832213-0.402235783221297
436.16.0752416084480.0247583915520039
445.85.97759087915082-0.177590879150825
456.15.815548357187420.284451642812577
467.26.848155234507150.351844765492855
477.37.50872061537512-0.208720615375115
486.97.09795779035395-0.197957790353950
496.16.39572916526077-0.295729165260766
505.85.86072660476531-0.0607266047653117
516.26.168663219506470.0313367804935349
527.16.95039387055290.149606129447097
537.77.70630140804968-0.00630140804967544
547.97.891439755944240.0085602440557647
557.77.8598844087899-0.159884408789902
567.47.396778561464790.00322143853521490
577.57.09916039104460.400839608955395
5887.859316233679640.140683766320358






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.04247554727642170.08495109455284350.957524452723578
200.02193402502212370.04386805004424740.978065974977876
210.04556729784080010.09113459568160010.9544327021592
220.5772448394848120.8455103210303750.422755160515188
230.5336838141024910.9326323717950190.466316185897509
240.4955001082737790.9910002165475590.50449989172622
250.4305093815731130.8610187631462250.569490618426887
260.3988720561804620.7977441123609230.601127943819538
270.4837559451619940.9675118903239870.516244054838006
280.3761102604876110.7522205209752220.623889739512389
290.293153261435820.586306522871640.70684673856418
300.2962106667173720.5924213334347450.703789333282628
310.3550436255244720.7100872510489450.644956374475528
320.3211789188376460.6423578376752920.678821081162354
330.4054201462816230.8108402925632470.594579853718377
340.3948693081485100.7897386162970190.605130691851490
350.3847460754111390.7694921508222770.615253924588861
360.3754680917055980.7509361834111970.624531908294402
370.7378989983867260.5242020032265470.262101001613274
380.615622512398320.768754975203360.38437748760168
390.5467821610568710.9064356778862590.453217838943129

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.0424755472764217 & 0.0849510945528435 & 0.957524452723578 \tabularnewline
20 & 0.0219340250221237 & 0.0438680500442474 & 0.978065974977876 \tabularnewline
21 & 0.0455672978408001 & 0.0911345956816001 & 0.9544327021592 \tabularnewline
22 & 0.577244839484812 & 0.845510321030375 & 0.422755160515188 \tabularnewline
23 & 0.533683814102491 & 0.932632371795019 & 0.466316185897509 \tabularnewline
24 & 0.495500108273779 & 0.991000216547559 & 0.50449989172622 \tabularnewline
25 & 0.430509381573113 & 0.861018763146225 & 0.569490618426887 \tabularnewline
26 & 0.398872056180462 & 0.797744112360923 & 0.601127943819538 \tabularnewline
27 & 0.483755945161994 & 0.967511890323987 & 0.516244054838006 \tabularnewline
28 & 0.376110260487611 & 0.752220520975222 & 0.623889739512389 \tabularnewline
29 & 0.29315326143582 & 0.58630652287164 & 0.70684673856418 \tabularnewline
30 & 0.296210666717372 & 0.592421333434745 & 0.703789333282628 \tabularnewline
31 & 0.355043625524472 & 0.710087251048945 & 0.644956374475528 \tabularnewline
32 & 0.321178918837646 & 0.642357837675292 & 0.678821081162354 \tabularnewline
33 & 0.405420146281623 & 0.810840292563247 & 0.594579853718377 \tabularnewline
34 & 0.394869308148510 & 0.789738616297019 & 0.605130691851490 \tabularnewline
35 & 0.384746075411139 & 0.769492150822277 & 0.615253924588861 \tabularnewline
36 & 0.375468091705598 & 0.750936183411197 & 0.624531908294402 \tabularnewline
37 & 0.737898998386726 & 0.524202003226547 & 0.262101001613274 \tabularnewline
38 & 0.61562251239832 & 0.76875497520336 & 0.38437748760168 \tabularnewline
39 & 0.546782161056871 & 0.906435677886259 & 0.453217838943129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58149&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]19[/C][C]0.0424755472764217[/C][C]0.0849510945528435[/C][C]0.957524452723578[/C][/ROW]
[ROW][C]20[/C][C]0.0219340250221237[/C][C]0.0438680500442474[/C][C]0.978065974977876[/C][/ROW]
[ROW][C]21[/C][C]0.0455672978408001[/C][C]0.0911345956816001[/C][C]0.9544327021592[/C][/ROW]
[ROW][C]22[/C][C]0.577244839484812[/C][C]0.845510321030375[/C][C]0.422755160515188[/C][/ROW]
[ROW][C]23[/C][C]0.533683814102491[/C][C]0.932632371795019[/C][C]0.466316185897509[/C][/ROW]
[ROW][C]24[/C][C]0.495500108273779[/C][C]0.991000216547559[/C][C]0.50449989172622[/C][/ROW]
[ROW][C]25[/C][C]0.430509381573113[/C][C]0.861018763146225[/C][C]0.569490618426887[/C][/ROW]
[ROW][C]26[/C][C]0.398872056180462[/C][C]0.797744112360923[/C][C]0.601127943819538[/C][/ROW]
[ROW][C]27[/C][C]0.483755945161994[/C][C]0.967511890323987[/C][C]0.516244054838006[/C][/ROW]
[ROW][C]28[/C][C]0.376110260487611[/C][C]0.752220520975222[/C][C]0.623889739512389[/C][/ROW]
[ROW][C]29[/C][C]0.29315326143582[/C][C]0.58630652287164[/C][C]0.70684673856418[/C][/ROW]
[ROW][C]30[/C][C]0.296210666717372[/C][C]0.592421333434745[/C][C]0.703789333282628[/C][/ROW]
[ROW][C]31[/C][C]0.355043625524472[/C][C]0.710087251048945[/C][C]0.644956374475528[/C][/ROW]
[ROW][C]32[/C][C]0.321178918837646[/C][C]0.642357837675292[/C][C]0.678821081162354[/C][/ROW]
[ROW][C]33[/C][C]0.405420146281623[/C][C]0.810840292563247[/C][C]0.594579853718377[/C][/ROW]
[ROW][C]34[/C][C]0.394869308148510[/C][C]0.789738616297019[/C][C]0.605130691851490[/C][/ROW]
[ROW][C]35[/C][C]0.384746075411139[/C][C]0.769492150822277[/C][C]0.615253924588861[/C][/ROW]
[ROW][C]36[/C][C]0.375468091705598[/C][C]0.750936183411197[/C][C]0.624531908294402[/C][/ROW]
[ROW][C]37[/C][C]0.737898998386726[/C][C]0.524202003226547[/C][C]0.262101001613274[/C][/ROW]
[ROW][C]38[/C][C]0.61562251239832[/C][C]0.76875497520336[/C][C]0.38437748760168[/C][/ROW]
[ROW][C]39[/C][C]0.546782161056871[/C][C]0.906435677886259[/C][C]0.453217838943129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58149&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58149&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
190.04247554727642170.08495109455284350.957524452723578
200.02193402502212370.04386805004424740.978065974977876
210.04556729784080010.09113459568160010.9544327021592
220.5772448394848120.8455103210303750.422755160515188
230.5336838141024910.9326323717950190.466316185897509
240.4955001082737790.9910002165475590.50449989172622
250.4305093815731130.8610187631462250.569490618426887
260.3988720561804620.7977441123609230.601127943819538
270.4837559451619940.9675118903239870.516244054838006
280.3761102604876110.7522205209752220.623889739512389
290.293153261435820.586306522871640.70684673856418
300.2962106667173720.5924213334347450.703789333282628
310.3550436255244720.7100872510489450.644956374475528
320.3211789188376460.6423578376752920.678821081162354
330.4054201462816230.8108402925632470.594579853718377
340.3948693081485100.7897386162970190.605130691851490
350.3847460754111390.7694921508222770.615253924588861
360.3754680917055980.7509361834111970.624531908294402
370.7378989983867260.5242020032265470.262101001613274
380.615622512398320.768754975203360.38437748760168
390.5467821610568710.9064356778862590.453217838943129






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0476190476190476OK
10% type I error level30.142857142857143NOK

\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 & 1 & 0.0476190476190476 & OK \tabularnewline
10% type I error level & 3 & 0.142857142857143 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58149&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]1[/C][C]0.0476190476190476[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.142857142857143[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58149&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58149&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 level10.0476190476190476OK
10% type I error level30.142857142857143NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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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')
}