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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 Thu, 28 Mar 2024 10:27:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58149, Retrieved Thu, 28 Mar 2024 10:27:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws72lags
Estimated Impact136
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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Dataseries X:
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




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:  

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:  

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:  

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:  

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:  

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:  

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:  

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



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')
}