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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 06:30:42 -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/t1258723943qeqc4t1hblhb0kn.htm/, Retrieved Wed, 24 Apr 2024 06:31:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58147, Retrieved Wed, 24 Apr 2024 06:31:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws73lags
Estimated Impact179

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] [2b548c9d2e9bba6e1eaf65bd4d551f41] [Current]
-    D          [Multiple Regression] [] [2009-11-20 13:35:13] [90f6d58d515a4caed6fb4b8be4e11eaa]
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Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58147&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]6 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=58147&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58147&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.98518401342828 -0.0145944931655954X[t] + 1.60214515152688Y1[t] -1.14767852541949Y2[t] + 0.354459259946489Y3[t] + 0.0193598686132426M1[t] + 0.082891000338969M2[t] + 0.0325486589288215M3[t] -0.0821859560428094M4[t] + 0.0890126310675888M5[t] + 0.00699035407687789M6[t] -0.128436830127242M7[t] + 0.0290728814144387M8[t] + 0.159023499959213M9[t] -0.5450041439469M10[t] + 0.185451716720582M11[t] -0.00279480398198670t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  2.98518401342828 -0.0145944931655954X[t] +  1.60214515152688Y1[t] -1.14767852541949Y2[t] +  0.354459259946489Y3[t] +  0.0193598686132426M1[t] +  0.082891000338969M2[t] +  0.0325486589288215M3[t] -0.0821859560428094M4[t] +  0.0890126310675888M5[t] +  0.00699035407687789M6[t] -0.128436830127242M7[t] +  0.0290728814144387M8[t] +  0.159023499959213M9[t] -0.5450041439469M10[t] +  0.185451716720582M11[t] -0.00279480398198670t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58147&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  2.98518401342828 -0.0145944931655954X[t] +  1.60214515152688Y1[t] -1.14767852541949Y2[t] +  0.354459259946489Y3[t] +  0.0193598686132426M1[t] +  0.082891000338969M2[t] +  0.0325486589288215M3[t] -0.0821859560428094M4[t] +  0.0890126310675888M5[t] +  0.00699035407687789M6[t] -0.128436830127242M7[t] +  0.0290728814144387M8[t] +  0.159023499959213M9[t] -0.5450041439469M10[t] +  0.185451716720582M11[t] -0.00279480398198670t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58147&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58147&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] = + 2.98518401342828 -0.0145944931655954X[t] + 1.60214515152688Y1[t] -1.14767852541949Y2[t] + 0.354459259946489Y3[t] + 0.0193598686132426M1[t] + 0.082891000338969M2[t] + 0.0325486589288215M3[t] -0.0821859560428094M4[t] + 0.0890126310675888M5[t] + 0.00699035407687789M6[t] -0.128436830127242M7[t] + 0.0290728814144387M8[t] + 0.159023499959213M9[t] -0.5450041439469M10[t] + 0.185451716720582M11[t] -0.00279480398198670t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.985184013428281.0325942.8910.006180.00309
X-0.01459449316559540.005253-2.77840.008280.00414
Y11.602145151526880.13476911.888100
Y2-1.147678525419490.215066-5.33644e-062e-06
Y30.3544592599464890.1411462.51130.0161690.008085
M10.01935986861324260.1434250.1350.8933030.446651
M20.0828910003389690.1598090.51870.6068360.303418
M30.03254865892882150.1618760.20110.8416620.420831
M4-0.08218595604280940.158924-0.51710.6079070.303954
M50.08901263106758880.1443480.61670.5409580.270479
M60.006990354076877890.1465450.04770.9621920.481096
M7-0.1284368301272420.146643-0.87580.3863410.193171
M80.02907288141443870.1387530.20950.8350980.417549
M90.1590234999592130.1959470.81160.4218460.210923
M10-0.54500414394690.176414-3.08940.0036410.00182
M110.1854517167205820.1546171.19940.237420.11871
t-0.002794803981986700.002487-1.12370.2678460.133923

\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) & 2.98518401342828 & 1.032594 & 2.891 & 0.00618 & 0.00309 \tabularnewline
X & -0.0145944931655954 & 0.005253 & -2.7784 & 0.00828 & 0.00414 \tabularnewline
Y1 & 1.60214515152688 & 0.134769 & 11.8881 & 0 & 0 \tabularnewline
Y2 & -1.14767852541949 & 0.215066 & -5.3364 & 4e-06 & 2e-06 \tabularnewline
Y3 & 0.354459259946489 & 0.141146 & 2.5113 & 0.016169 & 0.008085 \tabularnewline
M1 & 0.0193598686132426 & 0.143425 & 0.135 & 0.893303 & 0.446651 \tabularnewline
M2 & 0.082891000338969 & 0.159809 & 0.5187 & 0.606836 & 0.303418 \tabularnewline
M3 & 0.0325486589288215 & 0.161876 & 0.2011 & 0.841662 & 0.420831 \tabularnewline
M4 & -0.0821859560428094 & 0.158924 & -0.5171 & 0.607907 & 0.303954 \tabularnewline
M5 & 0.0890126310675888 & 0.144348 & 0.6167 & 0.540958 & 0.270479 \tabularnewline
M6 & 0.00699035407687789 & 0.146545 & 0.0477 & 0.962192 & 0.481096 \tabularnewline
M7 & -0.128436830127242 & 0.146643 & -0.8758 & 0.386341 & 0.193171 \tabularnewline
M8 & 0.0290728814144387 & 0.138753 & 0.2095 & 0.835098 & 0.417549 \tabularnewline
M9 & 0.159023499959213 & 0.195947 & 0.8116 & 0.421846 & 0.210923 \tabularnewline
M10 & -0.5450041439469 & 0.176414 & -3.0894 & 0.003641 & 0.00182 \tabularnewline
M11 & 0.185451716720582 & 0.154617 & 1.1994 & 0.23742 & 0.11871 \tabularnewline
t & -0.00279480398198670 & 0.002487 & -1.1237 & 0.267846 & 0.133923 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58147&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]2.98518401342828[/C][C]1.032594[/C][C]2.891[/C][C]0.00618[/C][C]0.00309[/C][/ROW]
[ROW][C]X[/C][C]-0.0145944931655954[/C][C]0.005253[/C][C]-2.7784[/C][C]0.00828[/C][C]0.00414[/C][/ROW]
[ROW][C]Y1[/C][C]1.60214515152688[/C][C]0.134769[/C][C]11.8881[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-1.14767852541949[/C][C]0.215066[/C][C]-5.3364[/C][C]4e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]Y3[/C][C]0.354459259946489[/C][C]0.141146[/C][C]2.5113[/C][C]0.016169[/C][C]0.008085[/C][/ROW]
[ROW][C]M1[/C][C]0.0193598686132426[/C][C]0.143425[/C][C]0.135[/C][C]0.893303[/C][C]0.446651[/C][/ROW]
[ROW][C]M2[/C][C]0.082891000338969[/C][C]0.159809[/C][C]0.5187[/C][C]0.606836[/C][C]0.303418[/C][/ROW]
[ROW][C]M3[/C][C]0.0325486589288215[/C][C]0.161876[/C][C]0.2011[/C][C]0.841662[/C][C]0.420831[/C][/ROW]
[ROW][C]M4[/C][C]-0.0821859560428094[/C][C]0.158924[/C][C]-0.5171[/C][C]0.607907[/C][C]0.303954[/C][/ROW]
[ROW][C]M5[/C][C]0.0890126310675888[/C][C]0.144348[/C][C]0.6167[/C][C]0.540958[/C][C]0.270479[/C][/ROW]
[ROW][C]M6[/C][C]0.00699035407687789[/C][C]0.146545[/C][C]0.0477[/C][C]0.962192[/C][C]0.481096[/C][/ROW]
[ROW][C]M7[/C][C]-0.128436830127242[/C][C]0.146643[/C][C]-0.8758[/C][C]0.386341[/C][C]0.193171[/C][/ROW]
[ROW][C]M8[/C][C]0.0290728814144387[/C][C]0.138753[/C][C]0.2095[/C][C]0.835098[/C][C]0.417549[/C][/ROW]
[ROW][C]M9[/C][C]0.159023499959213[/C][C]0.195947[/C][C]0.8116[/C][C]0.421846[/C][C]0.210923[/C][/ROW]
[ROW][C]M10[/C][C]-0.5450041439469[/C][C]0.176414[/C][C]-3.0894[/C][C]0.003641[/C][C]0.00182[/C][/ROW]
[ROW][C]M11[/C][C]0.185451716720582[/C][C]0.154617[/C][C]1.1994[/C][C]0.23742[/C][C]0.11871[/C][/ROW]
[ROW][C]t[/C][C]-0.00279480398198670[/C][C]0.002487[/C][C]-1.1237[/C][C]0.267846[/C][C]0.133923[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58147&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58147&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)2.985184013428281.0325942.8910.006180.00309
X-0.01459449316559540.005253-2.77840.008280.00414
Y11.602145151526880.13476911.888100
Y2-1.147678525419490.215066-5.33644e-062e-06
Y30.3544592599464890.1411462.51130.0161690.008085
M10.01935986861324260.1434250.1350.8933030.446651
M20.0828910003389690.1598090.51870.6068360.303418
M30.03254865892882150.1618760.20110.8416620.420831
M4-0.08218595604280940.158924-0.51710.6079070.303954
M50.08901263106758880.1443480.61670.5409580.270479
M60.006990354076877890.1465450.04770.9621920.481096
M7-0.1284368301272420.146643-0.87580.3863410.193171
M80.02907288141443870.1387530.20950.8350980.417549
M90.1590234999592130.1959470.81160.4218460.210923
M10-0.54500414394690.176414-3.08940.0036410.00182
M110.1854517167205820.1546171.19940.237420.11871
t-0.002794803981986700.002487-1.12370.2678460.133923






Multiple Linear Regression - Regression Statistics
Multiple R0.96434445443667
R-squared0.929960226802759
Adjusted R-squared0.901944317523863
F-TEST (value)33.1940047901022
F-TEST (DF numerator)16
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.203295340925834
Sum Squared Residuals1.65315982568604

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.96434445443667 \tabularnewline
R-squared & 0.929960226802759 \tabularnewline
Adjusted R-squared & 0.901944317523863 \tabularnewline
F-TEST (value) & 33.1940047901022 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 40 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.203295340925834 \tabularnewline
Sum Squared Residuals & 1.65315982568604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58147&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.96434445443667[/C][/ROW]
[ROW][C]R-squared[/C][C]0.929960226802759[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.901944317523863[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]33.1940047901022[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]40[/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]0.203295340925834[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.65315982568604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58147&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58147&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 R0.96434445443667
R-squared0.929960226802759
Adjusted R-squared0.901944317523863
F-TEST (value)33.1940047901022
F-TEST (DF numerator)16
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.203295340925834
Sum Squared Residuals1.65315982568604






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.57.361376928585220.138623071414778
27.67.62976889646691-0.0297688964669144
37.87.92675971949194-0.126759719491939
47.87.92502678519718-0.125026785197176
57.87.77090924937910.0290907506209001
67.57.78471355741033-0.284713557410331
77.57.234442141644460.265557858355541
87.17.50286761481359-0.402867614813591
97.57.364445865246330.135554134753674
107.57.54155438928596-0.0415543892859626
117.67.412956701427150.187043298572851
127.77.633248199964710.0667518000352907
137.77.652935897026480.0470641029735206
147.97.729214503799290.170785496200712
158.18.080114142153650.0198858578463546
168.28.028667410040.171332589960006
178.27.982643356375680.217356643624318
188.28.069948773701150.130051226298854
197.97.832903374386210.0670966256137905
207.37.43838061860954-0.138380618609543
216.97.37471210031743-0.47471210031743
226.66.388924082285830.211075917714166
236.76.673636195445150.0263638045548499
246.96.823313405161010.076686594838991
2576.991742044967890.00825795503211118
267.17.17768308428006-0.0776830842800585
277.27.182506480825580.0174935191744210
287.17.15608579569327-0.0560857956932686
296.96.887927479386150.0120725206138481
3076.818245209847740.181754790152260
316.86.98762513777366-0.187625137773663
326.46.52095481448853-0.120954814488530
336.76.632718180709320.067281819290682
346.66.62396326642031-0.0239632664203125
356.46.58418825307424-0.184188253074237
366.36.152132850252790.147867149747206
376.26.33538306662753-0.135383066627526
386.56.473887638873650.0261123611263514
396.86.824554888615-0.0245548886150067
406.86.777271095851210.0227289041487908
416.46.75149257883451-0.351492578834507
426.16.022696516493040.0773034835069607
435.85.98257723697454-0.182577236974543
446.15.759925899197380.340074100802625
457.26.896121452855470.303878547144526
467.37.44555826200789-0.145558262007891
476.96.92921885005346-0.0292188500534638
486.16.39130554462149-0.291305544621488
495.85.85856206279288-0.0585620627928845
506.26.28944587658009-0.0894458765800902
517.16.986064768913830.113935231086171
527.77.71294891321835-0.0129489132183525
537.97.807027336024560.0929726639754414
547.77.80439594254774-0.104395942547744
557.47.362452109221130.0375478907788737
567.57.177871052890960.322128947109039
5788.03200240087145-0.0320024008714517

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.5 & 7.36137692858522 & 0.138623071414778 \tabularnewline
2 & 7.6 & 7.62976889646691 & -0.0297688964669144 \tabularnewline
3 & 7.8 & 7.92675971949194 & -0.126759719491939 \tabularnewline
4 & 7.8 & 7.92502678519718 & -0.125026785197176 \tabularnewline
5 & 7.8 & 7.7709092493791 & 0.0290907506209001 \tabularnewline
6 & 7.5 & 7.78471355741033 & -0.284713557410331 \tabularnewline
7 & 7.5 & 7.23444214164446 & 0.265557858355541 \tabularnewline
8 & 7.1 & 7.50286761481359 & -0.402867614813591 \tabularnewline
9 & 7.5 & 7.36444586524633 & 0.135554134753674 \tabularnewline
10 & 7.5 & 7.54155438928596 & -0.0415543892859626 \tabularnewline
11 & 7.6 & 7.41295670142715 & 0.187043298572851 \tabularnewline
12 & 7.7 & 7.63324819996471 & 0.0667518000352907 \tabularnewline
13 & 7.7 & 7.65293589702648 & 0.0470641029735206 \tabularnewline
14 & 7.9 & 7.72921450379929 & 0.170785496200712 \tabularnewline
15 & 8.1 & 8.08011414215365 & 0.0198858578463546 \tabularnewline
16 & 8.2 & 8.02866741004 & 0.171332589960006 \tabularnewline
17 & 8.2 & 7.98264335637568 & 0.217356643624318 \tabularnewline
18 & 8.2 & 8.06994877370115 & 0.130051226298854 \tabularnewline
19 & 7.9 & 7.83290337438621 & 0.0670966256137905 \tabularnewline
20 & 7.3 & 7.43838061860954 & -0.138380618609543 \tabularnewline
21 & 6.9 & 7.37471210031743 & -0.47471210031743 \tabularnewline
22 & 6.6 & 6.38892408228583 & 0.211075917714166 \tabularnewline
23 & 6.7 & 6.67363619544515 & 0.0263638045548499 \tabularnewline
24 & 6.9 & 6.82331340516101 & 0.076686594838991 \tabularnewline
25 & 7 & 6.99174204496789 & 0.00825795503211118 \tabularnewline
26 & 7.1 & 7.17768308428006 & -0.0776830842800585 \tabularnewline
27 & 7.2 & 7.18250648082558 & 0.0174935191744210 \tabularnewline
28 & 7.1 & 7.15608579569327 & -0.0560857956932686 \tabularnewline
29 & 6.9 & 6.88792747938615 & 0.0120725206138481 \tabularnewline
30 & 7 & 6.81824520984774 & 0.181754790152260 \tabularnewline
31 & 6.8 & 6.98762513777366 & -0.187625137773663 \tabularnewline
32 & 6.4 & 6.52095481448853 & -0.120954814488530 \tabularnewline
33 & 6.7 & 6.63271818070932 & 0.067281819290682 \tabularnewline
34 & 6.6 & 6.62396326642031 & -0.0239632664203125 \tabularnewline
35 & 6.4 & 6.58418825307424 & -0.184188253074237 \tabularnewline
36 & 6.3 & 6.15213285025279 & 0.147867149747206 \tabularnewline
37 & 6.2 & 6.33538306662753 & -0.135383066627526 \tabularnewline
38 & 6.5 & 6.47388763887365 & 0.0261123611263514 \tabularnewline
39 & 6.8 & 6.824554888615 & -0.0245548886150067 \tabularnewline
40 & 6.8 & 6.77727109585121 & 0.0227289041487908 \tabularnewline
41 & 6.4 & 6.75149257883451 & -0.351492578834507 \tabularnewline
42 & 6.1 & 6.02269651649304 & 0.0773034835069607 \tabularnewline
43 & 5.8 & 5.98257723697454 & -0.182577236974543 \tabularnewline
44 & 6.1 & 5.75992589919738 & 0.340074100802625 \tabularnewline
45 & 7.2 & 6.89612145285547 & 0.303878547144526 \tabularnewline
46 & 7.3 & 7.44555826200789 & -0.145558262007891 \tabularnewline
47 & 6.9 & 6.92921885005346 & -0.0292188500534638 \tabularnewline
48 & 6.1 & 6.39130554462149 & -0.291305544621488 \tabularnewline
49 & 5.8 & 5.85856206279288 & -0.0585620627928845 \tabularnewline
50 & 6.2 & 6.28944587658009 & -0.0894458765800902 \tabularnewline
51 & 7.1 & 6.98606476891383 & 0.113935231086171 \tabularnewline
52 & 7.7 & 7.71294891321835 & -0.0129489132183525 \tabularnewline
53 & 7.9 & 7.80702733602456 & 0.0929726639754414 \tabularnewline
54 & 7.7 & 7.80439594254774 & -0.104395942547744 \tabularnewline
55 & 7.4 & 7.36245210922113 & 0.0375478907788737 \tabularnewline
56 & 7.5 & 7.17787105289096 & 0.322128947109039 \tabularnewline
57 & 8 & 8.03200240087145 & -0.0320024008714517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58147&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]7.5[/C][C]7.36137692858522[/C][C]0.138623071414778[/C][/ROW]
[ROW][C]2[/C][C]7.6[/C][C]7.62976889646691[/C][C]-0.0297688964669144[/C][/ROW]
[ROW][C]3[/C][C]7.8[/C][C]7.92675971949194[/C][C]-0.126759719491939[/C][/ROW]
[ROW][C]4[/C][C]7.8[/C][C]7.92502678519718[/C][C]-0.125026785197176[/C][/ROW]
[ROW][C]5[/C][C]7.8[/C][C]7.7709092493791[/C][C]0.0290907506209001[/C][/ROW]
[ROW][C]6[/C][C]7.5[/C][C]7.78471355741033[/C][C]-0.284713557410331[/C][/ROW]
[ROW][C]7[/C][C]7.5[/C][C]7.23444214164446[/C][C]0.265557858355541[/C][/ROW]
[ROW][C]8[/C][C]7.1[/C][C]7.50286761481359[/C][C]-0.402867614813591[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.36444586524633[/C][C]0.135554134753674[/C][/ROW]
[ROW][C]10[/C][C]7.5[/C][C]7.54155438928596[/C][C]-0.0415543892859626[/C][/ROW]
[ROW][C]11[/C][C]7.6[/C][C]7.41295670142715[/C][C]0.187043298572851[/C][/ROW]
[ROW][C]12[/C][C]7.7[/C][C]7.63324819996471[/C][C]0.0667518000352907[/C][/ROW]
[ROW][C]13[/C][C]7.7[/C][C]7.65293589702648[/C][C]0.0470641029735206[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.72921450379929[/C][C]0.170785496200712[/C][/ROW]
[ROW][C]15[/C][C]8.1[/C][C]8.08011414215365[/C][C]0.0198858578463546[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]8.02866741004[/C][C]0.171332589960006[/C][/ROW]
[ROW][C]17[/C][C]8.2[/C][C]7.98264335637568[/C][C]0.217356643624318[/C][/ROW]
[ROW][C]18[/C][C]8.2[/C][C]8.06994877370115[/C][C]0.130051226298854[/C][/ROW]
[ROW][C]19[/C][C]7.9[/C][C]7.83290337438621[/C][C]0.0670966256137905[/C][/ROW]
[ROW][C]20[/C][C]7.3[/C][C]7.43838061860954[/C][C]-0.138380618609543[/C][/ROW]
[ROW][C]21[/C][C]6.9[/C][C]7.37471210031743[/C][C]-0.47471210031743[/C][/ROW]
[ROW][C]22[/C][C]6.6[/C][C]6.38892408228583[/C][C]0.211075917714166[/C][/ROW]
[ROW][C]23[/C][C]6.7[/C][C]6.67363619544515[/C][C]0.0263638045548499[/C][/ROW]
[ROW][C]24[/C][C]6.9[/C][C]6.82331340516101[/C][C]0.076686594838991[/C][/ROW]
[ROW][C]25[/C][C]7[/C][C]6.99174204496789[/C][C]0.00825795503211118[/C][/ROW]
[ROW][C]26[/C][C]7.1[/C][C]7.17768308428006[/C][C]-0.0776830842800585[/C][/ROW]
[ROW][C]27[/C][C]7.2[/C][C]7.18250648082558[/C][C]0.0174935191744210[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.15608579569327[/C][C]-0.0560857956932686[/C][/ROW]
[ROW][C]29[/C][C]6.9[/C][C]6.88792747938615[/C][C]0.0120725206138481[/C][/ROW]
[ROW][C]30[/C][C]7[/C][C]6.81824520984774[/C][C]0.181754790152260[/C][/ROW]
[ROW][C]31[/C][C]6.8[/C][C]6.98762513777366[/C][C]-0.187625137773663[/C][/ROW]
[ROW][C]32[/C][C]6.4[/C][C]6.52095481448853[/C][C]-0.120954814488530[/C][/ROW]
[ROW][C]33[/C][C]6.7[/C][C]6.63271818070932[/C][C]0.067281819290682[/C][/ROW]
[ROW][C]34[/C][C]6.6[/C][C]6.62396326642031[/C][C]-0.0239632664203125[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]6.58418825307424[/C][C]-0.184188253074237[/C][/ROW]
[ROW][C]36[/C][C]6.3[/C][C]6.15213285025279[/C][C]0.147867149747206[/C][/ROW]
[ROW][C]37[/C][C]6.2[/C][C]6.33538306662753[/C][C]-0.135383066627526[/C][/ROW]
[ROW][C]38[/C][C]6.5[/C][C]6.47388763887365[/C][C]0.0261123611263514[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]6.824554888615[/C][C]-0.0245548886150067[/C][/ROW]
[ROW][C]40[/C][C]6.8[/C][C]6.77727109585121[/C][C]0.0227289041487908[/C][/ROW]
[ROW][C]41[/C][C]6.4[/C][C]6.75149257883451[/C][C]-0.351492578834507[/C][/ROW]
[ROW][C]42[/C][C]6.1[/C][C]6.02269651649304[/C][C]0.0773034835069607[/C][/ROW]
[ROW][C]43[/C][C]5.8[/C][C]5.98257723697454[/C][C]-0.182577236974543[/C][/ROW]
[ROW][C]44[/C][C]6.1[/C][C]5.75992589919738[/C][C]0.340074100802625[/C][/ROW]
[ROW][C]45[/C][C]7.2[/C][C]6.89612145285547[/C][C]0.303878547144526[/C][/ROW]
[ROW][C]46[/C][C]7.3[/C][C]7.44555826200789[/C][C]-0.145558262007891[/C][/ROW]
[ROW][C]47[/C][C]6.9[/C][C]6.92921885005346[/C][C]-0.0292188500534638[/C][/ROW]
[ROW][C]48[/C][C]6.1[/C][C]6.39130554462149[/C][C]-0.291305544621488[/C][/ROW]
[ROW][C]49[/C][C]5.8[/C][C]5.85856206279288[/C][C]-0.0585620627928845[/C][/ROW]
[ROW][C]50[/C][C]6.2[/C][C]6.28944587658009[/C][C]-0.0894458765800902[/C][/ROW]
[ROW][C]51[/C][C]7.1[/C][C]6.98606476891383[/C][C]0.113935231086171[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]7.71294891321835[/C][C]-0.0129489132183525[/C][/ROW]
[ROW][C]53[/C][C]7.9[/C][C]7.80702733602456[/C][C]0.0929726639754414[/C][/ROW]
[ROW][C]54[/C][C]7.7[/C][C]7.80439594254774[/C][C]-0.104395942547744[/C][/ROW]
[ROW][C]55[/C][C]7.4[/C][C]7.36245210922113[/C][C]0.0375478907788737[/C][/ROW]
[ROW][C]56[/C][C]7.5[/C][C]7.17787105289096[/C][C]0.322128947109039[/C][/ROW]
[ROW][C]57[/C][C]8[/C][C]8.03200240087145[/C][C]-0.0320024008714517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58147&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58147&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
17.57.361376928585220.138623071414778
27.67.62976889646691-0.0297688964669144
37.87.92675971949194-0.126759719491939
47.87.92502678519718-0.125026785197176
57.87.77090924937910.0290907506209001
67.57.78471355741033-0.284713557410331
77.57.234442141644460.265557858355541
87.17.50286761481359-0.402867614813591
97.57.364445865246330.135554134753674
107.57.54155438928596-0.0415543892859626
117.67.412956701427150.187043298572851
127.77.633248199964710.0667518000352907
137.77.652935897026480.0470641029735206
147.97.729214503799290.170785496200712
158.18.080114142153650.0198858578463546
168.28.028667410040.171332589960006
178.27.982643356375680.217356643624318
188.28.069948773701150.130051226298854
197.97.832903374386210.0670966256137905
207.37.43838061860954-0.138380618609543
216.97.37471210031743-0.47471210031743
226.66.388924082285830.211075917714166
236.76.673636195445150.0263638045548499
246.96.823313405161010.076686594838991
2576.991742044967890.00825795503211118
267.17.17768308428006-0.0776830842800585
277.27.182506480825580.0174935191744210
287.17.15608579569327-0.0560857956932686
296.96.887927479386150.0120725206138481
3076.818245209847740.181754790152260
316.86.98762513777366-0.187625137773663
326.46.52095481448853-0.120954814488530
336.76.632718180709320.067281819290682
346.66.62396326642031-0.0239632664203125
356.46.58418825307424-0.184188253074237
366.36.152132850252790.147867149747206
376.26.33538306662753-0.135383066627526
386.56.473887638873650.0261123611263514
396.86.824554888615-0.0245548886150067
406.86.777271095851210.0227289041487908
416.46.75149257883451-0.351492578834507
426.16.022696516493040.0773034835069607
435.85.98257723697454-0.182577236974543
446.15.759925899197380.340074100802625
457.26.896121452855470.303878547144526
467.37.44555826200789-0.145558262007891
476.96.92921885005346-0.0292188500534638
486.16.39130554462149-0.291305544621488
495.85.85856206279288-0.0585620627928845
506.26.28944587658009-0.0894458765800902
517.16.986064768913830.113935231086171
527.77.71294891321835-0.0129489132183525
537.97.807027336024560.0929726639754414
547.77.80439594254774-0.104395942547744
557.47.362452109221130.0375478907788737
567.57.177871052890960.322128947109039
5788.03200240087145-0.0320024008714517






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.1790662679532710.3581325359065430.820933732046729
210.7513637825601650.497272434879670.248636217439835
220.7606384265432750.4787231469134490.239361573456725
230.6801898582985890.6396202834028220.319810141701411
240.5599709817356970.8800580365286050.440029018264303
250.5059865564923420.9880268870153170.494013443507658
260.543706811893880.912586376212240.45629318810612
270.4293767682406730.8587535364813470.570623231759327
280.3223720167705680.6447440335411350.677627983229433
290.2635260612309640.5270521224619280.736473938769036
300.322893441638020.645786883276040.67710655836198
310.2476486327389990.4952972654779990.752351367261
320.3060281492972540.6120562985945090.693971850702746
330.2769135206567270.5538270413134540.723086479343273
340.2532225191616810.5064450383233620.746777480838319
350.2221042830763660.4442085661527320.777895716923634
360.739422362011720.5211552759765590.260577637988280
370.6626839337127230.6746321325745530.337316066287277

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.179066267953271 & 0.358132535906543 & 0.820933732046729 \tabularnewline
21 & 0.751363782560165 & 0.49727243487967 & 0.248636217439835 \tabularnewline
22 & 0.760638426543275 & 0.478723146913449 & 0.239361573456725 \tabularnewline
23 & 0.680189858298589 & 0.639620283402822 & 0.319810141701411 \tabularnewline
24 & 0.559970981735697 & 0.880058036528605 & 0.440029018264303 \tabularnewline
25 & 0.505986556492342 & 0.988026887015317 & 0.494013443507658 \tabularnewline
26 & 0.54370681189388 & 0.91258637621224 & 0.45629318810612 \tabularnewline
27 & 0.429376768240673 & 0.858753536481347 & 0.570623231759327 \tabularnewline
28 & 0.322372016770568 & 0.644744033541135 & 0.677627983229433 \tabularnewline
29 & 0.263526061230964 & 0.527052122461928 & 0.736473938769036 \tabularnewline
30 & 0.32289344163802 & 0.64578688327604 & 0.67710655836198 \tabularnewline
31 & 0.247648632738999 & 0.495297265477999 & 0.752351367261 \tabularnewline
32 & 0.306028149297254 & 0.612056298594509 & 0.693971850702746 \tabularnewline
33 & 0.276913520656727 & 0.553827041313454 & 0.723086479343273 \tabularnewline
34 & 0.253222519161681 & 0.506445038323362 & 0.746777480838319 \tabularnewline
35 & 0.222104283076366 & 0.444208566152732 & 0.777895716923634 \tabularnewline
36 & 0.73942236201172 & 0.521155275976559 & 0.260577637988280 \tabularnewline
37 & 0.662683933712723 & 0.674632132574553 & 0.337316066287277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58147&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]20[/C][C]0.179066267953271[/C][C]0.358132535906543[/C][C]0.820933732046729[/C][/ROW]
[ROW][C]21[/C][C]0.751363782560165[/C][C]0.49727243487967[/C][C]0.248636217439835[/C][/ROW]
[ROW][C]22[/C][C]0.760638426543275[/C][C]0.478723146913449[/C][C]0.239361573456725[/C][/ROW]
[ROW][C]23[/C][C]0.680189858298589[/C][C]0.639620283402822[/C][C]0.319810141701411[/C][/ROW]
[ROW][C]24[/C][C]0.559970981735697[/C][C]0.880058036528605[/C][C]0.440029018264303[/C][/ROW]
[ROW][C]25[/C][C]0.505986556492342[/C][C]0.988026887015317[/C][C]0.494013443507658[/C][/ROW]
[ROW][C]26[/C][C]0.54370681189388[/C][C]0.91258637621224[/C][C]0.45629318810612[/C][/ROW]
[ROW][C]27[/C][C]0.429376768240673[/C][C]0.858753536481347[/C][C]0.570623231759327[/C][/ROW]
[ROW][C]28[/C][C]0.322372016770568[/C][C]0.644744033541135[/C][C]0.677627983229433[/C][/ROW]
[ROW][C]29[/C][C]0.263526061230964[/C][C]0.527052122461928[/C][C]0.736473938769036[/C][/ROW]
[ROW][C]30[/C][C]0.32289344163802[/C][C]0.64578688327604[/C][C]0.67710655836198[/C][/ROW]
[ROW][C]31[/C][C]0.247648632738999[/C][C]0.495297265477999[/C][C]0.752351367261[/C][/ROW]
[ROW][C]32[/C][C]0.306028149297254[/C][C]0.612056298594509[/C][C]0.693971850702746[/C][/ROW]
[ROW][C]33[/C][C]0.276913520656727[/C][C]0.553827041313454[/C][C]0.723086479343273[/C][/ROW]
[ROW][C]34[/C][C]0.253222519161681[/C][C]0.506445038323362[/C][C]0.746777480838319[/C][/ROW]
[ROW][C]35[/C][C]0.222104283076366[/C][C]0.444208566152732[/C][C]0.777895716923634[/C][/ROW]
[ROW][C]36[/C][C]0.73942236201172[/C][C]0.521155275976559[/C][C]0.260577637988280[/C][/ROW]
[ROW][C]37[/C][C]0.662683933712723[/C][C]0.674632132574553[/C][C]0.337316066287277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58147&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58147&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.1790662679532710.3581325359065430.820933732046729
210.7513637825601650.497272434879670.248636217439835
220.7606384265432750.4787231469134490.239361573456725
230.6801898582985890.6396202834028220.319810141701411
240.5599709817356970.8800580365286050.440029018264303
250.5059865564923420.9880268870153170.494013443507658
260.543706811893880.912586376212240.45629318810612
270.4293767682406730.8587535364813470.570623231759327
280.3223720167705680.6447440335411350.677627983229433
290.2635260612309640.5270521224619280.736473938769036
300.322893441638020.645786883276040.67710655836198
310.2476486327389990.4952972654779990.752351367261
320.3060281492972540.6120562985945090.693971850702746
330.2769135206567270.5538270413134540.723086479343273
340.2532225191616810.5064450383233620.746777480838319
350.2221042830763660.4442085661527320.777895716923634
360.739422362011720.5211552759765590.260577637988280
370.6626839337127230.6746321325745530.337316066287277






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58147&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58147&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58147&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}