FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationMon, 14 Dec 2009 02:56:03 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/14/t12607846799mdxxrumay32f64.htm/, Retrieved Sun, 05 May 2024 16:10:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67485, Retrieved Sun, 05 May 2024 16:10:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192

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] [] [2009-12-14 09:56:03] [d39d4e1021a28f94dc953cf77db656ab] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97,4	123,5	102,9	112,7	97,0	95,1
111,4	124,0	97,4	102,9	112,7	97,0
87,4	127,4	111,4	97,4	102,9	112,7
96,8	127,6	87,4	111,4	97,4	102,9
114,1	128,4	96,8	87,4	111,4	97,4
110,3	131,4	114,1	96,8	87,4	111,4
103,9	135,1	110,3	114,1	96,8	87,4
101,6	134,0	103,9	110,3	114,1	96,8
94,6	144,5	101,6	103,9	110,3	114,1
95,9	147,3	94,6	101,6	103,9	110,3
104,7	150,9	95,9	94,6	101,6	103,9
102,8	148,7	104,7	95,9	94,6	101,6
98,1	141,4	102,8	104,7	95,9	94,6
113,9	138,9	98,1	102,8	104,7	95,9
80,9	139,8	113,9	98,1	102,8	104,7
95,7	145,6	80,9	113,9	98,1	102,8
113,2	147,9	95,7	80,9	113,9	98,1
105,9	148,5	113,2	95,7	80,9	113,9
108,8	151,1	105,9	113,2	95,7	80,9
102,3	157,5	108,8	105,9	113,2	95,7
99,0	167,5	102,3	108,8	105,9	113,2
100,7	172,3	99,0	102,3	108,8	105,9
115,5	173,5	100,7	99,0	102,3	108,8
100,7	187,5	115,5	100,7	99,0	102,3
109,9	205,5	100,7	115,5	100,7	99,0
114,6	195,1	109,9	100,7	115,5	100,7
85,4	204,5	114,6	109,9	100,7	115,5
100,5	204,5	85,4	114,6	109,9	100,7
114,8	201,7	100,5	85,4	114,6	109,9
116,5	207,0	114,8	100,5	85,4	114,6
112,9	206,6	116,5	114,8	100,5	85,4
102,0	210,6	112,9	116,5	114,8	100,5
106,0	211,1	102,0	112,9	116,5	114,8
105,3	215,0	106,0	102,0	112,9	116,5
118,8	223,9	105,3	106,0	102,0	112,9
106,1	238,2	118,8	105,3	106,0	102,0
109,3	238,9	106,1	118,8	105,3	106,0
117,2	229,6	109,3	106,1	118,8	105,3
92,5	232,2	117,2	109,3	106,1	118,8
104,2	222,1	92,5	117,2	109,3	106,1
112,5	221,6	104,2	92,5	117,2	109,3
122,4	227,3	112,5	104,2	92,5	117,2
113,3	221,0	122,4	112,5	104,2	92,5
100,0	213,6	113,3	122,4	112,5	104,2
110,7	243,4	100,0	113,3	122,4	112,5
112,8	253,8	110,7	100,0	113,3	122,4
109,8	265,3	112,8	110,7	100,0	113,3
117,3	268,2	109,8	112,8	110,7	100,0
109,1	268,5	117,3	109,8	112,8	110,7
115,9	266,9	109,1	117,3	109,8	112,8
96,0	268,4	115,9	109,1	117,3	109,8
99,8	250,8	96,0	115,9	109,1	117,3
116,8	231,2	99,8	96,0	115,9	109,1
115,7	192,0	116,8	99,8	96,0	115,9
99,4	171,4	115,7	116,8	99,8	96,0
94,3	160,0	99,4	115,7	116,8	99,8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67485&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=67485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67485&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
TIP[t] = + 102.462591005717 + 0.154745690029901Grondstofprijzen[t] -0.356082029627551Y1[t] -0.126709222006954Y2[t] + 0.333175994767932Y3[t] -0.0356040497354635Y4[t] -1.66280543858118M1[t] + 4.5877159356974M2[t] -16.1108173064501M3[t] -12.1798134767917M4[t] + 0.773361771582027M5[t] + 17.3617852801477M6[t] + 8.96502288148342M7[t] -5.06452385668755M8[t] -8.13728355878094M9[t] -6.99075060859638M10[t] + 3.88854064345828M11[t] -0.193613167038276t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TIP[t] =  +  102.462591005717 +  0.154745690029901Grondstofprijzen[t] -0.356082029627551Y1[t] -0.126709222006954Y2[t] +  0.333175994767932Y3[t] -0.0356040497354635Y4[t] -1.66280543858118M1[t] +  4.5877159356974M2[t] -16.1108173064501M3[t] -12.1798134767917M4[t] +  0.773361771582027M5[t] +  17.3617852801477M6[t] +  8.96502288148342M7[t] -5.06452385668755M8[t] -8.13728355878094M9[t] -6.99075060859638M10[t] +  3.88854064345828M11[t] -0.193613167038276t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67485&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TIP[t] =  +  102.462591005717 +  0.154745690029901Grondstofprijzen[t] -0.356082029627551Y1[t] -0.126709222006954Y2[t] +  0.333175994767932Y3[t] -0.0356040497354635Y4[t] -1.66280543858118M1[t] +  4.5877159356974M2[t] -16.1108173064501M3[t] -12.1798134767917M4[t] +  0.773361771582027M5[t] +  17.3617852801477M6[t] +  8.96502288148342M7[t] -5.06452385668755M8[t] -8.13728355878094M9[t] -6.99075060859638M10[t] +  3.88854064345828M11[t] -0.193613167038276t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67485&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
TIP[t] = + 102.462591005717 + 0.154745690029901Grondstofprijzen[t] -0.356082029627551Y1[t] -0.126709222006954Y2[t] + 0.333175994767932Y3[t] -0.0356040497354635Y4[t] -1.66280543858118M1[t] + 4.5877159356974M2[t] -16.1108173064501M3[t] -12.1798134767917M4[t] + 0.773361771582027M5[t] + 17.3617852801477M6[t] + 8.96502288148342M7[t] -5.06452385668755M8[t] -8.13728355878094M9[t] -6.99075060859638M10[t] + 3.88854064345828M11[t] -0.193613167038276t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)102.46259100571733.7860013.03270.0043520.002176
Grondstofprijzen0.1547456900299010.0316284.89271.9e-059e-06
Y1-0.3560820296275510.156319-2.27790.0284430.014221
Y2-0.1267092220069540.159644-0.79370.4322990.216149
Y30.3331759947679320.1555762.14160.0387020.019351
Y4-0.03560404973546350.15681-0.22710.82160.4108
M1-1.662805438581182.701879-0.61540.5419420.270971
M24.58771593569743.1491881.45680.1533880.076694
M3-16.11081730645013.098392-5.19977e-064e-06
M4-12.17981347679174.461054-2.73030.0095390.00477
M50.7733617715820274.2140360.18350.8553650.427683
M617.36178528014773.3007355.266e-063e-06
M78.965022881483423.9766972.25440.0300180.015009
M8-5.064523856687554.073894-1.24320.2214230.110711
M9-8.137283558780944.704216-1.72980.0917850.045892
M10-6.990750608596384.067739-1.71860.0938290.046914
M113.888540643458283.1876841.21990.2300340.115017
t-0.1936131670382760.067808-2.85530.0069290.003465

\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) & 102.462591005717 & 33.786001 & 3.0327 & 0.004352 & 0.002176 \tabularnewline
Grondstofprijzen & 0.154745690029901 & 0.031628 & 4.8927 & 1.9e-05 & 9e-06 \tabularnewline
Y1 & -0.356082029627551 & 0.156319 & -2.2779 & 0.028443 & 0.014221 \tabularnewline
Y2 & -0.126709222006954 & 0.159644 & -0.7937 & 0.432299 & 0.216149 \tabularnewline
Y3 & 0.333175994767932 & 0.155576 & 2.1416 & 0.038702 & 0.019351 \tabularnewline
Y4 & -0.0356040497354635 & 0.15681 & -0.2271 & 0.8216 & 0.4108 \tabularnewline
M1 & -1.66280543858118 & 2.701879 & -0.6154 & 0.541942 & 0.270971 \tabularnewline
M2 & 4.5877159356974 & 3.149188 & 1.4568 & 0.153388 & 0.076694 \tabularnewline
M3 & -16.1108173064501 & 3.098392 & -5.1997 & 7e-06 & 4e-06 \tabularnewline
M4 & -12.1798134767917 & 4.461054 & -2.7303 & 0.009539 & 0.00477 \tabularnewline
M5 & 0.773361771582027 & 4.214036 & 0.1835 & 0.855365 & 0.427683 \tabularnewline
M6 & 17.3617852801477 & 3.300735 & 5.26 & 6e-06 & 3e-06 \tabularnewline
M7 & 8.96502288148342 & 3.976697 & 2.2544 & 0.030018 & 0.015009 \tabularnewline
M8 & -5.06452385668755 & 4.073894 & -1.2432 & 0.221423 & 0.110711 \tabularnewline
M9 & -8.13728355878094 & 4.704216 & -1.7298 & 0.091785 & 0.045892 \tabularnewline
M10 & -6.99075060859638 & 4.067739 & -1.7186 & 0.093829 & 0.046914 \tabularnewline
M11 & 3.88854064345828 & 3.187684 & 1.2199 & 0.230034 & 0.115017 \tabularnewline
t & -0.193613167038276 & 0.067808 & -2.8553 & 0.006929 & 0.003465 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67485&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]102.462591005717[/C][C]33.786001[/C][C]3.0327[/C][C]0.004352[/C][C]0.002176[/C][/ROW]
[ROW][C]Grondstofprijzen[/C][C]0.154745690029901[/C][C]0.031628[/C][C]4.8927[/C][C]1.9e-05[/C][C]9e-06[/C][/ROW]
[ROW][C]Y1[/C][C]-0.356082029627551[/C][C]0.156319[/C][C]-2.2779[/C][C]0.028443[/C][C]0.014221[/C][/ROW]
[ROW][C]Y2[/C][C]-0.126709222006954[/C][C]0.159644[/C][C]-0.7937[/C][C]0.432299[/C][C]0.216149[/C][/ROW]
[ROW][C]Y3[/C][C]0.333175994767932[/C][C]0.155576[/C][C]2.1416[/C][C]0.038702[/C][C]0.019351[/C][/ROW]
[ROW][C]Y4[/C][C]-0.0356040497354635[/C][C]0.15681[/C][C]-0.2271[/C][C]0.8216[/C][C]0.4108[/C][/ROW]
[ROW][C]M1[/C][C]-1.66280543858118[/C][C]2.701879[/C][C]-0.6154[/C][C]0.541942[/C][C]0.270971[/C][/ROW]
[ROW][C]M2[/C][C]4.5877159356974[/C][C]3.149188[/C][C]1.4568[/C][C]0.153388[/C][C]0.076694[/C][/ROW]
[ROW][C]M3[/C][C]-16.1108173064501[/C][C]3.098392[/C][C]-5.1997[/C][C]7e-06[/C][C]4e-06[/C][/ROW]
[ROW][C]M4[/C][C]-12.1798134767917[/C][C]4.461054[/C][C]-2.7303[/C][C]0.009539[/C][C]0.00477[/C][/ROW]
[ROW][C]M5[/C][C]0.773361771582027[/C][C]4.214036[/C][C]0.1835[/C][C]0.855365[/C][C]0.427683[/C][/ROW]
[ROW][C]M6[/C][C]17.3617852801477[/C][C]3.300735[/C][C]5.26[/C][C]6e-06[/C][C]3e-06[/C][/ROW]
[ROW][C]M7[/C][C]8.96502288148342[/C][C]3.976697[/C][C]2.2544[/C][C]0.030018[/C][C]0.015009[/C][/ROW]
[ROW][C]M8[/C][C]-5.06452385668755[/C][C]4.073894[/C][C]-1.2432[/C][C]0.221423[/C][C]0.110711[/C][/ROW]
[ROW][C]M9[/C][C]-8.13728355878094[/C][C]4.704216[/C][C]-1.7298[/C][C]0.091785[/C][C]0.045892[/C][/ROW]
[ROW][C]M10[/C][C]-6.99075060859638[/C][C]4.067739[/C][C]-1.7186[/C][C]0.093829[/C][C]0.046914[/C][/ROW]
[ROW][C]M11[/C][C]3.88854064345828[/C][C]3.187684[/C][C]1.2199[/C][C]0.230034[/C][C]0.115017[/C][/ROW]
[ROW][C]t[/C][C]-0.193613167038276[/C][C]0.067808[/C][C]-2.8553[/C][C]0.006929[/C][C]0.003465[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67485&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)102.46259100571733.7860013.03270.0043520.002176
Grondstofprijzen0.1547456900299010.0316284.89271.9e-059e-06
Y1-0.3560820296275510.156319-2.27790.0284430.014221
Y2-0.1267092220069540.159644-0.79370.4322990.216149
Y30.3331759947679320.1555762.14160.0387020.019351
Y4-0.03560404973546350.15681-0.22710.82160.4108
M1-1.662805438581182.701879-0.61540.5419420.270971
M24.58771593569743.1491881.45680.1533880.076694
M3-16.11081730645013.098392-5.19977e-064e-06
M4-12.17981347679174.461054-2.73030.0095390.00477
M50.7733617715820274.2140360.18350.8553650.427683
M617.36178528014773.3007355.266e-063e-06
M78.965022881483423.9766972.25440.0300180.015009
M8-5.064523856687554.073894-1.24320.2214230.110711
M9-8.137283558780944.704216-1.72980.0917850.045892
M10-6.990750608596384.067739-1.71860.0938290.046914
M113.888540643458283.1876841.21990.2300340.115017
t-0.1936131670382760.067808-2.85530.0069290.003465






Multiple Linear Regression - Regression Statistics
Multiple R0.953775966980205
R-squared0.909688595189026
Adjusted R-squared0.869286124615695
F-TEST (value)22.5156675391407
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value8.99280649946377e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.28423946988512
Sum Squared Residuals409.876698030949

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.953775966980205 \tabularnewline
R-squared & 0.909688595189026 \tabularnewline
Adjusted R-squared & 0.869286124615695 \tabularnewline
F-TEST (value) & 22.5156675391407 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 8.99280649946377e-15 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.28423946988512 \tabularnewline
Sum Squared Residuals & 409.876698030949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67485&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.953775966980205[/C][/ROW]
[ROW][C]R-squared[/C][C]0.909688595189026[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.869286124615695[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]22.5156675391407[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]8.99280649946377e-15[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.28423946988512[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]409.876698030949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67485&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67485&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 R0.953775966980205
R-squared0.909688595189026
Adjusted R-squared0.869286124615695
F-TEST (value)22.5156675391407
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value8.99280649946377e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.28423946988512
Sum Squared Residuals409.876698030949






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
197.497.7284213125789-0.328421312578872
2111.4112.226119326813-0.826119326812827
387.483.74775224040873.65224775959126
496.892.80458336018263.99541663981735
5114.1110.2420784435063.85792155649397
6110.3111.255159484974-0.955159484974221
7103.9106.384736688716-2.48473668871642
8101.6100.1810431996891.41895680031111
994.698.2874089243174-3.68740892431741
1095.9100.460591080036-4.56059108003627
11104.7111.588972695034-6.88897269503388
12102.8101.6177918681561.18220813184390
1398.198.875601569296-0.775601569296084
14113.9109.3456421018264.55435789817398
1580.982.6158540612534-1.71585406125336
1695.795.50119151513440.198808484865657
17113.2112.9595787223700.240421277629707
18105.9109.783152660568-3.88315266056845
19108.8108.0830416839390.716958316061201
20102.3100.0462336020062.25376639799426
219997.21913844975551.78086155024451
22100.7102.139638133757-1.4396381337573
23115.5110.5549163188414.94508368115872
24100.7102.28572799341-1.58572799341010
25109.9107.2933419163462.60665808365379
26114.6115.210714598420-0.610714598420099
2785.487.4759226351517-2.07592263515166
28100.5104.607534307413-4.10753430741344
29114.8116.495249009735-1.69524900973521
30116.5116.808851151462-0.308851151461769
31112.9111.8098917579521.09010824204768
32102103.498999816286-1.49899981628597
33106104.7047083942231.29529160577704
34105.3104.9579783041370.342021695863387
35118.8113.2598697992085.5401302007922
36106.1108.39295653276-2.29295653276004
37109.3109.0808877940580.219112205941876
38117.2118.691204472882-1.49120447288240
3992.590.2708895083132.22911049168705
40104.2101.7579065944742.44209340552557
41112.5115.921811267238-3.42181126723753
42122.4120.2499742348672.15002576513281
43113.3110.8853813532572.4146186467434
4410099.85182188823690.148178111763143
45110.7110.0887442317040.61125576829586
46112.8107.1417924820705.65820751793018
47109.8113.396241186917-3.59624118691704
48117.3114.6035236056742.69647639432623
49109.1110.821747407721-1.72174740772072
50115.9117.526319500059-1.62631950005866
519698.0895815548733-2.08958155487328
5299.8102.328784222795-2.52878422279513
53116.8115.7812825571511.01871744284906
54115.7112.7028624681282.99713753187163
5599.4101.136948516136-1.73694851613586
5694.396.6219014937825-2.32190149378255

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 97.4 & 97.7284213125789 & -0.328421312578872 \tabularnewline
2 & 111.4 & 112.226119326813 & -0.826119326812827 \tabularnewline
3 & 87.4 & 83.7477522404087 & 3.65224775959126 \tabularnewline
4 & 96.8 & 92.8045833601826 & 3.99541663981735 \tabularnewline
5 & 114.1 & 110.242078443506 & 3.85792155649397 \tabularnewline
6 & 110.3 & 111.255159484974 & -0.955159484974221 \tabularnewline
7 & 103.9 & 106.384736688716 & -2.48473668871642 \tabularnewline
8 & 101.6 & 100.181043199689 & 1.41895680031111 \tabularnewline
9 & 94.6 & 98.2874089243174 & -3.68740892431741 \tabularnewline
10 & 95.9 & 100.460591080036 & -4.56059108003627 \tabularnewline
11 & 104.7 & 111.588972695034 & -6.88897269503388 \tabularnewline
12 & 102.8 & 101.617791868156 & 1.18220813184390 \tabularnewline
13 & 98.1 & 98.875601569296 & -0.775601569296084 \tabularnewline
14 & 113.9 & 109.345642101826 & 4.55435789817398 \tabularnewline
15 & 80.9 & 82.6158540612534 & -1.71585406125336 \tabularnewline
16 & 95.7 & 95.5011915151344 & 0.198808484865657 \tabularnewline
17 & 113.2 & 112.959578722370 & 0.240421277629707 \tabularnewline
18 & 105.9 & 109.783152660568 & -3.88315266056845 \tabularnewline
19 & 108.8 & 108.083041683939 & 0.716958316061201 \tabularnewline
20 & 102.3 & 100.046233602006 & 2.25376639799426 \tabularnewline
21 & 99 & 97.2191384497555 & 1.78086155024451 \tabularnewline
22 & 100.7 & 102.139638133757 & -1.4396381337573 \tabularnewline
23 & 115.5 & 110.554916318841 & 4.94508368115872 \tabularnewline
24 & 100.7 & 102.28572799341 & -1.58572799341010 \tabularnewline
25 & 109.9 & 107.293341916346 & 2.60665808365379 \tabularnewline
26 & 114.6 & 115.210714598420 & -0.610714598420099 \tabularnewline
27 & 85.4 & 87.4759226351517 & -2.07592263515166 \tabularnewline
28 & 100.5 & 104.607534307413 & -4.10753430741344 \tabularnewline
29 & 114.8 & 116.495249009735 & -1.69524900973521 \tabularnewline
30 & 116.5 & 116.808851151462 & -0.308851151461769 \tabularnewline
31 & 112.9 & 111.809891757952 & 1.09010824204768 \tabularnewline
32 & 102 & 103.498999816286 & -1.49899981628597 \tabularnewline
33 & 106 & 104.704708394223 & 1.29529160577704 \tabularnewline
34 & 105.3 & 104.957978304137 & 0.342021695863387 \tabularnewline
35 & 118.8 & 113.259869799208 & 5.5401302007922 \tabularnewline
36 & 106.1 & 108.39295653276 & -2.29295653276004 \tabularnewline
37 & 109.3 & 109.080887794058 & 0.219112205941876 \tabularnewline
38 & 117.2 & 118.691204472882 & -1.49120447288240 \tabularnewline
39 & 92.5 & 90.270889508313 & 2.22911049168705 \tabularnewline
40 & 104.2 & 101.757906594474 & 2.44209340552557 \tabularnewline
41 & 112.5 & 115.921811267238 & -3.42181126723753 \tabularnewline
42 & 122.4 & 120.249974234867 & 2.15002576513281 \tabularnewline
43 & 113.3 & 110.885381353257 & 2.4146186467434 \tabularnewline
44 & 100 & 99.8518218882369 & 0.148178111763143 \tabularnewline
45 & 110.7 & 110.088744231704 & 0.61125576829586 \tabularnewline
46 & 112.8 & 107.141792482070 & 5.65820751793018 \tabularnewline
47 & 109.8 & 113.396241186917 & -3.59624118691704 \tabularnewline
48 & 117.3 & 114.603523605674 & 2.69647639432623 \tabularnewline
49 & 109.1 & 110.821747407721 & -1.72174740772072 \tabularnewline
50 & 115.9 & 117.526319500059 & -1.62631950005866 \tabularnewline
51 & 96 & 98.0895815548733 & -2.08958155487328 \tabularnewline
52 & 99.8 & 102.328784222795 & -2.52878422279513 \tabularnewline
53 & 116.8 & 115.781282557151 & 1.01871744284906 \tabularnewline
54 & 115.7 & 112.702862468128 & 2.99713753187163 \tabularnewline
55 & 99.4 & 101.136948516136 & -1.73694851613586 \tabularnewline
56 & 94.3 & 96.6219014937825 & -2.32190149378255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67485&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]97.4[/C][C]97.7284213125789[/C][C]-0.328421312578872[/C][/ROW]
[ROW][C]2[/C][C]111.4[/C][C]112.226119326813[/C][C]-0.826119326812827[/C][/ROW]
[ROW][C]3[/C][C]87.4[/C][C]83.7477522404087[/C][C]3.65224775959126[/C][/ROW]
[ROW][C]4[/C][C]96.8[/C][C]92.8045833601826[/C][C]3.99541663981735[/C][/ROW]
[ROW][C]5[/C][C]114.1[/C][C]110.242078443506[/C][C]3.85792155649397[/C][/ROW]
[ROW][C]6[/C][C]110.3[/C][C]111.255159484974[/C][C]-0.955159484974221[/C][/ROW]
[ROW][C]7[/C][C]103.9[/C][C]106.384736688716[/C][C]-2.48473668871642[/C][/ROW]
[ROW][C]8[/C][C]101.6[/C][C]100.181043199689[/C][C]1.41895680031111[/C][/ROW]
[ROW][C]9[/C][C]94.6[/C][C]98.2874089243174[/C][C]-3.68740892431741[/C][/ROW]
[ROW][C]10[/C][C]95.9[/C][C]100.460591080036[/C][C]-4.56059108003627[/C][/ROW]
[ROW][C]11[/C][C]104.7[/C][C]111.588972695034[/C][C]-6.88897269503388[/C][/ROW]
[ROW][C]12[/C][C]102.8[/C][C]101.617791868156[/C][C]1.18220813184390[/C][/ROW]
[ROW][C]13[/C][C]98.1[/C][C]98.875601569296[/C][C]-0.775601569296084[/C][/ROW]
[ROW][C]14[/C][C]113.9[/C][C]109.345642101826[/C][C]4.55435789817398[/C][/ROW]
[ROW][C]15[/C][C]80.9[/C][C]82.6158540612534[/C][C]-1.71585406125336[/C][/ROW]
[ROW][C]16[/C][C]95.7[/C][C]95.5011915151344[/C][C]0.198808484865657[/C][/ROW]
[ROW][C]17[/C][C]113.2[/C][C]112.959578722370[/C][C]0.240421277629707[/C][/ROW]
[ROW][C]18[/C][C]105.9[/C][C]109.783152660568[/C][C]-3.88315266056845[/C][/ROW]
[ROW][C]19[/C][C]108.8[/C][C]108.083041683939[/C][C]0.716958316061201[/C][/ROW]
[ROW][C]20[/C][C]102.3[/C][C]100.046233602006[/C][C]2.25376639799426[/C][/ROW]
[ROW][C]21[/C][C]99[/C][C]97.2191384497555[/C][C]1.78086155024451[/C][/ROW]
[ROW][C]22[/C][C]100.7[/C][C]102.139638133757[/C][C]-1.4396381337573[/C][/ROW]
[ROW][C]23[/C][C]115.5[/C][C]110.554916318841[/C][C]4.94508368115872[/C][/ROW]
[ROW][C]24[/C][C]100.7[/C][C]102.28572799341[/C][C]-1.58572799341010[/C][/ROW]
[ROW][C]25[/C][C]109.9[/C][C]107.293341916346[/C][C]2.60665808365379[/C][/ROW]
[ROW][C]26[/C][C]114.6[/C][C]115.210714598420[/C][C]-0.610714598420099[/C][/ROW]
[ROW][C]27[/C][C]85.4[/C][C]87.4759226351517[/C][C]-2.07592263515166[/C][/ROW]
[ROW][C]28[/C][C]100.5[/C][C]104.607534307413[/C][C]-4.10753430741344[/C][/ROW]
[ROW][C]29[/C][C]114.8[/C][C]116.495249009735[/C][C]-1.69524900973521[/C][/ROW]
[ROW][C]30[/C][C]116.5[/C][C]116.808851151462[/C][C]-0.308851151461769[/C][/ROW]
[ROW][C]31[/C][C]112.9[/C][C]111.809891757952[/C][C]1.09010824204768[/C][/ROW]
[ROW][C]32[/C][C]102[/C][C]103.498999816286[/C][C]-1.49899981628597[/C][/ROW]
[ROW][C]33[/C][C]106[/C][C]104.704708394223[/C][C]1.29529160577704[/C][/ROW]
[ROW][C]34[/C][C]105.3[/C][C]104.957978304137[/C][C]0.342021695863387[/C][/ROW]
[ROW][C]35[/C][C]118.8[/C][C]113.259869799208[/C][C]5.5401302007922[/C][/ROW]
[ROW][C]36[/C][C]106.1[/C][C]108.39295653276[/C][C]-2.29295653276004[/C][/ROW]
[ROW][C]37[/C][C]109.3[/C][C]109.080887794058[/C][C]0.219112205941876[/C][/ROW]
[ROW][C]38[/C][C]117.2[/C][C]118.691204472882[/C][C]-1.49120447288240[/C][/ROW]
[ROW][C]39[/C][C]92.5[/C][C]90.270889508313[/C][C]2.22911049168705[/C][/ROW]
[ROW][C]40[/C][C]104.2[/C][C]101.757906594474[/C][C]2.44209340552557[/C][/ROW]
[ROW][C]41[/C][C]112.5[/C][C]115.921811267238[/C][C]-3.42181126723753[/C][/ROW]
[ROW][C]42[/C][C]122.4[/C][C]120.249974234867[/C][C]2.15002576513281[/C][/ROW]
[ROW][C]43[/C][C]113.3[/C][C]110.885381353257[/C][C]2.4146186467434[/C][/ROW]
[ROW][C]44[/C][C]100[/C][C]99.8518218882369[/C][C]0.148178111763143[/C][/ROW]
[ROW][C]45[/C][C]110.7[/C][C]110.088744231704[/C][C]0.61125576829586[/C][/ROW]
[ROW][C]46[/C][C]112.8[/C][C]107.141792482070[/C][C]5.65820751793018[/C][/ROW]
[ROW][C]47[/C][C]109.8[/C][C]113.396241186917[/C][C]-3.59624118691704[/C][/ROW]
[ROW][C]48[/C][C]117.3[/C][C]114.603523605674[/C][C]2.69647639432623[/C][/ROW]
[ROW][C]49[/C][C]109.1[/C][C]110.821747407721[/C][C]-1.72174740772072[/C][/ROW]
[ROW][C]50[/C][C]115.9[/C][C]117.526319500059[/C][C]-1.62631950005866[/C][/ROW]
[ROW][C]51[/C][C]96[/C][C]98.0895815548733[/C][C]-2.08958155487328[/C][/ROW]
[ROW][C]52[/C][C]99.8[/C][C]102.328784222795[/C][C]-2.52878422279513[/C][/ROW]
[ROW][C]53[/C][C]116.8[/C][C]115.781282557151[/C][C]1.01871744284906[/C][/ROW]
[ROW][C]54[/C][C]115.7[/C][C]112.702862468128[/C][C]2.99713753187163[/C][/ROW]
[ROW][C]55[/C][C]99.4[/C][C]101.136948516136[/C][C]-1.73694851613586[/C][/ROW]
[ROW][C]56[/C][C]94.3[/C][C]96.6219014937825[/C][C]-2.32190149378255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67485&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67485&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
197.497.7284213125789-0.328421312578872
2111.4112.226119326813-0.826119326812827
387.483.74775224040873.65224775959126
496.892.80458336018263.99541663981735
5114.1110.2420784435063.85792155649397
6110.3111.255159484974-0.955159484974221
7103.9106.384736688716-2.48473668871642
8101.6100.1810431996891.41895680031111
994.698.2874089243174-3.68740892431741
1095.9100.460591080036-4.56059108003627
11104.7111.588972695034-6.88897269503388
12102.8101.6177918681561.18220813184390
1398.198.875601569296-0.775601569296084
14113.9109.3456421018264.55435789817398
1580.982.6158540612534-1.71585406125336
1695.795.50119151513440.198808484865657
17113.2112.9595787223700.240421277629707
18105.9109.783152660568-3.88315266056845
19108.8108.0830416839390.716958316061201
20102.3100.0462336020062.25376639799426
219997.21913844975551.78086155024451
22100.7102.139638133757-1.4396381337573
23115.5110.5549163188414.94508368115872
24100.7102.28572799341-1.58572799341010
25109.9107.2933419163462.60665808365379
26114.6115.210714598420-0.610714598420099
2785.487.4759226351517-2.07592263515166
28100.5104.607534307413-4.10753430741344
29114.8116.495249009735-1.69524900973521
30116.5116.808851151462-0.308851151461769
31112.9111.8098917579521.09010824204768
32102103.498999816286-1.49899981628597
33106104.7047083942231.29529160577704
34105.3104.9579783041370.342021695863387
35118.8113.2598697992085.5401302007922
36106.1108.39295653276-2.29295653276004
37109.3109.0808877940580.219112205941876
38117.2118.691204472882-1.49120447288240
3992.590.2708895083132.22911049168705
40104.2101.7579065944742.44209340552557
41112.5115.921811267238-3.42181126723753
42122.4120.2499742348672.15002576513281
43113.3110.8853813532572.4146186467434
4410099.85182188823690.148178111763143
45110.7110.0887442317040.61125576829586
46112.8107.1417924820705.65820751793018
47109.8113.396241186917-3.59624118691704
48117.3114.6035236056742.69647639432623
49109.1110.821747407721-1.72174740772072
50115.9117.526319500059-1.62631950005866
519698.0895815548733-2.08958155487328
5299.8102.328784222795-2.52878422279513
53116.8115.7812825571511.01871744284906
54115.7112.7028624681282.99713753187163
5599.4101.136948516136-1.73694851613586
5694.396.6219014937825-2.32190149378255






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.2751027901634870.5502055803269750.724897209836513
220.2627284888622740.5254569777245480.737271511137726
230.740372739963570.5192545200728620.259627260036431
240.8369975094842680.3260049810314640.163002490515732
250.7967521491930180.4064957016139630.203247850806982
260.7358288749147450.528342250170510.264171125085255
270.7533440871342470.4933118257315050.246655912865753
280.7119901736654170.5760196526691670.288009826334583
290.6298872827119910.7402254345760180.370112717288009
300.5574308838250160.8851382323499670.442569116174984
310.4452511747186720.8905023494373430.554748825281328
320.3580873100396160.7161746200792320.641912689960384
330.2472738199874650.4945476399749290.752726180012535
340.2876186618785120.5752373237570240.712381338121488
350.3540150378161470.7080300756322940.645984962183853

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.275102790163487 & 0.550205580326975 & 0.724897209836513 \tabularnewline
22 & 0.262728488862274 & 0.525456977724548 & 0.737271511137726 \tabularnewline
23 & 0.74037273996357 & 0.519254520072862 & 0.259627260036431 \tabularnewline
24 & 0.836997509484268 & 0.326004981031464 & 0.163002490515732 \tabularnewline
25 & 0.796752149193018 & 0.406495701613963 & 0.203247850806982 \tabularnewline
26 & 0.735828874914745 & 0.52834225017051 & 0.264171125085255 \tabularnewline
27 & 0.753344087134247 & 0.493311825731505 & 0.246655912865753 \tabularnewline
28 & 0.711990173665417 & 0.576019652669167 & 0.288009826334583 \tabularnewline
29 & 0.629887282711991 & 0.740225434576018 & 0.370112717288009 \tabularnewline
30 & 0.557430883825016 & 0.885138232349967 & 0.442569116174984 \tabularnewline
31 & 0.445251174718672 & 0.890502349437343 & 0.554748825281328 \tabularnewline
32 & 0.358087310039616 & 0.716174620079232 & 0.641912689960384 \tabularnewline
33 & 0.247273819987465 & 0.494547639974929 & 0.752726180012535 \tabularnewline
34 & 0.287618661878512 & 0.575237323757024 & 0.712381338121488 \tabularnewline
35 & 0.354015037816147 & 0.708030075632294 & 0.645984962183853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67485&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]21[/C][C]0.275102790163487[/C][C]0.550205580326975[/C][C]0.724897209836513[/C][/ROW]
[ROW][C]22[/C][C]0.262728488862274[/C][C]0.525456977724548[/C][C]0.737271511137726[/C][/ROW]
[ROW][C]23[/C][C]0.74037273996357[/C][C]0.519254520072862[/C][C]0.259627260036431[/C][/ROW]
[ROW][C]24[/C][C]0.836997509484268[/C][C]0.326004981031464[/C][C]0.163002490515732[/C][/ROW]
[ROW][C]25[/C][C]0.796752149193018[/C][C]0.406495701613963[/C][C]0.203247850806982[/C][/ROW]
[ROW][C]26[/C][C]0.735828874914745[/C][C]0.52834225017051[/C][C]0.264171125085255[/C][/ROW]
[ROW][C]27[/C][C]0.753344087134247[/C][C]0.493311825731505[/C][C]0.246655912865753[/C][/ROW]
[ROW][C]28[/C][C]0.711990173665417[/C][C]0.576019652669167[/C][C]0.288009826334583[/C][/ROW]
[ROW][C]29[/C][C]0.629887282711991[/C][C]0.740225434576018[/C][C]0.370112717288009[/C][/ROW]
[ROW][C]30[/C][C]0.557430883825016[/C][C]0.885138232349967[/C][C]0.442569116174984[/C][/ROW]
[ROW][C]31[/C][C]0.445251174718672[/C][C]0.890502349437343[/C][C]0.554748825281328[/C][/ROW]
[ROW][C]32[/C][C]0.358087310039616[/C][C]0.716174620079232[/C][C]0.641912689960384[/C][/ROW]
[ROW][C]33[/C][C]0.247273819987465[/C][C]0.494547639974929[/C][C]0.752726180012535[/C][/ROW]
[ROW][C]34[/C][C]0.287618661878512[/C][C]0.575237323757024[/C][C]0.712381338121488[/C][/ROW]
[ROW][C]35[/C][C]0.354015037816147[/C][C]0.708030075632294[/C][C]0.645984962183853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67485&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67485&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.2751027901634870.5502055803269750.724897209836513
220.2627284888622740.5254569777245480.737271511137726
230.740372739963570.5192545200728620.259627260036431
240.8369975094842680.3260049810314640.163002490515732
250.7967521491930180.4064957016139630.203247850806982
260.7358288749147450.528342250170510.264171125085255
270.7533440871342470.4933118257315050.246655912865753
280.7119901736654170.5760196526691670.288009826334583
290.6298872827119910.7402254345760180.370112717288009
300.5574308838250160.8851382323499670.442569116174984
310.4452511747186720.8905023494373430.554748825281328
320.3580873100396160.7161746200792320.641912689960384
330.2472738199874650.4945476399749290.752726180012535
340.2876186618785120.5752373237570240.712381338121488
350.3540150378161470.7080300756322940.645984962183853






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=67485&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=67485&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67485&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
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 2
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 3
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 4
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 5
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 6
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 7
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 8
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 9
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 10
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


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')
}