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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 computationThu, 19 Nov 2009 11:27:34 -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/19/t12586553795zf596b5iq439t3.htm/, Retrieved Fri, 19 Apr 2024 06:40:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57879, Retrieved Fri, 19 Apr 2024 06:40:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190

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]
-   PD    [Multiple Regression] [] [2009-11-18 17:25:36] [96d96f181930b548ce74f8c3116c4873]
-   P         [Multiple Regression] [] [2009-11-19 18:27:34] [508aab72d879399b4187e5fcd8f7c773] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.2	2.4	7.5	8.3	8.8	8.9
7.4	2	7.2	7.5	8.3	8.8
8.8	2.1	7.4	7.2	7.5	8.3
9.3	2	8.8	7.4	7.2	7.5
9.3	1.8	9.3	8.8	7.4	7.2
8.7	2.7	9.3	9.3	8.8	7.4
8.2	2.3	8.7	9.3	9.3	8.8
8.3	1.9	8.2	8.7	9.3	9.3
8.5	2	8.3	8.2	8.7	9.3
8.6	2.3	8.5	8.3	8.2	8.7
8.5	2.8	8.6	8.5	8.3	8.2
8.2	2.4	8.5	8.6	8.5	8.3
8.1	2.3	8.2	8.5	8.6	8.5
7.9	2.7	8.1	8.2	8.5	8.6
8.6	2.7	7.9	8.1	8.2	8.5
8.7	2.9	8.6	7.9	8.1	8.2
8.7	3	8.7	8.6	7.9	8.1
8.5	2.2	8.7	8.7	8.6	7.9
8.4	2.3	8.5	8.7	8.7	8.6
8.5	2.8	8.4	8.5	8.7	8.7
8.7	2.8	8.5	8.4	8.5	8.7
8.7	2.8	8.7	8.5	8.4	8.5
8.6	2.2	8.7	8.7	8.5	8.4
8.5	2.6	8.6	8.7	8.7	8.5
8.3	2.8	8.5	8.6	8.7	8.7
8	2.5	8.3	8.5	8.6	8.7
8.2	2.4	8	8.3	8.5	8.6
8.1	2.3	8.2	8	8.3	8.5
8.1	1.9	8.1	8.2	8	8.3
8	1.7	8.1	8.1	8.2	8
7.9	2	8	8.1	8.1	8.2
7.9	2.1	7.9	8	8.1	8.1
8	1.7	7.9	7.9	8	8.1
8	1.8	8	7.9	7.9	8
7.9	1.8	8	8	7.9	7.9
8	1.8	7.9	8	8	7.9
7.7	1.3	8	7.9	8	8
7.2	1.3	7.7	8	7.9	8
7.5	1.3	7.2	7.7	8	7.9
7.3	1.2	7.5	7.2	7.7	8
7	1.4	7.3	7.5	7.2	7.7
7	2.2	7	7.3	7.5	7.2
7	2.9	7	7	7.3	7.5
7.2	3.1	7	7	7	7.3
7.3	3.5	7.2	7	7	7
7.1	3.6	7.3	7.2	7	7
6.8	4.4	7.1	7.3	7.2	7
6.4	4.1	6.8	7.1	7.3	7.2
6.1	5.1	6.4	6.8	7.1	7.3
6.5	5.8	6.1	6.4	6.8	7.1
7.7	5.9	6.5	6.1	6.4	6.8
7.9	5.4	7.7	6.5	6.1	6.4
7.5	5.5	7.9	7.7	6.5	6.1
6.9	4.8	7.5	7.9	7.7	6.5
6.6	3.2	6.9	7.5	7.9	7.7
6.9	2.7	6.6	6.9	7.5	7.9

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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57879&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]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57879&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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 0.998292328693155 + 0.0376630226888407`X(t)`[t] + 1.46957457460690`Y(t-1)`[t] -0.801806872557724`Y(t-2)`[t] -0.115732461513392`Y(t-3)`[t] + 0.329690799318938`Y(t-4) `[t] -0.144354348061105M1[t] -0.120706258608075M2[t] + 0.608263839578986M3[t] -0.390327570481754M4[t] + 0.0102407157144446M5[t] + 0.117272582800866M6[t] + 0.0204583804677823M7[t] + 0.172191674221844M8[t] + 0.0134046809351707M9[t] -0.0958526420642873M10[t] -0.0193853350638593M11[t] -0.00677880468999083t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  0.998292328693155 +  0.0376630226888407`X(t)`[t] +  1.46957457460690`Y(t-1)`[t] -0.801806872557724`Y(t-2)`[t] -0.115732461513392`Y(t-3)`[t] +  0.329690799318938`Y(t-4)
`[t] -0.144354348061105M1[t] -0.120706258608075M2[t] +  0.608263839578986M3[t] -0.390327570481754M4[t] +  0.0102407157144446M5[t] +  0.117272582800866M6[t] +  0.0204583804677823M7[t] +  0.172191674221844M8[t] +  0.0134046809351707M9[t] -0.0958526420642873M10[t] -0.0193853350638593M11[t] -0.00677880468999083t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57879&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  0.998292328693155 +  0.0376630226888407`X(t)`[t] +  1.46957457460690`Y(t-1)`[t] -0.801806872557724`Y(t-2)`[t] -0.115732461513392`Y(t-3)`[t] +  0.329690799318938`Y(t-4)
`[t] -0.144354348061105M1[t] -0.120706258608075M2[t] +  0.608263839578986M3[t] -0.390327570481754M4[t] +  0.0102407157144446M5[t] +  0.117272582800866M6[t] +  0.0204583804677823M7[t] +  0.172191674221844M8[t] +  0.0134046809351707M9[t] -0.0958526420642873M10[t] -0.0193853350638593M11[t] -0.00677880468999083t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57879&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)[t] = + 0.998292328693155 + 0.0376630226888407`X(t)`[t] + 1.46957457460690`Y(t-1)`[t] -0.801806872557724`Y(t-2)`[t] -0.115732461513392`Y(t-3)`[t] + 0.329690799318938`Y(t-4) `[t] -0.144354348061105M1[t] -0.120706258608075M2[t] + 0.608263839578986M3[t] -0.390327570481754M4[t] + 0.0102407157144446M5[t] + 0.117272582800866M6[t] + 0.0204583804677823M7[t] + 0.172191674221844M8[t] + 0.0134046809351707M9[t] -0.0958526420642873M10[t] -0.0193853350638593M11[t] -0.00677880468999083t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.9982923286931550.6689511.49230.1438710.071935
`X(t)`0.03766302268884070.0247011.52480.1355980.067799
`Y(t-1)`1.469574574606900.13794110.653700
`Y(t-2)`-0.8018068725577240.263589-3.04190.0042470.002123
`Y(t-3)`-0.1157324615133920.263607-0.4390.6631230.331562
`Y(t-4) `0.3296907993189380.1437872.29290.0274780.013739
M1-0.1443543480611050.103653-1.39270.1718130.085907
M2-0.1207062586080750.107018-1.12790.2664320.133216
M30.6082638395789860.1085445.60392e-061e-06
M4-0.3903275704817540.141671-2.75520.0089560.004478
M50.01024071571444460.1556340.06580.9478820.473941
M60.1172725828008660.1243250.94330.3514980.175749
M70.02045838046778230.101110.20230.8407320.420366
M80.1721916742218440.1038721.65770.1056080.052804
M90.01340468093517070.1127820.11890.9060160.453008
M10-0.09585264206428730.11389-0.84160.4052640.202632
M11-0.01938533506385930.107819-0.17980.8582680.429134
t-0.006778804689990830.002425-2.79570.0080770.004038

\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) & 0.998292328693155 & 0.668951 & 1.4923 & 0.143871 & 0.071935 \tabularnewline
`X(t)` & 0.0376630226888407 & 0.024701 & 1.5248 & 0.135598 & 0.067799 \tabularnewline
`Y(t-1)` & 1.46957457460690 & 0.137941 & 10.6537 & 0 & 0 \tabularnewline
`Y(t-2)` & -0.801806872557724 & 0.263589 & -3.0419 & 0.004247 & 0.002123 \tabularnewline
`Y(t-3)` & -0.115732461513392 & 0.263607 & -0.439 & 0.663123 & 0.331562 \tabularnewline
`Y(t-4)
` & 0.329690799318938 & 0.143787 & 2.2929 & 0.027478 & 0.013739 \tabularnewline
M1 & -0.144354348061105 & 0.103653 & -1.3927 & 0.171813 & 0.085907 \tabularnewline
M2 & -0.120706258608075 & 0.107018 & -1.1279 & 0.266432 & 0.133216 \tabularnewline
M3 & 0.608263839578986 & 0.108544 & 5.6039 & 2e-06 & 1e-06 \tabularnewline
M4 & -0.390327570481754 & 0.141671 & -2.7552 & 0.008956 & 0.004478 \tabularnewline
M5 & 0.0102407157144446 & 0.155634 & 0.0658 & 0.947882 & 0.473941 \tabularnewline
M6 & 0.117272582800866 & 0.124325 & 0.9433 & 0.351498 & 0.175749 \tabularnewline
M7 & 0.0204583804677823 & 0.10111 & 0.2023 & 0.840732 & 0.420366 \tabularnewline
M8 & 0.172191674221844 & 0.103872 & 1.6577 & 0.105608 & 0.052804 \tabularnewline
M9 & 0.0134046809351707 & 0.112782 & 0.1189 & 0.906016 & 0.453008 \tabularnewline
M10 & -0.0958526420642873 & 0.11389 & -0.8416 & 0.405264 & 0.202632 \tabularnewline
M11 & -0.0193853350638593 & 0.107819 & -0.1798 & 0.858268 & 0.429134 \tabularnewline
t & -0.00677880468999083 & 0.002425 & -2.7957 & 0.008077 & 0.004038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57879&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]0.998292328693155[/C][C]0.668951[/C][C]1.4923[/C][C]0.143871[/C][C]0.071935[/C][/ROW]
[ROW][C]`X(t)`[/C][C]0.0376630226888407[/C][C]0.024701[/C][C]1.5248[/C][C]0.135598[/C][C]0.067799[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]1.46957457460690[/C][C]0.137941[/C][C]10.6537[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]-0.801806872557724[/C][C]0.263589[/C][C]-3.0419[/C][C]0.004247[/C][C]0.002123[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.115732461513392[/C][C]0.263607[/C][C]-0.439[/C][C]0.663123[/C][C]0.331562[/C][/ROW]
[ROW][C]`Y(t-4)
`[/C][C]0.329690799318938[/C][C]0.143787[/C][C]2.2929[/C][C]0.027478[/C][C]0.013739[/C][/ROW]
[ROW][C]M1[/C][C]-0.144354348061105[/C][C]0.103653[/C][C]-1.3927[/C][C]0.171813[/C][C]0.085907[/C][/ROW]
[ROW][C]M2[/C][C]-0.120706258608075[/C][C]0.107018[/C][C]-1.1279[/C][C]0.266432[/C][C]0.133216[/C][/ROW]
[ROW][C]M3[/C][C]0.608263839578986[/C][C]0.108544[/C][C]5.6039[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M4[/C][C]-0.390327570481754[/C][C]0.141671[/C][C]-2.7552[/C][C]0.008956[/C][C]0.004478[/C][/ROW]
[ROW][C]M5[/C][C]0.0102407157144446[/C][C]0.155634[/C][C]0.0658[/C][C]0.947882[/C][C]0.473941[/C][/ROW]
[ROW][C]M6[/C][C]0.117272582800866[/C][C]0.124325[/C][C]0.9433[/C][C]0.351498[/C][C]0.175749[/C][/ROW]
[ROW][C]M7[/C][C]0.0204583804677823[/C][C]0.10111[/C][C]0.2023[/C][C]0.840732[/C][C]0.420366[/C][/ROW]
[ROW][C]M8[/C][C]0.172191674221844[/C][C]0.103872[/C][C]1.6577[/C][C]0.105608[/C][C]0.052804[/C][/ROW]
[ROW][C]M9[/C][C]0.0134046809351707[/C][C]0.112782[/C][C]0.1189[/C][C]0.906016[/C][C]0.453008[/C][/ROW]
[ROW][C]M10[/C][C]-0.0958526420642873[/C][C]0.11389[/C][C]-0.8416[/C][C]0.405264[/C][C]0.202632[/C][/ROW]
[ROW][C]M11[/C][C]-0.0193853350638593[/C][C]0.107819[/C][C]-0.1798[/C][C]0.858268[/C][C]0.429134[/C][/ROW]
[ROW][C]t[/C][C]-0.00677880468999083[/C][C]0.002425[/C][C]-2.7957[/C][C]0.008077[/C][C]0.004038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57879&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57879&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)0.9982923286931550.6689511.49230.1438710.071935
`X(t)`0.03766302268884070.0247011.52480.1355980.067799
`Y(t-1)`1.469574574606900.13794110.653700
`Y(t-2)`-0.8018068725577240.263589-3.04190.0042470.002123
`Y(t-3)`-0.1157324615133920.263607-0.4390.6631230.331562
`Y(t-4) `0.3296907993189380.1437872.29290.0274780.013739
M1-0.1443543480611050.103653-1.39270.1718130.085907
M2-0.1207062586080750.107018-1.12790.2664320.133216
M30.6082638395789860.1085445.60392e-061e-06
M4-0.3903275704817540.141671-2.75520.0089560.004478
M50.01024071571444460.1556340.06580.9478820.473941
M60.1172725828008660.1243250.94330.3514980.175749
M70.02045838046778230.101110.20230.8407320.420366
M80.1721916742218440.1038721.65770.1056080.052804
M90.01340468093517070.1127820.11890.9060160.453008
M10-0.09585264206428730.11389-0.84160.4052640.202632
M11-0.01938533506385930.107819-0.17980.8582680.429134
t-0.006778804689990830.002425-2.79570.0080770.004038






Multiple Linear Regression - Regression Statistics
Multiple R0.985993431228861
R-squared0.972183046426463
Adjusted R-squared0.959738619827776
F-TEST (value)78.121963974539
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.149249431800875
Sum Squared Residuals0.846464929929589

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.985993431228861 \tabularnewline
R-squared & 0.972183046426463 \tabularnewline
Adjusted R-squared & 0.959738619827776 \tabularnewline
F-TEST (value) & 78.121963974539 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.149249431800875 \tabularnewline
Sum Squared Residuals & 0.846464929929589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57879&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.985993431228861[/C][/ROW]
[ROW][C]R-squared[/C][C]0.972183046426463[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.959738619827776[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]78.121963974539[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.149249431800875[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.846464929929589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57879&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57879&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 R0.985993431228861
R-squared0.972183046426463
Adjusted R-squared0.959738619827776
F-TEST (value)78.121963974539
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.149249431800875
Sum Squared Residuals0.846464929929589






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.27.22016515033857-0.0201651503385712
27.47.447439502515-0.0474395025150006
38.88.63559464452090.164405355479107
49.39.294468256438260.00553174356174162
59.39.170929067030970.129070932969028
68.78.80808812731354-0.108088127313538
78.28.2113860547406-0.0113860547406046
88.38.25241757061980.0475824293802062
98.58.7079184455596-0.207918445559603
108.68.67696720350775-0.0769672035077447
118.58.57566465430094-0.0756646543009385
128.28.35589041851203-0.155890418512026
138.17.89466419207820.205335807921803
147.98.06472561630663-0.164725616306633
158.68.574933340660220.0250666593397786
168.78.678825313539290.0211746864607128
178.78.652251156355450.0477488436445533
188.58.495242230421870.0047577695781299
198.48.320710924118220.079289075881782
208.58.53086992150946-0.0308699215094584
218.78.615588760551930.0844112394480652
228.78.658921946815640.0410780531843564
238.68.5011089349180.098891065082001
248.58.391645804535930.108354195464070
258.38.247206645981470.0527933540185279
2688.0506160424236-0.0506160424235927
278.28.4671342020007-0.267134202000699
288.17.982632074040560.117367925959436
298.18.022819093089230.0771809069107674
3088.0736665061053-0.0736665061053069
317.97.91192635444332-0.0119263544433215
327.97.96090129563947-0.0609012956394656
3387.872024221994380.127975778005623
3487.885316020253950.114683979746053
357.97.841854755376720.0581452446232822
3687.695930582138560.304069417861442
377.77.7860731426914-0.0860731426913972
387.27.29346261396794-0.0934626139679346
397.57.476866355845640.0231336441543587
407.37.37719446587287-0.0771944658728678
4177.20301856618916-0.203018566189162
4276.853325910752660.146674089247345
4377.13869281347745-0.138692813477446
447.27.25996148566951-0.0599614856695144
457.37.30446857189408-0.00446857189408546
467.17.17879482942266-0.078794829422665
476.86.88137165540434-0.0813716554043448
486.46.65653319481349-0.256533194813486
496.16.25189086891036-0.151890868910363
506.56.143756224786840.356243775213161
517.77.645471456972550.0545285430274547
527.97.96687989010902-0.0668798901090223
537.57.55098211733519-0.0509821173351869
546.96.869677225406630.0303227745933704
556.66.517283853220410.0827161467795902
566.96.795849726561770.104150273438232

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.2 & 7.22016515033857 & -0.0201651503385712 \tabularnewline
2 & 7.4 & 7.447439502515 & -0.0474395025150006 \tabularnewline
3 & 8.8 & 8.6355946445209 & 0.164405355479107 \tabularnewline
4 & 9.3 & 9.29446825643826 & 0.00553174356174162 \tabularnewline
5 & 9.3 & 9.17092906703097 & 0.129070932969028 \tabularnewline
6 & 8.7 & 8.80808812731354 & -0.108088127313538 \tabularnewline
7 & 8.2 & 8.2113860547406 & -0.0113860547406046 \tabularnewline
8 & 8.3 & 8.2524175706198 & 0.0475824293802062 \tabularnewline
9 & 8.5 & 8.7079184455596 & -0.207918445559603 \tabularnewline
10 & 8.6 & 8.67696720350775 & -0.0769672035077447 \tabularnewline
11 & 8.5 & 8.57566465430094 & -0.0756646543009385 \tabularnewline
12 & 8.2 & 8.35589041851203 & -0.155890418512026 \tabularnewline
13 & 8.1 & 7.8946641920782 & 0.205335807921803 \tabularnewline
14 & 7.9 & 8.06472561630663 & -0.164725616306633 \tabularnewline
15 & 8.6 & 8.57493334066022 & 0.0250666593397786 \tabularnewline
16 & 8.7 & 8.67882531353929 & 0.0211746864607128 \tabularnewline
17 & 8.7 & 8.65225115635545 & 0.0477488436445533 \tabularnewline
18 & 8.5 & 8.49524223042187 & 0.0047577695781299 \tabularnewline
19 & 8.4 & 8.32071092411822 & 0.079289075881782 \tabularnewline
20 & 8.5 & 8.53086992150946 & -0.0308699215094584 \tabularnewline
21 & 8.7 & 8.61558876055193 & 0.0844112394480652 \tabularnewline
22 & 8.7 & 8.65892194681564 & 0.0410780531843564 \tabularnewline
23 & 8.6 & 8.501108934918 & 0.098891065082001 \tabularnewline
24 & 8.5 & 8.39164580453593 & 0.108354195464070 \tabularnewline
25 & 8.3 & 8.24720664598147 & 0.0527933540185279 \tabularnewline
26 & 8 & 8.0506160424236 & -0.0506160424235927 \tabularnewline
27 & 8.2 & 8.4671342020007 & -0.267134202000699 \tabularnewline
28 & 8.1 & 7.98263207404056 & 0.117367925959436 \tabularnewline
29 & 8.1 & 8.02281909308923 & 0.0771809069107674 \tabularnewline
30 & 8 & 8.0736665061053 & -0.0736665061053069 \tabularnewline
31 & 7.9 & 7.91192635444332 & -0.0119263544433215 \tabularnewline
32 & 7.9 & 7.96090129563947 & -0.0609012956394656 \tabularnewline
33 & 8 & 7.87202422199438 & 0.127975778005623 \tabularnewline
34 & 8 & 7.88531602025395 & 0.114683979746053 \tabularnewline
35 & 7.9 & 7.84185475537672 & 0.0581452446232822 \tabularnewline
36 & 8 & 7.69593058213856 & 0.304069417861442 \tabularnewline
37 & 7.7 & 7.7860731426914 & -0.0860731426913972 \tabularnewline
38 & 7.2 & 7.29346261396794 & -0.0934626139679346 \tabularnewline
39 & 7.5 & 7.47686635584564 & 0.0231336441543587 \tabularnewline
40 & 7.3 & 7.37719446587287 & -0.0771944658728678 \tabularnewline
41 & 7 & 7.20301856618916 & -0.203018566189162 \tabularnewline
42 & 7 & 6.85332591075266 & 0.146674089247345 \tabularnewline
43 & 7 & 7.13869281347745 & -0.138692813477446 \tabularnewline
44 & 7.2 & 7.25996148566951 & -0.0599614856695144 \tabularnewline
45 & 7.3 & 7.30446857189408 & -0.00446857189408546 \tabularnewline
46 & 7.1 & 7.17879482942266 & -0.078794829422665 \tabularnewline
47 & 6.8 & 6.88137165540434 & -0.0813716554043448 \tabularnewline
48 & 6.4 & 6.65653319481349 & -0.256533194813486 \tabularnewline
49 & 6.1 & 6.25189086891036 & -0.151890868910363 \tabularnewline
50 & 6.5 & 6.14375622478684 & 0.356243775213161 \tabularnewline
51 & 7.7 & 7.64547145697255 & 0.0545285430274547 \tabularnewline
52 & 7.9 & 7.96687989010902 & -0.0668798901090223 \tabularnewline
53 & 7.5 & 7.55098211733519 & -0.0509821173351869 \tabularnewline
54 & 6.9 & 6.86967722540663 & 0.0303227745933704 \tabularnewline
55 & 6.6 & 6.51728385322041 & 0.0827161467795902 \tabularnewline
56 & 6.9 & 6.79584972656177 & 0.104150273438232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57879&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]7.2[/C][C]7.22016515033857[/C][C]-0.0201651503385712[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]7.447439502515[/C][C]-0.0474395025150006[/C][/ROW]
[ROW][C]3[/C][C]8.8[/C][C]8.6355946445209[/C][C]0.164405355479107[/C][/ROW]
[ROW][C]4[/C][C]9.3[/C][C]9.29446825643826[/C][C]0.00553174356174162[/C][/ROW]
[ROW][C]5[/C][C]9.3[/C][C]9.17092906703097[/C][C]0.129070932969028[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.80808812731354[/C][C]-0.108088127313538[/C][/ROW]
[ROW][C]7[/C][C]8.2[/C][C]8.2113860547406[/C][C]-0.0113860547406046[/C][/ROW]
[ROW][C]8[/C][C]8.3[/C][C]8.2524175706198[/C][C]0.0475824293802062[/C][/ROW]
[ROW][C]9[/C][C]8.5[/C][C]8.7079184455596[/C][C]-0.207918445559603[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.67696720350775[/C][C]-0.0769672035077447[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.57566465430094[/C][C]-0.0756646543009385[/C][/ROW]
[ROW][C]12[/C][C]8.2[/C][C]8.35589041851203[/C][C]-0.155890418512026[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]7.8946641920782[/C][C]0.205335807921803[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.06472561630663[/C][C]-0.164725616306633[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.57493334066022[/C][C]0.0250666593397786[/C][/ROW]
[ROW][C]16[/C][C]8.7[/C][C]8.67882531353929[/C][C]0.0211746864607128[/C][/ROW]
[ROW][C]17[/C][C]8.7[/C][C]8.65225115635545[/C][C]0.0477488436445533[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.49524223042187[/C][C]0.0047577695781299[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.32071092411822[/C][C]0.079289075881782[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.53086992150946[/C][C]-0.0308699215094584[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.61558876055193[/C][C]0.0844112394480652[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]8.65892194681564[/C][C]0.0410780531843564[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.501108934918[/C][C]0.098891065082001[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.39164580453593[/C][C]0.108354195464070[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.24720664598147[/C][C]0.0527933540185279[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.0506160424236[/C][C]-0.0506160424235927[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.4671342020007[/C][C]-0.267134202000699[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]7.98263207404056[/C][C]0.117367925959436[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]8.02281909308923[/C][C]0.0771809069107674[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.0736665061053[/C][C]-0.0736665061053069[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]7.91192635444332[/C][C]-0.0119263544433215[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]7.96090129563947[/C][C]-0.0609012956394656[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.87202422199438[/C][C]0.127975778005623[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.88531602025395[/C][C]0.114683979746053[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.84185475537672[/C][C]0.0581452446232822[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.69593058213856[/C][C]0.304069417861442[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]7.7860731426914[/C][C]-0.0860731426913972[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.29346261396794[/C][C]-0.0934626139679346[/C][/ROW]
[ROW][C]39[/C][C]7.5[/C][C]7.47686635584564[/C][C]0.0231336441543587[/C][/ROW]
[ROW][C]40[/C][C]7.3[/C][C]7.37719446587287[/C][C]-0.0771944658728678[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.20301856618916[/C][C]-0.203018566189162[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.85332591075266[/C][C]0.146674089247345[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]7.13869281347745[/C][C]-0.138692813477446[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.25996148566951[/C][C]-0.0599614856695144[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.30446857189408[/C][C]-0.00446857189408546[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.17879482942266[/C][C]-0.078794829422665[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.88137165540434[/C][C]-0.0813716554043448[/C][/ROW]
[ROW][C]48[/C][C]6.4[/C][C]6.65653319481349[/C][C]-0.256533194813486[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.25189086891036[/C][C]-0.151890868910363[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.14375622478684[/C][C]0.356243775213161[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.64547145697255[/C][C]0.0545285430274547[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.96687989010902[/C][C]-0.0668798901090223[/C][/ROW]
[ROW][C]53[/C][C]7.5[/C][C]7.55098211733519[/C][C]-0.0509821173351869[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.86967722540663[/C][C]0.0303227745933704[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.51728385322041[/C][C]0.0827161467795902[/C][/ROW]
[ROW][C]56[/C][C]6.9[/C][C]6.79584972656177[/C][C]0.104150273438232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57879&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57879&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
17.27.22016515033857-0.0201651503385712
27.47.447439502515-0.0474395025150006
38.88.63559464452090.164405355479107
49.39.294468256438260.00553174356174162
59.39.170929067030970.129070932969028
68.78.80808812731354-0.108088127313538
78.28.2113860547406-0.0113860547406046
88.38.25241757061980.0475824293802062
98.58.7079184455596-0.207918445559603
108.68.67696720350775-0.0769672035077447
118.58.57566465430094-0.0756646543009385
128.28.35589041851203-0.155890418512026
138.17.89466419207820.205335807921803
147.98.06472561630663-0.164725616306633
158.68.574933340660220.0250666593397786
168.78.678825313539290.0211746864607128
178.78.652251156355450.0477488436445533
188.58.495242230421870.0047577695781299
198.48.320710924118220.079289075881782
208.58.53086992150946-0.0308699215094584
218.78.615588760551930.0844112394480652
228.78.658921946815640.0410780531843564
238.68.5011089349180.098891065082001
248.58.391645804535930.108354195464070
258.38.247206645981470.0527933540185279
2688.0506160424236-0.0506160424235927
278.28.4671342020007-0.267134202000699
288.17.982632074040560.117367925959436
298.18.022819093089230.0771809069107674
3088.0736665061053-0.0736665061053069
317.97.91192635444332-0.0119263544433215
327.97.96090129563947-0.0609012956394656
3387.872024221994380.127975778005623
3487.885316020253950.114683979746053
357.97.841854755376720.0581452446232822
3687.695930582138560.304069417861442
377.77.7860731426914-0.0860731426913972
387.27.29346261396794-0.0934626139679346
397.57.476866355845640.0231336441543587
407.37.37719446587287-0.0771944658728678
4177.20301856618916-0.203018566189162
4276.853325910752660.146674089247345
4377.13869281347745-0.138692813477446
447.27.25996148566951-0.0599614856695144
457.37.30446857189408-0.00446857189408546
467.17.17879482942266-0.078794829422665
476.86.88137165540434-0.0813716554043448
486.46.65653319481349-0.256533194813486
496.16.25189086891036-0.151890868910363
506.56.143756224786840.356243775213161
517.77.645471456972550.0545285430274547
527.97.96687989010902-0.0668798901090223
537.57.55098211733519-0.0509821173351869
546.96.869677225406630.0303227745933704
556.66.517283853220410.0827161467795902
566.96.795849726561770.104150273438232






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.09964282738495020.1992856547699000.90035717261505
220.1246857226260460.2493714452520920.875314277373954
230.05447877714434420.1089575542886880.945521222855656
240.05186546217400170.1037309243480030.948134537825998
250.0251744922236570.0503489844473140.974825507776343
260.01416094278481880.02832188556963760.985839057215181
270.3136850977814730.6273701955629460.686314902218527
280.2136394565590310.4272789131180630.786360543440969
290.140549500967410.281099001934820.85945049903259
300.1654514508064190.3309029016128380.834548549193581
310.1216225932306360.2432451864612730.878377406769363
320.1057664629832130.2115329259664250.894233537016787
330.07117735235949840.1423547047189970.928822647640502
340.04373570820363250.0874714164072650.956264291796368
350.02044093231002880.04088186462005760.97955906768997

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0996428273849502 & 0.199285654769900 & 0.90035717261505 \tabularnewline
22 & 0.124685722626046 & 0.249371445252092 & 0.875314277373954 \tabularnewline
23 & 0.0544787771443442 & 0.108957554288688 & 0.945521222855656 \tabularnewline
24 & 0.0518654621740017 & 0.103730924348003 & 0.948134537825998 \tabularnewline
25 & 0.025174492223657 & 0.050348984447314 & 0.974825507776343 \tabularnewline
26 & 0.0141609427848188 & 0.0283218855696376 & 0.985839057215181 \tabularnewline
27 & 0.313685097781473 & 0.627370195562946 & 0.686314902218527 \tabularnewline
28 & 0.213639456559031 & 0.427278913118063 & 0.786360543440969 \tabularnewline
29 & 0.14054950096741 & 0.28109900193482 & 0.85945049903259 \tabularnewline
30 & 0.165451450806419 & 0.330902901612838 & 0.834548549193581 \tabularnewline
31 & 0.121622593230636 & 0.243245186461273 & 0.878377406769363 \tabularnewline
32 & 0.105766462983213 & 0.211532925966425 & 0.894233537016787 \tabularnewline
33 & 0.0711773523594984 & 0.142354704718997 & 0.928822647640502 \tabularnewline
34 & 0.0437357082036325 & 0.087471416407265 & 0.956264291796368 \tabularnewline
35 & 0.0204409323100288 & 0.0408818646200576 & 0.97955906768997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57879&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]0.0996428273849502[/C][C]0.199285654769900[/C][C]0.90035717261505[/C][/ROW]
[ROW][C]22[/C][C]0.124685722626046[/C][C]0.249371445252092[/C][C]0.875314277373954[/C][/ROW]
[ROW][C]23[/C][C]0.0544787771443442[/C][C]0.108957554288688[/C][C]0.945521222855656[/C][/ROW]
[ROW][C]24[/C][C]0.0518654621740017[/C][C]0.103730924348003[/C][C]0.948134537825998[/C][/ROW]
[ROW][C]25[/C][C]0.025174492223657[/C][C]0.050348984447314[/C][C]0.974825507776343[/C][/ROW]
[ROW][C]26[/C][C]0.0141609427848188[/C][C]0.0283218855696376[/C][C]0.985839057215181[/C][/ROW]
[ROW][C]27[/C][C]0.313685097781473[/C][C]0.627370195562946[/C][C]0.686314902218527[/C][/ROW]
[ROW][C]28[/C][C]0.213639456559031[/C][C]0.427278913118063[/C][C]0.786360543440969[/C][/ROW]
[ROW][C]29[/C][C]0.14054950096741[/C][C]0.28109900193482[/C][C]0.85945049903259[/C][/ROW]
[ROW][C]30[/C][C]0.165451450806419[/C][C]0.330902901612838[/C][C]0.834548549193581[/C][/ROW]
[ROW][C]31[/C][C]0.121622593230636[/C][C]0.243245186461273[/C][C]0.878377406769363[/C][/ROW]
[ROW][C]32[/C][C]0.105766462983213[/C][C]0.211532925966425[/C][C]0.894233537016787[/C][/ROW]
[ROW][C]33[/C][C]0.0711773523594984[/C][C]0.142354704718997[/C][C]0.928822647640502[/C][/ROW]
[ROW][C]34[/C][C]0.0437357082036325[/C][C]0.087471416407265[/C][C]0.956264291796368[/C][/ROW]
[ROW][C]35[/C][C]0.0204409323100288[/C][C]0.0408818646200576[/C][C]0.97955906768997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57879&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57879&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
210.09964282738495020.1992856547699000.90035717261505
220.1246857226260460.2493714452520920.875314277373954
230.05447877714434420.1089575542886880.945521222855656
240.05186546217400170.1037309243480030.948134537825998
250.0251744922236570.0503489844473140.974825507776343
260.01416094278481880.02832188556963760.985839057215181
270.3136850977814730.6273701955629460.686314902218527
280.2136394565590310.4272789131180630.786360543440969
290.140549500967410.281099001934820.85945049903259
300.1654514508064190.3309029016128380.834548549193581
310.1216225932306360.2432451864612730.878377406769363
320.1057664629832130.2115329259664250.894233537016787
330.07117735235949840.1423547047189970.928822647640502
340.04373570820363250.0874714164072650.956264291796368
350.02044093231002880.04088186462005760.97955906768997






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.133333333333333NOK
10% type I error level40.266666666666667NOK

\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 & 2 & 0.133333333333333 & NOK \tabularnewline
10% type I error level & 4 & 0.266666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57879&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]2[/C][C]0.133333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.266666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57879&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57879&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 level20.133333333333333NOK
10% type I error level40.266666666666667NOK


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')
}