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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, 17 Dec 2009 07:24:39 -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/17/t1261059973wnubrb2m4h16t1h.htm/, Retrieved Tue, 30 Apr 2024 06:51:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68907, Retrieved Tue, 30 Apr 2024 06:51:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-18 16:22:43] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D      [Multiple Regression] [Multiple Regressi...] [2009-12-17 13:47:34] [90f6d58d515a4caed6fb4b8be4e11eaa]
-   PD          [Multiple Regression] [Multiple Regressi...] [2009-12-17 14:24:39] [2b548c9d2e9bba6e1eaf65bd4d551f41] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8,3	101,6	8,2	8,7	9,3	9,3
8,5	94,6	8,3	8,2	8,7	9,3
8,6	95,9	8,5	8,3	8,2	8,7
8,5	104,7	8,6	8,5	8,3	8,2
8,2	102,8	8,5	8,6	8,5	8,3
8,1	98,1	8,2	8,5	8,6	8,5
7,9	113,9	8,1	8,2	8,5	8,6
8,6	80,9	7,9	8,1	8,2	8,5
8,7	95,7	8,6	7,9	8,1	8,2
8,7	113,2	8,7	8,6	7,9	8,1
8,5	105,9	8,7	8,7	8,6	7,9
8,4	108,8	8,5	8,7	8,7	8,6
8,5	102,3	8,4	8,5	8,7	8,7
8,7	99	8,5	8,4	8,5	8,7
8,7	100,7	8,7	8,5	8,4	8,5
8,6	115,5	8,7	8,7	8,5	8,4
8,5	100,7	8,6	8,7	8,7	8,5
8,3	109,9	8,5	8,6	8,7	8,7
8	114,6	8,3	8,5	8,6	8,7
8,2	85,4	8	8,3	8,5	8,6
8,1	100,5	8,2	8	8,3	8,5
8,1	114,8	8,1	8,2	8	8,3
8	116,5	8,1	8,1	8,2	8
7,9	112,9	8	8,1	8,1	8,2
7,9	102	7,9	8	8,1	8,1
8	106	7,9	7,9	8	8,1
8	105,3	8	7,9	7,9	8
7,9	118,8	8	8	7,9	7,9
8	106,1	7,9	8	8	7,9
7,7	109,3	8	7,9	8	8
7,2	117,2	7,7	8	7,9	8
7,5	92,5	7,2	7,7	8	7,9
7,3	104,2	7,5	7,2	7,7	8
7	112,5	7,3	7,5	7,2	7,7
7	122,4	7	7,3	7,5	7,2
7	113,3	7	7	7,3	7,5
7,2	100	7	7	7	7,3
7,3	110,7	7,2	7	7	7
7,1	112,8	7,3	7,2	7	7
6,8	109,8	7,1	7,3	7,2	7
6,4	117,3	6,8	7,1	7,3	7,2
6,1	109,1	6,4	6,8	7,1	7,3
6,5	115,9	6,1	6,4	6,8	7,1
7,7	96	6,5	6,1	6,4	6,8
7,9	99,8	7,7	6,5	6,1	6,4
7,5	116,8	7,9	7,7	6,5	6,1
6,9	115,7	7,5	7,9	7,7	6,5
6,6	99,4	6,9	7,5	7,9	7,7
6,9	94,3	6,6	6,9	7,5	7,9
7,7	91	6,9	6,6	6,9	7,5
8	93,2	7,7	6,9	6,6	6,9
8	103,1	8	7,7	6,9	6,6
7,7	94,1	8	8	7,7	6,9
7,3	91,8	7,7	8	8	7,7
7,4	102,7	7,3	7,7	8	8
8,1	82,6	7,4	7,3	7,7	8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68907&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]3 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=68907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68907&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 1.98590756285012 -0.00943061190311762X[t] + 1.52598349264715Y1[t] -0.930814478092821Y2[t] + 0.083898441498005Y3[t] + 0.200460686192801Y4[t] + 0.0943347310193463M1[t] + 0.0323584890565962M2[t] -0.132720980590720M3[t] + 0.0607190532369926M4[t] -0.026252010278004M5[t] -0.155003542088029M6[t] + 0.0471044771517931M7[t] + 0.38169268214532M8[t] -0.486310067426483M9[t] + 0.0920046044556282M10[t] + 0.123841822712825M11[t] -0.00251557949133382t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  1.98590756285012 -0.00943061190311762X[t] +  1.52598349264715Y1[t] -0.930814478092821Y2[t] +  0.083898441498005Y3[t] +  0.200460686192801Y4[t] +  0.0943347310193463M1[t] +  0.0323584890565962M2[t] -0.132720980590720M3[t] +  0.0607190532369926M4[t] -0.026252010278004M5[t] -0.155003542088029M6[t] +  0.0471044771517931M7[t] +  0.38169268214532M8[t] -0.486310067426483M9[t] +  0.0920046044556282M10[t] +  0.123841822712825M11[t] -0.00251557949133382t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68907&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  1.98590756285012 -0.00943061190311762X[t] +  1.52598349264715Y1[t] -0.930814478092821Y2[t] +  0.083898441498005Y3[t] +  0.200460686192801Y4[t] +  0.0943347310193463M1[t] +  0.0323584890565962M2[t] -0.132720980590720M3[t] +  0.0607190532369926M4[t] -0.026252010278004M5[t] -0.155003542088029M6[t] +  0.0471044771517931M7[t] +  0.38169268214532M8[t] -0.486310067426483M9[t] +  0.0920046044556282M10[t] +  0.123841822712825M11[t] -0.00251557949133382t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68907&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] = + 1.98590756285012 -0.00943061190311762X[t] + 1.52598349264715Y1[t] -0.930814478092821Y2[t] + 0.083898441498005Y3[t] + 0.200460686192801Y4[t] + 0.0943347310193463M1[t] + 0.0323584890565962M2[t] -0.132720980590720M3[t] + 0.0607190532369926M4[t] -0.026252010278004M5[t] -0.155003542088029M6[t] + 0.0471044771517931M7[t] + 0.38169268214532M8[t] -0.486310067426483M9[t] + 0.0920046044556282M10[t] + 0.123841822712825M11[t] -0.00251557949133382t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.985907562850120.9814432.02350.0501010.02505
X-0.009430611903117620.004171-2.26070.0295850.014792
Y11.525983492647150.15062910.130700
Y2-0.9308144780928210.289905-3.21080.0026930.001347
Y30.0838984414980050.2897110.28960.7737020.386851
Y40.2004606861928010.1610511.24470.2208620.110431
M10.09433473101934630.1162150.81170.4220050.211003
M20.03235848905659620.1226340.26390.7933120.396656
M3-0.1327209805907200.125244-1.05970.295970.147985
M40.06071905323699260.1194330.50840.6141140.307057
M5-0.0262520102780040.115121-0.2280.820840.41042
M6-0.1550035420880290.110417-1.40380.1684980.084249
M70.04710447715179310.1120130.42050.6764690.338234
M80.381692682145320.1425362.67790.0108820.005441
M9-0.4863100674264830.15808-3.07630.0038740.001937
M100.09200460445562820.1703440.54010.5922720.296136
M110.1238418227128250.1411840.87720.3859080.192954
t-0.002515579491333820.00295-0.85280.3991130.199557

\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) & 1.98590756285012 & 0.981443 & 2.0235 & 0.050101 & 0.02505 \tabularnewline
X & -0.00943061190311762 & 0.004171 & -2.2607 & 0.029585 & 0.014792 \tabularnewline
Y1 & 1.52598349264715 & 0.150629 & 10.1307 & 0 & 0 \tabularnewline
Y2 & -0.930814478092821 & 0.289905 & -3.2108 & 0.002693 & 0.001347 \tabularnewline
Y3 & 0.083898441498005 & 0.289711 & 0.2896 & 0.773702 & 0.386851 \tabularnewline
Y4 & 0.200460686192801 & 0.161051 & 1.2447 & 0.220862 & 0.110431 \tabularnewline
M1 & 0.0943347310193463 & 0.116215 & 0.8117 & 0.422005 & 0.211003 \tabularnewline
M2 & 0.0323584890565962 & 0.122634 & 0.2639 & 0.793312 & 0.396656 \tabularnewline
M3 & -0.132720980590720 & 0.125244 & -1.0597 & 0.29597 & 0.147985 \tabularnewline
M4 & 0.0607190532369926 & 0.119433 & 0.5084 & 0.614114 & 0.307057 \tabularnewline
M5 & -0.026252010278004 & 0.115121 & -0.228 & 0.82084 & 0.41042 \tabularnewline
M6 & -0.155003542088029 & 0.110417 & -1.4038 & 0.168498 & 0.084249 \tabularnewline
M7 & 0.0471044771517931 & 0.112013 & 0.4205 & 0.676469 & 0.338234 \tabularnewline
M8 & 0.38169268214532 & 0.142536 & 2.6779 & 0.010882 & 0.005441 \tabularnewline
M9 & -0.486310067426483 & 0.15808 & -3.0763 & 0.003874 & 0.001937 \tabularnewline
M10 & 0.0920046044556282 & 0.170344 & 0.5401 & 0.592272 & 0.296136 \tabularnewline
M11 & 0.123841822712825 & 0.141184 & 0.8772 & 0.385908 & 0.192954 \tabularnewline
t & -0.00251557949133382 & 0.00295 & -0.8528 & 0.399113 & 0.199557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68907&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]1.98590756285012[/C][C]0.981443[/C][C]2.0235[/C][C]0.050101[/C][C]0.02505[/C][/ROW]
[ROW][C]X[/C][C]-0.00943061190311762[/C][C]0.004171[/C][C]-2.2607[/C][C]0.029585[/C][C]0.014792[/C][/ROW]
[ROW][C]Y1[/C][C]1.52598349264715[/C][C]0.150629[/C][C]10.1307[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.930814478092821[/C][C]0.289905[/C][C]-3.2108[/C][C]0.002693[/C][C]0.001347[/C][/ROW]
[ROW][C]Y3[/C][C]0.083898441498005[/C][C]0.289711[/C][C]0.2896[/C][C]0.773702[/C][C]0.386851[/C][/ROW]
[ROW][C]Y4[/C][C]0.200460686192801[/C][C]0.161051[/C][C]1.2447[/C][C]0.220862[/C][C]0.110431[/C][/ROW]
[ROW][C]M1[/C][C]0.0943347310193463[/C][C]0.116215[/C][C]0.8117[/C][C]0.422005[/C][C]0.211003[/C][/ROW]
[ROW][C]M2[/C][C]0.0323584890565962[/C][C]0.122634[/C][C]0.2639[/C][C]0.793312[/C][C]0.396656[/C][/ROW]
[ROW][C]M3[/C][C]-0.132720980590720[/C][C]0.125244[/C][C]-1.0597[/C][C]0.29597[/C][C]0.147985[/C][/ROW]
[ROW][C]M4[/C][C]0.0607190532369926[/C][C]0.119433[/C][C]0.5084[/C][C]0.614114[/C][C]0.307057[/C][/ROW]
[ROW][C]M5[/C][C]-0.026252010278004[/C][C]0.115121[/C][C]-0.228[/C][C]0.82084[/C][C]0.41042[/C][/ROW]
[ROW][C]M6[/C][C]-0.155003542088029[/C][C]0.110417[/C][C]-1.4038[/C][C]0.168498[/C][C]0.084249[/C][/ROW]
[ROW][C]M7[/C][C]0.0471044771517931[/C][C]0.112013[/C][C]0.4205[/C][C]0.676469[/C][C]0.338234[/C][/ROW]
[ROW][C]M8[/C][C]0.38169268214532[/C][C]0.142536[/C][C]2.6779[/C][C]0.010882[/C][C]0.005441[/C][/ROW]
[ROW][C]M9[/C][C]-0.486310067426483[/C][C]0.15808[/C][C]-3.0763[/C][C]0.003874[/C][C]0.001937[/C][/ROW]
[ROW][C]M10[/C][C]0.0920046044556282[/C][C]0.170344[/C][C]0.5401[/C][C]0.592272[/C][C]0.296136[/C][/ROW]
[ROW][C]M11[/C][C]0.123841822712825[/C][C]0.141184[/C][C]0.8772[/C][C]0.385908[/C][C]0.192954[/C][/ROW]
[ROW][C]t[/C][C]-0.00251557949133382[/C][C]0.00295[/C][C]-0.8528[/C][C]0.399113[/C][C]0.199557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68907&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)1.985907562850120.9814432.02350.0501010.02505
X-0.009430611903117620.004171-2.26070.0295850.014792
Y11.525983492647150.15062910.130700
Y2-0.9308144780928210.289905-3.21080.0026930.001347
Y30.0838984414980050.2897110.28960.7737020.386851
Y40.2004606861928010.1610511.24470.2208620.110431
M10.09433473101934630.1162150.81170.4220050.211003
M20.03235848905659620.1226340.26390.7933120.396656
M3-0.1327209805907200.125244-1.05970.295970.147985
M40.06071905323699260.1194330.50840.6141140.307057
M5-0.0262520102780040.115121-0.2280.820840.41042
M6-0.1550035420880290.110417-1.40380.1684980.084249
M70.04710447715179310.1120130.42050.6764690.338234
M80.381692682145320.1425362.67790.0108820.005441
M9-0.4863100674264830.15808-3.07630.0038740.001937
M100.09200460445562820.1703440.54010.5922720.296136
M110.1238418227128250.1411840.87720.3859080.192954
t-0.002515579491333820.00295-0.85280.3991130.199557






Multiple Linear Regression - Regression Statistics
Multiple R0.97925484748044
R-squared0.958940056313942
Adjusted R-squared0.9405711341386
F-TEST (value)52.2044814148763
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.162151251073433
Sum Squared Residuals0.999135072537818

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.97925484748044 \tabularnewline
R-squared & 0.958940056313942 \tabularnewline
Adjusted R-squared & 0.9405711341386 \tabularnewline
F-TEST (value) & 52.2044814148763 \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 & 0.162151251073433 \tabularnewline
Sum Squared Residuals & 0.999135072537818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68907&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.97925484748044[/C][/ROW]
[ROW][C]R-squared[/C][C]0.958940056313942[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.9405711341386[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]52.2044814148763[/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]0.162151251073433[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.999135072537818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68907&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68907&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 R0.97925484748044
R-squared0.958940056313942
Adjusted R-squared0.9405711341386
F-TEST (value)52.2044814148763
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.162151251073433
Sum Squared Residuals0.999135072537818






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.38.179095112844980.120904887155019
28.58.74828409812503-0.248284098125033
38.68.6183188717678-0.0183188717677956
48.58.60084889605629-0.100848896056286
58.28.32042637551077-0.120426375510767
68.17.917251521557560.182748478442443
77.98.1061425118694-0.206142511869397
88.68.492094478385640.107905521614356
98.78.66782638362030.0321736163797068
108.78.542792225387370.157207774612629
118.58.56651265504675-0.0665126550467537
128.48.256322104278890.143677895721114
138.58.463050848150290.0369491518497075
148.78.658580154750890.0414198452491076
158.78.638586334708730.0614136652912708
168.68.492118612790920.107881387209076
178.58.42643243360490.0735675663950994
188.38.188978928577990.111021071422013
1988.12374239751187-0.123742397511875
208.28.43112082564044-0.23112082564044
218.17.965815541878620.134184458121378
228.18.002733969483580.0972660305164226
2388.06574649826518-0.0657464982651822
247.97.852443242736290.0475567572637083
257.97.96749309393357-0.0674930939335735
2687.94997042852650.0500295714734993
2787.913139244215670.0868607557843335
287.97.86362292143140.0363770785686043
2987.749696544479750.250303455520255
307.77.85397734078169-0.153977340781686
317.27.41980160674232-0.219801606742319
327.57.489406718886310.0105932811136916
337.37.42662905356713-0.126629053567130
3477.23762559859791-0.237625598597911
3576.826891216700330.17310878329967
3677.10895524380063-0.108955243800627
377.27.26093986395214-0.060939863952142
387.37.34059898780629-0.0405989878062894
397.17.11963510731724-0.0196351073172426
406.86.95735293932386-0.157352939323864
416.46.57398653625693-0.173986536256931
426.16.1921677692498-0.0921677692498036
436.56.176901121812110.323098878187889
447.77.492583082216010.207416917783991
457.97.93972902093396-0.0397290209339552
467.57.51684820653114-0.0168482065311401
476.96.94084962998773-0.040849629987734
486.66.6822794091842-0.0822794091841953
496.96.92942108111901-0.0294210811190112
507.77.502566330791280.197433669208716
5188.11032044199057-0.110320441990566
5287.886056630397530.113943369602470
537.77.72945811014766-0.0294581101476566
547.37.34762443983297-0.047624439832967
557.47.17341236206430.226587637935702
568.18.1947948948716-0.0947948948715987

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.3 & 8.17909511284498 & 0.120904887155019 \tabularnewline
2 & 8.5 & 8.74828409812503 & -0.248284098125033 \tabularnewline
3 & 8.6 & 8.6183188717678 & -0.0183188717677956 \tabularnewline
4 & 8.5 & 8.60084889605629 & -0.100848896056286 \tabularnewline
5 & 8.2 & 8.32042637551077 & -0.120426375510767 \tabularnewline
6 & 8.1 & 7.91725152155756 & 0.182748478442443 \tabularnewline
7 & 7.9 & 8.1061425118694 & -0.206142511869397 \tabularnewline
8 & 8.6 & 8.49209447838564 & 0.107905521614356 \tabularnewline
9 & 8.7 & 8.6678263836203 & 0.0321736163797068 \tabularnewline
10 & 8.7 & 8.54279222538737 & 0.157207774612629 \tabularnewline
11 & 8.5 & 8.56651265504675 & -0.0665126550467537 \tabularnewline
12 & 8.4 & 8.25632210427889 & 0.143677895721114 \tabularnewline
13 & 8.5 & 8.46305084815029 & 0.0369491518497075 \tabularnewline
14 & 8.7 & 8.65858015475089 & 0.0414198452491076 \tabularnewline
15 & 8.7 & 8.63858633470873 & 0.0614136652912708 \tabularnewline
16 & 8.6 & 8.49211861279092 & 0.107881387209076 \tabularnewline
17 & 8.5 & 8.4264324336049 & 0.0735675663950994 \tabularnewline
18 & 8.3 & 8.18897892857799 & 0.111021071422013 \tabularnewline
19 & 8 & 8.12374239751187 & -0.123742397511875 \tabularnewline
20 & 8.2 & 8.43112082564044 & -0.23112082564044 \tabularnewline
21 & 8.1 & 7.96581554187862 & 0.134184458121378 \tabularnewline
22 & 8.1 & 8.00273396948358 & 0.0972660305164226 \tabularnewline
23 & 8 & 8.06574649826518 & -0.0657464982651822 \tabularnewline
24 & 7.9 & 7.85244324273629 & 0.0475567572637083 \tabularnewline
25 & 7.9 & 7.96749309393357 & -0.0674930939335735 \tabularnewline
26 & 8 & 7.9499704285265 & 0.0500295714734993 \tabularnewline
27 & 8 & 7.91313924421567 & 0.0868607557843335 \tabularnewline
28 & 7.9 & 7.8636229214314 & 0.0363770785686043 \tabularnewline
29 & 8 & 7.74969654447975 & 0.250303455520255 \tabularnewline
30 & 7.7 & 7.85397734078169 & -0.153977340781686 \tabularnewline
31 & 7.2 & 7.41980160674232 & -0.219801606742319 \tabularnewline
32 & 7.5 & 7.48940671888631 & 0.0105932811136916 \tabularnewline
33 & 7.3 & 7.42662905356713 & -0.126629053567130 \tabularnewline
34 & 7 & 7.23762559859791 & -0.237625598597911 \tabularnewline
35 & 7 & 6.82689121670033 & 0.17310878329967 \tabularnewline
36 & 7 & 7.10895524380063 & -0.108955243800627 \tabularnewline
37 & 7.2 & 7.26093986395214 & -0.060939863952142 \tabularnewline
38 & 7.3 & 7.34059898780629 & -0.0405989878062894 \tabularnewline
39 & 7.1 & 7.11963510731724 & -0.0196351073172426 \tabularnewline
40 & 6.8 & 6.95735293932386 & -0.157352939323864 \tabularnewline
41 & 6.4 & 6.57398653625693 & -0.173986536256931 \tabularnewline
42 & 6.1 & 6.1921677692498 & -0.0921677692498036 \tabularnewline
43 & 6.5 & 6.17690112181211 & 0.323098878187889 \tabularnewline
44 & 7.7 & 7.49258308221601 & 0.207416917783991 \tabularnewline
45 & 7.9 & 7.93972902093396 & -0.0397290209339552 \tabularnewline
46 & 7.5 & 7.51684820653114 & -0.0168482065311401 \tabularnewline
47 & 6.9 & 6.94084962998773 & -0.040849629987734 \tabularnewline
48 & 6.6 & 6.6822794091842 & -0.0822794091841953 \tabularnewline
49 & 6.9 & 6.92942108111901 & -0.0294210811190112 \tabularnewline
50 & 7.7 & 7.50256633079128 & 0.197433669208716 \tabularnewline
51 & 8 & 8.11032044199057 & -0.110320441990566 \tabularnewline
52 & 8 & 7.88605663039753 & 0.113943369602470 \tabularnewline
53 & 7.7 & 7.72945811014766 & -0.0294581101476566 \tabularnewline
54 & 7.3 & 7.34762443983297 & -0.047624439832967 \tabularnewline
55 & 7.4 & 7.1734123620643 & 0.226587637935702 \tabularnewline
56 & 8.1 & 8.1947948948716 & -0.0947948948715987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68907&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]8.3[/C][C]8.17909511284498[/C][C]0.120904887155019[/C][/ROW]
[ROW][C]2[/C][C]8.5[/C][C]8.74828409812503[/C][C]-0.248284098125033[/C][/ROW]
[ROW][C]3[/C][C]8.6[/C][C]8.6183188717678[/C][C]-0.0183188717677956[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]8.60084889605629[/C][C]-0.100848896056286[/C][/ROW]
[ROW][C]5[/C][C]8.2[/C][C]8.32042637551077[/C][C]-0.120426375510767[/C][/ROW]
[ROW][C]6[/C][C]8.1[/C][C]7.91725152155756[/C][C]0.182748478442443[/C][/ROW]
[ROW][C]7[/C][C]7.9[/C][C]8.1061425118694[/C][C]-0.206142511869397[/C][/ROW]
[ROW][C]8[/C][C]8.6[/C][C]8.49209447838564[/C][C]0.107905521614356[/C][/ROW]
[ROW][C]9[/C][C]8.7[/C][C]8.6678263836203[/C][C]0.0321736163797068[/C][/ROW]
[ROW][C]10[/C][C]8.7[/C][C]8.54279222538737[/C][C]0.157207774612629[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.56651265504675[/C][C]-0.0665126550467537[/C][/ROW]
[ROW][C]12[/C][C]8.4[/C][C]8.25632210427889[/C][C]0.143677895721114[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.46305084815029[/C][C]0.0369491518497075[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.65858015475089[/C][C]0.0414198452491076[/C][/ROW]
[ROW][C]15[/C][C]8.7[/C][C]8.63858633470873[/C][C]0.0614136652912708[/C][/ROW]
[ROW][C]16[/C][C]8.6[/C][C]8.49211861279092[/C][C]0.107881387209076[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.4264324336049[/C][C]0.0735675663950994[/C][/ROW]
[ROW][C]18[/C][C]8.3[/C][C]8.18897892857799[/C][C]0.111021071422013[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]8.12374239751187[/C][C]-0.123742397511875[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.43112082564044[/C][C]-0.23112082564044[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.96581554187862[/C][C]0.134184458121378[/C][/ROW]
[ROW][C]22[/C][C]8.1[/C][C]8.00273396948358[/C][C]0.0972660305164226[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.06574649826518[/C][C]-0.0657464982651822[/C][/ROW]
[ROW][C]24[/C][C]7.9[/C][C]7.85244324273629[/C][C]0.0475567572637083[/C][/ROW]
[ROW][C]25[/C][C]7.9[/C][C]7.96749309393357[/C][C]-0.0674930939335735[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]7.9499704285265[/C][C]0.0500295714734993[/C][/ROW]
[ROW][C]27[/C][C]8[/C][C]7.91313924421567[/C][C]0.0868607557843335[/C][/ROW]
[ROW][C]28[/C][C]7.9[/C][C]7.8636229214314[/C][C]0.0363770785686043[/C][/ROW]
[ROW][C]29[/C][C]8[/C][C]7.74969654447975[/C][C]0.250303455520255[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.85397734078169[/C][C]-0.153977340781686[/C][/ROW]
[ROW][C]31[/C][C]7.2[/C][C]7.41980160674232[/C][C]-0.219801606742319[/C][/ROW]
[ROW][C]32[/C][C]7.5[/C][C]7.48940671888631[/C][C]0.0105932811136916[/C][/ROW]
[ROW][C]33[/C][C]7.3[/C][C]7.42662905356713[/C][C]-0.126629053567130[/C][/ROW]
[ROW][C]34[/C][C]7[/C][C]7.23762559859791[/C][C]-0.237625598597911[/C][/ROW]
[ROW][C]35[/C][C]7[/C][C]6.82689121670033[/C][C]0.17310878329967[/C][/ROW]
[ROW][C]36[/C][C]7[/C][C]7.10895524380063[/C][C]-0.108955243800627[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.26093986395214[/C][C]-0.060939863952142[/C][/ROW]
[ROW][C]38[/C][C]7.3[/C][C]7.34059898780629[/C][C]-0.0405989878062894[/C][/ROW]
[ROW][C]39[/C][C]7.1[/C][C]7.11963510731724[/C][C]-0.0196351073172426[/C][/ROW]
[ROW][C]40[/C][C]6.8[/C][C]6.95735293932386[/C][C]-0.157352939323864[/C][/ROW]
[ROW][C]41[/C][C]6.4[/C][C]6.57398653625693[/C][C]-0.173986536256931[/C][/ROW]
[ROW][C]42[/C][C]6.1[/C][C]6.1921677692498[/C][C]-0.0921677692498036[/C][/ROW]
[ROW][C]43[/C][C]6.5[/C][C]6.17690112181211[/C][C]0.323098878187889[/C][/ROW]
[ROW][C]44[/C][C]7.7[/C][C]7.49258308221601[/C][C]0.207416917783991[/C][/ROW]
[ROW][C]45[/C][C]7.9[/C][C]7.93972902093396[/C][C]-0.0397290209339552[/C][/ROW]
[ROW][C]46[/C][C]7.5[/C][C]7.51684820653114[/C][C]-0.0168482065311401[/C][/ROW]
[ROW][C]47[/C][C]6.9[/C][C]6.94084962998773[/C][C]-0.040849629987734[/C][/ROW]
[ROW][C]48[/C][C]6.6[/C][C]6.6822794091842[/C][C]-0.0822794091841953[/C][/ROW]
[ROW][C]49[/C][C]6.9[/C][C]6.92942108111901[/C][C]-0.0294210811190112[/C][/ROW]
[ROW][C]50[/C][C]7.7[/C][C]7.50256633079128[/C][C]0.197433669208716[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8.11032044199057[/C][C]-0.110320441990566[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]7.88605663039753[/C][C]0.113943369602470[/C][/ROW]
[ROW][C]53[/C][C]7.7[/C][C]7.72945811014766[/C][C]-0.0294581101476566[/C][/ROW]
[ROW][C]54[/C][C]7.3[/C][C]7.34762443983297[/C][C]-0.047624439832967[/C][/ROW]
[ROW][C]55[/C][C]7.4[/C][C]7.1734123620643[/C][C]0.226587637935702[/C][/ROW]
[ROW][C]56[/C][C]8.1[/C][C]8.1947948948716[/C][C]-0.0947948948715987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68907&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68907&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
18.38.179095112844980.120904887155019
28.58.74828409812503-0.248284098125033
38.68.6183188717678-0.0183188717677956
48.58.60084889605629-0.100848896056286
58.28.32042637551077-0.120426375510767
68.17.917251521557560.182748478442443
77.98.1061425118694-0.206142511869397
88.68.492094478385640.107905521614356
98.78.66782638362030.0321736163797068
108.78.542792225387370.157207774612629
118.58.56651265504675-0.0665126550467537
128.48.256322104278890.143677895721114
138.58.463050848150290.0369491518497075
148.78.658580154750890.0414198452491076
158.78.638586334708730.0614136652912708
168.68.492118612790920.107881387209076
178.58.42643243360490.0735675663950994
188.38.188978928577990.111021071422013
1988.12374239751187-0.123742397511875
208.28.43112082564044-0.23112082564044
218.17.965815541878620.134184458121378
228.18.002733969483580.0972660305164226
2388.06574649826518-0.0657464982651822
247.97.852443242736290.0475567572637083
257.97.96749309393357-0.0674930939335735
2687.94997042852650.0500295714734993
2787.913139244215670.0868607557843335
287.97.86362292143140.0363770785686043
2987.749696544479750.250303455520255
307.77.85397734078169-0.153977340781686
317.27.41980160674232-0.219801606742319
327.57.489406718886310.0105932811136916
337.37.42662905356713-0.126629053567130
3477.23762559859791-0.237625598597911
3576.826891216700330.17310878329967
3677.10895524380063-0.108955243800627
377.27.26093986395214-0.060939863952142
387.37.34059898780629-0.0405989878062894
397.17.11963510731724-0.0196351073172426
406.86.95735293932386-0.157352939323864
416.46.57398653625693-0.173986536256931
426.16.1921677692498-0.0921677692498036
436.56.176901121812110.323098878187889
447.77.492583082216010.207416917783991
457.97.93972902093396-0.0397290209339552
467.57.51684820653114-0.0168482065311401
476.96.94084962998773-0.040849629987734
486.66.6822794091842-0.0822794091841953
496.96.92942108111901-0.0294210811190112
507.77.502566330791280.197433669208716
5188.11032044199057-0.110320441990566
5287.886056630397530.113943369602470
537.77.72945811014766-0.0294581101476566
547.37.34762443983297-0.047624439832967
557.47.17341236206430.226587637935702
568.18.1947948948716-0.0947948948715987






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.7171850902804730.5656298194390550.282814909719527
220.5963021082472730.8073957835054540.403697891752727
230.468598360624650.93719672124930.53140163937535
240.3617658025201820.7235316050403640.638234197479818
250.2653629201239550.530725840247910.734637079876045
260.1758022631879230.3516045263758460.824197736812077
270.1240936636531550.2481873273063090.875906336346845
280.0839721584756690.1679443169513380.916027841524331
290.3170151074097300.6340302148194610.68298489259027
300.3104022012157980.6208044024315950.689597798784202
310.4778520427786130.9557040855572250.522147957221387
320.344158942080350.68831788416070.65584105791965
330.3754329179152960.7508658358305930.624567082084704
340.3126443715393690.6252887430787380.687355628460631
350.4185791636942500.8371583273885010.58142083630575

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.717185090280473 & 0.565629819439055 & 0.282814909719527 \tabularnewline
22 & 0.596302108247273 & 0.807395783505454 & 0.403697891752727 \tabularnewline
23 & 0.46859836062465 & 0.9371967212493 & 0.53140163937535 \tabularnewline
24 & 0.361765802520182 & 0.723531605040364 & 0.638234197479818 \tabularnewline
25 & 0.265362920123955 & 0.53072584024791 & 0.734637079876045 \tabularnewline
26 & 0.175802263187923 & 0.351604526375846 & 0.824197736812077 \tabularnewline
27 & 0.124093663653155 & 0.248187327306309 & 0.875906336346845 \tabularnewline
28 & 0.083972158475669 & 0.167944316951338 & 0.916027841524331 \tabularnewline
29 & 0.317015107409730 & 0.634030214819461 & 0.68298489259027 \tabularnewline
30 & 0.310402201215798 & 0.620804402431595 & 0.689597798784202 \tabularnewline
31 & 0.477852042778613 & 0.955704085557225 & 0.522147957221387 \tabularnewline
32 & 0.34415894208035 & 0.6883178841607 & 0.65584105791965 \tabularnewline
33 & 0.375432917915296 & 0.750865835830593 & 0.624567082084704 \tabularnewline
34 & 0.312644371539369 & 0.625288743078738 & 0.687355628460631 \tabularnewline
35 & 0.418579163694250 & 0.837158327388501 & 0.58142083630575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68907&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]0.717185090280473[/C][C]0.565629819439055[/C][C]0.282814909719527[/C][/ROW]
[ROW][C]22[/C][C]0.596302108247273[/C][C]0.807395783505454[/C][C]0.403697891752727[/C][/ROW]
[ROW][C]23[/C][C]0.46859836062465[/C][C]0.9371967212493[/C][C]0.53140163937535[/C][/ROW]
[ROW][C]24[/C][C]0.361765802520182[/C][C]0.723531605040364[/C][C]0.638234197479818[/C][/ROW]
[ROW][C]25[/C][C]0.265362920123955[/C][C]0.53072584024791[/C][C]0.734637079876045[/C][/ROW]
[ROW][C]26[/C][C]0.175802263187923[/C][C]0.351604526375846[/C][C]0.824197736812077[/C][/ROW]
[ROW][C]27[/C][C]0.124093663653155[/C][C]0.248187327306309[/C][C]0.875906336346845[/C][/ROW]
[ROW][C]28[/C][C]0.083972158475669[/C][C]0.167944316951338[/C][C]0.916027841524331[/C][/ROW]
[ROW][C]29[/C][C]0.317015107409730[/C][C]0.634030214819461[/C][C]0.68298489259027[/C][/ROW]
[ROW][C]30[/C][C]0.310402201215798[/C][C]0.620804402431595[/C][C]0.689597798784202[/C][/ROW]
[ROW][C]31[/C][C]0.477852042778613[/C][C]0.955704085557225[/C][C]0.522147957221387[/C][/ROW]
[ROW][C]32[/C][C]0.34415894208035[/C][C]0.6883178841607[/C][C]0.65584105791965[/C][/ROW]
[ROW][C]33[/C][C]0.375432917915296[/C][C]0.750865835830593[/C][C]0.624567082084704[/C][/ROW]
[ROW][C]34[/C][C]0.312644371539369[/C][C]0.625288743078738[/C][C]0.687355628460631[/C][/ROW]
[ROW][C]35[/C][C]0.418579163694250[/C][C]0.837158327388501[/C][C]0.58142083630575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68907&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68907&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
210.7171850902804730.5656298194390550.282814909719527
220.5963021082472730.8073957835054540.403697891752727
230.468598360624650.93719672124930.53140163937535
240.3617658025201820.7235316050403640.638234197479818
250.2653629201239550.530725840247910.734637079876045
260.1758022631879230.3516045263758460.824197736812077
270.1240936636531550.2481873273063090.875906336346845
280.0839721584756690.1679443169513380.916027841524331
290.3170151074097300.6340302148194610.68298489259027
300.3104022012157980.6208044024315950.689597798784202
310.4778520427786130.9557040855572250.522147957221387
320.344158942080350.68831788416070.65584105791965
330.3754329179152960.7508658358305930.624567082084704
340.3126443715393690.6252887430787380.687355628460631
350.4185791636942500.8371583273885010.58142083630575






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=68907&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=68907&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68907&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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