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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, 26 Nov 2009 11:29:20 -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/26/t1259260256s9njq955vmvd47o.htm/, Retrieved Sun, 28 Apr 2024 23:56:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60243, Retrieved Sun, 28 Apr 2024 23:56:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93

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 14:14:11] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [WS 7: Multiple Re...] [2009-11-26 18:21:11] [b00a5c3d5f6ccb867aa9e2de58adfa61]
-    D      [Multiple Regression] [WS 7: Multiple Re...] [2009-11-26 18:26:06] [b00a5c3d5f6ccb867aa9e2de58adfa61]
-    D          [Multiple Regression] [WS 7: Multiple Re...] [2009-11-26 18:29:20] [63d6214c2814604a6f6cfa44dba5912e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.8	9.5	7.8	7.8	7.6	7.5	7.7	8.1
7.5	9.1	7.8	7.8	7.8	7.6	7.5	7.7
7.5	8.9	7.5	7.8	7.8	7.8	7.6	7.5
7.1	9	7.5	7.5	7.8	7.8	7.8	7.6
7.5	10.1	7.1	7.5	7.5	7.8	7.8	7.8
7.5	10.3	7.5	7.1	7.5	7.5	7.8	7.8
7.6	10.2	7.5	7.5	7.1	7.5	7.5	7.8
7.7	9.6	7.6	7.5	7.5	7.1	7.5	7.5
7.7	9.2	7.7	7.6	7.5	7.5	7.1	7.5
7.9	9.3	7.7	7.7	7.6	7.5	7.5	7.1
8.1	9.4	7.9	7.7	7.7	7.6	7.5	7.5
8.2	9.4	8.1	7.9	7.7	7.7	7.6	7.5
8.2	9.2	8.2	8.1	7.9	7.7	7.7	7.6
8.2	9	8.2	8.2	8.1	7.9	7.7	7.7
7.9	9	8.2	8.2	8.2	8.1	7.9	7.7
7.3	9	7.9	8.2	8.2	8.2	8.1	7.9
6.9	9.8	7.3	7.9	8.2	8.2	8.2	8.1
6.6	10	6.9	7.3	7.9	8.2	8.2	8.2
6.7	9.8	6.6	6.9	7.3	7.9	8.2	8.2
6.9	9.3	6.7	6.6	6.9	7.3	7.9	8.2
7	9	6.9	6.7	6.6	6.9	7.3	7.9
7.1	9	7	6.9	6.7	6.6	6.9	7.3
7.2	9.1	7.1	7	6.9	6.7	6.6	6.9
7.1	9.1	7.2	7.1	7	6.9	6.7	6.6
6.9	9.1	7.1	7.2	7.1	7	6.9	6.7
7	9.2	6.9	7.1	7.2	7.1	7	6.9
6.8	8.8	7	6.9	7.1	7.2	7.1	7
6.4	8.3	6.8	7	6.9	7.1	7.2	7.1
6.7	8.4	6.4	6.8	7	6.9	7.1	7.2
6.6	8.1	6.7	6.4	6.8	7	6.9	7.1
6.4	7.7	6.6	6.7	6.4	6.8	7	6.9
6.3	7.9	6.4	6.6	6.7	6.4	6.8	7
6.2	7.9	6.3	6.4	6.6	6.7	6.4	6.8
6.5	8	6.2	6.3	6.4	6.6	6.7	6.4
6.8	7.9	6.5	6.2	6.3	6.4	6.6	6.7
6.8	7.6	6.8	6.5	6.2	6.3	6.4	6.6
6.4	7.1	6.8	6.8	6.5	6.2	6.3	6.4
6.1	6.8	6.4	6.8	6.8	6.5	6.2	6.3
5.8	6.5	6.1	6.4	6.8	6.8	6.5	6.2
6.1	6.9	5.8	6.1	6.4	6.8	6.8	6.5
7.2	8.2	6.1	5.8	6.1	6.4	6.8	6.8
7.3	8.7	7.2	6.1	5.8	6.1	6.4	6.8
6.9	8.3	7.3	7.2	6.1	5.8	6.1	6.4
6.1	7.9	6.9	7.3	7.2	6.1	5.8	6.1
5.8	7.5	6.1	6.9	7.3	7.2	6.1	5.8
6.2	7.8	5.8	6.1	6.9	7.3	7.2	6.1
7.1	8.3	6.2	5.8	6.1	6.9	7.3	7.2
7.7	8.4	7.1	6.2	5.8	6.1	6.9	7.3
7.9	8.2	7.7	7.1	6.2	5.8	6.1	6.9
7.7	7.7	7.9	7.7	7.1	6.2	5.8	6.1
7.4	7.2	7.7	7.9	7.7	7.1	6.2	5.8
7.5	7.3	7.4	7.7	7.9	7.7	7.1	6.2
8	8.1	7.5	7.4	7.7	7.9	7.7	7.1
8.1	8.5	8	7.5	7.4	7.7	7.9	7.7

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=60243&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=60243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60243&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
Y[t] = + 0.0591462227848196 + 0.0660454365791428X[t] + 1.52512703254502`Y-1`[t] -0.620545370718424`Y-2`[t] -0.441317537172667`Y-3`[t] + 0.498373687006295`Y-4`[t] + 0.162625204980074`Y-5`[t] -0.231593669035930`Y-6`[t] + 0.111512253826071M1[t] + 0.193313373161585M2[t] -0.0219414502710726M3[t] -0.0762588111162378M4[t] + 0.453205779017736M5[t] -0.292372779576293M6[t] -0.0892150900311018M7[t] + 0.181115372158409M8[t] + 0.0796701373967479M9[t] + 0.213160532284749M10[t] + 0.225129629065532M11[t] + 0.00219583945301820t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.0591462227848196 +  0.0660454365791428X[t] +  1.52512703254502`Y-1`[t] -0.620545370718424`Y-2`[t] -0.441317537172667`Y-3`[t] +  0.498373687006295`Y-4`[t] +  0.162625204980074`Y-5`[t] -0.231593669035930`Y-6`[t] +  0.111512253826071M1[t] +  0.193313373161585M2[t] -0.0219414502710726M3[t] -0.0762588111162378M4[t] +  0.453205779017736M5[t] -0.292372779576293M6[t] -0.0892150900311018M7[t] +  0.181115372158409M8[t] +  0.0796701373967479M9[t] +  0.213160532284749M10[t] +  0.225129629065532M11[t] +  0.00219583945301820t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60243&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.0591462227848196 +  0.0660454365791428X[t] +  1.52512703254502`Y-1`[t] -0.620545370718424`Y-2`[t] -0.441317537172667`Y-3`[t] +  0.498373687006295`Y-4`[t] +  0.162625204980074`Y-5`[t] -0.231593669035930`Y-6`[t] +  0.111512253826071M1[t] +  0.193313373161585M2[t] -0.0219414502710726M3[t] -0.0762588111162378M4[t] +  0.453205779017736M5[t] -0.292372779576293M6[t] -0.0892150900311018M7[t] +  0.181115372158409M8[t] +  0.0796701373967479M9[t] +  0.213160532284749M10[t] +  0.225129629065532M11[t] +  0.00219583945301820t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60243&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] = + 0.0591462227848196 + 0.0660454365791428X[t] + 1.52512703254502`Y-1`[t] -0.620545370718424`Y-2`[t] -0.441317537172667`Y-3`[t] + 0.498373687006295`Y-4`[t] + 0.162625204980074`Y-5`[t] -0.231593669035930`Y-6`[t] + 0.111512253826071M1[t] + 0.193313373161585M2[t] -0.0219414502710726M3[t] -0.0762588111162378M4[t] + 0.453205779017736M5[t] -0.292372779576293M6[t] -0.0892150900311018M7[t] + 0.181115372158409M8[t] + 0.0796701373967479M9[t] + 0.213160532284749M10[t] + 0.225129629065532M11[t] + 0.00219583945301820t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.05914622278481960.7866120.07520.9405030.470252
X0.06604543657914280.0776280.85080.4008350.200417
`Y-1`1.525127032545020.1701558.963200
`Y-2`-0.6205453707184240.313336-1.98040.0557920.027896
`Y-3`-0.4413175371726670.337024-1.30950.1991610.09958
`Y-4`0.4983736870062950.3422291.45630.1544950.077248
`Y-5`0.1626252049800740.3336750.48740.629120.31456
`Y-6`-0.2315936690359300.201016-1.15210.2573110.128655
M10.1115122538260710.1534670.72660.4724320.236216
M20.1933133731615850.1636511.18130.2456990.12285
M3-0.02194145027107260.163436-0.13430.8939960.446998
M4-0.07625881111623780.165896-0.45970.6486730.324337
M50.4532057790177360.1675972.70410.0106180.005309
M6-0.2923727795762930.169298-1.7270.093250.046625
M7-0.08921509003110180.181994-0.49020.6271350.313568
M80.1811153721584090.2041580.88710.3812390.19062
M90.07967013739674790.1945210.40960.684690.342345
M100.2131605322847490.1704681.25040.2196750.109838
M110.2251296290655320.1573071.43110.1615170.080759
t0.002195839453018200.003890.56450.576110.288055

\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) & 0.0591462227848196 & 0.786612 & 0.0752 & 0.940503 & 0.470252 \tabularnewline
X & 0.0660454365791428 & 0.077628 & 0.8508 & 0.400835 & 0.200417 \tabularnewline
`Y-1` & 1.52512703254502 & 0.170155 & 8.9632 & 0 & 0 \tabularnewline
`Y-2` & -0.620545370718424 & 0.313336 & -1.9804 & 0.055792 & 0.027896 \tabularnewline
`Y-3` & -0.441317537172667 & 0.337024 & -1.3095 & 0.199161 & 0.09958 \tabularnewline
`Y-4` & 0.498373687006295 & 0.342229 & 1.4563 & 0.154495 & 0.077248 \tabularnewline
`Y-5` & 0.162625204980074 & 0.333675 & 0.4874 & 0.62912 & 0.31456 \tabularnewline
`Y-6` & -0.231593669035930 & 0.201016 & -1.1521 & 0.257311 & 0.128655 \tabularnewline
M1 & 0.111512253826071 & 0.153467 & 0.7266 & 0.472432 & 0.236216 \tabularnewline
M2 & 0.193313373161585 & 0.163651 & 1.1813 & 0.245699 & 0.12285 \tabularnewline
M3 & -0.0219414502710726 & 0.163436 & -0.1343 & 0.893996 & 0.446998 \tabularnewline
M4 & -0.0762588111162378 & 0.165896 & -0.4597 & 0.648673 & 0.324337 \tabularnewline
M5 & 0.453205779017736 & 0.167597 & 2.7041 & 0.010618 & 0.005309 \tabularnewline
M6 & -0.292372779576293 & 0.169298 & -1.727 & 0.09325 & 0.046625 \tabularnewline
M7 & -0.0892150900311018 & 0.181994 & -0.4902 & 0.627135 & 0.313568 \tabularnewline
M8 & 0.181115372158409 & 0.204158 & 0.8871 & 0.381239 & 0.19062 \tabularnewline
M9 & 0.0796701373967479 & 0.194521 & 0.4096 & 0.68469 & 0.342345 \tabularnewline
M10 & 0.213160532284749 & 0.170468 & 1.2504 & 0.219675 & 0.109838 \tabularnewline
M11 & 0.225129629065532 & 0.157307 & 1.4311 & 0.161517 & 0.080759 \tabularnewline
t & 0.00219583945301820 & 0.00389 & 0.5645 & 0.57611 & 0.288055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60243&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]0.0591462227848196[/C][C]0.786612[/C][C]0.0752[/C][C]0.940503[/C][C]0.470252[/C][/ROW]
[ROW][C]X[/C][C]0.0660454365791428[/C][C]0.077628[/C][C]0.8508[/C][C]0.400835[/C][C]0.200417[/C][/ROW]
[ROW][C]`Y-1`[/C][C]1.52512703254502[/C][C]0.170155[/C][C]8.9632[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y-2`[/C][C]-0.620545370718424[/C][C]0.313336[/C][C]-1.9804[/C][C]0.055792[/C][C]0.027896[/C][/ROW]
[ROW][C]`Y-3`[/C][C]-0.441317537172667[/C][C]0.337024[/C][C]-1.3095[/C][C]0.199161[/C][C]0.09958[/C][/ROW]
[ROW][C]`Y-4`[/C][C]0.498373687006295[/C][C]0.342229[/C][C]1.4563[/C][C]0.154495[/C][C]0.077248[/C][/ROW]
[ROW][C]`Y-5`[/C][C]0.162625204980074[/C][C]0.333675[/C][C]0.4874[/C][C]0.62912[/C][C]0.31456[/C][/ROW]
[ROW][C]`Y-6`[/C][C]-0.231593669035930[/C][C]0.201016[/C][C]-1.1521[/C][C]0.257311[/C][C]0.128655[/C][/ROW]
[ROW][C]M1[/C][C]0.111512253826071[/C][C]0.153467[/C][C]0.7266[/C][C]0.472432[/C][C]0.236216[/C][/ROW]
[ROW][C]M2[/C][C]0.193313373161585[/C][C]0.163651[/C][C]1.1813[/C][C]0.245699[/C][C]0.12285[/C][/ROW]
[ROW][C]M3[/C][C]-0.0219414502710726[/C][C]0.163436[/C][C]-0.1343[/C][C]0.893996[/C][C]0.446998[/C][/ROW]
[ROW][C]M4[/C][C]-0.0762588111162378[/C][C]0.165896[/C][C]-0.4597[/C][C]0.648673[/C][C]0.324337[/C][/ROW]
[ROW][C]M5[/C][C]0.453205779017736[/C][C]0.167597[/C][C]2.7041[/C][C]0.010618[/C][C]0.005309[/C][/ROW]
[ROW][C]M6[/C][C]-0.292372779576293[/C][C]0.169298[/C][C]-1.727[/C][C]0.09325[/C][C]0.046625[/C][/ROW]
[ROW][C]M7[/C][C]-0.0892150900311018[/C][C]0.181994[/C][C]-0.4902[/C][C]0.627135[/C][C]0.313568[/C][/ROW]
[ROW][C]M8[/C][C]0.181115372158409[/C][C]0.204158[/C][C]0.8871[/C][C]0.381239[/C][C]0.19062[/C][/ROW]
[ROW][C]M9[/C][C]0.0796701373967479[/C][C]0.194521[/C][C]0.4096[/C][C]0.68469[/C][C]0.342345[/C][/ROW]
[ROW][C]M10[/C][C]0.213160532284749[/C][C]0.170468[/C][C]1.2504[/C][C]0.219675[/C][C]0.109838[/C][/ROW]
[ROW][C]M11[/C][C]0.225129629065532[/C][C]0.157307[/C][C]1.4311[/C][C]0.161517[/C][C]0.080759[/C][/ROW]
[ROW][C]t[/C][C]0.00219583945301820[/C][C]0.00389[/C][C]0.5645[/C][C]0.57611[/C][C]0.288055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60243&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)0.05914622278481960.7866120.07520.9405030.470252
X0.06604543657914280.0776280.85080.4008350.200417
`Y-1`1.525127032545020.1701558.963200
`Y-2`-0.6205453707184240.313336-1.98040.0557920.027896
`Y-3`-0.4413175371726670.337024-1.30950.1991610.09958
`Y-4`0.4983736870062950.3422291.45630.1544950.077248
`Y-5`0.1626252049800740.3336750.48740.629120.31456
`Y-6`-0.2315936690359300.201016-1.15210.2573110.128655
M10.1115122538260710.1534670.72660.4724320.236216
M20.1933133731615850.1636511.18130.2456990.12285
M3-0.02194145027107260.163436-0.13430.8939960.446998
M4-0.07625881111623780.165896-0.45970.6486730.324337
M50.4532057790177360.1675972.70410.0106180.005309
M6-0.2923727795762930.169298-1.7270.093250.046625
M7-0.08921509003110180.181994-0.49020.6271350.313568
M80.1811153721584090.2041580.88710.3812390.19062
M90.07967013739674790.1945210.40960.684690.342345
M100.2131605322847490.1704681.25040.2196750.109838
M110.2251296290655320.1573071.43110.1615170.080759
t0.002195839453018200.003890.56450.576110.288055






Multiple Linear Regression - Regression Statistics
Multiple R0.966793725165996
R-squared0.934690107020344
Adjusted R-squared0.898193402119949
F-TEST (value)25.6102601473540
F-TEST (DF numerator)19
F-TEST (DF denominator)34
p-value7.7715611723761e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.211400014540384
Sum Squared Residuals1.51945884902094

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.966793725165996 \tabularnewline
R-squared & 0.934690107020344 \tabularnewline
Adjusted R-squared & 0.898193402119949 \tabularnewline
F-TEST (value) & 25.6102601473540 \tabularnewline
F-TEST (DF numerator) & 19 \tabularnewline
F-TEST (DF denominator) & 34 \tabularnewline
p-value & 7.7715611723761e-15 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.211400014540384 \tabularnewline
Sum Squared Residuals & 1.51945884902094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60243&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.966793725165996[/C][/ROW]
[ROW][C]R-squared[/C][C]0.934690107020344[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.898193402119949[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]25.6102601473540[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]19[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]7.7715611723761e-15[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.211400014540384[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.51945884902094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60243&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60243&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 R0.966793725165996
R-squared0.934690107020344
Adjusted R-squared0.898193402119949
F-TEST (value)25.6102601473540
F-TEST (DF numerator)19
F-TEST (DF denominator)34
p-value7.7715611723761e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.211400014540384
Sum Squared Residuals1.51945884902094






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.87.616117655003720.183882344996277
27.57.69538272704505-0.195382727045054
37.57.173832537692530.32616746230747
47.17.32384484526625-0.223844845266247
57.57.40418096941690.0958190305830996
67.57.382764192795210.117235807204791
77.67.461034483223180.138965516776820
87.77.540047837211920.159952162788082
97.77.639137826264770.0608621737352328
107.97.8329298630810.0670701369190068
118.18.07179289685070.0282071031492954
128.28.095875328802150.104124671197852
138.28.12961761003610.0703823899638934
148.28.12660280750010.073397192499899
157.98.00161184820047-0.101611848200468
167.37.52799589293427-0.227995892934273
176.97.35352385016391-0.453523850163913
186.66.494862521999980.105137478000016
196.76.592965418407940.107034581592062
206.96.9998605574022-0.0998605574021935
2177.02871716462899-0.0287171646289862
227.17.07306928769120.0269307123088047
237.27.189720701152020.0102792988479844
247.17.19852868261494-0.098528682614943
256.97.11274082464347-0.212740824643470
2676.936020859326940.0639791406730605
276.87.06023775412614-0.260237754126141
286.46.63954286319189-0.239542863191892
296.76.508637719042350.191362280957651
306.66.579932829021210.0200671709787864
316.46.55962540069074-0.159625400690735
326.36.214960776358010.0850392236419927
336.26.26222026357286-0.0622202635728567
346.56.493904043231430.00609595676857139
356.86.87977347774989-0.0797734777498863
366.86.89332926663582-0.0933292666358247
376.46.63567461386656-0.235674613866564
386.16.11382082001902-0.0138208200190193
395.85.893087278089-0.0930872780890019
406.15.751845908432840.348154091567157
417.26.876634812190260.323365187809742
427.37.5755840089807-0.2755840089807
436.96.98637469767815-0.0863746976781471
446.16.24513082902788-0.145130829027881
455.85.769924745533390.0300752544666105
466.26.30009680599638-0.100096805996383
477.17.05871292424740.0412870757526068
487.77.612266721947090.0877332780529151
497.97.705849296450140.194150703549864
507.77.628172786108890.0718272138911134
517.47.271230581891860.128769418108140
527.57.156770490174740.343229509825256
5388.15702264918658-0.15702264918658
548.18.06685644720290.0331435527971063

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.8 & 7.61611765500372 & 0.183882344996277 \tabularnewline
2 & 7.5 & 7.69538272704505 & -0.195382727045054 \tabularnewline
3 & 7.5 & 7.17383253769253 & 0.32616746230747 \tabularnewline
4 & 7.1 & 7.32384484526625 & -0.223844845266247 \tabularnewline
5 & 7.5 & 7.4041809694169 & 0.0958190305830996 \tabularnewline
6 & 7.5 & 7.38276419279521 & 0.117235807204791 \tabularnewline
7 & 7.6 & 7.46103448322318 & 0.138965516776820 \tabularnewline
8 & 7.7 & 7.54004783721192 & 0.159952162788082 \tabularnewline
9 & 7.7 & 7.63913782626477 & 0.0608621737352328 \tabularnewline
10 & 7.9 & 7.832929863081 & 0.0670701369190068 \tabularnewline
11 & 8.1 & 8.0717928968507 & 0.0282071031492954 \tabularnewline
12 & 8.2 & 8.09587532880215 & 0.104124671197852 \tabularnewline
13 & 8.2 & 8.1296176100361 & 0.0703823899638934 \tabularnewline
14 & 8.2 & 8.1266028075001 & 0.073397192499899 \tabularnewline
15 & 7.9 & 8.00161184820047 & -0.101611848200468 \tabularnewline
16 & 7.3 & 7.52799589293427 & -0.227995892934273 \tabularnewline
17 & 6.9 & 7.35352385016391 & -0.453523850163913 \tabularnewline
18 & 6.6 & 6.49486252199998 & 0.105137478000016 \tabularnewline
19 & 6.7 & 6.59296541840794 & 0.107034581592062 \tabularnewline
20 & 6.9 & 6.9998605574022 & -0.0998605574021935 \tabularnewline
21 & 7 & 7.02871716462899 & -0.0287171646289862 \tabularnewline
22 & 7.1 & 7.0730692876912 & 0.0269307123088047 \tabularnewline
23 & 7.2 & 7.18972070115202 & 0.0102792988479844 \tabularnewline
24 & 7.1 & 7.19852868261494 & -0.098528682614943 \tabularnewline
25 & 6.9 & 7.11274082464347 & -0.212740824643470 \tabularnewline
26 & 7 & 6.93602085932694 & 0.0639791406730605 \tabularnewline
27 & 6.8 & 7.06023775412614 & -0.260237754126141 \tabularnewline
28 & 6.4 & 6.63954286319189 & -0.239542863191892 \tabularnewline
29 & 6.7 & 6.50863771904235 & 0.191362280957651 \tabularnewline
30 & 6.6 & 6.57993282902121 & 0.0200671709787864 \tabularnewline
31 & 6.4 & 6.55962540069074 & -0.159625400690735 \tabularnewline
32 & 6.3 & 6.21496077635801 & 0.0850392236419927 \tabularnewline
33 & 6.2 & 6.26222026357286 & -0.0622202635728567 \tabularnewline
34 & 6.5 & 6.49390404323143 & 0.00609595676857139 \tabularnewline
35 & 6.8 & 6.87977347774989 & -0.0797734777498863 \tabularnewline
36 & 6.8 & 6.89332926663582 & -0.0933292666358247 \tabularnewline
37 & 6.4 & 6.63567461386656 & -0.235674613866564 \tabularnewline
38 & 6.1 & 6.11382082001902 & -0.0138208200190193 \tabularnewline
39 & 5.8 & 5.893087278089 & -0.0930872780890019 \tabularnewline
40 & 6.1 & 5.75184590843284 & 0.348154091567157 \tabularnewline
41 & 7.2 & 6.87663481219026 & 0.323365187809742 \tabularnewline
42 & 7.3 & 7.5755840089807 & -0.2755840089807 \tabularnewline
43 & 6.9 & 6.98637469767815 & -0.0863746976781471 \tabularnewline
44 & 6.1 & 6.24513082902788 & -0.145130829027881 \tabularnewline
45 & 5.8 & 5.76992474553339 & 0.0300752544666105 \tabularnewline
46 & 6.2 & 6.30009680599638 & -0.100096805996383 \tabularnewline
47 & 7.1 & 7.0587129242474 & 0.0412870757526068 \tabularnewline
48 & 7.7 & 7.61226672194709 & 0.0877332780529151 \tabularnewline
49 & 7.9 & 7.70584929645014 & 0.194150703549864 \tabularnewline
50 & 7.7 & 7.62817278610889 & 0.0718272138911134 \tabularnewline
51 & 7.4 & 7.27123058189186 & 0.128769418108140 \tabularnewline
52 & 7.5 & 7.15677049017474 & 0.343229509825256 \tabularnewline
53 & 8 & 8.15702264918658 & -0.15702264918658 \tabularnewline
54 & 8.1 & 8.0668564472029 & 0.0331435527971063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60243&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]7.8[/C][C]7.61611765500372[/C][C]0.183882344996277[/C][/ROW]
[ROW][C]2[/C][C]7.5[/C][C]7.69538272704505[/C][C]-0.195382727045054[/C][/ROW]
[ROW][C]3[/C][C]7.5[/C][C]7.17383253769253[/C][C]0.32616746230747[/C][/ROW]
[ROW][C]4[/C][C]7.1[/C][C]7.32384484526625[/C][C]-0.223844845266247[/C][/ROW]
[ROW][C]5[/C][C]7.5[/C][C]7.4041809694169[/C][C]0.0958190305830996[/C][/ROW]
[ROW][C]6[/C][C]7.5[/C][C]7.38276419279521[/C][C]0.117235807204791[/C][/ROW]
[ROW][C]7[/C][C]7.6[/C][C]7.46103448322318[/C][C]0.138965516776820[/C][/ROW]
[ROW][C]8[/C][C]7.7[/C][C]7.54004783721192[/C][C]0.159952162788082[/C][/ROW]
[ROW][C]9[/C][C]7.7[/C][C]7.63913782626477[/C][C]0.0608621737352328[/C][/ROW]
[ROW][C]10[/C][C]7.9[/C][C]7.832929863081[/C][C]0.0670701369190068[/C][/ROW]
[ROW][C]11[/C][C]8.1[/C][C]8.0717928968507[/C][C]0.0282071031492954[/C][/ROW]
[ROW][C]12[/C][C]8.2[/C][C]8.09587532880215[/C][C]0.104124671197852[/C][/ROW]
[ROW][C]13[/C][C]8.2[/C][C]8.1296176100361[/C][C]0.0703823899638934[/C][/ROW]
[ROW][C]14[/C][C]8.2[/C][C]8.1266028075001[/C][C]0.073397192499899[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]8.00161184820047[/C][C]-0.101611848200468[/C][/ROW]
[ROW][C]16[/C][C]7.3[/C][C]7.52799589293427[/C][C]-0.227995892934273[/C][/ROW]
[ROW][C]17[/C][C]6.9[/C][C]7.35352385016391[/C][C]-0.453523850163913[/C][/ROW]
[ROW][C]18[/C][C]6.6[/C][C]6.49486252199998[/C][C]0.105137478000016[/C][/ROW]
[ROW][C]19[/C][C]6.7[/C][C]6.59296541840794[/C][C]0.107034581592062[/C][/ROW]
[ROW][C]20[/C][C]6.9[/C][C]6.9998605574022[/C][C]-0.0998605574021935[/C][/ROW]
[ROW][C]21[/C][C]7[/C][C]7.02871716462899[/C][C]-0.0287171646289862[/C][/ROW]
[ROW][C]22[/C][C]7.1[/C][C]7.0730692876912[/C][C]0.0269307123088047[/C][/ROW]
[ROW][C]23[/C][C]7.2[/C][C]7.18972070115202[/C][C]0.0102792988479844[/C][/ROW]
[ROW][C]24[/C][C]7.1[/C][C]7.19852868261494[/C][C]-0.098528682614943[/C][/ROW]
[ROW][C]25[/C][C]6.9[/C][C]7.11274082464347[/C][C]-0.212740824643470[/C][/ROW]
[ROW][C]26[/C][C]7[/C][C]6.93602085932694[/C][C]0.0639791406730605[/C][/ROW]
[ROW][C]27[/C][C]6.8[/C][C]7.06023775412614[/C][C]-0.260237754126141[/C][/ROW]
[ROW][C]28[/C][C]6.4[/C][C]6.63954286319189[/C][C]-0.239542863191892[/C][/ROW]
[ROW][C]29[/C][C]6.7[/C][C]6.50863771904235[/C][C]0.191362280957651[/C][/ROW]
[ROW][C]30[/C][C]6.6[/C][C]6.57993282902121[/C][C]0.0200671709787864[/C][/ROW]
[ROW][C]31[/C][C]6.4[/C][C]6.55962540069074[/C][C]-0.159625400690735[/C][/ROW]
[ROW][C]32[/C][C]6.3[/C][C]6.21496077635801[/C][C]0.0850392236419927[/C][/ROW]
[ROW][C]33[/C][C]6.2[/C][C]6.26222026357286[/C][C]-0.0622202635728567[/C][/ROW]
[ROW][C]34[/C][C]6.5[/C][C]6.49390404323143[/C][C]0.00609595676857139[/C][/ROW]
[ROW][C]35[/C][C]6.8[/C][C]6.87977347774989[/C][C]-0.0797734777498863[/C][/ROW]
[ROW][C]36[/C][C]6.8[/C][C]6.89332926663582[/C][C]-0.0933292666358247[/C][/ROW]
[ROW][C]37[/C][C]6.4[/C][C]6.63567461386656[/C][C]-0.235674613866564[/C][/ROW]
[ROW][C]38[/C][C]6.1[/C][C]6.11382082001902[/C][C]-0.0138208200190193[/C][/ROW]
[ROW][C]39[/C][C]5.8[/C][C]5.893087278089[/C][C]-0.0930872780890019[/C][/ROW]
[ROW][C]40[/C][C]6.1[/C][C]5.75184590843284[/C][C]0.348154091567157[/C][/ROW]
[ROW][C]41[/C][C]7.2[/C][C]6.87663481219026[/C][C]0.323365187809742[/C][/ROW]
[ROW][C]42[/C][C]7.3[/C][C]7.5755840089807[/C][C]-0.2755840089807[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]6.98637469767815[/C][C]-0.0863746976781471[/C][/ROW]
[ROW][C]44[/C][C]6.1[/C][C]6.24513082902788[/C][C]-0.145130829027881[/C][/ROW]
[ROW][C]45[/C][C]5.8[/C][C]5.76992474553339[/C][C]0.0300752544666105[/C][/ROW]
[ROW][C]46[/C][C]6.2[/C][C]6.30009680599638[/C][C]-0.100096805996383[/C][/ROW]
[ROW][C]47[/C][C]7.1[/C][C]7.0587129242474[/C][C]0.0412870757526068[/C][/ROW]
[ROW][C]48[/C][C]7.7[/C][C]7.61226672194709[/C][C]0.0877332780529151[/C][/ROW]
[ROW][C]49[/C][C]7.9[/C][C]7.70584929645014[/C][C]0.194150703549864[/C][/ROW]
[ROW][C]50[/C][C]7.7[/C][C]7.62817278610889[/C][C]0.0718272138911134[/C][/ROW]
[ROW][C]51[/C][C]7.4[/C][C]7.27123058189186[/C][C]0.128769418108140[/C][/ROW]
[ROW][C]52[/C][C]7.5[/C][C]7.15677049017474[/C][C]0.343229509825256[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]8.15702264918658[/C][C]-0.15702264918658[/C][/ROW]
[ROW][C]54[/C][C]8.1[/C][C]8.0668564472029[/C][C]0.0331435527971063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60243&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60243&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
17.87.616117655003720.183882344996277
27.57.69538272704505-0.195382727045054
37.57.173832537692530.32616746230747
47.17.32384484526625-0.223844845266247
57.57.40418096941690.0958190305830996
67.57.382764192795210.117235807204791
77.67.461034483223180.138965516776820
87.77.540047837211920.159952162788082
97.77.639137826264770.0608621737352328
107.97.8329298630810.0670701369190068
118.18.07179289685070.0282071031492954
128.28.095875328802150.104124671197852
138.28.12961761003610.0703823899638934
148.28.12660280750010.073397192499899
157.98.00161184820047-0.101611848200468
167.37.52799589293427-0.227995892934273
176.97.35352385016391-0.453523850163913
186.66.494862521999980.105137478000016
196.76.592965418407940.107034581592062
206.96.9998605574022-0.0998605574021935
2177.02871716462899-0.0287171646289862
227.17.07306928769120.0269307123088047
237.27.189720701152020.0102792988479844
247.17.19852868261494-0.098528682614943
256.97.11274082464347-0.212740824643470
2676.936020859326940.0639791406730605
276.87.06023775412614-0.260237754126141
286.46.63954286319189-0.239542863191892
296.76.508637719042350.191362280957651
306.66.579932829021210.0200671709787864
316.46.55962540069074-0.159625400690735
326.36.214960776358010.0850392236419927
336.26.26222026357286-0.0622202635728567
346.56.493904043231430.00609595676857139
356.86.87977347774989-0.0797734777498863
366.86.89332926663582-0.0933292666358247
376.46.63567461386656-0.235674613866564
386.16.11382082001902-0.0138208200190193
395.85.893087278089-0.0930872780890019
406.15.751845908432840.348154091567157
417.26.876634812190260.323365187809742
427.37.5755840089807-0.2755840089807
436.96.98637469767815-0.0863746976781471
446.16.24513082902788-0.145130829027881
455.85.769924745533390.0300752544666105
466.26.30009680599638-0.100096805996383
477.17.05871292424740.0412870757526068
487.77.612266721947090.0877332780529151
497.97.705849296450140.194150703549864
507.77.628172786108890.0718272138911134
517.47.271230581891860.128769418108140
527.57.156770490174740.343229509825256
5388.15702264918658-0.15702264918658
548.18.06685644720290.0331435527971063






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
230.5971932449504060.8056135100991890.402806755049594
240.4769812871817680.9539625743635360.523018712818232
250.3501473941978450.7002947883956890.649852605802155
260.3662101282773440.7324202565546880.633789871722656
270.2370939481210460.4741878962420910.762906051878954
280.4152350685797510.8304701371595030.584764931420249
290.8837420246853280.2325159506293440.116257975314672
300.911282092783570.1774358144328590.0887179072164294
310.922702329146160.1545953417076800.0772976708538401

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
23 & 0.597193244950406 & 0.805613510099189 & 0.402806755049594 \tabularnewline
24 & 0.476981287181768 & 0.953962574363536 & 0.523018712818232 \tabularnewline
25 & 0.350147394197845 & 0.700294788395689 & 0.649852605802155 \tabularnewline
26 & 0.366210128277344 & 0.732420256554688 & 0.633789871722656 \tabularnewline
27 & 0.237093948121046 & 0.474187896242091 & 0.762906051878954 \tabularnewline
28 & 0.415235068579751 & 0.830470137159503 & 0.584764931420249 \tabularnewline
29 & 0.883742024685328 & 0.232515950629344 & 0.116257975314672 \tabularnewline
30 & 0.91128209278357 & 0.177435814432859 & 0.0887179072164294 \tabularnewline
31 & 0.92270232914616 & 0.154595341707680 & 0.0772976708538401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60243&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]23[/C][C]0.597193244950406[/C][C]0.805613510099189[/C][C]0.402806755049594[/C][/ROW]
[ROW][C]24[/C][C]0.476981287181768[/C][C]0.953962574363536[/C][C]0.523018712818232[/C][/ROW]
[ROW][C]25[/C][C]0.350147394197845[/C][C]0.700294788395689[/C][C]0.649852605802155[/C][/ROW]
[ROW][C]26[/C][C]0.366210128277344[/C][C]0.732420256554688[/C][C]0.633789871722656[/C][/ROW]
[ROW][C]27[/C][C]0.237093948121046[/C][C]0.474187896242091[/C][C]0.762906051878954[/C][/ROW]
[ROW][C]28[/C][C]0.415235068579751[/C][C]0.830470137159503[/C][C]0.584764931420249[/C][/ROW]
[ROW][C]29[/C][C]0.883742024685328[/C][C]0.232515950629344[/C][C]0.116257975314672[/C][/ROW]
[ROW][C]30[/C][C]0.91128209278357[/C][C]0.177435814432859[/C][C]0.0887179072164294[/C][/ROW]
[ROW][C]31[/C][C]0.92270232914616[/C][C]0.154595341707680[/C][C]0.0772976708538401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60243&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60243&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
230.5971932449504060.8056135100991890.402806755049594
240.4769812871817680.9539625743635360.523018712818232
250.3501473941978450.7002947883956890.649852605802155
260.3662101282773440.7324202565546880.633789871722656
270.2370939481210460.4741878962420910.762906051878954
280.4152350685797510.8304701371595030.584764931420249
290.8837420246853280.2325159506293440.116257975314672
300.911282092783570.1774358144328590.0887179072164294
310.922702329146160.1545953417076800.0772976708538401






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=60243&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=60243&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60243&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')
}