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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 10:18:30 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t12587375792x6y1gtedmjj6n8.htm/, Retrieved Tue, 23 Apr 2024 08:39:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58345, Retrieved Tue, 23 Apr 2024 08:39:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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] [ws7 Multiple Regr...] [2009-11-20 16:50:31] [95cead3ebb75668735f848316249436a]
-   PD        [Multiple Regression] [WS7 Multiple Regr...] [2009-11-20 17:18:30] [95523ebdb89b97dbf680ec91e0b4bca2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.08	1.00	2.05	2.09	2.11	2.05
2.06	1.00	2.08	2.05	2.09	2.11
2.06	1.00	2.06	2.08	2.05	2.09
2.08	1.00	2.06	2.06	2.08	2.05
2.07	1.00	2.08	2.06	2.06	2.08
2.06	1.00	2.07	2.08	2.06	2.06
2.07	1.00	2.06	2.07	2.08	2.06
2.06	1.00	2.07	2.06	2.07	2.08
2.09	1.00	2.06	2.07	2.06	2.07
2.07	1.00	2.09	2.06	2.07	2.06
2.09	1.00	2.07	2.09	2.06	2.07
2.28	1.25	2.09	2.07	2.09	2.06
2.33	1.25	2.28	2.09	2.07	2.09
2.35	1.25	2.33	2.28	2.09	2.07
2.52	1.50	2.35	2.33	2.28	2.09
2.63	1.50	2.52	2.35	2.33	2.28
2.58	1.50	2.63	2.52	2.35	2.33
2.70	1.75	2.58	2.63	2.52	2.35
2.81	1.75	2.70	2.58	2.63	2.52
2.97	2.00	2.81	2.70	2.58	2.63
3.04	2.00	2.97	2.81	2.70	2.58
3.28	2.25	3.04	2.97	2.81	2.70
3.33	2.25	3.28	3.04	2.97	2.81
3.50	2.50	3.33	3.28	3.04	2.97
3.56	2.50	3.50	3.33	3.28	3.04
3.57	2.50	3.56	3.50	3.33	3.28
3.69	2.75	3.57	3.56	3.50	3.33
3.82	2.75	3.69	3.57	3.56	3.50
3.79	2.75	3.82	3.69	3.57	3.56
3.96	3.00	3.79	3.82	3.69	3.57
4.06	3.00	3.96	3.79	3.82	3.69
4.05	3.00	4.06	3.96	3.79	3.82
4.03	3.00	4.05	4.06	3.96	3.79
3.94	3.00	4.03	4.05	4.06	3.96
4.02	3.00	3.94	4.03	4.05	4.06
3.88	3.00	4.02	3.94	4.03	4.05
4.02	3.00	3.88	4.02	3.94	4.03
4.03	3.00	4.02	3.88	4.02	3.94
4.09	3.00	4.03	4.02	3.88	4.02
3.99	3.00	4.09	4.03	4.02	3.88
4.01	3.00	3.99	4.09	4.03	4.02
4.01	3.00	4.01	3.99	4.09	4.03
4.19	3.25	4.01	4.01	3.99	4.09
4.30	3.25	4.19	4.01	4.01	3.99
4.27	3.25	4.30	4.19	4.01	4.01
3.82	3.25	4.27	4.30	4.19	4.01
3.15	2.75	3.82	4.27	4.30	4.19
2.49	2.00	3.15	3.82	4.27	4.30
1.81	1.00	2.49	3.15	3.82	4.27
1.26	1.00	1.81	2.49	3.15	3.82
1.06	0.50	1.26	1.81	2.49	3.15
0.84	0.25	1.06	1.26	1.81	2.49
0.78	0.25	0.84	1.06	1.26	1.81
0.70	0.25	0.78	0.84	1.06	1.26
0.36	0.25	0.70	0.78	0.84	1.06
0.35	0.25	0.36	0.70	0.78	0.84

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=58345&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=58345&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58345&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] = + 0.685919050525686 + 0.845278920723775X[t] + 0.788576291718117`Y-1`[t] -0.607030562122719`Y-2`[t] -0.244013538273027`Y-3`[t] + 0.345411574379241`Y-4`[t] + 0.0826560113300043M1[t] -0.0160550741627145M2[t] + 0.0737205235477154M3[t] + 0.0404901747252967M4[t] + 0.0548013033823734M5[t] + 0.0782958665809638M6[t] -0.00171463003041461M7[t] + 0.0275101232145196M8[t] + 0.0666278757530691M9[t] -0.0270275012858383M10[t] + 0.0108858432721366M11[t] -0.0108698053993793t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.685919050525686 +  0.845278920723775X[t] +  0.788576291718117`Y-1`[t] -0.607030562122719`Y-2`[t] -0.244013538273027`Y-3`[t] +  0.345411574379241`Y-4`[t] +  0.0826560113300043M1[t] -0.0160550741627145M2[t] +  0.0737205235477154M3[t] +  0.0404901747252967M4[t] +  0.0548013033823734M5[t] +  0.0782958665809638M6[t] -0.00171463003041461M7[t] +  0.0275101232145196M8[t] +  0.0666278757530691M9[t] -0.0270275012858383M10[t] +  0.0108858432721366M11[t] -0.0108698053993793t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58345&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.685919050525686 +  0.845278920723775X[t] +  0.788576291718117`Y-1`[t] -0.607030562122719`Y-2`[t] -0.244013538273027`Y-3`[t] +  0.345411574379241`Y-4`[t] +  0.0826560113300043M1[t] -0.0160550741627145M2[t] +  0.0737205235477154M3[t] +  0.0404901747252967M4[t] +  0.0548013033823734M5[t] +  0.0782958665809638M6[t] -0.00171463003041461M7[t] +  0.0275101232145196M8[t] +  0.0666278757530691M9[t] -0.0270275012858383M10[t] +  0.0108858432721366M11[t] -0.0108698053993793t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58345&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58345&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] = + 0.685919050525686 + 0.845278920723775X[t] + 0.788576291718117`Y-1`[t] -0.607030562122719`Y-2`[t] -0.244013538273027`Y-3`[t] + 0.345411574379241`Y-4`[t] + 0.0826560113300043M1[t] -0.0160550741627145M2[t] + 0.0737205235477154M3[t] + 0.0404901747252967M4[t] + 0.0548013033823734M5[t] + 0.0782958665809638M6[t] -0.00171463003041461M7[t] + 0.0275101232145196M8[t] + 0.0666278757530691M9[t] -0.0270275012858383M10[t] + 0.0108858432721366M11[t] -0.0108698053993793t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.6859190505256860.1122176.112400
X0.8452789207237750.1242686.80200
`Y-1`0.7885762917181170.1624674.85382.1e-051e-05
`Y-2`-0.6070305621227190.220893-2.74810.0091190.004559
`Y-3`-0.2440135382730270.232627-1.04890.3008280.150414
`Y-4`0.3454115743792410.1283042.69210.01050.00525
M10.08265601133000430.0664211.24440.2209610.11048
M2-0.01605507416271450.066433-0.24170.8103340.405167
M30.07372052354771540.0656861.12230.2687680.134384
M40.04049017472529670.0685640.59050.5583190.27916
M50.05480130338237340.0709230.77270.4444840.222242
M60.07829586658096380.0659711.18680.2426650.121332
M7-0.001714630030414610.067359-0.02550.9798250.489913
M80.02751012321451960.0677210.40620.6868550.343428
M90.06662787575306910.0717310.92890.3588240.179412
M10-0.02702750128583830.069232-0.39040.6984290.349214
M110.01088584327213660.0691510.15740.8757470.437874
t-0.01086980539937930.001735-6.263400

\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) & 0.685919050525686 & 0.112217 & 6.1124 & 0 & 0 \tabularnewline
X & 0.845278920723775 & 0.124268 & 6.802 & 0 & 0 \tabularnewline
`Y-1` & 0.788576291718117 & 0.162467 & 4.8538 & 2.1e-05 & 1e-05 \tabularnewline
`Y-2` & -0.607030562122719 & 0.220893 & -2.7481 & 0.009119 & 0.004559 \tabularnewline
`Y-3` & -0.244013538273027 & 0.232627 & -1.0489 & 0.300828 & 0.150414 \tabularnewline
`Y-4` & 0.345411574379241 & 0.128304 & 2.6921 & 0.0105 & 0.00525 \tabularnewline
M1 & 0.0826560113300043 & 0.066421 & 1.2444 & 0.220961 & 0.11048 \tabularnewline
M2 & -0.0160550741627145 & 0.066433 & -0.2417 & 0.810334 & 0.405167 \tabularnewline
M3 & 0.0737205235477154 & 0.065686 & 1.1223 & 0.268768 & 0.134384 \tabularnewline
M4 & 0.0404901747252967 & 0.068564 & 0.5905 & 0.558319 & 0.27916 \tabularnewline
M5 & 0.0548013033823734 & 0.070923 & 0.7727 & 0.444484 & 0.222242 \tabularnewline
M6 & 0.0782958665809638 & 0.065971 & 1.1868 & 0.242665 & 0.121332 \tabularnewline
M7 & -0.00171463003041461 & 0.067359 & -0.0255 & 0.979825 & 0.489913 \tabularnewline
M8 & 0.0275101232145196 & 0.067721 & 0.4062 & 0.686855 & 0.343428 \tabularnewline
M9 & 0.0666278757530691 & 0.071731 & 0.9289 & 0.358824 & 0.179412 \tabularnewline
M10 & -0.0270275012858383 & 0.069232 & -0.3904 & 0.698429 & 0.349214 \tabularnewline
M11 & 0.0108858432721366 & 0.069151 & 0.1574 & 0.875747 & 0.437874 \tabularnewline
t & -0.0108698053993793 & 0.001735 & -6.2634 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58345&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]0.685919050525686[/C][C]0.112217[/C][C]6.1124[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]0.845278920723775[/C][C]0.124268[/C][C]6.802[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y-1`[/C][C]0.788576291718117[/C][C]0.162467[/C][C]4.8538[/C][C]2.1e-05[/C][C]1e-05[/C][/ROW]
[ROW][C]`Y-2`[/C][C]-0.607030562122719[/C][C]0.220893[/C][C]-2.7481[/C][C]0.009119[/C][C]0.004559[/C][/ROW]
[ROW][C]`Y-3`[/C][C]-0.244013538273027[/C][C]0.232627[/C][C]-1.0489[/C][C]0.300828[/C][C]0.150414[/C][/ROW]
[ROW][C]`Y-4`[/C][C]0.345411574379241[/C][C]0.128304[/C][C]2.6921[/C][C]0.0105[/C][C]0.00525[/C][/ROW]
[ROW][C]M1[/C][C]0.0826560113300043[/C][C]0.066421[/C][C]1.2444[/C][C]0.220961[/C][C]0.11048[/C][/ROW]
[ROW][C]M2[/C][C]-0.0160550741627145[/C][C]0.066433[/C][C]-0.2417[/C][C]0.810334[/C][C]0.405167[/C][/ROW]
[ROW][C]M3[/C][C]0.0737205235477154[/C][C]0.065686[/C][C]1.1223[/C][C]0.268768[/C][C]0.134384[/C][/ROW]
[ROW][C]M4[/C][C]0.0404901747252967[/C][C]0.068564[/C][C]0.5905[/C][C]0.558319[/C][C]0.27916[/C][/ROW]
[ROW][C]M5[/C][C]0.0548013033823734[/C][C]0.070923[/C][C]0.7727[/C][C]0.444484[/C][C]0.222242[/C][/ROW]
[ROW][C]M6[/C][C]0.0782958665809638[/C][C]0.065971[/C][C]1.1868[/C][C]0.242665[/C][C]0.121332[/C][/ROW]
[ROW][C]M7[/C][C]-0.00171463003041461[/C][C]0.067359[/C][C]-0.0255[/C][C]0.979825[/C][C]0.489913[/C][/ROW]
[ROW][C]M8[/C][C]0.0275101232145196[/C][C]0.067721[/C][C]0.4062[/C][C]0.686855[/C][C]0.343428[/C][/ROW]
[ROW][C]M9[/C][C]0.0666278757530691[/C][C]0.071731[/C][C]0.9289[/C][C]0.358824[/C][C]0.179412[/C][/ROW]
[ROW][C]M10[/C][C]-0.0270275012858383[/C][C]0.069232[/C][C]-0.3904[/C][C]0.698429[/C][C]0.349214[/C][/ROW]
[ROW][C]M11[/C][C]0.0108858432721366[/C][C]0.069151[/C][C]0.1574[/C][C]0.875747[/C][C]0.437874[/C][/ROW]
[ROW][C]t[/C][C]-0.0108698053993793[/C][C]0.001735[/C][C]-6.2634[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58345&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58345&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)0.6859190505256860.1122176.112400
X0.8452789207237750.1242686.80200
`Y-1`0.7885762917181170.1624674.85382.1e-051e-05
`Y-2`-0.6070305621227190.220893-2.74810.0091190.004559
`Y-3`-0.2440135382730270.232627-1.04890.3008280.150414
`Y-4`0.3454115743792410.1283042.69210.01050.00525
M10.08265601133000430.0664211.24440.2209610.11048
M2-0.01605507416271450.066433-0.24170.8103340.405167
M30.07372052354771540.0656861.12230.2687680.134384
M40.04049017472529670.0685640.59050.5583190.27916
M50.05480130338237340.0709230.77270.4444840.222242
M60.07829586658096380.0659711.18680.2426650.121332
M7-0.001714630030414610.067359-0.02550.9798250.489913
M80.02751012321451960.0677210.40620.6868550.343428
M90.06662787575306910.0717310.92890.3588240.179412
M10-0.02702750128583830.069232-0.39040.6984290.349214
M110.01088584327213660.0691510.15740.8757470.437874
t-0.01086980539937930.001735-6.263400






Multiple Linear Regression - Regression Statistics
Multiple R0.99746800308064
R-squared0.99494241716968
Adjusted R-squared0.992679814324536
F-TEST (value)439.733565837805
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.095774680561324
Sum Squared Residuals0.348565998591699

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99746800308064 \tabularnewline
R-squared & 0.99494241716968 \tabularnewline
Adjusted R-squared & 0.992679814324536 \tabularnewline
F-TEST (value) & 439.733565837805 \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 & 0.095774680561324 \tabularnewline
Sum Squared Residuals & 0.348565998591699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58345&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99746800308064[/C][/ROW]
[ROW][C]R-squared[/C][C]0.99494241716968[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.992679814324536[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]439.733565837805[/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]0.095774680561324[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.348565998591699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58345&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58345&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 R0.99746800308064
R-squared0.99494241716968
Adjusted R-squared0.992679814324536
F-TEST (value)439.733565837805
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.095774680561324
Sum Squared Residuals0.348565998591699






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.082.1440968620871-0.0640968620871015
22.062.10805944765967-0.0480594476596719
32.062.15583510731601-0.0958351073160126
42.082.10273869521331-0.0227386952133087
52.072.13719416230221-0.0671941623022063
62.062.12288431445420-0.0628843144541967
72.072.025308284382020.0446917156179751
82.062.06696766763630-0.00696766763630282
92.092.080245565876000.00975443412399725
102.071.999553726683960.070446273316036
112.091.998509074271040.0914909257289616
122.282.20521077096530.0747892290346999
132.332.42992847907675-0.0999284790767505
142.352.232652093714200.117347906285803
152.522.468843273150130.0511567268498732
162.632.600087999496360.0299120005036413
172.582.59946782723569-0.0194678272356881
182.72.682636068777610.0173639312223915
192.812.74861492831360.0613850716864012
202.973.04238528106973-0.0723852810697316
213.043.08347986973858-0.0434798697385766
223.283.162957767677340.117042232322657
233.333.33572058455773-0.00572058455772807
243.53.457211049965180.0427889500348235
253.563.59831925840277-0.0383192584027656
263.573.503555850390260.0664441496097411
273.693.74103357928462-0.0510335792846186
283.823.82957142979586-0.00957142979585707
293.793.88096856260221-0.0909685626022074
303.963.97651427990589-0.0165142799058946
314.064.047630493300910.0123695066990860
324.054.09387178557491-0.04387178557491
334.034.001686264846840.0283137351531647
343.943.921778476012580.0182215239874179
354.023.926972052979660.0930279470203444
363.884.0243614132583-0.144361413258301
374.023.952237480335560.0677625196644388
384.033.987433424225210.0425665757747948
394.094.051035522064820.0389644779351797
403.993.965660123953560.0243398760464363
414.013.899739469342450.110260530657550
424.013.977652112635710.0323478873642938
434.194.13107697785350.0589230221465051
444.34.251954230004930.0480457699950725
454.274.264588299538580.0054117004614147
463.824.02571002962611-0.205710029626111
473.153.32879828819158-0.178798288191578
482.492.463216765811220.026783234188778
491.811.675417920097820.134582079902179
501.261.43829918401067-0.178299184010667
511.061.003252518184420.0567474818155784
520.840.861941751540912-0.0219417515409118
530.780.7126299785174480.067370021482552
540.70.6703132242265940.0296867757734061
550.360.537369316149968-0.177369316149968
560.350.2748210357141280.075178964285872

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.08 & 2.1440968620871 & -0.0640968620871015 \tabularnewline
2 & 2.06 & 2.10805944765967 & -0.0480594476596719 \tabularnewline
3 & 2.06 & 2.15583510731601 & -0.0958351073160126 \tabularnewline
4 & 2.08 & 2.10273869521331 & -0.0227386952133087 \tabularnewline
5 & 2.07 & 2.13719416230221 & -0.0671941623022063 \tabularnewline
6 & 2.06 & 2.12288431445420 & -0.0628843144541967 \tabularnewline
7 & 2.07 & 2.02530828438202 & 0.0446917156179751 \tabularnewline
8 & 2.06 & 2.06696766763630 & -0.00696766763630282 \tabularnewline
9 & 2.09 & 2.08024556587600 & 0.00975443412399725 \tabularnewline
10 & 2.07 & 1.99955372668396 & 0.070446273316036 \tabularnewline
11 & 2.09 & 1.99850907427104 & 0.0914909257289616 \tabularnewline
12 & 2.28 & 2.2052107709653 & 0.0747892290346999 \tabularnewline
13 & 2.33 & 2.42992847907675 & -0.0999284790767505 \tabularnewline
14 & 2.35 & 2.23265209371420 & 0.117347906285803 \tabularnewline
15 & 2.52 & 2.46884327315013 & 0.0511567268498732 \tabularnewline
16 & 2.63 & 2.60008799949636 & 0.0299120005036413 \tabularnewline
17 & 2.58 & 2.59946782723569 & -0.0194678272356881 \tabularnewline
18 & 2.7 & 2.68263606877761 & 0.0173639312223915 \tabularnewline
19 & 2.81 & 2.7486149283136 & 0.0613850716864012 \tabularnewline
20 & 2.97 & 3.04238528106973 & -0.0723852810697316 \tabularnewline
21 & 3.04 & 3.08347986973858 & -0.0434798697385766 \tabularnewline
22 & 3.28 & 3.16295776767734 & 0.117042232322657 \tabularnewline
23 & 3.33 & 3.33572058455773 & -0.00572058455772807 \tabularnewline
24 & 3.5 & 3.45721104996518 & 0.0427889500348235 \tabularnewline
25 & 3.56 & 3.59831925840277 & -0.0383192584027656 \tabularnewline
26 & 3.57 & 3.50355585039026 & 0.0664441496097411 \tabularnewline
27 & 3.69 & 3.74103357928462 & -0.0510335792846186 \tabularnewline
28 & 3.82 & 3.82957142979586 & -0.00957142979585707 \tabularnewline
29 & 3.79 & 3.88096856260221 & -0.0909685626022074 \tabularnewline
30 & 3.96 & 3.97651427990589 & -0.0165142799058946 \tabularnewline
31 & 4.06 & 4.04763049330091 & 0.0123695066990860 \tabularnewline
32 & 4.05 & 4.09387178557491 & -0.04387178557491 \tabularnewline
33 & 4.03 & 4.00168626484684 & 0.0283137351531647 \tabularnewline
34 & 3.94 & 3.92177847601258 & 0.0182215239874179 \tabularnewline
35 & 4.02 & 3.92697205297966 & 0.0930279470203444 \tabularnewline
36 & 3.88 & 4.0243614132583 & -0.144361413258301 \tabularnewline
37 & 4.02 & 3.95223748033556 & 0.0677625196644388 \tabularnewline
38 & 4.03 & 3.98743342422521 & 0.0425665757747948 \tabularnewline
39 & 4.09 & 4.05103552206482 & 0.0389644779351797 \tabularnewline
40 & 3.99 & 3.96566012395356 & 0.0243398760464363 \tabularnewline
41 & 4.01 & 3.89973946934245 & 0.110260530657550 \tabularnewline
42 & 4.01 & 3.97765211263571 & 0.0323478873642938 \tabularnewline
43 & 4.19 & 4.1310769778535 & 0.0589230221465051 \tabularnewline
44 & 4.3 & 4.25195423000493 & 0.0480457699950725 \tabularnewline
45 & 4.27 & 4.26458829953858 & 0.0054117004614147 \tabularnewline
46 & 3.82 & 4.02571002962611 & -0.205710029626111 \tabularnewline
47 & 3.15 & 3.32879828819158 & -0.178798288191578 \tabularnewline
48 & 2.49 & 2.46321676581122 & 0.026783234188778 \tabularnewline
49 & 1.81 & 1.67541792009782 & 0.134582079902179 \tabularnewline
50 & 1.26 & 1.43829918401067 & -0.178299184010667 \tabularnewline
51 & 1.06 & 1.00325251818442 & 0.0567474818155784 \tabularnewline
52 & 0.84 & 0.861941751540912 & -0.0219417515409118 \tabularnewline
53 & 0.78 & 0.712629978517448 & 0.067370021482552 \tabularnewline
54 & 0.7 & 0.670313224226594 & 0.0296867757734061 \tabularnewline
55 & 0.36 & 0.537369316149968 & -0.177369316149968 \tabularnewline
56 & 0.35 & 0.274821035714128 & 0.075178964285872 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58345&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]2.08[/C][C]2.1440968620871[/C][C]-0.0640968620871015[/C][/ROW]
[ROW][C]2[/C][C]2.06[/C][C]2.10805944765967[/C][C]-0.0480594476596719[/C][/ROW]
[ROW][C]3[/C][C]2.06[/C][C]2.15583510731601[/C][C]-0.0958351073160126[/C][/ROW]
[ROW][C]4[/C][C]2.08[/C][C]2.10273869521331[/C][C]-0.0227386952133087[/C][/ROW]
[ROW][C]5[/C][C]2.07[/C][C]2.13719416230221[/C][C]-0.0671941623022063[/C][/ROW]
[ROW][C]6[/C][C]2.06[/C][C]2.12288431445420[/C][C]-0.0628843144541967[/C][/ROW]
[ROW][C]7[/C][C]2.07[/C][C]2.02530828438202[/C][C]0.0446917156179751[/C][/ROW]
[ROW][C]8[/C][C]2.06[/C][C]2.06696766763630[/C][C]-0.00696766763630282[/C][/ROW]
[ROW][C]9[/C][C]2.09[/C][C]2.08024556587600[/C][C]0.00975443412399725[/C][/ROW]
[ROW][C]10[/C][C]2.07[/C][C]1.99955372668396[/C][C]0.070446273316036[/C][/ROW]
[ROW][C]11[/C][C]2.09[/C][C]1.99850907427104[/C][C]0.0914909257289616[/C][/ROW]
[ROW][C]12[/C][C]2.28[/C][C]2.2052107709653[/C][C]0.0747892290346999[/C][/ROW]
[ROW][C]13[/C][C]2.33[/C][C]2.42992847907675[/C][C]-0.0999284790767505[/C][/ROW]
[ROW][C]14[/C][C]2.35[/C][C]2.23265209371420[/C][C]0.117347906285803[/C][/ROW]
[ROW][C]15[/C][C]2.52[/C][C]2.46884327315013[/C][C]0.0511567268498732[/C][/ROW]
[ROW][C]16[/C][C]2.63[/C][C]2.60008799949636[/C][C]0.0299120005036413[/C][/ROW]
[ROW][C]17[/C][C]2.58[/C][C]2.59946782723569[/C][C]-0.0194678272356881[/C][/ROW]
[ROW][C]18[/C][C]2.7[/C][C]2.68263606877761[/C][C]0.0173639312223915[/C][/ROW]
[ROW][C]19[/C][C]2.81[/C][C]2.7486149283136[/C][C]0.0613850716864012[/C][/ROW]
[ROW][C]20[/C][C]2.97[/C][C]3.04238528106973[/C][C]-0.0723852810697316[/C][/ROW]
[ROW][C]21[/C][C]3.04[/C][C]3.08347986973858[/C][C]-0.0434798697385766[/C][/ROW]
[ROW][C]22[/C][C]3.28[/C][C]3.16295776767734[/C][C]0.117042232322657[/C][/ROW]
[ROW][C]23[/C][C]3.33[/C][C]3.33572058455773[/C][C]-0.00572058455772807[/C][/ROW]
[ROW][C]24[/C][C]3.5[/C][C]3.45721104996518[/C][C]0.0427889500348235[/C][/ROW]
[ROW][C]25[/C][C]3.56[/C][C]3.59831925840277[/C][C]-0.0383192584027656[/C][/ROW]
[ROW][C]26[/C][C]3.57[/C][C]3.50355585039026[/C][C]0.0664441496097411[/C][/ROW]
[ROW][C]27[/C][C]3.69[/C][C]3.74103357928462[/C][C]-0.0510335792846186[/C][/ROW]
[ROW][C]28[/C][C]3.82[/C][C]3.82957142979586[/C][C]-0.00957142979585707[/C][/ROW]
[ROW][C]29[/C][C]3.79[/C][C]3.88096856260221[/C][C]-0.0909685626022074[/C][/ROW]
[ROW][C]30[/C][C]3.96[/C][C]3.97651427990589[/C][C]-0.0165142799058946[/C][/ROW]
[ROW][C]31[/C][C]4.06[/C][C]4.04763049330091[/C][C]0.0123695066990860[/C][/ROW]
[ROW][C]32[/C][C]4.05[/C][C]4.09387178557491[/C][C]-0.04387178557491[/C][/ROW]
[ROW][C]33[/C][C]4.03[/C][C]4.00168626484684[/C][C]0.0283137351531647[/C][/ROW]
[ROW][C]34[/C][C]3.94[/C][C]3.92177847601258[/C][C]0.0182215239874179[/C][/ROW]
[ROW][C]35[/C][C]4.02[/C][C]3.92697205297966[/C][C]0.0930279470203444[/C][/ROW]
[ROW][C]36[/C][C]3.88[/C][C]4.0243614132583[/C][C]-0.144361413258301[/C][/ROW]
[ROW][C]37[/C][C]4.02[/C][C]3.95223748033556[/C][C]0.0677625196644388[/C][/ROW]
[ROW][C]38[/C][C]4.03[/C][C]3.98743342422521[/C][C]0.0425665757747948[/C][/ROW]
[ROW][C]39[/C][C]4.09[/C][C]4.05103552206482[/C][C]0.0389644779351797[/C][/ROW]
[ROW][C]40[/C][C]3.99[/C][C]3.96566012395356[/C][C]0.0243398760464363[/C][/ROW]
[ROW][C]41[/C][C]4.01[/C][C]3.89973946934245[/C][C]0.110260530657550[/C][/ROW]
[ROW][C]42[/C][C]4.01[/C][C]3.97765211263571[/C][C]0.0323478873642938[/C][/ROW]
[ROW][C]43[/C][C]4.19[/C][C]4.1310769778535[/C][C]0.0589230221465051[/C][/ROW]
[ROW][C]44[/C][C]4.3[/C][C]4.25195423000493[/C][C]0.0480457699950725[/C][/ROW]
[ROW][C]45[/C][C]4.27[/C][C]4.26458829953858[/C][C]0.0054117004614147[/C][/ROW]
[ROW][C]46[/C][C]3.82[/C][C]4.02571002962611[/C][C]-0.205710029626111[/C][/ROW]
[ROW][C]47[/C][C]3.15[/C][C]3.32879828819158[/C][C]-0.178798288191578[/C][/ROW]
[ROW][C]48[/C][C]2.49[/C][C]2.46321676581122[/C][C]0.026783234188778[/C][/ROW]
[ROW][C]49[/C][C]1.81[/C][C]1.67541792009782[/C][C]0.134582079902179[/C][/ROW]
[ROW][C]50[/C][C]1.26[/C][C]1.43829918401067[/C][C]-0.178299184010667[/C][/ROW]
[ROW][C]51[/C][C]1.06[/C][C]1.00325251818442[/C][C]0.0567474818155784[/C][/ROW]
[ROW][C]52[/C][C]0.84[/C][C]0.861941751540912[/C][C]-0.0219417515409118[/C][/ROW]
[ROW][C]53[/C][C]0.78[/C][C]0.712629978517448[/C][C]0.067370021482552[/C][/ROW]
[ROW][C]54[/C][C]0.7[/C][C]0.670313224226594[/C][C]0.0296867757734061[/C][/ROW]
[ROW][C]55[/C][C]0.36[/C][C]0.537369316149968[/C][C]-0.177369316149968[/C][/ROW]
[ROW][C]56[/C][C]0.35[/C][C]0.274821035714128[/C][C]0.075178964285872[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58345&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58345&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
12.082.1440968620871-0.0640968620871015
22.062.10805944765967-0.0480594476596719
32.062.15583510731601-0.0958351073160126
42.082.10273869521331-0.0227386952133087
52.072.13719416230221-0.0671941623022063
62.062.12288431445420-0.0628843144541967
72.072.025308284382020.0446917156179751
82.062.06696766763630-0.00696766763630282
92.092.080245565876000.00975443412399725
102.071.999553726683960.070446273316036
112.091.998509074271040.0914909257289616
122.282.20521077096530.0747892290346999
132.332.42992847907675-0.0999284790767505
142.352.232652093714200.117347906285803
152.522.468843273150130.0511567268498732
162.632.600087999496360.0299120005036413
172.582.59946782723569-0.0194678272356881
182.72.682636068777610.0173639312223915
192.812.74861492831360.0613850716864012
202.973.04238528106973-0.0723852810697316
213.043.08347986973858-0.0434798697385766
223.283.162957767677340.117042232322657
233.333.33572058455773-0.00572058455772807
243.53.457211049965180.0427889500348235
253.563.59831925840277-0.0383192584027656
263.573.503555850390260.0664441496097411
273.693.74103357928462-0.0510335792846186
283.823.82957142979586-0.00957142979585707
293.793.88096856260221-0.0909685626022074
303.963.97651427990589-0.0165142799058946
314.064.047630493300910.0123695066990860
324.054.09387178557491-0.04387178557491
334.034.001686264846840.0283137351531647
343.943.921778476012580.0182215239874179
354.023.926972052979660.0930279470203444
363.884.0243614132583-0.144361413258301
374.023.952237480335560.0677625196644388
384.033.987433424225210.0425665757747948
394.094.051035522064820.0389644779351797
403.993.965660123953560.0243398760464363
414.013.899739469342450.110260530657550
424.013.977652112635710.0323478873642938
434.194.13107697785350.0589230221465051
444.34.251954230004930.0480457699950725
454.274.264588299538580.0054117004614147
463.824.02571002962611-0.205710029626111
473.153.32879828819158-0.178798288191578
482.492.463216765811220.026783234188778
491.811.675417920097820.134582079902179
501.261.43829918401067-0.178299184010667
511.061.003252518184420.0567474818155784
520.840.861941751540912-0.0219417515409118
530.780.7126299785174480.067370021482552
540.70.6703132242265940.0296867757734061
550.360.537369316149968-0.177369316149968
560.350.2748210357141280.075178964285872






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.01974015583155800.03948031166311590.980259844168442
220.01569490906542810.03138981813085620.984305090934572
230.003804517284719220.007609034569438430.99619548271528
240.001012387224479870.002024774448959740.99898761277552
250.0002800837043139990.0005601674086279980.999719916295686
260.0001629921308870810.0003259842617741620.999837007869113
270.0001043242056071900.0002086484112143800.999895675794393
282.98189529391630e-055.96379058783261e-050.99997018104706
292.54620718564248e-055.09241437128496e-050.999974537928144
308.13562944900058e-061.62712588980012e-050.999991864370551
313.45168331209004e-066.90336662418008e-060.999996548316688
328.55482100914298e-071.71096420182860e-060.999999144517899
331.10014839048648e-062.20029678097297e-060.99999889985161
344.81055231117813e-069.62110462235626e-060.99999518944769
350.0001247375823808540.0002494751647617080.99987526241762

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0197401558315580 & 0.0394803116631159 & 0.980259844168442 \tabularnewline
22 & 0.0156949090654281 & 0.0313898181308562 & 0.984305090934572 \tabularnewline
23 & 0.00380451728471922 & 0.00760903456943843 & 0.99619548271528 \tabularnewline
24 & 0.00101238722447987 & 0.00202477444895974 & 0.99898761277552 \tabularnewline
25 & 0.000280083704313999 & 0.000560167408627998 & 0.999719916295686 \tabularnewline
26 & 0.000162992130887081 & 0.000325984261774162 & 0.999837007869113 \tabularnewline
27 & 0.000104324205607190 & 0.000208648411214380 & 0.999895675794393 \tabularnewline
28 & 2.98189529391630e-05 & 5.96379058783261e-05 & 0.99997018104706 \tabularnewline
29 & 2.54620718564248e-05 & 5.09241437128496e-05 & 0.999974537928144 \tabularnewline
30 & 8.13562944900058e-06 & 1.62712588980012e-05 & 0.999991864370551 \tabularnewline
31 & 3.45168331209004e-06 & 6.90336662418008e-06 & 0.999996548316688 \tabularnewline
32 & 8.55482100914298e-07 & 1.71096420182860e-06 & 0.999999144517899 \tabularnewline
33 & 1.10014839048648e-06 & 2.20029678097297e-06 & 0.99999889985161 \tabularnewline
34 & 4.81055231117813e-06 & 9.62110462235626e-06 & 0.99999518944769 \tabularnewline
35 & 0.000124737582380854 & 0.000249475164761708 & 0.99987526241762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58345&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]0.0197401558315580[/C][C]0.0394803116631159[/C][C]0.980259844168442[/C][/ROW]
[ROW][C]22[/C][C]0.0156949090654281[/C][C]0.0313898181308562[/C][C]0.984305090934572[/C][/ROW]
[ROW][C]23[/C][C]0.00380451728471922[/C][C]0.00760903456943843[/C][C]0.99619548271528[/C][/ROW]
[ROW][C]24[/C][C]0.00101238722447987[/C][C]0.00202477444895974[/C][C]0.99898761277552[/C][/ROW]
[ROW][C]25[/C][C]0.000280083704313999[/C][C]0.000560167408627998[/C][C]0.999719916295686[/C][/ROW]
[ROW][C]26[/C][C]0.000162992130887081[/C][C]0.000325984261774162[/C][C]0.999837007869113[/C][/ROW]
[ROW][C]27[/C][C]0.000104324205607190[/C][C]0.000208648411214380[/C][C]0.999895675794393[/C][/ROW]
[ROW][C]28[/C][C]2.98189529391630e-05[/C][C]5.96379058783261e-05[/C][C]0.99997018104706[/C][/ROW]
[ROW][C]29[/C][C]2.54620718564248e-05[/C][C]5.09241437128496e-05[/C][C]0.999974537928144[/C][/ROW]
[ROW][C]30[/C][C]8.13562944900058e-06[/C][C]1.62712588980012e-05[/C][C]0.999991864370551[/C][/ROW]
[ROW][C]31[/C][C]3.45168331209004e-06[/C][C]6.90336662418008e-06[/C][C]0.999996548316688[/C][/ROW]
[ROW][C]32[/C][C]8.55482100914298e-07[/C][C]1.71096420182860e-06[/C][C]0.999999144517899[/C][/ROW]
[ROW][C]33[/C][C]1.10014839048648e-06[/C][C]2.20029678097297e-06[/C][C]0.99999889985161[/C][/ROW]
[ROW][C]34[/C][C]4.81055231117813e-06[/C][C]9.62110462235626e-06[/C][C]0.99999518944769[/C][/ROW]
[ROW][C]35[/C][C]0.000124737582380854[/C][C]0.000249475164761708[/C][C]0.99987526241762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58345&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58345&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
210.01974015583155800.03948031166311590.980259844168442
220.01569490906542810.03138981813085620.984305090934572
230.003804517284719220.007609034569438430.99619548271528
240.001012387224479870.002024774448959740.99898761277552
250.0002800837043139990.0005601674086279980.999719916295686
260.0001629921308870810.0003259842617741620.999837007869113
270.0001043242056071900.0002086484112143800.999895675794393
282.98189529391630e-055.96379058783261e-050.99997018104706
292.54620718564248e-055.09241437128496e-050.999974537928144
308.13562944900058e-061.62712588980012e-050.999991864370551
313.45168331209004e-066.90336662418008e-060.999996548316688
328.55482100914298e-071.71096420182860e-060.999999144517899
331.10014839048648e-062.20029678097297e-060.99999889985161
344.81055231117813e-069.62110462235626e-060.99999518944769
350.0001247375823808540.0002494751647617080.99987526241762






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level130.866666666666667NOK
5% type I error level151NOK
10% type I error level151NOK

\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 & 13 & 0.866666666666667 & NOK \tabularnewline
5% type I error level & 15 & 1 & NOK \tabularnewline
10% type I error level & 15 & 1 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58345&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]13[/C][C]0.866666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]15[/C][C]1[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]1[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58345&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58345&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 level130.866666666666667NOK
5% type I error level151NOK
10% type I error level151NOK


Figures (Output of Computation)

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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')
}