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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSun, 28 Nov 2010 10:58:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/28/t1290941941kuhwseonw48x8hd.htm/, Retrieved Sat, 04 May 2024 16:03:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102481, Retrieved Sat, 04 May 2024 16:03:16 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193
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 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [WS 8, maandelijks...] [2010-11-28 10:58:16] [99c051a77087383325372ff23bc64341] [Current]
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Dataseries X:
4.803	0
4.672	0
4.560	0
4.289	0
3.961	0
3.943	0
3.932	0
3.816	0
3.834	0
4.130	0
4.467	0
4.447	0
4.683	1
4.441	1
4.465	1
4.187	1
3.991	1
3.816	1
3.903	1
3.784	1
3.817	1
4.189	1
4.345	1
4.183	1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 10 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102481&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]10 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102481&T=0

As an alternative you can also use a 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 time10 seconds
R Server'George Udny Yule' @ 72.249.76.132







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 4.35875 -0.0875000000000003X[t] + 0.428000000000001M1[t] + 0.2415M2[t] + 0.197500000000000M3[t] -0.0769999999999999M4[t] -0.339M5[t] -0.4355M6[t] -0.3975M7[t] -0.515M8[t] -0.4895M9[t] -0.1555M10[t] + 0.0909999999999999M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  4.35875 -0.0875000000000003X[t] +  0.428000000000001M1[t] +  0.2415M2[t] +  0.197500000000000M3[t] -0.0769999999999999M4[t] -0.339M5[t] -0.4355M6[t] -0.3975M7[t] -0.515M8[t] -0.4895M9[t] -0.1555M10[t] +  0.0909999999999999M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102481&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  4.35875 -0.0875000000000003X[t] +  0.428000000000001M1[t] +  0.2415M2[t] +  0.197500000000000M3[t] -0.0769999999999999M4[t] -0.339M5[t] -0.4355M6[t] -0.3975M7[t] -0.515M8[t] -0.4895M9[t] -0.1555M10[t] +  0.0909999999999999M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102481&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 4.35875 -0.0875000000000003X[t] + 0.428000000000001M1[t] + 0.2415M2[t] + 0.197500000000000M3[t] -0.0769999999999999M4[t] -0.339M5[t] -0.4355M6[t] -0.3975M7[t] -0.515M8[t] -0.4895M9[t] -0.1555M10[t] + 0.0909999999999999M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)4.358750.05025186.740200
X-0.08750000000000030.027874-3.13910.0094230.004712
M10.4280000000000010.0682776.26866.1e-053e-05
M20.24150.0682773.53710.0046570.002328
M30.1975000000000000.0682772.89260.0146370.007319
M4-0.07699999999999990.068277-1.12780.2834210.14171
M5-0.3390.068277-4.96510.0004250.000213
M6-0.43550.068277-6.37845.2e-052.6e-05
M7-0.39750.068277-5.82190.0001165.8e-05
M8-0.5150.068277-7.54281.1e-056e-06
M9-0.48950.068277-7.16931.8e-059e-06
M10-0.15550.068277-2.27750.0437290.021865
M110.09099999999999990.0682771.33280.2095450.104772

\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) & 4.35875 & 0.050251 & 86.7402 & 0 & 0 \tabularnewline
X & -0.0875000000000003 & 0.027874 & -3.1391 & 0.009423 & 0.004712 \tabularnewline
M1 & 0.428000000000001 & 0.068277 & 6.2686 & 6.1e-05 & 3e-05 \tabularnewline
M2 & 0.2415 & 0.068277 & 3.5371 & 0.004657 & 0.002328 \tabularnewline
M3 & 0.197500000000000 & 0.068277 & 2.8926 & 0.014637 & 0.007319 \tabularnewline
M4 & -0.0769999999999999 & 0.068277 & -1.1278 & 0.283421 & 0.14171 \tabularnewline
M5 & -0.339 & 0.068277 & -4.9651 & 0.000425 & 0.000213 \tabularnewline
M6 & -0.4355 & 0.068277 & -6.3784 & 5.2e-05 & 2.6e-05 \tabularnewline
M7 & -0.3975 & 0.068277 & -5.8219 & 0.000116 & 5.8e-05 \tabularnewline
M8 & -0.515 & 0.068277 & -7.5428 & 1.1e-05 & 6e-06 \tabularnewline
M9 & -0.4895 & 0.068277 & -7.1693 & 1.8e-05 & 9e-06 \tabularnewline
M10 & -0.1555 & 0.068277 & -2.2775 & 0.043729 & 0.021865 \tabularnewline
M11 & 0.0909999999999999 & 0.068277 & 1.3328 & 0.209545 & 0.104772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102481&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]4.35875[/C][C]0.050251[/C][C]86.7402[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-0.0875000000000003[/C][C]0.027874[/C][C]-3.1391[/C][C]0.009423[/C][C]0.004712[/C][/ROW]
[ROW][C]M1[/C][C]0.428000000000001[/C][C]0.068277[/C][C]6.2686[/C][C]6.1e-05[/C][C]3e-05[/C][/ROW]
[ROW][C]M2[/C][C]0.2415[/C][C]0.068277[/C][C]3.5371[/C][C]0.004657[/C][C]0.002328[/C][/ROW]
[ROW][C]M3[/C][C]0.197500000000000[/C][C]0.068277[/C][C]2.8926[/C][C]0.014637[/C][C]0.007319[/C][/ROW]
[ROW][C]M4[/C][C]-0.0769999999999999[/C][C]0.068277[/C][C]-1.1278[/C][C]0.283421[/C][C]0.14171[/C][/ROW]
[ROW][C]M5[/C][C]-0.339[/C][C]0.068277[/C][C]-4.9651[/C][C]0.000425[/C][C]0.000213[/C][/ROW]
[ROW][C]M6[/C][C]-0.4355[/C][C]0.068277[/C][C]-6.3784[/C][C]5.2e-05[/C][C]2.6e-05[/C][/ROW]
[ROW][C]M7[/C][C]-0.3975[/C][C]0.068277[/C][C]-5.8219[/C][C]0.000116[/C][C]5.8e-05[/C][/ROW]
[ROW][C]M8[/C][C]-0.515[/C][C]0.068277[/C][C]-7.5428[/C][C]1.1e-05[/C][C]6e-06[/C][/ROW]
[ROW][C]M9[/C][C]-0.4895[/C][C]0.068277[/C][C]-7.1693[/C][C]1.8e-05[/C][C]9e-06[/C][/ROW]
[ROW][C]M10[/C][C]-0.1555[/C][C]0.068277[/C][C]-2.2775[/C][C]0.043729[/C][C]0.021865[/C][/ROW]
[ROW][C]M11[/C][C]0.0909999999999999[/C][C]0.068277[/C][C]1.3328[/C][C]0.209545[/C][C]0.104772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102481&T=2

As an alternative you can also use a 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)4.358750.05025186.740200
X-0.08750000000000030.027874-3.13910.0094230.004712
M10.4280000000000010.0682776.26866.1e-053e-05
M20.24150.0682773.53710.0046570.002328
M30.1975000000000000.0682772.89260.0146370.007319
M4-0.07699999999999990.068277-1.12780.2834210.14171
M5-0.3390.068277-4.96510.0004250.000213
M6-0.43550.068277-6.37845.2e-052.6e-05
M7-0.39750.068277-5.82190.0001165.8e-05
M8-0.5150.068277-7.54281.1e-056e-06
M9-0.48950.068277-7.16931.8e-059e-06
M10-0.15550.068277-2.27750.0437290.021865
M110.09099999999999990.0682771.33280.2095450.104772







Multiple Linear Regression - Regression Statistics
Multiple R0.988881655785396
R-squared0.977886929148866
Adjusted R-squared0.953763579129448
F-TEST (value)40.5369456713803
F-TEST (DF numerator)12
F-TEST (DF denominator)11
p-value2.46443835116850e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0682771757417714
Sum Squared Residuals0.0512795000000002

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.988881655785396 \tabularnewline
R-squared & 0.977886929148866 \tabularnewline
Adjusted R-squared & 0.953763579129448 \tabularnewline
F-TEST (value) & 40.5369456713803 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 11 \tabularnewline
p-value & 2.46443835116850e-07 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0682771757417714 \tabularnewline
Sum Squared Residuals & 0.0512795000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102481&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.988881655785396[/C][/ROW]
[ROW][C]R-squared[/C][C]0.977886929148866[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.953763579129448[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]40.5369456713803[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]11[/C][/ROW]
[ROW][C]p-value[/C][C]2.46443835116850e-07[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0682771757417714[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0512795000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102481&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102481&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.988881655785396
R-squared0.977886929148866
Adjusted R-squared0.953763579129448
F-TEST (value)40.5369456713803
F-TEST (DF numerator)12
F-TEST (DF denominator)11
p-value2.46443835116850e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0682771757417714
Sum Squared Residuals0.0512795000000002







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
14.8034.786750.0162500000000014
24.6724.600250.0717500
34.564.556250.00374999999999966
44.2894.281750.00724999999999955
53.9614.01975-0.0587500000000001
63.9433.923250.0197499999999999
73.9323.96125-0.0292500000000001
83.8163.84375-0.0277500000000000
93.8343.86925-0.0352500000000001
104.134.20325-0.0732500000000002
114.4674.449750.0172500000000000
124.4474.358750.08825
134.6834.69925-0.0162500000000013
144.4414.51275-0.0717499999999999
154.4654.46875-0.00374999999999974
164.1874.19425-0.00724999999999958
173.9913.932250.0587500000000002
183.8163.83575-0.0197499999999999
193.9033.873750.0292500000000001
203.7843.756250.02775
213.8173.781750.0352500000000001
224.1894.115750.0732500000000002
234.3454.36225-0.0172500000000000
244.1834.27125-0.08825

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 4.803 & 4.78675 & 0.0162500000000014 \tabularnewline
2 & 4.672 & 4.60025 & 0.0717500 \tabularnewline
3 & 4.56 & 4.55625 & 0.00374999999999966 \tabularnewline
4 & 4.289 & 4.28175 & 0.00724999999999955 \tabularnewline
5 & 3.961 & 4.01975 & -0.0587500000000001 \tabularnewline
6 & 3.943 & 3.92325 & 0.0197499999999999 \tabularnewline
7 & 3.932 & 3.96125 & -0.0292500000000001 \tabularnewline
8 & 3.816 & 3.84375 & -0.0277500000000000 \tabularnewline
9 & 3.834 & 3.86925 & -0.0352500000000001 \tabularnewline
10 & 4.13 & 4.20325 & -0.0732500000000002 \tabularnewline
11 & 4.467 & 4.44975 & 0.0172500000000000 \tabularnewline
12 & 4.447 & 4.35875 & 0.08825 \tabularnewline
13 & 4.683 & 4.69925 & -0.0162500000000013 \tabularnewline
14 & 4.441 & 4.51275 & -0.0717499999999999 \tabularnewline
15 & 4.465 & 4.46875 & -0.00374999999999974 \tabularnewline
16 & 4.187 & 4.19425 & -0.00724999999999958 \tabularnewline
17 & 3.991 & 3.93225 & 0.0587500000000002 \tabularnewline
18 & 3.816 & 3.83575 & -0.0197499999999999 \tabularnewline
19 & 3.903 & 3.87375 & 0.0292500000000001 \tabularnewline
20 & 3.784 & 3.75625 & 0.02775 \tabularnewline
21 & 3.817 & 3.78175 & 0.0352500000000001 \tabularnewline
22 & 4.189 & 4.11575 & 0.0732500000000002 \tabularnewline
23 & 4.345 & 4.36225 & -0.0172500000000000 \tabularnewline
24 & 4.183 & 4.27125 & -0.08825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102481&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]4.803[/C][C]4.78675[/C][C]0.0162500000000014[/C][/ROW]
[ROW][C]2[/C][C]4.672[/C][C]4.60025[/C][C]0.0717500[/C][/ROW]
[ROW][C]3[/C][C]4.56[/C][C]4.55625[/C][C]0.00374999999999966[/C][/ROW]
[ROW][C]4[/C][C]4.289[/C][C]4.28175[/C][C]0.00724999999999955[/C][/ROW]
[ROW][C]5[/C][C]3.961[/C][C]4.01975[/C][C]-0.0587500000000001[/C][/ROW]
[ROW][C]6[/C][C]3.943[/C][C]3.92325[/C][C]0.0197499999999999[/C][/ROW]
[ROW][C]7[/C][C]3.932[/C][C]3.96125[/C][C]-0.0292500000000001[/C][/ROW]
[ROW][C]8[/C][C]3.816[/C][C]3.84375[/C][C]-0.0277500000000000[/C][/ROW]
[ROW][C]9[/C][C]3.834[/C][C]3.86925[/C][C]-0.0352500000000001[/C][/ROW]
[ROW][C]10[/C][C]4.13[/C][C]4.20325[/C][C]-0.0732500000000002[/C][/ROW]
[ROW][C]11[/C][C]4.467[/C][C]4.44975[/C][C]0.0172500000000000[/C][/ROW]
[ROW][C]12[/C][C]4.447[/C][C]4.35875[/C][C]0.08825[/C][/ROW]
[ROW][C]13[/C][C]4.683[/C][C]4.69925[/C][C]-0.0162500000000013[/C][/ROW]
[ROW][C]14[/C][C]4.441[/C][C]4.51275[/C][C]-0.0717499999999999[/C][/ROW]
[ROW][C]15[/C][C]4.465[/C][C]4.46875[/C][C]-0.00374999999999974[/C][/ROW]
[ROW][C]16[/C][C]4.187[/C][C]4.19425[/C][C]-0.00724999999999958[/C][/ROW]
[ROW][C]17[/C][C]3.991[/C][C]3.93225[/C][C]0.0587500000000002[/C][/ROW]
[ROW][C]18[/C][C]3.816[/C][C]3.83575[/C][C]-0.0197499999999999[/C][/ROW]
[ROW][C]19[/C][C]3.903[/C][C]3.87375[/C][C]0.0292500000000001[/C][/ROW]
[ROW][C]20[/C][C]3.784[/C][C]3.75625[/C][C]0.02775[/C][/ROW]
[ROW][C]21[/C][C]3.817[/C][C]3.78175[/C][C]0.0352500000000001[/C][/ROW]
[ROW][C]22[/C][C]4.189[/C][C]4.11575[/C][C]0.0732500000000002[/C][/ROW]
[ROW][C]23[/C][C]4.345[/C][C]4.36225[/C][C]-0.0172500000000000[/C][/ROW]
[ROW][C]24[/C][C]4.183[/C][C]4.27125[/C][C]-0.08825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102481&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102481&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
14.8034.786750.0162500000000014
24.6724.600250.0717500
34.564.556250.00374999999999966
44.2894.281750.00724999999999955
53.9614.01975-0.0587500000000001
63.9433.923250.0197499999999999
73.9323.96125-0.0292500000000001
83.8163.84375-0.0277500000000000
93.8343.86925-0.0352500000000001
104.134.20325-0.0732500000000002
114.4674.449750.0172500000000000
124.4474.358750.08825
134.6834.69925-0.0162500000000013
144.4414.51275-0.0717499999999999
154.4654.46875-0.00374999999999974
164.1874.19425-0.00724999999999958
173.9913.932250.0587500000000002
183.8163.83575-0.0197499999999999
193.9033.873750.0292500000000001
203.7843.756250.02775
213.8173.781750.0352500000000001
224.1894.115750.0732500000000002
234.3454.36225-0.0172500000000000
244.1834.27125-0.08825



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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')
}