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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 computationMon, 23 Jan 2017 09:25:28 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/23/t1485160097rt24t1ynoqex7d9.htm/, Retrieved Thu, 31 Oct 2024 23:44:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=303839, Retrieved Thu, 31 Oct 2024 23:44:03 +0000
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User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [] [2017-01-23 08:25:28] [bde5266f17215258f6d7c4cd7e531432] [Current]
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Dataseries X:
6 1 1 0 0 0 3.2 10.24 3.2
7 0 0 1 0 1 3.3 10.89 0
2 1 0 1 1 1 3 9 3
11 0 0 1 0 1 3.5 12.25 0
13 1 0 1 0 0 3.7 13.69 3.7
3 0 1 0 0 0 2.7 7.29 0
17 1 0 1 1 1 3.6 12.96 3.6
10 0 0 1 0 1 3.5 12.25 0
4 1 1 0 0 0 3.8 14.44 3.8
12 0 0 1 0 0 3.4 11.56 0
7 1 0 0 0 1 3.7 13.69 3.7
11 0 0 1 0 0 3.5 12.25 0
3 1 0 0 1 0 2.8 7.84 2.8
5 0 1 0 1 0 3.8 14.44 0
1 1 0 1 0 0 4.3 18.49 4.3
12 0 0 0 0 1 3.3 10.89 0
18 1 0 0 0 0 3.6 12.96 3.6
8 0 1 0 1 0 3.6 12.96 0
6 1 1 1 0 0 3.3 10.89 3.3
1 0 0 0 0 0 2.8 7.84 0




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303839&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]7 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=303839&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303839&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R ServerBig Analytics Cloud Computing Center







Multiple Linear Regression - Estimated Regression Equation
Score[t] = -257.794 -44.4619Geslacht[t] -4.8654X1[t] -0.217231X2[t] + 3.22869X3[t] -2.92673X4[t] + 163.222X5[t] -24.6204X6[t] + 13.1261Inter[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Score[t] =  -257.794 -44.4619Geslacht[t] -4.8654X1[t] -0.217231X2[t] +  3.22869X3[t] -2.92673X4[t] +  163.222X5[t] -24.6204X6[t] +  13.1261Inter[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303839&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Score[t] =  -257.794 -44.4619Geslacht[t] -4.8654X1[t] -0.217231X2[t] +  3.22869X3[t] -2.92673X4[t] +  163.222X5[t] -24.6204X6[t] +  13.1261Inter[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303839&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303839&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
Score[t] = -257.794 -44.4619Geslacht[t] -4.8654X1[t] -0.217231X2[t] + 3.22869X3[t] -2.92673X4[t] + 163.222X5[t] -24.6204X6[t] + 13.1261Inter[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-257.8 57.75-4.4640e+00 0.0009567 0.0004784
Geslacht-44.46 24.95-1.7820e+00 0.1023 0.05116
X1-4.865 2.155-2.2580e+00 0.04529 0.02264
X2-0.2172 1.849-1.1750e-01 0.9086 0.4543
X3+3.229 2.606+1.2390e+00 0.2412 0.1206
X4-2.927 2.123-1.3780e+00 0.1955 0.09773
X5+163.2 36.71+4.4460e+00 0.0009849 0.0004925
X6-24.62 5.804-4.2420e+00 0.001384 0.0006921
Inter+13.13 7.328+1.7910e+00 0.1008 0.05038

\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) & -257.8 &  57.75 & -4.4640e+00 &  0.0009567 &  0.0004784 \tabularnewline
Geslacht & -44.46 &  24.95 & -1.7820e+00 &  0.1023 &  0.05116 \tabularnewline
X1 & -4.865 &  2.155 & -2.2580e+00 &  0.04529 &  0.02264 \tabularnewline
X2 & -0.2172 &  1.849 & -1.1750e-01 &  0.9086 &  0.4543 \tabularnewline
X3 & +3.229 &  2.606 & +1.2390e+00 &  0.2412 &  0.1206 \tabularnewline
X4 & -2.927 &  2.123 & -1.3780e+00 &  0.1955 &  0.09773 \tabularnewline
X5 & +163.2 &  36.71 & +4.4460e+00 &  0.0009849 &  0.0004925 \tabularnewline
X6 & -24.62 &  5.804 & -4.2420e+00 &  0.001384 &  0.0006921 \tabularnewline
Inter & +13.13 &  7.328 & +1.7910e+00 &  0.1008 &  0.05038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303839&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]-257.8[/C][C] 57.75[/C][C]-4.4640e+00[/C][C] 0.0009567[/C][C] 0.0004784[/C][/ROW]
[ROW][C]Geslacht[/C][C]-44.46[/C][C] 24.95[/C][C]-1.7820e+00[/C][C] 0.1023[/C][C] 0.05116[/C][/ROW]
[ROW][C]X1[/C][C]-4.865[/C][C] 2.155[/C][C]-2.2580e+00[/C][C] 0.04529[/C][C] 0.02264[/C][/ROW]
[ROW][C]X2[/C][C]-0.2172[/C][C] 1.849[/C][C]-1.1750e-01[/C][C] 0.9086[/C][C] 0.4543[/C][/ROW]
[ROW][C]X3[/C][C]+3.229[/C][C] 2.606[/C][C]+1.2390e+00[/C][C] 0.2412[/C][C] 0.1206[/C][/ROW]
[ROW][C]X4[/C][C]-2.927[/C][C] 2.123[/C][C]-1.3780e+00[/C][C] 0.1955[/C][C] 0.09773[/C][/ROW]
[ROW][C]X5[/C][C]+163.2[/C][C] 36.71[/C][C]+4.4460e+00[/C][C] 0.0009849[/C][C] 0.0004925[/C][/ROW]
[ROW][C]X6[/C][C]-24.62[/C][C] 5.804[/C][C]-4.2420e+00[/C][C] 0.001384[/C][C] 0.0006921[/C][/ROW]
[ROW][C]Inter[/C][C]+13.13[/C][C] 7.328[/C][C]+1.7910e+00[/C][C] 0.1008[/C][C] 0.05038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303839&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303839&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)-257.8 57.75-4.4640e+00 0.0009567 0.0004784
Geslacht-44.46 24.95-1.7820e+00 0.1023 0.05116
X1-4.865 2.155-2.2580e+00 0.04529 0.02264
X2-0.2172 1.849-1.1750e-01 0.9086 0.4543
X3+3.229 2.606+1.2390e+00 0.2412 0.1206
X4-2.927 2.123-1.3780e+00 0.1955 0.09773
X5+163.2 36.71+4.4460e+00 0.0009849 0.0004925
X6-24.62 5.804-4.2420e+00 0.001384 0.0006921
Inter+13.13 7.328+1.7910e+00 0.1008 0.05038







Multiple Linear Regression - Regression Statistics
Multiple R 0.8474
R-squared 0.7181
Adjusted R-squared 0.5131
F-TEST (value) 3.502
F-TEST (DF numerator)8
F-TEST (DF denominator)11
p-value 0.02904
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 3.502
Sum Squared Residuals 134.9

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.8474 \tabularnewline
R-squared &  0.7181 \tabularnewline
Adjusted R-squared &  0.5131 \tabularnewline
F-TEST (value) &  3.502 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 11 \tabularnewline
p-value &  0.02904 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  3.502 \tabularnewline
Sum Squared Residuals &  134.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303839&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.8474[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.7181[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.5131[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 3.502[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]8[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]11[/C][/ROW]
[ROW][C]p-value[/C][C] 0.02904[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 3.502[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 134.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303839&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303839&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 R 0.8474
R-squared 0.7181
Adjusted R-squared 0.5131
F-TEST (value) 3.502
F-TEST (DF numerator)8
F-TEST (DF denominator)11
p-value 0.02904
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 3.502
Sum Squared Residuals 134.9







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1 6 5.08 0.9198
2 7 9.579-2.579
3 2 5.29-3.29
4 11 8.74 2.26
5 13 12.96 0.03781
6 3-1.442 4.442
7 17 13.6 3.398
8 10 8.74 1.26
9 4 7.484-3.484
10 12 12.33-0.3324
11 7 10.25-3.253
12 11 11.67-0.6666
13 3 1.724 1.276
14 5 5.295-0.2951
15 1 0.5933 0.4067
16 12 9.796 2.204
17 18 13.52 4.483
18 8 9.089-1.089
19 6 6.495-0.4945
20 1 6.204-5.204

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  6 &  5.08 &  0.9198 \tabularnewline
2 &  7 &  9.579 & -2.579 \tabularnewline
3 &  2 &  5.29 & -3.29 \tabularnewline
4 &  11 &  8.74 &  2.26 \tabularnewline
5 &  13 &  12.96 &  0.03781 \tabularnewline
6 &  3 & -1.442 &  4.442 \tabularnewline
7 &  17 &  13.6 &  3.398 \tabularnewline
8 &  10 &  8.74 &  1.26 \tabularnewline
9 &  4 &  7.484 & -3.484 \tabularnewline
10 &  12 &  12.33 & -0.3324 \tabularnewline
11 &  7 &  10.25 & -3.253 \tabularnewline
12 &  11 &  11.67 & -0.6666 \tabularnewline
13 &  3 &  1.724 &  1.276 \tabularnewline
14 &  5 &  5.295 & -0.2951 \tabularnewline
15 &  1 &  0.5933 &  0.4067 \tabularnewline
16 &  12 &  9.796 &  2.204 \tabularnewline
17 &  18 &  13.52 &  4.483 \tabularnewline
18 &  8 &  9.089 & -1.089 \tabularnewline
19 &  6 &  6.495 & -0.4945 \tabularnewline
20 &  1 &  6.204 & -5.204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303839&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] 6[/C][C] 5.08[/C][C] 0.9198[/C][/ROW]
[ROW][C]2[/C][C] 7[/C][C] 9.579[/C][C]-2.579[/C][/ROW]
[ROW][C]3[/C][C] 2[/C][C] 5.29[/C][C]-3.29[/C][/ROW]
[ROW][C]4[/C][C] 11[/C][C] 8.74[/C][C] 2.26[/C][/ROW]
[ROW][C]5[/C][C] 13[/C][C] 12.96[/C][C] 0.03781[/C][/ROW]
[ROW][C]6[/C][C] 3[/C][C]-1.442[/C][C] 4.442[/C][/ROW]
[ROW][C]7[/C][C] 17[/C][C] 13.6[/C][C] 3.398[/C][/ROW]
[ROW][C]8[/C][C] 10[/C][C] 8.74[/C][C] 1.26[/C][/ROW]
[ROW][C]9[/C][C] 4[/C][C] 7.484[/C][C]-3.484[/C][/ROW]
[ROW][C]10[/C][C] 12[/C][C] 12.33[/C][C]-0.3324[/C][/ROW]
[ROW][C]11[/C][C] 7[/C][C] 10.25[/C][C]-3.253[/C][/ROW]
[ROW][C]12[/C][C] 11[/C][C] 11.67[/C][C]-0.6666[/C][/ROW]
[ROW][C]13[/C][C] 3[/C][C] 1.724[/C][C] 1.276[/C][/ROW]
[ROW][C]14[/C][C] 5[/C][C] 5.295[/C][C]-0.2951[/C][/ROW]
[ROW][C]15[/C][C] 1[/C][C] 0.5933[/C][C] 0.4067[/C][/ROW]
[ROW][C]16[/C][C] 12[/C][C] 9.796[/C][C] 2.204[/C][/ROW]
[ROW][C]17[/C][C] 18[/C][C] 13.52[/C][C] 4.483[/C][/ROW]
[ROW][C]18[/C][C] 8[/C][C] 9.089[/C][C]-1.089[/C][/ROW]
[ROW][C]19[/C][C] 6[/C][C] 6.495[/C][C]-0.4945[/C][/ROW]
[ROW][C]20[/C][C] 1[/C][C] 6.204[/C][C]-5.204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303839&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303839&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
1 6 5.08 0.9198
2 7 9.579-2.579
3 2 5.29-3.29
4 11 8.74 2.26
5 13 12.96 0.03781
6 3-1.442 4.442
7 17 13.6 3.398
8 10 8.74 1.26
9 4 7.484-3.484
10 12 12.33-0.3324
11 7 10.25-3.253
12 11 11.67-0.6666
13 3 1.724 1.276
14 5 5.295-0.2951
15 1 0.5933 0.4067
16 12 9.796 2.204
17 18 13.52 4.483
18 8 9.089-1.089
19 6 6.495-0.4945
20 1 6.204-5.204







Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 19.324, df1 = 2, df2 = 9, p-value = 0.0005533
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = -0.97854, df1 = 16, df2 = -5, p-value = NA
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.92151, df1 = 2, df2 = 9, p-value = 0.4324

\begin{tabular}{lllllllll}
\hline
Ramsey RESET F-Test for powers (2 and 3) of fitted values \tabularnewline
> reset_test_fitted
	RESET test
data:  mylm
RESET = 19.324, df1 = 2, df2 = 9, p-value = 0.0005533
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = -0.97854, df1 = 16, df2 = -5, p-value = NA
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.92151, df1 = 2, df2 = 9, p-value = 0.4324
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=303839&T=5

[TABLE]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of fitted values[/C][/ROW]
[ROW][C]
> reset_test_fitted
	RESET test
data:  mylm
RESET = 19.324, df1 = 2, df2 = 9, p-value = 0.0005533
[/C][/ROW] [ROW][C]Ramsey RESET F-Test for powers (2 and 3) of regressors[/C][/ROW] [ROW][C]
> reset_test_regressors
	RESET test
data:  mylm
RESET = -0.97854, df1 = 16, df2 = -5, p-value = NA
[/C][/ROW] [ROW][C]Ramsey RESET F-Test for powers (2 and 3) of principal components[/C][/ROW] [ROW][C]
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.92151, df1 = 2, df2 = 9, p-value = 0.4324
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=303839&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303839&T=5

As an alternative you can also use a QR Code:  

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

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 19.324, df1 = 2, df2 = 9, p-value = 0.0005533
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = -0.97854, df1 = 16, df2 = -5, p-value = NA
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.92151, df1 = 2, df2 = 9, p-value = 0.4324







Variance Inflation Factors (Multicollinearity)
> vif
  Geslacht         X1         X2         X3         X4         X5         X6 
253.760008   1.590610   1.393797   2.076499   1.672483 317.781701 370.696086 
     Inter 
275.595478 

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
  Geslacht         X1         X2         X3         X4         X5         X6 
253.760008   1.590610   1.393797   2.076499   1.672483 317.781701 370.696086 
     Inter 
275.595478 
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=303839&T=6

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]
> vif
  Geslacht         X1         X2         X3         X4         X5         X6 
253.760008   1.590610   1.393797   2.076499   1.672483 317.781701 370.696086 
     Inter 
275.595478 
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=303839&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303839&T=6

As an alternative you can also use a QR Code:  

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

Variance Inflation Factors (Multicollinearity)
> vif
  Geslacht         X1         X2         X3         X4         X5         X6 
253.760008   1.590610   1.393797   2.076499   1.672483 317.781701 370.696086 
     Inter 
275.595478 



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = ; par5 = ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
library(car)
library(MASS)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
x <- na.omit(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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s=12)'){
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s=12)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,j] - x[i,j]
}
}
x <- x2
}
if(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
if(par5 > 0) {
x2 <- array(0, dim=c(n-par5*12,par5), dimnames=list(1:(n-par5*12), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*12)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*12-j*12,par1]
}
}
x <- cbind(x[(par5*12+1):n,], x2)
n <- n - par5*12
}
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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
print(x)
(k <- length(x[n,]))
head(x)
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$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
sresid <- studres(mylm)
hist(sresid, freq=FALSE, main='Distribution of Studentized Residuals')
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqPlot(mylm, main='QQ Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
print(z)
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$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, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$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.row.start(a)
a<-table.element(a, mywarning)
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,'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$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
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,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
myr <- as.numeric(mysum$resid)
myr
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
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,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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')
}
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of fitted values',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_fitted <- resettest(mylm,power=2:3,type='fitted')
a<-table.element(a,paste('
',RC.texteval('reset_test_fitted'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of regressors',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_regressors <- resettest(mylm,power=2:3,type='regressor')
a<-table.element(a,paste('
',RC.texteval('reset_test_regressors'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of principal components',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_principal_components <- resettest(mylm,power=2:3,type='princomp')
a<-table.element(a,paste('
',RC.texteval('reset_test_principal_components'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable8.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Inflation Factors (Multicollinearity)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
vif <- vif(mylm)
a<-table.element(a,paste('
',RC.texteval('vif'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable9.tab')