Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 02 Feb 2017 09:54:06 +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/Feb/02/t1486025660ihfi7adcd0h6o96.htm/, Retrieved Thu, 31 Oct 2024 23:25:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306627, Retrieved Thu, 31 Oct 2024 23:25:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [rm 1] [2017-02-02 08:54:06] [c383a3f496d779b12e2493a523dfe438] [Current]
Feedback Forum

Post a new message
Dataseries X:
6 1 0 0 0 3.2 3.2
7 0 1 0 1 3.3 0
2 0 1 1 1 3 3
11 0 1 0 1 3.5 0
13 0 1 0 0 3.7 3.7
3 1 0 0 0 2.7 0
17 0 1 1 1 3.6 3.6
10 0 1 0 1 3.5 0
4 1 0 0 0 3.8 3.8
12 0 1 0 0 3.4 0
7 0 0 0 1 3.7 3.7
11 0 1 0 0 3.5 0
3 0 0 1 0 2.8 2.8
5 1 0 1 0 3.8 0
1 0 1 0 0 4.3 4.3
12 0 0 0 1 3.3 0
18 0 0 0 0 3.6 3.6
8 1 0 1 0 3.6 0
6 1 1 0 0 3.3 3.3
1 0 0 0 0 2.8 0





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=306627&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [ROW]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306627&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306627&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 time5 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Multiple Linear Regression - Estimated Regression Equation
Score[t] = -3.89483 -2.87878X1[t] + 0.156245X2[t] -0.448907X3[t] + 0.98967X4[t] + 3.73413X5[t] -0.271171Inter[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Score[t] =  -3.89483 -2.87878X1[t] +  0.156245X2[t] -0.448907X3[t] +  0.98967X4[t] +  3.73413X5[t] -0.271171Inter[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306627&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Score[t] =  -3.89483 -2.87878X1[t] +  0.156245X2[t] -0.448907X3[t] +  0.98967X4[t] +  3.73413X5[t] -0.271171Inter[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306627&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306627&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] = -3.89483 -2.87878X1[t] + 0.156245X2[t] -0.448907X3[t] + 0.98967X4[t] + 3.73413X5[t] -0.271171Inter[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-3.895 11.6-3.3570e-01 0.7425 0.3712
X1-2.879 3.26-8.8300e-01 0.3933 0.1966
X2+0.1562 2.819+5.5420e-02 0.9566 0.4783
X3-0.4489 2.88-1.5590e-01 0.8785 0.4393
X4+0.9897 2.991+3.3090e-01 0.746 0.373
X5+3.734 3.514+1.0630e+00 0.3073 0.1536
Inter-0.2712 0.7357-3.6860e-01 0.7184 0.3592

\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) & -3.895 &  11.6 & -3.3570e-01 &  0.7425 &  0.3712 \tabularnewline
X1 & -2.879 &  3.26 & -8.8300e-01 &  0.3933 &  0.1966 \tabularnewline
X2 & +0.1562 &  2.819 & +5.5420e-02 &  0.9566 &  0.4783 \tabularnewline
X3 & -0.4489 &  2.88 & -1.5590e-01 &  0.8785 &  0.4393 \tabularnewline
X4 & +0.9897 &  2.991 & +3.3090e-01 &  0.746 &  0.373 \tabularnewline
X5 & +3.734 &  3.514 & +1.0630e+00 &  0.3073 &  0.1536 \tabularnewline
Inter & -0.2712 &  0.7357 & -3.6860e-01 &  0.7184 &  0.3592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306627&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]-3.895[/C][C] 11.6[/C][C]-3.3570e-01[/C][C] 0.7425[/C][C] 0.3712[/C][/ROW]
[ROW][C]X1[/C][C]-2.879[/C][C] 3.26[/C][C]-8.8300e-01[/C][C] 0.3933[/C][C] 0.1966[/C][/ROW]
[ROW][C]X2[/C][C]+0.1562[/C][C] 2.819[/C][C]+5.5420e-02[/C][C] 0.9566[/C][C] 0.4783[/C][/ROW]
[ROW][C]X3[/C][C]-0.4489[/C][C] 2.88[/C][C]-1.5590e-01[/C][C] 0.8785[/C][C] 0.4393[/C][/ROW]
[ROW][C]X4[/C][C]+0.9897[/C][C] 2.991[/C][C]+3.3090e-01[/C][C] 0.746[/C][C] 0.373[/C][/ROW]
[ROW][C]X5[/C][C]+3.734[/C][C] 3.514[/C][C]+1.0630e+00[/C][C] 0.3073[/C][C] 0.1536[/C][/ROW]
[ROW][C]Inter[/C][C]-0.2712[/C][C] 0.7357[/C][C]-3.6860e-01[/C][C] 0.7184[/C][C] 0.3592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306627&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306627&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)-3.895 11.6-3.3570e-01 0.7425 0.3712
X1-2.879 3.26-8.8300e-01 0.3933 0.1966
X2+0.1562 2.819+5.5420e-02 0.9566 0.4783
X3-0.4489 2.88-1.5590e-01 0.8785 0.4393
X4+0.9897 2.991+3.3090e-01 0.746 0.373
X5+3.734 3.514+1.0630e+00 0.3073 0.1536
Inter-0.2712 0.7357-3.6860e-01 0.7184 0.3592







Multiple Linear Regression - Regression Statistics
Multiple R 0.4492
R-squared 0.2018
Adjusted R-squared-0.1667
F-TEST (value) 0.5476
F-TEST (DF numerator)6
F-TEST (DF denominator)13
p-value 0.7636
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 5.421
Sum Squared Residuals 382

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.4492 \tabularnewline
R-squared &  0.2018 \tabularnewline
Adjusted R-squared & -0.1667 \tabularnewline
F-TEST (value) &  0.5476 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 13 \tabularnewline
p-value &  0.7636 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  5.421 \tabularnewline
Sum Squared Residuals &  382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306627&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.4492[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.2018[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.1667[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 0.5476[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]13[/C][/ROW]
[ROW][C]p-value[/C][C] 0.7636[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 5.421[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306627&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306627&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 0.4492
R-squared 0.2018
Adjusted R-squared-0.1667
F-TEST (value) 0.5476
F-TEST (DF numerator)6
F-TEST (DF denominator)13
p-value 0.7636
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 5.421
Sum Squared Residuals 382







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1 6 4.308 1.692
2 7 9.574-2.574
3 2 7.191-5.191
4 11 10.32 0.6795
5 13 9.074 3.926
6 3 3.309-0.3085
7 17 9.269 7.731
8 10 10.32-0.3205
9 4 6.386-2.386
10 12 8.957 3.043
11 7 9.908-2.908
12 11 9.331 1.669
13 3 5.353-2.353
14 5 6.967-1.967
15 1 11.15-10.15
16 12 9.417 2.583
17 18 8.572 9.428
18 8 6.22 1.78
19 6 4.81 1.19
20 1 6.561-5.561

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  6 &  4.308 &  1.692 \tabularnewline
2 &  7 &  9.574 & -2.574 \tabularnewline
3 &  2 &  7.191 & -5.191 \tabularnewline
4 &  11 &  10.32 &  0.6795 \tabularnewline
5 &  13 &  9.074 &  3.926 \tabularnewline
6 &  3 &  3.309 & -0.3085 \tabularnewline
7 &  17 &  9.269 &  7.731 \tabularnewline
8 &  10 &  10.32 & -0.3205 \tabularnewline
9 &  4 &  6.386 & -2.386 \tabularnewline
10 &  12 &  8.957 &  3.043 \tabularnewline
11 &  7 &  9.908 & -2.908 \tabularnewline
12 &  11 &  9.331 &  1.669 \tabularnewline
13 &  3 &  5.353 & -2.353 \tabularnewline
14 &  5 &  6.967 & -1.967 \tabularnewline
15 &  1 &  11.15 & -10.15 \tabularnewline
16 &  12 &  9.417 &  2.583 \tabularnewline
17 &  18 &  8.572 &  9.428 \tabularnewline
18 &  8 &  6.22 &  1.78 \tabularnewline
19 &  6 &  4.81 &  1.19 \tabularnewline
20 &  1 &  6.561 & -5.561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306627&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] 4.308[/C][C] 1.692[/C][/ROW]
[ROW][C]2[/C][C] 7[/C][C] 9.574[/C][C]-2.574[/C][/ROW]
[ROW][C]3[/C][C] 2[/C][C] 7.191[/C][C]-5.191[/C][/ROW]
[ROW][C]4[/C][C] 11[/C][C] 10.32[/C][C] 0.6795[/C][/ROW]
[ROW][C]5[/C][C] 13[/C][C] 9.074[/C][C] 3.926[/C][/ROW]
[ROW][C]6[/C][C] 3[/C][C] 3.309[/C][C]-0.3085[/C][/ROW]
[ROW][C]7[/C][C] 17[/C][C] 9.269[/C][C] 7.731[/C][/ROW]
[ROW][C]8[/C][C] 10[/C][C] 10.32[/C][C]-0.3205[/C][/ROW]
[ROW][C]9[/C][C] 4[/C][C] 6.386[/C][C]-2.386[/C][/ROW]
[ROW][C]10[/C][C] 12[/C][C] 8.957[/C][C] 3.043[/C][/ROW]
[ROW][C]11[/C][C] 7[/C][C] 9.908[/C][C]-2.908[/C][/ROW]
[ROW][C]12[/C][C] 11[/C][C] 9.331[/C][C] 1.669[/C][/ROW]
[ROW][C]13[/C][C] 3[/C][C] 5.353[/C][C]-2.353[/C][/ROW]
[ROW][C]14[/C][C] 5[/C][C] 6.967[/C][C]-1.967[/C][/ROW]
[ROW][C]15[/C][C] 1[/C][C] 11.15[/C][C]-10.15[/C][/ROW]
[ROW][C]16[/C][C] 12[/C][C] 9.417[/C][C] 2.583[/C][/ROW]
[ROW][C]17[/C][C] 18[/C][C] 8.572[/C][C] 9.428[/C][/ROW]
[ROW][C]18[/C][C] 8[/C][C] 6.22[/C][C] 1.78[/C][/ROW]
[ROW][C]19[/C][C] 6[/C][C] 4.81[/C][C] 1.19[/C][/ROW]
[ROW][C]20[/C][C] 1[/C][C] 6.561[/C][C]-5.561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306627&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306627&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 4.308 1.692
2 7 9.574-2.574
3 2 7.191-5.191
4 11 10.32 0.6795
5 13 9.074 3.926
6 3 3.309-0.3085
7 17 9.269 7.731
8 10 10.32-0.3205
9 4 6.386-2.386
10 12 8.957 3.043
11 7 9.908-2.908
12 11 9.331 1.669
13 3 5.353-2.353
14 5 6.967-1.967
15 1 11.15-10.15
16 12 9.417 2.583
17 18 8.572 9.428
18 8 6.22 1.78
19 6 4.81 1.19
20 1 6.561-5.561







Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 5.4682, df1 = 2, df2 = 11, p-value = 0.02245
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.15599, df1 = 12, df2 = 1, p-value = 0.9737
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 9.5913, df1 = 2, df2 = 11, p-value = 0.003882

\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 = 5.4682, df1 = 2, df2 = 11, p-value = 0.02245
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.15599, df1 = 12, df2 = 1, p-value = 0.9737
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 9.5913, df1 = 2, df2 = 11, p-value = 0.003882
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=306627&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 = 5.4682, df1 = 2, df2 = 11, p-value = 0.02245
[/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 = 0.15599, df1 = 12, df2 = 1, p-value = 0.9737
[/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 = 9.5913, df1 = 2, df2 = 11, p-value = 0.003882
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306627&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306627&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 = 5.4682, df1 = 2, df2 = 11, p-value = 0.02245
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.15599, df1 = 12, df2 = 1, p-value = 0.9737
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 9.5913, df1 = 2, df2 = 11, p-value = 0.003882







Variance Inflation Factors (Multicollinearity)
> vif
      X1       X2       X3       X4       X5    Inter 
1.519129 1.352560 1.058179 1.385193 1.215344 1.159644 

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
      X1       X2       X3       X4       X5    Inter 
1.519129 1.352560 1.058179 1.385193 1.215344 1.159644 
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=306627&T=6

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]
> vif
      X1       X2       X3       X4       X5    Inter 
1.519129 1.352560 1.058179 1.385193 1.215344 1.159644 
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306627&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306627&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
      X1       X2       X3       X4       X5    Inter 
1.519129 1.352560 1.058179 1.385193 1.215344 1.159644 



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')