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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, 11 Dec 2017 09:43:33 +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/Dec/11/t1512981903lb0uoyvfkayq6yy.htm/, Retrieved Wed, 15 May 2024 08:29:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308952, Retrieved Wed, 15 May 2024 08:29:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Dataset 3: Multip...] [2017-12-11 08:43:33] [b4c215a57d838e3992780a1253393c3b] [Current]
- RMPD    [Skewness-Kurtosis Plot] [] [2017-12-17 13:42:53] [c468faea9a2856906f4b319427cb0317]
- RMPD    [Skewness-Kurtosis Plot] [] [2017-12-17 13:45:53] [c468faea9a2856906f4b319427cb0317]
- RMPD    [Skewness-Kurtosis Plot] [] [2017-12-17 13:48:45] [c468faea9a2856906f4b319427cb0317]
- RMPD    [Skewness and Kurtosis Test] [] [2017-12-17 13:50:31] [c468faea9a2856906f4b319427cb0317]
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Dataseries X:
52.20	78.70	56.90
63.90	88.60	69.60
70.30	104.20	82.60
64.30	88.20	71.20
77.20	94.70	74.10
71.90	112.00	67.60
46.30	78.90	56.30
61.50	111.40	54.40
73.30	132.50	65.00
75.00	121.60	68.60
74.40	116.10	80.30
74.70	123.30	72.50
71.70	107.90	88.30
66.60	107.00	89.80
75.10	115.80	103.50
67.50	91.80	78.80
74.60	93.50	85.70
76.40	107.10	96.90
53.90	80.50	66.90
70.10	100.50	71.50
76.10	100.20	89.50
79.40	100.30	86.60
74.80	96.60	91.20
65.30	86.00	75.60
63.50	76.90	75.60
64.40	79.70	80.40
70.30	93.10	91.60
74.50	79.50	90.10
69.40	80.30	90.80
74.50	88.80	94.60
52.80	72.40	62.60
61.50	75.50	65.00
73.90	92.90	87.60
79.40	101.50	99.90
69.80	94.70	85.10
77.40	93.00	71.00
69.40	79.80	73.00
75.00	82.20	83.50
76.40	87.60	86.50
75.90	83.20	80.90
70.30	81.60	80.80
89.50	85.90	81.20
62.50	71.90	61.90
59.00	71.80	49.40
89.50	98.30	79.20
83.50	93.60	76.80
76.00	86.10	81.20
85.80	96.20	79.40
66.90	78.60	74.00
75.40	82.10	78.20
84.60	94.40	98.90
81.80	86.40	88.30
75.00	82.20	79.30
92.60	96.70	104.00
66.40	84.20	60.50
75.70	73.60	75.30
91.30	94.90	106.20
88.60	96.90	106.70
85.80	90.20	95.40
86.70	104.20	90.50
71.00	78.40	113.80
83.20	81.50	94.10
85.00	96.70	109.90
79.30	87.50	104.30
77.50	86.20	80.70
96.50	105.10	121.10
56.50	72.90	68.80
75.20	76.40	73.70
86.30	100.50	104.20
84.80	92.40	87.20
91.60	96.30	94.50
110.70	103.60	120.90
81.00	75.10	88.50
81.50	78.80	102.50
91.00	93.70	118.60
81.30	82.50	86.00
93.50	88.30	110.60
100.70	95.70	114.00
68.50	73.30	72.60
77.60	72.40	76.00
102.70	94.00	114.60
113.10	96.90	113.50
98.50	92.40	115.20
108.20	90.90	102.00
89.60	93.50	101.50
93.30	92.00	99.60
104.60	115.90	113.80
94.30	97.80	94.80
100.70	97.70	102.00
111.80	116.90	119.50
76.10	96.70	88.00
102.10	97.70	82.80
149.20	103.90	112.10
172.30	124.10	131.50
125.60	117.30	110.00
132.20	113.80	96.50
106.50	100.00	101.90
116.60	114.20	103.10
110.80	116.30	103.50
121.90	111.40	111.80
117.20	103.40	100.30
123.90	125.30	111.00
98.00	92.50	84.60
93.50	92.00	73.30
136.30	121.60	112.00
131.00	113.30	111.20
113.20	92.50	82.40
101.00	100.30	75.60
88.70	83.20	64.20
96.90	81.20	72.20
105.80	94.50	80.80
95.20	87.70	71.10
88.00	82.30	153.20
107.70	99.00	89.80
71.10	72.40	57.30
72.30	80.80	83.60
101.50	105.50	88.40
103.20	98.40	84.10
103.00	94.50	95.50
88.30	109.20	74.60
78.00	84.10	79.80
91.80	88.40	85.40
111.50	111.30	106.40
100.20	93.20	94.60
94.30	86.30	94.60
118.20	111.40	113.70
80.50	85.40	66.70
92.60	89.70	78.90
113.10	110.90	126.30
111.80	119.40	118.10
101.70	109.30	117.30
106.50	110.70	118.10
88.90	101.30	108.60
101.20	99.00	118.10
119.00	117.90	141.00
104.60	89.30	112.70
120.20	105.40	131.90
112.60	99.90	123.50
88.10	79.50	81.30
99.20	88.30	85.40
126.50	116.20	138.50
113.20	110.60	124.60
114.20	99.30	125.80
128.10	105.40	125.30
109.20	89.90	111.00
107.00	100.70	120.40
142.30	122.50	141.40
106.00	97.40	113.10
115.20	97.90	114.00
129.70	124.30	131.30
90.40	94.70	77.80
97.50	85.20	105.10
118.30	101.90	125.40
121.20	110.90	123.60
117.50	102.00	107.90
105.50	95.80	86.10
97.30	86.90	97.80
98.00	90.30	98.40
114.80	97.90	118.00
109.80	91.90	115.60
121.90	90.40	114.50
123.00	98.90	124.00
104.10	81.30	101.80
99.90	79.80	80.60
128.50	93.70	129.70
127.70	101.50	137.00
116.70	88.60	127.30
112.10	94.60	110.30
102.80	84.20	134.90
110.80	86.50	126.20
117.80	92.60	130.50
122.40	84.20	127.60
120.40	85.90	134.80
119.20	90.00	128.90
101.30	79.10	101.10
101.20	75.60	86.00
136.10	97.00	139.20
133.60	96.40	126.80
109.60	85.20	117.10
115.80	100.30	103.00
104.30	76.70	108.70
115.00	79.00	115.00
124.60	94.40	133.20
123.10	82.80	131.30
120.00	74.60	119.60
132.00	92.80	146.70
107.20	69.70	101.00
101.00	68.90	88.70
153.10	97.50	143.70
144.50	92.90	138.10
125.80	93.40	139.80
125.40	92.10	121.60
111.70	80.60	112.60
118.40	86.00	136.70
135.60	93.60	147.40
130.70	90.30	128.10
128.50	81.30	117.50
137.10	98.40	148.20
92.10	73.30	101.60
103.70	77.10	90.40
139.00	91.40	148.60
125.00	89.00	133.80
130.20	94.10	130.30
116.40	94.70	113.60
106.40	80.70	105.80
121.20	85.20	136.10
147.60	107.90	160.30
116.00	81.60	127.70
137.50	83.80	141.80
136.40	98.80	149.30
95.80	75.60	94.50
127.00	80.70	95.20




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=308952&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=308952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308952&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
a[t] = -2.19076 + 0.238156b[t] + 0.774831c[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
a[t] =  -2.19076 +  0.238156b[t] +  0.774831c[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308952&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]a[t] =  -2.19076 +  0.238156b[t] +  0.774831c[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308952&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
a[t] = -2.19076 + 0.238156b[t] + 0.774831c[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-2.191 6.941-3.1560e-01 0.7526 0.3763
b+0.2382 0.07307+3.2590e+00 0.001304 0.0006518
c+0.7748 0.04+1.9370e+01 1.518e-48 7.591e-49

\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) & -2.191 &  6.941 & -3.1560e-01 &  0.7526 &  0.3763 \tabularnewline
b & +0.2382 &  0.07307 & +3.2590e+00 &  0.001304 &  0.0006518 \tabularnewline
c & +0.7748 &  0.04 & +1.9370e+01 &  1.518e-48 &  7.591e-49 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308952&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]-2.191[/C][C] 6.941[/C][C]-3.1560e-01[/C][C] 0.7526[/C][C] 0.3763[/C][/ROW]
[ROW][C]b[/C][C]+0.2382[/C][C] 0.07307[/C][C]+3.2590e+00[/C][C] 0.001304[/C][C] 0.0006518[/C][/ROW]
[ROW][C]c[/C][C]+0.7748[/C][C] 0.04[/C][C]+1.9370e+01[/C][C] 1.518e-48[/C][C] 7.591e-49[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308952&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308952&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)-2.191 6.941-3.1560e-01 0.7526 0.3763
b+0.2382 0.07307+3.2590e+00 0.001304 0.0006518
c+0.7748 0.04+1.9370e+01 1.518e-48 7.591e-49







Multiple Linear Regression - Regression Statistics
Multiple R 0.829
R-squared 0.6872
Adjusted R-squared 0.6842
F-TEST (value) 229.6
F-TEST (DF numerator)2
F-TEST (DF denominator)209
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 13.13
Sum Squared Residuals 3.602e+04

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.829 \tabularnewline
R-squared &  0.6872 \tabularnewline
Adjusted R-squared &  0.6842 \tabularnewline
F-TEST (value) &  229.6 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 209 \tabularnewline
p-value &  0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  13.13 \tabularnewline
Sum Squared Residuals &  3.602e+04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308952&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.829[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.6872[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.6842[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 229.6[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]209[/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] 13.13[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 3.602e+04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308952&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308952&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 0.829
R-squared 0.6872
Adjusted R-squared 0.6842
F-TEST (value) 229.6
F-TEST (DF numerator)2
F-TEST (DF denominator)209
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 13.13
Sum Squared Residuals 3.602e+04







Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute

\begin{tabular}{lllllllll}
\hline
Menu of Residual Diagnostics \tabularnewline
Description & Link \tabularnewline
Histogram & Compute \tabularnewline
Central Tendency & Compute \tabularnewline
QQ Plot & Compute \tabularnewline
Kernel Density Plot & Compute \tabularnewline
Skewness/Kurtosis Test & Compute \tabularnewline
Skewness-Kurtosis Plot & Compute \tabularnewline
Harrell-Davis Plot & Compute \tabularnewline
Bootstrap Plot -- Central Tendency & Compute \tabularnewline
Blocked Bootstrap Plot -- Central Tendency & Compute \tabularnewline
(Partial) Autocorrelation Plot & Compute \tabularnewline
Spectral Analysis & Compute \tabularnewline
Tukey lambda PPCC Plot & Compute \tabularnewline
Box-Cox Normality Plot & Compute \tabularnewline
Summary Statistics & Compute \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308952&T=4

[TABLE]
[ROW][C]Menu of Residual Diagnostics[/C][/ROW]
[ROW][C]Description[/C][C]Link[/C][/ROW]
[ROW][C]Histogram[/C][C]Compute[/C][/ROW]
[ROW][C]Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]QQ Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Kernel Density Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness/Kurtosis Test[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness-Kurtosis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Harrell-Davis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]Blocked Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C](Partial) Autocorrelation Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Spectral Analysis[/C][C]Compute[/C][/ROW]
[ROW][C]Tukey lambda PPCC Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Box-Cox Normality Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Summary Statistics[/C][C]Compute[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308952&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308952&T=4

As an alternative you can also use a QR Code:  

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

Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute







Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.03869, df1 = 2, df2 = 207, p-value = 0.9621
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.44095, df1 = 4, df2 = 205, p-value = 0.7789
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.098225, df1 = 2, df2 = 207, p-value = 0.9065

\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 = 0.03869, df1 = 2, df2 = 207, p-value = 0.9621
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.44095, df1 = 4, df2 = 205, p-value = 0.7789
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.098225, df1 = 2, df2 = 207, p-value = 0.9065
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=308952&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 = 0.03869, df1 = 2, df2 = 207, p-value = 0.9621
[/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 = 0.44095, df1 = 4, df2 = 205, p-value = 0.7789
[/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 = 0.098225, df1 = 2, df2 = 207, p-value = 0.9065
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308952&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308952&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 = 0.03869, df1 = 2, df2 = 207, p-value = 0.9621
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.44095, df1 = 4, df2 = 205, p-value = 0.7789
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.098225, df1 = 2, df2 = 207, p-value = 0.9065







Variance Inflation Factors (Multicollinearity)
> vif
       b        c 
1.088388 1.088388 

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
       b        c 
1.088388 1.088388 
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=308952&T=6

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]
> vif
       b        c 
1.088388 1.088388 
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308952&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308952&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
       b        c 
1.088388 1.088388 



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;
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 <- ''
par6 <- as.numeric(par6)
if(is.na(par6)) {
par6 <- 12
mywarning = 'Warning: you did not specify the seasonality. The seasonal period was set to s = 12.'
}
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 (!is.numeric(par4)) par4 <- 0
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
if (!is.numeric(par5)) par5 <- 0
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)'){
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s)'){
(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 - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,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*par6,par5), dimnames=list(1:(n-par5*par6), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*par6)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*par6-j*par6,par1]
}
}
x <- cbind(x[(par5*par6+1):n,], x2)
n <- n - par5*par6
}
if (par2 == 'Include Seasonal Dummies'){
x2 <- array(0, dim=c(n,par6-1), dimnames=list(1:n, paste('M', seq(1:(par6-1)), sep ='')))
for (i in 1:(par6-1)){
x2[seq(i,n,par6),i] <- 1
}
x <- cbind(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[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$resid)
myr
a <-table.start()
a <- table.row.start(a)
a <- table.element(a,'Menu of Residual Diagnostics',2,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Description',1,TRUE)
a <- table.element(a,'Link',1,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Histogram',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_histogram.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_centraltendency.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'QQ Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_fitdistrnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Kernel Density Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_density.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness/Kurtosis Test',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness-Kurtosis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis_plot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Harrell-Davis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_harrell_davis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Blocked Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'(Partial) Autocorrelation Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_autocorrelation.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Spectral Analysis',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_spectrum.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Tukey lambda PPCC Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_tukeylambda.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Box-Cox Normality Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_boxcoxnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Summary Statistics',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_summary1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable7.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$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')