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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 06:57:48 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t125872580731i3ia3drwallq0.htm/, Retrieved Fri, 29 Mar 2024 13:32:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58172, Retrieved Fri, 29 Mar 2024 13:32:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [Model 4] [2009-11-20 13:57:48] [cf272a759dc2b193d9a85354803ede7b] [Current]
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Dataseries X:
108.5	98.71	115.5	116.6	112.3	108.5
112.3	98.54	120.1	115.5	116.6	112.3
116.6	98.2	132.9	120.1	115.5	116.6
115.5	96.92	128.1	132.9	120.1	115.5
120.1	99.06	129.3	128.1	132.9	120.1
132.9	99.65	132.5	129.3	128.1	132.9
128.1	99.82	131	132.5	129.3	128.1
129.3	99.99	124.9	131	132.5	129.3
132.5	100.33	120.8	124.9	131	132.5
131	99.31	122	120.8	124.9	131
124.9	101.1	122.1	122	120.8	124.9
120.8	101.1	127.4	122.1	122	120.8
122	100.93	135.2	127.4	122.1	122
122.1	100.85	137.3	135.2	127.4	122.1
127.4	100.93	135	137.3	135.2	127.4
135.2	99.6	136	135	137.3	135.2
137.3	101.88	138.4	136	135	137.3
135	101.81	134.7	138.4	136	135
136	102.38	138.4	134.7	138.4	136
138.4	102.74	133.9	138.4	134.7	138.4
134.7	102.82	133.6	133.9	138.4	134.7
138.4	101.72	141.2	133.6	133.9	138.4
133.9	103.47	151.8	141.2	133.6	133.9
133.6	102.98	155.4	151.8	141.2	133.6
141.2	102.68	156.6	155.4	151.8	141.2
151.8	102.9	161.6	156.6	155.4	151.8
155.4	103.03	160.7	161.6	156.6	155.4
156.6	101.29	156	160.7	161.6	156.6
161.6	103.69	159.5	156	160.7	161.6
160.7	103.68	168.7	159.5	156	160.7
156	104.2	169.9	168.7	159.5	156
159.5	104.08	169.9	169.9	168.7	159.5
168.7	104.16	185.9	169.9	169.9	168.7
169.9	103.05	190.8	185.9	169.9	169.9
169.9	104.66	195.8	190.8	185.9	169.9
185.9	104.46	211.9	195.8	190.8	185.9
190.8	104.95	227.1	211.9	195.8	190.8
195.8	105.85	251.3	227.1	211.9	195.8
211.9	106.23	256.7	251.3	227.1	211.9
227.1	104.86	251.9	256.7	251.3	227.1
251.3	107.44	251.2	251.9	256.7	251.3
256.7	108.23	270.3	251.2	251.9	256.7
251.9	108.45	267.2	270.3	251.2	251.9
251.2	109.39	243	267.2	270.3	251.2
270.3	110.15	229.9	243	267.2	270.3
267.2	109.13	187.2	229.9	243	267.2
243	110.28	178.2	187.2	229.9	243
229.9	110.17	175.2	178.2	187.2	229.9
187.2	109.99	192.4	175.2	178.2	187.2
178.2	109.26	187	192.4	175.2	178.2
175.2	109.11	184	187	192.4	175.2
192.4	107.06	194.1	184	187	192.4
187	109.53	212.7	194.1	184	187
184	108.92	217.5	212.7	194.1	184
194.1	109.24	200.5	217.5	212.7	194.1
212.7	109.12	205.9	200.5	217.5	212.7
217.5	109	196.5	205.9	200.5	217.5
200.5	107.23	206.3	196.5	205.9	200.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58172&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58172&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58172&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.16355186150491e-14 -5.16431325155128e-16X[t] + 1.59090058226580e-16Y1[t] -7.92762271926817e-17Y2[t] -4.19119738909473e-16Y3[t] + 1Y4[t] -4.8940746873282e-16M1[t] -6.66523909077379e-16M2[t] + 5.34026133594919e-16M3[t] + 2.1568677450766e-16M4[t] + 2.34962547286129e-16M5[t] + 6.20006976066222e-15M6[t] + 8.96894589098686e-16M7[t] + 1.85692333379998e-16M8[t] + 7.64820214041699e-16M9[t] -2.31022629128203e-16M10[t] -7.89915010542167e-17M11[t] + 6.3286818349455e-18t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  2.16355186150491e-14 -5.16431325155128e-16X[t] +  1.59090058226580e-16Y1[t] -7.92762271926817e-17Y2[t] -4.19119738909473e-16Y3[t] +  1Y4[t] -4.8940746873282e-16M1[t] -6.66523909077379e-16M2[t] +  5.34026133594919e-16M3[t] +  2.1568677450766e-16M4[t] +  2.34962547286129e-16M5[t] +  6.20006976066222e-15M6[t] +  8.96894589098686e-16M7[t] +  1.85692333379998e-16M8[t] +  7.64820214041699e-16M9[t] -2.31022629128203e-16M10[t] -7.89915010542167e-17M11[t] +  6.3286818349455e-18t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58172&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  2.16355186150491e-14 -5.16431325155128e-16X[t] +  1.59090058226580e-16Y1[t] -7.92762271926817e-17Y2[t] -4.19119738909473e-16Y3[t] +  1Y4[t] -4.8940746873282e-16M1[t] -6.66523909077379e-16M2[t] +  5.34026133594919e-16M3[t] +  2.1568677450766e-16M4[t] +  2.34962547286129e-16M5[t] +  6.20006976066222e-15M6[t] +  8.96894589098686e-16M7[t] +  1.85692333379998e-16M8[t] +  7.64820214041699e-16M9[t] -2.31022629128203e-16M10[t] -7.89915010542167e-17M11[t] +  6.3286818349455e-18t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58172&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58172&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.16355186150491e-14 -5.16431325155128e-16X[t] + 1.59090058226580e-16Y1[t] -7.92762271926817e-17Y2[t] -4.19119738909473e-16Y3[t] + 1Y4[t] -4.8940746873282e-16M1[t] -6.66523909077379e-16M2[t] + 5.34026133594919e-16M3[t] + 2.1568677450766e-16M4[t] + 2.34962547286129e-16M5[t] + 6.20006976066222e-15M6[t] + 8.96894589098686e-16M7[t] + 1.85692333379998e-16M8[t] + 7.64820214041699e-16M9[t] -2.31022629128203e-16M10[t] -7.89915010542167e-17M11[t] + 6.3286818349455e-18t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.16355186150491e-1400.24910.8045760.402288
X-5.16431325155128e-160-0.57420.5690730.284536
Y11.59090058226580e-1602.53680.0151920.007596
Y2-7.92762271926817e-170-0.86190.3938660.196933
Y3-4.19119738909473e-160-4.40667.7e-053.8e-05
Y4101388601244710942600
M1-4.8940746873282e-160-0.18330.8554940.427747
M2-6.66523909077379e-160-0.24640.8066550.403328
M35.34026133594919e-1600.19370.8474020.423701
M42.1568677450766e-1600.06430.9490520.474526
M52.34962547286129e-1600.08770.9305150.465257
M66.20006976066222e-1502.35020.0237810.011891
M78.96894589098686e-1600.32450.7472330.373616
M81.85692333379998e-1600.06530.9482420.474121
M97.64820214041699e-1600.28260.7789670.389483
M10-2.31022629128203e-160-0.07440.9410310.470515
M11-7.89915010542167e-170-0.02760.9781090.489054
t6.3286818349455e-1800.03730.9703950.485197

\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) & 2.16355186150491e-14 & 0 & 0.2491 & 0.804576 & 0.402288 \tabularnewline
X & -5.16431325155128e-16 & 0 & -0.5742 & 0.569073 & 0.284536 \tabularnewline
Y1 & 1.59090058226580e-16 & 0 & 2.5368 & 0.015192 & 0.007596 \tabularnewline
Y2 & -7.92762271926817e-17 & 0 & -0.8619 & 0.393866 & 0.196933 \tabularnewline
Y3 & -4.19119738909473e-16 & 0 & -4.4066 & 7.7e-05 & 3.8e-05 \tabularnewline
Y4 & 1 & 0 & 13886012447109426 & 0 & 0 \tabularnewline
M1 & -4.8940746873282e-16 & 0 & -0.1833 & 0.855494 & 0.427747 \tabularnewline
M2 & -6.66523909077379e-16 & 0 & -0.2464 & 0.806655 & 0.403328 \tabularnewline
M3 & 5.34026133594919e-16 & 0 & 0.1937 & 0.847402 & 0.423701 \tabularnewline
M4 & 2.1568677450766e-16 & 0 & 0.0643 & 0.949052 & 0.474526 \tabularnewline
M5 & 2.34962547286129e-16 & 0 & 0.0877 & 0.930515 & 0.465257 \tabularnewline
M6 & 6.20006976066222e-15 & 0 & 2.3502 & 0.023781 & 0.011891 \tabularnewline
M7 & 8.96894589098686e-16 & 0 & 0.3245 & 0.747233 & 0.373616 \tabularnewline
M8 & 1.85692333379998e-16 & 0 & 0.0653 & 0.948242 & 0.474121 \tabularnewline
M9 & 7.64820214041699e-16 & 0 & 0.2826 & 0.778967 & 0.389483 \tabularnewline
M10 & -2.31022629128203e-16 & 0 & -0.0744 & 0.941031 & 0.470515 \tabularnewline
M11 & -7.89915010542167e-17 & 0 & -0.0276 & 0.978109 & 0.489054 \tabularnewline
t & 6.3286818349455e-18 & 0 & 0.0373 & 0.970395 & 0.485197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58172&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]2.16355186150491e-14[/C][C]0[/C][C]0.2491[/C][C]0.804576[/C][C]0.402288[/C][/ROW]
[ROW][C]X[/C][C]-5.16431325155128e-16[/C][C]0[/C][C]-0.5742[/C][C]0.569073[/C][C]0.284536[/C][/ROW]
[ROW][C]Y1[/C][C]1.59090058226580e-16[/C][C]0[/C][C]2.5368[/C][C]0.015192[/C][C]0.007596[/C][/ROW]
[ROW][C]Y2[/C][C]-7.92762271926817e-17[/C][C]0[/C][C]-0.8619[/C][C]0.393866[/C][C]0.196933[/C][/ROW]
[ROW][C]Y3[/C][C]-4.19119738909473e-16[/C][C]0[/C][C]-4.4066[/C][C]7.7e-05[/C][C]3.8e-05[/C][/ROW]
[ROW][C]Y4[/C][C]1[/C][C]0[/C][C]13886012447109426[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-4.8940746873282e-16[/C][C]0[/C][C]-0.1833[/C][C]0.855494[/C][C]0.427747[/C][/ROW]
[ROW][C]M2[/C][C]-6.66523909077379e-16[/C][C]0[/C][C]-0.2464[/C][C]0.806655[/C][C]0.403328[/C][/ROW]
[ROW][C]M3[/C][C]5.34026133594919e-16[/C][C]0[/C][C]0.1937[/C][C]0.847402[/C][C]0.423701[/C][/ROW]
[ROW][C]M4[/C][C]2.1568677450766e-16[/C][C]0[/C][C]0.0643[/C][C]0.949052[/C][C]0.474526[/C][/ROW]
[ROW][C]M5[/C][C]2.34962547286129e-16[/C][C]0[/C][C]0.0877[/C][C]0.930515[/C][C]0.465257[/C][/ROW]
[ROW][C]M6[/C][C]6.20006976066222e-15[/C][C]0[/C][C]2.3502[/C][C]0.023781[/C][C]0.011891[/C][/ROW]
[ROW][C]M7[/C][C]8.96894589098686e-16[/C][C]0[/C][C]0.3245[/C][C]0.747233[/C][C]0.373616[/C][/ROW]
[ROW][C]M8[/C][C]1.85692333379998e-16[/C][C]0[/C][C]0.0653[/C][C]0.948242[/C][C]0.474121[/C][/ROW]
[ROW][C]M9[/C][C]7.64820214041699e-16[/C][C]0[/C][C]0.2826[/C][C]0.778967[/C][C]0.389483[/C][/ROW]
[ROW][C]M10[/C][C]-2.31022629128203e-16[/C][C]0[/C][C]-0.0744[/C][C]0.941031[/C][C]0.470515[/C][/ROW]
[ROW][C]M11[/C][C]-7.89915010542167e-17[/C][C]0[/C][C]-0.0276[/C][C]0.978109[/C][C]0.489054[/C][/ROW]
[ROW][C]t[/C][C]6.3286818349455e-18[/C][C]0[/C][C]0.0373[/C][C]0.970395[/C][C]0.485197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58172&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58172&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)2.16355186150491e-1400.24910.8045760.402288
X-5.16431325155128e-160-0.57420.5690730.284536
Y11.59090058226580e-1602.53680.0151920.007596
Y2-7.92762271926817e-170-0.86190.3938660.196933
Y3-4.19119738909473e-160-4.40667.7e-053.8e-05
Y4101388601244710942600
M1-4.8940746873282e-160-0.18330.8554940.427747
M2-6.66523909077379e-160-0.24640.8066550.403328
M35.34026133594919e-1600.19370.8474020.423701
M42.1568677450766e-1600.06430.9490520.474526
M52.34962547286129e-1600.08770.9305150.465257
M66.20006976066222e-1502.35020.0237810.011891
M78.96894589098686e-1600.32450.7472330.373616
M81.85692333379998e-1600.06530.9482420.474121
M97.64820214041699e-1600.28260.7789670.389483
M10-2.31022629128203e-160-0.07440.9410310.470515
M11-7.89915010542167e-170-0.02760.9781090.489054
t6.3286818349455e-1800.03730.9703950.485197







Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)4.52444903618255e+32
F-TEST (DF numerator)17
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.87735021444872e-15
Sum Squared Residuals6.0135378741942e-28

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 1 \tabularnewline
R-squared & 1 \tabularnewline
Adjusted R-squared & 1 \tabularnewline
F-TEST (value) & 4.52444903618255e+32 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 40 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.87735021444872e-15 \tabularnewline
Sum Squared Residuals & 6.0135378741942e-28 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58172&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]1[/C][/ROW]
[ROW][C]R-squared[/C][C]1[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.52444903618255e+32[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]40[/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]3.87735021444872e-15[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6.0135378741942e-28[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58172&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58172&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 R1
R-squared1
Adjusted R-squared1
F-TEST (value)4.52444903618255e+32
F-TEST (DF numerator)17
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.87735021444872e-15
Sum Squared Residuals6.0135378741942e-28







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1108.5108.5-3.29839737165348e-15
2112.3112.3-3.31188053484745e-15
3116.6116.6-8.7702089918852e-16
4115.5115.57.66183023220705e-16
5120.1120.1-6.90367191252025e-16
6132.9132.92.07067720305347e-14
7128.1128.1-1.32810811567139e-15
8129.3129.3-5.37845267868493e-16
9132.5132.5-1.19166692565931e-15
101311311.32277310495672e-15
11124.9124.9-2.12531021700543e-16
12120.8120.8-3.78968191426067e-16
131221221.51822237918604e-16
14122.1122.11.63671240851298e-16
15127.4127.4-1.28941037949949e-15
16135.2135.2-6.37088015179162e-16
17137.3137.3-6.66357580906015e-16
18135135-6.35588633253829e-15
19136136-8.2670096221065e-16
20138.4138.45.89012223373722e-17
21134.7134.7-4.19994524298056e-16
22138.4138.4-5.08821517908562e-16
23133.9133.98.21087703693914e-17
24133.6133.62.31936918400157e-16
25141.2141.27.14767053144733e-16
26151.8151.85.97773544280951e-16
27155.4155.4-5.10718457794993e-16
28156.6156.6-3.24521495346969e-16
29161.6161.6-1.27127440080524e-16
30160.7160.7-5.38004752110076e-15
31156156-6.64972065519288e-16
32159.5159.5-3.19322440161124e-16
33168.7168.7-5.78494052175696e-16
34169.9169.93.38287751156981e-16
35169.9169.9-4.46588138668727e-16
36185.9185.97.88101720294903e-16
37190.8190.81.13786614676900e-15
38195.8195.81.12055944976226e-15
39211.9211.96.81518275785871e-16
40227.1227.1-1.21550103846306e-16
41251.3251.38.68429397992201e-16
42256.7256.7-5.07283619535942e-15
43251.9251.94.7903201794652e-16
44251.2251.24.28768690935868e-16
45270.3270.35.22020997050886e-16
46267.2267.2-1.98233932561599e-15
472432435.77010389999881e-16
48229.9229.9-6.4107044726898e-16
49187.2187.21.29394193382115e-15
50178.2178.21.42987629995295e-15
51175.2175.21.99563146069713e-15
52192.4192.43.1697659115173e-16
531871876.15422814246362e-16
54184184-3.89800198153627e-15
55194.1194.12.34074912545480e-15
56212.7212.73.6949779475638e-16
57217.5217.51.66813450508217e-15
58200.5200.58.30099987410848e-16

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 108.5 & 108.5 & -3.29839737165348e-15 \tabularnewline
2 & 112.3 & 112.3 & -3.31188053484745e-15 \tabularnewline
3 & 116.6 & 116.6 & -8.7702089918852e-16 \tabularnewline
4 & 115.5 & 115.5 & 7.66183023220705e-16 \tabularnewline
5 & 120.1 & 120.1 & -6.90367191252025e-16 \tabularnewline
6 & 132.9 & 132.9 & 2.07067720305347e-14 \tabularnewline
7 & 128.1 & 128.1 & -1.32810811567139e-15 \tabularnewline
8 & 129.3 & 129.3 & -5.37845267868493e-16 \tabularnewline
9 & 132.5 & 132.5 & -1.19166692565931e-15 \tabularnewline
10 & 131 & 131 & 1.32277310495672e-15 \tabularnewline
11 & 124.9 & 124.9 & -2.12531021700543e-16 \tabularnewline
12 & 120.8 & 120.8 & -3.78968191426067e-16 \tabularnewline
13 & 122 & 122 & 1.51822237918604e-16 \tabularnewline
14 & 122.1 & 122.1 & 1.63671240851298e-16 \tabularnewline
15 & 127.4 & 127.4 & -1.28941037949949e-15 \tabularnewline
16 & 135.2 & 135.2 & -6.37088015179162e-16 \tabularnewline
17 & 137.3 & 137.3 & -6.66357580906015e-16 \tabularnewline
18 & 135 & 135 & -6.35588633253829e-15 \tabularnewline
19 & 136 & 136 & -8.2670096221065e-16 \tabularnewline
20 & 138.4 & 138.4 & 5.89012223373722e-17 \tabularnewline
21 & 134.7 & 134.7 & -4.19994524298056e-16 \tabularnewline
22 & 138.4 & 138.4 & -5.08821517908562e-16 \tabularnewline
23 & 133.9 & 133.9 & 8.21087703693914e-17 \tabularnewline
24 & 133.6 & 133.6 & 2.31936918400157e-16 \tabularnewline
25 & 141.2 & 141.2 & 7.14767053144733e-16 \tabularnewline
26 & 151.8 & 151.8 & 5.97773544280951e-16 \tabularnewline
27 & 155.4 & 155.4 & -5.10718457794993e-16 \tabularnewline
28 & 156.6 & 156.6 & -3.24521495346969e-16 \tabularnewline
29 & 161.6 & 161.6 & -1.27127440080524e-16 \tabularnewline
30 & 160.7 & 160.7 & -5.38004752110076e-15 \tabularnewline
31 & 156 & 156 & -6.64972065519288e-16 \tabularnewline
32 & 159.5 & 159.5 & -3.19322440161124e-16 \tabularnewline
33 & 168.7 & 168.7 & -5.78494052175696e-16 \tabularnewline
34 & 169.9 & 169.9 & 3.38287751156981e-16 \tabularnewline
35 & 169.9 & 169.9 & -4.46588138668727e-16 \tabularnewline
36 & 185.9 & 185.9 & 7.88101720294903e-16 \tabularnewline
37 & 190.8 & 190.8 & 1.13786614676900e-15 \tabularnewline
38 & 195.8 & 195.8 & 1.12055944976226e-15 \tabularnewline
39 & 211.9 & 211.9 & 6.81518275785871e-16 \tabularnewline
40 & 227.1 & 227.1 & -1.21550103846306e-16 \tabularnewline
41 & 251.3 & 251.3 & 8.68429397992201e-16 \tabularnewline
42 & 256.7 & 256.7 & -5.07283619535942e-15 \tabularnewline
43 & 251.9 & 251.9 & 4.7903201794652e-16 \tabularnewline
44 & 251.2 & 251.2 & 4.28768690935868e-16 \tabularnewline
45 & 270.3 & 270.3 & 5.22020997050886e-16 \tabularnewline
46 & 267.2 & 267.2 & -1.98233932561599e-15 \tabularnewline
47 & 243 & 243 & 5.77010389999881e-16 \tabularnewline
48 & 229.9 & 229.9 & -6.4107044726898e-16 \tabularnewline
49 & 187.2 & 187.2 & 1.29394193382115e-15 \tabularnewline
50 & 178.2 & 178.2 & 1.42987629995295e-15 \tabularnewline
51 & 175.2 & 175.2 & 1.99563146069713e-15 \tabularnewline
52 & 192.4 & 192.4 & 3.1697659115173e-16 \tabularnewline
53 & 187 & 187 & 6.15422814246362e-16 \tabularnewline
54 & 184 & 184 & -3.89800198153627e-15 \tabularnewline
55 & 194.1 & 194.1 & 2.34074912545480e-15 \tabularnewline
56 & 212.7 & 212.7 & 3.6949779475638e-16 \tabularnewline
57 & 217.5 & 217.5 & 1.66813450508217e-15 \tabularnewline
58 & 200.5 & 200.5 & 8.30099987410848e-16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58172&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]108.5[/C][C]108.5[/C][C]-3.29839737165348e-15[/C][/ROW]
[ROW][C]2[/C][C]112.3[/C][C]112.3[/C][C]-3.31188053484745e-15[/C][/ROW]
[ROW][C]3[/C][C]116.6[/C][C]116.6[/C][C]-8.7702089918852e-16[/C][/ROW]
[ROW][C]4[/C][C]115.5[/C][C]115.5[/C][C]7.66183023220705e-16[/C][/ROW]
[ROW][C]5[/C][C]120.1[/C][C]120.1[/C][C]-6.90367191252025e-16[/C][/ROW]
[ROW][C]6[/C][C]132.9[/C][C]132.9[/C][C]2.07067720305347e-14[/C][/ROW]
[ROW][C]7[/C][C]128.1[/C][C]128.1[/C][C]-1.32810811567139e-15[/C][/ROW]
[ROW][C]8[/C][C]129.3[/C][C]129.3[/C][C]-5.37845267868493e-16[/C][/ROW]
[ROW][C]9[/C][C]132.5[/C][C]132.5[/C][C]-1.19166692565931e-15[/C][/ROW]
[ROW][C]10[/C][C]131[/C][C]131[/C][C]1.32277310495672e-15[/C][/ROW]
[ROW][C]11[/C][C]124.9[/C][C]124.9[/C][C]-2.12531021700543e-16[/C][/ROW]
[ROW][C]12[/C][C]120.8[/C][C]120.8[/C][C]-3.78968191426067e-16[/C][/ROW]
[ROW][C]13[/C][C]122[/C][C]122[/C][C]1.51822237918604e-16[/C][/ROW]
[ROW][C]14[/C][C]122.1[/C][C]122.1[/C][C]1.63671240851298e-16[/C][/ROW]
[ROW][C]15[/C][C]127.4[/C][C]127.4[/C][C]-1.28941037949949e-15[/C][/ROW]
[ROW][C]16[/C][C]135.2[/C][C]135.2[/C][C]-6.37088015179162e-16[/C][/ROW]
[ROW][C]17[/C][C]137.3[/C][C]137.3[/C][C]-6.66357580906015e-16[/C][/ROW]
[ROW][C]18[/C][C]135[/C][C]135[/C][C]-6.35588633253829e-15[/C][/ROW]
[ROW][C]19[/C][C]136[/C][C]136[/C][C]-8.2670096221065e-16[/C][/ROW]
[ROW][C]20[/C][C]138.4[/C][C]138.4[/C][C]5.89012223373722e-17[/C][/ROW]
[ROW][C]21[/C][C]134.7[/C][C]134.7[/C][C]-4.19994524298056e-16[/C][/ROW]
[ROW][C]22[/C][C]138.4[/C][C]138.4[/C][C]-5.08821517908562e-16[/C][/ROW]
[ROW][C]23[/C][C]133.9[/C][C]133.9[/C][C]8.21087703693914e-17[/C][/ROW]
[ROW][C]24[/C][C]133.6[/C][C]133.6[/C][C]2.31936918400157e-16[/C][/ROW]
[ROW][C]25[/C][C]141.2[/C][C]141.2[/C][C]7.14767053144733e-16[/C][/ROW]
[ROW][C]26[/C][C]151.8[/C][C]151.8[/C][C]5.97773544280951e-16[/C][/ROW]
[ROW][C]27[/C][C]155.4[/C][C]155.4[/C][C]-5.10718457794993e-16[/C][/ROW]
[ROW][C]28[/C][C]156.6[/C][C]156.6[/C][C]-3.24521495346969e-16[/C][/ROW]
[ROW][C]29[/C][C]161.6[/C][C]161.6[/C][C]-1.27127440080524e-16[/C][/ROW]
[ROW][C]30[/C][C]160.7[/C][C]160.7[/C][C]-5.38004752110076e-15[/C][/ROW]
[ROW][C]31[/C][C]156[/C][C]156[/C][C]-6.64972065519288e-16[/C][/ROW]
[ROW][C]32[/C][C]159.5[/C][C]159.5[/C][C]-3.19322440161124e-16[/C][/ROW]
[ROW][C]33[/C][C]168.7[/C][C]168.7[/C][C]-5.78494052175696e-16[/C][/ROW]
[ROW][C]34[/C][C]169.9[/C][C]169.9[/C][C]3.38287751156981e-16[/C][/ROW]
[ROW][C]35[/C][C]169.9[/C][C]169.9[/C][C]-4.46588138668727e-16[/C][/ROW]
[ROW][C]36[/C][C]185.9[/C][C]185.9[/C][C]7.88101720294903e-16[/C][/ROW]
[ROW][C]37[/C][C]190.8[/C][C]190.8[/C][C]1.13786614676900e-15[/C][/ROW]
[ROW][C]38[/C][C]195.8[/C][C]195.8[/C][C]1.12055944976226e-15[/C][/ROW]
[ROW][C]39[/C][C]211.9[/C][C]211.9[/C][C]6.81518275785871e-16[/C][/ROW]
[ROW][C]40[/C][C]227.1[/C][C]227.1[/C][C]-1.21550103846306e-16[/C][/ROW]
[ROW][C]41[/C][C]251.3[/C][C]251.3[/C][C]8.68429397992201e-16[/C][/ROW]
[ROW][C]42[/C][C]256.7[/C][C]256.7[/C][C]-5.07283619535942e-15[/C][/ROW]
[ROW][C]43[/C][C]251.9[/C][C]251.9[/C][C]4.7903201794652e-16[/C][/ROW]
[ROW][C]44[/C][C]251.2[/C][C]251.2[/C][C]4.28768690935868e-16[/C][/ROW]
[ROW][C]45[/C][C]270.3[/C][C]270.3[/C][C]5.22020997050886e-16[/C][/ROW]
[ROW][C]46[/C][C]267.2[/C][C]267.2[/C][C]-1.98233932561599e-15[/C][/ROW]
[ROW][C]47[/C][C]243[/C][C]243[/C][C]5.77010389999881e-16[/C][/ROW]
[ROW][C]48[/C][C]229.9[/C][C]229.9[/C][C]-6.4107044726898e-16[/C][/ROW]
[ROW][C]49[/C][C]187.2[/C][C]187.2[/C][C]1.29394193382115e-15[/C][/ROW]
[ROW][C]50[/C][C]178.2[/C][C]178.2[/C][C]1.42987629995295e-15[/C][/ROW]
[ROW][C]51[/C][C]175.2[/C][C]175.2[/C][C]1.99563146069713e-15[/C][/ROW]
[ROW][C]52[/C][C]192.4[/C][C]192.4[/C][C]3.1697659115173e-16[/C][/ROW]
[ROW][C]53[/C][C]187[/C][C]187[/C][C]6.15422814246362e-16[/C][/ROW]
[ROW][C]54[/C][C]184[/C][C]184[/C][C]-3.89800198153627e-15[/C][/ROW]
[ROW][C]55[/C][C]194.1[/C][C]194.1[/C][C]2.34074912545480e-15[/C][/ROW]
[ROW][C]56[/C][C]212.7[/C][C]212.7[/C][C]3.6949779475638e-16[/C][/ROW]
[ROW][C]57[/C][C]217.5[/C][C]217.5[/C][C]1.66813450508217e-15[/C][/ROW]
[ROW][C]58[/C][C]200.5[/C][C]200.5[/C][C]8.30099987410848e-16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58172&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58172&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
1108.5108.5-3.29839737165348e-15
2112.3112.3-3.31188053484745e-15
3116.6116.6-8.7702089918852e-16
4115.5115.57.66183023220705e-16
5120.1120.1-6.90367191252025e-16
6132.9132.92.07067720305347e-14
7128.1128.1-1.32810811567139e-15
8129.3129.3-5.37845267868493e-16
9132.5132.5-1.19166692565931e-15
101311311.32277310495672e-15
11124.9124.9-2.12531021700543e-16
12120.8120.8-3.78968191426067e-16
131221221.51822237918604e-16
14122.1122.11.63671240851298e-16
15127.4127.4-1.28941037949949e-15
16135.2135.2-6.37088015179162e-16
17137.3137.3-6.66357580906015e-16
18135135-6.35588633253829e-15
19136136-8.2670096221065e-16
20138.4138.45.89012223373722e-17
21134.7134.7-4.19994524298056e-16
22138.4138.4-5.08821517908562e-16
23133.9133.98.21087703693914e-17
24133.6133.62.31936918400157e-16
25141.2141.27.14767053144733e-16
26151.8151.85.97773544280951e-16
27155.4155.4-5.10718457794993e-16
28156.6156.6-3.24521495346969e-16
29161.6161.6-1.27127440080524e-16
30160.7160.7-5.38004752110076e-15
31156156-6.64972065519288e-16
32159.5159.5-3.19322440161124e-16
33168.7168.7-5.78494052175696e-16
34169.9169.93.38287751156981e-16
35169.9169.9-4.46588138668727e-16
36185.9185.97.88101720294903e-16
37190.8190.81.13786614676900e-15
38195.8195.81.12055944976226e-15
39211.9211.96.81518275785871e-16
40227.1227.1-1.21550103846306e-16
41251.3251.38.68429397992201e-16
42256.7256.7-5.07283619535942e-15
43251.9251.94.7903201794652e-16
44251.2251.24.28768690935868e-16
45270.3270.35.22020997050886e-16
46267.2267.2-1.98233932561599e-15
472432435.77010389999881e-16
48229.9229.9-6.4107044726898e-16
49187.2187.21.29394193382115e-15
50178.2178.21.42987629995295e-15
51175.2175.21.99563146069713e-15
52192.4192.43.1697659115173e-16
531871876.15422814246362e-16
54184184-3.89800198153627e-15
55194.1194.12.34074912545480e-15
56212.7212.73.6949779475638e-16
57217.5217.51.66813450508217e-15
58200.5200.58.30099987410848e-16







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.003549221857218760.007098443714437530.996450778142781
226.72744556507772e-050.0001345489113015540.99993272554435
230.0358208133518090.0716416267036180.96417918664819
240.9038894774880950.1922210450238090.0961105225119047
250.000831219002047950.00166243800409590.999168780997952
260.9854102469214320.02917950615713700.0145897530785685
271.44931085613560e-072.89862171227120e-070.999999855068914
280.9999866246790322.67506419367588e-051.33753209683794e-05
290.004183704872341420.008367409744682830.995816295127659
300.9881849150424690.0236301699150630.0118150849575315
310.4556925292930270.9113850585860530.544307470706973
321.37538503310616e-072.75077006621231e-070.999999862461497
330.0002001860547045490.0004003721094090990.999799813945295
340.9999899321747252.01356505507558e-051.00678252753779e-05
350.7040509824428040.5918980351143920.295949017557196
366.15482274481323e-141.23096454896265e-130.999999999999938
370.0002474344014296310.0004948688028592610.99975256559857

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.00354922185721876 & 0.00709844371443753 & 0.996450778142781 \tabularnewline
22 & 6.72744556507772e-05 & 0.000134548911301554 & 0.99993272554435 \tabularnewline
23 & 0.035820813351809 & 0.071641626703618 & 0.96417918664819 \tabularnewline
24 & 0.903889477488095 & 0.192221045023809 & 0.0961105225119047 \tabularnewline
25 & 0.00083121900204795 & 0.0016624380040959 & 0.999168780997952 \tabularnewline
26 & 0.985410246921432 & 0.0291795061571370 & 0.0145897530785685 \tabularnewline
27 & 1.44931085613560e-07 & 2.89862171227120e-07 & 0.999999855068914 \tabularnewline
28 & 0.999986624679032 & 2.67506419367588e-05 & 1.33753209683794e-05 \tabularnewline
29 & 0.00418370487234142 & 0.00836740974468283 & 0.995816295127659 \tabularnewline
30 & 0.988184915042469 & 0.023630169915063 & 0.0118150849575315 \tabularnewline
31 & 0.455692529293027 & 0.911385058586053 & 0.544307470706973 \tabularnewline
32 & 1.37538503310616e-07 & 2.75077006621231e-07 & 0.999999862461497 \tabularnewline
33 & 0.000200186054704549 & 0.000400372109409099 & 0.999799813945295 \tabularnewline
34 & 0.999989932174725 & 2.01356505507558e-05 & 1.00678252753779e-05 \tabularnewline
35 & 0.704050982442804 & 0.591898035114392 & 0.295949017557196 \tabularnewline
36 & 6.15482274481323e-14 & 1.23096454896265e-13 & 0.999999999999938 \tabularnewline
37 & 0.000247434401429631 & 0.000494868802859261 & 0.99975256559857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58172&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]21[/C][C]0.00354922185721876[/C][C]0.00709844371443753[/C][C]0.996450778142781[/C][/ROW]
[ROW][C]22[/C][C]6.72744556507772e-05[/C][C]0.000134548911301554[/C][C]0.99993272554435[/C][/ROW]
[ROW][C]23[/C][C]0.035820813351809[/C][C]0.071641626703618[/C][C]0.96417918664819[/C][/ROW]
[ROW][C]24[/C][C]0.903889477488095[/C][C]0.192221045023809[/C][C]0.0961105225119047[/C][/ROW]
[ROW][C]25[/C][C]0.00083121900204795[/C][C]0.0016624380040959[/C][C]0.999168780997952[/C][/ROW]
[ROW][C]26[/C][C]0.985410246921432[/C][C]0.0291795061571370[/C][C]0.0145897530785685[/C][/ROW]
[ROW][C]27[/C][C]1.44931085613560e-07[/C][C]2.89862171227120e-07[/C][C]0.999999855068914[/C][/ROW]
[ROW][C]28[/C][C]0.999986624679032[/C][C]2.67506419367588e-05[/C][C]1.33753209683794e-05[/C][/ROW]
[ROW][C]29[/C][C]0.00418370487234142[/C][C]0.00836740974468283[/C][C]0.995816295127659[/C][/ROW]
[ROW][C]30[/C][C]0.988184915042469[/C][C]0.023630169915063[/C][C]0.0118150849575315[/C][/ROW]
[ROW][C]31[/C][C]0.455692529293027[/C][C]0.911385058586053[/C][C]0.544307470706973[/C][/ROW]
[ROW][C]32[/C][C]1.37538503310616e-07[/C][C]2.75077006621231e-07[/C][C]0.999999862461497[/C][/ROW]
[ROW][C]33[/C][C]0.000200186054704549[/C][C]0.000400372109409099[/C][C]0.999799813945295[/C][/ROW]
[ROW][C]34[/C][C]0.999989932174725[/C][C]2.01356505507558e-05[/C][C]1.00678252753779e-05[/C][/ROW]
[ROW][C]35[/C][C]0.704050982442804[/C][C]0.591898035114392[/C][C]0.295949017557196[/C][/ROW]
[ROW][C]36[/C][C]6.15482274481323e-14[/C][C]1.23096454896265e-13[/C][C]0.999999999999938[/C][/ROW]
[ROW][C]37[/C][C]0.000247434401429631[/C][C]0.000494868802859261[/C][C]0.99975256559857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58172&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58172&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.003549221857218760.007098443714437530.996450778142781
226.72744556507772e-050.0001345489113015540.99993272554435
230.0358208133518090.0716416267036180.96417918664819
240.9038894774880950.1922210450238090.0961105225119047
250.000831219002047950.00166243800409590.999168780997952
260.9854102469214320.02917950615713700.0145897530785685
271.44931085613560e-072.89862171227120e-070.999999855068914
280.9999866246790322.67506419367588e-051.33753209683794e-05
290.004183704872341420.008367409744682830.995816295127659
300.9881849150424690.0236301699150630.0118150849575315
310.4556925292930270.9113850585860530.544307470706973
321.37538503310616e-072.75077006621231e-070.999999862461497
330.0002001860547045490.0004003721094090990.999799813945295
340.9999899321747252.01356505507558e-051.00678252753779e-05
350.7040509824428040.5918980351143920.295949017557196
366.15482274481323e-141.23096454896265e-130.999999999999938
370.0002474344014296310.0004948688028592610.99975256559857







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level110.647058823529412NOK
5% type I error level130.764705882352941NOK
10% type I error level140.823529411764706NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 11 & 0.647058823529412 & NOK \tabularnewline
5% type I error level & 13 & 0.764705882352941 & NOK \tabularnewline
10% type I error level & 14 & 0.823529411764706 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58172&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]11[/C][C]0.647058823529412[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]13[/C][C]0.764705882352941[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]14[/C][C]0.823529411764706[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58172&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58172&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level110.647058823529412NOK
5% type I error level130.764705882352941NOK
10% type I error level140.823529411764706NOK



Parameters (Session):
par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}