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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationWed, 18 Nov 2009 10:56:09 -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/18/t125856709607u38cnus9iypdn.htm/, Retrieved Sun, 05 May 2024 19:43:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57560, Retrieved Sun, 05 May 2024 19:43:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

Tree of Dependent Computations

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 14:14:11] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2009-11-18 17:49:39] [96d96f181930b548ce74f8c3116c4873]
-   P         [Multiple Regression] [] [2009-11-18 17:56:09] [508aab72d879399b4187e5fcd8f7c773] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.2	2.4	7.5	8.3	8.9
7.4	2	7.2	7.5	8.8
8.8	2.1	7.4	7.2	8.3
9.3	2	8.8	7.4	7.5
9.3	1.8	9.3	8.8	7.2
8.7	2.7	9.3	9.3	7.4
8.2	2.3	8.7	9.3	8.8
8.3	1.9	8.2	8.7	9.3
8.5	2	8.3	8.2	9.3
8.6	2.3	8.5	8.3	8.7
8.5	2.8	8.6	8.5	8.2
8.2	2.4	8.5	8.6	8.3
8.1	2.3	8.2	8.5	8.5
7.9	2.7	8.1	8.2	8.6
8.6	2.7	7.9	8.1	8.5
8.7	2.9	8.6	7.9	8.2
8.7	3	8.7	8.6	8.1
8.5	2.2	8.7	8.7	7.9
8.4	2.3	8.5	8.7	8.6
8.5	2.8	8.4	8.5	8.7
8.7	2.8	8.5	8.4	8.7
8.7	2.8	8.7	8.5	8.5
8.6	2.2	8.7	8.7	8.4
8.5	2.6	8.6	8.7	8.5
8.3	2.8	8.5	8.6	8.7
8	2.5	8.3	8.5	8.7
8.2	2.4	8	8.3	8.6
8.1	2.3	8.2	8	8.5
8.1	1.9	8.1	8.2	8.3
8	1.7	8.1	8.1	8
7.9	2	8	8.1	8.2
7.9	2.1	7.9	8	8.1
8	1.7	7.9	7.9	8.1
8	1.8	8	7.9	8
7.9	1.8	8	8	7.9
8	1.8	7.9	8	7.9
7.7	1.3	8	7.9	8
7.2	1.3	7.7	8	8
7.5	1.3	7.2	7.7	7.9
7.3	1.2	7.5	7.2	8
7	1.4	7.3	7.5	7.7
7	2.2	7	7.3	7.2
7	2.9	7	7	7.5
7.2	3.1	7	7	7.3
7.3	3.5	7.2	7	7
7.1	3.6	7.3	7.2	7
6.8	4.4	7.1	7.3	7
6.4	4.1	6.8	7.1	7.2
6.1	5.1	6.4	6.8	7.3
6.5	5.8	6.1	6.4	7.1
7.7	5.9	6.5	6.1	6.8
7.9	5.4	7.7	6.5	6.4
7.5	5.5	7.9	7.7	6.1
6.9	4.8	7.5	7.9	6.5
6.6	3.2	6.9	7.5	7.7
6.9	2.7	6.6	6.9	7.9

Tables (Output of Computation)





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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57560&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]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57560&T=0

As an alternative you can also use a QR Code:  
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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 1.02127911876007 + 0.0360414799421969`X(t)`[t] + 1.51084525441126`Y(t-1)`[t] -0.906467676335996`Y(t-2)`[t] + 0.274643095535908`Y(t-4) `[t] -0.139705169919118M1[t] -0.114153458576846M2[t] + 0.615649318632783M3[t] -0.411605834814504M4[t] + 0.0603678236443447M5[t] + 0.0912911222967044M6[t] + 0.0221846854736586M7[t] + 0.172456701258676M8[t] + 0.0136298025154064M9[t] -0.0832739587515652M10[t] -0.0109906454536734M11[t] -0.00678674775831158t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  1.02127911876007 +  0.0360414799421969`X(t)`[t] +  1.51084525441126`Y(t-1)`[t] -0.906467676335996`Y(t-2)`[t] +  0.274643095535908`Y(t-4)
`[t] -0.139705169919118M1[t] -0.114153458576846M2[t] +  0.615649318632783M3[t] -0.411605834814504M4[t] +  0.0603678236443447M5[t] +  0.0912911222967044M6[t] +  0.0221846854736586M7[t] +  0.172456701258676M8[t] +  0.0136298025154064M9[t] -0.0832739587515652M10[t] -0.0109906454536734M11[t] -0.00678674775831158t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57560&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  1.02127911876007 +  0.0360414799421969`X(t)`[t] +  1.51084525441126`Y(t-1)`[t] -0.906467676335996`Y(t-2)`[t] +  0.274643095535908`Y(t-4)
`[t] -0.139705169919118M1[t] -0.114153458576846M2[t] +  0.615649318632783M3[t] -0.411605834814504M4[t] +  0.0603678236443447M5[t] +  0.0912911222967044M6[t] +  0.0221846854736586M7[t] +  0.172456701258676M8[t] +  0.0136298025154064M9[t] -0.0832739587515652M10[t] -0.0109906454536734M11[t] -0.00678674775831158t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57560&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 1.02127911876007 + 0.0360414799421969`X(t)`[t] + 1.51084525441126`Y(t-1)`[t] -0.906467676335996`Y(t-2)`[t] + 0.274643095535908`Y(t-4) `[t] -0.139705169919118M1[t] -0.114153458576846M2[t] + 0.615649318632783M3[t] -0.411605834814504M4[t] + 0.0603678236443447M5[t] + 0.0912911222967044M6[t] + 0.0221846854736586M7[t] + 0.172456701258676M8[t] + 0.0136298025154064M9[t] -0.0832739587515652M10[t] -0.0109906454536734M11[t] -0.00678674775831158t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.021279118760070.6599611.54750.1298240.064912
`X(t)`0.03604147994219690.0241691.49120.1439470.071974
`Y(t-1)`1.510845254411260.099915.123600
`Y(t-2)`-0.9064676763359960.111302-8.144200
`Y(t-4) `0.2746430955359080.069653.94320.0003240.000162
M1-0.1397051699191180.102037-1.36920.1787840.089392
M2-0.1141534585768460.10487-1.08850.2830450.141522
M30.6156493186327830.1061175.80161e-060
M4-0.4116058348145040.131738-3.12440.0033550.001678
M50.06036782364434470.1046630.57680.5674020.283701
M60.09129112229670440.1081990.84370.4039650.201983
M70.02218468547365860.0999830.22190.8255610.41278
M80.1724567012586760.102791.67780.1013920.050696
M90.01362980251540640.1116070.12210.9034290.451714
M10-0.08327395875156520.109081-0.76340.4498090.224905
M11-0.01099064545367340.105006-0.10470.9171760.458588
t-0.006786747758311580.002399-2.82850.0073480.003674

\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) & 1.02127911876007 & 0.659961 & 1.5475 & 0.129824 & 0.064912 \tabularnewline
`X(t)` & 0.0360414799421969 & 0.024169 & 1.4912 & 0.143947 & 0.071974 \tabularnewline
`Y(t-1)` & 1.51084525441126 & 0.0999 & 15.1236 & 0 & 0 \tabularnewline
`Y(t-2)` & -0.906467676335996 & 0.111302 & -8.1442 & 0 & 0 \tabularnewline
`Y(t-4)
` & 0.274643095535908 & 0.06965 & 3.9432 & 0.000324 & 0.000162 \tabularnewline
M1 & -0.139705169919118 & 0.102037 & -1.3692 & 0.178784 & 0.089392 \tabularnewline
M2 & -0.114153458576846 & 0.10487 & -1.0885 & 0.283045 & 0.141522 \tabularnewline
M3 & 0.615649318632783 & 0.106117 & 5.8016 & 1e-06 & 0 \tabularnewline
M4 & -0.411605834814504 & 0.131738 & -3.1244 & 0.003355 & 0.001678 \tabularnewline
M5 & 0.0603678236443447 & 0.104663 & 0.5768 & 0.567402 & 0.283701 \tabularnewline
M6 & 0.0912911222967044 & 0.108199 & 0.8437 & 0.403965 & 0.201983 \tabularnewline
M7 & 0.0221846854736586 & 0.099983 & 0.2219 & 0.825561 & 0.41278 \tabularnewline
M8 & 0.172456701258676 & 0.10279 & 1.6778 & 0.101392 & 0.050696 \tabularnewline
M9 & 0.0136298025154064 & 0.111607 & 0.1221 & 0.903429 & 0.451714 \tabularnewline
M10 & -0.0832739587515652 & 0.109081 & -0.7634 & 0.449809 & 0.224905 \tabularnewline
M11 & -0.0109906454536734 & 0.105006 & -0.1047 & 0.917176 & 0.458588 \tabularnewline
t & -0.00678674775831158 & 0.002399 & -2.8285 & 0.007348 & 0.003674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57560&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]1.02127911876007[/C][C]0.659961[/C][C]1.5475[/C][C]0.129824[/C][C]0.064912[/C][/ROW]
[ROW][C]`X(t)`[/C][C]0.0360414799421969[/C][C]0.024169[/C][C]1.4912[/C][C]0.143947[/C][C]0.071974[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]1.51084525441126[/C][C]0.0999[/C][C]15.1236[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]-0.906467676335996[/C][C]0.111302[/C][C]-8.1442[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-4)
`[/C][C]0.274643095535908[/C][C]0.06965[/C][C]3.9432[/C][C]0.000324[/C][C]0.000162[/C][/ROW]
[ROW][C]M1[/C][C]-0.139705169919118[/C][C]0.102037[/C][C]-1.3692[/C][C]0.178784[/C][C]0.089392[/C][/ROW]
[ROW][C]M2[/C][C]-0.114153458576846[/C][C]0.10487[/C][C]-1.0885[/C][C]0.283045[/C][C]0.141522[/C][/ROW]
[ROW][C]M3[/C][C]0.615649318632783[/C][C]0.106117[/C][C]5.8016[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-0.411605834814504[/C][C]0.131738[/C][C]-3.1244[/C][C]0.003355[/C][C]0.001678[/C][/ROW]
[ROW][C]M5[/C][C]0.0603678236443447[/C][C]0.104663[/C][C]0.5768[/C][C]0.567402[/C][C]0.283701[/C][/ROW]
[ROW][C]M6[/C][C]0.0912911222967044[/C][C]0.108199[/C][C]0.8437[/C][C]0.403965[/C][C]0.201983[/C][/ROW]
[ROW][C]M7[/C][C]0.0221846854736586[/C][C]0.099983[/C][C]0.2219[/C][C]0.825561[/C][C]0.41278[/C][/ROW]
[ROW][C]M8[/C][C]0.172456701258676[/C][C]0.10279[/C][C]1.6778[/C][C]0.101392[/C][C]0.050696[/C][/ROW]
[ROW][C]M9[/C][C]0.0136298025154064[/C][C]0.111607[/C][C]0.1221[/C][C]0.903429[/C][C]0.451714[/C][/ROW]
[ROW][C]M10[/C][C]-0.0832739587515652[/C][C]0.109081[/C][C]-0.7634[/C][C]0.449809[/C][C]0.224905[/C][/ROW]
[ROW][C]M11[/C][C]-0.0109906454536734[/C][C]0.105006[/C][C]-0.1047[/C][C]0.917176[/C][C]0.458588[/C][/ROW]
[ROW][C]t[/C][C]-0.00678674775831158[/C][C]0.002399[/C][C]-2.8285[/C][C]0.007348[/C][C]0.003674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57560&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57560&T=2

As an alternative you can also use a QR Code:  
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)1.021279118760070.6599611.54750.1298240.064912
`X(t)`0.03604147994219690.0241691.49120.1439470.071974
`Y(t-1)`1.510845254411260.099915.123600
`Y(t-2)`-0.9064676763359960.111302-8.144200
`Y(t-4) `0.2746430955359080.069653.94320.0003240.000162
M1-0.1397051699191180.102037-1.36920.1787840.089392
M2-0.1141534585768460.10487-1.08850.2830450.141522
M30.6156493186327830.1061175.80161e-060
M4-0.4116058348145040.131738-3.12440.0033550.001678
M50.06036782364434470.1046630.57680.5674020.283701
M60.09129112229670440.1081990.84370.4039650.201983
M70.02218468547365860.0999830.22190.8255610.41278
M80.1724567012586760.102791.67780.1013920.050696
M90.01362980251540640.1116070.12210.9034290.451714
M10-0.08327395875156520.109081-0.76340.4498090.224905
M11-0.01099064545367340.105006-0.10470.9171760.458588
t-0.006786747758311580.002399-2.82850.0073480.003674






Multiple Linear Regression - Regression Statistics
Multiple R0.98592187717783
R-squared0.972041947897856
Adjusted R-squared0.960571977804668
F-TEST (value)84.7466854752484
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.147696720877349
Sum Squared Residuals0.850758532958944

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.98592187717783 \tabularnewline
R-squared & 0.972041947897856 \tabularnewline
Adjusted R-squared & 0.960571977804668 \tabularnewline
F-TEST (value) & 84.7466854752484 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.147696720877349 \tabularnewline
Sum Squared Residuals & 0.850758532958944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57560&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.98592187717783[/C][/ROW]
[ROW][C]R-squared[/C][C]0.972041947897856[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.960571977804668[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]84.7466854752484[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/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]0.147696720877349[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.850758532958944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57560&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57560&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.98592187717783
R-squared0.972041947897856
Adjusted R-squared0.960571977804668
F-TEST (value)84.7466854752484
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.147696720877349
Sum Squared Residuals0.850758532958944






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.27.21326799770914-0.0132679977091398
27.47.46207262450806-0.0620726245080646
38.88.62548060796870.174519392031305
49.39.30200990324871-0.00200990324871326
59.39.163963469635270.136036530364729
68.78.82223213341648-0.122232133416482
78.28.20991553796176-0.00991553796176193
88.38.264763740375510.0352362596244875
98.58.70707260547728-0.207072605477277
108.68.66093096636176-0.0609309663617573
118.58.57691771427841-0.0769177142784081
128.28.35243803647576-0.152438036475759
138.17.894663781221510.205336218778488
147.98.07616542379562-0.176165423795615
158.68.560194860444690.0398051395553082
168.78.689853539921840.0101464600781625
178.78.647737441068930.0522625589310682
188.58.497465421268440.00253457873155903
198.48.315257500674190.0847424993258116
208.58.53443682805166-0.0344368280516576
218.78.61055447462480.089445525375199
228.78.663457629740990.0365423702590125
238.68.498571462494460.101428537505540
248.58.393571736279170.106428263720834
258.38.248778975889830.0512210241101695
2688.04520921224248-0.0452092122424815
278.28.46519674308981-0.26519674308981
288.17.974195738119450.12580426188055
298.18.03765937702760.0623406229723969
3088.06284147090604-0.0628414709060379
317.97.9016048239734-0.00160482397339572
327.97.9607921726332-0.0607921726332048
3387.871408701788340.128591298211656
3487.894942556644820.105057443355185
357.97.84232804499720.057671955002795
3687.695447417251440.304552582748558
377.77.80013036223123-0.100130362231229
387.27.27499498185821-0.0749949818582132
397.57.487064377451110.0129356225488890
407.37.38337005229626-0.083370052296258
4177.19926297654141-0.199262976541412
4276.842951122565090.157048877434914
4377.14662020550484-0.146620205504838
447.27.2423851504128-0.042385150412801
457.37.31096421810958-0.0109642181095777
467.17.18066884725244-0.0806688472524402
476.86.88218277822993-0.082182778229927
486.46.65854280999363-0.258542809993634
496.16.24315888294829-0.143158882948289
506.56.141557757595630.358442242404375
517.77.662063411045690.0379365889543076
527.97.95057076641374-0.0505707664137413
537.57.55137673572678-0.051376735726782
546.96.874509851843950.0254901481560472
556.66.526601931885820.0733980681141836
566.96.797622108526820.102377891473176

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.2 & 7.21326799770914 & -0.0132679977091398 \tabularnewline
2 & 7.4 & 7.46207262450806 & -0.0620726245080646 \tabularnewline
3 & 8.8 & 8.6254806079687 & 0.174519392031305 \tabularnewline
4 & 9.3 & 9.30200990324871 & -0.00200990324871326 \tabularnewline
5 & 9.3 & 9.16396346963527 & 0.136036530364729 \tabularnewline
6 & 8.7 & 8.82223213341648 & -0.122232133416482 \tabularnewline
7 & 8.2 & 8.20991553796176 & -0.00991553796176193 \tabularnewline
8 & 8.3 & 8.26476374037551 & 0.0352362596244875 \tabularnewline
9 & 8.5 & 8.70707260547728 & -0.207072605477277 \tabularnewline
10 & 8.6 & 8.66093096636176 & -0.0609309663617573 \tabularnewline
11 & 8.5 & 8.57691771427841 & -0.0769177142784081 \tabularnewline
12 & 8.2 & 8.35243803647576 & -0.152438036475759 \tabularnewline
13 & 8.1 & 7.89466378122151 & 0.205336218778488 \tabularnewline
14 & 7.9 & 8.07616542379562 & -0.176165423795615 \tabularnewline
15 & 8.6 & 8.56019486044469 & 0.0398051395553082 \tabularnewline
16 & 8.7 & 8.68985353992184 & 0.0101464600781625 \tabularnewline
17 & 8.7 & 8.64773744106893 & 0.0522625589310682 \tabularnewline
18 & 8.5 & 8.49746542126844 & 0.00253457873155903 \tabularnewline
19 & 8.4 & 8.31525750067419 & 0.0847424993258116 \tabularnewline
20 & 8.5 & 8.53443682805166 & -0.0344368280516576 \tabularnewline
21 & 8.7 & 8.6105544746248 & 0.089445525375199 \tabularnewline
22 & 8.7 & 8.66345762974099 & 0.0365423702590125 \tabularnewline
23 & 8.6 & 8.49857146249446 & 0.101428537505540 \tabularnewline
24 & 8.5 & 8.39357173627917 & 0.106428263720834 \tabularnewline
25 & 8.3 & 8.24877897588983 & 0.0512210241101695 \tabularnewline
26 & 8 & 8.04520921224248 & -0.0452092122424815 \tabularnewline
27 & 8.2 & 8.46519674308981 & -0.26519674308981 \tabularnewline
28 & 8.1 & 7.97419573811945 & 0.12580426188055 \tabularnewline
29 & 8.1 & 8.0376593770276 & 0.0623406229723969 \tabularnewline
30 & 8 & 8.06284147090604 & -0.0628414709060379 \tabularnewline
31 & 7.9 & 7.9016048239734 & -0.00160482397339572 \tabularnewline
32 & 7.9 & 7.9607921726332 & -0.0607921726332048 \tabularnewline
33 & 8 & 7.87140870178834 & 0.128591298211656 \tabularnewline
34 & 8 & 7.89494255664482 & 0.105057443355185 \tabularnewline
35 & 7.9 & 7.8423280449972 & 0.057671955002795 \tabularnewline
36 & 8 & 7.69544741725144 & 0.304552582748558 \tabularnewline
37 & 7.7 & 7.80013036223123 & -0.100130362231229 \tabularnewline
38 & 7.2 & 7.27499498185821 & -0.0749949818582132 \tabularnewline
39 & 7.5 & 7.48706437745111 & 0.0129356225488890 \tabularnewline
40 & 7.3 & 7.38337005229626 & -0.083370052296258 \tabularnewline
41 & 7 & 7.19926297654141 & -0.199262976541412 \tabularnewline
42 & 7 & 6.84295112256509 & 0.157048877434914 \tabularnewline
43 & 7 & 7.14662020550484 & -0.146620205504838 \tabularnewline
44 & 7.2 & 7.2423851504128 & -0.042385150412801 \tabularnewline
45 & 7.3 & 7.31096421810958 & -0.0109642181095777 \tabularnewline
46 & 7.1 & 7.18066884725244 & -0.0806688472524402 \tabularnewline
47 & 6.8 & 6.88218277822993 & -0.082182778229927 \tabularnewline
48 & 6.4 & 6.65854280999363 & -0.258542809993634 \tabularnewline
49 & 6.1 & 6.24315888294829 & -0.143158882948289 \tabularnewline
50 & 6.5 & 6.14155775759563 & 0.358442242404375 \tabularnewline
51 & 7.7 & 7.66206341104569 & 0.0379365889543076 \tabularnewline
52 & 7.9 & 7.95057076641374 & -0.0505707664137413 \tabularnewline
53 & 7.5 & 7.55137673572678 & -0.051376735726782 \tabularnewline
54 & 6.9 & 6.87450985184395 & 0.0254901481560472 \tabularnewline
55 & 6.6 & 6.52660193188582 & 0.0733980681141836 \tabularnewline
56 & 6.9 & 6.79762210852682 & 0.102377891473176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57560&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]7.2[/C][C]7.21326799770914[/C][C]-0.0132679977091398[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]7.46207262450806[/C][C]-0.0620726245080646[/C][/ROW]
[ROW][C]3[/C][C]8.8[/C][C]8.6254806079687[/C][C]0.174519392031305[/C][/ROW]
[ROW][C]4[/C][C]9.3[/C][C]9.30200990324871[/C][C]-0.00200990324871326[/C][/ROW]
[ROW][C]5[/C][C]9.3[/C][C]9.16396346963527[/C][C]0.136036530364729[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.82223213341648[/C][C]-0.122232133416482[/C][/ROW]
[ROW][C]7[/C][C]8.2[/C][C]8.20991553796176[/C][C]-0.00991553796176193[/C][/ROW]
[ROW][C]8[/C][C]8.3[/C][C]8.26476374037551[/C][C]0.0352362596244875[/C][/ROW]
[ROW][C]9[/C][C]8.5[/C][C]8.70707260547728[/C][C]-0.207072605477277[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.66093096636176[/C][C]-0.0609309663617573[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.57691771427841[/C][C]-0.0769177142784081[/C][/ROW]
[ROW][C]12[/C][C]8.2[/C][C]8.35243803647576[/C][C]-0.152438036475759[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]7.89466378122151[/C][C]0.205336218778488[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.07616542379562[/C][C]-0.176165423795615[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.56019486044469[/C][C]0.0398051395553082[/C][/ROW]
[ROW][C]16[/C][C]8.7[/C][C]8.68985353992184[/C][C]0.0101464600781625[/C][/ROW]
[ROW][C]17[/C][C]8.7[/C][C]8.64773744106893[/C][C]0.0522625589310682[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.49746542126844[/C][C]0.00253457873155903[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.31525750067419[/C][C]0.0847424993258116[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.53443682805166[/C][C]-0.0344368280516576[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.6105544746248[/C][C]0.089445525375199[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]8.66345762974099[/C][C]0.0365423702590125[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.49857146249446[/C][C]0.101428537505540[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.39357173627917[/C][C]0.106428263720834[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.24877897588983[/C][C]0.0512210241101695[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.04520921224248[/C][C]-0.0452092122424815[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.46519674308981[/C][C]-0.26519674308981[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]7.97419573811945[/C][C]0.12580426188055[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]8.0376593770276[/C][C]0.0623406229723969[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.06284147090604[/C][C]-0.0628414709060379[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]7.9016048239734[/C][C]-0.00160482397339572[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]7.9607921726332[/C][C]-0.0607921726332048[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.87140870178834[/C][C]0.128591298211656[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.89494255664482[/C][C]0.105057443355185[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.8423280449972[/C][C]0.057671955002795[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.69544741725144[/C][C]0.304552582748558[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]7.80013036223123[/C][C]-0.100130362231229[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.27499498185821[/C][C]-0.0749949818582132[/C][/ROW]
[ROW][C]39[/C][C]7.5[/C][C]7.48706437745111[/C][C]0.0129356225488890[/C][/ROW]
[ROW][C]40[/C][C]7.3[/C][C]7.38337005229626[/C][C]-0.083370052296258[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.19926297654141[/C][C]-0.199262976541412[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.84295112256509[/C][C]0.157048877434914[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]7.14662020550484[/C][C]-0.146620205504838[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.2423851504128[/C][C]-0.042385150412801[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.31096421810958[/C][C]-0.0109642181095777[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.18066884725244[/C][C]-0.0806688472524402[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.88218277822993[/C][C]-0.082182778229927[/C][/ROW]
[ROW][C]48[/C][C]6.4[/C][C]6.65854280999363[/C][C]-0.258542809993634[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.24315888294829[/C][C]-0.143158882948289[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.14155775759563[/C][C]0.358442242404375[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.66206341104569[/C][C]0.0379365889543076[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.95057076641374[/C][C]-0.0505707664137413[/C][/ROW]
[ROW][C]53[/C][C]7.5[/C][C]7.55137673572678[/C][C]-0.051376735726782[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.87450985184395[/C][C]0.0254901481560472[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.52660193188582[/C][C]0.0733980681141836[/C][/ROW]
[ROW][C]56[/C][C]6.9[/C][C]6.79762210852682[/C][C]0.102377891473176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57560&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57560&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.27.21326799770914-0.0132679977091398
27.47.46207262450806-0.0620726245080646
38.88.62548060796870.174519392031305
49.39.30200990324871-0.00200990324871326
59.39.163963469635270.136036530364729
68.78.82223213341648-0.122232133416482
78.28.20991553796176-0.00991553796176193
88.38.264763740375510.0352362596244875
98.58.70707260547728-0.207072605477277
108.68.66093096636176-0.0609309663617573
118.58.57691771427841-0.0769177142784081
128.28.35243803647576-0.152438036475759
138.17.894663781221510.205336218778488
147.98.07616542379562-0.176165423795615
158.68.560194860444690.0398051395553082
168.78.689853539921840.0101464600781625
178.78.647737441068930.0522625589310682
188.58.497465421268440.00253457873155903
198.48.315257500674190.0847424993258116
208.58.53443682805166-0.0344368280516576
218.78.61055447462480.089445525375199
228.78.663457629740990.0365423702590125
238.68.498571462494460.101428537505540
248.58.393571736279170.106428263720834
258.38.248778975889830.0512210241101695
2688.04520921224248-0.0452092122424815
278.28.46519674308981-0.26519674308981
288.17.974195738119450.12580426188055
298.18.03765937702760.0623406229723969
3088.06284147090604-0.0628414709060379
317.97.9016048239734-0.00160482397339572
327.97.9607921726332-0.0607921726332048
3387.871408701788340.128591298211656
3487.894942556644820.105057443355185
357.97.84232804499720.057671955002795
3687.695447417251440.304552582748558
377.77.80013036223123-0.100130362231229
387.27.27499498185821-0.0749949818582132
397.57.487064377451110.0129356225488890
407.37.38337005229626-0.083370052296258
4177.19926297654141-0.199262976541412
4276.842951122565090.157048877434914
4377.14662020550484-0.146620205504838
447.27.2423851504128-0.042385150412801
457.37.31096421810958-0.0109642181095777
467.17.18066884725244-0.0806688472524402
476.86.88218277822993-0.082182778229927
486.46.65854280999363-0.258542809993634
496.16.24315888294829-0.143158882948289
506.56.141557757595630.358442242404375
517.77.662063411045690.0379365889543076
527.97.95057076641374-0.0505707664137413
537.57.55137673572678-0.051376735726782
546.96.874509851843950.0254901481560472
556.66.526601931885820.0733980681141836
566.96.797622108526820.102377891473176






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.1415185501551110.2830371003102220.85848144984489
210.1873300884187730.3746601768375460.812669911581227
220.09139235182227070.1827847036445410.90860764817773
230.04125363391813060.08250726783626110.95874636608187
240.05131280405272120.1026256081054420.94868719594728
250.0257548064378520.0515096128757040.974245193562148
260.01429215740458550.02858431480917110.985707842595414
270.292784385989140.585568771978280.70721561401086
280.2037136736189180.4074273472378360.796286326381082
290.1633275641492770.3266551282985550.836672435850723
300.1815879460983730.3631758921967450.818412053901627
310.1403154332866830.2806308665733660.859684566713317
320.1244576602627750.248915320525550.875542339737225
330.08956880553190420.1791376110638080.910431194468096
340.05982341521688260.1196468304337650.940176584783117
350.03230955755099280.06461911510198560.967690442449007
360.1992798818733620.3985597637467240.800720118126638

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.141518550155111 & 0.283037100310222 & 0.85848144984489 \tabularnewline
21 & 0.187330088418773 & 0.374660176837546 & 0.812669911581227 \tabularnewline
22 & 0.0913923518222707 & 0.182784703644541 & 0.90860764817773 \tabularnewline
23 & 0.0412536339181306 & 0.0825072678362611 & 0.95874636608187 \tabularnewline
24 & 0.0513128040527212 & 0.102625608105442 & 0.94868719594728 \tabularnewline
25 & 0.025754806437852 & 0.051509612875704 & 0.974245193562148 \tabularnewline
26 & 0.0142921574045855 & 0.0285843148091711 & 0.985707842595414 \tabularnewline
27 & 0.29278438598914 & 0.58556877197828 & 0.70721561401086 \tabularnewline
28 & 0.203713673618918 & 0.407427347237836 & 0.796286326381082 \tabularnewline
29 & 0.163327564149277 & 0.326655128298555 & 0.836672435850723 \tabularnewline
30 & 0.181587946098373 & 0.363175892196745 & 0.818412053901627 \tabularnewline
31 & 0.140315433286683 & 0.280630866573366 & 0.859684566713317 \tabularnewline
32 & 0.124457660262775 & 0.24891532052555 & 0.875542339737225 \tabularnewline
33 & 0.0895688055319042 & 0.179137611063808 & 0.910431194468096 \tabularnewline
34 & 0.0598234152168826 & 0.119646830433765 & 0.940176584783117 \tabularnewline
35 & 0.0323095575509928 & 0.0646191151019856 & 0.967690442449007 \tabularnewline
36 & 0.199279881873362 & 0.398559763746724 & 0.800720118126638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57560&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]20[/C][C]0.141518550155111[/C][C]0.283037100310222[/C][C]0.85848144984489[/C][/ROW]
[ROW][C]21[/C][C]0.187330088418773[/C][C]0.374660176837546[/C][C]0.812669911581227[/C][/ROW]
[ROW][C]22[/C][C]0.0913923518222707[/C][C]0.182784703644541[/C][C]0.90860764817773[/C][/ROW]
[ROW][C]23[/C][C]0.0412536339181306[/C][C]0.0825072678362611[/C][C]0.95874636608187[/C][/ROW]
[ROW][C]24[/C][C]0.0513128040527212[/C][C]0.102625608105442[/C][C]0.94868719594728[/C][/ROW]
[ROW][C]25[/C][C]0.025754806437852[/C][C]0.051509612875704[/C][C]0.974245193562148[/C][/ROW]
[ROW][C]26[/C][C]0.0142921574045855[/C][C]0.0285843148091711[/C][C]0.985707842595414[/C][/ROW]
[ROW][C]27[/C][C]0.29278438598914[/C][C]0.58556877197828[/C][C]0.70721561401086[/C][/ROW]
[ROW][C]28[/C][C]0.203713673618918[/C][C]0.407427347237836[/C][C]0.796286326381082[/C][/ROW]
[ROW][C]29[/C][C]0.163327564149277[/C][C]0.326655128298555[/C][C]0.836672435850723[/C][/ROW]
[ROW][C]30[/C][C]0.181587946098373[/C][C]0.363175892196745[/C][C]0.818412053901627[/C][/ROW]
[ROW][C]31[/C][C]0.140315433286683[/C][C]0.280630866573366[/C][C]0.859684566713317[/C][/ROW]
[ROW][C]32[/C][C]0.124457660262775[/C][C]0.24891532052555[/C][C]0.875542339737225[/C][/ROW]
[ROW][C]33[/C][C]0.0895688055319042[/C][C]0.179137611063808[/C][C]0.910431194468096[/C][/ROW]
[ROW][C]34[/C][C]0.0598234152168826[/C][C]0.119646830433765[/C][C]0.940176584783117[/C][/ROW]
[ROW][C]35[/C][C]0.0323095575509928[/C][C]0.0646191151019856[/C][C]0.967690442449007[/C][/ROW]
[ROW][C]36[/C][C]0.199279881873362[/C][C]0.398559763746724[/C][C]0.800720118126638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57560&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57560&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.1415185501551110.2830371003102220.85848144984489
210.1873300884187730.3746601768375460.812669911581227
220.09139235182227070.1827847036445410.90860764817773
230.04125363391813060.08250726783626110.95874636608187
240.05131280405272120.1026256081054420.94868719594728
250.0257548064378520.0515096128757040.974245193562148
260.01429215740458550.02858431480917110.985707842595414
270.292784385989140.585568771978280.70721561401086
280.2037136736189180.4074273472378360.796286326381082
290.1633275641492770.3266551282985550.836672435850723
300.1815879460983730.3631758921967450.818412053901627
310.1403154332866830.2806308665733660.859684566713317
320.1244576602627750.248915320525550.875542339737225
330.08956880553190420.1791376110638080.910431194468096
340.05982341521688260.1196468304337650.940176584783117
350.03230955755099280.06461911510198560.967690442449007
360.1992798818733620.3985597637467240.800720118126638






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0588235294117647NOK
10% type I error level40.235294117647059NOK

\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 & 0 & 0 & OK \tabularnewline
5% type I error level & 1 & 0.0588235294117647 & NOK \tabularnewline
10% type I error level & 4 & 0.235294117647059 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57560&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]1[/C][C]0.0588235294117647[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.235294117647059[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57560&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57560&T=6

As an alternative you can also use a QR Code:  
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 level00OK
5% type I error level10.0588235294117647NOK
10% type I error level40.235294117647059NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; 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')
}