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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 computationThu, 19 Nov 2009 14:28:01 -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/19/t1258666223bgcop1ly9ip7j40.htm/, Retrieved Thu, 18 Apr 2024 03:05:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57964, Retrieved Thu, 18 Apr 2024 03:05:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Model 5] [2009-11-19 21:28:01] [e458b4e05bf28a297f8af8d9f96e59d6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.1	96.8	96.2
3.9	109.9	96.8
3.8	88	109.9
3.7	91.1	88
3.7	106.4	91.1
4.1	68.6	106.4
4.1	100.1	68.6
3.8	108	100.1
3.7	106	108
3.5	108.6	106
3.6	91.5	108.6
4.1	99.2	91.5
3.8	98	99.2
3.7	96.6	98
3.6	102.8	96.6
3.3	96.9	102.8
3.4	110	96.9
3.7	70.5	110
3.7	101.9	70.5
3.4	109.6	101.9
3.3	107.8	109.6
3	113	107.8
3	93.8	113
3.3	108	93.8
3	102.8	108
2.9	116.3	102.8
2.8	89.2	116.3
2.5	106.7	89.2
2.6	112.1	106.7
2.8	74.2	112.1
2.7	108.8	74.2
2.4	111.5	108.8
2.2	118.8	111.5
2.1	118.9	118.8
2.1	97.6	118.9
2.3	116.4	97.6
2.1	107.9	116.4
2	121.2	107.9
1.9	97.9	121.2
1.7	113.4	97.9
1.8	117.6	113.4
2.1	79.6	117.6
2	115.9	79.6
1.8	115.7	115.9
1.7	129.1	115.7
1.6	123.3	129.1
1.6	96.7	123.3
1.8	121.2	96.7
1.7	118.2	121.2
1.7	102.1	118.2
1.5	125.4	102.1
1.5	116.7	125.4
1.5	121.3	116.7
1.8	85.3	121.3
1.8	114.2	85.3
1.7	124.4	114.2
1.7	131	124.4
1.8	118.3	131
2	99.6	118.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57964&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]4 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=57964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57964&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
unempl[t] = + 6.95863385692966 -0.0172255661383461proman[t] -0.0105823825619524`Y(t-1)`[t] -0.0995119353824613M1[t] -0.120160349506485M2[t] -0.301406028532639M3[t] -0.459125195627519M4[t] -0.168063033871873M5[t] -0.390920463878512M6[t] -0.232041804640464M7[t] + 0.00860172150904735M8[t] + 0.0882542609004675M9[t] + 0.020269351968893M10[t] -0.257871356949066M11[t] -0.038796093240543t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
unempl[t] =  +  6.95863385692966 -0.0172255661383461proman[t] -0.0105823825619524`Y(t-1)`[t] -0.0995119353824613M1[t] -0.120160349506485M2[t] -0.301406028532639M3[t] -0.459125195627519M4[t] -0.168063033871873M5[t] -0.390920463878512M6[t] -0.232041804640464M7[t] +  0.00860172150904735M8[t] +  0.0882542609004675M9[t] +  0.020269351968893M10[t] -0.257871356949066M11[t] -0.038796093240543t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57964&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]unempl[t] =  +  6.95863385692966 -0.0172255661383461proman[t] -0.0105823825619524`Y(t-1)`[t] -0.0995119353824613M1[t] -0.120160349506485M2[t] -0.301406028532639M3[t] -0.459125195627519M4[t] -0.168063033871873M5[t] -0.390920463878512M6[t] -0.232041804640464M7[t] +  0.00860172150904735M8[t] +  0.0882542609004675M9[t] +  0.020269351968893M10[t] -0.257871356949066M11[t] -0.038796093240543t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57964&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
unempl[t] = + 6.95863385692966 -0.0172255661383461proman[t] -0.0105823825619524`Y(t-1)`[t] -0.0995119353824613M1[t] -0.120160349506485M2[t] -0.301406028532639M3[t] -0.459125195627519M4[t] -0.168063033871873M5[t] -0.390920463878512M6[t] -0.232041804640464M7[t] + 0.00860172150904735M8[t] + 0.0882542609004675M9[t] + 0.020269351968893M10[t] -0.257871356949066M11[t] -0.038796093240543t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)6.958633856929661.0851426.412600
proman-0.01722556613834610.006944-2.48060.0170150.008507
`Y(t-1)`-0.01058238256195240.007009-1.50980.1382360.069118
M1-0.09951193538246130.189178-0.5260.6015150.300757
M2-0.1201603495064850.179817-0.66820.5074740.253737
M3-0.3014060285326390.190444-1.58260.1206640.060332
M4-0.4591251956275190.16797-2.73340.0089950.004497
M5-0.1680630338718730.181497-0.9260.3595070.179753
M6-0.3909204638785120.277812-1.40710.1664110.083206
M7-0.2320418046404640.219876-1.05530.2970350.148517
M80.008601721509047350.1868890.0460.9634980.481749
M90.08825426090046750.2190930.40280.6890340.344517
M100.0202693519688930.2326320.08710.9309630.465482
M11-0.2578713569490660.213585-1.20730.2337480.116874
t-0.0387960932405430.004869-7.968100

\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) & 6.95863385692966 & 1.085142 & 6.4126 & 0 & 0 \tabularnewline
proman & -0.0172255661383461 & 0.006944 & -2.4806 & 0.017015 & 0.008507 \tabularnewline
`Y(t-1)` & -0.0105823825619524 & 0.007009 & -1.5098 & 0.138236 & 0.069118 \tabularnewline
M1 & -0.0995119353824613 & 0.189178 & -0.526 & 0.601515 & 0.300757 \tabularnewline
M2 & -0.120160349506485 & 0.179817 & -0.6682 & 0.507474 & 0.253737 \tabularnewline
M3 & -0.301406028532639 & 0.190444 & -1.5826 & 0.120664 & 0.060332 \tabularnewline
M4 & -0.459125195627519 & 0.16797 & -2.7334 & 0.008995 & 0.004497 \tabularnewline
M5 & -0.168063033871873 & 0.181497 & -0.926 & 0.359507 & 0.179753 \tabularnewline
M6 & -0.390920463878512 & 0.277812 & -1.4071 & 0.166411 & 0.083206 \tabularnewline
M7 & -0.232041804640464 & 0.219876 & -1.0553 & 0.297035 & 0.148517 \tabularnewline
M8 & 0.00860172150904735 & 0.186889 & 0.046 & 0.963498 & 0.481749 \tabularnewline
M9 & 0.0882542609004675 & 0.219093 & 0.4028 & 0.689034 & 0.344517 \tabularnewline
M10 & 0.020269351968893 & 0.232632 & 0.0871 & 0.930963 & 0.465482 \tabularnewline
M11 & -0.257871356949066 & 0.213585 & -1.2073 & 0.233748 & 0.116874 \tabularnewline
t & -0.038796093240543 & 0.004869 & -7.9681 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57964&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]6.95863385692966[/C][C]1.085142[/C][C]6.4126[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]proman[/C][C]-0.0172255661383461[/C][C]0.006944[/C][C]-2.4806[/C][C]0.017015[/C][C]0.008507[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]-0.0105823825619524[/C][C]0.007009[/C][C]-1.5098[/C][C]0.138236[/C][C]0.069118[/C][/ROW]
[ROW][C]M1[/C][C]-0.0995119353824613[/C][C]0.189178[/C][C]-0.526[/C][C]0.601515[/C][C]0.300757[/C][/ROW]
[ROW][C]M2[/C][C]-0.120160349506485[/C][C]0.179817[/C][C]-0.6682[/C][C]0.507474[/C][C]0.253737[/C][/ROW]
[ROW][C]M3[/C][C]-0.301406028532639[/C][C]0.190444[/C][C]-1.5826[/C][C]0.120664[/C][C]0.060332[/C][/ROW]
[ROW][C]M4[/C][C]-0.459125195627519[/C][C]0.16797[/C][C]-2.7334[/C][C]0.008995[/C][C]0.004497[/C][/ROW]
[ROW][C]M5[/C][C]-0.168063033871873[/C][C]0.181497[/C][C]-0.926[/C][C]0.359507[/C][C]0.179753[/C][/ROW]
[ROW][C]M6[/C][C]-0.390920463878512[/C][C]0.277812[/C][C]-1.4071[/C][C]0.166411[/C][C]0.083206[/C][/ROW]
[ROW][C]M7[/C][C]-0.232041804640464[/C][C]0.219876[/C][C]-1.0553[/C][C]0.297035[/C][C]0.148517[/C][/ROW]
[ROW][C]M8[/C][C]0.00860172150904735[/C][C]0.186889[/C][C]0.046[/C][C]0.963498[/C][C]0.481749[/C][/ROW]
[ROW][C]M9[/C][C]0.0882542609004675[/C][C]0.219093[/C][C]0.4028[/C][C]0.689034[/C][C]0.344517[/C][/ROW]
[ROW][C]M10[/C][C]0.020269351968893[/C][C]0.232632[/C][C]0.0871[/C][C]0.930963[/C][C]0.465482[/C][/ROW]
[ROW][C]M11[/C][C]-0.257871356949066[/C][C]0.213585[/C][C]-1.2073[/C][C]0.233748[/C][C]0.116874[/C][/ROW]
[ROW][C]t[/C][C]-0.038796093240543[/C][C]0.004869[/C][C]-7.9681[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57964&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57964&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)6.958633856929661.0851426.412600
proman-0.01722556613834610.006944-2.48060.0170150.008507
`Y(t-1)`-0.01058238256195240.007009-1.50980.1382360.069118
M1-0.09951193538246130.189178-0.5260.6015150.300757
M2-0.1201603495064850.179817-0.66820.5074740.253737
M3-0.3014060285326390.190444-1.58260.1206640.060332
M4-0.4591251956275190.16797-2.73340.0089950.004497
M5-0.1680630338718730.181497-0.9260.3595070.179753
M6-0.3909204638785120.277812-1.40710.1664110.083206
M7-0.2320418046404640.219876-1.05530.2970350.148517
M80.008601721509047350.1868890.0460.9634980.481749
M90.08825426090046750.2190930.40280.6890340.344517
M100.0202693519688930.2326320.08710.9309630.465482
M11-0.2578713569490660.213585-1.20730.2337480.116874
t-0.0387960932405430.004869-7.968100






Multiple Linear Regression - Regression Statistics
Multiple R0.97138574167357
R-squared0.94359025912671
Adjusted R-squared0.925641705212483
F-TEST (value)52.5719377525283
F-TEST (DF numerator)14
F-TEST (DF denominator)44
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.240855151191974
Sum Squared Residuals2.55249296965118

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.97138574167357 \tabularnewline
R-squared & 0.94359025912671 \tabularnewline
Adjusted R-squared & 0.925641705212483 \tabularnewline
F-TEST (value) & 52.5719377525283 \tabularnewline
F-TEST (DF numerator) & 14 \tabularnewline
F-TEST (DF denominator) & 44 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.240855151191974 \tabularnewline
Sum Squared Residuals & 2.55249296965118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57964&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.97138574167357[/C][/ROW]
[ROW][C]R-squared[/C][C]0.94359025912671[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.925641705212483[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]52.5719377525283[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]14[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]44[/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]0.240855151191974[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.55249296965118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57964&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57964&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 R0.97138574167357
R-squared0.94359025912671
Adjusted R-squared0.925641705212483
F-TEST (value)52.5719377525283
F-TEST (DF numerator)14
F-TEST (DF denominator)44
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.240855151191974
Sum Squared Residuals2.55249296965118






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
14.14.13486582365492-0.0348658236549180
23.93.843416970340860.0565830296591427
33.83.86198588494237-0.0619858849423663
43.73.84382554768483-0.143825547684825
53.73.79973506834118-0.0997350683411813
64.14.027297491925610.0727025080743886
74.14.004788785407010.0952112145929868
83.83.737209195121550.0627908048784517
93.73.72891595130969-0.0289159513096931
103.53.59851324230178-0.0985132423017812
113.63.548619426447920.0513805735520787
124.13.816016572700570.283983427299435
133.83.616894877716540.183105122283458
143.73.594265022020.105734977979997
153.63.282240075282290.317759924717706
163.33.121744883279010.178255116720993
173.43.210792092497300.189207907502704
183.73.490919220153210.209080779846791
193.73.488123120603760.211876879396236
203.43.225046881802160.174953118197836
213.33.215425001275030.0845749987249688
2233.03811934379503-0.038119343795028
2332.996885022170620.00311497782938105
243.33.174538991904110.125461008095887
2532.975534074820780.0244659251792153
262.92.73857281391070.161427186089302
272.82.84248171940682-0.0424817194068233
282.52.63130161907925-0.131301619079252
292.62.60535793561312-0.00535793561312037
302.82.93940850317471-0.139408503174713
312.72.86455877988344-0.164558779883437
322.42.65374674757532-0.253746747575319
332.22.540284127999-0.340284127998998
342.12.35452917651079-0.254529176510794
352.12.40343869484287-0.303438694842869
362.32.52407806372007-0.224078063720071
372.12.33323855510830-0.233238555108303
3822.13464426988033-0.134644269880329
391.92.17521250056313-0.275212500563130
401.71.95827047877683-0.258270478776832
411.81.97416223980062-0.174162239800621
422.12.32263422305039-0.22263422305039
4322.21955927558012-0.219559275580121
441.82.04071133471789-0.240711334717888
451.71.85286167112732-0.152861671127318
461.61.70418502622745-0.104185026227446
471.61.90682610220827-0.306826102208274
481.81.98536637167525-0.185366371675251
491.71.639466668699450.0605333313005481
501.71.88910092384811-0.189100923848114
511.51.438079819805390.0619201801946135
521.51.144857471180080.355142528819916
531.51.409952663747780.0900473362522189
541.81.719740561696080.0802594383039226
551.81.722970038525660.0770299614743352
561.71.443285840783080.256714159216920
571.71.262513248288960.437486751711041
581.81.304653211164950.495346788835049
5921.444230754330320.555769245669683

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 4.1 & 4.13486582365492 & -0.0348658236549180 \tabularnewline
2 & 3.9 & 3.84341697034086 & 0.0565830296591427 \tabularnewline
3 & 3.8 & 3.86198588494237 & -0.0619858849423663 \tabularnewline
4 & 3.7 & 3.84382554768483 & -0.143825547684825 \tabularnewline
5 & 3.7 & 3.79973506834118 & -0.0997350683411813 \tabularnewline
6 & 4.1 & 4.02729749192561 & 0.0727025080743886 \tabularnewline
7 & 4.1 & 4.00478878540701 & 0.0952112145929868 \tabularnewline
8 & 3.8 & 3.73720919512155 & 0.0627908048784517 \tabularnewline
9 & 3.7 & 3.72891595130969 & -0.0289159513096931 \tabularnewline
10 & 3.5 & 3.59851324230178 & -0.0985132423017812 \tabularnewline
11 & 3.6 & 3.54861942644792 & 0.0513805735520787 \tabularnewline
12 & 4.1 & 3.81601657270057 & 0.283983427299435 \tabularnewline
13 & 3.8 & 3.61689487771654 & 0.183105122283458 \tabularnewline
14 & 3.7 & 3.59426502202 & 0.105734977979997 \tabularnewline
15 & 3.6 & 3.28224007528229 & 0.317759924717706 \tabularnewline
16 & 3.3 & 3.12174488327901 & 0.178255116720993 \tabularnewline
17 & 3.4 & 3.21079209249730 & 0.189207907502704 \tabularnewline
18 & 3.7 & 3.49091922015321 & 0.209080779846791 \tabularnewline
19 & 3.7 & 3.48812312060376 & 0.211876879396236 \tabularnewline
20 & 3.4 & 3.22504688180216 & 0.174953118197836 \tabularnewline
21 & 3.3 & 3.21542500127503 & 0.0845749987249688 \tabularnewline
22 & 3 & 3.03811934379503 & -0.038119343795028 \tabularnewline
23 & 3 & 2.99688502217062 & 0.00311497782938105 \tabularnewline
24 & 3.3 & 3.17453899190411 & 0.125461008095887 \tabularnewline
25 & 3 & 2.97553407482078 & 0.0244659251792153 \tabularnewline
26 & 2.9 & 2.7385728139107 & 0.161427186089302 \tabularnewline
27 & 2.8 & 2.84248171940682 & -0.0424817194068233 \tabularnewline
28 & 2.5 & 2.63130161907925 & -0.131301619079252 \tabularnewline
29 & 2.6 & 2.60535793561312 & -0.00535793561312037 \tabularnewline
30 & 2.8 & 2.93940850317471 & -0.139408503174713 \tabularnewline
31 & 2.7 & 2.86455877988344 & -0.164558779883437 \tabularnewline
32 & 2.4 & 2.65374674757532 & -0.253746747575319 \tabularnewline
33 & 2.2 & 2.540284127999 & -0.340284127998998 \tabularnewline
34 & 2.1 & 2.35452917651079 & -0.254529176510794 \tabularnewline
35 & 2.1 & 2.40343869484287 & -0.303438694842869 \tabularnewline
36 & 2.3 & 2.52407806372007 & -0.224078063720071 \tabularnewline
37 & 2.1 & 2.33323855510830 & -0.233238555108303 \tabularnewline
38 & 2 & 2.13464426988033 & -0.134644269880329 \tabularnewline
39 & 1.9 & 2.17521250056313 & -0.275212500563130 \tabularnewline
40 & 1.7 & 1.95827047877683 & -0.258270478776832 \tabularnewline
41 & 1.8 & 1.97416223980062 & -0.174162239800621 \tabularnewline
42 & 2.1 & 2.32263422305039 & -0.22263422305039 \tabularnewline
43 & 2 & 2.21955927558012 & -0.219559275580121 \tabularnewline
44 & 1.8 & 2.04071133471789 & -0.240711334717888 \tabularnewline
45 & 1.7 & 1.85286167112732 & -0.152861671127318 \tabularnewline
46 & 1.6 & 1.70418502622745 & -0.104185026227446 \tabularnewline
47 & 1.6 & 1.90682610220827 & -0.306826102208274 \tabularnewline
48 & 1.8 & 1.98536637167525 & -0.185366371675251 \tabularnewline
49 & 1.7 & 1.63946666869945 & 0.0605333313005481 \tabularnewline
50 & 1.7 & 1.88910092384811 & -0.189100923848114 \tabularnewline
51 & 1.5 & 1.43807981980539 & 0.0619201801946135 \tabularnewline
52 & 1.5 & 1.14485747118008 & 0.355142528819916 \tabularnewline
53 & 1.5 & 1.40995266374778 & 0.0900473362522189 \tabularnewline
54 & 1.8 & 1.71974056169608 & 0.0802594383039226 \tabularnewline
55 & 1.8 & 1.72297003852566 & 0.0770299614743352 \tabularnewline
56 & 1.7 & 1.44328584078308 & 0.256714159216920 \tabularnewline
57 & 1.7 & 1.26251324828896 & 0.437486751711041 \tabularnewline
58 & 1.8 & 1.30465321116495 & 0.495346788835049 \tabularnewline
59 & 2 & 1.44423075433032 & 0.555769245669683 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57964&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]4.1[/C][C]4.13486582365492[/C][C]-0.0348658236549180[/C][/ROW]
[ROW][C]2[/C][C]3.9[/C][C]3.84341697034086[/C][C]0.0565830296591427[/C][/ROW]
[ROW][C]3[/C][C]3.8[/C][C]3.86198588494237[/C][C]-0.0619858849423663[/C][/ROW]
[ROW][C]4[/C][C]3.7[/C][C]3.84382554768483[/C][C]-0.143825547684825[/C][/ROW]
[ROW][C]5[/C][C]3.7[/C][C]3.79973506834118[/C][C]-0.0997350683411813[/C][/ROW]
[ROW][C]6[/C][C]4.1[/C][C]4.02729749192561[/C][C]0.0727025080743886[/C][/ROW]
[ROW][C]7[/C][C]4.1[/C][C]4.00478878540701[/C][C]0.0952112145929868[/C][/ROW]
[ROW][C]8[/C][C]3.8[/C][C]3.73720919512155[/C][C]0.0627908048784517[/C][/ROW]
[ROW][C]9[/C][C]3.7[/C][C]3.72891595130969[/C][C]-0.0289159513096931[/C][/ROW]
[ROW][C]10[/C][C]3.5[/C][C]3.59851324230178[/C][C]-0.0985132423017812[/C][/ROW]
[ROW][C]11[/C][C]3.6[/C][C]3.54861942644792[/C][C]0.0513805735520787[/C][/ROW]
[ROW][C]12[/C][C]4.1[/C][C]3.81601657270057[/C][C]0.283983427299435[/C][/ROW]
[ROW][C]13[/C][C]3.8[/C][C]3.61689487771654[/C][C]0.183105122283458[/C][/ROW]
[ROW][C]14[/C][C]3.7[/C][C]3.59426502202[/C][C]0.105734977979997[/C][/ROW]
[ROW][C]15[/C][C]3.6[/C][C]3.28224007528229[/C][C]0.317759924717706[/C][/ROW]
[ROW][C]16[/C][C]3.3[/C][C]3.12174488327901[/C][C]0.178255116720993[/C][/ROW]
[ROW][C]17[/C][C]3.4[/C][C]3.21079209249730[/C][C]0.189207907502704[/C][/ROW]
[ROW][C]18[/C][C]3.7[/C][C]3.49091922015321[/C][C]0.209080779846791[/C][/ROW]
[ROW][C]19[/C][C]3.7[/C][C]3.48812312060376[/C][C]0.211876879396236[/C][/ROW]
[ROW][C]20[/C][C]3.4[/C][C]3.22504688180216[/C][C]0.174953118197836[/C][/ROW]
[ROW][C]21[/C][C]3.3[/C][C]3.21542500127503[/C][C]0.0845749987249688[/C][/ROW]
[ROW][C]22[/C][C]3[/C][C]3.03811934379503[/C][C]-0.038119343795028[/C][/ROW]
[ROW][C]23[/C][C]3[/C][C]2.99688502217062[/C][C]0.00311497782938105[/C][/ROW]
[ROW][C]24[/C][C]3.3[/C][C]3.17453899190411[/C][C]0.125461008095887[/C][/ROW]
[ROW][C]25[/C][C]3[/C][C]2.97553407482078[/C][C]0.0244659251792153[/C][/ROW]
[ROW][C]26[/C][C]2.9[/C][C]2.7385728139107[/C][C]0.161427186089302[/C][/ROW]
[ROW][C]27[/C][C]2.8[/C][C]2.84248171940682[/C][C]-0.0424817194068233[/C][/ROW]
[ROW][C]28[/C][C]2.5[/C][C]2.63130161907925[/C][C]-0.131301619079252[/C][/ROW]
[ROW][C]29[/C][C]2.6[/C][C]2.60535793561312[/C][C]-0.00535793561312037[/C][/ROW]
[ROW][C]30[/C][C]2.8[/C][C]2.93940850317471[/C][C]-0.139408503174713[/C][/ROW]
[ROW][C]31[/C][C]2.7[/C][C]2.86455877988344[/C][C]-0.164558779883437[/C][/ROW]
[ROW][C]32[/C][C]2.4[/C][C]2.65374674757532[/C][C]-0.253746747575319[/C][/ROW]
[ROW][C]33[/C][C]2.2[/C][C]2.540284127999[/C][C]-0.340284127998998[/C][/ROW]
[ROW][C]34[/C][C]2.1[/C][C]2.35452917651079[/C][C]-0.254529176510794[/C][/ROW]
[ROW][C]35[/C][C]2.1[/C][C]2.40343869484287[/C][C]-0.303438694842869[/C][/ROW]
[ROW][C]36[/C][C]2.3[/C][C]2.52407806372007[/C][C]-0.224078063720071[/C][/ROW]
[ROW][C]37[/C][C]2.1[/C][C]2.33323855510830[/C][C]-0.233238555108303[/C][/ROW]
[ROW][C]38[/C][C]2[/C][C]2.13464426988033[/C][C]-0.134644269880329[/C][/ROW]
[ROW][C]39[/C][C]1.9[/C][C]2.17521250056313[/C][C]-0.275212500563130[/C][/ROW]
[ROW][C]40[/C][C]1.7[/C][C]1.95827047877683[/C][C]-0.258270478776832[/C][/ROW]
[ROW][C]41[/C][C]1.8[/C][C]1.97416223980062[/C][C]-0.174162239800621[/C][/ROW]
[ROW][C]42[/C][C]2.1[/C][C]2.32263422305039[/C][C]-0.22263422305039[/C][/ROW]
[ROW][C]43[/C][C]2[/C][C]2.21955927558012[/C][C]-0.219559275580121[/C][/ROW]
[ROW][C]44[/C][C]1.8[/C][C]2.04071133471789[/C][C]-0.240711334717888[/C][/ROW]
[ROW][C]45[/C][C]1.7[/C][C]1.85286167112732[/C][C]-0.152861671127318[/C][/ROW]
[ROW][C]46[/C][C]1.6[/C][C]1.70418502622745[/C][C]-0.104185026227446[/C][/ROW]
[ROW][C]47[/C][C]1.6[/C][C]1.90682610220827[/C][C]-0.306826102208274[/C][/ROW]
[ROW][C]48[/C][C]1.8[/C][C]1.98536637167525[/C][C]-0.185366371675251[/C][/ROW]
[ROW][C]49[/C][C]1.7[/C][C]1.63946666869945[/C][C]0.0605333313005481[/C][/ROW]
[ROW][C]50[/C][C]1.7[/C][C]1.88910092384811[/C][C]-0.189100923848114[/C][/ROW]
[ROW][C]51[/C][C]1.5[/C][C]1.43807981980539[/C][C]0.0619201801946135[/C][/ROW]
[ROW][C]52[/C][C]1.5[/C][C]1.14485747118008[/C][C]0.355142528819916[/C][/ROW]
[ROW][C]53[/C][C]1.5[/C][C]1.40995266374778[/C][C]0.0900473362522189[/C][/ROW]
[ROW][C]54[/C][C]1.8[/C][C]1.71974056169608[/C][C]0.0802594383039226[/C][/ROW]
[ROW][C]55[/C][C]1.8[/C][C]1.72297003852566[/C][C]0.0770299614743352[/C][/ROW]
[ROW][C]56[/C][C]1.7[/C][C]1.44328584078308[/C][C]0.256714159216920[/C][/ROW]
[ROW][C]57[/C][C]1.7[/C][C]1.26251324828896[/C][C]0.437486751711041[/C][/ROW]
[ROW][C]58[/C][C]1.8[/C][C]1.30465321116495[/C][C]0.495346788835049[/C][/ROW]
[ROW][C]59[/C][C]2[/C][C]1.44423075433032[/C][C]0.555769245669683[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57964&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57964&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
14.14.13486582365492-0.0348658236549180
23.93.843416970340860.0565830296591427
33.83.86198588494237-0.0619858849423663
43.73.84382554768483-0.143825547684825
53.73.79973506834118-0.0997350683411813
64.14.027297491925610.0727025080743886
74.14.004788785407010.0952112145929868
83.83.737209195121550.0627908048784517
93.73.72891595130969-0.0289159513096931
103.53.59851324230178-0.0985132423017812
113.63.548619426447920.0513805735520787
124.13.816016572700570.283983427299435
133.83.616894877716540.183105122283458
143.73.594265022020.105734977979997
153.63.282240075282290.317759924717706
163.33.121744883279010.178255116720993
173.43.210792092497300.189207907502704
183.73.490919220153210.209080779846791
193.73.488123120603760.211876879396236
203.43.225046881802160.174953118197836
213.33.215425001275030.0845749987249688
2233.03811934379503-0.038119343795028
2332.996885022170620.00311497782938105
243.33.174538991904110.125461008095887
2532.975534074820780.0244659251792153
262.92.73857281391070.161427186089302
272.82.84248171940682-0.0424817194068233
282.52.63130161907925-0.131301619079252
292.62.60535793561312-0.00535793561312037
302.82.93940850317471-0.139408503174713
312.72.86455877988344-0.164558779883437
322.42.65374674757532-0.253746747575319
332.22.540284127999-0.340284127998998
342.12.35452917651079-0.254529176510794
352.12.40343869484287-0.303438694842869
362.32.52407806372007-0.224078063720071
372.12.33323855510830-0.233238555108303
3822.13464426988033-0.134644269880329
391.92.17521250056313-0.275212500563130
401.71.95827047877683-0.258270478776832
411.81.97416223980062-0.174162239800621
422.12.32263422305039-0.22263422305039
4322.21955927558012-0.219559275580121
441.82.04071133471789-0.240711334717888
451.71.85286167112732-0.152861671127318
461.61.70418502622745-0.104185026227446
471.61.90682610220827-0.306826102208274
481.81.98536637167525-0.185366371675251
491.71.639466668699450.0605333313005481
501.71.88910092384811-0.189100923848114
511.51.438079819805390.0619201801946135
521.51.144857471180080.355142528819916
531.51.409952663747780.0900473362522189
541.81.719740561696080.0802594383039226
551.81.722970038525660.0770299614743352
561.71.443285840783080.256714159216920
571.71.262513248288960.437486751711041
581.81.304653211164950.495346788835049
5921.444230754330320.555769245669683






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
180.005514626550459170.01102925310091830.99448537344954
190.002906748920837620.005813497841675240.997093251079162
200.001229790817871510.002459581635743020.998770209182128
210.0004351577111134950.000870315422226990.999564842288887
220.000457480682099760.000914961364199520.9995425193179
230.001096201207377250.002192402414754490.998903798792623
240.01198342324747340.02396684649494680.988016576752527
250.01538287493976720.03076574987953450.984617125060233
260.0224352687236490.0448705374472980.977564731276351
270.030182630079780.060365260159560.96981736992022
280.05661207461050590.1132241492210120.943387925389494
290.06736308010905630.1347261602181130.932636919890944
300.1496172345757090.2992344691514190.85038276542429
310.3040914195841340.6081828391682690.695908580415866
320.4083361651127420.8166723302254840.591663834887258
330.426023678965350.85204735793070.57397632103465
340.3415667549473910.6831335098947810.65843324505261
350.2917489755383010.5834979510766030.708251024461699
360.3824814196874310.7649628393748620.617518580312569
370.316672381810940.633344763621880.68332761818906
380.5346340061197140.9307319877605720.465365993880286
390.4085225438358110.8170450876716230.591477456164189
400.5377819961606220.9244360076787560.462218003839378
410.4695717100045630.9391434200091260.530428289995437

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
18 & 0.00551462655045917 & 0.0110292531009183 & 0.99448537344954 \tabularnewline
19 & 0.00290674892083762 & 0.00581349784167524 & 0.997093251079162 \tabularnewline
20 & 0.00122979081787151 & 0.00245958163574302 & 0.998770209182128 \tabularnewline
21 & 0.000435157711113495 & 0.00087031542222699 & 0.999564842288887 \tabularnewline
22 & 0.00045748068209976 & 0.00091496136419952 & 0.9995425193179 \tabularnewline
23 & 0.00109620120737725 & 0.00219240241475449 & 0.998903798792623 \tabularnewline
24 & 0.0119834232474734 & 0.0239668464949468 & 0.988016576752527 \tabularnewline
25 & 0.0153828749397672 & 0.0307657498795345 & 0.984617125060233 \tabularnewline
26 & 0.022435268723649 & 0.044870537447298 & 0.977564731276351 \tabularnewline
27 & 0.03018263007978 & 0.06036526015956 & 0.96981736992022 \tabularnewline
28 & 0.0566120746105059 & 0.113224149221012 & 0.943387925389494 \tabularnewline
29 & 0.0673630801090563 & 0.134726160218113 & 0.932636919890944 \tabularnewline
30 & 0.149617234575709 & 0.299234469151419 & 0.85038276542429 \tabularnewline
31 & 0.304091419584134 & 0.608182839168269 & 0.695908580415866 \tabularnewline
32 & 0.408336165112742 & 0.816672330225484 & 0.591663834887258 \tabularnewline
33 & 0.42602367896535 & 0.8520473579307 & 0.57397632103465 \tabularnewline
34 & 0.341566754947391 & 0.683133509894781 & 0.65843324505261 \tabularnewline
35 & 0.291748975538301 & 0.583497951076603 & 0.708251024461699 \tabularnewline
36 & 0.382481419687431 & 0.764962839374862 & 0.617518580312569 \tabularnewline
37 & 0.31667238181094 & 0.63334476362188 & 0.68332761818906 \tabularnewline
38 & 0.534634006119714 & 0.930731987760572 & 0.465365993880286 \tabularnewline
39 & 0.408522543835811 & 0.817045087671623 & 0.591477456164189 \tabularnewline
40 & 0.537781996160622 & 0.924436007678756 & 0.462218003839378 \tabularnewline
41 & 0.469571710004563 & 0.939143420009126 & 0.530428289995437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57964&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]18[/C][C]0.00551462655045917[/C][C]0.0110292531009183[/C][C]0.99448537344954[/C][/ROW]
[ROW][C]19[/C][C]0.00290674892083762[/C][C]0.00581349784167524[/C][C]0.997093251079162[/C][/ROW]
[ROW][C]20[/C][C]0.00122979081787151[/C][C]0.00245958163574302[/C][C]0.998770209182128[/C][/ROW]
[ROW][C]21[/C][C]0.000435157711113495[/C][C]0.00087031542222699[/C][C]0.999564842288887[/C][/ROW]
[ROW][C]22[/C][C]0.00045748068209976[/C][C]0.00091496136419952[/C][C]0.9995425193179[/C][/ROW]
[ROW][C]23[/C][C]0.00109620120737725[/C][C]0.00219240241475449[/C][C]0.998903798792623[/C][/ROW]
[ROW][C]24[/C][C]0.0119834232474734[/C][C]0.0239668464949468[/C][C]0.988016576752527[/C][/ROW]
[ROW][C]25[/C][C]0.0153828749397672[/C][C]0.0307657498795345[/C][C]0.984617125060233[/C][/ROW]
[ROW][C]26[/C][C]0.022435268723649[/C][C]0.044870537447298[/C][C]0.977564731276351[/C][/ROW]
[ROW][C]27[/C][C]0.03018263007978[/C][C]0.06036526015956[/C][C]0.96981736992022[/C][/ROW]
[ROW][C]28[/C][C]0.0566120746105059[/C][C]0.113224149221012[/C][C]0.943387925389494[/C][/ROW]
[ROW][C]29[/C][C]0.0673630801090563[/C][C]0.134726160218113[/C][C]0.932636919890944[/C][/ROW]
[ROW][C]30[/C][C]0.149617234575709[/C][C]0.299234469151419[/C][C]0.85038276542429[/C][/ROW]
[ROW][C]31[/C][C]0.304091419584134[/C][C]0.608182839168269[/C][C]0.695908580415866[/C][/ROW]
[ROW][C]32[/C][C]0.408336165112742[/C][C]0.816672330225484[/C][C]0.591663834887258[/C][/ROW]
[ROW][C]33[/C][C]0.42602367896535[/C][C]0.8520473579307[/C][C]0.57397632103465[/C][/ROW]
[ROW][C]34[/C][C]0.341566754947391[/C][C]0.683133509894781[/C][C]0.65843324505261[/C][/ROW]
[ROW][C]35[/C][C]0.291748975538301[/C][C]0.583497951076603[/C][C]0.708251024461699[/C][/ROW]
[ROW][C]36[/C][C]0.382481419687431[/C][C]0.764962839374862[/C][C]0.617518580312569[/C][/ROW]
[ROW][C]37[/C][C]0.31667238181094[/C][C]0.63334476362188[/C][C]0.68332761818906[/C][/ROW]
[ROW][C]38[/C][C]0.534634006119714[/C][C]0.930731987760572[/C][C]0.465365993880286[/C][/ROW]
[ROW][C]39[/C][C]0.408522543835811[/C][C]0.817045087671623[/C][C]0.591477456164189[/C][/ROW]
[ROW][C]40[/C][C]0.537781996160622[/C][C]0.924436007678756[/C][C]0.462218003839378[/C][/ROW]
[ROW][C]41[/C][C]0.469571710004563[/C][C]0.939143420009126[/C][C]0.530428289995437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57964&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57964&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
180.005514626550459170.01102925310091830.99448537344954
190.002906748920837620.005813497841675240.997093251079162
200.001229790817871510.002459581635743020.998770209182128
210.0004351577111134950.000870315422226990.999564842288887
220.000457480682099760.000914961364199520.9995425193179
230.001096201207377250.002192402414754490.998903798792623
240.01198342324747340.02396684649494680.988016576752527
250.01538287493976720.03076574987953450.984617125060233
260.0224352687236490.0448705374472980.977564731276351
270.030182630079780.060365260159560.96981736992022
280.05661207461050590.1132241492210120.943387925389494
290.06736308010905630.1347261602181130.932636919890944
300.1496172345757090.2992344691514190.85038276542429
310.3040914195841340.6081828391682690.695908580415866
320.4083361651127420.8166723302254840.591663834887258
330.426023678965350.85204735793070.57397632103465
340.3415667549473910.6831335098947810.65843324505261
350.2917489755383010.5834979510766030.708251024461699
360.3824814196874310.7649628393748620.617518580312569
370.316672381810940.633344763621880.68332761818906
380.5346340061197140.9307319877605720.465365993880286
390.4085225438358110.8170450876716230.591477456164189
400.5377819961606220.9244360076787560.462218003839378
410.4695717100045630.9391434200091260.530428289995437






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.208333333333333NOK
5% type I error level90.375NOK
10% type I error level100.416666666666667NOK

\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 & 5 & 0.208333333333333 & NOK \tabularnewline
5% type I error level & 9 & 0.375 & NOK \tabularnewline
10% type I error level & 10 & 0.416666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57964&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]5[/C][C]0.208333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]9[/C][C]0.375[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]10[/C][C]0.416666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57964&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57964&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 level50.208333333333333NOK
5% type I error level90.375NOK
10% type I error level100.416666666666667NOK


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')
}