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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 06:15:54 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258723056xarh0f8fc7fxppx.htm/, Retrieved Thu, 28 Mar 2024 15:15:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58127, Retrieved Thu, 28 Mar 2024 15:15:27 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-20 12:09:50] [badc6a9acdc45286bea7f74742e15a21]
-   PD      [Multiple Regression] [] [2009-11-20 12:36:54] [badc6a9acdc45286bea7f74742e15a21]
-   P         [Multiple Regression] [] [2009-11-20 12:53:28] [badc6a9acdc45286bea7f74742e15a21]
-   P             [Multiple Regression] [] [2009-11-20 13:15:54] [fbab597368601c68e80be601720d8ff9] [Current]
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Dataseries X:
1.4	2
1.2	2
1	2
1.7	2
2.4	2
2	2
2.1	2
2	2
1.8	2
2.7	2
2.3	2
1.9	2
2	2
2.3	2
2.8	2
2.4	2
2.3	2
2.7	2
2.7	2
2.9	2
3	2
2.2	2
2.3	2
2.8	2.21
2.8	2.25
2.8	2.25
2.2	2.45
2.6	2.5
2.8	2.5
2.5	2.64
2.4	2.75
2.3	2.93
1.9	3
1.7	3.17
2	3.25
2.1	3.39
1.7	3.5
1.8	3.5
1.8	3.65
1.8	3.75
1.3	3.75
1.3	3.9
1.3	4
1.2	4
1.4	4
2.2	4
2.9	4
3.1	4
3.5	4
3.6	4
4.4	4
4.1	4
5.1	4
5.8	4
5.9	4.18
5.4	4.25
5.5	4.25
4.8	3.97
3.2	3.42
2.7	2.75




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58127&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58127&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58127&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.07836940516536 -0.776305498871819X[t] + 0.482562816317725M1[t] + 0.468406500301148M2[t] + 0.548591569205598M3[t] + 0.577724418155176M4[t] + 0.7635681021386M5[t] + 0.814437505056589M6[t] + 0.820833017952014M7[t] + 0.665491976879028M8[t] + 0.562203937846657M9[t] + 0.47096890085490M10[t] + 0.143839867944373M11[t] + 0.0741563160165766t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  2.07836940516536 -0.776305498871819X[t] +  0.482562816317725M1[t] +  0.468406500301148M2[t] +  0.548591569205598M3[t] +  0.577724418155176M4[t] +  0.7635681021386M5[t] +  0.814437505056589M6[t] +  0.820833017952014M7[t] +  0.665491976879028M8[t] +  0.562203937846657M9[t] +  0.47096890085490M10[t] +  0.143839867944373M11[t] +  0.0741563160165766t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58127&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  2.07836940516536 -0.776305498871819X[t] +  0.482562816317725M1[t] +  0.468406500301148M2[t] +  0.548591569205598M3[t] +  0.577724418155176M4[t] +  0.7635681021386M5[t] +  0.814437505056589M6[t] +  0.820833017952014M7[t] +  0.665491976879028M8[t] +  0.562203937846657M9[t] +  0.47096890085490M10[t] +  0.143839867944373M11[t] +  0.0741563160165766t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58127&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58127&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.07836940516536 -0.776305498871819X[t] + 0.482562816317725M1[t] + 0.468406500301148M2[t] + 0.548591569205598M3[t] + 0.577724418155176M4[t] + 0.7635681021386M5[t] + 0.814437505056589M6[t] + 0.820833017952014M7[t] + 0.665491976879028M8[t] + 0.562203937846657M9[t] + 0.47096890085490M10[t] + 0.143839867944373M11[t] + 0.0741563160165766t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.078369405165360.7028562.9570.0048890.002445
X-0.7763054988718190.379015-2.04820.0462710.023135
M10.4825628163177250.6753220.71460.4784880.239244
M20.4684065003011480.6706390.69840.4884130.244207
M30.5485915692055980.671550.81690.4181950.209097
M40.5777244181551760.6694560.8630.3926280.196314
M50.76356810213860.6654211.14750.2571090.128555
M60.8144375050565890.6655721.22370.227310.113655
M70.8208330179520140.667311.23010.2249280.112464
M80.6654919768790280.6671320.99750.3237210.16186
M90.5622039378466570.6644190.84620.4018440.200922
M100.470968900854900.6599110.71370.4790270.239514
M110.1438398679443730.6541870.21990.8269410.41347
t0.07415631601657660.0194193.81874e-042e-04

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 2.07836940516536 & 0.702856 & 2.957 & 0.004889 & 0.002445 \tabularnewline
X & -0.776305498871819 & 0.379015 & -2.0482 & 0.046271 & 0.023135 \tabularnewline
M1 & 0.482562816317725 & 0.675322 & 0.7146 & 0.478488 & 0.239244 \tabularnewline
M2 & 0.468406500301148 & 0.670639 & 0.6984 & 0.488413 & 0.244207 \tabularnewline
M3 & 0.548591569205598 & 0.67155 & 0.8169 & 0.418195 & 0.209097 \tabularnewline
M4 & 0.577724418155176 & 0.669456 & 0.863 & 0.392628 & 0.196314 \tabularnewline
M5 & 0.7635681021386 & 0.665421 & 1.1475 & 0.257109 & 0.128555 \tabularnewline
M6 & 0.814437505056589 & 0.665572 & 1.2237 & 0.22731 & 0.113655 \tabularnewline
M7 & 0.820833017952014 & 0.66731 & 1.2301 & 0.224928 & 0.112464 \tabularnewline
M8 & 0.665491976879028 & 0.667132 & 0.9975 & 0.323721 & 0.16186 \tabularnewline
M9 & 0.562203937846657 & 0.664419 & 0.8462 & 0.401844 & 0.200922 \tabularnewline
M10 & 0.47096890085490 & 0.659911 & 0.7137 & 0.479027 & 0.239514 \tabularnewline
M11 & 0.143839867944373 & 0.654187 & 0.2199 & 0.826941 & 0.41347 \tabularnewline
t & 0.0741563160165766 & 0.019419 & 3.8187 & 4e-04 & 2e-04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58127&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]2.07836940516536[/C][C]0.702856[/C][C]2.957[/C][C]0.004889[/C][C]0.002445[/C][/ROW]
[ROW][C]X[/C][C]-0.776305498871819[/C][C]0.379015[/C][C]-2.0482[/C][C]0.046271[/C][C]0.023135[/C][/ROW]
[ROW][C]M1[/C][C]0.482562816317725[/C][C]0.675322[/C][C]0.7146[/C][C]0.478488[/C][C]0.239244[/C][/ROW]
[ROW][C]M2[/C][C]0.468406500301148[/C][C]0.670639[/C][C]0.6984[/C][C]0.488413[/C][C]0.244207[/C][/ROW]
[ROW][C]M3[/C][C]0.548591569205598[/C][C]0.67155[/C][C]0.8169[/C][C]0.418195[/C][C]0.209097[/C][/ROW]
[ROW][C]M4[/C][C]0.577724418155176[/C][C]0.669456[/C][C]0.863[/C][C]0.392628[/C][C]0.196314[/C][/ROW]
[ROW][C]M5[/C][C]0.7635681021386[/C][C]0.665421[/C][C]1.1475[/C][C]0.257109[/C][C]0.128555[/C][/ROW]
[ROW][C]M6[/C][C]0.814437505056589[/C][C]0.665572[/C][C]1.2237[/C][C]0.22731[/C][C]0.113655[/C][/ROW]
[ROW][C]M7[/C][C]0.820833017952014[/C][C]0.66731[/C][C]1.2301[/C][C]0.224928[/C][C]0.112464[/C][/ROW]
[ROW][C]M8[/C][C]0.665491976879028[/C][C]0.667132[/C][C]0.9975[/C][C]0.323721[/C][C]0.16186[/C][/ROW]
[ROW][C]M9[/C][C]0.562203937846657[/C][C]0.664419[/C][C]0.8462[/C][C]0.401844[/C][C]0.200922[/C][/ROW]
[ROW][C]M10[/C][C]0.47096890085490[/C][C]0.659911[/C][C]0.7137[/C][C]0.479027[/C][C]0.239514[/C][/ROW]
[ROW][C]M11[/C][C]0.143839867944373[/C][C]0.654187[/C][C]0.2199[/C][C]0.826941[/C][C]0.41347[/C][/ROW]
[ROW][C]t[/C][C]0.0741563160165766[/C][C]0.019419[/C][C]3.8187[/C][C]4e-04[/C][C]2e-04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58127&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58127&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.078369405165360.7028562.9570.0048890.002445
X-0.7763054988718190.379015-2.04820.0462710.023135
M10.4825628163177250.6753220.71460.4784880.239244
M20.4684065003011480.6706390.69840.4884130.244207
M30.5485915692055980.671550.81690.4181950.209097
M40.5777244181551760.6694560.8630.3926280.196314
M50.76356810213860.6654211.14750.2571090.128555
M60.8144375050565890.6655721.22370.227310.113655
M70.8208330179520140.667311.23010.2249280.112464
M80.6654919768790280.6671320.99750.3237210.16186
M90.5622039378466570.6644190.84620.4018440.200922
M100.470968900854900.6599110.71370.4790270.239514
M110.1438398679443730.6541870.21990.8269410.41347
t0.07415631601657660.0194193.81874e-042e-04







Multiple Linear Regression - Regression Statistics
Multiple R0.624576730303413
R-squared0.390096092036502
Adjusted R-squared0.217731944133774
F-TEST (value)2.26320900711121
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.0211618067216435
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.03215027135484
Sum Squared Residuals49.0053724022618

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.624576730303413 \tabularnewline
R-squared & 0.390096092036502 \tabularnewline
Adjusted R-squared & 0.217731944133774 \tabularnewline
F-TEST (value) & 2.26320900711121 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.0211618067216435 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.03215027135484 \tabularnewline
Sum Squared Residuals & 49.0053724022618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58127&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.624576730303413[/C][/ROW]
[ROW][C]R-squared[/C][C]0.390096092036502[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.217731944133774[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.26320900711121[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0.0211618067216435[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.03215027135484[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]49.0053724022618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58127&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58127&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.624576730303413
R-squared0.390096092036502
Adjusted R-squared0.217731944133774
F-TEST (value)2.26320900711121
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.0211618067216435
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.03215027135484
Sum Squared Residuals49.0053724022618







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.41.082477539756020.317522460243977
21.21.142477539756020.057522460243976
311.29681892467705-0.296818924677053
41.71.400108089643210.299891910356793
52.41.660108089643210.739891910356793
621.785133808577770.214866191422228
72.11.865685637489770.234314362510226
821.784500912433370.215499087566634
91.81.755369189417570.0446308105824288
102.71.738290468442390.961709531557609
112.31.485317751548440.81468224845156
121.91.415634199620640.484365800379356
1321.972353331954950.0276466680450549
142.32.032353331954940.267646668045055
152.82.186694716875970.613305283124028
162.42.289983881842130.110016118157873
172.32.54998388184213-0.249983881842126
182.72.675009600776690.0249903992233081
192.72.75556142968869-0.0555614296886936
202.92.674376704632290.225623295367715
2132.645244981616490.35475501838351
222.22.62816626064131-0.42816626064131
232.32.37519354374736-0.0751935437473595
242.82.142485837056480.657514162943519
252.82.668152749435910.13184725056409
262.82.728152749435910.0718472505640904
272.22.72723303458257-0.527233034582573
282.62.79170692460514-0.191706924605136
292.83.05170692460514-0.251706924605136
302.53.06804987369765-0.568049873697647
312.43.06320809773375-0.66320809773375
322.32.84228838288041-0.542288382880413
331.92.75881527494359-0.858815274943591
341.72.6097646191602-0.909764619160202
3522.29468746235651-0.294687462356506
362.12.11632114058665-0.0163211405866546
371.72.58764666804506-0.887646668045056
381.82.64764666804506-0.847646668045056
391.82.68554222813531-0.88554222813531
401.82.71120084321428-0.911200843214282
411.32.97120084321428-1.67120084321428
421.32.97978073731808-1.67978073731808
431.32.98270201634290-1.68270201634290
441.22.90151729128649-1.70151729128649
451.42.87238556827069-1.47238556827069
462.22.85530684729551-0.655306847295512
472.92.602334130401560.297665869598439
483.12.532650578473760.567349421526235
493.53.089369710808070.410630289191934
503.63.149369710808070.450630289191934
514.43.303711095729091.09628890427091
524.13.407000260695250.692999739304753
535.13.667000260695251.43299973930475
545.83.792025979629812.00797402037019
555.93.732842818744892.16715718125511
565.43.597316708767451.80268329123255
575.53.568184985751661.93181501424834
584.83.768471804460591.03152819553941
593.23.94246711194613-0.742467111946135
602.74.39290824426246-1.69290824426246

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.4 & 1.08247753975602 & 0.317522460243977 \tabularnewline
2 & 1.2 & 1.14247753975602 & 0.057522460243976 \tabularnewline
3 & 1 & 1.29681892467705 & -0.296818924677053 \tabularnewline
4 & 1.7 & 1.40010808964321 & 0.299891910356793 \tabularnewline
5 & 2.4 & 1.66010808964321 & 0.739891910356793 \tabularnewline
6 & 2 & 1.78513380857777 & 0.214866191422228 \tabularnewline
7 & 2.1 & 1.86568563748977 & 0.234314362510226 \tabularnewline
8 & 2 & 1.78450091243337 & 0.215499087566634 \tabularnewline
9 & 1.8 & 1.75536918941757 & 0.0446308105824288 \tabularnewline
10 & 2.7 & 1.73829046844239 & 0.961709531557609 \tabularnewline
11 & 2.3 & 1.48531775154844 & 0.81468224845156 \tabularnewline
12 & 1.9 & 1.41563419962064 & 0.484365800379356 \tabularnewline
13 & 2 & 1.97235333195495 & 0.0276466680450549 \tabularnewline
14 & 2.3 & 2.03235333195494 & 0.267646668045055 \tabularnewline
15 & 2.8 & 2.18669471687597 & 0.613305283124028 \tabularnewline
16 & 2.4 & 2.28998388184213 & 0.110016118157873 \tabularnewline
17 & 2.3 & 2.54998388184213 & -0.249983881842126 \tabularnewline
18 & 2.7 & 2.67500960077669 & 0.0249903992233081 \tabularnewline
19 & 2.7 & 2.75556142968869 & -0.0555614296886936 \tabularnewline
20 & 2.9 & 2.67437670463229 & 0.225623295367715 \tabularnewline
21 & 3 & 2.64524498161649 & 0.35475501838351 \tabularnewline
22 & 2.2 & 2.62816626064131 & -0.42816626064131 \tabularnewline
23 & 2.3 & 2.37519354374736 & -0.0751935437473595 \tabularnewline
24 & 2.8 & 2.14248583705648 & 0.657514162943519 \tabularnewline
25 & 2.8 & 2.66815274943591 & 0.13184725056409 \tabularnewline
26 & 2.8 & 2.72815274943591 & 0.0718472505640904 \tabularnewline
27 & 2.2 & 2.72723303458257 & -0.527233034582573 \tabularnewline
28 & 2.6 & 2.79170692460514 & -0.191706924605136 \tabularnewline
29 & 2.8 & 3.05170692460514 & -0.251706924605136 \tabularnewline
30 & 2.5 & 3.06804987369765 & -0.568049873697647 \tabularnewline
31 & 2.4 & 3.06320809773375 & -0.66320809773375 \tabularnewline
32 & 2.3 & 2.84228838288041 & -0.542288382880413 \tabularnewline
33 & 1.9 & 2.75881527494359 & -0.858815274943591 \tabularnewline
34 & 1.7 & 2.6097646191602 & -0.909764619160202 \tabularnewline
35 & 2 & 2.29468746235651 & -0.294687462356506 \tabularnewline
36 & 2.1 & 2.11632114058665 & -0.0163211405866546 \tabularnewline
37 & 1.7 & 2.58764666804506 & -0.887646668045056 \tabularnewline
38 & 1.8 & 2.64764666804506 & -0.847646668045056 \tabularnewline
39 & 1.8 & 2.68554222813531 & -0.88554222813531 \tabularnewline
40 & 1.8 & 2.71120084321428 & -0.911200843214282 \tabularnewline
41 & 1.3 & 2.97120084321428 & -1.67120084321428 \tabularnewline
42 & 1.3 & 2.97978073731808 & -1.67978073731808 \tabularnewline
43 & 1.3 & 2.98270201634290 & -1.68270201634290 \tabularnewline
44 & 1.2 & 2.90151729128649 & -1.70151729128649 \tabularnewline
45 & 1.4 & 2.87238556827069 & -1.47238556827069 \tabularnewline
46 & 2.2 & 2.85530684729551 & -0.655306847295512 \tabularnewline
47 & 2.9 & 2.60233413040156 & 0.297665869598439 \tabularnewline
48 & 3.1 & 2.53265057847376 & 0.567349421526235 \tabularnewline
49 & 3.5 & 3.08936971080807 & 0.410630289191934 \tabularnewline
50 & 3.6 & 3.14936971080807 & 0.450630289191934 \tabularnewline
51 & 4.4 & 3.30371109572909 & 1.09628890427091 \tabularnewline
52 & 4.1 & 3.40700026069525 & 0.692999739304753 \tabularnewline
53 & 5.1 & 3.66700026069525 & 1.43299973930475 \tabularnewline
54 & 5.8 & 3.79202597962981 & 2.00797402037019 \tabularnewline
55 & 5.9 & 3.73284281874489 & 2.16715718125511 \tabularnewline
56 & 5.4 & 3.59731670876745 & 1.80268329123255 \tabularnewline
57 & 5.5 & 3.56818498575166 & 1.93181501424834 \tabularnewline
58 & 4.8 & 3.76847180446059 & 1.03152819553941 \tabularnewline
59 & 3.2 & 3.94246711194613 & -0.742467111946135 \tabularnewline
60 & 2.7 & 4.39290824426246 & -1.69290824426246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58127&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]1.4[/C][C]1.08247753975602[/C][C]0.317522460243977[/C][/ROW]
[ROW][C]2[/C][C]1.2[/C][C]1.14247753975602[/C][C]0.057522460243976[/C][/ROW]
[ROW][C]3[/C][C]1[/C][C]1.29681892467705[/C][C]-0.296818924677053[/C][/ROW]
[ROW][C]4[/C][C]1.7[/C][C]1.40010808964321[/C][C]0.299891910356793[/C][/ROW]
[ROW][C]5[/C][C]2.4[/C][C]1.66010808964321[/C][C]0.739891910356793[/C][/ROW]
[ROW][C]6[/C][C]2[/C][C]1.78513380857777[/C][C]0.214866191422228[/C][/ROW]
[ROW][C]7[/C][C]2.1[/C][C]1.86568563748977[/C][C]0.234314362510226[/C][/ROW]
[ROW][C]8[/C][C]2[/C][C]1.78450091243337[/C][C]0.215499087566634[/C][/ROW]
[ROW][C]9[/C][C]1.8[/C][C]1.75536918941757[/C][C]0.0446308105824288[/C][/ROW]
[ROW][C]10[/C][C]2.7[/C][C]1.73829046844239[/C][C]0.961709531557609[/C][/ROW]
[ROW][C]11[/C][C]2.3[/C][C]1.48531775154844[/C][C]0.81468224845156[/C][/ROW]
[ROW][C]12[/C][C]1.9[/C][C]1.41563419962064[/C][C]0.484365800379356[/C][/ROW]
[ROW][C]13[/C][C]2[/C][C]1.97235333195495[/C][C]0.0276466680450549[/C][/ROW]
[ROW][C]14[/C][C]2.3[/C][C]2.03235333195494[/C][C]0.267646668045055[/C][/ROW]
[ROW][C]15[/C][C]2.8[/C][C]2.18669471687597[/C][C]0.613305283124028[/C][/ROW]
[ROW][C]16[/C][C]2.4[/C][C]2.28998388184213[/C][C]0.110016118157873[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]2.54998388184213[/C][C]-0.249983881842126[/C][/ROW]
[ROW][C]18[/C][C]2.7[/C][C]2.67500960077669[/C][C]0.0249903992233081[/C][/ROW]
[ROW][C]19[/C][C]2.7[/C][C]2.75556142968869[/C][C]-0.0555614296886936[/C][/ROW]
[ROW][C]20[/C][C]2.9[/C][C]2.67437670463229[/C][C]0.225623295367715[/C][/ROW]
[ROW][C]21[/C][C]3[/C][C]2.64524498161649[/C][C]0.35475501838351[/C][/ROW]
[ROW][C]22[/C][C]2.2[/C][C]2.62816626064131[/C][C]-0.42816626064131[/C][/ROW]
[ROW][C]23[/C][C]2.3[/C][C]2.37519354374736[/C][C]-0.0751935437473595[/C][/ROW]
[ROW][C]24[/C][C]2.8[/C][C]2.14248583705648[/C][C]0.657514162943519[/C][/ROW]
[ROW][C]25[/C][C]2.8[/C][C]2.66815274943591[/C][C]0.13184725056409[/C][/ROW]
[ROW][C]26[/C][C]2.8[/C][C]2.72815274943591[/C][C]0.0718472505640904[/C][/ROW]
[ROW][C]27[/C][C]2.2[/C][C]2.72723303458257[/C][C]-0.527233034582573[/C][/ROW]
[ROW][C]28[/C][C]2.6[/C][C]2.79170692460514[/C][C]-0.191706924605136[/C][/ROW]
[ROW][C]29[/C][C]2.8[/C][C]3.05170692460514[/C][C]-0.251706924605136[/C][/ROW]
[ROW][C]30[/C][C]2.5[/C][C]3.06804987369765[/C][C]-0.568049873697647[/C][/ROW]
[ROW][C]31[/C][C]2.4[/C][C]3.06320809773375[/C][C]-0.66320809773375[/C][/ROW]
[ROW][C]32[/C][C]2.3[/C][C]2.84228838288041[/C][C]-0.542288382880413[/C][/ROW]
[ROW][C]33[/C][C]1.9[/C][C]2.75881527494359[/C][C]-0.858815274943591[/C][/ROW]
[ROW][C]34[/C][C]1.7[/C][C]2.6097646191602[/C][C]-0.909764619160202[/C][/ROW]
[ROW][C]35[/C][C]2[/C][C]2.29468746235651[/C][C]-0.294687462356506[/C][/ROW]
[ROW][C]36[/C][C]2.1[/C][C]2.11632114058665[/C][C]-0.0163211405866546[/C][/ROW]
[ROW][C]37[/C][C]1.7[/C][C]2.58764666804506[/C][C]-0.887646668045056[/C][/ROW]
[ROW][C]38[/C][C]1.8[/C][C]2.64764666804506[/C][C]-0.847646668045056[/C][/ROW]
[ROW][C]39[/C][C]1.8[/C][C]2.68554222813531[/C][C]-0.88554222813531[/C][/ROW]
[ROW][C]40[/C][C]1.8[/C][C]2.71120084321428[/C][C]-0.911200843214282[/C][/ROW]
[ROW][C]41[/C][C]1.3[/C][C]2.97120084321428[/C][C]-1.67120084321428[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]2.97978073731808[/C][C]-1.67978073731808[/C][/ROW]
[ROW][C]43[/C][C]1.3[/C][C]2.98270201634290[/C][C]-1.68270201634290[/C][/ROW]
[ROW][C]44[/C][C]1.2[/C][C]2.90151729128649[/C][C]-1.70151729128649[/C][/ROW]
[ROW][C]45[/C][C]1.4[/C][C]2.87238556827069[/C][C]-1.47238556827069[/C][/ROW]
[ROW][C]46[/C][C]2.2[/C][C]2.85530684729551[/C][C]-0.655306847295512[/C][/ROW]
[ROW][C]47[/C][C]2.9[/C][C]2.60233413040156[/C][C]0.297665869598439[/C][/ROW]
[ROW][C]48[/C][C]3.1[/C][C]2.53265057847376[/C][C]0.567349421526235[/C][/ROW]
[ROW][C]49[/C][C]3.5[/C][C]3.08936971080807[/C][C]0.410630289191934[/C][/ROW]
[ROW][C]50[/C][C]3.6[/C][C]3.14936971080807[/C][C]0.450630289191934[/C][/ROW]
[ROW][C]51[/C][C]4.4[/C][C]3.30371109572909[/C][C]1.09628890427091[/C][/ROW]
[ROW][C]52[/C][C]4.1[/C][C]3.40700026069525[/C][C]0.692999739304753[/C][/ROW]
[ROW][C]53[/C][C]5.1[/C][C]3.66700026069525[/C][C]1.43299973930475[/C][/ROW]
[ROW][C]54[/C][C]5.8[/C][C]3.79202597962981[/C][C]2.00797402037019[/C][/ROW]
[ROW][C]55[/C][C]5.9[/C][C]3.73284281874489[/C][C]2.16715718125511[/C][/ROW]
[ROW][C]56[/C][C]5.4[/C][C]3.59731670876745[/C][C]1.80268329123255[/C][/ROW]
[ROW][C]57[/C][C]5.5[/C][C]3.56818498575166[/C][C]1.93181501424834[/C][/ROW]
[ROW][C]58[/C][C]4.8[/C][C]3.76847180446059[/C][C]1.03152819553941[/C][/ROW]
[ROW][C]59[/C][C]3.2[/C][C]3.94246711194613[/C][C]-0.742467111946135[/C][/ROW]
[ROW][C]60[/C][C]2.7[/C][C]4.39290824426246[/C][C]-1.69290824426246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58127&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58127&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.41.082477539756020.317522460243977
21.21.142477539756020.057522460243976
311.29681892467705-0.296818924677053
41.71.400108089643210.299891910356793
52.41.660108089643210.739891910356793
621.785133808577770.214866191422228
72.11.865685637489770.234314362510226
821.784500912433370.215499087566634
91.81.755369189417570.0446308105824288
102.71.738290468442390.961709531557609
112.31.485317751548440.81468224845156
121.91.415634199620640.484365800379356
1321.972353331954950.0276466680450549
142.32.032353331954940.267646668045055
152.82.186694716875970.613305283124028
162.42.289983881842130.110016118157873
172.32.54998388184213-0.249983881842126
182.72.675009600776690.0249903992233081
192.72.75556142968869-0.0555614296886936
202.92.674376704632290.225623295367715
2132.645244981616490.35475501838351
222.22.62816626064131-0.42816626064131
232.32.37519354374736-0.0751935437473595
242.82.142485837056480.657514162943519
252.82.668152749435910.13184725056409
262.82.728152749435910.0718472505640904
272.22.72723303458257-0.527233034582573
282.62.79170692460514-0.191706924605136
292.83.05170692460514-0.251706924605136
302.53.06804987369765-0.568049873697647
312.43.06320809773375-0.66320809773375
322.32.84228838288041-0.542288382880413
331.92.75881527494359-0.858815274943591
341.72.6097646191602-0.909764619160202
3522.29468746235651-0.294687462356506
362.12.11632114058665-0.0163211405866546
371.72.58764666804506-0.887646668045056
381.82.64764666804506-0.847646668045056
391.82.68554222813531-0.88554222813531
401.82.71120084321428-0.911200843214282
411.32.97120084321428-1.67120084321428
421.32.97978073731808-1.67978073731808
431.32.98270201634290-1.68270201634290
441.22.90151729128649-1.70151729128649
451.42.87238556827069-1.47238556827069
462.22.85530684729551-0.655306847295512
472.92.602334130401560.297665869598439
483.12.532650578473760.567349421526235
493.53.089369710808070.410630289191934
503.63.149369710808070.450630289191934
514.43.303711095729091.09628890427091
524.13.407000260695250.692999739304753
535.13.667000260695251.43299973930475
545.83.792025979629812.00797402037019
555.93.732842818744892.16715718125511
565.43.597316708767451.80268329123255
575.53.568184985751661.93181501424834
584.83.768471804460591.03152819553941
593.23.94246711194613-0.742467111946135
602.74.39290824426246-1.69290824426246







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1260075415665080.2520150831330160.873992458433492
180.04786747211171470.09573494422342950.952132527888285
190.01682422977932900.03364845955865810.98317577022067
200.005493324082715540.01098664816543110.994506675917284
210.00212885514836790.00425771029673580.997871144851632
220.004252879414654460.008505758829308920.995747120585346
230.002393004712019780.004786009424039550.99760699528798
240.001216210111160590.002432420222321190.99878378988884
250.0004768569079774150.000953713815954830.999523143092023
260.0001866820923049660.0003733641846099310.999813317907695
270.0001088855747223190.0002177711494446390.999891114425278
284.14383915722353e-058.28767831444706e-050.999958561608428
291.72779775627681e-053.45559551255361e-050.999982722022437
306.55690455161648e-061.31138091032330e-050.999993443095448
312.50258945404973e-065.00517890809946e-060.999997497410546
321.36765347839472e-062.73530695678945e-060.999998632346522
339.789827975231e-071.9579655950462e-060.999999021017203
348.31081662289104e-071.66216332457821e-060.999999168918338
354.75537323903766e-069.51074647807532e-060.999995244626761
366.07590257616875e-050.0001215180515233750.999939240974238
370.0001332117460737370.0002664234921474740.999866788253926
380.001694840100952960.003389680201905920.998305159899047
390.004790877396164250.00958175479232850.995209122603836
400.05270314162732460.1054062832546490.947296858372675
410.04995681261400360.09991362522800710.950043187385996
420.06979864947804530.1395972989560910.930201350521955
430.1130313657849530.2260627315699060.886968634215047

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.126007541566508 & 0.252015083133016 & 0.873992458433492 \tabularnewline
18 & 0.0478674721117147 & 0.0957349442234295 & 0.952132527888285 \tabularnewline
19 & 0.0168242297793290 & 0.0336484595586581 & 0.98317577022067 \tabularnewline
20 & 0.00549332408271554 & 0.0109866481654311 & 0.994506675917284 \tabularnewline
21 & 0.0021288551483679 & 0.0042577102967358 & 0.997871144851632 \tabularnewline
22 & 0.00425287941465446 & 0.00850575882930892 & 0.995747120585346 \tabularnewline
23 & 0.00239300471201978 & 0.00478600942403955 & 0.99760699528798 \tabularnewline
24 & 0.00121621011116059 & 0.00243242022232119 & 0.99878378988884 \tabularnewline
25 & 0.000476856907977415 & 0.00095371381595483 & 0.999523143092023 \tabularnewline
26 & 0.000186682092304966 & 0.000373364184609931 & 0.999813317907695 \tabularnewline
27 & 0.000108885574722319 & 0.000217771149444639 & 0.999891114425278 \tabularnewline
28 & 4.14383915722353e-05 & 8.28767831444706e-05 & 0.999958561608428 \tabularnewline
29 & 1.72779775627681e-05 & 3.45559551255361e-05 & 0.999982722022437 \tabularnewline
30 & 6.55690455161648e-06 & 1.31138091032330e-05 & 0.999993443095448 \tabularnewline
31 & 2.50258945404973e-06 & 5.00517890809946e-06 & 0.999997497410546 \tabularnewline
32 & 1.36765347839472e-06 & 2.73530695678945e-06 & 0.999998632346522 \tabularnewline
33 & 9.789827975231e-07 & 1.9579655950462e-06 & 0.999999021017203 \tabularnewline
34 & 8.31081662289104e-07 & 1.66216332457821e-06 & 0.999999168918338 \tabularnewline
35 & 4.75537323903766e-06 & 9.51074647807532e-06 & 0.999995244626761 \tabularnewline
36 & 6.07590257616875e-05 & 0.000121518051523375 & 0.999939240974238 \tabularnewline
37 & 0.000133211746073737 & 0.000266423492147474 & 0.999866788253926 \tabularnewline
38 & 0.00169484010095296 & 0.00338968020190592 & 0.998305159899047 \tabularnewline
39 & 0.00479087739616425 & 0.0095817547923285 & 0.995209122603836 \tabularnewline
40 & 0.0527031416273246 & 0.105406283254649 & 0.947296858372675 \tabularnewline
41 & 0.0499568126140036 & 0.0999136252280071 & 0.950043187385996 \tabularnewline
42 & 0.0697986494780453 & 0.139597298956091 & 0.930201350521955 \tabularnewline
43 & 0.113031365784953 & 0.226062731569906 & 0.886968634215047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58127&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]17[/C][C]0.126007541566508[/C][C]0.252015083133016[/C][C]0.873992458433492[/C][/ROW]
[ROW][C]18[/C][C]0.0478674721117147[/C][C]0.0957349442234295[/C][C]0.952132527888285[/C][/ROW]
[ROW][C]19[/C][C]0.0168242297793290[/C][C]0.0336484595586581[/C][C]0.98317577022067[/C][/ROW]
[ROW][C]20[/C][C]0.00549332408271554[/C][C]0.0109866481654311[/C][C]0.994506675917284[/C][/ROW]
[ROW][C]21[/C][C]0.0021288551483679[/C][C]0.0042577102967358[/C][C]0.997871144851632[/C][/ROW]
[ROW][C]22[/C][C]0.00425287941465446[/C][C]0.00850575882930892[/C][C]0.995747120585346[/C][/ROW]
[ROW][C]23[/C][C]0.00239300471201978[/C][C]0.00478600942403955[/C][C]0.99760699528798[/C][/ROW]
[ROW][C]24[/C][C]0.00121621011116059[/C][C]0.00243242022232119[/C][C]0.99878378988884[/C][/ROW]
[ROW][C]25[/C][C]0.000476856907977415[/C][C]0.00095371381595483[/C][C]0.999523143092023[/C][/ROW]
[ROW][C]26[/C][C]0.000186682092304966[/C][C]0.000373364184609931[/C][C]0.999813317907695[/C][/ROW]
[ROW][C]27[/C][C]0.000108885574722319[/C][C]0.000217771149444639[/C][C]0.999891114425278[/C][/ROW]
[ROW][C]28[/C][C]4.14383915722353e-05[/C][C]8.28767831444706e-05[/C][C]0.999958561608428[/C][/ROW]
[ROW][C]29[/C][C]1.72779775627681e-05[/C][C]3.45559551255361e-05[/C][C]0.999982722022437[/C][/ROW]
[ROW][C]30[/C][C]6.55690455161648e-06[/C][C]1.31138091032330e-05[/C][C]0.999993443095448[/C][/ROW]
[ROW][C]31[/C][C]2.50258945404973e-06[/C][C]5.00517890809946e-06[/C][C]0.999997497410546[/C][/ROW]
[ROW][C]32[/C][C]1.36765347839472e-06[/C][C]2.73530695678945e-06[/C][C]0.999998632346522[/C][/ROW]
[ROW][C]33[/C][C]9.789827975231e-07[/C][C]1.9579655950462e-06[/C][C]0.999999021017203[/C][/ROW]
[ROW][C]34[/C][C]8.31081662289104e-07[/C][C]1.66216332457821e-06[/C][C]0.999999168918338[/C][/ROW]
[ROW][C]35[/C][C]4.75537323903766e-06[/C][C]9.51074647807532e-06[/C][C]0.999995244626761[/C][/ROW]
[ROW][C]36[/C][C]6.07590257616875e-05[/C][C]0.000121518051523375[/C][C]0.999939240974238[/C][/ROW]
[ROW][C]37[/C][C]0.000133211746073737[/C][C]0.000266423492147474[/C][C]0.999866788253926[/C][/ROW]
[ROW][C]38[/C][C]0.00169484010095296[/C][C]0.00338968020190592[/C][C]0.998305159899047[/C][/ROW]
[ROW][C]39[/C][C]0.00479087739616425[/C][C]0.0095817547923285[/C][C]0.995209122603836[/C][/ROW]
[ROW][C]40[/C][C]0.0527031416273246[/C][C]0.105406283254649[/C][C]0.947296858372675[/C][/ROW]
[ROW][C]41[/C][C]0.0499568126140036[/C][C]0.0999136252280071[/C][C]0.950043187385996[/C][/ROW]
[ROW][C]42[/C][C]0.0697986494780453[/C][C]0.139597298956091[/C][C]0.930201350521955[/C][/ROW]
[ROW][C]43[/C][C]0.113031365784953[/C][C]0.226062731569906[/C][C]0.886968634215047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58127&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58127&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1260075415665080.2520150831330160.873992458433492
180.04786747211171470.09573494422342950.952132527888285
190.01682422977932900.03364845955865810.98317577022067
200.005493324082715540.01098664816543110.994506675917284
210.00212885514836790.00425771029673580.997871144851632
220.004252879414654460.008505758829308920.995747120585346
230.002393004712019780.004786009424039550.99760699528798
240.001216210111160590.002432420222321190.99878378988884
250.0004768569079774150.000953713815954830.999523143092023
260.0001866820923049660.0003733641846099310.999813317907695
270.0001088855747223190.0002177711494446390.999891114425278
284.14383915722353e-058.28767831444706e-050.999958561608428
291.72779775627681e-053.45559551255361e-050.999982722022437
306.55690455161648e-061.31138091032330e-050.999993443095448
312.50258945404973e-065.00517890809946e-060.999997497410546
321.36765347839472e-062.73530695678945e-060.999998632346522
339.789827975231e-071.9579655950462e-060.999999021017203
348.31081662289104e-071.66216332457821e-060.999999168918338
354.75537323903766e-069.51074647807532e-060.999995244626761
366.07590257616875e-050.0001215180515233750.999939240974238
370.0001332117460737370.0002664234921474740.999866788253926
380.001694840100952960.003389680201905920.998305159899047
390.004790877396164250.00958175479232850.995209122603836
400.05270314162732460.1054062832546490.947296858372675
410.04995681261400360.09991362522800710.950043187385996
420.06979864947804530.1395972989560910.930201350521955
430.1130313657849530.2260627315699060.886968634215047







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.703703703703704NOK
5% type I error level210.777777777777778NOK
10% type I error level230.851851851851852NOK

\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 & 19 & 0.703703703703704 & NOK \tabularnewline
5% type I error level & 21 & 0.777777777777778 & NOK \tabularnewline
10% type I error level & 23 & 0.851851851851852 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58127&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]19[/C][C]0.703703703703704[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]21[/C][C]0.777777777777778[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]23[/C][C]0.851851851851852[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58127&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58127&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.703703703703704NOK
5% type I error level210.777777777777778NOK
10% type I error level230.851851851851852NOK



Parameters (Session):
par2 = Do not include Seasonal Dummies ; par3 = No 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')
}