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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 02:11:16 -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/t12587083662ruk95ekfo6vgf7.htm/, Retrieved Fri, 29 Mar 2024 08:05:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57992, Retrieved Fri, 29 Mar 2024 08:05:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
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 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [Workshop 7] [2009-11-20 09:11:16] [a18540c86166a2b66550d1fef0503cc2] [Current]
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Dataseries X:
8,9	8,6
8,9	8,5
8,9	8,3
8,9	7,8
9	7,8
9	8
9	8,6
9	8,9
9	8,9
9	8,6
9	8,3
9,1	8,3
9	8,3
9,1	8,4
9,1	8,5
9	8,4
9	8,6
9	8,5
9	8,5
8,9	8,4
8,9	8,5
8,9	8,5
8,9	8,5
8,8	8,5
8,8	8,5
8,7	8,5
8,7	8,5
8,5	8,5
8,5	8,6
8,4	8,4
8,2	8,1
8,2	8
8,1	8
8,1	8
8	8
7,9	7,9
7,8	7,8
7,7	7,8
7,6	7,9
7,5	8,1
7,5	8
7,5	7,6
7,5	7,3
7,5	7
7,4	6,8
7,4	7
7,3	7,1
7,3	7,2
7,3	7,1
7,2	6,9
7,2	6,7
7,3	6,7
7,4	6,6
7,4	6,9
7,5	7,3
7,6	7,5
7,7	7,3
7,9	7,1
8	6,9
8,2	7,1




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=57992&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=57992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57992&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] = + 1.29280924113589 + 0.893229584469757X[t] -0.132239691962144M1[t] -0.136510508583347M2[t] -0.120781325204556M3[t] -0.109322958446975M4[t] -0.0871875501363702M5[t] -0.0714583667575799M6[t] -0.162916733515161M7[t] -0.162916733515161M8[t] -0.129322958446975M9[t] -0.0357291833787896M10[t] + 0.0157291833787906M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  1.29280924113589 +  0.893229584469757X[t] -0.132239691962144M1[t] -0.136510508583347M2[t] -0.120781325204556M3[t] -0.109322958446975M4[t] -0.0871875501363702M5[t] -0.0714583667575799M6[t] -0.162916733515161M7[t] -0.162916733515161M8[t] -0.129322958446975M9[t] -0.0357291833787896M10[t] +  0.0157291833787906M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57992&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  1.29280924113589 +  0.893229584469757X[t] -0.132239691962144M1[t] -0.136510508583347M2[t] -0.120781325204556M3[t] -0.109322958446975M4[t] -0.0871875501363702M5[t] -0.0714583667575799M6[t] -0.162916733515161M7[t] -0.162916733515161M8[t] -0.129322958446975M9[t] -0.0357291833787896M10[t] +  0.0157291833787906M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57992&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] = + 1.29280924113589 + 0.893229584469757X[t] -0.132239691962144M1[t] -0.136510508583347M2[t] -0.120781325204556M3[t] -0.109322958446975M4[t] -0.0871875501363702M5[t] -0.0714583667575799M6[t] -0.162916733515161M7[t] -0.162916733515161M8[t] -0.129322958446975M9[t] -0.0357291833787896M10[t] + 0.0157291833787906M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.292809241135890.6537351.97760.0538570.026929
X0.8932295844697570.08057511.085700
M1-0.1322396919621440.255315-0.51790.6069250.303463
M2-0.1365105085833470.255071-0.53520.5950440.297522
M3-0.1207813252045560.254867-0.47390.6377660.318883
M4-0.1093229584469750.254582-0.42940.6695790.334789
M5-0.08718755013637020.254638-0.34240.7335780.366789
M6-0.07145836675757990.254536-0.28070.7801420.390071
M7-0.1629167335151610.254781-0.63940.5256420.262821
M8-0.1629167335151610.254781-0.63940.5256420.262821
M9-0.1293229584469750.254582-0.5080.6138420.306921
M10-0.03572918337878960.254475-0.14040.8889410.444471
M110.01572918337879060.2544750.06180.9509760.475488

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 1.29280924113589 & 0.653735 & 1.9776 & 0.053857 & 0.026929 \tabularnewline
X & 0.893229584469757 & 0.080575 & 11.0857 & 0 & 0 \tabularnewline
M1 & -0.132239691962144 & 0.255315 & -0.5179 & 0.606925 & 0.303463 \tabularnewline
M2 & -0.136510508583347 & 0.255071 & -0.5352 & 0.595044 & 0.297522 \tabularnewline
M3 & -0.120781325204556 & 0.254867 & -0.4739 & 0.637766 & 0.318883 \tabularnewline
M4 & -0.109322958446975 & 0.254582 & -0.4294 & 0.669579 & 0.334789 \tabularnewline
M5 & -0.0871875501363702 & 0.254638 & -0.3424 & 0.733578 & 0.366789 \tabularnewline
M6 & -0.0714583667575799 & 0.254536 & -0.2807 & 0.780142 & 0.390071 \tabularnewline
M7 & -0.162916733515161 & 0.254781 & -0.6394 & 0.525642 & 0.262821 \tabularnewline
M8 & -0.162916733515161 & 0.254781 & -0.6394 & 0.525642 & 0.262821 \tabularnewline
M9 & -0.129322958446975 & 0.254582 & -0.508 & 0.613842 & 0.306921 \tabularnewline
M10 & -0.0357291833787896 & 0.254475 & -0.1404 & 0.888941 & 0.444471 \tabularnewline
M11 & 0.0157291833787906 & 0.254475 & 0.0618 & 0.950976 & 0.475488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57992&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]1.29280924113589[/C][C]0.653735[/C][C]1.9776[/C][C]0.053857[/C][C]0.026929[/C][/ROW]
[ROW][C]X[/C][C]0.893229584469757[/C][C]0.080575[/C][C]11.0857[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.132239691962144[/C][C]0.255315[/C][C]-0.5179[/C][C]0.606925[/C][C]0.303463[/C][/ROW]
[ROW][C]M2[/C][C]-0.136510508583347[/C][C]0.255071[/C][C]-0.5352[/C][C]0.595044[/C][C]0.297522[/C][/ROW]
[ROW][C]M3[/C][C]-0.120781325204556[/C][C]0.254867[/C][C]-0.4739[/C][C]0.637766[/C][C]0.318883[/C][/ROW]
[ROW][C]M4[/C][C]-0.109322958446975[/C][C]0.254582[/C][C]-0.4294[/C][C]0.669579[/C][C]0.334789[/C][/ROW]
[ROW][C]M5[/C][C]-0.0871875501363702[/C][C]0.254638[/C][C]-0.3424[/C][C]0.733578[/C][C]0.366789[/C][/ROW]
[ROW][C]M6[/C][C]-0.0714583667575799[/C][C]0.254536[/C][C]-0.2807[/C][C]0.780142[/C][C]0.390071[/C][/ROW]
[ROW][C]M7[/C][C]-0.162916733515161[/C][C]0.254781[/C][C]-0.6394[/C][C]0.525642[/C][C]0.262821[/C][/ROW]
[ROW][C]M8[/C][C]-0.162916733515161[/C][C]0.254781[/C][C]-0.6394[/C][C]0.525642[/C][C]0.262821[/C][/ROW]
[ROW][C]M9[/C][C]-0.129322958446975[/C][C]0.254582[/C][C]-0.508[/C][C]0.613842[/C][C]0.306921[/C][/ROW]
[ROW][C]M10[/C][C]-0.0357291833787896[/C][C]0.254475[/C][C]-0.1404[/C][C]0.888941[/C][C]0.444471[/C][/ROW]
[ROW][C]M11[/C][C]0.0157291833787906[/C][C]0.254475[/C][C]0.0618[/C][C]0.950976[/C][C]0.475488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57992&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)1.292809241135890.6537351.97760.0538570.026929
X0.8932295844697570.08057511.085700
M1-0.1322396919621440.255315-0.51790.6069250.303463
M2-0.1365105085833470.255071-0.53520.5950440.297522
M3-0.1207813252045560.254867-0.47390.6377660.318883
M4-0.1093229584469750.254582-0.42940.6695790.334789
M5-0.08718755013637020.254638-0.34240.7335780.366789
M6-0.07145836675757990.254536-0.28070.7801420.390071
M7-0.1629167335151610.254781-0.63940.5256420.262821
M8-0.1629167335151610.254781-0.63940.5256420.262821
M9-0.1293229584469750.254582-0.5080.6138420.306921
M10-0.03572918337878960.254475-0.14040.8889410.444471
M110.01572918337879060.2544750.06180.9509760.475488







Multiple Linear Regression - Regression Statistics
Multiple R0.851031331526163
R-squared0.724254327239195
Adjusted R-squared0.653851176747074
F-TEST (value)10.2872431443285
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value1.65884173064512e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.40232772588807
Sum Squared Residuals7.60777715385849

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.851031331526163 \tabularnewline
R-squared & 0.724254327239195 \tabularnewline
Adjusted R-squared & 0.653851176747074 \tabularnewline
F-TEST (value) & 10.2872431443285 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 1.65884173064512e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.40232772588807 \tabularnewline
Sum Squared Residuals & 7.60777715385849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57992&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.851031331526163[/C][/ROW]
[ROW][C]R-squared[/C][C]0.724254327239195[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.653851176747074[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]10.2872431443285[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]1.65884173064512e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.40232772588807[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7.60777715385849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57992&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57992&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 R0.851031331526163
R-squared0.724254327239195
Adjusted R-squared0.653851176747074
F-TEST (value)10.2872431443285
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value1.65884173064512e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.40232772588807
Sum Squared Residuals7.60777715385849







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.98.84234397561370.0576560243863022
28.98.748750200545480.151249799454517
38.98.585833467030320.314166532969678
48.98.150677041553020.749322958446976
598.172812449863630.82718755013637
698.367187550136370.632812449863629
798.811666934060640.188333065939356
899.07963580940157-0.0796358094015717
999.11322958446976-0.113229584469757
1098.938854484197020.0611455158029848
1198.722343975613670.277656024386331
129.18.706614792234880.393385207765121
1398.574375100272740.425624899727265
149.18.65942724209850.440572757901492
159.18.764479383924270.335520616075726
1698.686614792234880.313385207765121
1798.887396117439430.112603882560565
1898.813802342371250.186197657628751
1998.722343975613670.277656024386331
208.98.633021017166690.266978982833307
218.98.755937750681850.144062249318146
228.98.849531525750040.0504684742499605
238.98.90098989250762-0.000989892507619604
248.88.88526070912883-0.0852607091288288
258.88.753021017166690.0469789828333149
268.78.74875020054548-0.0487502005454838
278.78.76447938392427-0.0644793839242739
288.58.77593775068185-0.275937750681854
298.58.88739611743943-0.387396117439435
308.48.72447938392427-0.324479383924274
318.28.36505214182577-0.165052141825766
328.28.27572918337879-0.0757291833787907
338.18.30932295844697-0.209322958446976
348.18.40291673351516-0.302916733515162
3588.45437510027274-0.454375100272742
367.98.34932295844698-0.449322958446975
377.88.12776030803786-0.327760308037856
387.78.12348949141665-0.423489491416653
397.68.22854163324242-0.62854163324242
407.58.41864591689395-0.918645916893951
417.58.35145836675758-0.85145836675758
427.58.00989571634847-0.509895716348468
437.57.65046847424996-0.150468474249960
447.57.382499598909030.117500401090967
457.47.237447457083270.162552542916733
467.47.5096871490454-0.109687149045404
477.37.65046847424996-0.35046847424996
487.37.72406224931815-0.424062249318146
497.37.50249959890903-0.202499598909026
507.27.31958286539387-0.119582865393872
517.27.156666131878710.0433338681212891
527.37.168124498636290.131875501363708
537.47.100936948499920.299063051500079
547.47.384635007219640.0153649927803616
557.57.65046847424996-0.150468474249960
567.67.82911439114391-0.229114391143912
577.77.684062249318150.0159377506818545
587.97.599010107492380.300989892507620
5987.471822557356010.528177442643991
608.27.634739290871170.56526070912883

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.9 & 8.8423439756137 & 0.0576560243863022 \tabularnewline
2 & 8.9 & 8.74875020054548 & 0.151249799454517 \tabularnewline
3 & 8.9 & 8.58583346703032 & 0.314166532969678 \tabularnewline
4 & 8.9 & 8.15067704155302 & 0.749322958446976 \tabularnewline
5 & 9 & 8.17281244986363 & 0.82718755013637 \tabularnewline
6 & 9 & 8.36718755013637 & 0.632812449863629 \tabularnewline
7 & 9 & 8.81166693406064 & 0.188333065939356 \tabularnewline
8 & 9 & 9.07963580940157 & -0.0796358094015717 \tabularnewline
9 & 9 & 9.11322958446976 & -0.113229584469757 \tabularnewline
10 & 9 & 8.93885448419702 & 0.0611455158029848 \tabularnewline
11 & 9 & 8.72234397561367 & 0.277656024386331 \tabularnewline
12 & 9.1 & 8.70661479223488 & 0.393385207765121 \tabularnewline
13 & 9 & 8.57437510027274 & 0.425624899727265 \tabularnewline
14 & 9.1 & 8.6594272420985 & 0.440572757901492 \tabularnewline
15 & 9.1 & 8.76447938392427 & 0.335520616075726 \tabularnewline
16 & 9 & 8.68661479223488 & 0.313385207765121 \tabularnewline
17 & 9 & 8.88739611743943 & 0.112603882560565 \tabularnewline
18 & 9 & 8.81380234237125 & 0.186197657628751 \tabularnewline
19 & 9 & 8.72234397561367 & 0.277656024386331 \tabularnewline
20 & 8.9 & 8.63302101716669 & 0.266978982833307 \tabularnewline
21 & 8.9 & 8.75593775068185 & 0.144062249318146 \tabularnewline
22 & 8.9 & 8.84953152575004 & 0.0504684742499605 \tabularnewline
23 & 8.9 & 8.90098989250762 & -0.000989892507619604 \tabularnewline
24 & 8.8 & 8.88526070912883 & -0.0852607091288288 \tabularnewline
25 & 8.8 & 8.75302101716669 & 0.0469789828333149 \tabularnewline
26 & 8.7 & 8.74875020054548 & -0.0487502005454838 \tabularnewline
27 & 8.7 & 8.76447938392427 & -0.0644793839242739 \tabularnewline
28 & 8.5 & 8.77593775068185 & -0.275937750681854 \tabularnewline
29 & 8.5 & 8.88739611743943 & -0.387396117439435 \tabularnewline
30 & 8.4 & 8.72447938392427 & -0.324479383924274 \tabularnewline
31 & 8.2 & 8.36505214182577 & -0.165052141825766 \tabularnewline
32 & 8.2 & 8.27572918337879 & -0.0757291833787907 \tabularnewline
33 & 8.1 & 8.30932295844697 & -0.209322958446976 \tabularnewline
34 & 8.1 & 8.40291673351516 & -0.302916733515162 \tabularnewline
35 & 8 & 8.45437510027274 & -0.454375100272742 \tabularnewline
36 & 7.9 & 8.34932295844698 & -0.449322958446975 \tabularnewline
37 & 7.8 & 8.12776030803786 & -0.327760308037856 \tabularnewline
38 & 7.7 & 8.12348949141665 & -0.423489491416653 \tabularnewline
39 & 7.6 & 8.22854163324242 & -0.62854163324242 \tabularnewline
40 & 7.5 & 8.41864591689395 & -0.918645916893951 \tabularnewline
41 & 7.5 & 8.35145836675758 & -0.85145836675758 \tabularnewline
42 & 7.5 & 8.00989571634847 & -0.509895716348468 \tabularnewline
43 & 7.5 & 7.65046847424996 & -0.150468474249960 \tabularnewline
44 & 7.5 & 7.38249959890903 & 0.117500401090967 \tabularnewline
45 & 7.4 & 7.23744745708327 & 0.162552542916733 \tabularnewline
46 & 7.4 & 7.5096871490454 & -0.109687149045404 \tabularnewline
47 & 7.3 & 7.65046847424996 & -0.35046847424996 \tabularnewline
48 & 7.3 & 7.72406224931815 & -0.424062249318146 \tabularnewline
49 & 7.3 & 7.50249959890903 & -0.202499598909026 \tabularnewline
50 & 7.2 & 7.31958286539387 & -0.119582865393872 \tabularnewline
51 & 7.2 & 7.15666613187871 & 0.0433338681212891 \tabularnewline
52 & 7.3 & 7.16812449863629 & 0.131875501363708 \tabularnewline
53 & 7.4 & 7.10093694849992 & 0.299063051500079 \tabularnewline
54 & 7.4 & 7.38463500721964 & 0.0153649927803616 \tabularnewline
55 & 7.5 & 7.65046847424996 & -0.150468474249960 \tabularnewline
56 & 7.6 & 7.82911439114391 & -0.229114391143912 \tabularnewline
57 & 7.7 & 7.68406224931815 & 0.0159377506818545 \tabularnewline
58 & 7.9 & 7.59901010749238 & 0.300989892507620 \tabularnewline
59 & 8 & 7.47182255735601 & 0.528177442643991 \tabularnewline
60 & 8.2 & 7.63473929087117 & 0.56526070912883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57992&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]8.9[/C][C]8.8423439756137[/C][C]0.0576560243863022[/C][/ROW]
[ROW][C]2[/C][C]8.9[/C][C]8.74875020054548[/C][C]0.151249799454517[/C][/ROW]
[ROW][C]3[/C][C]8.9[/C][C]8.58583346703032[/C][C]0.314166532969678[/C][/ROW]
[ROW][C]4[/C][C]8.9[/C][C]8.15067704155302[/C][C]0.749322958446976[/C][/ROW]
[ROW][C]5[/C][C]9[/C][C]8.17281244986363[/C][C]0.82718755013637[/C][/ROW]
[ROW][C]6[/C][C]9[/C][C]8.36718755013637[/C][C]0.632812449863629[/C][/ROW]
[ROW][C]7[/C][C]9[/C][C]8.81166693406064[/C][C]0.188333065939356[/C][/ROW]
[ROW][C]8[/C][C]9[/C][C]9.07963580940157[/C][C]-0.0796358094015717[/C][/ROW]
[ROW][C]9[/C][C]9[/C][C]9.11322958446976[/C][C]-0.113229584469757[/C][/ROW]
[ROW][C]10[/C][C]9[/C][C]8.93885448419702[/C][C]0.0611455158029848[/C][/ROW]
[ROW][C]11[/C][C]9[/C][C]8.72234397561367[/C][C]0.277656024386331[/C][/ROW]
[ROW][C]12[/C][C]9.1[/C][C]8.70661479223488[/C][C]0.393385207765121[/C][/ROW]
[ROW][C]13[/C][C]9[/C][C]8.57437510027274[/C][C]0.425624899727265[/C][/ROW]
[ROW][C]14[/C][C]9.1[/C][C]8.6594272420985[/C][C]0.440572757901492[/C][/ROW]
[ROW][C]15[/C][C]9.1[/C][C]8.76447938392427[/C][C]0.335520616075726[/C][/ROW]
[ROW][C]16[/C][C]9[/C][C]8.68661479223488[/C][C]0.313385207765121[/C][/ROW]
[ROW][C]17[/C][C]9[/C][C]8.88739611743943[/C][C]0.112603882560565[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]8.81380234237125[/C][C]0.186197657628751[/C][/ROW]
[ROW][C]19[/C][C]9[/C][C]8.72234397561367[/C][C]0.277656024386331[/C][/ROW]
[ROW][C]20[/C][C]8.9[/C][C]8.63302101716669[/C][C]0.266978982833307[/C][/ROW]
[ROW][C]21[/C][C]8.9[/C][C]8.75593775068185[/C][C]0.144062249318146[/C][/ROW]
[ROW][C]22[/C][C]8.9[/C][C]8.84953152575004[/C][C]0.0504684742499605[/C][/ROW]
[ROW][C]23[/C][C]8.9[/C][C]8.90098989250762[/C][C]-0.000989892507619604[/C][/ROW]
[ROW][C]24[/C][C]8.8[/C][C]8.88526070912883[/C][C]-0.0852607091288288[/C][/ROW]
[ROW][C]25[/C][C]8.8[/C][C]8.75302101716669[/C][C]0.0469789828333149[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.74875020054548[/C][C]-0.0487502005454838[/C][/ROW]
[ROW][C]27[/C][C]8.7[/C][C]8.76447938392427[/C][C]-0.0644793839242739[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.77593775068185[/C][C]-0.275937750681854[/C][/ROW]
[ROW][C]29[/C][C]8.5[/C][C]8.88739611743943[/C][C]-0.387396117439435[/C][/ROW]
[ROW][C]30[/C][C]8.4[/C][C]8.72447938392427[/C][C]-0.324479383924274[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.36505214182577[/C][C]-0.165052141825766[/C][/ROW]
[ROW][C]32[/C][C]8.2[/C][C]8.27572918337879[/C][C]-0.0757291833787907[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.30932295844697[/C][C]-0.209322958446976[/C][/ROW]
[ROW][C]34[/C][C]8.1[/C][C]8.40291673351516[/C][C]-0.302916733515162[/C][/ROW]
[ROW][C]35[/C][C]8[/C][C]8.45437510027274[/C][C]-0.454375100272742[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]8.34932295844698[/C][C]-0.449322958446975[/C][/ROW]
[ROW][C]37[/C][C]7.8[/C][C]8.12776030803786[/C][C]-0.327760308037856[/C][/ROW]
[ROW][C]38[/C][C]7.7[/C][C]8.12348949141665[/C][C]-0.423489491416653[/C][/ROW]
[ROW][C]39[/C][C]7.6[/C][C]8.22854163324242[/C][C]-0.62854163324242[/C][/ROW]
[ROW][C]40[/C][C]7.5[/C][C]8.41864591689395[/C][C]-0.918645916893951[/C][/ROW]
[ROW][C]41[/C][C]7.5[/C][C]8.35145836675758[/C][C]-0.85145836675758[/C][/ROW]
[ROW][C]42[/C][C]7.5[/C][C]8.00989571634847[/C][C]-0.509895716348468[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]7.65046847424996[/C][C]-0.150468474249960[/C][/ROW]
[ROW][C]44[/C][C]7.5[/C][C]7.38249959890903[/C][C]0.117500401090967[/C][/ROW]
[ROW][C]45[/C][C]7.4[/C][C]7.23744745708327[/C][C]0.162552542916733[/C][/ROW]
[ROW][C]46[/C][C]7.4[/C][C]7.5096871490454[/C][C]-0.109687149045404[/C][/ROW]
[ROW][C]47[/C][C]7.3[/C][C]7.65046847424996[/C][C]-0.35046847424996[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]7.72406224931815[/C][C]-0.424062249318146[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.50249959890903[/C][C]-0.202499598909026[/C][/ROW]
[ROW][C]50[/C][C]7.2[/C][C]7.31958286539387[/C][C]-0.119582865393872[/C][/ROW]
[ROW][C]51[/C][C]7.2[/C][C]7.15666613187871[/C][C]0.0433338681212891[/C][/ROW]
[ROW][C]52[/C][C]7.3[/C][C]7.16812449863629[/C][C]0.131875501363708[/C][/ROW]
[ROW][C]53[/C][C]7.4[/C][C]7.10093694849992[/C][C]0.299063051500079[/C][/ROW]
[ROW][C]54[/C][C]7.4[/C][C]7.38463500721964[/C][C]0.0153649927803616[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7.65046847424996[/C][C]-0.150468474249960[/C][/ROW]
[ROW][C]56[/C][C]7.6[/C][C]7.82911439114391[/C][C]-0.229114391143912[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]7.68406224931815[/C][C]0.0159377506818545[/C][/ROW]
[ROW][C]58[/C][C]7.9[/C][C]7.59901010749238[/C][C]0.300989892507620[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]7.47182255735601[/C][C]0.528177442643991[/C][/ROW]
[ROW][C]60[/C][C]8.2[/C][C]7.63473929087117[/C][C]0.56526070912883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57992&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57992&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
18.98.84234397561370.0576560243863022
28.98.748750200545480.151249799454517
38.98.585833467030320.314166532969678
48.98.150677041553020.749322958446976
598.172812449863630.82718755013637
698.367187550136370.632812449863629
798.811666934060640.188333065939356
899.07963580940157-0.0796358094015717
999.11322958446976-0.113229584469757
1098.938854484197020.0611455158029848
1198.722343975613670.277656024386331
129.18.706614792234880.393385207765121
1398.574375100272740.425624899727265
149.18.65942724209850.440572757901492
159.18.764479383924270.335520616075726
1698.686614792234880.313385207765121
1798.887396117439430.112603882560565
1898.813802342371250.186197657628751
1998.722343975613670.277656024386331
208.98.633021017166690.266978982833307
218.98.755937750681850.144062249318146
228.98.849531525750040.0504684742499605
238.98.90098989250762-0.000989892507619604
248.88.88526070912883-0.0852607091288288
258.88.753021017166690.0469789828333149
268.78.74875020054548-0.0487502005454838
278.78.76447938392427-0.0644793839242739
288.58.77593775068185-0.275937750681854
298.58.88739611743943-0.387396117439435
308.48.72447938392427-0.324479383924274
318.28.36505214182577-0.165052141825766
328.28.27572918337879-0.0757291833787907
338.18.30932295844697-0.209322958446976
348.18.40291673351516-0.302916733515162
3588.45437510027274-0.454375100272742
367.98.34932295844698-0.449322958446975
377.88.12776030803786-0.327760308037856
387.78.12348949141665-0.423489491416653
397.68.22854163324242-0.62854163324242
407.58.41864591689395-0.918645916893951
417.58.35145836675758-0.85145836675758
427.58.00989571634847-0.509895716348468
437.57.65046847424996-0.150468474249960
447.57.382499598909030.117500401090967
457.47.237447457083270.162552542916733
467.47.5096871490454-0.109687149045404
477.37.65046847424996-0.35046847424996
487.37.72406224931815-0.424062249318146
497.37.50249959890903-0.202499598909026
507.27.31958286539387-0.119582865393872
517.27.156666131878710.0433338681212891
527.37.168124498636290.131875501363708
537.47.100936948499920.299063051500079
547.47.384635007219640.0153649927803616
557.57.65046847424996-0.150468474249960
567.67.82911439114391-0.229114391143912
577.77.684062249318150.0159377506818545
587.97.599010107492380.300989892507620
5987.471822557356010.528177442643991
608.27.634739290871170.56526070912883







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.05914363586427620.1182872717285520.940856364135724
170.01957068444276280.03914136888552560.980429315557237
180.006132969865119460.01226593973023890.99386703013488
190.001882436511591890.003764873023183780.998117563488408
200.0006458448649090.0012916897298180.99935415513509
210.0002038878736368620.0004077757472737250.999796112126363
227.00172062510889e-050.0001400344125021780.999929982793749
232.97533403541544e-055.95066807083089e-050.999970246659646
240.0001187751227353360.0002375502454706720.999881224877265
250.0001069805085530510.0002139610171061030.999893019491447
260.0004503939792648590.0009007879585297170.999549606020735
270.001593089075655760.003186178151311520.998406910924344
280.009693145771974460.01938629154394890.990306854228026
290.02969071959288440.05938143918576870.970309280407116
300.1120753048378000.2241506096756010.8879246951622
310.42557213364630.85114426729260.5744278663537
320.6042560052213890.7914879895572210.395743994778611
330.6786734696586770.6426530606826450.321326530341323
340.6992143759690720.6015712480618570.300785624030928
350.720717418912260.5585651621754790.279282581087740
360.7173055135315320.5653889729369360.282694486468468
370.7206705287927880.5586589424144240.279329471207212
380.7160039766452260.5679920467095470.283996023354774
390.7056546987866970.5886906024266050.294345301213303
400.7198910516628430.5602178966743140.280108948337157
410.6706283592985180.6587432814029640.329371640701482
420.5520333196999040.8959333606001930.447966680300096
430.3994733849745390.7989467699490790.600526615025461
440.2602536038190890.5205072076381770.739746396180911

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0591436358642762 & 0.118287271728552 & 0.940856364135724 \tabularnewline
17 & 0.0195706844427628 & 0.0391413688855256 & 0.980429315557237 \tabularnewline
18 & 0.00613296986511946 & 0.0122659397302389 & 0.99386703013488 \tabularnewline
19 & 0.00188243651159189 & 0.00376487302318378 & 0.998117563488408 \tabularnewline
20 & 0.000645844864909 & 0.001291689729818 & 0.99935415513509 \tabularnewline
21 & 0.000203887873636862 & 0.000407775747273725 & 0.999796112126363 \tabularnewline
22 & 7.00172062510889e-05 & 0.000140034412502178 & 0.999929982793749 \tabularnewline
23 & 2.97533403541544e-05 & 5.95066807083089e-05 & 0.999970246659646 \tabularnewline
24 & 0.000118775122735336 & 0.000237550245470672 & 0.999881224877265 \tabularnewline
25 & 0.000106980508553051 & 0.000213961017106103 & 0.999893019491447 \tabularnewline
26 & 0.000450393979264859 & 0.000900787958529717 & 0.999549606020735 \tabularnewline
27 & 0.00159308907565576 & 0.00318617815131152 & 0.998406910924344 \tabularnewline
28 & 0.00969314577197446 & 0.0193862915439489 & 0.990306854228026 \tabularnewline
29 & 0.0296907195928844 & 0.0593814391857687 & 0.970309280407116 \tabularnewline
30 & 0.112075304837800 & 0.224150609675601 & 0.8879246951622 \tabularnewline
31 & 0.4255721336463 & 0.8511442672926 & 0.5744278663537 \tabularnewline
32 & 0.604256005221389 & 0.791487989557221 & 0.395743994778611 \tabularnewline
33 & 0.678673469658677 & 0.642653060682645 & 0.321326530341323 \tabularnewline
34 & 0.699214375969072 & 0.601571248061857 & 0.300785624030928 \tabularnewline
35 & 0.72071741891226 & 0.558565162175479 & 0.279282581087740 \tabularnewline
36 & 0.717305513531532 & 0.565388972936936 & 0.282694486468468 \tabularnewline
37 & 0.720670528792788 & 0.558658942414424 & 0.279329471207212 \tabularnewline
38 & 0.716003976645226 & 0.567992046709547 & 0.283996023354774 \tabularnewline
39 & 0.705654698786697 & 0.588690602426605 & 0.294345301213303 \tabularnewline
40 & 0.719891051662843 & 0.560217896674314 & 0.280108948337157 \tabularnewline
41 & 0.670628359298518 & 0.658743281402964 & 0.329371640701482 \tabularnewline
42 & 0.552033319699904 & 0.895933360600193 & 0.447966680300096 \tabularnewline
43 & 0.399473384974539 & 0.798946769949079 & 0.600526615025461 \tabularnewline
44 & 0.260253603819089 & 0.520507207638177 & 0.739746396180911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57992&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]16[/C][C]0.0591436358642762[/C][C]0.118287271728552[/C][C]0.940856364135724[/C][/ROW]
[ROW][C]17[/C][C]0.0195706844427628[/C][C]0.0391413688855256[/C][C]0.980429315557237[/C][/ROW]
[ROW][C]18[/C][C]0.00613296986511946[/C][C]0.0122659397302389[/C][C]0.99386703013488[/C][/ROW]
[ROW][C]19[/C][C]0.00188243651159189[/C][C]0.00376487302318378[/C][C]0.998117563488408[/C][/ROW]
[ROW][C]20[/C][C]0.000645844864909[/C][C]0.001291689729818[/C][C]0.99935415513509[/C][/ROW]
[ROW][C]21[/C][C]0.000203887873636862[/C][C]0.000407775747273725[/C][C]0.999796112126363[/C][/ROW]
[ROW][C]22[/C][C]7.00172062510889e-05[/C][C]0.000140034412502178[/C][C]0.999929982793749[/C][/ROW]
[ROW][C]23[/C][C]2.97533403541544e-05[/C][C]5.95066807083089e-05[/C][C]0.999970246659646[/C][/ROW]
[ROW][C]24[/C][C]0.000118775122735336[/C][C]0.000237550245470672[/C][C]0.999881224877265[/C][/ROW]
[ROW][C]25[/C][C]0.000106980508553051[/C][C]0.000213961017106103[/C][C]0.999893019491447[/C][/ROW]
[ROW][C]26[/C][C]0.000450393979264859[/C][C]0.000900787958529717[/C][C]0.999549606020735[/C][/ROW]
[ROW][C]27[/C][C]0.00159308907565576[/C][C]0.00318617815131152[/C][C]0.998406910924344[/C][/ROW]
[ROW][C]28[/C][C]0.00969314577197446[/C][C]0.0193862915439489[/C][C]0.990306854228026[/C][/ROW]
[ROW][C]29[/C][C]0.0296907195928844[/C][C]0.0593814391857687[/C][C]0.970309280407116[/C][/ROW]
[ROW][C]30[/C][C]0.112075304837800[/C][C]0.224150609675601[/C][C]0.8879246951622[/C][/ROW]
[ROW][C]31[/C][C]0.4255721336463[/C][C]0.8511442672926[/C][C]0.5744278663537[/C][/ROW]
[ROW][C]32[/C][C]0.604256005221389[/C][C]0.791487989557221[/C][C]0.395743994778611[/C][/ROW]
[ROW][C]33[/C][C]0.678673469658677[/C][C]0.642653060682645[/C][C]0.321326530341323[/C][/ROW]
[ROW][C]34[/C][C]0.699214375969072[/C][C]0.601571248061857[/C][C]0.300785624030928[/C][/ROW]
[ROW][C]35[/C][C]0.72071741891226[/C][C]0.558565162175479[/C][C]0.279282581087740[/C][/ROW]
[ROW][C]36[/C][C]0.717305513531532[/C][C]0.565388972936936[/C][C]0.282694486468468[/C][/ROW]
[ROW][C]37[/C][C]0.720670528792788[/C][C]0.558658942414424[/C][C]0.279329471207212[/C][/ROW]
[ROW][C]38[/C][C]0.716003976645226[/C][C]0.567992046709547[/C][C]0.283996023354774[/C][/ROW]
[ROW][C]39[/C][C]0.705654698786697[/C][C]0.588690602426605[/C][C]0.294345301213303[/C][/ROW]
[ROW][C]40[/C][C]0.719891051662843[/C][C]0.560217896674314[/C][C]0.280108948337157[/C][/ROW]
[ROW][C]41[/C][C]0.670628359298518[/C][C]0.658743281402964[/C][C]0.329371640701482[/C][/ROW]
[ROW][C]42[/C][C]0.552033319699904[/C][C]0.895933360600193[/C][C]0.447966680300096[/C][/ROW]
[ROW][C]43[/C][C]0.399473384974539[/C][C]0.798946769949079[/C][C]0.600526615025461[/C][/ROW]
[ROW][C]44[/C][C]0.260253603819089[/C][C]0.520507207638177[/C][C]0.739746396180911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57992&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57992&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
160.05914363586427620.1182872717285520.940856364135724
170.01957068444276280.03914136888552560.980429315557237
180.006132969865119460.01226593973023890.99386703013488
190.001882436511591890.003764873023183780.998117563488408
200.0006458448649090.0012916897298180.99935415513509
210.0002038878736368620.0004077757472737250.999796112126363
227.00172062510889e-050.0001400344125021780.999929982793749
232.97533403541544e-055.95066807083089e-050.999970246659646
240.0001187751227353360.0002375502454706720.999881224877265
250.0001069805085530510.0002139610171061030.999893019491447
260.0004503939792648590.0009007879585297170.999549606020735
270.001593089075655760.003186178151311520.998406910924344
280.009693145771974460.01938629154394890.990306854228026
290.02969071959288440.05938143918576870.970309280407116
300.1120753048378000.2241506096756010.8879246951622
310.42557213364630.85114426729260.5744278663537
320.6042560052213890.7914879895572210.395743994778611
330.6786734696586770.6426530606826450.321326530341323
340.6992143759690720.6015712480618570.300785624030928
350.720717418912260.5585651621754790.279282581087740
360.7173055135315320.5653889729369360.282694486468468
370.7206705287927880.5586589424144240.279329471207212
380.7160039766452260.5679920467095470.283996023354774
390.7056546987866970.5886906024266050.294345301213303
400.7198910516628430.5602178966743140.280108948337157
410.6706283592985180.6587432814029640.329371640701482
420.5520333196999040.8959333606001930.447966680300096
430.3994733849745390.7989467699490790.600526615025461
440.2602536038190890.5205072076381770.739746396180911







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level90.310344827586207NOK
5% type I error level120.413793103448276NOK
10% type I error level130.448275862068966NOK

\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 & 9 & 0.310344827586207 & NOK \tabularnewline
5% type I error level & 12 & 0.413793103448276 & NOK \tabularnewline
10% type I error level & 13 & 0.448275862068966 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57992&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]9[/C][C]0.310344827586207[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]12[/C][C]0.413793103448276[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]13[/C][C]0.448275862068966[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57992&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57992&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 level90.310344827586207NOK
5% type I error level120.413793103448276NOK
10% type I error level130.448275862068966NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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')
}