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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 25 Nov 2011 15:22:16 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/25/t1322252567h79p65qexh08v14.htm/, Retrieved Mon, 24 Jun 2024 12:09:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147357, Retrieved Mon, 24 Jun 2024 12:09:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- R P         [Univariate Data Series] [WS8 Time Series A...] [2010-11-30 09:10:08] [afe9379cca749d06b3d6872e02cc47ed]
- R PD          [Univariate Data Series] [] [2011-11-25 19:20:16] [f1de53e71fac758e9834be8effee591f]
- RMPD              [Multiple Regression] [] [2011-11-25 20:22:16] [13d85cac30d4a10947636c080219d4f4] [Current]
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Dataseries X:
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
10.943
9.867
10.203
10.837
10.573
10.647
11.502
10.656
10.866
10.835
9.945
10.331




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

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147357&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147357&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147357&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' @ jenkins.wessa.net







Multiple Linear Regression - Estimated Regression Equation
Births[t] = + 9.470475 + 0.345771527777781M1[t] -0.529098611111111M2[t] + 0.30883125M3[t] -0.0318388888888881M4[t] + 0.184290972222223M5[t] + 0.224020833333334M6[t] + 0.683950694444445M7[t] + 0.635480555555556M8[t] + 0.400410416666667M9[t] + 0.461940277777779M10[t] -0.354729861111111M11[t] + 0.0168701388888889t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Births[t] =  +  9.470475 +  0.345771527777781M1[t] -0.529098611111111M2[t] +  0.30883125M3[t] -0.0318388888888881M4[t] +  0.184290972222223M5[t] +  0.224020833333334M6[t] +  0.683950694444445M7[t] +  0.635480555555556M8[t] +  0.400410416666667M9[t] +  0.461940277777779M10[t] -0.354729861111111M11[t] +  0.0168701388888889t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147357&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Births[t] =  +  9.470475 +  0.345771527777781M1[t] -0.529098611111111M2[t] +  0.30883125M3[t] -0.0318388888888881M4[t] +  0.184290972222223M5[t] +  0.224020833333334M6[t] +  0.683950694444445M7[t] +  0.635480555555556M8[t] +  0.400410416666667M9[t] +  0.461940277777779M10[t] -0.354729861111111M11[t] +  0.0168701388888889t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147357&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147357&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
Births[t] = + 9.470475 + 0.345771527777781M1[t] -0.529098611111111M2[t] + 0.30883125M3[t] -0.0318388888888881M4[t] + 0.184290972222223M5[t] + 0.224020833333334M6[t] + 0.683950694444445M7[t] + 0.635480555555556M8[t] + 0.400410416666667M9[t] + 0.461940277777779M10[t] -0.354729861111111M11[t] + 0.0168701388888889t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)9.4704750.13300971.201600
M10.3457715277777810.1618132.13690.0378450.018922
M2-0.5290986111111110.161571-3.27470.001990.000995
M30.308831250.1613521.9140.0617180.030859
M4-0.03183888888888810.161156-0.19760.8442370.422119
M50.1842909722222230.1609831.14480.2580940.129047
M60.2240208333333340.1608321.39290.1702090.085105
M70.6839506944444450.1607054.25599.9e-054.9e-05
M80.6354805555555560.1606013.95690.0002550.000128
M90.4004104166666670.160522.49450.0161880.008094
M100.4619402777777790.1604622.87880.005990.002995
M11-0.3547298611111110.160427-2.21120.0319250.015963
t0.01687013888888890.0019298.743300

\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) & 9.470475 & 0.133009 & 71.2016 & 0 & 0 \tabularnewline
M1 & 0.345771527777781 & 0.161813 & 2.1369 & 0.037845 & 0.018922 \tabularnewline
M2 & -0.529098611111111 & 0.161571 & -3.2747 & 0.00199 & 0.000995 \tabularnewline
M3 & 0.30883125 & 0.161352 & 1.914 & 0.061718 & 0.030859 \tabularnewline
M4 & -0.0318388888888881 & 0.161156 & -0.1976 & 0.844237 & 0.422119 \tabularnewline
M5 & 0.184290972222223 & 0.160983 & 1.1448 & 0.258094 & 0.129047 \tabularnewline
M6 & 0.224020833333334 & 0.160832 & 1.3929 & 0.170209 & 0.085105 \tabularnewline
M7 & 0.683950694444445 & 0.160705 & 4.2559 & 9.9e-05 & 4.9e-05 \tabularnewline
M8 & 0.635480555555556 & 0.160601 & 3.9569 & 0.000255 & 0.000128 \tabularnewline
M9 & 0.400410416666667 & 0.16052 & 2.4945 & 0.016188 & 0.008094 \tabularnewline
M10 & 0.461940277777779 & 0.160462 & 2.8788 & 0.00599 & 0.002995 \tabularnewline
M11 & -0.354729861111111 & 0.160427 & -2.2112 & 0.031925 & 0.015963 \tabularnewline
t & 0.0168701388888889 & 0.001929 & 8.7433 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147357&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]9.470475[/C][C]0.133009[/C][C]71.2016[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.345771527777781[/C][C]0.161813[/C][C]2.1369[/C][C]0.037845[/C][C]0.018922[/C][/ROW]
[ROW][C]M2[/C][C]-0.529098611111111[/C][C]0.161571[/C][C]-3.2747[/C][C]0.00199[/C][C]0.000995[/C][/ROW]
[ROW][C]M3[/C][C]0.30883125[/C][C]0.161352[/C][C]1.914[/C][C]0.061718[/C][C]0.030859[/C][/ROW]
[ROW][C]M4[/C][C]-0.0318388888888881[/C][C]0.161156[/C][C]-0.1976[/C][C]0.844237[/C][C]0.422119[/C][/ROW]
[ROW][C]M5[/C][C]0.184290972222223[/C][C]0.160983[/C][C]1.1448[/C][C]0.258094[/C][C]0.129047[/C][/ROW]
[ROW][C]M6[/C][C]0.224020833333334[/C][C]0.160832[/C][C]1.3929[/C][C]0.170209[/C][C]0.085105[/C][/ROW]
[ROW][C]M7[/C][C]0.683950694444445[/C][C]0.160705[/C][C]4.2559[/C][C]9.9e-05[/C][C]4.9e-05[/C][/ROW]
[ROW][C]M8[/C][C]0.635480555555556[/C][C]0.160601[/C][C]3.9569[/C][C]0.000255[/C][C]0.000128[/C][/ROW]
[ROW][C]M9[/C][C]0.400410416666667[/C][C]0.16052[/C][C]2.4945[/C][C]0.016188[/C][C]0.008094[/C][/ROW]
[ROW][C]M10[/C][C]0.461940277777779[/C][C]0.160462[/C][C]2.8788[/C][C]0.00599[/C][C]0.002995[/C][/ROW]
[ROW][C]M11[/C][C]-0.354729861111111[/C][C]0.160427[/C][C]-2.2112[/C][C]0.031925[/C][C]0.015963[/C][/ROW]
[ROW][C]t[/C][C]0.0168701388888889[/C][C]0.001929[/C][C]8.7433[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147357&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147357&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)9.4704750.13300971.201600
M10.3457715277777810.1618132.13690.0378450.018922
M2-0.5290986111111110.161571-3.27470.001990.000995
M30.308831250.1613521.9140.0617180.030859
M4-0.03183888888888810.161156-0.19760.8442370.422119
M50.1842909722222230.1609831.14480.2580940.129047
M60.2240208333333340.1608321.39290.1702090.085105
M70.6839506944444450.1607054.25599.9e-054.9e-05
M80.6354805555555560.1606013.95690.0002550.000128
M90.4004104166666670.160522.49450.0161880.008094
M100.4619402777777790.1604622.87880.005990.002995
M11-0.3547298611111110.160427-2.21120.0319250.015963
t0.01687013888888890.0019298.743300







Multiple Linear Regression - Regression Statistics
Multiple R0.899762836842612
R-squared0.809573162563065
Adjusted R-squared0.76095354449406
F-TEST (value)16.6511625289622
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value4.67736960274578e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.253638769423387
Sum Squared Residuals3.02363339166666

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.899762836842612 \tabularnewline
R-squared & 0.809573162563065 \tabularnewline
Adjusted R-squared & 0.76095354449406 \tabularnewline
F-TEST (value) & 16.6511625289622 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 4.67736960274578e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.253638769423387 \tabularnewline
Sum Squared Residuals & 3.02363339166666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147357&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.899762836842612[/C][/ROW]
[ROW][C]R-squared[/C][C]0.809573162563065[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.76095354449406[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]16.6511625289622[/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]4.67736960274578e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.253638769423387[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3.02363339166666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147357&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147357&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 R0.899762836842612
R-squared0.809573162563065
Adjusted R-squared0.76095354449406
F-TEST (value)16.6511625289622
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value4.67736960274578e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.253638769423387
Sum Squared Residuals3.02363339166666







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
19.8299.83311666666666-0.00411666666665606
29.1258.975116666666670.149883333333333
39.7829.82991666666667-0.0479166666666673
49.4419.50611666666667-0.0651166666666668
59.1629.73911666666667-0.577116666666667
69.9159.795716666666670.119283333333332
710.44410.27251666666670.171483333333333
810.20910.2409166666667-0.0319166666666677
99.98510.0227166666667-0.0377166666666679
109.84210.1011166666667-0.259116666666667
119.4299.301316666666670.127683333333333
1210.1329.672916666666670.459083333333333
139.84910.0355583333333-0.186558333333336
149.1729.17755833333333-0.00555833333333307
1510.31310.03235833333330.280641666666667
169.8199.708558333333330.110441666666667
179.9559.941558333333330.0134416666666663
1810.0489.998158333333330.0498416666666664
1910.08210.4749583333333-0.392958333333333
2010.54110.44335833333330.0976416666666666
2110.20810.2251583333333-0.0171583333333334
2210.23310.3035583333333-0.0705583333333334
239.4399.50375833333333-0.0647583333333336
249.9639.875358333333330.0876416666666661
2510.15810.238-0.0800000000000031
269.2259.38-0.155
2710.47410.23480.2392
289.7579.911-0.154000000000001
2910.4910.1440.346
3010.28110.20060.0804000000000006
3110.44410.6774-0.2334
3210.6410.6458-0.00579999999999958
3310.69510.42760.2674
3410.78610.5060.279999999999999
359.8329.70620.125800000000001
369.74710.0778-0.3308
3710.41110.4404416666667-0.0294416666666694
389.5119.58244166666667-0.0714416666666671
3910.40210.4372416666667-0.035241666666667
409.70110.1134416666667-0.412441666666666
4110.5410.34644166666670.193558333333333
4210.11210.4030416666667-0.291041666666666
4310.91510.87984166666670.0351583333333324
4411.18310.84824166666670.334758333333333
4510.38410.6300416666667-0.246041666666666
4610.83410.70844166666670.125558333333333
479.8869.90864166666667-0.0226416666666673
4810.21610.2802416666667-0.0642416666666665
4910.94310.64288333333330.300116666666664
509.8679.784883333333330.082116666666668
5110.20310.6396833333333-0.436683333333333
5210.83710.31588333333330.521116666666667
5310.57310.54888333333330.0241166666666674
5410.64710.60548333333330.0415166666666676
5511.50211.08228333333330.419716666666667
5610.65611.0506833333333-0.394683333333332
5710.86610.83248333333330.0335166666666669
5810.83510.9108833333333-0.075883333333332
599.94510.1110833333333-0.166083333333333
6010.33110.4826833333333-0.151683333333333

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9.829 & 9.83311666666666 & -0.00411666666665606 \tabularnewline
2 & 9.125 & 8.97511666666667 & 0.149883333333333 \tabularnewline
3 & 9.782 & 9.82991666666667 & -0.0479166666666673 \tabularnewline
4 & 9.441 & 9.50611666666667 & -0.0651166666666668 \tabularnewline
5 & 9.162 & 9.73911666666667 & -0.577116666666667 \tabularnewline
6 & 9.915 & 9.79571666666667 & 0.119283333333332 \tabularnewline
7 & 10.444 & 10.2725166666667 & 0.171483333333333 \tabularnewline
8 & 10.209 & 10.2409166666667 & -0.0319166666666677 \tabularnewline
9 & 9.985 & 10.0227166666667 & -0.0377166666666679 \tabularnewline
10 & 9.842 & 10.1011166666667 & -0.259116666666667 \tabularnewline
11 & 9.429 & 9.30131666666667 & 0.127683333333333 \tabularnewline
12 & 10.132 & 9.67291666666667 & 0.459083333333333 \tabularnewline
13 & 9.849 & 10.0355583333333 & -0.186558333333336 \tabularnewline
14 & 9.172 & 9.17755833333333 & -0.00555833333333307 \tabularnewline
15 & 10.313 & 10.0323583333333 & 0.280641666666667 \tabularnewline
16 & 9.819 & 9.70855833333333 & 0.110441666666667 \tabularnewline
17 & 9.955 & 9.94155833333333 & 0.0134416666666663 \tabularnewline
18 & 10.048 & 9.99815833333333 & 0.0498416666666664 \tabularnewline
19 & 10.082 & 10.4749583333333 & -0.392958333333333 \tabularnewline
20 & 10.541 & 10.4433583333333 & 0.0976416666666666 \tabularnewline
21 & 10.208 & 10.2251583333333 & -0.0171583333333334 \tabularnewline
22 & 10.233 & 10.3035583333333 & -0.0705583333333334 \tabularnewline
23 & 9.439 & 9.50375833333333 & -0.0647583333333336 \tabularnewline
24 & 9.963 & 9.87535833333333 & 0.0876416666666661 \tabularnewline
25 & 10.158 & 10.238 & -0.0800000000000031 \tabularnewline
26 & 9.225 & 9.38 & -0.155 \tabularnewline
27 & 10.474 & 10.2348 & 0.2392 \tabularnewline
28 & 9.757 & 9.911 & -0.154000000000001 \tabularnewline
29 & 10.49 & 10.144 & 0.346 \tabularnewline
30 & 10.281 & 10.2006 & 0.0804000000000006 \tabularnewline
31 & 10.444 & 10.6774 & -0.2334 \tabularnewline
32 & 10.64 & 10.6458 & -0.00579999999999958 \tabularnewline
33 & 10.695 & 10.4276 & 0.2674 \tabularnewline
34 & 10.786 & 10.506 & 0.279999999999999 \tabularnewline
35 & 9.832 & 9.7062 & 0.125800000000001 \tabularnewline
36 & 9.747 & 10.0778 & -0.3308 \tabularnewline
37 & 10.411 & 10.4404416666667 & -0.0294416666666694 \tabularnewline
38 & 9.511 & 9.58244166666667 & -0.0714416666666671 \tabularnewline
39 & 10.402 & 10.4372416666667 & -0.035241666666667 \tabularnewline
40 & 9.701 & 10.1134416666667 & -0.412441666666666 \tabularnewline
41 & 10.54 & 10.3464416666667 & 0.193558333333333 \tabularnewline
42 & 10.112 & 10.4030416666667 & -0.291041666666666 \tabularnewline
43 & 10.915 & 10.8798416666667 & 0.0351583333333324 \tabularnewline
44 & 11.183 & 10.8482416666667 & 0.334758333333333 \tabularnewline
45 & 10.384 & 10.6300416666667 & -0.246041666666666 \tabularnewline
46 & 10.834 & 10.7084416666667 & 0.125558333333333 \tabularnewline
47 & 9.886 & 9.90864166666667 & -0.0226416666666673 \tabularnewline
48 & 10.216 & 10.2802416666667 & -0.0642416666666665 \tabularnewline
49 & 10.943 & 10.6428833333333 & 0.300116666666664 \tabularnewline
50 & 9.867 & 9.78488333333333 & 0.082116666666668 \tabularnewline
51 & 10.203 & 10.6396833333333 & -0.436683333333333 \tabularnewline
52 & 10.837 & 10.3158833333333 & 0.521116666666667 \tabularnewline
53 & 10.573 & 10.5488833333333 & 0.0241166666666674 \tabularnewline
54 & 10.647 & 10.6054833333333 & 0.0415166666666676 \tabularnewline
55 & 11.502 & 11.0822833333333 & 0.419716666666667 \tabularnewline
56 & 10.656 & 11.0506833333333 & -0.394683333333332 \tabularnewline
57 & 10.866 & 10.8324833333333 & 0.0335166666666669 \tabularnewline
58 & 10.835 & 10.9108833333333 & -0.075883333333332 \tabularnewline
59 & 9.945 & 10.1110833333333 & -0.166083333333333 \tabularnewline
60 & 10.331 & 10.4826833333333 & -0.151683333333333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147357&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]9.829[/C][C]9.83311666666666[/C][C]-0.00411666666665606[/C][/ROW]
[ROW][C]2[/C][C]9.125[/C][C]8.97511666666667[/C][C]0.149883333333333[/C][/ROW]
[ROW][C]3[/C][C]9.782[/C][C]9.82991666666667[/C][C]-0.0479166666666673[/C][/ROW]
[ROW][C]4[/C][C]9.441[/C][C]9.50611666666667[/C][C]-0.0651166666666668[/C][/ROW]
[ROW][C]5[/C][C]9.162[/C][C]9.73911666666667[/C][C]-0.577116666666667[/C][/ROW]
[ROW][C]6[/C][C]9.915[/C][C]9.79571666666667[/C][C]0.119283333333332[/C][/ROW]
[ROW][C]7[/C][C]10.444[/C][C]10.2725166666667[/C][C]0.171483333333333[/C][/ROW]
[ROW][C]8[/C][C]10.209[/C][C]10.2409166666667[/C][C]-0.0319166666666677[/C][/ROW]
[ROW][C]9[/C][C]9.985[/C][C]10.0227166666667[/C][C]-0.0377166666666679[/C][/ROW]
[ROW][C]10[/C][C]9.842[/C][C]10.1011166666667[/C][C]-0.259116666666667[/C][/ROW]
[ROW][C]11[/C][C]9.429[/C][C]9.30131666666667[/C][C]0.127683333333333[/C][/ROW]
[ROW][C]12[/C][C]10.132[/C][C]9.67291666666667[/C][C]0.459083333333333[/C][/ROW]
[ROW][C]13[/C][C]9.849[/C][C]10.0355583333333[/C][C]-0.186558333333336[/C][/ROW]
[ROW][C]14[/C][C]9.172[/C][C]9.17755833333333[/C][C]-0.00555833333333307[/C][/ROW]
[ROW][C]15[/C][C]10.313[/C][C]10.0323583333333[/C][C]0.280641666666667[/C][/ROW]
[ROW][C]16[/C][C]9.819[/C][C]9.70855833333333[/C][C]0.110441666666667[/C][/ROW]
[ROW][C]17[/C][C]9.955[/C][C]9.94155833333333[/C][C]0.0134416666666663[/C][/ROW]
[ROW][C]18[/C][C]10.048[/C][C]9.99815833333333[/C][C]0.0498416666666664[/C][/ROW]
[ROW][C]19[/C][C]10.082[/C][C]10.4749583333333[/C][C]-0.392958333333333[/C][/ROW]
[ROW][C]20[/C][C]10.541[/C][C]10.4433583333333[/C][C]0.0976416666666666[/C][/ROW]
[ROW][C]21[/C][C]10.208[/C][C]10.2251583333333[/C][C]-0.0171583333333334[/C][/ROW]
[ROW][C]22[/C][C]10.233[/C][C]10.3035583333333[/C][C]-0.0705583333333334[/C][/ROW]
[ROW][C]23[/C][C]9.439[/C][C]9.50375833333333[/C][C]-0.0647583333333336[/C][/ROW]
[ROW][C]24[/C][C]9.963[/C][C]9.87535833333333[/C][C]0.0876416666666661[/C][/ROW]
[ROW][C]25[/C][C]10.158[/C][C]10.238[/C][C]-0.0800000000000031[/C][/ROW]
[ROW][C]26[/C][C]9.225[/C][C]9.38[/C][C]-0.155[/C][/ROW]
[ROW][C]27[/C][C]10.474[/C][C]10.2348[/C][C]0.2392[/C][/ROW]
[ROW][C]28[/C][C]9.757[/C][C]9.911[/C][C]-0.154000000000001[/C][/ROW]
[ROW][C]29[/C][C]10.49[/C][C]10.144[/C][C]0.346[/C][/ROW]
[ROW][C]30[/C][C]10.281[/C][C]10.2006[/C][C]0.0804000000000006[/C][/ROW]
[ROW][C]31[/C][C]10.444[/C][C]10.6774[/C][C]-0.2334[/C][/ROW]
[ROW][C]32[/C][C]10.64[/C][C]10.6458[/C][C]-0.00579999999999958[/C][/ROW]
[ROW][C]33[/C][C]10.695[/C][C]10.4276[/C][C]0.2674[/C][/ROW]
[ROW][C]34[/C][C]10.786[/C][C]10.506[/C][C]0.279999999999999[/C][/ROW]
[ROW][C]35[/C][C]9.832[/C][C]9.7062[/C][C]0.125800000000001[/C][/ROW]
[ROW][C]36[/C][C]9.747[/C][C]10.0778[/C][C]-0.3308[/C][/ROW]
[ROW][C]37[/C][C]10.411[/C][C]10.4404416666667[/C][C]-0.0294416666666694[/C][/ROW]
[ROW][C]38[/C][C]9.511[/C][C]9.58244166666667[/C][C]-0.0714416666666671[/C][/ROW]
[ROW][C]39[/C][C]10.402[/C][C]10.4372416666667[/C][C]-0.035241666666667[/C][/ROW]
[ROW][C]40[/C][C]9.701[/C][C]10.1134416666667[/C][C]-0.412441666666666[/C][/ROW]
[ROW][C]41[/C][C]10.54[/C][C]10.3464416666667[/C][C]0.193558333333333[/C][/ROW]
[ROW][C]42[/C][C]10.112[/C][C]10.4030416666667[/C][C]-0.291041666666666[/C][/ROW]
[ROW][C]43[/C][C]10.915[/C][C]10.8798416666667[/C][C]0.0351583333333324[/C][/ROW]
[ROW][C]44[/C][C]11.183[/C][C]10.8482416666667[/C][C]0.334758333333333[/C][/ROW]
[ROW][C]45[/C][C]10.384[/C][C]10.6300416666667[/C][C]-0.246041666666666[/C][/ROW]
[ROW][C]46[/C][C]10.834[/C][C]10.7084416666667[/C][C]0.125558333333333[/C][/ROW]
[ROW][C]47[/C][C]9.886[/C][C]9.90864166666667[/C][C]-0.0226416666666673[/C][/ROW]
[ROW][C]48[/C][C]10.216[/C][C]10.2802416666667[/C][C]-0.0642416666666665[/C][/ROW]
[ROW][C]49[/C][C]10.943[/C][C]10.6428833333333[/C][C]0.300116666666664[/C][/ROW]
[ROW][C]50[/C][C]9.867[/C][C]9.78488333333333[/C][C]0.082116666666668[/C][/ROW]
[ROW][C]51[/C][C]10.203[/C][C]10.6396833333333[/C][C]-0.436683333333333[/C][/ROW]
[ROW][C]52[/C][C]10.837[/C][C]10.3158833333333[/C][C]0.521116666666667[/C][/ROW]
[ROW][C]53[/C][C]10.573[/C][C]10.5488833333333[/C][C]0.0241166666666674[/C][/ROW]
[ROW][C]54[/C][C]10.647[/C][C]10.6054833333333[/C][C]0.0415166666666676[/C][/ROW]
[ROW][C]55[/C][C]11.502[/C][C]11.0822833333333[/C][C]0.419716666666667[/C][/ROW]
[ROW][C]56[/C][C]10.656[/C][C]11.0506833333333[/C][C]-0.394683333333332[/C][/ROW]
[ROW][C]57[/C][C]10.866[/C][C]10.8324833333333[/C][C]0.0335166666666669[/C][/ROW]
[ROW][C]58[/C][C]10.835[/C][C]10.9108833333333[/C][C]-0.075883333333332[/C][/ROW]
[ROW][C]59[/C][C]9.945[/C][C]10.1110833333333[/C][C]-0.166083333333333[/C][/ROW]
[ROW][C]60[/C][C]10.331[/C][C]10.4826833333333[/C][C]-0.151683333333333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147357&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147357&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
19.8299.83311666666666-0.00411666666665606
29.1258.975116666666670.149883333333333
39.7829.82991666666667-0.0479166666666673
49.4419.50611666666667-0.0651166666666668
59.1629.73911666666667-0.577116666666667
69.9159.795716666666670.119283333333332
710.44410.27251666666670.171483333333333
810.20910.2409166666667-0.0319166666666677
99.98510.0227166666667-0.0377166666666679
109.84210.1011166666667-0.259116666666667
119.4299.301316666666670.127683333333333
1210.1329.672916666666670.459083333333333
139.84910.0355583333333-0.186558333333336
149.1729.17755833333333-0.00555833333333307
1510.31310.03235833333330.280641666666667
169.8199.708558333333330.110441666666667
179.9559.941558333333330.0134416666666663
1810.0489.998158333333330.0498416666666664
1910.08210.4749583333333-0.392958333333333
2010.54110.44335833333330.0976416666666666
2110.20810.2251583333333-0.0171583333333334
2210.23310.3035583333333-0.0705583333333334
239.4399.50375833333333-0.0647583333333336
249.9639.875358333333330.0876416666666661
2510.15810.238-0.0800000000000031
269.2259.38-0.155
2710.47410.23480.2392
289.7579.911-0.154000000000001
2910.4910.1440.346
3010.28110.20060.0804000000000006
3110.44410.6774-0.2334
3210.6410.6458-0.00579999999999958
3310.69510.42760.2674
3410.78610.5060.279999999999999
359.8329.70620.125800000000001
369.74710.0778-0.3308
3710.41110.4404416666667-0.0294416666666694
389.5119.58244166666667-0.0714416666666671
3910.40210.4372416666667-0.035241666666667
409.70110.1134416666667-0.412441666666666
4110.5410.34644166666670.193558333333333
4210.11210.4030416666667-0.291041666666666
4310.91510.87984166666670.0351583333333324
4411.18310.84824166666670.334758333333333
4510.38410.6300416666667-0.246041666666666
4610.83410.70844166666670.125558333333333
479.8869.90864166666667-0.0226416666666673
4810.21610.2802416666667-0.0642416666666665
4910.94310.64288333333330.300116666666664
509.8679.784883333333330.082116666666668
5110.20310.6396833333333-0.436683333333333
5210.83710.31588333333330.521116666666667
5310.57310.54888333333330.0241166666666674
5410.64710.60548333333330.0415166666666676
5511.50211.08228333333330.419716666666667
5610.65611.0506833333333-0.394683333333332
5710.86610.83248333333330.0335166666666669
5810.83510.9108833333333-0.075883333333332
599.94510.1110833333333-0.166083333333333
6010.33110.4826833333333-0.151683333333333







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.3099888504856890.6199777009713780.690011149514311
170.4779487202213010.9558974404426020.522051279778699
180.3711000379860320.7422000759720640.628899962013968
190.6283974849296920.7432050301406160.371602515070308
200.5133225603726930.9733548792546130.486677439627307
210.3923346545134980.7846693090269970.607665345486502
220.309081141782310.618162283564620.69091885821769
230.2465144465311290.4930288930622580.753485553468871
240.251034944299060.502069888598120.74896505570094
250.1836264811685660.3672529623371330.816373518831434
260.1464818776815420.2929637553630840.853518122318458
270.1359045045795450.2718090091590890.864095495420455
280.1024666532214120.2049333064428230.897533346778588
290.221710310643060.4434206212861210.77828968935694
300.1652159515628320.3304319031256630.834784048437168
310.1665850515034440.3331701030068880.833414948496556
320.1126708122780890.2253416245561770.887329187721911
330.1135248390486960.2270496780973930.886475160951304
340.1259272661264250.2518545322528510.874072733873575
350.0996100949856340.1992201899712680.900389905014366
360.1481748273876030.2963496547752050.851825172612397
370.1097975711568550.219595142313710.890202428843145
380.07094475562032670.1418895112406530.929055244379673
390.06731526089744710.1346305217948940.932684739102553
400.3075833903241320.6151667806482640.692416609675868
410.2371711118667960.4743422237335930.762828888133204
420.249711385445530.4994227708910610.75028861455447
430.3349397657274730.6698795314549460.665060234272527
440.7380717409676690.5238565180646620.261928259032331

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.309988850485689 & 0.619977700971378 & 0.690011149514311 \tabularnewline
17 & 0.477948720221301 & 0.955897440442602 & 0.522051279778699 \tabularnewline
18 & 0.371100037986032 & 0.742200075972064 & 0.628899962013968 \tabularnewline
19 & 0.628397484929692 & 0.743205030140616 & 0.371602515070308 \tabularnewline
20 & 0.513322560372693 & 0.973354879254613 & 0.486677439627307 \tabularnewline
21 & 0.392334654513498 & 0.784669309026997 & 0.607665345486502 \tabularnewline
22 & 0.30908114178231 & 0.61816228356462 & 0.69091885821769 \tabularnewline
23 & 0.246514446531129 & 0.493028893062258 & 0.753485553468871 \tabularnewline
24 & 0.25103494429906 & 0.50206988859812 & 0.74896505570094 \tabularnewline
25 & 0.183626481168566 & 0.367252962337133 & 0.816373518831434 \tabularnewline
26 & 0.146481877681542 & 0.292963755363084 & 0.853518122318458 \tabularnewline
27 & 0.135904504579545 & 0.271809009159089 & 0.864095495420455 \tabularnewline
28 & 0.102466653221412 & 0.204933306442823 & 0.897533346778588 \tabularnewline
29 & 0.22171031064306 & 0.443420621286121 & 0.77828968935694 \tabularnewline
30 & 0.165215951562832 & 0.330431903125663 & 0.834784048437168 \tabularnewline
31 & 0.166585051503444 & 0.333170103006888 & 0.833414948496556 \tabularnewline
32 & 0.112670812278089 & 0.225341624556177 & 0.887329187721911 \tabularnewline
33 & 0.113524839048696 & 0.227049678097393 & 0.886475160951304 \tabularnewline
34 & 0.125927266126425 & 0.251854532252851 & 0.874072733873575 \tabularnewline
35 & 0.099610094985634 & 0.199220189971268 & 0.900389905014366 \tabularnewline
36 & 0.148174827387603 & 0.296349654775205 & 0.851825172612397 \tabularnewline
37 & 0.109797571156855 & 0.21959514231371 & 0.890202428843145 \tabularnewline
38 & 0.0709447556203267 & 0.141889511240653 & 0.929055244379673 \tabularnewline
39 & 0.0673152608974471 & 0.134630521794894 & 0.932684739102553 \tabularnewline
40 & 0.307583390324132 & 0.615166780648264 & 0.692416609675868 \tabularnewline
41 & 0.237171111866796 & 0.474342223733593 & 0.762828888133204 \tabularnewline
42 & 0.24971138544553 & 0.499422770891061 & 0.75028861455447 \tabularnewline
43 & 0.334939765727473 & 0.669879531454946 & 0.665060234272527 \tabularnewline
44 & 0.738071740967669 & 0.523856518064662 & 0.261928259032331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147357&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]0.309988850485689[/C][C]0.619977700971378[/C][C]0.690011149514311[/C][/ROW]
[ROW][C]17[/C][C]0.477948720221301[/C][C]0.955897440442602[/C][C]0.522051279778699[/C][/ROW]
[ROW][C]18[/C][C]0.371100037986032[/C][C]0.742200075972064[/C][C]0.628899962013968[/C][/ROW]
[ROW][C]19[/C][C]0.628397484929692[/C][C]0.743205030140616[/C][C]0.371602515070308[/C][/ROW]
[ROW][C]20[/C][C]0.513322560372693[/C][C]0.973354879254613[/C][C]0.486677439627307[/C][/ROW]
[ROW][C]21[/C][C]0.392334654513498[/C][C]0.784669309026997[/C][C]0.607665345486502[/C][/ROW]
[ROW][C]22[/C][C]0.30908114178231[/C][C]0.61816228356462[/C][C]0.69091885821769[/C][/ROW]
[ROW][C]23[/C][C]0.246514446531129[/C][C]0.493028893062258[/C][C]0.753485553468871[/C][/ROW]
[ROW][C]24[/C][C]0.25103494429906[/C][C]0.50206988859812[/C][C]0.74896505570094[/C][/ROW]
[ROW][C]25[/C][C]0.183626481168566[/C][C]0.367252962337133[/C][C]0.816373518831434[/C][/ROW]
[ROW][C]26[/C][C]0.146481877681542[/C][C]0.292963755363084[/C][C]0.853518122318458[/C][/ROW]
[ROW][C]27[/C][C]0.135904504579545[/C][C]0.271809009159089[/C][C]0.864095495420455[/C][/ROW]
[ROW][C]28[/C][C]0.102466653221412[/C][C]0.204933306442823[/C][C]0.897533346778588[/C][/ROW]
[ROW][C]29[/C][C]0.22171031064306[/C][C]0.443420621286121[/C][C]0.77828968935694[/C][/ROW]
[ROW][C]30[/C][C]0.165215951562832[/C][C]0.330431903125663[/C][C]0.834784048437168[/C][/ROW]
[ROW][C]31[/C][C]0.166585051503444[/C][C]0.333170103006888[/C][C]0.833414948496556[/C][/ROW]
[ROW][C]32[/C][C]0.112670812278089[/C][C]0.225341624556177[/C][C]0.887329187721911[/C][/ROW]
[ROW][C]33[/C][C]0.113524839048696[/C][C]0.227049678097393[/C][C]0.886475160951304[/C][/ROW]
[ROW][C]34[/C][C]0.125927266126425[/C][C]0.251854532252851[/C][C]0.874072733873575[/C][/ROW]
[ROW][C]35[/C][C]0.099610094985634[/C][C]0.199220189971268[/C][C]0.900389905014366[/C][/ROW]
[ROW][C]36[/C][C]0.148174827387603[/C][C]0.296349654775205[/C][C]0.851825172612397[/C][/ROW]
[ROW][C]37[/C][C]0.109797571156855[/C][C]0.21959514231371[/C][C]0.890202428843145[/C][/ROW]
[ROW][C]38[/C][C]0.0709447556203267[/C][C]0.141889511240653[/C][C]0.929055244379673[/C][/ROW]
[ROW][C]39[/C][C]0.0673152608974471[/C][C]0.134630521794894[/C][C]0.932684739102553[/C][/ROW]
[ROW][C]40[/C][C]0.307583390324132[/C][C]0.615166780648264[/C][C]0.692416609675868[/C][/ROW]
[ROW][C]41[/C][C]0.237171111866796[/C][C]0.474342223733593[/C][C]0.762828888133204[/C][/ROW]
[ROW][C]42[/C][C]0.24971138544553[/C][C]0.499422770891061[/C][C]0.75028861455447[/C][/ROW]
[ROW][C]43[/C][C]0.334939765727473[/C][C]0.669879531454946[/C][C]0.665060234272527[/C][/ROW]
[ROW][C]44[/C][C]0.738071740967669[/C][C]0.523856518064662[/C][C]0.261928259032331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147357&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147357&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
160.3099888504856890.6199777009713780.690011149514311
170.4779487202213010.9558974404426020.522051279778699
180.3711000379860320.7422000759720640.628899962013968
190.6283974849296920.7432050301406160.371602515070308
200.5133225603726930.9733548792546130.486677439627307
210.3923346545134980.7846693090269970.607665345486502
220.309081141782310.618162283564620.69091885821769
230.2465144465311290.4930288930622580.753485553468871
240.251034944299060.502069888598120.74896505570094
250.1836264811685660.3672529623371330.816373518831434
260.1464818776815420.2929637553630840.853518122318458
270.1359045045795450.2718090091590890.864095495420455
280.1024666532214120.2049333064428230.897533346778588
290.221710310643060.4434206212861210.77828968935694
300.1652159515628320.3304319031256630.834784048437168
310.1665850515034440.3331701030068880.833414948496556
320.1126708122780890.2253416245561770.887329187721911
330.1135248390486960.2270496780973930.886475160951304
340.1259272661264250.2518545322528510.874072733873575
350.0996100949856340.1992201899712680.900389905014366
360.1481748273876030.2963496547752050.851825172612397
370.1097975711568550.219595142313710.890202428843145
380.07094475562032670.1418895112406530.929055244379673
390.06731526089744710.1346305217948940.932684739102553
400.3075833903241320.6151667806482640.692416609675868
410.2371711118667960.4743422237335930.762828888133204
420.249711385445530.4994227708910610.75028861455447
430.3349397657274730.6698795314549460.665060234272527
440.7380717409676690.5238565180646620.261928259032331







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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147357&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147357&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147357&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 level00OK
5% type I error level00OK
10% type I error level00OK



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