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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, 05 Dec 2008 07:02:35 -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/2008/Dec/05/t12284858810vok74pshmpz3mk.htm/, Retrieved Thu, 31 Oct 2024 23:18:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29272, Retrieved Thu, 31 Oct 2024 23:18:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact247
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [paper regression ...] [2008-12-05 12:51:10] [077ffec662d24c06be4c491541a44245]
-   P   [Multiple Regression] [paper regressie z...] [2008-12-05 13:36:01] [077ffec662d24c06be4c491541a44245]
-   P       [Multiple Regression] [paper regression ...] [2008-12-05 14:02:35] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
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Dataseries X:
12300.00	0
12092.80	0
12380.80	0
12196.90	0
9455.00	0
13168.00	0
13427.90	0
11980.50	0
11884.80	0
11691.70	0
12233.80	0
14341.40	0
13130.70	0
12421.10	0
14285.80	0
12864.60	0
11160.20	0
14316.20	0
14388.70	0
14013.90	0
13419.00	0
12769.60	0
13315.50	0
15332.90	0
14243.00	0
13824.40	0
14962.90	0
13202.90	0
12199.00	0
15508.90	0
14199.80	0
15169.60	0
14058.00	0
13786.20	0
14147.90	0
16541.70	0
13587.50	0
15582.40	0
15802.80	0
14130.50	0
12923.20	0
15612.20	1
16033.70	1
16036.60	1
14037.80	1
15330.60	1
15038.30	1
17401.80	1
14992.50	1
16043.70	1
16929.60	1
15921.30	1
14417.20	1
15961.00	1
17851.90	1
16483.90	1
14215.50	1
17429.70	1
17839.50	1
17629.20	1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29272&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29272&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 13325.2037950664 + 16.9434535104332D[t] -1703.83777988615M1[t] -1442.73719165085M2[t] -644.276603415561M3[t] -1934.45601518026M4[t] -3647.81542694497M5[t] -849.903529411764M6[t] -663.802941176471M7[t] -1188.34235294117M8[t] -2483.26176470588M9[t] -1885.76117647059M10[t] -1653.36058823529M11[t] + 81.039411764706t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  13325.2037950664 +  16.9434535104332D[t] -1703.83777988615M1[t] -1442.73719165085M2[t] -644.276603415561M3[t] -1934.45601518026M4[t] -3647.81542694497M5[t] -849.903529411764M6[t] -663.802941176471M7[t] -1188.34235294117M8[t] -2483.26176470588M9[t] -1885.76117647059M10[t] -1653.36058823529M11[t] +  81.039411764706t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29272&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  13325.2037950664 +  16.9434535104332D[t] -1703.83777988615M1[t] -1442.73719165085M2[t] -644.276603415561M3[t] -1934.45601518026M4[t] -3647.81542694497M5[t] -849.903529411764M6[t] -663.802941176471M7[t] -1188.34235294117M8[t] -2483.26176470588M9[t] -1885.76117647059M10[t] -1653.36058823529M11[t] +  81.039411764706t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29272&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] = + 13325.2037950664 + 16.9434535104332D[t] -1703.83777988615M1[t] -1442.73719165085M2[t] -644.276603415561M3[t] -1934.45601518026M4[t] -3647.81542694497M5[t] -849.903529411764M6[t] -663.802941176471M7[t] -1188.34235294117M8[t] -2483.26176470588M9[t] -1885.76117647059M10[t] -1653.36058823529M11[t] + 81.039411764706t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)13325.2037950664339.12763339.292600
D16.9434535104332292.0549310.0580.9539880.476994
M1-1703.83777988615390.608938-4.3627.2e-053.6e-05
M2-1442.73719165085389.903157-3.70020.0005740.000287
M3-644.276603415561389.353331-1.65470.1047870.052393
M4-1934.45601518026388.960123-4.97341e-055e-06
M5-3647.81542694497388.724008-9.384100
M6-849.903529411764389.923412-2.17970.0344380.017219
M7-663.802941176471389.059097-1.70620.0947190.04736
M8-1188.34235294117388.350499-3.060.0036870.001843
M9-2483.26176470588387.798473-6.403500
M10-1885.76117647059387.403687-4.86771.4e-057e-06
M11-1653.36058823529387.166622-4.27049.7e-054.8e-05
t81.0394117647067.82354410.358400

\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) & 13325.2037950664 & 339.127633 & 39.2926 & 0 & 0 \tabularnewline
D & 16.9434535104332 & 292.054931 & 0.058 & 0.953988 & 0.476994 \tabularnewline
M1 & -1703.83777988615 & 390.608938 & -4.362 & 7.2e-05 & 3.6e-05 \tabularnewline
M2 & -1442.73719165085 & 389.903157 & -3.7002 & 0.000574 & 0.000287 \tabularnewline
M3 & -644.276603415561 & 389.353331 & -1.6547 & 0.104787 & 0.052393 \tabularnewline
M4 & -1934.45601518026 & 388.960123 & -4.9734 & 1e-05 & 5e-06 \tabularnewline
M5 & -3647.81542694497 & 388.724008 & -9.3841 & 0 & 0 \tabularnewline
M6 & -849.903529411764 & 389.923412 & -2.1797 & 0.034438 & 0.017219 \tabularnewline
M7 & -663.802941176471 & 389.059097 & -1.7062 & 0.094719 & 0.04736 \tabularnewline
M8 & -1188.34235294117 & 388.350499 & -3.06 & 0.003687 & 0.001843 \tabularnewline
M9 & -2483.26176470588 & 387.798473 & -6.4035 & 0 & 0 \tabularnewline
M10 & -1885.76117647059 & 387.403687 & -4.8677 & 1.4e-05 & 7e-06 \tabularnewline
M11 & -1653.36058823529 & 387.166622 & -4.2704 & 9.7e-05 & 4.8e-05 \tabularnewline
t & 81.039411764706 & 7.823544 & 10.3584 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29272&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]13325.2037950664[/C][C]339.127633[/C][C]39.2926[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]D[/C][C]16.9434535104332[/C][C]292.054931[/C][C]0.058[/C][C]0.953988[/C][C]0.476994[/C][/ROW]
[ROW][C]M1[/C][C]-1703.83777988615[/C][C]390.608938[/C][C]-4.362[/C][C]7.2e-05[/C][C]3.6e-05[/C][/ROW]
[ROW][C]M2[/C][C]-1442.73719165085[/C][C]389.903157[/C][C]-3.7002[/C][C]0.000574[/C][C]0.000287[/C][/ROW]
[ROW][C]M3[/C][C]-644.276603415561[/C][C]389.353331[/C][C]-1.6547[/C][C]0.104787[/C][C]0.052393[/C][/ROW]
[ROW][C]M4[/C][C]-1934.45601518026[/C][C]388.960123[/C][C]-4.9734[/C][C]1e-05[/C][C]5e-06[/C][/ROW]
[ROW][C]M5[/C][C]-3647.81542694497[/C][C]388.724008[/C][C]-9.3841[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-849.903529411764[/C][C]389.923412[/C][C]-2.1797[/C][C]0.034438[/C][C]0.017219[/C][/ROW]
[ROW][C]M7[/C][C]-663.802941176471[/C][C]389.059097[/C][C]-1.7062[/C][C]0.094719[/C][C]0.04736[/C][/ROW]
[ROW][C]M8[/C][C]-1188.34235294117[/C][C]388.350499[/C][C]-3.06[/C][C]0.003687[/C][C]0.001843[/C][/ROW]
[ROW][C]M9[/C][C]-2483.26176470588[/C][C]387.798473[/C][C]-6.4035[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-1885.76117647059[/C][C]387.403687[/C][C]-4.8677[/C][C]1.4e-05[/C][C]7e-06[/C][/ROW]
[ROW][C]M11[/C][C]-1653.36058823529[/C][C]387.166622[/C][C]-4.2704[/C][C]9.7e-05[/C][C]4.8e-05[/C][/ROW]
[ROW][C]t[/C][C]81.039411764706[/C][C]7.823544[/C][C]10.3584[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29272&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)13325.2037950664339.12763339.292600
D16.9434535104332292.0549310.0580.9539880.476994
M1-1703.83777988615390.608938-4.3627.2e-053.6e-05
M2-1442.73719165085389.903157-3.70020.0005740.000287
M3-644.276603415561389.353331-1.65470.1047870.052393
M4-1934.45601518026388.960123-4.97341e-055e-06
M5-3647.81542694497388.724008-9.384100
M6-849.903529411764389.923412-2.17970.0344380.017219
M7-663.802941176471389.059097-1.70620.0947190.04736
M8-1188.34235294117388.350499-3.060.0036870.001843
M9-2483.26176470588387.798473-6.403500
M10-1885.76117647059387.403687-4.86771.4e-057e-06
M11-1653.36058823529387.166622-4.27049.7e-054.8e-05
t81.0394117647067.82354410.358400







Multiple Linear Regression - Regression Statistics
Multiple R0.9542519941186
R-squared0.910596868279325
Adjusted R-squared0.885330765836525
F-TEST (value)36.0402586960473
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation612.039183841238
Sum Squared Residuals17231230.2776242

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.9542519941186 \tabularnewline
R-squared & 0.910596868279325 \tabularnewline
Adjusted R-squared & 0.885330765836525 \tabularnewline
F-TEST (value) & 36.0402586960473 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 612.039183841238 \tabularnewline
Sum Squared Residuals & 17231230.2776242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29272&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.9542519941186[/C][/ROW]
[ROW][C]R-squared[/C][C]0.910596868279325[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.885330765836525[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]36.0402586960473[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]612.039183841238[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]17231230.2776242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29272&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29272&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 R0.9542519941186
R-squared0.910596868279325
Adjusted R-squared0.885330765836525
F-TEST (value)36.0402586960473
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation612.039183841238
Sum Squared Residuals17231230.2776242







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11230011702.405426945597.594573054989
212092.812044.545426945048.2545730550292
312380.812924.0454269450-543.245426944971
412196.911714.9054269450481.994573055034
5945510082.5854269450-627.585426944965
61316812961.5367362429206.463263757115
713427.913228.6767362429199.223263757114
811980.512785.1767362429-804.676736242883
911884.811571.2967362429313.503263757121
1011691.712249.8367362429-558.136736242882
1112233.812563.2767362429-329.476736242883
1214341.414297.676736242943.7232637571157
1313130.712674.8783681214455.82163187857
1412421.113017.0183681214-595.918368121441
1514285.813896.5183681214389.28163187856
1612864.612687.3783681214177.221631878559
1711160.211055.0583681214105.141631878559
1814316.213934.0096774194382.190322580647
1914388.714201.1496774194187.550322580647
2014013.913757.6496774194256.250322580645
211341912543.7696774194875.230322580645
2212769.613222.3096774194-452.709677419354
2313315.513535.7496774194-220.249677419354
2415332.915270.149677419462.7503225806468
251424313647.3513092979595.648690702097
2613824.413989.4913092979-165.091309297913
2714962.914868.991309297993.9086907020875
2813202.913659.8513092979-456.951309297914
291219912027.5313092979171.468690702085
3015508.914906.4826185958602.417381404173
3114199.815173.6226185958-973.822618595827
3215169.614730.1226185958439.477381404173
331405813516.2426185958541.757381404172
3413786.214194.7826185958-408.582618595827
3514147.914508.2226185958-360.322618595827
3616541.716242.6226185958299.077381404175
3713587.514619.8242504744-1032.32425047438
3815582.414961.9642504744620.435749525614
3915802.815841.4642504744-38.6642504743856
4014130.514632.3242504744-501.824250474387
4112923.213000.0042504744-76.804250474387
4215612.215895.8990132827-283.69901328273
4316033.716163.0390132827-129.339013282731
4416036.615719.5390132827317.060986717268
4514037.814505.6590132827-467.859013282734
4615330.615184.1990132827146.400986717268
4715038.315497.6390132827-459.339013282732
4817401.817232.0390132827169.760986717268
4914992.515609.2406451613-616.740645161281
5016043.715951.380645161392.3193548387102
5116929.616830.880645161398.7193548387087
5215921.315621.7406451613299.559354838707
5314417.213989.4206451613427.779354838708
541596116868.3719544592-907.371954459204
5517851.917135.5119544592716.388045540797
5616483.916692.0119544592-208.111954459204
5714215.515478.1319544592-1262.63195445921
5817429.716156.67195445921273.02804554080
5917839.516470.11195445921369.38804554080
6017629.218204.5119544592-575.311954459204

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12300 & 11702.405426945 & 597.594573054989 \tabularnewline
2 & 12092.8 & 12044.5454269450 & 48.2545730550292 \tabularnewline
3 & 12380.8 & 12924.0454269450 & -543.245426944971 \tabularnewline
4 & 12196.9 & 11714.9054269450 & 481.994573055034 \tabularnewline
5 & 9455 & 10082.5854269450 & -627.585426944965 \tabularnewline
6 & 13168 & 12961.5367362429 & 206.463263757115 \tabularnewline
7 & 13427.9 & 13228.6767362429 & 199.223263757114 \tabularnewline
8 & 11980.5 & 12785.1767362429 & -804.676736242883 \tabularnewline
9 & 11884.8 & 11571.2967362429 & 313.503263757121 \tabularnewline
10 & 11691.7 & 12249.8367362429 & -558.136736242882 \tabularnewline
11 & 12233.8 & 12563.2767362429 & -329.476736242883 \tabularnewline
12 & 14341.4 & 14297.6767362429 & 43.7232637571157 \tabularnewline
13 & 13130.7 & 12674.8783681214 & 455.82163187857 \tabularnewline
14 & 12421.1 & 13017.0183681214 & -595.918368121441 \tabularnewline
15 & 14285.8 & 13896.5183681214 & 389.28163187856 \tabularnewline
16 & 12864.6 & 12687.3783681214 & 177.221631878559 \tabularnewline
17 & 11160.2 & 11055.0583681214 & 105.141631878559 \tabularnewline
18 & 14316.2 & 13934.0096774194 & 382.190322580647 \tabularnewline
19 & 14388.7 & 14201.1496774194 & 187.550322580647 \tabularnewline
20 & 14013.9 & 13757.6496774194 & 256.250322580645 \tabularnewline
21 & 13419 & 12543.7696774194 & 875.230322580645 \tabularnewline
22 & 12769.6 & 13222.3096774194 & -452.709677419354 \tabularnewline
23 & 13315.5 & 13535.7496774194 & -220.249677419354 \tabularnewline
24 & 15332.9 & 15270.1496774194 & 62.7503225806468 \tabularnewline
25 & 14243 & 13647.3513092979 & 595.648690702097 \tabularnewline
26 & 13824.4 & 13989.4913092979 & -165.091309297913 \tabularnewline
27 & 14962.9 & 14868.9913092979 & 93.9086907020875 \tabularnewline
28 & 13202.9 & 13659.8513092979 & -456.951309297914 \tabularnewline
29 & 12199 & 12027.5313092979 & 171.468690702085 \tabularnewline
30 & 15508.9 & 14906.4826185958 & 602.417381404173 \tabularnewline
31 & 14199.8 & 15173.6226185958 & -973.822618595827 \tabularnewline
32 & 15169.6 & 14730.1226185958 & 439.477381404173 \tabularnewline
33 & 14058 & 13516.2426185958 & 541.757381404172 \tabularnewline
34 & 13786.2 & 14194.7826185958 & -408.582618595827 \tabularnewline
35 & 14147.9 & 14508.2226185958 & -360.322618595827 \tabularnewline
36 & 16541.7 & 16242.6226185958 & 299.077381404175 \tabularnewline
37 & 13587.5 & 14619.8242504744 & -1032.32425047438 \tabularnewline
38 & 15582.4 & 14961.9642504744 & 620.435749525614 \tabularnewline
39 & 15802.8 & 15841.4642504744 & -38.6642504743856 \tabularnewline
40 & 14130.5 & 14632.3242504744 & -501.824250474387 \tabularnewline
41 & 12923.2 & 13000.0042504744 & -76.804250474387 \tabularnewline
42 & 15612.2 & 15895.8990132827 & -283.69901328273 \tabularnewline
43 & 16033.7 & 16163.0390132827 & -129.339013282731 \tabularnewline
44 & 16036.6 & 15719.5390132827 & 317.060986717268 \tabularnewline
45 & 14037.8 & 14505.6590132827 & -467.859013282734 \tabularnewline
46 & 15330.6 & 15184.1990132827 & 146.400986717268 \tabularnewline
47 & 15038.3 & 15497.6390132827 & -459.339013282732 \tabularnewline
48 & 17401.8 & 17232.0390132827 & 169.760986717268 \tabularnewline
49 & 14992.5 & 15609.2406451613 & -616.740645161281 \tabularnewline
50 & 16043.7 & 15951.3806451613 & 92.3193548387102 \tabularnewline
51 & 16929.6 & 16830.8806451613 & 98.7193548387087 \tabularnewline
52 & 15921.3 & 15621.7406451613 & 299.559354838707 \tabularnewline
53 & 14417.2 & 13989.4206451613 & 427.779354838708 \tabularnewline
54 & 15961 & 16868.3719544592 & -907.371954459204 \tabularnewline
55 & 17851.9 & 17135.5119544592 & 716.388045540797 \tabularnewline
56 & 16483.9 & 16692.0119544592 & -208.111954459204 \tabularnewline
57 & 14215.5 & 15478.1319544592 & -1262.63195445921 \tabularnewline
58 & 17429.7 & 16156.6719544592 & 1273.02804554080 \tabularnewline
59 & 17839.5 & 16470.1119544592 & 1369.38804554080 \tabularnewline
60 & 17629.2 & 18204.5119544592 & -575.311954459204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29272&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]12300[/C][C]11702.405426945[/C][C]597.594573054989[/C][/ROW]
[ROW][C]2[/C][C]12092.8[/C][C]12044.5454269450[/C][C]48.2545730550292[/C][/ROW]
[ROW][C]3[/C][C]12380.8[/C][C]12924.0454269450[/C][C]-543.245426944971[/C][/ROW]
[ROW][C]4[/C][C]12196.9[/C][C]11714.9054269450[/C][C]481.994573055034[/C][/ROW]
[ROW][C]5[/C][C]9455[/C][C]10082.5854269450[/C][C]-627.585426944965[/C][/ROW]
[ROW][C]6[/C][C]13168[/C][C]12961.5367362429[/C][C]206.463263757115[/C][/ROW]
[ROW][C]7[/C][C]13427.9[/C][C]13228.6767362429[/C][C]199.223263757114[/C][/ROW]
[ROW][C]8[/C][C]11980.5[/C][C]12785.1767362429[/C][C]-804.676736242883[/C][/ROW]
[ROW][C]9[/C][C]11884.8[/C][C]11571.2967362429[/C][C]313.503263757121[/C][/ROW]
[ROW][C]10[/C][C]11691.7[/C][C]12249.8367362429[/C][C]-558.136736242882[/C][/ROW]
[ROW][C]11[/C][C]12233.8[/C][C]12563.2767362429[/C][C]-329.476736242883[/C][/ROW]
[ROW][C]12[/C][C]14341.4[/C][C]14297.6767362429[/C][C]43.7232637571157[/C][/ROW]
[ROW][C]13[/C][C]13130.7[/C][C]12674.8783681214[/C][C]455.82163187857[/C][/ROW]
[ROW][C]14[/C][C]12421.1[/C][C]13017.0183681214[/C][C]-595.918368121441[/C][/ROW]
[ROW][C]15[/C][C]14285.8[/C][C]13896.5183681214[/C][C]389.28163187856[/C][/ROW]
[ROW][C]16[/C][C]12864.6[/C][C]12687.3783681214[/C][C]177.221631878559[/C][/ROW]
[ROW][C]17[/C][C]11160.2[/C][C]11055.0583681214[/C][C]105.141631878559[/C][/ROW]
[ROW][C]18[/C][C]14316.2[/C][C]13934.0096774194[/C][C]382.190322580647[/C][/ROW]
[ROW][C]19[/C][C]14388.7[/C][C]14201.1496774194[/C][C]187.550322580647[/C][/ROW]
[ROW][C]20[/C][C]14013.9[/C][C]13757.6496774194[/C][C]256.250322580645[/C][/ROW]
[ROW][C]21[/C][C]13419[/C][C]12543.7696774194[/C][C]875.230322580645[/C][/ROW]
[ROW][C]22[/C][C]12769.6[/C][C]13222.3096774194[/C][C]-452.709677419354[/C][/ROW]
[ROW][C]23[/C][C]13315.5[/C][C]13535.7496774194[/C][C]-220.249677419354[/C][/ROW]
[ROW][C]24[/C][C]15332.9[/C][C]15270.1496774194[/C][C]62.7503225806468[/C][/ROW]
[ROW][C]25[/C][C]14243[/C][C]13647.3513092979[/C][C]595.648690702097[/C][/ROW]
[ROW][C]26[/C][C]13824.4[/C][C]13989.4913092979[/C][C]-165.091309297913[/C][/ROW]
[ROW][C]27[/C][C]14962.9[/C][C]14868.9913092979[/C][C]93.9086907020875[/C][/ROW]
[ROW][C]28[/C][C]13202.9[/C][C]13659.8513092979[/C][C]-456.951309297914[/C][/ROW]
[ROW][C]29[/C][C]12199[/C][C]12027.5313092979[/C][C]171.468690702085[/C][/ROW]
[ROW][C]30[/C][C]15508.9[/C][C]14906.4826185958[/C][C]602.417381404173[/C][/ROW]
[ROW][C]31[/C][C]14199.8[/C][C]15173.6226185958[/C][C]-973.822618595827[/C][/ROW]
[ROW][C]32[/C][C]15169.6[/C][C]14730.1226185958[/C][C]439.477381404173[/C][/ROW]
[ROW][C]33[/C][C]14058[/C][C]13516.2426185958[/C][C]541.757381404172[/C][/ROW]
[ROW][C]34[/C][C]13786.2[/C][C]14194.7826185958[/C][C]-408.582618595827[/C][/ROW]
[ROW][C]35[/C][C]14147.9[/C][C]14508.2226185958[/C][C]-360.322618595827[/C][/ROW]
[ROW][C]36[/C][C]16541.7[/C][C]16242.6226185958[/C][C]299.077381404175[/C][/ROW]
[ROW][C]37[/C][C]13587.5[/C][C]14619.8242504744[/C][C]-1032.32425047438[/C][/ROW]
[ROW][C]38[/C][C]15582.4[/C][C]14961.9642504744[/C][C]620.435749525614[/C][/ROW]
[ROW][C]39[/C][C]15802.8[/C][C]15841.4642504744[/C][C]-38.6642504743856[/C][/ROW]
[ROW][C]40[/C][C]14130.5[/C][C]14632.3242504744[/C][C]-501.824250474387[/C][/ROW]
[ROW][C]41[/C][C]12923.2[/C][C]13000.0042504744[/C][C]-76.804250474387[/C][/ROW]
[ROW][C]42[/C][C]15612.2[/C][C]15895.8990132827[/C][C]-283.69901328273[/C][/ROW]
[ROW][C]43[/C][C]16033.7[/C][C]16163.0390132827[/C][C]-129.339013282731[/C][/ROW]
[ROW][C]44[/C][C]16036.6[/C][C]15719.5390132827[/C][C]317.060986717268[/C][/ROW]
[ROW][C]45[/C][C]14037.8[/C][C]14505.6590132827[/C][C]-467.859013282734[/C][/ROW]
[ROW][C]46[/C][C]15330.6[/C][C]15184.1990132827[/C][C]146.400986717268[/C][/ROW]
[ROW][C]47[/C][C]15038.3[/C][C]15497.6390132827[/C][C]-459.339013282732[/C][/ROW]
[ROW][C]48[/C][C]17401.8[/C][C]17232.0390132827[/C][C]169.760986717268[/C][/ROW]
[ROW][C]49[/C][C]14992.5[/C][C]15609.2406451613[/C][C]-616.740645161281[/C][/ROW]
[ROW][C]50[/C][C]16043.7[/C][C]15951.3806451613[/C][C]92.3193548387102[/C][/ROW]
[ROW][C]51[/C][C]16929.6[/C][C]16830.8806451613[/C][C]98.7193548387087[/C][/ROW]
[ROW][C]52[/C][C]15921.3[/C][C]15621.7406451613[/C][C]299.559354838707[/C][/ROW]
[ROW][C]53[/C][C]14417.2[/C][C]13989.4206451613[/C][C]427.779354838708[/C][/ROW]
[ROW][C]54[/C][C]15961[/C][C]16868.3719544592[/C][C]-907.371954459204[/C][/ROW]
[ROW][C]55[/C][C]17851.9[/C][C]17135.5119544592[/C][C]716.388045540797[/C][/ROW]
[ROW][C]56[/C][C]16483.9[/C][C]16692.0119544592[/C][C]-208.111954459204[/C][/ROW]
[ROW][C]57[/C][C]14215.5[/C][C]15478.1319544592[/C][C]-1262.63195445921[/C][/ROW]
[ROW][C]58[/C][C]17429.7[/C][C]16156.6719544592[/C][C]1273.02804554080[/C][/ROW]
[ROW][C]59[/C][C]17839.5[/C][C]16470.1119544592[/C][C]1369.38804554080[/C][/ROW]
[ROW][C]60[/C][C]17629.2[/C][C]18204.5119544592[/C][C]-575.311954459204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29272&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29272&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
11230011702.405426945597.594573054989
212092.812044.545426945048.2545730550292
312380.812924.0454269450-543.245426944971
412196.911714.9054269450481.994573055034
5945510082.5854269450-627.585426944965
61316812961.5367362429206.463263757115
713427.913228.6767362429199.223263757114
811980.512785.1767362429-804.676736242883
911884.811571.2967362429313.503263757121
1011691.712249.8367362429-558.136736242882
1112233.812563.2767362429-329.476736242883
1214341.414297.676736242943.7232637571157
1313130.712674.8783681214455.82163187857
1412421.113017.0183681214-595.918368121441
1514285.813896.5183681214389.28163187856
1612864.612687.3783681214177.221631878559
1711160.211055.0583681214105.141631878559
1814316.213934.0096774194382.190322580647
1914388.714201.1496774194187.550322580647
2014013.913757.6496774194256.250322580645
211341912543.7696774194875.230322580645
2212769.613222.3096774194-452.709677419354
2313315.513535.7496774194-220.249677419354
2415332.915270.149677419462.7503225806468
251424313647.3513092979595.648690702097
2613824.413989.4913092979-165.091309297913
2714962.914868.991309297993.9086907020875
2813202.913659.8513092979-456.951309297914
291219912027.5313092979171.468690702085
3015508.914906.4826185958602.417381404173
3114199.815173.6226185958-973.822618595827
3215169.614730.1226185958439.477381404173
331405813516.2426185958541.757381404172
3413786.214194.7826185958-408.582618595827
3514147.914508.2226185958-360.322618595827
3616541.716242.6226185958299.077381404175
3713587.514619.8242504744-1032.32425047438
3815582.414961.9642504744620.435749525614
3915802.815841.4642504744-38.6642504743856
4014130.514632.3242504744-501.824250474387
4112923.213000.0042504744-76.804250474387
4215612.215895.8990132827-283.69901328273
4316033.716163.0390132827-129.339013282731
4416036.615719.5390132827317.060986717268
4514037.814505.6590132827-467.859013282734
4615330.615184.1990132827146.400986717268
4715038.315497.6390132827-459.339013282732
4817401.817232.0390132827169.760986717268
4914992.515609.2406451613-616.740645161281
5016043.715951.380645161392.3193548387102
5116929.616830.880645161398.7193548387087
5215921.315621.7406451613299.559354838707
5314417.213989.4206451613427.779354838708
541596116868.3719544592-907.371954459204
5517851.917135.5119544592716.388045540797
5616483.916692.0119544592-208.111954459204
5714215.515478.1319544592-1262.63195445921
5817429.716156.67195445921273.02804554080
5917839.516470.11195445921369.38804554080
6017629.218204.5119544592-575.311954459204







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.442251436059720.884502872119440.55774856394028
180.2770063897217420.5540127794434850.722993610278257
190.1590727792152570.3181455584305140.840927220784743
200.170697679447040.341395358894080.82930232055296
210.1340346071846410.2680692143692830.865965392815359
220.08314254970425190.1662850994085040.916857450295748
230.04628009395288350.09256018790576710.953719906047116
240.02443263898568670.04886527797137340.975567361014313
250.02233271011329390.04466542022658780.977667289886706
260.01178001982456730.02356003964913460.988219980175433
270.005502994562418310.01100598912483660.994497005437582
280.01254196938239140.02508393876478280.987458030617609
290.006971655196678670.01394331039335730.993028344803321
300.006929885392336360.01385977078467270.993070114607664
310.03767907662763240.07535815325526490.962320923372368
320.03346625240106530.06693250480213060.966533747598935
330.07219978338451720.1443995667690340.927800216615483
340.05985295988741470.1197059197748290.940147040112585
350.04443608181493520.08887216362987030.955563918185065
360.03704743254666910.07409486509333820.96295256745333
370.1106167334514910.2212334669029830.889383266548509
380.1301141963643630.2602283927287260.869885803635637
390.08511292263770370.1702258452754070.914887077362296
400.05542824824833510.1108564964966700.944571751751665
410.02810645331894190.05621290663788390.971893546681058
420.01971554921280570.03943109842561140.980284450787194
430.01158171815771840.02316343631543670.988418281842282

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.44225143605972 & 0.88450287211944 & 0.55774856394028 \tabularnewline
18 & 0.277006389721742 & 0.554012779443485 & 0.722993610278257 \tabularnewline
19 & 0.159072779215257 & 0.318145558430514 & 0.840927220784743 \tabularnewline
20 & 0.17069767944704 & 0.34139535889408 & 0.82930232055296 \tabularnewline
21 & 0.134034607184641 & 0.268069214369283 & 0.865965392815359 \tabularnewline
22 & 0.0831425497042519 & 0.166285099408504 & 0.916857450295748 \tabularnewline
23 & 0.0462800939528835 & 0.0925601879057671 & 0.953719906047116 \tabularnewline
24 & 0.0244326389856867 & 0.0488652779713734 & 0.975567361014313 \tabularnewline
25 & 0.0223327101132939 & 0.0446654202265878 & 0.977667289886706 \tabularnewline
26 & 0.0117800198245673 & 0.0235600396491346 & 0.988219980175433 \tabularnewline
27 & 0.00550299456241831 & 0.0110059891248366 & 0.994497005437582 \tabularnewline
28 & 0.0125419693823914 & 0.0250839387647828 & 0.987458030617609 \tabularnewline
29 & 0.00697165519667867 & 0.0139433103933573 & 0.993028344803321 \tabularnewline
30 & 0.00692988539233636 & 0.0138597707846727 & 0.993070114607664 \tabularnewline
31 & 0.0376790766276324 & 0.0753581532552649 & 0.962320923372368 \tabularnewline
32 & 0.0334662524010653 & 0.0669325048021306 & 0.966533747598935 \tabularnewline
33 & 0.0721997833845172 & 0.144399566769034 & 0.927800216615483 \tabularnewline
34 & 0.0598529598874147 & 0.119705919774829 & 0.940147040112585 \tabularnewline
35 & 0.0444360818149352 & 0.0888721636298703 & 0.955563918185065 \tabularnewline
36 & 0.0370474325466691 & 0.0740948650933382 & 0.96295256745333 \tabularnewline
37 & 0.110616733451491 & 0.221233466902983 & 0.889383266548509 \tabularnewline
38 & 0.130114196364363 & 0.260228392728726 & 0.869885803635637 \tabularnewline
39 & 0.0851129226377037 & 0.170225845275407 & 0.914887077362296 \tabularnewline
40 & 0.0554282482483351 & 0.110856496496670 & 0.944571751751665 \tabularnewline
41 & 0.0281064533189419 & 0.0562129066378839 & 0.971893546681058 \tabularnewline
42 & 0.0197155492128057 & 0.0394310984256114 & 0.980284450787194 \tabularnewline
43 & 0.0115817181577184 & 0.0231634363154367 & 0.988418281842282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29272&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.44225143605972[/C][C]0.88450287211944[/C][C]0.55774856394028[/C][/ROW]
[ROW][C]18[/C][C]0.277006389721742[/C][C]0.554012779443485[/C][C]0.722993610278257[/C][/ROW]
[ROW][C]19[/C][C]0.159072779215257[/C][C]0.318145558430514[/C][C]0.840927220784743[/C][/ROW]
[ROW][C]20[/C][C]0.17069767944704[/C][C]0.34139535889408[/C][C]0.82930232055296[/C][/ROW]
[ROW][C]21[/C][C]0.134034607184641[/C][C]0.268069214369283[/C][C]0.865965392815359[/C][/ROW]
[ROW][C]22[/C][C]0.0831425497042519[/C][C]0.166285099408504[/C][C]0.916857450295748[/C][/ROW]
[ROW][C]23[/C][C]0.0462800939528835[/C][C]0.0925601879057671[/C][C]0.953719906047116[/C][/ROW]
[ROW][C]24[/C][C]0.0244326389856867[/C][C]0.0488652779713734[/C][C]0.975567361014313[/C][/ROW]
[ROW][C]25[/C][C]0.0223327101132939[/C][C]0.0446654202265878[/C][C]0.977667289886706[/C][/ROW]
[ROW][C]26[/C][C]0.0117800198245673[/C][C]0.0235600396491346[/C][C]0.988219980175433[/C][/ROW]
[ROW][C]27[/C][C]0.00550299456241831[/C][C]0.0110059891248366[/C][C]0.994497005437582[/C][/ROW]
[ROW][C]28[/C][C]0.0125419693823914[/C][C]0.0250839387647828[/C][C]0.987458030617609[/C][/ROW]
[ROW][C]29[/C][C]0.00697165519667867[/C][C]0.0139433103933573[/C][C]0.993028344803321[/C][/ROW]
[ROW][C]30[/C][C]0.00692988539233636[/C][C]0.0138597707846727[/C][C]0.993070114607664[/C][/ROW]
[ROW][C]31[/C][C]0.0376790766276324[/C][C]0.0753581532552649[/C][C]0.962320923372368[/C][/ROW]
[ROW][C]32[/C][C]0.0334662524010653[/C][C]0.0669325048021306[/C][C]0.966533747598935[/C][/ROW]
[ROW][C]33[/C][C]0.0721997833845172[/C][C]0.144399566769034[/C][C]0.927800216615483[/C][/ROW]
[ROW][C]34[/C][C]0.0598529598874147[/C][C]0.119705919774829[/C][C]0.940147040112585[/C][/ROW]
[ROW][C]35[/C][C]0.0444360818149352[/C][C]0.0888721636298703[/C][C]0.955563918185065[/C][/ROW]
[ROW][C]36[/C][C]0.0370474325466691[/C][C]0.0740948650933382[/C][C]0.96295256745333[/C][/ROW]
[ROW][C]37[/C][C]0.110616733451491[/C][C]0.221233466902983[/C][C]0.889383266548509[/C][/ROW]
[ROW][C]38[/C][C]0.130114196364363[/C][C]0.260228392728726[/C][C]0.869885803635637[/C][/ROW]
[ROW][C]39[/C][C]0.0851129226377037[/C][C]0.170225845275407[/C][C]0.914887077362296[/C][/ROW]
[ROW][C]40[/C][C]0.0554282482483351[/C][C]0.110856496496670[/C][C]0.944571751751665[/C][/ROW]
[ROW][C]41[/C][C]0.0281064533189419[/C][C]0.0562129066378839[/C][C]0.971893546681058[/C][/ROW]
[ROW][C]42[/C][C]0.0197155492128057[/C][C]0.0394310984256114[/C][C]0.980284450787194[/C][/ROW]
[ROW][C]43[/C][C]0.0115817181577184[/C][C]0.0231634363154367[/C][C]0.988418281842282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29272&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29272&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.442251436059720.884502872119440.55774856394028
180.2770063897217420.5540127794434850.722993610278257
190.1590727792152570.3181455584305140.840927220784743
200.170697679447040.341395358894080.82930232055296
210.1340346071846410.2680692143692830.865965392815359
220.08314254970425190.1662850994085040.916857450295748
230.04628009395288350.09256018790576710.953719906047116
240.02443263898568670.04886527797137340.975567361014313
250.02233271011329390.04466542022658780.977667289886706
260.01178001982456730.02356003964913460.988219980175433
270.005502994562418310.01100598912483660.994497005437582
280.01254196938239140.02508393876478280.987458030617609
290.006971655196678670.01394331039335730.993028344803321
300.006929885392336360.01385977078467270.993070114607664
310.03767907662763240.07535815325526490.962320923372368
320.03346625240106530.06693250480213060.966533747598935
330.07219978338451720.1443995667690340.927800216615483
340.05985295988741470.1197059197748290.940147040112585
350.04443608181493520.08887216362987030.955563918185065
360.03704743254666910.07409486509333820.96295256745333
370.1106167334514910.2212334669029830.889383266548509
380.1301141963643630.2602283927287260.869885803635637
390.08511292263770370.1702258452754070.914887077362296
400.05542824824833510.1108564964966700.944571751751665
410.02810645331894190.05621290663788390.971893546681058
420.01971554921280570.03943109842561140.980284450787194
430.01158171815771840.02316343631543670.988418281842282







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level90.333333333333333NOK
10% type I error level150.555555555555556NOK

\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 & 9 & 0.333333333333333 & NOK \tabularnewline
10% type I error level & 15 & 0.555555555555556 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29272&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]9[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]0.555555555555556[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29272&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29272&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 level90.333333333333333NOK
10% type I error level150.555555555555556NOK



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')
}