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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 26 Dec 2009 11:13:42 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/26/t1261851272uhl8cpyjzk1owj5.htm/, Retrieved Mon, 29 Apr 2024 00:54:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70766, Retrieved Mon, 29 Apr 2024 00:54:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2009-11-20 12:03:21] [0750c128064677e728c9436fc3f45ae7]
-   PD    [Multiple Regression] [ws7] [2009-12-26 18:13:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.2	2.2	1.4	1.1	1.2	1.3
1.5	2.3	1.2	1.4	1.1	1.2
1.1	2.3	1.5	1.2	1.4	1.1
1.3	2.2	1.1	1.5	1.2	1.4
1.5	2.2	1.3	1.1	1.5	1.2
1.1	1.6	1.5	1.3	1.1	1.5
1.4	1.8	1.1	1.5	1.3	1.1
1.3	1.7	1.4	1.1	1.5	1.3
1.5	1.9	1.3	1.4	1.1	1.5
1.6	1.8	1.5	1.3	1.4	1.1
1.7	1.9	1.6	1.5	1.3	1.4
1.1	1.5	1.7	1.6	1.5	1.3
1.6	1	1.1	1.7	1.6	1.5
1.3	0.8	1.6	1.1	1.7	1.6
1.7	1.1	1.3	1.6	1.1	1.7
1.6	1.5	1.7	1.3	1.6	1.1
1.7	1.7	1.6	1.7	1.3	1.6
1.9	2.3	1.7	1.6	1.7	1.3
1.8	2.4	1.9	1.7	1.6	1.7
1.9	3	1.8	1.9	1.7	1.6
1.6	3	1.9	1.8	1.9	1.7
1.5	3.2	1.6	1.9	1.8	1.9
1.6	3.2	1.5	1.6	1.9	1.8
1.6	3.2	1.6	1.5	1.6	1.9
1.7	3.5	1.6	1.6	1.5	1.6
2	4	1.7	1.6	1.6	1.5
2	4.3	2	1.7	1.6	1.6
1.9	4.1	2	2	1.7	1.6
1.7	4	1.9	2	2	1.7
1.8	4.1	1.7	1.9	2	2
1.9	4.2	1.8	1.7	1.9	2
1.7	4.5	1.9	1.8	1.7	1.9
2	5.6	1.7	1.9	1.8	1.7
2.1	6.5	2	1.7	1.9	1.8
2.4	7.6	2.1	2	1.7	1.9
2.5	8.5	2.4	2.1	2	1.7
2.5	8.7	2.5	2.4	2.1	2
2.6	8.3	2.5	2.5	2.4	2.1
2.2	8.3	2.6	2.5	2.5	2.4
2.5	8.5	2.2	2.6	2.5	2.5
2.8	8.7	2.5	2.2	2.6	2.5
2.8	8.7	2.8	2.5	2.2	2.6
2.9	8.5	2.8	2.8	2.5	2.2
3	7.9	2.9	2.8	2.8	2.5
3.1	7	3	2.9	2.8	2.8
2.9	5.8	3.1	3	2.9	2.8
2.7	4.5	2.9	3.1	3	2.9
2.2	3.7	2.7	2.9	3.1	3
2.5	3.1	2.2	2.7	2.9	3.1
2.3	2.7	2.5	2.2	2.7	2.9
2.6	2.3	2.3	2.5	2.2	2.7
2.3	1.8	2.6	2.3	2.5	2.2
2.2	1.5	2.3	2.6	2.3	2.5
1.8	1.2	2.2	2.3	2.6	2.3
1.8	1	1.8	2.2	2.3	2.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70766&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]5 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=70766&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70766&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.445876947317449 + 0.0630464964599403X[t] + 0.333944163747943Y1[t] + 0.330677338008161Y2[t] -0.156978631392103Y3[t] + 0.0624645597720463Y4[t] + 0.00560319987550132t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.445876947317449 +  0.0630464964599403X[t] +  0.333944163747943Y1[t] +  0.330677338008161Y2[t] -0.156978631392103Y3[t] +  0.0624645597720463Y4[t] +  0.00560319987550132t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70766&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.445876947317449 +  0.0630464964599403X[t] +  0.333944163747943Y1[t] +  0.330677338008161Y2[t] -0.156978631392103Y3[t] +  0.0624645597720463Y4[t] +  0.00560319987550132t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70766&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70766&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.445876947317449 + 0.0630464964599403X[t] + 0.333944163747943Y1[t] + 0.330677338008161Y2[t] -0.156978631392103Y3[t] + 0.0624645597720463Y4[t] + 0.00560319987550132t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.4458769473174490.1548992.87850.005950.002975
X0.06304649645994030.0151384.16490.0001296.4e-05
Y10.3339441637479430.1395412.39320.0206640.010332
Y20.3306773380081610.1463542.25940.0284330.014217
Y3-0.1569786313921030.146334-1.07270.288750.144375
Y40.06246455977204630.1370120.45590.6505140.325257
t0.005603199875501320.0043371.2920.2025320.101266

\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) & 0.445876947317449 & 0.154899 & 2.8785 & 0.00595 & 0.002975 \tabularnewline
X & 0.0630464964599403 & 0.015138 & 4.1649 & 0.000129 & 6.4e-05 \tabularnewline
Y1 & 0.333944163747943 & 0.139541 & 2.3932 & 0.020664 & 0.010332 \tabularnewline
Y2 & 0.330677338008161 & 0.146354 & 2.2594 & 0.028433 & 0.014217 \tabularnewline
Y3 & -0.156978631392103 & 0.146334 & -1.0727 & 0.28875 & 0.144375 \tabularnewline
Y4 & 0.0624645597720463 & 0.137012 & 0.4559 & 0.650514 & 0.325257 \tabularnewline
t & 0.00560319987550132 & 0.004337 & 1.292 & 0.202532 & 0.101266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70766&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]0.445876947317449[/C][C]0.154899[/C][C]2.8785[/C][C]0.00595[/C][C]0.002975[/C][/ROW]
[ROW][C]X[/C][C]0.0630464964599403[/C][C]0.015138[/C][C]4.1649[/C][C]0.000129[/C][C]6.4e-05[/C][/ROW]
[ROW][C]Y1[/C][C]0.333944163747943[/C][C]0.139541[/C][C]2.3932[/C][C]0.020664[/C][C]0.010332[/C][/ROW]
[ROW][C]Y2[/C][C]0.330677338008161[/C][C]0.146354[/C][C]2.2594[/C][C]0.028433[/C][C]0.014217[/C][/ROW]
[ROW][C]Y3[/C][C]-0.156978631392103[/C][C]0.146334[/C][C]-1.0727[/C][C]0.28875[/C][C]0.144375[/C][/ROW]
[ROW][C]Y4[/C][C]0.0624645597720463[/C][C]0.137012[/C][C]0.4559[/C][C]0.650514[/C][C]0.325257[/C][/ROW]
[ROW][C]t[/C][C]0.00560319987550132[/C][C]0.004337[/C][C]1.292[/C][C]0.202532[/C][C]0.101266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70766&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70766&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.4458769473174490.1548992.87850.005950.002975
X0.06304649645994030.0151384.16490.0001296.4e-05
Y10.3339441637479430.1395412.39320.0206640.010332
Y20.3306773380081610.1463542.25940.0284330.014217
Y3-0.1569786313921030.146334-1.07270.288750.144375
Y40.06246455977204630.1370120.45590.6505140.325257
t0.005603199875501320.0043371.2920.2025320.101266






Multiple Linear Regression - Regression Statistics
Multiple R0.936908177184696
R-squared0.87779693247555
Adjusted R-squared0.862521549034993
F-TEST (value)57.4648051154637
F-TEST (DF numerator)6
F-TEST (DF denominator)48
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.197210679275923
Sum Squared Residuals1.86681849698261

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.936908177184696 \tabularnewline
R-squared & 0.87779693247555 \tabularnewline
Adjusted R-squared & 0.862521549034993 \tabularnewline
F-TEST (value) & 57.4648051154637 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.197210679275923 \tabularnewline
Sum Squared Residuals & 1.86681849698261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70766&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.936908177184696[/C][/ROW]
[ROW][C]R-squared[/C][C]0.87779693247555[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.862521549034993[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]57.4648051154637[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.197210679275923[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.86681849698261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70766&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70766&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.936908177184696
R-squared0.87779693247555
Adjusted R-squared0.862521549034993
F-TEST (value)57.4648051154637
F-TEST (DF numerator)6
F-TEST (DF denominator)48
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.197210679275923
Sum Squared Residuals1.86681849698261






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.21.31427891049405-0.114278910494052
21.51.368052535830410.131947464169587
31.11.35436347183383-0.254363471833830
41.31.36942265217664-0.0694226521766431
51.51.249957248226430.250042751773572
61.11.43218767106564-0.332187671065641
71.41.326576422148350.0734235778516534
81.31.274884471974960.0251155280250395
91.51.434190120681350.0658098793186456
101.61.395130356533180.204869643466815
111.71.541005321101930.158994678898069
121.11.55020989031344-0.450209890313441
131.61.353786126326220.246213873673778
141.31.30589429881680-0.0058942988168041
151.71.496000502322450.203999497677548
161.61.445228713319380.154771286680622
171.71.640643600618990.0593563993810077
181.91.602870560455980.297129439544019
191.81.755318663575910.0446813364240905
201.91.80954649343780.0904535065622017
211.61.79032710558606-0.190327105586062
221.51.76961486452360-0.269614864523604
231.61.62067612750545-0.0206761275054478
241.61.67994605534976-0.0799460553497627
251.71.73448943317166-0.0344894331716588
2621.783065978535510.216934021464490
2721.947080566251400.0529194337486037
281.92.02357980509815-0.123579805098148
291.71.94863680551243-0.248636805512435
301.81.87942745641514-0.0794274564151391
311.91.874292117849010.0257078821509930
321.71.99042068713932-0.290420687139317
3322.00346315907836-0.00346315907836029
342.12.090404580128550.00959541987144743
352.42.335598726142860.0644012738571437
362.52.471608254385460.0283917456145374
372.52.6254598761226-0.125459876122598
382.62.598065077774510.00193492222548675
392.22.64010419881721-0.440104198817212
402.52.56405322226355-0.0640532222635459
412.82.534480172212940.265519827787057
422.82.80850773114932-0.00850773114932122
432.92.828625419808830.0713745801911665
4432.801440916697150.198559083302852
453.12.835503787865930.264496212134073
462.92.81621547902590.0837845209740996
472.72.69668572739270.00331427260729896
482.22.50947602258702-0.309476022587024
492.52.281785957366580.218214042633417
502.32.215917953102420.0840820468975784
512.62.294713326788450.305286673211552
522.32.224515190653080.0754848093469237
532.22.26035948807870-0.0603594880786954
541.82.05486461986693-0.254864619866932
551.81.94704607849970-0.147046078499697

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.2 & 1.31427891049405 & -0.114278910494052 \tabularnewline
2 & 1.5 & 1.36805253583041 & 0.131947464169587 \tabularnewline
3 & 1.1 & 1.35436347183383 & -0.254363471833830 \tabularnewline
4 & 1.3 & 1.36942265217664 & -0.0694226521766431 \tabularnewline
5 & 1.5 & 1.24995724822643 & 0.250042751773572 \tabularnewline
6 & 1.1 & 1.43218767106564 & -0.332187671065641 \tabularnewline
7 & 1.4 & 1.32657642214835 & 0.0734235778516534 \tabularnewline
8 & 1.3 & 1.27488447197496 & 0.0251155280250395 \tabularnewline
9 & 1.5 & 1.43419012068135 & 0.0658098793186456 \tabularnewline
10 & 1.6 & 1.39513035653318 & 0.204869643466815 \tabularnewline
11 & 1.7 & 1.54100532110193 & 0.158994678898069 \tabularnewline
12 & 1.1 & 1.55020989031344 & -0.450209890313441 \tabularnewline
13 & 1.6 & 1.35378612632622 & 0.246213873673778 \tabularnewline
14 & 1.3 & 1.30589429881680 & -0.0058942988168041 \tabularnewline
15 & 1.7 & 1.49600050232245 & 0.203999497677548 \tabularnewline
16 & 1.6 & 1.44522871331938 & 0.154771286680622 \tabularnewline
17 & 1.7 & 1.64064360061899 & 0.0593563993810077 \tabularnewline
18 & 1.9 & 1.60287056045598 & 0.297129439544019 \tabularnewline
19 & 1.8 & 1.75531866357591 & 0.0446813364240905 \tabularnewline
20 & 1.9 & 1.8095464934378 & 0.0904535065622017 \tabularnewline
21 & 1.6 & 1.79032710558606 & -0.190327105586062 \tabularnewline
22 & 1.5 & 1.76961486452360 & -0.269614864523604 \tabularnewline
23 & 1.6 & 1.62067612750545 & -0.0206761275054478 \tabularnewline
24 & 1.6 & 1.67994605534976 & -0.0799460553497627 \tabularnewline
25 & 1.7 & 1.73448943317166 & -0.0344894331716588 \tabularnewline
26 & 2 & 1.78306597853551 & 0.216934021464490 \tabularnewline
27 & 2 & 1.94708056625140 & 0.0529194337486037 \tabularnewline
28 & 1.9 & 2.02357980509815 & -0.123579805098148 \tabularnewline
29 & 1.7 & 1.94863680551243 & -0.248636805512435 \tabularnewline
30 & 1.8 & 1.87942745641514 & -0.0794274564151391 \tabularnewline
31 & 1.9 & 1.87429211784901 & 0.0257078821509930 \tabularnewline
32 & 1.7 & 1.99042068713932 & -0.290420687139317 \tabularnewline
33 & 2 & 2.00346315907836 & -0.00346315907836029 \tabularnewline
34 & 2.1 & 2.09040458012855 & 0.00959541987144743 \tabularnewline
35 & 2.4 & 2.33559872614286 & 0.0644012738571437 \tabularnewline
36 & 2.5 & 2.47160825438546 & 0.0283917456145374 \tabularnewline
37 & 2.5 & 2.6254598761226 & -0.125459876122598 \tabularnewline
38 & 2.6 & 2.59806507777451 & 0.00193492222548675 \tabularnewline
39 & 2.2 & 2.64010419881721 & -0.440104198817212 \tabularnewline
40 & 2.5 & 2.56405322226355 & -0.0640532222635459 \tabularnewline
41 & 2.8 & 2.53448017221294 & 0.265519827787057 \tabularnewline
42 & 2.8 & 2.80850773114932 & -0.00850773114932122 \tabularnewline
43 & 2.9 & 2.82862541980883 & 0.0713745801911665 \tabularnewline
44 & 3 & 2.80144091669715 & 0.198559083302852 \tabularnewline
45 & 3.1 & 2.83550378786593 & 0.264496212134073 \tabularnewline
46 & 2.9 & 2.8162154790259 & 0.0837845209740996 \tabularnewline
47 & 2.7 & 2.6966857273927 & 0.00331427260729896 \tabularnewline
48 & 2.2 & 2.50947602258702 & -0.309476022587024 \tabularnewline
49 & 2.5 & 2.28178595736658 & 0.218214042633417 \tabularnewline
50 & 2.3 & 2.21591795310242 & 0.0840820468975784 \tabularnewline
51 & 2.6 & 2.29471332678845 & 0.305286673211552 \tabularnewline
52 & 2.3 & 2.22451519065308 & 0.0754848093469237 \tabularnewline
53 & 2.2 & 2.26035948807870 & -0.0603594880786954 \tabularnewline
54 & 1.8 & 2.05486461986693 & -0.254864619866932 \tabularnewline
55 & 1.8 & 1.94704607849970 & -0.147046078499697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70766&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]1.2[/C][C]1.31427891049405[/C][C]-0.114278910494052[/C][/ROW]
[ROW][C]2[/C][C]1.5[/C][C]1.36805253583041[/C][C]0.131947464169587[/C][/ROW]
[ROW][C]3[/C][C]1.1[/C][C]1.35436347183383[/C][C]-0.254363471833830[/C][/ROW]
[ROW][C]4[/C][C]1.3[/C][C]1.36942265217664[/C][C]-0.0694226521766431[/C][/ROW]
[ROW][C]5[/C][C]1.5[/C][C]1.24995724822643[/C][C]0.250042751773572[/C][/ROW]
[ROW][C]6[/C][C]1.1[/C][C]1.43218767106564[/C][C]-0.332187671065641[/C][/ROW]
[ROW][C]7[/C][C]1.4[/C][C]1.32657642214835[/C][C]0.0734235778516534[/C][/ROW]
[ROW][C]8[/C][C]1.3[/C][C]1.27488447197496[/C][C]0.0251155280250395[/C][/ROW]
[ROW][C]9[/C][C]1.5[/C][C]1.43419012068135[/C][C]0.0658098793186456[/C][/ROW]
[ROW][C]10[/C][C]1.6[/C][C]1.39513035653318[/C][C]0.204869643466815[/C][/ROW]
[ROW][C]11[/C][C]1.7[/C][C]1.54100532110193[/C][C]0.158994678898069[/C][/ROW]
[ROW][C]12[/C][C]1.1[/C][C]1.55020989031344[/C][C]-0.450209890313441[/C][/ROW]
[ROW][C]13[/C][C]1.6[/C][C]1.35378612632622[/C][C]0.246213873673778[/C][/ROW]
[ROW][C]14[/C][C]1.3[/C][C]1.30589429881680[/C][C]-0.0058942988168041[/C][/ROW]
[ROW][C]15[/C][C]1.7[/C][C]1.49600050232245[/C][C]0.203999497677548[/C][/ROW]
[ROW][C]16[/C][C]1.6[/C][C]1.44522871331938[/C][C]0.154771286680622[/C][/ROW]
[ROW][C]17[/C][C]1.7[/C][C]1.64064360061899[/C][C]0.0593563993810077[/C][/ROW]
[ROW][C]18[/C][C]1.9[/C][C]1.60287056045598[/C][C]0.297129439544019[/C][/ROW]
[ROW][C]19[/C][C]1.8[/C][C]1.75531866357591[/C][C]0.0446813364240905[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]1.8095464934378[/C][C]0.0904535065622017[/C][/ROW]
[ROW][C]21[/C][C]1.6[/C][C]1.79032710558606[/C][C]-0.190327105586062[/C][/ROW]
[ROW][C]22[/C][C]1.5[/C][C]1.76961486452360[/C][C]-0.269614864523604[/C][/ROW]
[ROW][C]23[/C][C]1.6[/C][C]1.62067612750545[/C][C]-0.0206761275054478[/C][/ROW]
[ROW][C]24[/C][C]1.6[/C][C]1.67994605534976[/C][C]-0.0799460553497627[/C][/ROW]
[ROW][C]25[/C][C]1.7[/C][C]1.73448943317166[/C][C]-0.0344894331716588[/C][/ROW]
[ROW][C]26[/C][C]2[/C][C]1.78306597853551[/C][C]0.216934021464490[/C][/ROW]
[ROW][C]27[/C][C]2[/C][C]1.94708056625140[/C][C]0.0529194337486037[/C][/ROW]
[ROW][C]28[/C][C]1.9[/C][C]2.02357980509815[/C][C]-0.123579805098148[/C][/ROW]
[ROW][C]29[/C][C]1.7[/C][C]1.94863680551243[/C][C]-0.248636805512435[/C][/ROW]
[ROW][C]30[/C][C]1.8[/C][C]1.87942745641514[/C][C]-0.0794274564151391[/C][/ROW]
[ROW][C]31[/C][C]1.9[/C][C]1.87429211784901[/C][C]0.0257078821509930[/C][/ROW]
[ROW][C]32[/C][C]1.7[/C][C]1.99042068713932[/C][C]-0.290420687139317[/C][/ROW]
[ROW][C]33[/C][C]2[/C][C]2.00346315907836[/C][C]-0.00346315907836029[/C][/ROW]
[ROW][C]34[/C][C]2.1[/C][C]2.09040458012855[/C][C]0.00959541987144743[/C][/ROW]
[ROW][C]35[/C][C]2.4[/C][C]2.33559872614286[/C][C]0.0644012738571437[/C][/ROW]
[ROW][C]36[/C][C]2.5[/C][C]2.47160825438546[/C][C]0.0283917456145374[/C][/ROW]
[ROW][C]37[/C][C]2.5[/C][C]2.6254598761226[/C][C]-0.125459876122598[/C][/ROW]
[ROW][C]38[/C][C]2.6[/C][C]2.59806507777451[/C][C]0.00193492222548675[/C][/ROW]
[ROW][C]39[/C][C]2.2[/C][C]2.64010419881721[/C][C]-0.440104198817212[/C][/ROW]
[ROW][C]40[/C][C]2.5[/C][C]2.56405322226355[/C][C]-0.0640532222635459[/C][/ROW]
[ROW][C]41[/C][C]2.8[/C][C]2.53448017221294[/C][C]0.265519827787057[/C][/ROW]
[ROW][C]42[/C][C]2.8[/C][C]2.80850773114932[/C][C]-0.00850773114932122[/C][/ROW]
[ROW][C]43[/C][C]2.9[/C][C]2.82862541980883[/C][C]0.0713745801911665[/C][/ROW]
[ROW][C]44[/C][C]3[/C][C]2.80144091669715[/C][C]0.198559083302852[/C][/ROW]
[ROW][C]45[/C][C]3.1[/C][C]2.83550378786593[/C][C]0.264496212134073[/C][/ROW]
[ROW][C]46[/C][C]2.9[/C][C]2.8162154790259[/C][C]0.0837845209740996[/C][/ROW]
[ROW][C]47[/C][C]2.7[/C][C]2.6966857273927[/C][C]0.00331427260729896[/C][/ROW]
[ROW][C]48[/C][C]2.2[/C][C]2.50947602258702[/C][C]-0.309476022587024[/C][/ROW]
[ROW][C]49[/C][C]2.5[/C][C]2.28178595736658[/C][C]0.218214042633417[/C][/ROW]
[ROW][C]50[/C][C]2.3[/C][C]2.21591795310242[/C][C]0.0840820468975784[/C][/ROW]
[ROW][C]51[/C][C]2.6[/C][C]2.29471332678845[/C][C]0.305286673211552[/C][/ROW]
[ROW][C]52[/C][C]2.3[/C][C]2.22451519065308[/C][C]0.0754848093469237[/C][/ROW]
[ROW][C]53[/C][C]2.2[/C][C]2.26035948807870[/C][C]-0.0603594880786954[/C][/ROW]
[ROW][C]54[/C][C]1.8[/C][C]2.05486461986693[/C][C]-0.254864619866932[/C][/ROW]
[ROW][C]55[/C][C]1.8[/C][C]1.94704607849970[/C][C]-0.147046078499697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70766&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70766&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.21.31427891049405-0.114278910494052
21.51.368052535830410.131947464169587
31.11.35436347183383-0.254363471833830
41.31.36942265217664-0.0694226521766431
51.51.249957248226430.250042751773572
61.11.43218767106564-0.332187671065641
71.41.326576422148350.0734235778516534
81.31.274884471974960.0251155280250395
91.51.434190120681350.0658098793186456
101.61.395130356533180.204869643466815
111.71.541005321101930.158994678898069
121.11.55020989031344-0.450209890313441
131.61.353786126326220.246213873673778
141.31.30589429881680-0.0058942988168041
151.71.496000502322450.203999497677548
161.61.445228713319380.154771286680622
171.71.640643600618990.0593563993810077
181.91.602870560455980.297129439544019
191.81.755318663575910.0446813364240905
201.91.80954649343780.0904535065622017
211.61.79032710558606-0.190327105586062
221.51.76961486452360-0.269614864523604
231.61.62067612750545-0.0206761275054478
241.61.67994605534976-0.0799460553497627
251.71.73448943317166-0.0344894331716588
2621.783065978535510.216934021464490
2721.947080566251400.0529194337486037
281.92.02357980509815-0.123579805098148
291.71.94863680551243-0.248636805512435
301.81.87942745641514-0.0794274564151391
311.91.874292117849010.0257078821509930
321.71.99042068713932-0.290420687139317
3322.00346315907836-0.00346315907836029
342.12.090404580128550.00959541987144743
352.42.335598726142860.0644012738571437
362.52.471608254385460.0283917456145374
372.52.6254598761226-0.125459876122598
382.62.598065077774510.00193492222548675
392.22.64010419881721-0.440104198817212
402.52.56405322226355-0.0640532222635459
412.82.534480172212940.265519827787057
422.82.80850773114932-0.00850773114932122
432.92.828625419808830.0713745801911665
4432.801440916697150.198559083302852
453.12.835503787865930.264496212134073
462.92.81621547902590.0837845209740996
472.72.69668572739270.00331427260729896
482.22.50947602258702-0.309476022587024
492.52.281785957366580.218214042633417
502.32.215917953102420.0840820468975784
512.62.294713326788450.305286673211552
522.32.224515190653080.0754848093469237
532.22.26035948807870-0.0603594880786954
541.82.05486461986693-0.254864619866932
551.81.94704607849970-0.147046078499697






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
100.2114201738562090.4228403477124170.788579826143791
110.318024055039390.636048110078780.68197594496061
120.2684396437094980.5368792874189960.731560356290502
130.5429038194484850.914192361103030.457096180551515
140.4222742926943620.8445485853887240.577725707305638
150.3284678812276380.6569357624552770.671532118772362
160.2468615402644470.4937230805288930.753138459735553
170.1827051445188650.3654102890377300.817294855481135
180.1762051266380440.3524102532760880.823794873361956
190.1182649326241380.2365298652482770.881735067375862
200.1142493722857980.2284987445715960.885750627714202
210.1709020937551590.3418041875103190.82909790624484
220.4329825292689140.8659650585378270.567017470731086
230.4471216426913580.8942432853827160.552878357308642
240.429117229759120.858234459518240.57088277024088
250.4110048524543630.8220097049087260.588995147545637
260.4389732117649350.877946423529870.561026788235065
270.3768949339121730.7537898678243460.623105066087827
280.3130940966232380.6261881932464760.686905903376762
290.2815347018541430.5630694037082870.718465298145857
300.2147263294296440.4294526588592880.785273670570356
310.1774902876377380.3549805752754760.822509712362262
320.211906091047640.423812182095280.78809390895236
330.1679826183142960.3359652366285920.832017381685704
340.1334825198295780.2669650396591560.866517480170422
350.1314859435454010.2629718870908020.868514056454599
360.1289913600338380.2579827200676770.871008639966162
370.09271681413486840.1854336282697370.907283185865132
380.1258354331800920.2516708663601830.874164566819909
390.2078617129123170.4157234258246330.792138287087683
400.1840352246546840.3680704493093680.815964775345316
410.2301811628824470.4603623257648940.769818837117553
420.54982346197820.90035307604360.4501765380218
430.7431424153589710.5137151692820580.256857584641029
440.8901798135335160.2196403729329690.109820186466484
450.8509799343505820.2980401312988370.149020065649419

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 & 0.211420173856209 & 0.422840347712417 & 0.788579826143791 \tabularnewline
11 & 0.31802405503939 & 0.63604811007878 & 0.68197594496061 \tabularnewline
12 & 0.268439643709498 & 0.536879287418996 & 0.731560356290502 \tabularnewline
13 & 0.542903819448485 & 0.91419236110303 & 0.457096180551515 \tabularnewline
14 & 0.422274292694362 & 0.844548585388724 & 0.577725707305638 \tabularnewline
15 & 0.328467881227638 & 0.656935762455277 & 0.671532118772362 \tabularnewline
16 & 0.246861540264447 & 0.493723080528893 & 0.753138459735553 \tabularnewline
17 & 0.182705144518865 & 0.365410289037730 & 0.817294855481135 \tabularnewline
18 & 0.176205126638044 & 0.352410253276088 & 0.823794873361956 \tabularnewline
19 & 0.118264932624138 & 0.236529865248277 & 0.881735067375862 \tabularnewline
20 & 0.114249372285798 & 0.228498744571596 & 0.885750627714202 \tabularnewline
21 & 0.170902093755159 & 0.341804187510319 & 0.82909790624484 \tabularnewline
22 & 0.432982529268914 & 0.865965058537827 & 0.567017470731086 \tabularnewline
23 & 0.447121642691358 & 0.894243285382716 & 0.552878357308642 \tabularnewline
24 & 0.42911722975912 & 0.85823445951824 & 0.57088277024088 \tabularnewline
25 & 0.411004852454363 & 0.822009704908726 & 0.588995147545637 \tabularnewline
26 & 0.438973211764935 & 0.87794642352987 & 0.561026788235065 \tabularnewline
27 & 0.376894933912173 & 0.753789867824346 & 0.623105066087827 \tabularnewline
28 & 0.313094096623238 & 0.626188193246476 & 0.686905903376762 \tabularnewline
29 & 0.281534701854143 & 0.563069403708287 & 0.718465298145857 \tabularnewline
30 & 0.214726329429644 & 0.429452658859288 & 0.785273670570356 \tabularnewline
31 & 0.177490287637738 & 0.354980575275476 & 0.822509712362262 \tabularnewline
32 & 0.21190609104764 & 0.42381218209528 & 0.78809390895236 \tabularnewline
33 & 0.167982618314296 & 0.335965236628592 & 0.832017381685704 \tabularnewline
34 & 0.133482519829578 & 0.266965039659156 & 0.866517480170422 \tabularnewline
35 & 0.131485943545401 & 0.262971887090802 & 0.868514056454599 \tabularnewline
36 & 0.128991360033838 & 0.257982720067677 & 0.871008639966162 \tabularnewline
37 & 0.0927168141348684 & 0.185433628269737 & 0.907283185865132 \tabularnewline
38 & 0.125835433180092 & 0.251670866360183 & 0.874164566819909 \tabularnewline
39 & 0.207861712912317 & 0.415723425824633 & 0.792138287087683 \tabularnewline
40 & 0.184035224654684 & 0.368070449309368 & 0.815964775345316 \tabularnewline
41 & 0.230181162882447 & 0.460362325764894 & 0.769818837117553 \tabularnewline
42 & 0.5498234619782 & 0.9003530760436 & 0.4501765380218 \tabularnewline
43 & 0.743142415358971 & 0.513715169282058 & 0.256857584641029 \tabularnewline
44 & 0.890179813533516 & 0.219640372932969 & 0.109820186466484 \tabularnewline
45 & 0.850979934350582 & 0.298040131298837 & 0.149020065649419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70766&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]10[/C][C]0.211420173856209[/C][C]0.422840347712417[/C][C]0.788579826143791[/C][/ROW]
[ROW][C]11[/C][C]0.31802405503939[/C][C]0.63604811007878[/C][C]0.68197594496061[/C][/ROW]
[ROW][C]12[/C][C]0.268439643709498[/C][C]0.536879287418996[/C][C]0.731560356290502[/C][/ROW]
[ROW][C]13[/C][C]0.542903819448485[/C][C]0.91419236110303[/C][C]0.457096180551515[/C][/ROW]
[ROW][C]14[/C][C]0.422274292694362[/C][C]0.844548585388724[/C][C]0.577725707305638[/C][/ROW]
[ROW][C]15[/C][C]0.328467881227638[/C][C]0.656935762455277[/C][C]0.671532118772362[/C][/ROW]
[ROW][C]16[/C][C]0.246861540264447[/C][C]0.493723080528893[/C][C]0.753138459735553[/C][/ROW]
[ROW][C]17[/C][C]0.182705144518865[/C][C]0.365410289037730[/C][C]0.817294855481135[/C][/ROW]
[ROW][C]18[/C][C]0.176205126638044[/C][C]0.352410253276088[/C][C]0.823794873361956[/C][/ROW]
[ROW][C]19[/C][C]0.118264932624138[/C][C]0.236529865248277[/C][C]0.881735067375862[/C][/ROW]
[ROW][C]20[/C][C]0.114249372285798[/C][C]0.228498744571596[/C][C]0.885750627714202[/C][/ROW]
[ROW][C]21[/C][C]0.170902093755159[/C][C]0.341804187510319[/C][C]0.82909790624484[/C][/ROW]
[ROW][C]22[/C][C]0.432982529268914[/C][C]0.865965058537827[/C][C]0.567017470731086[/C][/ROW]
[ROW][C]23[/C][C]0.447121642691358[/C][C]0.894243285382716[/C][C]0.552878357308642[/C][/ROW]
[ROW][C]24[/C][C]0.42911722975912[/C][C]0.85823445951824[/C][C]0.57088277024088[/C][/ROW]
[ROW][C]25[/C][C]0.411004852454363[/C][C]0.822009704908726[/C][C]0.588995147545637[/C][/ROW]
[ROW][C]26[/C][C]0.438973211764935[/C][C]0.87794642352987[/C][C]0.561026788235065[/C][/ROW]
[ROW][C]27[/C][C]0.376894933912173[/C][C]0.753789867824346[/C][C]0.623105066087827[/C][/ROW]
[ROW][C]28[/C][C]0.313094096623238[/C][C]0.626188193246476[/C][C]0.686905903376762[/C][/ROW]
[ROW][C]29[/C][C]0.281534701854143[/C][C]0.563069403708287[/C][C]0.718465298145857[/C][/ROW]
[ROW][C]30[/C][C]0.214726329429644[/C][C]0.429452658859288[/C][C]0.785273670570356[/C][/ROW]
[ROW][C]31[/C][C]0.177490287637738[/C][C]0.354980575275476[/C][C]0.822509712362262[/C][/ROW]
[ROW][C]32[/C][C]0.21190609104764[/C][C]0.42381218209528[/C][C]0.78809390895236[/C][/ROW]
[ROW][C]33[/C][C]0.167982618314296[/C][C]0.335965236628592[/C][C]0.832017381685704[/C][/ROW]
[ROW][C]34[/C][C]0.133482519829578[/C][C]0.266965039659156[/C][C]0.866517480170422[/C][/ROW]
[ROW][C]35[/C][C]0.131485943545401[/C][C]0.262971887090802[/C][C]0.868514056454599[/C][/ROW]
[ROW][C]36[/C][C]0.128991360033838[/C][C]0.257982720067677[/C][C]0.871008639966162[/C][/ROW]
[ROW][C]37[/C][C]0.0927168141348684[/C][C]0.185433628269737[/C][C]0.907283185865132[/C][/ROW]
[ROW][C]38[/C][C]0.125835433180092[/C][C]0.251670866360183[/C][C]0.874164566819909[/C][/ROW]
[ROW][C]39[/C][C]0.207861712912317[/C][C]0.415723425824633[/C][C]0.792138287087683[/C][/ROW]
[ROW][C]40[/C][C]0.184035224654684[/C][C]0.368070449309368[/C][C]0.815964775345316[/C][/ROW]
[ROW][C]41[/C][C]0.230181162882447[/C][C]0.460362325764894[/C][C]0.769818837117553[/C][/ROW]
[ROW][C]42[/C][C]0.5498234619782[/C][C]0.9003530760436[/C][C]0.4501765380218[/C][/ROW]
[ROW][C]43[/C][C]0.743142415358971[/C][C]0.513715169282058[/C][C]0.256857584641029[/C][/ROW]
[ROW][C]44[/C][C]0.890179813533516[/C][C]0.219640372932969[/C][C]0.109820186466484[/C][/ROW]
[ROW][C]45[/C][C]0.850979934350582[/C][C]0.298040131298837[/C][C]0.149020065649419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70766&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70766&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
100.2114201738562090.4228403477124170.788579826143791
110.318024055039390.636048110078780.68197594496061
120.2684396437094980.5368792874189960.731560356290502
130.5429038194484850.914192361103030.457096180551515
140.4222742926943620.8445485853887240.577725707305638
150.3284678812276380.6569357624552770.671532118772362
160.2468615402644470.4937230805288930.753138459735553
170.1827051445188650.3654102890377300.817294855481135
180.1762051266380440.3524102532760880.823794873361956
190.1182649326241380.2365298652482770.881735067375862
200.1142493722857980.2284987445715960.885750627714202
210.1709020937551590.3418041875103190.82909790624484
220.4329825292689140.8659650585378270.567017470731086
230.4471216426913580.8942432853827160.552878357308642
240.429117229759120.858234459518240.57088277024088
250.4110048524543630.8220097049087260.588995147545637
260.4389732117649350.877946423529870.561026788235065
270.3768949339121730.7537898678243460.623105066087827
280.3130940966232380.6261881932464760.686905903376762
290.2815347018541430.5630694037082870.718465298145857
300.2147263294296440.4294526588592880.785273670570356
310.1774902876377380.3549805752754760.822509712362262
320.211906091047640.423812182095280.78809390895236
330.1679826183142960.3359652366285920.832017381685704
340.1334825198295780.2669650396591560.866517480170422
350.1314859435454010.2629718870908020.868514056454599
360.1289913600338380.2579827200676770.871008639966162
370.09271681413486840.1854336282697370.907283185865132
380.1258354331800920.2516708663601830.874164566819909
390.2078617129123170.4157234258246330.792138287087683
400.1840352246546840.3680704493093680.815964775345316
410.2301811628824470.4603623257648940.769818837117553
420.54982346197820.90035307604360.4501765380218
430.7431424153589710.5137151692820580.256857584641029
440.8901798135335160.2196403729329690.109820186466484
450.8509799343505820.2980401312988370.149020065649419






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=70766&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=70766&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70766&T=6

As an alternative you can also use a QR Code:  
QR Code


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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')
}