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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 computationThu, 19 Nov 2009 14:01:04 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t125866454421v2frsgrk563o3.htm/, Retrieved Thu, 28 Mar 2024 10:08:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57955, Retrieved Thu, 28 Mar 2024 10:08:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [Model 1] [2009-11-19 20:45:20] [2c014794d4323c20be9bea6a55dac7b2]
-   PD      [Multiple Regression] [Model 2] [2009-11-19 20:56:07] [2c014794d4323c20be9bea6a55dac7b2]
-   P           [Multiple Regression] [Model 3] [2009-11-19 21:01:04] [a25640248f5f3c4d92f02a597edd3aef] [Current]
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Dataseries X:
109.8	8.4
111.7	8.4
98.6	8.4
96.9	8.6
95.1	8.9
97	8.8
112.7	8.3
102.9	7.5
97.4	7.2
111.4	7.4
87.4	8.8
96.8	9.3
114.1	9.3
110.3	8.7
103.9	8.2
101.6	8.3
94.6	8.5
95.9	8.6
104.7	8.5
102.8	8.2
98.1	8.1
113.9	7.9
80.9	8.6
95.7	8.7
113.2	8.7
105.9	8.5
108.8	8.4
102.3	8.5
99	8.7
100.7	8.7
115.5	8.6
100.7	8.5
109.9	8.3
114.6	8
85.4	8.2
100.5	8.1
114.8	8.1
116.5	8
112.9	7.9
102	7.9
106	8
105.3	8
118.8	7.9
106.1	8
109.3	7.7
117.2	7.2
92.5	7.5
104.2	7.3
112.5	7
122.4	7
113.3	7
100	7.2
110.7	7.3
112.8	7.1
109.8	6.8
117.3	6.4
109.1	6.1
115.9	6.5
96	7.7
99.8	7.9
116.8	7.5
115.7	6.9




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57955&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57955&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
X[t] = + 10.0715783709973 -0.00873369273130395Y[t] -0.100931769606700M1[t] -0.322832544139754M2[t] -0.445119417252861M3[t] -0.359524319432952M4[t] -0.148775873837516M5[t] -0.151564495620915M6[t] -0.258369990641970M7[t] -0.587534677183279M8[t] -0.811808183085685M9[t] -0.779661721234496M10[t] -0.221928197710249M11[t] -0.0262069253751581t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X[t] =  +  10.0715783709973 -0.00873369273130395Y[t] -0.100931769606700M1[t] -0.322832544139754M2[t] -0.445119417252861M3[t] -0.359524319432952M4[t] -0.148775873837516M5[t] -0.151564495620915M6[t] -0.258369990641970M7[t] -0.587534677183279M8[t] -0.811808183085685M9[t] -0.779661721234496M10[t] -0.221928197710249M11[t] -0.0262069253751581t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57955&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X[t] =  +  10.0715783709973 -0.00873369273130395Y[t] -0.100931769606700M1[t] -0.322832544139754M2[t] -0.445119417252861M3[t] -0.359524319432952M4[t] -0.148775873837516M5[t] -0.151564495620915M6[t] -0.258369990641970M7[t] -0.587534677183279M8[t] -0.811808183085685M9[t] -0.779661721234496M10[t] -0.221928197710249M11[t] -0.0262069253751581t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57955&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
X[t] = + 10.0715783709973 -0.00873369273130395Y[t] -0.100931769606700M1[t] -0.322832544139754M2[t] -0.445119417252861M3[t] -0.359524319432952M4[t] -0.148775873837516M5[t] -0.151564495620915M6[t] -0.258369990641970M7[t] -0.587534677183279M8[t] -0.811808183085685M9[t] -0.779661721234496M10[t] -0.221928197710249M11[t] -0.0262069253751581t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)10.07157837099731.6517386.097600
Y-0.008733692731303950.017653-0.49470.623040.31152
M1-0.1009317696067000.390912-0.25820.797360.39868
M2-0.3228325441397540.391096-0.82550.4131970.206598
M3-0.4451194172528610.346364-1.28510.2049170.102459
M4-0.3595243194329520.303319-1.18530.2417330.120867
M5-0.1487758738375160.303999-0.48940.6267910.313396
M6-0.1515644956209150.307623-0.49270.6244740.312237
M7-0.2583699906419700.386147-0.66910.5066380.253319
M8-0.5875346771832790.325445-1.80530.0772980.038649
M9-0.8118081830856850.316373-2.5660.0134650.006733
M10-0.7796617212344960.405862-1.9210.0606820.030341
M11-0.2219281977102490.353809-0.62730.5334650.266732
t-0.02620692537515810.00477-5.4941e-061e-06

\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) & 10.0715783709973 & 1.651738 & 6.0976 & 0 & 0 \tabularnewline
Y & -0.00873369273130395 & 0.017653 & -0.4947 & 0.62304 & 0.31152 \tabularnewline
M1 & -0.100931769606700 & 0.390912 & -0.2582 & 0.79736 & 0.39868 \tabularnewline
M2 & -0.322832544139754 & 0.391096 & -0.8255 & 0.413197 & 0.206598 \tabularnewline
M3 & -0.445119417252861 & 0.346364 & -1.2851 & 0.204917 & 0.102459 \tabularnewline
M4 & -0.359524319432952 & 0.303319 & -1.1853 & 0.241733 & 0.120867 \tabularnewline
M5 & -0.148775873837516 & 0.303999 & -0.4894 & 0.626791 & 0.313396 \tabularnewline
M6 & -0.151564495620915 & 0.307623 & -0.4927 & 0.624474 & 0.312237 \tabularnewline
M7 & -0.258369990641970 & 0.386147 & -0.6691 & 0.506638 & 0.253319 \tabularnewline
M8 & -0.587534677183279 & 0.325445 & -1.8053 & 0.077298 & 0.038649 \tabularnewline
M9 & -0.811808183085685 & 0.316373 & -2.566 & 0.013465 & 0.006733 \tabularnewline
M10 & -0.779661721234496 & 0.405862 & -1.921 & 0.060682 & 0.030341 \tabularnewline
M11 & -0.221928197710249 & 0.353809 & -0.6273 & 0.533465 & 0.266732 \tabularnewline
t & -0.0262069253751581 & 0.00477 & -5.494 & 1e-06 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57955&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]10.0715783709973[/C][C]1.651738[/C][C]6.0976[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y[/C][C]-0.00873369273130395[/C][C]0.017653[/C][C]-0.4947[/C][C]0.62304[/C][C]0.31152[/C][/ROW]
[ROW][C]M1[/C][C]-0.100931769606700[/C][C]0.390912[/C][C]-0.2582[/C][C]0.79736[/C][C]0.39868[/C][/ROW]
[ROW][C]M2[/C][C]-0.322832544139754[/C][C]0.391096[/C][C]-0.8255[/C][C]0.413197[/C][C]0.206598[/C][/ROW]
[ROW][C]M3[/C][C]-0.445119417252861[/C][C]0.346364[/C][C]-1.2851[/C][C]0.204917[/C][C]0.102459[/C][/ROW]
[ROW][C]M4[/C][C]-0.359524319432952[/C][C]0.303319[/C][C]-1.1853[/C][C]0.241733[/C][C]0.120867[/C][/ROW]
[ROW][C]M5[/C][C]-0.148775873837516[/C][C]0.303999[/C][C]-0.4894[/C][C]0.626791[/C][C]0.313396[/C][/ROW]
[ROW][C]M6[/C][C]-0.151564495620915[/C][C]0.307623[/C][C]-0.4927[/C][C]0.624474[/C][C]0.312237[/C][/ROW]
[ROW][C]M7[/C][C]-0.258369990641970[/C][C]0.386147[/C][C]-0.6691[/C][C]0.506638[/C][C]0.253319[/C][/ROW]
[ROW][C]M8[/C][C]-0.587534677183279[/C][C]0.325445[/C][C]-1.8053[/C][C]0.077298[/C][C]0.038649[/C][/ROW]
[ROW][C]M9[/C][C]-0.811808183085685[/C][C]0.316373[/C][C]-2.566[/C][C]0.013465[/C][C]0.006733[/C][/ROW]
[ROW][C]M10[/C][C]-0.779661721234496[/C][C]0.405862[/C][C]-1.921[/C][C]0.060682[/C][C]0.030341[/C][/ROW]
[ROW][C]M11[/C][C]-0.221928197710249[/C][C]0.353809[/C][C]-0.6273[/C][C]0.533465[/C][C]0.266732[/C][/ROW]
[ROW][C]t[/C][C]-0.0262069253751581[/C][C]0.00477[/C][C]-5.494[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57955&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)10.07157837099731.6517386.097600
Y-0.008733692731303950.017653-0.49470.623040.31152
M1-0.1009317696067000.390912-0.25820.797360.39868
M2-0.3228325441397540.391096-0.82550.4131970.206598
M3-0.4451194172528610.346364-1.28510.2049170.102459
M4-0.3595243194329520.303319-1.18530.2417330.120867
M5-0.1487758738375160.303999-0.48940.6267910.313396
M6-0.1515644956209150.307623-0.49270.6244740.312237
M7-0.2583699906419700.386147-0.66910.5066380.253319
M8-0.5875346771832790.325445-1.80530.0772980.038649
M9-0.8118081830856850.316373-2.5660.0134650.006733
M10-0.7796617212344960.405862-1.9210.0606820.030341
M11-0.2219281977102490.353809-0.62730.5334650.266732
t-0.02620692537515810.00477-5.4941e-061e-06







Multiple Linear Regression - Regression Statistics
Multiple R0.807916145521653
R-squared0.652728498194565
Adjusted R-squared0.558675799788926
F-TEST (value)6.94002946496464
F-TEST (DF numerator)13
F-TEST (DF denominator)48
p-value2.76054716197294e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.471765822725034
Sum Squared Residuals10.6830235915885

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.807916145521653 \tabularnewline
R-squared & 0.652728498194565 \tabularnewline
Adjusted R-squared & 0.558675799788926 \tabularnewline
F-TEST (value) & 6.94002946496464 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 2.76054716197294e-07 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.471765822725034 \tabularnewline
Sum Squared Residuals & 10.6830235915885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57955&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.807916145521653[/C][/ROW]
[ROW][C]R-squared[/C][C]0.652728498194565[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.558675799788926[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]6.94002946496464[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]2.76054716197294e-07[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.471765822725034[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]10.6830235915885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57955&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57955&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 R0.807916145521653
R-squared0.652728498194565
Adjusted R-squared0.558675799788926
F-TEST (value)6.94002946496464
F-TEST (DF numerator)13
F-TEST (DF denominator)48
p-value2.76054716197294e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.471765822725034
Sum Squared Residuals10.6830235915885







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.48.9854802141183-0.585480214118304
28.48.72077849802058-0.320778498020583
38.48.6866960743124-0.286696074312398
48.68.76093152440037-0.160931524400368
58.98.96119369153699-0.061193691536991
68.88.91560412818896-0.115604128188956
78.38.64547273191127-0.345472731911272
87.58.37569130876158-0.875691308761584
97.28.17324618750619-0.97324618750619
107.48.05691402574397-0.656914025743966
118.88.798049249444350.00195075055565072
129.38.911673810105190.388326189894816
139.38.633442230871770.666557769128233
148.78.418522563342510.281477436657489
158.28.3259243983346-0.125924398334592
168.38.40540006406134-0.105400064061340
178.58.65107743340075-0.151077433400746
188.68.6107280856915-0.0107280856914942
198.58.40085916925980.0991408307401932
208.28.062081573532820.137918426467182
218.17.852649498092380.247350501907618
227.97.720596689413810.179403310586191
238.68.540335147695930.0596648523040709
248.78.606797767607720.0932022323922777
258.78.326819449828040.373180550171955
268.58.142467706858350.357532293141649
278.47.96864619944930.431353800550695
288.58.084803374647530.415196625352469
298.78.298166080881110.401833919118887
308.78.254323256079340.445676743920661
318.67.992052183259830.607947816740172
328.57.765939223766660.734060776233341
338.37.43510881936110.864891180638903
3487.40.6
358.28.186550425903160.0134495740968354
368.18.25039293799557-0.150392937995566
378.17.998362436956060.101637563043939
3887.735407459404630.264592540595368
397.97.618354954749060.281645045250939
407.97.772940377965030.127059622034975
4187.922547127260090.0774528727399124
4287.899665165013440.100334834986557
437.97.648747892744630.251252107255373
4487.404294178515720.59570582148428
457.77.125865930497980.574134069502017
467.27.062809294396710.137190705603287
477.57.81005810300901-0.310058103009009
487.37.90359517038784-0.603595170387844
4977.70396682573616-0.703966825736163
5077.36939556778804-0.369395567788042
5177.30037837315464-0.300378373154644
527.27.47592465892574-0.275924658925736
537.37.56701566692106-0.267015666921062
547.17.51967936502677-0.419679365026767
556.87.41286802282447-0.612868022824466
566.46.99199371542322-0.591993715423219
576.16.81312956454235-0.713129564542348
586.56.75967999044551-0.259679990445511
597.77.465007073947550.234992926052452
607.97.627540313903690.272459686096316
617.57.351928842489660.148071157510341
626.97.11342820458588-0.213428204585881

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.4 & 8.9854802141183 & -0.585480214118304 \tabularnewline
2 & 8.4 & 8.72077849802058 & -0.320778498020583 \tabularnewline
3 & 8.4 & 8.6866960743124 & -0.286696074312398 \tabularnewline
4 & 8.6 & 8.76093152440037 & -0.160931524400368 \tabularnewline
5 & 8.9 & 8.96119369153699 & -0.061193691536991 \tabularnewline
6 & 8.8 & 8.91560412818896 & -0.115604128188956 \tabularnewline
7 & 8.3 & 8.64547273191127 & -0.345472731911272 \tabularnewline
8 & 7.5 & 8.37569130876158 & -0.875691308761584 \tabularnewline
9 & 7.2 & 8.17324618750619 & -0.97324618750619 \tabularnewline
10 & 7.4 & 8.05691402574397 & -0.656914025743966 \tabularnewline
11 & 8.8 & 8.79804924944435 & 0.00195075055565072 \tabularnewline
12 & 9.3 & 8.91167381010519 & 0.388326189894816 \tabularnewline
13 & 9.3 & 8.63344223087177 & 0.666557769128233 \tabularnewline
14 & 8.7 & 8.41852256334251 & 0.281477436657489 \tabularnewline
15 & 8.2 & 8.3259243983346 & -0.125924398334592 \tabularnewline
16 & 8.3 & 8.40540006406134 & -0.105400064061340 \tabularnewline
17 & 8.5 & 8.65107743340075 & -0.151077433400746 \tabularnewline
18 & 8.6 & 8.6107280856915 & -0.0107280856914942 \tabularnewline
19 & 8.5 & 8.4008591692598 & 0.0991408307401932 \tabularnewline
20 & 8.2 & 8.06208157353282 & 0.137918426467182 \tabularnewline
21 & 8.1 & 7.85264949809238 & 0.247350501907618 \tabularnewline
22 & 7.9 & 7.72059668941381 & 0.179403310586191 \tabularnewline
23 & 8.6 & 8.54033514769593 & 0.0596648523040709 \tabularnewline
24 & 8.7 & 8.60679776760772 & 0.0932022323922777 \tabularnewline
25 & 8.7 & 8.32681944982804 & 0.373180550171955 \tabularnewline
26 & 8.5 & 8.14246770685835 & 0.357532293141649 \tabularnewline
27 & 8.4 & 7.9686461994493 & 0.431353800550695 \tabularnewline
28 & 8.5 & 8.08480337464753 & 0.415196625352469 \tabularnewline
29 & 8.7 & 8.29816608088111 & 0.401833919118887 \tabularnewline
30 & 8.7 & 8.25432325607934 & 0.445676743920661 \tabularnewline
31 & 8.6 & 7.99205218325983 & 0.607947816740172 \tabularnewline
32 & 8.5 & 7.76593922376666 & 0.734060776233341 \tabularnewline
33 & 8.3 & 7.4351088193611 & 0.864891180638903 \tabularnewline
34 & 8 & 7.4 & 0.6 \tabularnewline
35 & 8.2 & 8.18655042590316 & 0.0134495740968354 \tabularnewline
36 & 8.1 & 8.25039293799557 & -0.150392937995566 \tabularnewline
37 & 8.1 & 7.99836243695606 & 0.101637563043939 \tabularnewline
38 & 8 & 7.73540745940463 & 0.264592540595368 \tabularnewline
39 & 7.9 & 7.61835495474906 & 0.281645045250939 \tabularnewline
40 & 7.9 & 7.77294037796503 & 0.127059622034975 \tabularnewline
41 & 8 & 7.92254712726009 & 0.0774528727399124 \tabularnewline
42 & 8 & 7.89966516501344 & 0.100334834986557 \tabularnewline
43 & 7.9 & 7.64874789274463 & 0.251252107255373 \tabularnewline
44 & 8 & 7.40429417851572 & 0.59570582148428 \tabularnewline
45 & 7.7 & 7.12586593049798 & 0.574134069502017 \tabularnewline
46 & 7.2 & 7.06280929439671 & 0.137190705603287 \tabularnewline
47 & 7.5 & 7.81005810300901 & -0.310058103009009 \tabularnewline
48 & 7.3 & 7.90359517038784 & -0.603595170387844 \tabularnewline
49 & 7 & 7.70396682573616 & -0.703966825736163 \tabularnewline
50 & 7 & 7.36939556778804 & -0.369395567788042 \tabularnewline
51 & 7 & 7.30037837315464 & -0.300378373154644 \tabularnewline
52 & 7.2 & 7.47592465892574 & -0.275924658925736 \tabularnewline
53 & 7.3 & 7.56701566692106 & -0.267015666921062 \tabularnewline
54 & 7.1 & 7.51967936502677 & -0.419679365026767 \tabularnewline
55 & 6.8 & 7.41286802282447 & -0.612868022824466 \tabularnewline
56 & 6.4 & 6.99199371542322 & -0.591993715423219 \tabularnewline
57 & 6.1 & 6.81312956454235 & -0.713129564542348 \tabularnewline
58 & 6.5 & 6.75967999044551 & -0.259679990445511 \tabularnewline
59 & 7.7 & 7.46500707394755 & 0.234992926052452 \tabularnewline
60 & 7.9 & 7.62754031390369 & 0.272459686096316 \tabularnewline
61 & 7.5 & 7.35192884248966 & 0.148071157510341 \tabularnewline
62 & 6.9 & 7.11342820458588 & -0.213428204585881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57955&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]8.4[/C][C]8.9854802141183[/C][C]-0.585480214118304[/C][/ROW]
[ROW][C]2[/C][C]8.4[/C][C]8.72077849802058[/C][C]-0.320778498020583[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]8.6866960743124[/C][C]-0.286696074312398[/C][/ROW]
[ROW][C]4[/C][C]8.6[/C][C]8.76093152440037[/C][C]-0.160931524400368[/C][/ROW]
[ROW][C]5[/C][C]8.9[/C][C]8.96119369153699[/C][C]-0.061193691536991[/C][/ROW]
[ROW][C]6[/C][C]8.8[/C][C]8.91560412818896[/C][C]-0.115604128188956[/C][/ROW]
[ROW][C]7[/C][C]8.3[/C][C]8.64547273191127[/C][C]-0.345472731911272[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]8.37569130876158[/C][C]-0.875691308761584[/C][/ROW]
[ROW][C]9[/C][C]7.2[/C][C]8.17324618750619[/C][C]-0.97324618750619[/C][/ROW]
[ROW][C]10[/C][C]7.4[/C][C]8.05691402574397[/C][C]-0.656914025743966[/C][/ROW]
[ROW][C]11[/C][C]8.8[/C][C]8.79804924944435[/C][C]0.00195075055565072[/C][/ROW]
[ROW][C]12[/C][C]9.3[/C][C]8.91167381010519[/C][C]0.388326189894816[/C][/ROW]
[ROW][C]13[/C][C]9.3[/C][C]8.63344223087177[/C][C]0.666557769128233[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.41852256334251[/C][C]0.281477436657489[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]8.3259243983346[/C][C]-0.125924398334592[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]8.40540006406134[/C][C]-0.105400064061340[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.65107743340075[/C][C]-0.151077433400746[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.6107280856915[/C][C]-0.0107280856914942[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]8.4008591692598[/C][C]0.0991408307401932[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.06208157353282[/C][C]0.137918426467182[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.85264949809238[/C][C]0.247350501907618[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.72059668941381[/C][C]0.179403310586191[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.54033514769593[/C][C]0.0596648523040709[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]8.60679776760772[/C][C]0.0932022323922777[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.32681944982804[/C][C]0.373180550171955[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.14246770685835[/C][C]0.357532293141649[/C][/ROW]
[ROW][C]27[/C][C]8.4[/C][C]7.9686461994493[/C][C]0.431353800550695[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.08480337464753[/C][C]0.415196625352469[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.29816608088111[/C][C]0.401833919118887[/C][/ROW]
[ROW][C]30[/C][C]8.7[/C][C]8.25432325607934[/C][C]0.445676743920661[/C][/ROW]
[ROW][C]31[/C][C]8.6[/C][C]7.99205218325983[/C][C]0.607947816740172[/C][/ROW]
[ROW][C]32[/C][C]8.5[/C][C]7.76593922376666[/C][C]0.734060776233341[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]7.4351088193611[/C][C]0.864891180638903[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.4[/C][C]0.6[/C][/ROW]
[ROW][C]35[/C][C]8.2[/C][C]8.18655042590316[/C][C]0.0134495740968354[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.25039293799557[/C][C]-0.150392937995566[/C][/ROW]
[ROW][C]37[/C][C]8.1[/C][C]7.99836243695606[/C][C]0.101637563043939[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]7.73540745940463[/C][C]0.264592540595368[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.61835495474906[/C][C]0.281645045250939[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.77294037796503[/C][C]0.127059622034975[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]7.92254712726009[/C][C]0.0774528727399124[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]7.89966516501344[/C][C]0.100334834986557[/C][/ROW]
[ROW][C]43[/C][C]7.9[/C][C]7.64874789274463[/C][C]0.251252107255373[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]7.40429417851572[/C][C]0.59570582148428[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]7.12586593049798[/C][C]0.574134069502017[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]7.06280929439671[/C][C]0.137190705603287[/C][/ROW]
[ROW][C]47[/C][C]7.5[/C][C]7.81005810300901[/C][C]-0.310058103009009[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]7.90359517038784[/C][C]-0.603595170387844[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]7.70396682573616[/C][C]-0.703966825736163[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]7.36939556778804[/C][C]-0.369395567788042[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]7.30037837315464[/C][C]-0.300378373154644[/C][/ROW]
[ROW][C]52[/C][C]7.2[/C][C]7.47592465892574[/C][C]-0.275924658925736[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.56701566692106[/C][C]-0.267015666921062[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]7.51967936502677[/C][C]-0.419679365026767[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]7.41286802282447[/C][C]-0.612868022824466[/C][/ROW]
[ROW][C]56[/C][C]6.4[/C][C]6.99199371542322[/C][C]-0.591993715423219[/C][/ROW]
[ROW][C]57[/C][C]6.1[/C][C]6.81312956454235[/C][C]-0.713129564542348[/C][/ROW]
[ROW][C]58[/C][C]6.5[/C][C]6.75967999044551[/C][C]-0.259679990445511[/C][/ROW]
[ROW][C]59[/C][C]7.7[/C][C]7.46500707394755[/C][C]0.234992926052452[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.62754031390369[/C][C]0.272459686096316[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.35192884248966[/C][C]0.148071157510341[/C][/ROW]
[ROW][C]62[/C][C]6.9[/C][C]7.11342820458588[/C][C]-0.213428204585881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57955&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57955&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.48.9854802141183-0.585480214118304
28.48.72077849802058-0.320778498020583
38.48.6866960743124-0.286696074312398
48.68.76093152440037-0.160931524400368
58.98.96119369153699-0.061193691536991
68.88.91560412818896-0.115604128188956
78.38.64547273191127-0.345472731911272
87.58.37569130876158-0.875691308761584
97.28.17324618750619-0.97324618750619
107.48.05691402574397-0.656914025743966
118.88.798049249444350.00195075055565072
129.38.911673810105190.388326189894816
139.38.633442230871770.666557769128233
148.78.418522563342510.281477436657489
158.28.3259243983346-0.125924398334592
168.38.40540006406134-0.105400064061340
178.58.65107743340075-0.151077433400746
188.68.6107280856915-0.0107280856914942
198.58.40085916925980.0991408307401932
208.28.062081573532820.137918426467182
218.17.852649498092380.247350501907618
227.97.720596689413810.179403310586191
238.68.540335147695930.0596648523040709
248.78.606797767607720.0932022323922777
258.78.326819449828040.373180550171955
268.58.142467706858350.357532293141649
278.47.96864619944930.431353800550695
288.58.084803374647530.415196625352469
298.78.298166080881110.401833919118887
308.78.254323256079340.445676743920661
318.67.992052183259830.607947816740172
328.57.765939223766660.734060776233341
338.37.43510881936110.864891180638903
3487.40.6
358.28.186550425903160.0134495740968354
368.18.25039293799557-0.150392937995566
378.17.998362436956060.101637563043939
3887.735407459404630.264592540595368
397.97.618354954749060.281645045250939
407.97.772940377965030.127059622034975
4187.922547127260090.0774528727399124
4287.899665165013440.100334834986557
437.97.648747892744630.251252107255373
4487.404294178515720.59570582148428
457.77.125865930497980.574134069502017
467.27.062809294396710.137190705603287
477.57.81005810300901-0.310058103009009
487.37.90359517038784-0.603595170387844
4977.70396682573616-0.703966825736163
5077.36939556778804-0.369395567788042
5177.30037837315464-0.300378373154644
527.27.47592465892574-0.275924658925736
537.37.56701566692106-0.267015666921062
547.17.51967936502677-0.419679365026767
556.87.41286802282447-0.612868022824466
566.46.99199371542322-0.591993715423219
576.16.81312956454235-0.713129564542348
586.56.75967999044551-0.259679990445511
597.77.465007073947550.234992926052452
607.97.627540313903690.272459686096316
617.57.351928842489660.148071157510341
626.97.11342820458588-0.213428204585881







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.7115890091356270.5768219817287470.288410990864373
180.5796220995106950.840755800978610.420377900489305
190.4636383069385510.9272766138771010.536361693061449
200.5043917215437180.9912165569125630.495608278456282
210.5802601350055790.8394797299888410.419739864994421
220.5148809591263330.9702380817473350.485119040873667
230.4706919189501930.9413838379003850.529308081049807
240.5295373503703080.9409252992593830.470462649629692
250.4596911820116980.9193823640233950.540308817988302
260.3654690135496920.7309380270993830.634530986450308
270.2771784544121070.5543569088242150.722821545587893
280.1993543546531130.3987087093062250.800645645346888
290.1388142288906800.2776284577813600.86118577110932
300.09229404448225460.1845880889645090.907705955517745
310.06347128539256210.1269425707851240.936528714607438
320.06644977824459670.1328995564891930.933550221755403
330.06557128581387890.1311425716277580.934428714186121
340.04523745495378410.09047490990756820.954762545046216
350.05432100589908730.1086420117981750.945678994100913
360.1107448230254050.221489646050810.889255176974595
370.1127486655351060.2254973310702130.887251334464894
380.09133329084302460.1826665816860490.908666709156975
390.0674080957405840.1348161914811680.932591904259416
400.04757729959620730.09515459919241460.952422700403793
410.03325207918873490.06650415837746970.966747920811265
420.02128788858045270.04257577716090550.978712111419547
430.02891612475459290.05783224950918580.971083875245407
440.03397575426251980.06795150852503970.96602424573748
450.3133214620551440.6266429241102890.686678537944855

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.711589009135627 & 0.576821981728747 & 0.288410990864373 \tabularnewline
18 & 0.579622099510695 & 0.84075580097861 & 0.420377900489305 \tabularnewline
19 & 0.463638306938551 & 0.927276613877101 & 0.536361693061449 \tabularnewline
20 & 0.504391721543718 & 0.991216556912563 & 0.495608278456282 \tabularnewline
21 & 0.580260135005579 & 0.839479729988841 & 0.419739864994421 \tabularnewline
22 & 0.514880959126333 & 0.970238081747335 & 0.485119040873667 \tabularnewline
23 & 0.470691918950193 & 0.941383837900385 & 0.529308081049807 \tabularnewline
24 & 0.529537350370308 & 0.940925299259383 & 0.470462649629692 \tabularnewline
25 & 0.459691182011698 & 0.919382364023395 & 0.540308817988302 \tabularnewline
26 & 0.365469013549692 & 0.730938027099383 & 0.634530986450308 \tabularnewline
27 & 0.277178454412107 & 0.554356908824215 & 0.722821545587893 \tabularnewline
28 & 0.199354354653113 & 0.398708709306225 & 0.800645645346888 \tabularnewline
29 & 0.138814228890680 & 0.277628457781360 & 0.86118577110932 \tabularnewline
30 & 0.0922940444822546 & 0.184588088964509 & 0.907705955517745 \tabularnewline
31 & 0.0634712853925621 & 0.126942570785124 & 0.936528714607438 \tabularnewline
32 & 0.0664497782445967 & 0.132899556489193 & 0.933550221755403 \tabularnewline
33 & 0.0655712858138789 & 0.131142571627758 & 0.934428714186121 \tabularnewline
34 & 0.0452374549537841 & 0.0904749099075682 & 0.954762545046216 \tabularnewline
35 & 0.0543210058990873 & 0.108642011798175 & 0.945678994100913 \tabularnewline
36 & 0.110744823025405 & 0.22148964605081 & 0.889255176974595 \tabularnewline
37 & 0.112748665535106 & 0.225497331070213 & 0.887251334464894 \tabularnewline
38 & 0.0913332908430246 & 0.182666581686049 & 0.908666709156975 \tabularnewline
39 & 0.067408095740584 & 0.134816191481168 & 0.932591904259416 \tabularnewline
40 & 0.0475772995962073 & 0.0951545991924146 & 0.952422700403793 \tabularnewline
41 & 0.0332520791887349 & 0.0665041583774697 & 0.966747920811265 \tabularnewline
42 & 0.0212878885804527 & 0.0425757771609055 & 0.978712111419547 \tabularnewline
43 & 0.0289161247545929 & 0.0578322495091858 & 0.971083875245407 \tabularnewline
44 & 0.0339757542625198 & 0.0679515085250397 & 0.96602424573748 \tabularnewline
45 & 0.313321462055144 & 0.626642924110289 & 0.686678537944855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57955&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]0.711589009135627[/C][C]0.576821981728747[/C][C]0.288410990864373[/C][/ROW]
[ROW][C]18[/C][C]0.579622099510695[/C][C]0.84075580097861[/C][C]0.420377900489305[/C][/ROW]
[ROW][C]19[/C][C]0.463638306938551[/C][C]0.927276613877101[/C][C]0.536361693061449[/C][/ROW]
[ROW][C]20[/C][C]0.504391721543718[/C][C]0.991216556912563[/C][C]0.495608278456282[/C][/ROW]
[ROW][C]21[/C][C]0.580260135005579[/C][C]0.839479729988841[/C][C]0.419739864994421[/C][/ROW]
[ROW][C]22[/C][C]0.514880959126333[/C][C]0.970238081747335[/C][C]0.485119040873667[/C][/ROW]
[ROW][C]23[/C][C]0.470691918950193[/C][C]0.941383837900385[/C][C]0.529308081049807[/C][/ROW]
[ROW][C]24[/C][C]0.529537350370308[/C][C]0.940925299259383[/C][C]0.470462649629692[/C][/ROW]
[ROW][C]25[/C][C]0.459691182011698[/C][C]0.919382364023395[/C][C]0.540308817988302[/C][/ROW]
[ROW][C]26[/C][C]0.365469013549692[/C][C]0.730938027099383[/C][C]0.634530986450308[/C][/ROW]
[ROW][C]27[/C][C]0.277178454412107[/C][C]0.554356908824215[/C][C]0.722821545587893[/C][/ROW]
[ROW][C]28[/C][C]0.199354354653113[/C][C]0.398708709306225[/C][C]0.800645645346888[/C][/ROW]
[ROW][C]29[/C][C]0.138814228890680[/C][C]0.277628457781360[/C][C]0.86118577110932[/C][/ROW]
[ROW][C]30[/C][C]0.0922940444822546[/C][C]0.184588088964509[/C][C]0.907705955517745[/C][/ROW]
[ROW][C]31[/C][C]0.0634712853925621[/C][C]0.126942570785124[/C][C]0.936528714607438[/C][/ROW]
[ROW][C]32[/C][C]0.0664497782445967[/C][C]0.132899556489193[/C][C]0.933550221755403[/C][/ROW]
[ROW][C]33[/C][C]0.0655712858138789[/C][C]0.131142571627758[/C][C]0.934428714186121[/C][/ROW]
[ROW][C]34[/C][C]0.0452374549537841[/C][C]0.0904749099075682[/C][C]0.954762545046216[/C][/ROW]
[ROW][C]35[/C][C]0.0543210058990873[/C][C]0.108642011798175[/C][C]0.945678994100913[/C][/ROW]
[ROW][C]36[/C][C]0.110744823025405[/C][C]0.22148964605081[/C][C]0.889255176974595[/C][/ROW]
[ROW][C]37[/C][C]0.112748665535106[/C][C]0.225497331070213[/C][C]0.887251334464894[/C][/ROW]
[ROW][C]38[/C][C]0.0913332908430246[/C][C]0.182666581686049[/C][C]0.908666709156975[/C][/ROW]
[ROW][C]39[/C][C]0.067408095740584[/C][C]0.134816191481168[/C][C]0.932591904259416[/C][/ROW]
[ROW][C]40[/C][C]0.0475772995962073[/C][C]0.0951545991924146[/C][C]0.952422700403793[/C][/ROW]
[ROW][C]41[/C][C]0.0332520791887349[/C][C]0.0665041583774697[/C][C]0.966747920811265[/C][/ROW]
[ROW][C]42[/C][C]0.0212878885804527[/C][C]0.0425757771609055[/C][C]0.978712111419547[/C][/ROW]
[ROW][C]43[/C][C]0.0289161247545929[/C][C]0.0578322495091858[/C][C]0.971083875245407[/C][/ROW]
[ROW][C]44[/C][C]0.0339757542625198[/C][C]0.0679515085250397[/C][C]0.96602424573748[/C][/ROW]
[ROW][C]45[/C][C]0.313321462055144[/C][C]0.626642924110289[/C][C]0.686678537944855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57955&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57955&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
170.7115890091356270.5768219817287470.288410990864373
180.5796220995106950.840755800978610.420377900489305
190.4636383069385510.9272766138771010.536361693061449
200.5043917215437180.9912165569125630.495608278456282
210.5802601350055790.8394797299888410.419739864994421
220.5148809591263330.9702380817473350.485119040873667
230.4706919189501930.9413838379003850.529308081049807
240.5295373503703080.9409252992593830.470462649629692
250.4596911820116980.9193823640233950.540308817988302
260.3654690135496920.7309380270993830.634530986450308
270.2771784544121070.5543569088242150.722821545587893
280.1993543546531130.3987087093062250.800645645346888
290.1388142288906800.2776284577813600.86118577110932
300.09229404448225460.1845880889645090.907705955517745
310.06347128539256210.1269425707851240.936528714607438
320.06644977824459670.1328995564891930.933550221755403
330.06557128581387890.1311425716277580.934428714186121
340.04523745495378410.09047490990756820.954762545046216
350.05432100589908730.1086420117981750.945678994100913
360.1107448230254050.221489646050810.889255176974595
370.1127486655351060.2254973310702130.887251334464894
380.09133329084302460.1826665816860490.908666709156975
390.0674080957405840.1348161914811680.932591904259416
400.04757729959620730.09515459919241460.952422700403793
410.03325207918873490.06650415837746970.966747920811265
420.02128788858045270.04257577716090550.978712111419547
430.02891612475459290.05783224950918580.971083875245407
440.03397575426251980.06795150852503970.96602424573748
450.3133214620551440.6266429241102890.686678537944855







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0344827586206897OK
10% type I error level60.206896551724138NOK

\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 & 1 & 0.0344827586206897 & OK \tabularnewline
10% type I error level & 6 & 0.206896551724138 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57955&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]1[/C][C]0.0344827586206897[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]6[/C][C]0.206896551724138[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57955&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57955&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 level10.0344827586206897OK
10% type I error level60.206896551724138NOK



Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 2 ; 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')
}