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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 24 Nov 2011 08:45:03 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/24/t13221430748x751bktz3w009a.htm/, Retrieved Fri, 29 Mar 2024 13:46:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=146816, Retrieved Fri, 29 Mar 2024 13:46:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Life expectancy] [2011-11-24 13:45:03] [e524eb56e6915a531809c7eb50783bc6] [Current]
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Dataseries X:
70.5	4.0	370
53.5	315.0	6166
65.0	4.0	684
76.5	1.7	449
70.0	8.0	643
71.0	5.6	1551
60.5	15.0	616
51.5	503.0	36660
78.0	2.6	403
76.0	2.6	346
57.5	44.0	2471
61.0	24.0	7427
64.5	23.0	2992
78.5	3.8	233
79.0	1.8	609
61.0	96.0	7615
70.0	90.0	370
70.0	4.9	1066
72.0	6.6	600
64.5	21.0	4873
54.5	592.0	3485
56.5	73.0	2364
64.5	14.0	1016
64.5	8.8	1062
73.0	3.9	480
72.0	6.0	559
69.0	3.2	259
64.0	11.0	1340
78.5	2.6	275
53.0	23.0	12550
75.0	3.2	965
68.5	11.0	4883
70.0	5.0	1189
70.5	3.0	226
76.0	3.0	611
75.5	1.3	404
74.5	5.6	576
65.0	29.0	3096




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146816&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146816&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 time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Multiple Linear Regression - Estimated Regression Equation
le[t] = + 70.2519572819284 -0.0234953652984406ppt[t] -0.000432047030747009ppp[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
le[t] =  +  70.2519572819284 -0.0234953652984406ppt[t] -0.000432047030747009ppp[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146816&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]le[t] =  +  70.2519572819284 -0.0234953652984406ppt[t] -0.000432047030747009ppp[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146816&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
le[t] = + 70.2519572819284 -0.0234953652984406ppt[t] -0.000432047030747009ppp[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)70.25195728192841.08770564.587300
ppt-0.02349536529844060.009647-2.43550.0201030.010051
ppp-0.0004320470307470090.000202-2.13590.0397630.019882

\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) & 70.2519572819284 & 1.087705 & 64.5873 & 0 & 0 \tabularnewline
ppt & -0.0234953652984406 & 0.009647 & -2.4355 & 0.020103 & 0.010051 \tabularnewline
ppp & -0.000432047030747009 & 0.000202 & -2.1359 & 0.039763 & 0.019882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146816&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]70.2519572819284[/C][C]1.087705[/C][C]64.5873[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]ppt[/C][C]-0.0234953652984406[/C][C]0.009647[/C][C]-2.4355[/C][C]0.020103[/C][C]0.010051[/C][/ROW]
[ROW][C]ppp[/C][C]-0.000432047030747009[/C][C]0.000202[/C][C]-2.1359[/C][C]0.039763[/C][C]0.019882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146816&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146816&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)70.25195728192841.08770564.587300
ppt-0.02349536529844060.009647-2.43550.0201030.010051
ppp-0.0004320470307470090.000202-2.13590.0397630.019882







Multiple Linear Regression - Regression Statistics
Multiple R0.663352260036241
R-squared0.440036220895189
Adjusted R-squared0.408038290660628
F-TEST (value)13.7520213860555
F-TEST (DF numerator)2
F-TEST (DF denominator)35
p-value3.91560502785993e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.00296291839995
Sum Squared Residuals1261.24473298897

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.663352260036241 \tabularnewline
R-squared & 0.440036220895189 \tabularnewline
Adjusted R-squared & 0.408038290660628 \tabularnewline
F-TEST (value) & 13.7520213860555 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 35 \tabularnewline
p-value & 3.91560502785993e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.00296291839995 \tabularnewline
Sum Squared Residuals & 1261.24473298897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146816&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.663352260036241[/C][/ROW]
[ROW][C]R-squared[/C][C]0.440036220895189[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.408038290660628[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]13.7520213860555[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]35[/C][/ROW]
[ROW][C]p-value[/C][C]3.91560502785993e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]6.00296291839995[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1261.24473298897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146816&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146816&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 R0.663352260036241
R-squared0.440036220895189
Adjusted R-squared0.408038290660628
F-TEST (value)13.7520213860555
F-TEST (DF numerator)2
F-TEST (DF denominator)35
p-value3.91560502785993e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.00296291839995
Sum Squared Residuals1261.24473298897







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
170.569.99811841935820.501881580641828
253.560.1869152213336-6.68691522133357
36569.8624556517037-4.86245565170369
476.570.01802604411566.48197395588435
57069.78618811877060.213811881229445
67169.45027829156851.54972170843147
760.569.6333858315116-9.13338583151164
851.542.59494438962758.90505561037254
97870.01675437876147.98324562123858
107670.0413810595145.958618940486
1157.568.1505729958212-10.6505729958212
126166.4792552174078-5.4792552174078
1364.568.4188791640692-3.91887916406922
1478.570.06200793563038.43799206436972
157969.94654898266639.05345101733372
166164.7063640741396-3.70636407413964
177067.97751700369242.02248299630764
187069.67626785718970.323732142810264
197269.83765965251052.16234034748951
2064.567.653189429831-3.15318942983098
2154.554.8370171230983-0.337017123098257
2256.567.5154364344563-11.0154364344563
2364.569.4840623845113-4.98406238451128
2464.569.5863641206488-5.08636412064881
257369.95294278250593.04705721749408
267269.86947079995022.13052920004982
276970.0648719320099-1.06487193200992
286469.4145652424446-5.41456524244457
2978.570.0720563986978.42794360130297
305364.2893736441893-11.2893736441893
317569.75984672830255.24015327169747
3268.567.88382261250790.616177387492084
337069.6207765358780.37922346412199
3470.570.08382855708430.41617144291574
357669.91749045024676.08250954975334
3675.570.04686630661865.45313369338136
3774.569.87152414654694.62847585345314
386568.2329740810809-3.23297408108089

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 70.5 & 69.9981184193582 & 0.501881580641828 \tabularnewline
2 & 53.5 & 60.1869152213336 & -6.68691522133357 \tabularnewline
3 & 65 & 69.8624556517037 & -4.86245565170369 \tabularnewline
4 & 76.5 & 70.0180260441156 & 6.48197395588435 \tabularnewline
5 & 70 & 69.7861881187706 & 0.213811881229445 \tabularnewline
6 & 71 & 69.4502782915685 & 1.54972170843147 \tabularnewline
7 & 60.5 & 69.6333858315116 & -9.13338583151164 \tabularnewline
8 & 51.5 & 42.5949443896275 & 8.90505561037254 \tabularnewline
9 & 78 & 70.0167543787614 & 7.98324562123858 \tabularnewline
10 & 76 & 70.041381059514 & 5.958618940486 \tabularnewline
11 & 57.5 & 68.1505729958212 & -10.6505729958212 \tabularnewline
12 & 61 & 66.4792552174078 & -5.4792552174078 \tabularnewline
13 & 64.5 & 68.4188791640692 & -3.91887916406922 \tabularnewline
14 & 78.5 & 70.0620079356303 & 8.43799206436972 \tabularnewline
15 & 79 & 69.9465489826663 & 9.05345101733372 \tabularnewline
16 & 61 & 64.7063640741396 & -3.70636407413964 \tabularnewline
17 & 70 & 67.9775170036924 & 2.02248299630764 \tabularnewline
18 & 70 & 69.6762678571897 & 0.323732142810264 \tabularnewline
19 & 72 & 69.8376596525105 & 2.16234034748951 \tabularnewline
20 & 64.5 & 67.653189429831 & -3.15318942983098 \tabularnewline
21 & 54.5 & 54.8370171230983 & -0.337017123098257 \tabularnewline
22 & 56.5 & 67.5154364344563 & -11.0154364344563 \tabularnewline
23 & 64.5 & 69.4840623845113 & -4.98406238451128 \tabularnewline
24 & 64.5 & 69.5863641206488 & -5.08636412064881 \tabularnewline
25 & 73 & 69.9529427825059 & 3.04705721749408 \tabularnewline
26 & 72 & 69.8694707999502 & 2.13052920004982 \tabularnewline
27 & 69 & 70.0648719320099 & -1.06487193200992 \tabularnewline
28 & 64 & 69.4145652424446 & -5.41456524244457 \tabularnewline
29 & 78.5 & 70.072056398697 & 8.42794360130297 \tabularnewline
30 & 53 & 64.2893736441893 & -11.2893736441893 \tabularnewline
31 & 75 & 69.7598467283025 & 5.24015327169747 \tabularnewline
32 & 68.5 & 67.8838226125079 & 0.616177387492084 \tabularnewline
33 & 70 & 69.620776535878 & 0.37922346412199 \tabularnewline
34 & 70.5 & 70.0838285570843 & 0.41617144291574 \tabularnewline
35 & 76 & 69.9174904502467 & 6.08250954975334 \tabularnewline
36 & 75.5 & 70.0468663066186 & 5.45313369338136 \tabularnewline
37 & 74.5 & 69.8715241465469 & 4.62847585345314 \tabularnewline
38 & 65 & 68.2329740810809 & -3.23297408108089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146816&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]70.5[/C][C]69.9981184193582[/C][C]0.501881580641828[/C][/ROW]
[ROW][C]2[/C][C]53.5[/C][C]60.1869152213336[/C][C]-6.68691522133357[/C][/ROW]
[ROW][C]3[/C][C]65[/C][C]69.8624556517037[/C][C]-4.86245565170369[/C][/ROW]
[ROW][C]4[/C][C]76.5[/C][C]70.0180260441156[/C][C]6.48197395588435[/C][/ROW]
[ROW][C]5[/C][C]70[/C][C]69.7861881187706[/C][C]0.213811881229445[/C][/ROW]
[ROW][C]6[/C][C]71[/C][C]69.4502782915685[/C][C]1.54972170843147[/C][/ROW]
[ROW][C]7[/C][C]60.5[/C][C]69.6333858315116[/C][C]-9.13338583151164[/C][/ROW]
[ROW][C]8[/C][C]51.5[/C][C]42.5949443896275[/C][C]8.90505561037254[/C][/ROW]
[ROW][C]9[/C][C]78[/C][C]70.0167543787614[/C][C]7.98324562123858[/C][/ROW]
[ROW][C]10[/C][C]76[/C][C]70.041381059514[/C][C]5.958618940486[/C][/ROW]
[ROW][C]11[/C][C]57.5[/C][C]68.1505729958212[/C][C]-10.6505729958212[/C][/ROW]
[ROW][C]12[/C][C]61[/C][C]66.4792552174078[/C][C]-5.4792552174078[/C][/ROW]
[ROW][C]13[/C][C]64.5[/C][C]68.4188791640692[/C][C]-3.91887916406922[/C][/ROW]
[ROW][C]14[/C][C]78.5[/C][C]70.0620079356303[/C][C]8.43799206436972[/C][/ROW]
[ROW][C]15[/C][C]79[/C][C]69.9465489826663[/C][C]9.05345101733372[/C][/ROW]
[ROW][C]16[/C][C]61[/C][C]64.7063640741396[/C][C]-3.70636407413964[/C][/ROW]
[ROW][C]17[/C][C]70[/C][C]67.9775170036924[/C][C]2.02248299630764[/C][/ROW]
[ROW][C]18[/C][C]70[/C][C]69.6762678571897[/C][C]0.323732142810264[/C][/ROW]
[ROW][C]19[/C][C]72[/C][C]69.8376596525105[/C][C]2.16234034748951[/C][/ROW]
[ROW][C]20[/C][C]64.5[/C][C]67.653189429831[/C][C]-3.15318942983098[/C][/ROW]
[ROW][C]21[/C][C]54.5[/C][C]54.8370171230983[/C][C]-0.337017123098257[/C][/ROW]
[ROW][C]22[/C][C]56.5[/C][C]67.5154364344563[/C][C]-11.0154364344563[/C][/ROW]
[ROW][C]23[/C][C]64.5[/C][C]69.4840623845113[/C][C]-4.98406238451128[/C][/ROW]
[ROW][C]24[/C][C]64.5[/C][C]69.5863641206488[/C][C]-5.08636412064881[/C][/ROW]
[ROW][C]25[/C][C]73[/C][C]69.9529427825059[/C][C]3.04705721749408[/C][/ROW]
[ROW][C]26[/C][C]72[/C][C]69.8694707999502[/C][C]2.13052920004982[/C][/ROW]
[ROW][C]27[/C][C]69[/C][C]70.0648719320099[/C][C]-1.06487193200992[/C][/ROW]
[ROW][C]28[/C][C]64[/C][C]69.4145652424446[/C][C]-5.41456524244457[/C][/ROW]
[ROW][C]29[/C][C]78.5[/C][C]70.072056398697[/C][C]8.42794360130297[/C][/ROW]
[ROW][C]30[/C][C]53[/C][C]64.2893736441893[/C][C]-11.2893736441893[/C][/ROW]
[ROW][C]31[/C][C]75[/C][C]69.7598467283025[/C][C]5.24015327169747[/C][/ROW]
[ROW][C]32[/C][C]68.5[/C][C]67.8838226125079[/C][C]0.616177387492084[/C][/ROW]
[ROW][C]33[/C][C]70[/C][C]69.620776535878[/C][C]0.37922346412199[/C][/ROW]
[ROW][C]34[/C][C]70.5[/C][C]70.0838285570843[/C][C]0.41617144291574[/C][/ROW]
[ROW][C]35[/C][C]76[/C][C]69.9174904502467[/C][C]6.08250954975334[/C][/ROW]
[ROW][C]36[/C][C]75.5[/C][C]70.0468663066186[/C][C]5.45313369338136[/C][/ROW]
[ROW][C]37[/C][C]74.5[/C][C]69.8715241465469[/C][C]4.62847585345314[/C][/ROW]
[ROW][C]38[/C][C]65[/C][C]68.2329740810809[/C][C]-3.23297408108089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146816&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146816&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
170.569.99811841935820.501881580641828
253.560.1869152213336-6.68691522133357
36569.8624556517037-4.86245565170369
476.570.01802604411566.48197395588435
57069.78618811877060.213811881229445
67169.45027829156851.54972170843147
760.569.6333858315116-9.13338583151164
851.542.59494438962758.90505561037254
97870.01675437876147.98324562123858
107670.0413810595145.958618940486
1157.568.1505729958212-10.6505729958212
126166.4792552174078-5.4792552174078
1364.568.4188791640692-3.91887916406922
1478.570.06200793563038.43799206436972
157969.94654898266639.05345101733372
166164.7063640741396-3.70636407413964
177067.97751700369242.02248299630764
187069.67626785718970.323732142810264
197269.83765965251052.16234034748951
2064.567.653189429831-3.15318942983098
2154.554.8370171230983-0.337017123098257
2256.567.5154364344563-11.0154364344563
2364.569.4840623845113-4.98406238451128
2464.569.5863641206488-5.08636412064881
257369.95294278250593.04705721749408
267269.86947079995022.13052920004982
276970.0648719320099-1.06487193200992
286469.4145652424446-5.41456524244457
2978.570.0720563986978.42794360130297
305364.2893736441893-11.2893736441893
317569.75984672830255.24015327169747
3268.567.88382261250790.616177387492084
337069.6207765358780.37922346412199
3470.570.08382855708430.41617144291574
357669.91749045024676.08250954975334
3675.570.04686630661865.45313369338136
3774.569.87152414654694.62847585345314
386568.2329740810809-3.23297408108089







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.3463105790461940.6926211580923890.653689420953806
70.5329962496256590.9340075007486820.467003750374341
80.6691158186087840.6617683627824310.330884181391216
90.78998078295170.42003843409660.2100192170483
100.7738891581624680.4522216836750640.226110841837532
110.9430488963650960.1139022072698080.0569511036349041
120.952390594639770.09521881072046080.0476094053602304
130.9324837121551860.1350325756896270.0675162878448137
140.9603650524311250.07926989513775010.039634947568875
150.9802175269055870.0395649461888260.019782473094413
160.9719638654337660.05607226913246830.0280361345662342
170.955053842660270.08989231467946070.0449461573397303
180.924905119709370.1501897605812590.0750948802906296
190.8842337165914140.2315325668171720.115766283408586
200.8408458116408070.3183083767183860.159154188359193
210.9692252776018440.06154944479631180.0307747223981559
220.9783038057209280.0433923885581450.0216961942790725
230.9734986231948060.0530027536103880.026501376805194
240.9829577145768910.03408457084621880.0170422854231094
250.9676395893192390.0647208213615220.032360410680761
260.9401170891635560.1197658216728880.0598829108364438
270.9396543056645970.1206913886708050.0603456943354027
280.9829482397690140.03410352046197270.0170517602309863
290.9850257557172530.02994848856549380.0149742442827469
300.978309962744180.04338007451164040.0216900372558202
310.9510656119925260.09786877601494730.0489343880074736
320.8712952373949410.2574095252101190.128704762605059

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
6 & 0.346310579046194 & 0.692621158092389 & 0.653689420953806 \tabularnewline
7 & 0.532996249625659 & 0.934007500748682 & 0.467003750374341 \tabularnewline
8 & 0.669115818608784 & 0.661768362782431 & 0.330884181391216 \tabularnewline
9 & 0.7899807829517 & 0.4200384340966 & 0.2100192170483 \tabularnewline
10 & 0.773889158162468 & 0.452221683675064 & 0.226110841837532 \tabularnewline
11 & 0.943048896365096 & 0.113902207269808 & 0.0569511036349041 \tabularnewline
12 & 0.95239059463977 & 0.0952188107204608 & 0.0476094053602304 \tabularnewline
13 & 0.932483712155186 & 0.135032575689627 & 0.0675162878448137 \tabularnewline
14 & 0.960365052431125 & 0.0792698951377501 & 0.039634947568875 \tabularnewline
15 & 0.980217526905587 & 0.039564946188826 & 0.019782473094413 \tabularnewline
16 & 0.971963865433766 & 0.0560722691324683 & 0.0280361345662342 \tabularnewline
17 & 0.95505384266027 & 0.0898923146794607 & 0.0449461573397303 \tabularnewline
18 & 0.92490511970937 & 0.150189760581259 & 0.0750948802906296 \tabularnewline
19 & 0.884233716591414 & 0.231532566817172 & 0.115766283408586 \tabularnewline
20 & 0.840845811640807 & 0.318308376718386 & 0.159154188359193 \tabularnewline
21 & 0.969225277601844 & 0.0615494447963118 & 0.0307747223981559 \tabularnewline
22 & 0.978303805720928 & 0.043392388558145 & 0.0216961942790725 \tabularnewline
23 & 0.973498623194806 & 0.053002753610388 & 0.026501376805194 \tabularnewline
24 & 0.982957714576891 & 0.0340845708462188 & 0.0170422854231094 \tabularnewline
25 & 0.967639589319239 & 0.064720821361522 & 0.032360410680761 \tabularnewline
26 & 0.940117089163556 & 0.119765821672888 & 0.0598829108364438 \tabularnewline
27 & 0.939654305664597 & 0.120691388670805 & 0.0603456943354027 \tabularnewline
28 & 0.982948239769014 & 0.0341035204619727 & 0.0170517602309863 \tabularnewline
29 & 0.985025755717253 & 0.0299484885654938 & 0.0149742442827469 \tabularnewline
30 & 0.97830996274418 & 0.0433800745116404 & 0.0216900372558202 \tabularnewline
31 & 0.951065611992526 & 0.0978687760149473 & 0.0489343880074736 \tabularnewline
32 & 0.871295237394941 & 0.257409525210119 & 0.128704762605059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146816&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]6[/C][C]0.346310579046194[/C][C]0.692621158092389[/C][C]0.653689420953806[/C][/ROW]
[ROW][C]7[/C][C]0.532996249625659[/C][C]0.934007500748682[/C][C]0.467003750374341[/C][/ROW]
[ROW][C]8[/C][C]0.669115818608784[/C][C]0.661768362782431[/C][C]0.330884181391216[/C][/ROW]
[ROW][C]9[/C][C]0.7899807829517[/C][C]0.4200384340966[/C][C]0.2100192170483[/C][/ROW]
[ROW][C]10[/C][C]0.773889158162468[/C][C]0.452221683675064[/C][C]0.226110841837532[/C][/ROW]
[ROW][C]11[/C][C]0.943048896365096[/C][C]0.113902207269808[/C][C]0.0569511036349041[/C][/ROW]
[ROW][C]12[/C][C]0.95239059463977[/C][C]0.0952188107204608[/C][C]0.0476094053602304[/C][/ROW]
[ROW][C]13[/C][C]0.932483712155186[/C][C]0.135032575689627[/C][C]0.0675162878448137[/C][/ROW]
[ROW][C]14[/C][C]0.960365052431125[/C][C]0.0792698951377501[/C][C]0.039634947568875[/C][/ROW]
[ROW][C]15[/C][C]0.980217526905587[/C][C]0.039564946188826[/C][C]0.019782473094413[/C][/ROW]
[ROW][C]16[/C][C]0.971963865433766[/C][C]0.0560722691324683[/C][C]0.0280361345662342[/C][/ROW]
[ROW][C]17[/C][C]0.95505384266027[/C][C]0.0898923146794607[/C][C]0.0449461573397303[/C][/ROW]
[ROW][C]18[/C][C]0.92490511970937[/C][C]0.150189760581259[/C][C]0.0750948802906296[/C][/ROW]
[ROW][C]19[/C][C]0.884233716591414[/C][C]0.231532566817172[/C][C]0.115766283408586[/C][/ROW]
[ROW][C]20[/C][C]0.840845811640807[/C][C]0.318308376718386[/C][C]0.159154188359193[/C][/ROW]
[ROW][C]21[/C][C]0.969225277601844[/C][C]0.0615494447963118[/C][C]0.0307747223981559[/C][/ROW]
[ROW][C]22[/C][C]0.978303805720928[/C][C]0.043392388558145[/C][C]0.0216961942790725[/C][/ROW]
[ROW][C]23[/C][C]0.973498623194806[/C][C]0.053002753610388[/C][C]0.026501376805194[/C][/ROW]
[ROW][C]24[/C][C]0.982957714576891[/C][C]0.0340845708462188[/C][C]0.0170422854231094[/C][/ROW]
[ROW][C]25[/C][C]0.967639589319239[/C][C]0.064720821361522[/C][C]0.032360410680761[/C][/ROW]
[ROW][C]26[/C][C]0.940117089163556[/C][C]0.119765821672888[/C][C]0.0598829108364438[/C][/ROW]
[ROW][C]27[/C][C]0.939654305664597[/C][C]0.120691388670805[/C][C]0.0603456943354027[/C][/ROW]
[ROW][C]28[/C][C]0.982948239769014[/C][C]0.0341035204619727[/C][C]0.0170517602309863[/C][/ROW]
[ROW][C]29[/C][C]0.985025755717253[/C][C]0.0299484885654938[/C][C]0.0149742442827469[/C][/ROW]
[ROW][C]30[/C][C]0.97830996274418[/C][C]0.0433800745116404[/C][C]0.0216900372558202[/C][/ROW]
[ROW][C]31[/C][C]0.951065611992526[/C][C]0.0978687760149473[/C][C]0.0489343880074736[/C][/ROW]
[ROW][C]32[/C][C]0.871295237394941[/C][C]0.257409525210119[/C][C]0.128704762605059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146816&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146816&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
60.3463105790461940.6926211580923890.653689420953806
70.5329962496256590.9340075007486820.467003750374341
80.6691158186087840.6617683627824310.330884181391216
90.78998078295170.42003843409660.2100192170483
100.7738891581624680.4522216836750640.226110841837532
110.9430488963650960.1139022072698080.0569511036349041
120.952390594639770.09521881072046080.0476094053602304
130.9324837121551860.1350325756896270.0675162878448137
140.9603650524311250.07926989513775010.039634947568875
150.9802175269055870.0395649461888260.019782473094413
160.9719638654337660.05607226913246830.0280361345662342
170.955053842660270.08989231467946070.0449461573397303
180.924905119709370.1501897605812590.0750948802906296
190.8842337165914140.2315325668171720.115766283408586
200.8408458116408070.3183083767183860.159154188359193
210.9692252776018440.06154944479631180.0307747223981559
220.9783038057209280.0433923885581450.0216961942790725
230.9734986231948060.0530027536103880.026501376805194
240.9829577145768910.03408457084621880.0170422854231094
250.9676395893192390.0647208213615220.032360410680761
260.9401170891635560.1197658216728880.0598829108364438
270.9396543056645970.1206913886708050.0603456943354027
280.9829482397690140.03410352046197270.0170517602309863
290.9850257557172530.02994848856549380.0149742442827469
300.978309962744180.04338007451164040.0216900372558202
310.9510656119925260.09786877601494730.0489343880074736
320.8712952373949410.2574095252101190.128704762605059







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level60.222222222222222NOK
10% type I error level140.518518518518518NOK

\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 & 6 & 0.222222222222222 & NOK \tabularnewline
10% type I error level & 14 & 0.518518518518518 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146816&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]6[/C][C]0.222222222222222[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]14[/C][C]0.518518518518518[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146816&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146816&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 level60.222222222222222NOK
10% type I error level140.518518518518518NOK



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}