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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 computationTue, 23 Nov 2010 14:55:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/23/t1290524074deeysgbtfsyziad.htm/, Retrieved Fri, 29 Mar 2024 11:25:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=99202, Retrieved Fri, 29 Mar 2024 11:25:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [Workshop 7 - regr...] [2010-11-23 14:55:54] [0605ea080d54454c99180f574351b8e4] [Current]
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Dataseries X:
70,5	4	370	 74
53,5	315	6166	 53
65	4	684	 68
76,5	17	449	 80
70	8	643	 72
71	56	1551	 74
60,5	15	616	 61
51,5	503	36660 53
78	26	403	 82
76	26	346	 79
57,5	44	2471	 58
61	24	7427	 63
64,5	23	2992	 65
78,5	38	233	 82
79	18	609	 82
61	96	7615	 63
70	90	370	 73
70	49	1066	 73
72	66	600	 76
64,5	21	4873	 66
54,5	592	3485	 56
56,5	73	2364	 57
64,5	14	1016	 67
64,5	88	1062	 67
73	39	480	 77
72	6	559	 75
69	32	259	 74
64	11	1340	 67
78,5	26	275	 82
53	23	12550 54
75	32	965	 78
52,5	NA	25229 55
68,5	11	4883	 71
70	5	1189	 72
70,5	3	226	 75
76	3	611	 79
75,5	13	404	 79
74,5	56	576	 78
65	29	3096	 67
54	NA	23193 56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99202&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]6 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=99202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99202&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
X2t[t] = + 25578.1303782642 -990.437503041272Yt[t] + 18.5570105455728X1t[t] + 615.08893959725X3t[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X2t[t] =  +  25578.1303782642 -990.437503041272Yt[t] +  18.5570105455728X1t[t] +  615.08893959725X3t[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99202&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X2t[t] =  +  25578.1303782642 -990.437503041272Yt[t] +  18.5570105455728X1t[t] +  615.08893959725X3t[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99202&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
X2t[t] = + 25578.1303782642 -990.437503041272Yt[t] + 18.5570105455728X1t[t] + 615.08893959725X3t[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)25578.130378264210607.7856652.41130.0214480.010724
Yt-990.4375030412721127.032157-0.87880.3856780.192839
X1t18.55701054557287.5134092.46990.0186940.009347
X3t615.08893959725990.8272110.62080.5388820.269441

\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) & 25578.1303782642 & 10607.785665 & 2.4113 & 0.021448 & 0.010724 \tabularnewline
Yt & -990.437503041272 & 1127.032157 & -0.8788 & 0.385678 & 0.192839 \tabularnewline
X1t & 18.5570105455728 & 7.513409 & 2.4699 & 0.018694 & 0.009347 \tabularnewline
X3t & 615.08893959725 & 990.827211 & 0.6208 & 0.538882 & 0.269441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99202&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]25578.1303782642[/C][C]10607.785665[/C][C]2.4113[/C][C]0.021448[/C][C]0.010724[/C][/ROW]
[ROW][C]Yt[/C][C]-990.437503041272[/C][C]1127.032157[/C][C]-0.8788[/C][C]0.385678[/C][C]0.192839[/C][/ROW]
[ROW][C]X1t[/C][C]18.5570105455728[/C][C]7.513409[/C][C]2.4699[/C][C]0.018694[/C][C]0.009347[/C][/ROW]
[ROW][C]X3t[/C][C]615.08893959725[/C][C]990.827211[/C][C]0.6208[/C][C]0.538882[/C][C]0.269441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99202&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99202&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)25578.130378264210607.7856652.41130.0214480.010724
Yt-990.4375030412721127.032157-0.87880.3856780.192839
X1t18.55701054557287.5134092.46990.0186940.009347
X3t615.08893959725990.8272110.62080.5388820.269441







Multiple Linear Regression - Regression Statistics
Multiple R0.676420411214375
R-squared0.457544572707424
Adjusted R-squared0.40968085853455
F-TEST (value)9.55932026200189
F-TEST (DF numerator)3
F-TEST (DF denominator)34
p-value0.000101194092399060
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4776.13028631606
Sum Squared Residuals775588297.403426

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.676420411214375 \tabularnewline
R-squared & 0.457544572707424 \tabularnewline
Adjusted R-squared & 0.40968085853455 \tabularnewline
F-TEST (value) & 9.55932026200189 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 34 \tabularnewline
p-value & 0.000101194092399060 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4776.13028631606 \tabularnewline
Sum Squared Residuals & 775588297.403426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99202&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.676420411214375[/C][/ROW]
[ROW][C]R-squared[/C][C]0.457544572707424[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.40968085853455[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]9.55932026200189[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]0.000101194092399060[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4776.13028631606[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]775588297.403426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99202&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99202&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 R0.676420411214375
R-squared0.457544572707424
Adjusted R-squared0.40968085853455
F-TEST (value)9.55932026200189
F-TEST (DF numerator)3
F-TEST (DF denominator)34
p-value0.000101194092399060
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4776.13028631606
Sum Squared Residuals775588297.403426







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13701343.09598623306-973.09598623306
2616611034.8960860658-4868.89608606576
36843099.96861537675-2415.96861537675
4449-667.7542573384341116.75425733843
5643682.364900741679-39.3649007416788
615511812.8417830824-261.8417830824
76163455.44191788303-2839.44191788303
83666016504.48907471620155.510925284
9403-756.219537795691159.21953779569
10346-620.611350504895966.611350504895
1124715119.6409140367-2648.64091403670
1274274357.414140467043069.58585953296
1329922102.50374847152889.49625152848
14233-1028.754162769451261.75416276945
15609-1895.113125201542504.11312520154
1676155693.518899748291921.48110025171
173702819.12870507590-2449.12870507590
1810662058.29127270741-992.291272707413
196002238.15226469135-1638.15226469135
2048732680.478666977622192.52133302238
21348517030.0173229399-13545.0173229399
2223646033.14278330234-3669.14278330234
2310163165.66853275586-2149.66853275586
2410624538.88731312825-3476.88731312825
254801361.76441651687-881.764416516867
26559509.64269235973849.3573076402622
272593348.34853607119-3089.34853607119
2813403605.21625263978-2265.21625263978
29275-1251.438289316331526.43828931633
30125506726.55669787645823.4433021236
31965-133.9207237874361098.92072378744
322522921954.60324734313274.39675265694
3348834320.69386910496562.306130895039
3411892902.62791528493-1713.62791528493
35226-1432.422593053071658.42259305307
36611-159.633736076705770.633736076705
37404634.666280826947-230.666280826947
38576428.804939418818147.195060581182
393096NANA
4023193NANA

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 370 & 1343.09598623306 & -973.09598623306 \tabularnewline
2 & 6166 & 11034.8960860658 & -4868.89608606576 \tabularnewline
3 & 684 & 3099.96861537675 & -2415.96861537675 \tabularnewline
4 & 449 & -667.754257338434 & 1116.75425733843 \tabularnewline
5 & 643 & 682.364900741679 & -39.3649007416788 \tabularnewline
6 & 1551 & 1812.8417830824 & -261.8417830824 \tabularnewline
7 & 616 & 3455.44191788303 & -2839.44191788303 \tabularnewline
8 & 36660 & 16504.489074716 & 20155.510925284 \tabularnewline
9 & 403 & -756.21953779569 & 1159.21953779569 \tabularnewline
10 & 346 & -620.611350504895 & 966.611350504895 \tabularnewline
11 & 2471 & 5119.6409140367 & -2648.64091403670 \tabularnewline
12 & 7427 & 4357.41414046704 & 3069.58585953296 \tabularnewline
13 & 2992 & 2102.50374847152 & 889.49625152848 \tabularnewline
14 & 233 & -1028.75416276945 & 1261.75416276945 \tabularnewline
15 & 609 & -1895.11312520154 & 2504.11312520154 \tabularnewline
16 & 7615 & 5693.51889974829 & 1921.48110025171 \tabularnewline
17 & 370 & 2819.12870507590 & -2449.12870507590 \tabularnewline
18 & 1066 & 2058.29127270741 & -992.291272707413 \tabularnewline
19 & 600 & 2238.15226469135 & -1638.15226469135 \tabularnewline
20 & 4873 & 2680.47866697762 & 2192.52133302238 \tabularnewline
21 & 3485 & 17030.0173229399 & -13545.0173229399 \tabularnewline
22 & 2364 & 6033.14278330234 & -3669.14278330234 \tabularnewline
23 & 1016 & 3165.66853275586 & -2149.66853275586 \tabularnewline
24 & 1062 & 4538.88731312825 & -3476.88731312825 \tabularnewline
25 & 480 & 1361.76441651687 & -881.764416516867 \tabularnewline
26 & 559 & 509.642692359738 & 49.3573076402622 \tabularnewline
27 & 259 & 3348.34853607119 & -3089.34853607119 \tabularnewline
28 & 1340 & 3605.21625263978 & -2265.21625263978 \tabularnewline
29 & 275 & -1251.43828931633 & 1526.43828931633 \tabularnewline
30 & 12550 & 6726.5566978764 & 5823.4433021236 \tabularnewline
31 & 965 & -133.920723787436 & 1098.92072378744 \tabularnewline
32 & 25229 & 21954.6032473431 & 3274.39675265694 \tabularnewline
33 & 4883 & 4320.69386910496 & 562.306130895039 \tabularnewline
34 & 1189 & 2902.62791528493 & -1713.62791528493 \tabularnewline
35 & 226 & -1432.42259305307 & 1658.42259305307 \tabularnewline
36 & 611 & -159.633736076705 & 770.633736076705 \tabularnewline
37 & 404 & 634.666280826947 & -230.666280826947 \tabularnewline
38 & 576 & 428.804939418818 & 147.195060581182 \tabularnewline
39 & 3096 & NA & NA \tabularnewline
40 & 23193 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99202&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]370[/C][C]1343.09598623306[/C][C]-973.09598623306[/C][/ROW]
[ROW][C]2[/C][C]6166[/C][C]11034.8960860658[/C][C]-4868.89608606576[/C][/ROW]
[ROW][C]3[/C][C]684[/C][C]3099.96861537675[/C][C]-2415.96861537675[/C][/ROW]
[ROW][C]4[/C][C]449[/C][C]-667.754257338434[/C][C]1116.75425733843[/C][/ROW]
[ROW][C]5[/C][C]643[/C][C]682.364900741679[/C][C]-39.3649007416788[/C][/ROW]
[ROW][C]6[/C][C]1551[/C][C]1812.8417830824[/C][C]-261.8417830824[/C][/ROW]
[ROW][C]7[/C][C]616[/C][C]3455.44191788303[/C][C]-2839.44191788303[/C][/ROW]
[ROW][C]8[/C][C]36660[/C][C]16504.489074716[/C][C]20155.510925284[/C][/ROW]
[ROW][C]9[/C][C]403[/C][C]-756.21953779569[/C][C]1159.21953779569[/C][/ROW]
[ROW][C]10[/C][C]346[/C][C]-620.611350504895[/C][C]966.611350504895[/C][/ROW]
[ROW][C]11[/C][C]2471[/C][C]5119.6409140367[/C][C]-2648.64091403670[/C][/ROW]
[ROW][C]12[/C][C]7427[/C][C]4357.41414046704[/C][C]3069.58585953296[/C][/ROW]
[ROW][C]13[/C][C]2992[/C][C]2102.50374847152[/C][C]889.49625152848[/C][/ROW]
[ROW][C]14[/C][C]233[/C][C]-1028.75416276945[/C][C]1261.75416276945[/C][/ROW]
[ROW][C]15[/C][C]609[/C][C]-1895.11312520154[/C][C]2504.11312520154[/C][/ROW]
[ROW][C]16[/C][C]7615[/C][C]5693.51889974829[/C][C]1921.48110025171[/C][/ROW]
[ROW][C]17[/C][C]370[/C][C]2819.12870507590[/C][C]-2449.12870507590[/C][/ROW]
[ROW][C]18[/C][C]1066[/C][C]2058.29127270741[/C][C]-992.291272707413[/C][/ROW]
[ROW][C]19[/C][C]600[/C][C]2238.15226469135[/C][C]-1638.15226469135[/C][/ROW]
[ROW][C]20[/C][C]4873[/C][C]2680.47866697762[/C][C]2192.52133302238[/C][/ROW]
[ROW][C]21[/C][C]3485[/C][C]17030.0173229399[/C][C]-13545.0173229399[/C][/ROW]
[ROW][C]22[/C][C]2364[/C][C]6033.14278330234[/C][C]-3669.14278330234[/C][/ROW]
[ROW][C]23[/C][C]1016[/C][C]3165.66853275586[/C][C]-2149.66853275586[/C][/ROW]
[ROW][C]24[/C][C]1062[/C][C]4538.88731312825[/C][C]-3476.88731312825[/C][/ROW]
[ROW][C]25[/C][C]480[/C][C]1361.76441651687[/C][C]-881.764416516867[/C][/ROW]
[ROW][C]26[/C][C]559[/C][C]509.642692359738[/C][C]49.3573076402622[/C][/ROW]
[ROW][C]27[/C][C]259[/C][C]3348.34853607119[/C][C]-3089.34853607119[/C][/ROW]
[ROW][C]28[/C][C]1340[/C][C]3605.21625263978[/C][C]-2265.21625263978[/C][/ROW]
[ROW][C]29[/C][C]275[/C][C]-1251.43828931633[/C][C]1526.43828931633[/C][/ROW]
[ROW][C]30[/C][C]12550[/C][C]6726.5566978764[/C][C]5823.4433021236[/C][/ROW]
[ROW][C]31[/C][C]965[/C][C]-133.920723787436[/C][C]1098.92072378744[/C][/ROW]
[ROW][C]32[/C][C]25229[/C][C]21954.6032473431[/C][C]3274.39675265694[/C][/ROW]
[ROW][C]33[/C][C]4883[/C][C]4320.69386910496[/C][C]562.306130895039[/C][/ROW]
[ROW][C]34[/C][C]1189[/C][C]2902.62791528493[/C][C]-1713.62791528493[/C][/ROW]
[ROW][C]35[/C][C]226[/C][C]-1432.42259305307[/C][C]1658.42259305307[/C][/ROW]
[ROW][C]36[/C][C]611[/C][C]-159.633736076705[/C][C]770.633736076705[/C][/ROW]
[ROW][C]37[/C][C]404[/C][C]634.666280826947[/C][C]-230.666280826947[/C][/ROW]
[ROW][C]38[/C][C]576[/C][C]428.804939418818[/C][C]147.195060581182[/C][/ROW]
[ROW][C]39[/C][C]3096[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]40[/C][C]23193[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99202&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99202&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
13701343.09598623306-973.09598623306
2616611034.8960860658-4868.89608606576
36843099.96861537675-2415.96861537675
4449-667.7542573384341116.75425733843
5643682.364900741679-39.3649007416788
615511812.8417830824-261.8417830824
76163455.44191788303-2839.44191788303
83666016504.48907471620155.510925284
9403-756.219537795691159.21953779569
10346-620.611350504895966.611350504895
1124715119.6409140367-2648.64091403670
1274274357.414140467043069.58585953296
1329922102.50374847152889.49625152848
14233-1028.754162769451261.75416276945
15609-1895.113125201542504.11312520154
1676155693.518899748291921.48110025171
173702819.12870507590-2449.12870507590
1810662058.29127270741-992.291272707413
196002238.15226469135-1638.15226469135
2048732680.478666977622192.52133302238
21348517030.0173229399-13545.0173229399
2223646033.14278330234-3669.14278330234
2310163165.66853275586-2149.66853275586
2410624538.88731312825-3476.88731312825
254801361.76441651687-881.764416516867
26559509.64269235973849.3573076402622
272593348.34853607119-3089.34853607119
2813403605.21625263978-2265.21625263978
29275-1251.438289316331526.43828931633
30125506726.55669787645823.4433021236
31965-133.9207237874361098.92072378744
322522921954.60324734313274.39675265694
3348834320.69386910496562.306130895039
3411892902.62791528493-1713.62791528493
35226-1432.422593053071658.42259305307
36611-159.633736076705770.633736076705
37404634.666280826947-230.666280826947
38576428.804939418818147.195060581182
393096NANA
4023193NANA







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
77.35156510979815e-050.0001470313021959630.999926484348902
80.999031561648340.001936876703321260.000968438351660631
90.9975752719760560.004849456047887060.00242472802394353
100.994769061699550.01046187660089890.00523093830044946
110.9954720904764330.009055819047132990.00452790952356649
120.9960437184306130.007912563138773260.00395628156938663
130.9984411747029880.003117650594025030.00155882529701251
140.996588061167680.006823877664641670.00341193883232083
150.9947427026902760.01051459461944790.00525729730972396
160.9949978023829260.01000439523414820.00500219761707409
170.9952507056380120.00949858872397580.0047492943619879
180.991172019983720.01765596003255950.00882798001627974
190.9885740373903530.02285192521929310.0114259626096466
200.9838005414569620.0323989170860750.0161994585430375
210.9997742534419420.0004514931161165140.000225746558058257
220.9998447059098560.0003105881802883540.000155294090144177
230.9998455318492520.0003089363014969240.000154468150748462
240.9998816801965550.0002366396068898910.000118319803444946
250.9995656717628770.0008686564742454550.000434328237122727
260.9985873069662840.002825386067431570.00141269303371578
270.9957255201550970.00854895968980660.0042744798449033
280.9958869640452850.008226071909430980.00411303595471549
290.99009888386960.01980223226079820.00990111613039912
300.9909087749638070.01818245007238560.00909122503619282
310.9625704379276130.07485912414477370.0374295620723869
320.9885563971950280.02288720560994450.0114436028049722
330.9887333865295620.02253322694087530.0112666134704377

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
7 & 7.35156510979815e-05 & 0.000147031302195963 & 0.999926484348902 \tabularnewline
8 & 0.99903156164834 & 0.00193687670332126 & 0.000968438351660631 \tabularnewline
9 & 0.997575271976056 & 0.00484945604788706 & 0.00242472802394353 \tabularnewline
10 & 0.99476906169955 & 0.0104618766008989 & 0.00523093830044946 \tabularnewline
11 & 0.995472090476433 & 0.00905581904713299 & 0.00452790952356649 \tabularnewline
12 & 0.996043718430613 & 0.00791256313877326 & 0.00395628156938663 \tabularnewline
13 & 0.998441174702988 & 0.00311765059402503 & 0.00155882529701251 \tabularnewline
14 & 0.99658806116768 & 0.00682387766464167 & 0.00341193883232083 \tabularnewline
15 & 0.994742702690276 & 0.0105145946194479 & 0.00525729730972396 \tabularnewline
16 & 0.994997802382926 & 0.0100043952341482 & 0.00500219761707409 \tabularnewline
17 & 0.995250705638012 & 0.0094985887239758 & 0.0047492943619879 \tabularnewline
18 & 0.99117201998372 & 0.0176559600325595 & 0.00882798001627974 \tabularnewline
19 & 0.988574037390353 & 0.0228519252192931 & 0.0114259626096466 \tabularnewline
20 & 0.983800541456962 & 0.032398917086075 & 0.0161994585430375 \tabularnewline
21 & 0.999774253441942 & 0.000451493116116514 & 0.000225746558058257 \tabularnewline
22 & 0.999844705909856 & 0.000310588180288354 & 0.000155294090144177 \tabularnewline
23 & 0.999845531849252 & 0.000308936301496924 & 0.000154468150748462 \tabularnewline
24 & 0.999881680196555 & 0.000236639606889891 & 0.000118319803444946 \tabularnewline
25 & 0.999565671762877 & 0.000868656474245455 & 0.000434328237122727 \tabularnewline
26 & 0.998587306966284 & 0.00282538606743157 & 0.00141269303371578 \tabularnewline
27 & 0.995725520155097 & 0.0085489596898066 & 0.0042744798449033 \tabularnewline
28 & 0.995886964045285 & 0.00822607190943098 & 0.00411303595471549 \tabularnewline
29 & 0.9900988838696 & 0.0198022322607982 & 0.00990111613039912 \tabularnewline
30 & 0.990908774963807 & 0.0181824500723856 & 0.00909122503619282 \tabularnewline
31 & 0.962570437927613 & 0.0748591241447737 & 0.0374295620723869 \tabularnewline
32 & 0.988556397195028 & 0.0228872056099445 & 0.0114436028049722 \tabularnewline
33 & 0.988733386529562 & 0.0225332269408753 & 0.0112666134704377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99202&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]7[/C][C]7.35156510979815e-05[/C][C]0.000147031302195963[/C][C]0.999926484348902[/C][/ROW]
[ROW][C]8[/C][C]0.99903156164834[/C][C]0.00193687670332126[/C][C]0.000968438351660631[/C][/ROW]
[ROW][C]9[/C][C]0.997575271976056[/C][C]0.00484945604788706[/C][C]0.00242472802394353[/C][/ROW]
[ROW][C]10[/C][C]0.99476906169955[/C][C]0.0104618766008989[/C][C]0.00523093830044946[/C][/ROW]
[ROW][C]11[/C][C]0.995472090476433[/C][C]0.00905581904713299[/C][C]0.00452790952356649[/C][/ROW]
[ROW][C]12[/C][C]0.996043718430613[/C][C]0.00791256313877326[/C][C]0.00395628156938663[/C][/ROW]
[ROW][C]13[/C][C]0.998441174702988[/C][C]0.00311765059402503[/C][C]0.00155882529701251[/C][/ROW]
[ROW][C]14[/C][C]0.99658806116768[/C][C]0.00682387766464167[/C][C]0.00341193883232083[/C][/ROW]
[ROW][C]15[/C][C]0.994742702690276[/C][C]0.0105145946194479[/C][C]0.00525729730972396[/C][/ROW]
[ROW][C]16[/C][C]0.994997802382926[/C][C]0.0100043952341482[/C][C]0.00500219761707409[/C][/ROW]
[ROW][C]17[/C][C]0.995250705638012[/C][C]0.0094985887239758[/C][C]0.0047492943619879[/C][/ROW]
[ROW][C]18[/C][C]0.99117201998372[/C][C]0.0176559600325595[/C][C]0.00882798001627974[/C][/ROW]
[ROW][C]19[/C][C]0.988574037390353[/C][C]0.0228519252192931[/C][C]0.0114259626096466[/C][/ROW]
[ROW][C]20[/C][C]0.983800541456962[/C][C]0.032398917086075[/C][C]0.0161994585430375[/C][/ROW]
[ROW][C]21[/C][C]0.999774253441942[/C][C]0.000451493116116514[/C][C]0.000225746558058257[/C][/ROW]
[ROW][C]22[/C][C]0.999844705909856[/C][C]0.000310588180288354[/C][C]0.000155294090144177[/C][/ROW]
[ROW][C]23[/C][C]0.999845531849252[/C][C]0.000308936301496924[/C][C]0.000154468150748462[/C][/ROW]
[ROW][C]24[/C][C]0.999881680196555[/C][C]0.000236639606889891[/C][C]0.000118319803444946[/C][/ROW]
[ROW][C]25[/C][C]0.999565671762877[/C][C]0.000868656474245455[/C][C]0.000434328237122727[/C][/ROW]
[ROW][C]26[/C][C]0.998587306966284[/C][C]0.00282538606743157[/C][C]0.00141269303371578[/C][/ROW]
[ROW][C]27[/C][C]0.995725520155097[/C][C]0.0085489596898066[/C][C]0.0042744798449033[/C][/ROW]
[ROW][C]28[/C][C]0.995886964045285[/C][C]0.00822607190943098[/C][C]0.00411303595471549[/C][/ROW]
[ROW][C]29[/C][C]0.9900988838696[/C][C]0.0198022322607982[/C][C]0.00990111613039912[/C][/ROW]
[ROW][C]30[/C][C]0.990908774963807[/C][C]0.0181824500723856[/C][C]0.00909122503619282[/C][/ROW]
[ROW][C]31[/C][C]0.962570437927613[/C][C]0.0748591241447737[/C][C]0.0374295620723869[/C][/ROW]
[ROW][C]32[/C][C]0.988556397195028[/C][C]0.0228872056099445[/C][C]0.0114436028049722[/C][/ROW]
[ROW][C]33[/C][C]0.988733386529562[/C][C]0.0225332269408753[/C][C]0.0112666134704377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99202&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99202&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
77.35156510979815e-050.0001470313021959630.999926484348902
80.999031561648340.001936876703321260.000968438351660631
90.9975752719760560.004849456047887060.00242472802394353
100.994769061699550.01046187660089890.00523093830044946
110.9954720904764330.009055819047132990.00452790952356649
120.9960437184306130.007912563138773260.00395628156938663
130.9984411747029880.003117650594025030.00155882529701251
140.996588061167680.006823877664641670.00341193883232083
150.9947427026902760.01051459461944790.00525729730972396
160.9949978023829260.01000439523414820.00500219761707409
170.9952507056380120.00949858872397580.0047492943619879
180.991172019983720.01765596003255950.00882798001627974
190.9885740373903530.02285192521929310.0114259626096466
200.9838005414569620.0323989170860750.0161994585430375
210.9997742534419420.0004514931161165140.000225746558058257
220.9998447059098560.0003105881802883540.000155294090144177
230.9998455318492520.0003089363014969240.000154468150748462
240.9998816801965550.0002366396068898910.000118319803444946
250.9995656717628770.0008686564742454550.000434328237122727
260.9985873069662840.002825386067431570.00141269303371578
270.9957255201550970.00854895968980660.0042744798449033
280.9958869640452850.008226071909430980.00411303595471549
290.99009888386960.01980223226079820.00990111613039912
300.9909087749638070.01818245007238560.00909122503619282
310.9625704379276130.07485912414477370.0374295620723869
320.9885563971950280.02288720560994450.0114436028049722
330.9887333865295620.02253322694087530.0112666134704377







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level160.592592592592593NOK
5% type I error level260.962962962962963NOK
10% type I error level271NOK

\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 & 16 & 0.592592592592593 & NOK \tabularnewline
5% type I error level & 26 & 0.962962962962963 & NOK \tabularnewline
10% type I error level & 27 & 1 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99202&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]16[/C][C]0.592592592592593[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]26[/C][C]0.962962962962963[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]27[/C][C]1[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99202&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99202&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 level160.592592592592593NOK
5% type I error level260.962962962962963NOK
10% type I error level271NOK



Parameters (Session):
par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 3 ; 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')
}