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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 13:24:21 -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/t1258662414kn86nnphoao4py0.htm/, Retrieved Fri, 29 Mar 2024 06:31:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57936, Retrieved Fri, 29 Mar 2024 06:31:37 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
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 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [Multiple Regressi...] [2009-11-19 20:24:21] [f97f6131ca109ba89501d75ae11b45c9] [Current]
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Dataseries X:
10	24.1
9.2	24.1
9.2	24.1
9.5	21.3
9.6	21.3
9.5	21.3
9.1	19.1
8.9	19.1
9	19.1
10.1	26.2
10.3	26.2
10.2	26.2
9.6	21.7
9.2	21.7
9.3	21.7
9.4	19.4
9.4	19.4
9.2	19.4
9	19.5
9	19.5
9	19.5
9.8	28.7
10	28.7
9.8	28.7
9.3	21.8
9	21.8
9	21.8
9.1	20
9.1	20
9.1	20
9.2	22.6
8.8	22.6
8.3	22.6
8.4	22.4
8.1	22.4
7.7	22.4
7.9	18.6
7.9	18.6
8	18.6
7.9	16.2
7.6	16.2
7.1	16.2
6.8	13.8
6.5	13.8
6.9	13.8
8.2	24.1
8.7	24.1
8.3	24.1
7.9	19.9
7.5	19.9
7.8	19.9
8.3	22.3
8.4	22.3
8.2	22.3
7.7	20.9
7.2	20.9
7.3	20.9
8.1	25.5
8.5	25.5
8.4	25.5




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57936&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57936&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
TWV[t] = + 2.53000723423698 + 0.250196720479237`WV-25`[t] + 1.10081835719362M1[t] + 0.720818357193624M2[t] + 0.820818357193624M3[t] + 1.34608983145497M4[t] + 1.32608983145497M5[t] + 1.12608983145497M6[t] + 1.03121966697127M7[t] + 0.751219666971267M8[t] + 0.771219666971266M9[t] + 0.0400000000000001M10[t] + 0.24M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TWV[t] =  +  2.53000723423698 +  0.250196720479237`WV-25`[t] +  1.10081835719362M1[t] +  0.720818357193624M2[t] +  0.820818357193624M3[t] +  1.34608983145497M4[t] +  1.32608983145497M5[t] +  1.12608983145497M6[t] +  1.03121966697127M7[t] +  0.751219666971267M8[t] +  0.771219666971266M9[t] +  0.0400000000000001M10[t] +  0.24M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57936&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TWV[t] =  +  2.53000723423698 +  0.250196720479237`WV-25`[t] +  1.10081835719362M1[t] +  0.720818357193624M2[t] +  0.820818357193624M3[t] +  1.34608983145497M4[t] +  1.32608983145497M5[t] +  1.12608983145497M6[t] +  1.03121966697127M7[t] +  0.751219666971267M8[t] +  0.771219666971266M9[t] +  0.0400000000000001M10[t] +  0.24M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57936&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
TWV[t] = + 2.53000723423698 + 0.250196720479237`WV-25`[t] + 1.10081835719362M1[t] + 0.720818357193624M2[t] + 0.820818357193624M3[t] + 1.34608983145497M4[t] + 1.32608983145497M5[t] + 1.12608983145497M6[t] + 1.03121966697127M7[t] + 0.751219666971267M8[t] + 0.771219666971266M9[t] + 0.0400000000000001M10[t] + 0.24M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.530007234236981.0414512.42930.0190040.009502
`WV-25`0.2501967204792370.0391636.388600
M11.100818357193620.468932.34750.0231620.011581
M20.7208183571936240.468931.53720.1309610.06548
M30.8208183571936240.468931.75040.0865740.043287
M41.346089831454970.4903322.74530.0085390.004269
M51.326089831454970.4903322.70450.0094970.004748
M61.126089831454970.4903322.29660.0261450.013073
M71.031219666971270.5023042.0530.0456650.022832
M80.7512196669712670.5023041.49550.1414570.070728
M90.7712196669712660.5023041.53540.13140.0657
M100.04000000000000010.4397190.0910.9279050.463953
M110.240.4397190.54580.5877830.293891

\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) & 2.53000723423698 & 1.041451 & 2.4293 & 0.019004 & 0.009502 \tabularnewline
`WV-25` & 0.250196720479237 & 0.039163 & 6.3886 & 0 & 0 \tabularnewline
M1 & 1.10081835719362 & 0.46893 & 2.3475 & 0.023162 & 0.011581 \tabularnewline
M2 & 0.720818357193624 & 0.46893 & 1.5372 & 0.130961 & 0.06548 \tabularnewline
M3 & 0.820818357193624 & 0.46893 & 1.7504 & 0.086574 & 0.043287 \tabularnewline
M4 & 1.34608983145497 & 0.490332 & 2.7453 & 0.008539 & 0.004269 \tabularnewline
M5 & 1.32608983145497 & 0.490332 & 2.7045 & 0.009497 & 0.004748 \tabularnewline
M6 & 1.12608983145497 & 0.490332 & 2.2966 & 0.026145 & 0.013073 \tabularnewline
M7 & 1.03121966697127 & 0.502304 & 2.053 & 0.045665 & 0.022832 \tabularnewline
M8 & 0.751219666971267 & 0.502304 & 1.4955 & 0.141457 & 0.070728 \tabularnewline
M9 & 0.771219666971266 & 0.502304 & 1.5354 & 0.1314 & 0.0657 \tabularnewline
M10 & 0.0400000000000001 & 0.439719 & 0.091 & 0.927905 & 0.463953 \tabularnewline
M11 & 0.24 & 0.439719 & 0.5458 & 0.587783 & 0.293891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57936&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]2.53000723423698[/C][C]1.041451[/C][C]2.4293[/C][C]0.019004[/C][C]0.009502[/C][/ROW]
[ROW][C]`WV-25`[/C][C]0.250196720479237[/C][C]0.039163[/C][C]6.3886[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]1.10081835719362[/C][C]0.46893[/C][C]2.3475[/C][C]0.023162[/C][C]0.011581[/C][/ROW]
[ROW][C]M2[/C][C]0.720818357193624[/C][C]0.46893[/C][C]1.5372[/C][C]0.130961[/C][C]0.06548[/C][/ROW]
[ROW][C]M3[/C][C]0.820818357193624[/C][C]0.46893[/C][C]1.7504[/C][C]0.086574[/C][C]0.043287[/C][/ROW]
[ROW][C]M4[/C][C]1.34608983145497[/C][C]0.490332[/C][C]2.7453[/C][C]0.008539[/C][C]0.004269[/C][/ROW]
[ROW][C]M5[/C][C]1.32608983145497[/C][C]0.490332[/C][C]2.7045[/C][C]0.009497[/C][C]0.004748[/C][/ROW]
[ROW][C]M6[/C][C]1.12608983145497[/C][C]0.490332[/C][C]2.2966[/C][C]0.026145[/C][C]0.013073[/C][/ROW]
[ROW][C]M7[/C][C]1.03121966697127[/C][C]0.502304[/C][C]2.053[/C][C]0.045665[/C][C]0.022832[/C][/ROW]
[ROW][C]M8[/C][C]0.751219666971267[/C][C]0.502304[/C][C]1.4955[/C][C]0.141457[/C][C]0.070728[/C][/ROW]
[ROW][C]M9[/C][C]0.771219666971266[/C][C]0.502304[/C][C]1.5354[/C][C]0.1314[/C][C]0.0657[/C][/ROW]
[ROW][C]M10[/C][C]0.0400000000000001[/C][C]0.439719[/C][C]0.091[/C][C]0.927905[/C][C]0.463953[/C][/ROW]
[ROW][C]M11[/C][C]0.24[/C][C]0.439719[/C][C]0.5458[/C][C]0.587783[/C][C]0.293891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57936&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57936&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)2.530007234236981.0414512.42930.0190040.009502
`WV-25`0.2501967204792370.0391636.388600
M11.100818357193620.468932.34750.0231620.011581
M20.7208183571936240.468931.53720.1309610.06548
M30.8208183571936240.468931.75040.0865740.043287
M41.346089831454970.4903322.74530.0085390.004269
M51.326089831454970.4903322.70450.0094970.004748
M61.126089831454970.4903322.29660.0261450.013073
M71.031219666971270.5023042.0530.0456650.022832
M80.7512196669712670.5023041.49550.1414570.070728
M90.7712196669712660.5023041.53540.13140.0657
M100.04000000000000010.4397190.0910.9279050.463953
M110.240.4397190.54580.5877830.293891







Multiple Linear Regression - Regression Statistics
Multiple R0.729257593587251
R-squared0.531816637804669
Adjusted R-squared0.412280460222882
F-TEST (value)4.44900153713548
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value9.98343333580287e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.695257304326818
Sum Squared Residuals22.7189878033303

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.729257593587251 \tabularnewline
R-squared & 0.531816637804669 \tabularnewline
Adjusted R-squared & 0.412280460222882 \tabularnewline
F-TEST (value) & 4.44900153713548 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 9.98343333580287e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.695257304326818 \tabularnewline
Sum Squared Residuals & 22.7189878033303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57936&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.729257593587251[/C][/ROW]
[ROW][C]R-squared[/C][C]0.531816637804669[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.412280460222882[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.44900153713548[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]9.98343333580287e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.695257304326818[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]22.7189878033303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57936&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57936&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 R0.729257593587251
R-squared0.531816637804669
Adjusted R-squared0.412280460222882
F-TEST (value)4.44900153713548
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value9.98343333580287e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.695257304326818
Sum Squared Residuals22.7189878033303







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1109.66056655498020.339433445019795
29.29.2805665549802-0.0805665549802007
39.29.3805665549802-0.180566554980201
49.59.205287211899680.294712788100315
59.69.185287211899680.414712788100316
69.58.985287211899680.514712788100314
79.18.339984262361660.760015737638337
88.98.059984262361660.840015737638338
998.079984262361660.920015737638338
1010.19.125161310792970.974838689207026
1110.39.325161310792970.974838689207027
1210.29.085161310792971.11483868920703
139.69.060094425830030.539905574169967
149.28.680094425830030.519905574169966
159.38.780094425830030.519905574169967
169.48.729913442989140.670086557010864
179.48.709913442989140.690086557010864
189.28.509913442989140.690086557010864
1998.440062950553350.559937049446645
2098.160062950553360.839937049446644
2198.180062950553350.819937049446645
229.89.750653111991070.0493468880089356
23109.950653111991060.0493468880089351
249.89.710653111991060.089346888008936
259.39.085114097877960.214885902122044
2698.705114097877960.294885902122043
2798.805114097877960.194885902122043
289.18.880031475276680.219968524723321
299.18.860031475276680.239968524723322
309.18.660031475276680.439968524723322
319.29.21567278403899-0.0156727840389892
328.88.93567278403899-0.135672784038989
338.38.95567278403899-0.655672784038989
348.48.174413772971870.225586227028125
358.18.37441377297188-0.274413772971875
367.78.13441377297188-0.434413772971875
377.98.2844845923444-0.384484592344400
387.97.9044845923444-0.00448459234440062
3988.0044845923444-0.00448459234440128
407.97.92928393745558-0.0292839374555795
417.67.90928393745558-0.30928393745558
427.17.70928393745558-0.609283937455579
436.87.01394164382171-0.213941643821708
446.56.73394164382171-0.233941643821708
456.96.753941643821710.146058356178292
468.28.59974819778658-0.399748197786578
478.78.79974819778658-0.0997481977865782
488.38.55974819778658-0.259748197786576
497.98.6097403289674-0.709740328967406
507.58.2297403289674-0.729740328967407
517.88.3297403289674-0.529740328967408
528.39.45548393237892-1.15548393237892
538.49.43548393237892-1.03548393237892
548.29.23548393237892-1.03548393237892
557.78.79033835922429-1.09033835922429
567.28.51033835922429-1.31033835922429
577.38.53033835922429-1.23033835922429
588.18.9500236064575-0.850023606457509
598.59.1500236064575-0.650023606457508
608.48.9100236064575-0.510023606457508

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 10 & 9.6605665549802 & 0.339433445019795 \tabularnewline
2 & 9.2 & 9.2805665549802 & -0.0805665549802007 \tabularnewline
3 & 9.2 & 9.3805665549802 & -0.180566554980201 \tabularnewline
4 & 9.5 & 9.20528721189968 & 0.294712788100315 \tabularnewline
5 & 9.6 & 9.18528721189968 & 0.414712788100316 \tabularnewline
6 & 9.5 & 8.98528721189968 & 0.514712788100314 \tabularnewline
7 & 9.1 & 8.33998426236166 & 0.760015737638337 \tabularnewline
8 & 8.9 & 8.05998426236166 & 0.840015737638338 \tabularnewline
9 & 9 & 8.07998426236166 & 0.920015737638338 \tabularnewline
10 & 10.1 & 9.12516131079297 & 0.974838689207026 \tabularnewline
11 & 10.3 & 9.32516131079297 & 0.974838689207027 \tabularnewline
12 & 10.2 & 9.08516131079297 & 1.11483868920703 \tabularnewline
13 & 9.6 & 9.06009442583003 & 0.539905574169967 \tabularnewline
14 & 9.2 & 8.68009442583003 & 0.519905574169966 \tabularnewline
15 & 9.3 & 8.78009442583003 & 0.519905574169967 \tabularnewline
16 & 9.4 & 8.72991344298914 & 0.670086557010864 \tabularnewline
17 & 9.4 & 8.70991344298914 & 0.690086557010864 \tabularnewline
18 & 9.2 & 8.50991344298914 & 0.690086557010864 \tabularnewline
19 & 9 & 8.44006295055335 & 0.559937049446645 \tabularnewline
20 & 9 & 8.16006295055336 & 0.839937049446644 \tabularnewline
21 & 9 & 8.18006295055335 & 0.819937049446645 \tabularnewline
22 & 9.8 & 9.75065311199107 & 0.0493468880089356 \tabularnewline
23 & 10 & 9.95065311199106 & 0.0493468880089351 \tabularnewline
24 & 9.8 & 9.71065311199106 & 0.089346888008936 \tabularnewline
25 & 9.3 & 9.08511409787796 & 0.214885902122044 \tabularnewline
26 & 9 & 8.70511409787796 & 0.294885902122043 \tabularnewline
27 & 9 & 8.80511409787796 & 0.194885902122043 \tabularnewline
28 & 9.1 & 8.88003147527668 & 0.219968524723321 \tabularnewline
29 & 9.1 & 8.86003147527668 & 0.239968524723322 \tabularnewline
30 & 9.1 & 8.66003147527668 & 0.439968524723322 \tabularnewline
31 & 9.2 & 9.21567278403899 & -0.0156727840389892 \tabularnewline
32 & 8.8 & 8.93567278403899 & -0.135672784038989 \tabularnewline
33 & 8.3 & 8.95567278403899 & -0.655672784038989 \tabularnewline
34 & 8.4 & 8.17441377297187 & 0.225586227028125 \tabularnewline
35 & 8.1 & 8.37441377297188 & -0.274413772971875 \tabularnewline
36 & 7.7 & 8.13441377297188 & -0.434413772971875 \tabularnewline
37 & 7.9 & 8.2844845923444 & -0.384484592344400 \tabularnewline
38 & 7.9 & 7.9044845923444 & -0.00448459234440062 \tabularnewline
39 & 8 & 8.0044845923444 & -0.00448459234440128 \tabularnewline
40 & 7.9 & 7.92928393745558 & -0.0292839374555795 \tabularnewline
41 & 7.6 & 7.90928393745558 & -0.30928393745558 \tabularnewline
42 & 7.1 & 7.70928393745558 & -0.609283937455579 \tabularnewline
43 & 6.8 & 7.01394164382171 & -0.213941643821708 \tabularnewline
44 & 6.5 & 6.73394164382171 & -0.233941643821708 \tabularnewline
45 & 6.9 & 6.75394164382171 & 0.146058356178292 \tabularnewline
46 & 8.2 & 8.59974819778658 & -0.399748197786578 \tabularnewline
47 & 8.7 & 8.79974819778658 & -0.0997481977865782 \tabularnewline
48 & 8.3 & 8.55974819778658 & -0.259748197786576 \tabularnewline
49 & 7.9 & 8.6097403289674 & -0.709740328967406 \tabularnewline
50 & 7.5 & 8.2297403289674 & -0.729740328967407 \tabularnewline
51 & 7.8 & 8.3297403289674 & -0.529740328967408 \tabularnewline
52 & 8.3 & 9.45548393237892 & -1.15548393237892 \tabularnewline
53 & 8.4 & 9.43548393237892 & -1.03548393237892 \tabularnewline
54 & 8.2 & 9.23548393237892 & -1.03548393237892 \tabularnewline
55 & 7.7 & 8.79033835922429 & -1.09033835922429 \tabularnewline
56 & 7.2 & 8.51033835922429 & -1.31033835922429 \tabularnewline
57 & 7.3 & 8.53033835922429 & -1.23033835922429 \tabularnewline
58 & 8.1 & 8.9500236064575 & -0.850023606457509 \tabularnewline
59 & 8.5 & 9.1500236064575 & -0.650023606457508 \tabularnewline
60 & 8.4 & 8.9100236064575 & -0.510023606457508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57936&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]10[/C][C]9.6605665549802[/C][C]0.339433445019795[/C][/ROW]
[ROW][C]2[/C][C]9.2[/C][C]9.2805665549802[/C][C]-0.0805665549802007[/C][/ROW]
[ROW][C]3[/C][C]9.2[/C][C]9.3805665549802[/C][C]-0.180566554980201[/C][/ROW]
[ROW][C]4[/C][C]9.5[/C][C]9.20528721189968[/C][C]0.294712788100315[/C][/ROW]
[ROW][C]5[/C][C]9.6[/C][C]9.18528721189968[/C][C]0.414712788100316[/C][/ROW]
[ROW][C]6[/C][C]9.5[/C][C]8.98528721189968[/C][C]0.514712788100314[/C][/ROW]
[ROW][C]7[/C][C]9.1[/C][C]8.33998426236166[/C][C]0.760015737638337[/C][/ROW]
[ROW][C]8[/C][C]8.9[/C][C]8.05998426236166[/C][C]0.840015737638338[/C][/ROW]
[ROW][C]9[/C][C]9[/C][C]8.07998426236166[/C][C]0.920015737638338[/C][/ROW]
[ROW][C]10[/C][C]10.1[/C][C]9.12516131079297[/C][C]0.974838689207026[/C][/ROW]
[ROW][C]11[/C][C]10.3[/C][C]9.32516131079297[/C][C]0.974838689207027[/C][/ROW]
[ROW][C]12[/C][C]10.2[/C][C]9.08516131079297[/C][C]1.11483868920703[/C][/ROW]
[ROW][C]13[/C][C]9.6[/C][C]9.06009442583003[/C][C]0.539905574169967[/C][/ROW]
[ROW][C]14[/C][C]9.2[/C][C]8.68009442583003[/C][C]0.519905574169966[/C][/ROW]
[ROW][C]15[/C][C]9.3[/C][C]8.78009442583003[/C][C]0.519905574169967[/C][/ROW]
[ROW][C]16[/C][C]9.4[/C][C]8.72991344298914[/C][C]0.670086557010864[/C][/ROW]
[ROW][C]17[/C][C]9.4[/C][C]8.70991344298914[/C][C]0.690086557010864[/C][/ROW]
[ROW][C]18[/C][C]9.2[/C][C]8.50991344298914[/C][C]0.690086557010864[/C][/ROW]
[ROW][C]19[/C][C]9[/C][C]8.44006295055335[/C][C]0.559937049446645[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]8.16006295055336[/C][C]0.839937049446644[/C][/ROW]
[ROW][C]21[/C][C]9[/C][C]8.18006295055335[/C][C]0.819937049446645[/C][/ROW]
[ROW][C]22[/C][C]9.8[/C][C]9.75065311199107[/C][C]0.0493468880089356[/C][/ROW]
[ROW][C]23[/C][C]10[/C][C]9.95065311199106[/C][C]0.0493468880089351[/C][/ROW]
[ROW][C]24[/C][C]9.8[/C][C]9.71065311199106[/C][C]0.089346888008936[/C][/ROW]
[ROW][C]25[/C][C]9.3[/C][C]9.08511409787796[/C][C]0.214885902122044[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]8.70511409787796[/C][C]0.294885902122043[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]8.80511409787796[/C][C]0.194885902122043[/C][/ROW]
[ROW][C]28[/C][C]9.1[/C][C]8.88003147527668[/C][C]0.219968524723321[/C][/ROW]
[ROW][C]29[/C][C]9.1[/C][C]8.86003147527668[/C][C]0.239968524723322[/C][/ROW]
[ROW][C]30[/C][C]9.1[/C][C]8.66003147527668[/C][C]0.439968524723322[/C][/ROW]
[ROW][C]31[/C][C]9.2[/C][C]9.21567278403899[/C][C]-0.0156727840389892[/C][/ROW]
[ROW][C]32[/C][C]8.8[/C][C]8.93567278403899[/C][C]-0.135672784038989[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]8.95567278403899[/C][C]-0.655672784038989[/C][/ROW]
[ROW][C]34[/C][C]8.4[/C][C]8.17441377297187[/C][C]0.225586227028125[/C][/ROW]
[ROW][C]35[/C][C]8.1[/C][C]8.37441377297188[/C][C]-0.274413772971875[/C][/ROW]
[ROW][C]36[/C][C]7.7[/C][C]8.13441377297188[/C][C]-0.434413772971875[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]8.2844845923444[/C][C]-0.384484592344400[/C][/ROW]
[ROW][C]38[/C][C]7.9[/C][C]7.9044845923444[/C][C]-0.00448459234440062[/C][/ROW]
[ROW][C]39[/C][C]8[/C][C]8.0044845923444[/C][C]-0.00448459234440128[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.92928393745558[/C][C]-0.0292839374555795[/C][/ROW]
[ROW][C]41[/C][C]7.6[/C][C]7.90928393745558[/C][C]-0.30928393745558[/C][/ROW]
[ROW][C]42[/C][C]7.1[/C][C]7.70928393745558[/C][C]-0.609283937455579[/C][/ROW]
[ROW][C]43[/C][C]6.8[/C][C]7.01394164382171[/C][C]-0.213941643821708[/C][/ROW]
[ROW][C]44[/C][C]6.5[/C][C]6.73394164382171[/C][C]-0.233941643821708[/C][/ROW]
[ROW][C]45[/C][C]6.9[/C][C]6.75394164382171[/C][C]0.146058356178292[/C][/ROW]
[ROW][C]46[/C][C]8.2[/C][C]8.59974819778658[/C][C]-0.399748197786578[/C][/ROW]
[ROW][C]47[/C][C]8.7[/C][C]8.79974819778658[/C][C]-0.0997481977865782[/C][/ROW]
[ROW][C]48[/C][C]8.3[/C][C]8.55974819778658[/C][C]-0.259748197786576[/C][/ROW]
[ROW][C]49[/C][C]7.9[/C][C]8.6097403289674[/C][C]-0.709740328967406[/C][/ROW]
[ROW][C]50[/C][C]7.5[/C][C]8.2297403289674[/C][C]-0.729740328967407[/C][/ROW]
[ROW][C]51[/C][C]7.8[/C][C]8.3297403289674[/C][C]-0.529740328967408[/C][/ROW]
[ROW][C]52[/C][C]8.3[/C][C]9.45548393237892[/C][C]-1.15548393237892[/C][/ROW]
[ROW][C]53[/C][C]8.4[/C][C]9.43548393237892[/C][C]-1.03548393237892[/C][/ROW]
[ROW][C]54[/C][C]8.2[/C][C]9.23548393237892[/C][C]-1.03548393237892[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]8.79033835922429[/C][C]-1.09033835922429[/C][/ROW]
[ROW][C]56[/C][C]7.2[/C][C]8.51033835922429[/C][C]-1.31033835922429[/C][/ROW]
[ROW][C]57[/C][C]7.3[/C][C]8.53033835922429[/C][C]-1.23033835922429[/C][/ROW]
[ROW][C]58[/C][C]8.1[/C][C]8.9500236064575[/C][C]-0.850023606457509[/C][/ROW]
[ROW][C]59[/C][C]8.5[/C][C]9.1500236064575[/C][C]-0.650023606457508[/C][/ROW]
[ROW][C]60[/C][C]8.4[/C][C]8.9100236064575[/C][C]-0.510023606457508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57936&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57936&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
1109.66056655498020.339433445019795
29.29.2805665549802-0.0805665549802007
39.29.3805665549802-0.180566554980201
49.59.205287211899680.294712788100315
59.69.185287211899680.414712788100316
69.58.985287211899680.514712788100314
79.18.339984262361660.760015737638337
88.98.059984262361660.840015737638338
998.079984262361660.920015737638338
1010.19.125161310792970.974838689207026
1110.39.325161310792970.974838689207027
1210.29.085161310792971.11483868920703
139.69.060094425830030.539905574169967
149.28.680094425830030.519905574169966
159.38.780094425830030.519905574169967
169.48.729913442989140.670086557010864
179.48.709913442989140.690086557010864
189.28.509913442989140.690086557010864
1998.440062950553350.559937049446645
2098.160062950553360.839937049446644
2198.180062950553350.819937049446645
229.89.750653111991070.0493468880089356
23109.950653111991060.0493468880089351
249.89.710653111991060.089346888008936
259.39.085114097877960.214885902122044
2698.705114097877960.294885902122043
2798.805114097877960.194885902122043
289.18.880031475276680.219968524723321
299.18.860031475276680.239968524723322
309.18.660031475276680.439968524723322
319.29.21567278403899-0.0156727840389892
328.88.93567278403899-0.135672784038989
338.38.95567278403899-0.655672784038989
348.48.174413772971870.225586227028125
358.18.37441377297188-0.274413772971875
367.78.13441377297188-0.434413772971875
377.98.2844845923444-0.384484592344400
387.97.9044845923444-0.00448459234440062
3988.0044845923444-0.00448459234440128
407.97.92928393745558-0.0292839374555795
417.67.90928393745558-0.30928393745558
427.17.70928393745558-0.609283937455579
436.87.01394164382171-0.213941643821708
446.56.73394164382171-0.233941643821708
456.96.753941643821710.146058356178292
468.28.59974819778658-0.399748197786578
478.78.79974819778658-0.0997481977865782
488.38.55974819778658-0.259748197786576
497.98.6097403289674-0.709740328967406
507.58.2297403289674-0.729740328967407
517.88.3297403289674-0.529740328967408
528.39.45548393237892-1.15548393237892
538.49.43548393237892-1.03548393237892
548.29.23548393237892-1.03548393237892
557.78.79033835922429-1.09033835922429
567.28.51033835922429-1.31033835922429
577.38.53033835922429-1.23033835922429
588.18.9500236064575-0.850023606457509
598.59.1500236064575-0.650023606457508
608.48.9100236064575-0.510023606457508







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.01735080215790160.03470160431580330.982649197842098
170.00426406078980980.00852812157961960.99573593921019
180.001493280905012980.002986561810025950.998506719094987
190.000427088789720790.000854177579441580.99957291121028
200.0001416134780351560.0002832269560703130.999858386521965
215.21703675492622e-050.0001043407350985240.99994782963245
220.0001479137428292230.0002958274856584460.99985208625717
230.0001486559997138560.0002973119994277110.999851344000286
240.0001943239959589990.0003886479919179990.99980567600404
250.0007507957868056770.001501591573611350.999249204213194
260.0005200471533028950.001040094306605790.999479952846697
270.000361615374506580.000723230749013160.999638384625493
280.0004949365369807670.0009898730739615350.999505063463019
290.001031980855768860.002063961711537720.99896801914423
300.003728711010928130.007457422021856260.996271288989072
310.01125187889584290.02250375779168580.988748121104157
320.1378728873501920.2757457747003830.862127112649808
330.4522741613298040.9045483226596080.547725838670196
340.9370382987409020.1259234025181960.0629617012590978
350.9858442907099730.02831141858005410.0141557092900271
360.99608559058810.007828818823799620.00391440941189981
370.9943327775815810.01133444483683760.00566722241841879
380.9960694483435710.007861103312857310.00393055165642866
390.9942171903842860.01156561923142700.00578280961571351
400.9896911772544860.02061764549102740.0103088227455137
410.979062055157590.04187588968481880.0209379448424094
420.98983162321960.02033675356080110.0101683767804006
430.9864524685842970.0270950628314050.0135475314157025
440.9772516689206270.04549666215874670.0227483310793733

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0173508021579016 & 0.0347016043158033 & 0.982649197842098 \tabularnewline
17 & 0.0042640607898098 & 0.0085281215796196 & 0.99573593921019 \tabularnewline
18 & 0.00149328090501298 & 0.00298656181002595 & 0.998506719094987 \tabularnewline
19 & 0.00042708878972079 & 0.00085417757944158 & 0.99957291121028 \tabularnewline
20 & 0.000141613478035156 & 0.000283226956070313 & 0.999858386521965 \tabularnewline
21 & 5.21703675492622e-05 & 0.000104340735098524 & 0.99994782963245 \tabularnewline
22 & 0.000147913742829223 & 0.000295827485658446 & 0.99985208625717 \tabularnewline
23 & 0.000148655999713856 & 0.000297311999427711 & 0.999851344000286 \tabularnewline
24 & 0.000194323995958999 & 0.000388647991917999 & 0.99980567600404 \tabularnewline
25 & 0.000750795786805677 & 0.00150159157361135 & 0.999249204213194 \tabularnewline
26 & 0.000520047153302895 & 0.00104009430660579 & 0.999479952846697 \tabularnewline
27 & 0.00036161537450658 & 0.00072323074901316 & 0.999638384625493 \tabularnewline
28 & 0.000494936536980767 & 0.000989873073961535 & 0.999505063463019 \tabularnewline
29 & 0.00103198085576886 & 0.00206396171153772 & 0.99896801914423 \tabularnewline
30 & 0.00372871101092813 & 0.00745742202185626 & 0.996271288989072 \tabularnewline
31 & 0.0112518788958429 & 0.0225037577916858 & 0.988748121104157 \tabularnewline
32 & 0.137872887350192 & 0.275745774700383 & 0.862127112649808 \tabularnewline
33 & 0.452274161329804 & 0.904548322659608 & 0.547725838670196 \tabularnewline
34 & 0.937038298740902 & 0.125923402518196 & 0.0629617012590978 \tabularnewline
35 & 0.985844290709973 & 0.0283114185800541 & 0.0141557092900271 \tabularnewline
36 & 0.9960855905881 & 0.00782881882379962 & 0.00391440941189981 \tabularnewline
37 & 0.994332777581581 & 0.0113344448368376 & 0.00566722241841879 \tabularnewline
38 & 0.996069448343571 & 0.00786110331285731 & 0.00393055165642866 \tabularnewline
39 & 0.994217190384286 & 0.0115656192314270 & 0.00578280961571351 \tabularnewline
40 & 0.989691177254486 & 0.0206176454910274 & 0.0103088227455137 \tabularnewline
41 & 0.97906205515759 & 0.0418758896848188 & 0.0209379448424094 \tabularnewline
42 & 0.9898316232196 & 0.0203367535608011 & 0.0101683767804006 \tabularnewline
43 & 0.986452468584297 & 0.027095062831405 & 0.0135475314157025 \tabularnewline
44 & 0.977251668920627 & 0.0454966621587467 & 0.0227483310793733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57936&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]16[/C][C]0.0173508021579016[/C][C]0.0347016043158033[/C][C]0.982649197842098[/C][/ROW]
[ROW][C]17[/C][C]0.0042640607898098[/C][C]0.0085281215796196[/C][C]0.99573593921019[/C][/ROW]
[ROW][C]18[/C][C]0.00149328090501298[/C][C]0.00298656181002595[/C][C]0.998506719094987[/C][/ROW]
[ROW][C]19[/C][C]0.00042708878972079[/C][C]0.00085417757944158[/C][C]0.99957291121028[/C][/ROW]
[ROW][C]20[/C][C]0.000141613478035156[/C][C]0.000283226956070313[/C][C]0.999858386521965[/C][/ROW]
[ROW][C]21[/C][C]5.21703675492622e-05[/C][C]0.000104340735098524[/C][C]0.99994782963245[/C][/ROW]
[ROW][C]22[/C][C]0.000147913742829223[/C][C]0.000295827485658446[/C][C]0.99985208625717[/C][/ROW]
[ROW][C]23[/C][C]0.000148655999713856[/C][C]0.000297311999427711[/C][C]0.999851344000286[/C][/ROW]
[ROW][C]24[/C][C]0.000194323995958999[/C][C]0.000388647991917999[/C][C]0.99980567600404[/C][/ROW]
[ROW][C]25[/C][C]0.000750795786805677[/C][C]0.00150159157361135[/C][C]0.999249204213194[/C][/ROW]
[ROW][C]26[/C][C]0.000520047153302895[/C][C]0.00104009430660579[/C][C]0.999479952846697[/C][/ROW]
[ROW][C]27[/C][C]0.00036161537450658[/C][C]0.00072323074901316[/C][C]0.999638384625493[/C][/ROW]
[ROW][C]28[/C][C]0.000494936536980767[/C][C]0.000989873073961535[/C][C]0.999505063463019[/C][/ROW]
[ROW][C]29[/C][C]0.00103198085576886[/C][C]0.00206396171153772[/C][C]0.99896801914423[/C][/ROW]
[ROW][C]30[/C][C]0.00372871101092813[/C][C]0.00745742202185626[/C][C]0.996271288989072[/C][/ROW]
[ROW][C]31[/C][C]0.0112518788958429[/C][C]0.0225037577916858[/C][C]0.988748121104157[/C][/ROW]
[ROW][C]32[/C][C]0.137872887350192[/C][C]0.275745774700383[/C][C]0.862127112649808[/C][/ROW]
[ROW][C]33[/C][C]0.452274161329804[/C][C]0.904548322659608[/C][C]0.547725838670196[/C][/ROW]
[ROW][C]34[/C][C]0.937038298740902[/C][C]0.125923402518196[/C][C]0.0629617012590978[/C][/ROW]
[ROW][C]35[/C][C]0.985844290709973[/C][C]0.0283114185800541[/C][C]0.0141557092900271[/C][/ROW]
[ROW][C]36[/C][C]0.9960855905881[/C][C]0.00782881882379962[/C][C]0.00391440941189981[/C][/ROW]
[ROW][C]37[/C][C]0.994332777581581[/C][C]0.0113344448368376[/C][C]0.00566722241841879[/C][/ROW]
[ROW][C]38[/C][C]0.996069448343571[/C][C]0.00786110331285731[/C][C]0.00393055165642866[/C][/ROW]
[ROW][C]39[/C][C]0.994217190384286[/C][C]0.0115656192314270[/C][C]0.00578280961571351[/C][/ROW]
[ROW][C]40[/C][C]0.989691177254486[/C][C]0.0206176454910274[/C][C]0.0103088227455137[/C][/ROW]
[ROW][C]41[/C][C]0.97906205515759[/C][C]0.0418758896848188[/C][C]0.0209379448424094[/C][/ROW]
[ROW][C]42[/C][C]0.9898316232196[/C][C]0.0203367535608011[/C][C]0.0101683767804006[/C][/ROW]
[ROW][C]43[/C][C]0.986452468584297[/C][C]0.027095062831405[/C][C]0.0135475314157025[/C][/ROW]
[ROW][C]44[/C][C]0.977251668920627[/C][C]0.0454966621587467[/C][C]0.0227483310793733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57936&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57936&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
160.01735080215790160.03470160431580330.982649197842098
170.00426406078980980.00852812157961960.99573593921019
180.001493280905012980.002986561810025950.998506719094987
190.000427088789720790.000854177579441580.99957291121028
200.0001416134780351560.0002832269560703130.999858386521965
215.21703675492622e-050.0001043407350985240.99994782963245
220.0001479137428292230.0002958274856584460.99985208625717
230.0001486559997138560.0002973119994277110.999851344000286
240.0001943239959589990.0003886479919179990.99980567600404
250.0007507957868056770.001501591573611350.999249204213194
260.0005200471533028950.001040094306605790.999479952846697
270.000361615374506580.000723230749013160.999638384625493
280.0004949365369807670.0009898730739615350.999505063463019
290.001031980855768860.002063961711537720.99896801914423
300.003728711010928130.007457422021856260.996271288989072
310.01125187889584290.02250375779168580.988748121104157
320.1378728873501920.2757457747003830.862127112649808
330.4522741613298040.9045483226596080.547725838670196
340.9370382987409020.1259234025181960.0629617012590978
350.9858442907099730.02831141858005410.0141557092900271
360.99608559058810.007828818823799620.00391440941189981
370.9943327775815810.01133444483683760.00566722241841879
380.9960694483435710.007861103312857310.00393055165642866
390.9942171903842860.01156561923142700.00578280961571351
400.9896911772544860.02061764549102740.0103088227455137
410.979062055157590.04187588968481880.0209379448424094
420.98983162321960.02033675356080110.0101683767804006
430.9864524685842970.0270950628314050.0135475314157025
440.9772516689206270.04549666215874670.0227483310793733







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level160.551724137931034NOK
5% type I error level260.896551724137931NOK
10% type I error level260.896551724137931NOK

\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 & 0.551724137931034 & NOK \tabularnewline
5% type I error level & 26 & 0.896551724137931 & NOK \tabularnewline
10% type I error level & 26 & 0.896551724137931 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57936&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]0.551724137931034[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]26[/C][C]0.896551724137931[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]26[/C][C]0.896551724137931[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57936&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57936&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 level160.551724137931034NOK
5% type I error level260.896551724137931NOK
10% type I error level260.896551724137931NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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')
}