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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 computationFri, 20 Nov 2009 03:31:28 -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/20/t1258713218ixnpk6xakd3o8ac.htm/, Retrieved Fri, 29 Mar 2024 09:34:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58013, Retrieved Fri, 29 Mar 2024 09:34:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185
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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 10:31:28] [30970b478e356ce7f8c2e9fca280b230] [Current]
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Dataseries X:
10.9	96.8
10	114.1
9.2	110.3
9.2	103.9
9.5	101.6
9.6	94.6
9.5	95.9
9.1	104.7
8.9	102.8
9	98.1
10.1	113.9
10.3	80.9
10.2	95.7
9.6	113.2
9.2	105.9
9.3	108.8
9.4	102.3
9.4	99
9.2	100.7
9	115.5
9	100.7
9	109.9
9.8	114.6
10	85.4
9.8	100.5
9.3	114.8
9	116.5
9	112.9
9.1	102
9.1	106
9.1	105.3
9.2	118.8
8.8	106.1
8.3	109.3
8.4	117.2
8.1	92.5
7.7	104.2
7.9	112.5
7.9	122.4
8	113.3
7.9	100
7.6	110.7
7.1	112.8
6.8	109.8
6.5	117.3
6.9	109.1
8.2	115.9
8.7	96
8.3	99.8
7.9	116.8
7.5	115.7
7.8	99.4
8.3	94.3
8.4	91
8.2	93.2
7.7	103.1
7.2	94.1
7.3	91.8
8.1	102.7
8.5	82.6




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=58013&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=58013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58013&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
Y[t] = + 13.0765375758616 -0.0275289865833972X[t] + 0.115053294379473M1[t] + 0.127692998894482M2[t] -0.212602095341469M3[t] -0.248532123979495M4[t] -0.235294617590926M5[t] -0.206229856388522M6[t] -0.326883209944381M7[t] -0.301619743856429M8[t] -0.708740496787767M9[t] -0.661148345120413M10[t] + 0.455677295332566M11[t] -0.0430083841540564t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  13.0765375758616 -0.0275289865833972X[t] +  0.115053294379473M1[t] +  0.127692998894482M2[t] -0.212602095341469M3[t] -0.248532123979495M4[t] -0.235294617590926M5[t] -0.206229856388522M6[t] -0.326883209944381M7[t] -0.301619743856429M8[t] -0.708740496787767M9[t] -0.661148345120413M10[t] +  0.455677295332566M11[t] -0.0430083841540564t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58013&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  13.0765375758616 -0.0275289865833972X[t] +  0.115053294379473M1[t] +  0.127692998894482M2[t] -0.212602095341469M3[t] -0.248532123979495M4[t] -0.235294617590926M5[t] -0.206229856388522M6[t] -0.326883209944381M7[t] -0.301619743856429M8[t] -0.708740496787767M9[t] -0.661148345120413M10[t] +  0.455677295332566M11[t] -0.0430083841540564t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58013&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
Y[t] = + 13.0765375758616 -0.0275289865833972X[t] + 0.115053294379473M1[t] + 0.127692998894482M2[t] -0.212602095341469M3[t] -0.248532123979495M4[t] -0.235294617590926M5[t] -0.206229856388522M6[t] -0.326883209944381M7[t] -0.301619743856429M8[t] -0.708740496787767M9[t] -0.661148345120413M10[t] + 0.455677295332566M11[t] -0.0430083841540564t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)13.07653757586161.01814712.843500
X-0.02752898658339720.011268-2.44310.0184610.00923
M10.1150532943794730.3453970.33310.7405690.370285
M20.1276929988944820.438520.29120.7722150.386107
M3-0.2126020953414690.437244-0.48620.6291110.314555
M4-0.2485321239794950.390101-0.63710.527220.26361
M5-0.2352946175909260.346709-0.67870.5007580.250379
M6-0.2062298563885220.347442-0.59360.5557090.277855
M7-0.3268832099443810.353633-0.92440.3601240.180062
M8-0.3016197438564290.407789-0.73960.4632720.231636
M9-0.7087404967877670.367501-1.92850.0599730.029986
M10-0.6611483451204130.364181-1.81540.0759790.037989
M110.4556772953325660.4256851.07050.2899980.144999
t-0.04300838415405640.003792-11.341700

\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) & 13.0765375758616 & 1.018147 & 12.8435 & 0 & 0 \tabularnewline
X & -0.0275289865833972 & 0.011268 & -2.4431 & 0.018461 & 0.00923 \tabularnewline
M1 & 0.115053294379473 & 0.345397 & 0.3331 & 0.740569 & 0.370285 \tabularnewline
M2 & 0.127692998894482 & 0.43852 & 0.2912 & 0.772215 & 0.386107 \tabularnewline
M3 & -0.212602095341469 & 0.437244 & -0.4862 & 0.629111 & 0.314555 \tabularnewline
M4 & -0.248532123979495 & 0.390101 & -0.6371 & 0.52722 & 0.26361 \tabularnewline
M5 & -0.235294617590926 & 0.346709 & -0.6787 & 0.500758 & 0.250379 \tabularnewline
M6 & -0.206229856388522 & 0.347442 & -0.5936 & 0.555709 & 0.277855 \tabularnewline
M7 & -0.326883209944381 & 0.353633 & -0.9244 & 0.360124 & 0.180062 \tabularnewline
M8 & -0.301619743856429 & 0.407789 & -0.7396 & 0.463272 & 0.231636 \tabularnewline
M9 & -0.708740496787767 & 0.367501 & -1.9285 & 0.059973 & 0.029986 \tabularnewline
M10 & -0.661148345120413 & 0.364181 & -1.8154 & 0.075979 & 0.037989 \tabularnewline
M11 & 0.455677295332566 & 0.425685 & 1.0705 & 0.289998 & 0.144999 \tabularnewline
t & -0.0430083841540564 & 0.003792 & -11.3417 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58013&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]13.0765375758616[/C][C]1.018147[/C][C]12.8435[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-0.0275289865833972[/C][C]0.011268[/C][C]-2.4431[/C][C]0.018461[/C][C]0.00923[/C][/ROW]
[ROW][C]M1[/C][C]0.115053294379473[/C][C]0.345397[/C][C]0.3331[/C][C]0.740569[/C][C]0.370285[/C][/ROW]
[ROW][C]M2[/C][C]0.127692998894482[/C][C]0.43852[/C][C]0.2912[/C][C]0.772215[/C][C]0.386107[/C][/ROW]
[ROW][C]M3[/C][C]-0.212602095341469[/C][C]0.437244[/C][C]-0.4862[/C][C]0.629111[/C][C]0.314555[/C][/ROW]
[ROW][C]M4[/C][C]-0.248532123979495[/C][C]0.390101[/C][C]-0.6371[/C][C]0.52722[/C][C]0.26361[/C][/ROW]
[ROW][C]M5[/C][C]-0.235294617590926[/C][C]0.346709[/C][C]-0.6787[/C][C]0.500758[/C][C]0.250379[/C][/ROW]
[ROW][C]M6[/C][C]-0.206229856388522[/C][C]0.347442[/C][C]-0.5936[/C][C]0.555709[/C][C]0.277855[/C][/ROW]
[ROW][C]M7[/C][C]-0.326883209944381[/C][C]0.353633[/C][C]-0.9244[/C][C]0.360124[/C][C]0.180062[/C][/ROW]
[ROW][C]M8[/C][C]-0.301619743856429[/C][C]0.407789[/C][C]-0.7396[/C][C]0.463272[/C][C]0.231636[/C][/ROW]
[ROW][C]M9[/C][C]-0.708740496787767[/C][C]0.367501[/C][C]-1.9285[/C][C]0.059973[/C][C]0.029986[/C][/ROW]
[ROW][C]M10[/C][C]-0.661148345120413[/C][C]0.364181[/C][C]-1.8154[/C][C]0.075979[/C][C]0.037989[/C][/ROW]
[ROW][C]M11[/C][C]0.455677295332566[/C][C]0.425685[/C][C]1.0705[/C][C]0.289998[/C][C]0.144999[/C][/ROW]
[ROW][C]t[/C][C]-0.0430083841540564[/C][C]0.003792[/C][C]-11.3417[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58013&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)13.07653757586161.01814712.843500
X-0.02752898658339720.011268-2.44310.0184610.00923
M10.1150532943794730.3453970.33310.7405690.370285
M20.1276929988944820.438520.29120.7722150.386107
M3-0.2126020953414690.437244-0.48620.6291110.314555
M4-0.2485321239794950.390101-0.63710.527220.26361
M5-0.2352946175909260.346709-0.67870.5007580.250379
M6-0.2062298563885220.347442-0.59360.5557090.277855
M7-0.3268832099443810.353633-0.92440.3601240.180062
M8-0.3016197438564290.407789-0.73960.4632720.231636
M9-0.7087404967877670.367501-1.92850.0599730.029986
M10-0.6611483451204130.364181-1.81540.0759790.037989
M110.4556772953325660.4256851.07050.2899980.144999
t-0.04300838415405640.003792-11.341700







Multiple Linear Regression - Regression Statistics
Multiple R0.886512797926374
R-squared0.785904940887249
Adjusted R-squared0.725399815485819
F-TEST (value)12.9890639127355
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value2.49942289087812e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.49844092265694
Sum Squared Residuals11.4283942554387

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.886512797926374 \tabularnewline
R-squared & 0.785904940887249 \tabularnewline
Adjusted R-squared & 0.725399815485819 \tabularnewline
F-TEST (value) & 12.9890639127355 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 2.49942289087812e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.49844092265694 \tabularnewline
Sum Squared Residuals & 11.4283942554387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58013&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.886512797926374[/C][/ROW]
[ROW][C]R-squared[/C][C]0.785904940887249[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.725399815485819[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]12.9890639127355[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]2.49942289087812e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.49844092265694[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]11.4283942554387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58013&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 R0.886512797926374
R-squared0.785904940887249
Adjusted R-squared0.725399815485819
F-TEST (value)12.9890639127355
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value2.49942289087812e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.49844092265694
Sum Squared Residuals11.4283942554387







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
110.910.48377658481420.416223415185806
2109.977156437282370.0228435627176335
39.29.69846310790927-0.498463107909269
49.29.79571020925093-0.595710209250928
59.59.82925600062725-0.329256000627255
69.610.0080152837594-0.408015283759383
79.59.80856586349105-0.30856586349105
89.19.54856586349105-0.44856586349105
98.99.15074180091411-0.250741800914110
1099.28471180536937-0.284711805369375
1110.19.923571073650620.176428926349378
1210.310.3333419514161-0.0333419514161077
1310.29.997957860207250.202042139792754
149.69.485831915358750.114168084641254
159.29.30349003902754-0.103490039027539
169.39.14471756514360.155282434856397
179.49.29388510017020.106114899829801
189.49.370787132943760.0292128670562426
199.29.160326118042070.0396738819579330
2098.735152198541680.264847801458317
2198.692452062890570.307547937109433
2298.443769153836610.55623084616339
239.89.388200173193570.411799826806435
24109.693360901942140.306639098057856
259.89.349718114758260.450281885241739
269.38.925684926976630.374315073023367
2798.495582171394850.50441782860515
2898.5157481103030.484251889697002
299.18.786043186296540.313956813703458
309.18.66198361701130.4380163829887
319.18.517592169909760.582407830090238
329.28.12820593296781.07179406703220
338.88.027694925491550.772305074508455
348.37.944185935937970.355814064062029
358.48.80052419822806-0.400524198228056
368.18.98180448735135-0.881804487351346
377.78.73176025455101-1.03176025455101
387.98.47290098626977-0.57290098626977
397.97.817060540704130.082939459295871
4087.988635905820960.0113640941790377
417.98.32500054961466-0.425000549614658
427.68.01649677022066-0.416496770220656
437.17.7950241606856-0.695024160685606
446.87.85986620236969-1.05986620236969
456.57.20326966590882-0.70326966590882
466.97.43359112340597-0.533591123405974
478.28.3202112709378-0.120211270937795
488.78.369352424460780.330647575539221
498.38.33678718566929-0.0367871856692847
507.97.838425734112480.0615742658875157
517.57.485404140964210.0145958590357862
527.87.8551882094815-0.0551882094815067
538.37.965815163291350.334184836708655
548.48.04271719606490.357282803935096
558.27.818491687871510.381508312128485
567.77.528209802629780.171790197370222
577.27.32584154479496-0.125841544794958
587.37.39374198145007-0.0937419814500695
598.18.16749328398996-0.0674932839899622
608.58.222140234829630.277859765170375

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 10.9 & 10.4837765848142 & 0.416223415185806 \tabularnewline
2 & 10 & 9.97715643728237 & 0.0228435627176335 \tabularnewline
3 & 9.2 & 9.69846310790927 & -0.498463107909269 \tabularnewline
4 & 9.2 & 9.79571020925093 & -0.595710209250928 \tabularnewline
5 & 9.5 & 9.82925600062725 & -0.329256000627255 \tabularnewline
6 & 9.6 & 10.0080152837594 & -0.408015283759383 \tabularnewline
7 & 9.5 & 9.80856586349105 & -0.30856586349105 \tabularnewline
8 & 9.1 & 9.54856586349105 & -0.44856586349105 \tabularnewline
9 & 8.9 & 9.15074180091411 & -0.250741800914110 \tabularnewline
10 & 9 & 9.28471180536937 & -0.284711805369375 \tabularnewline
11 & 10.1 & 9.92357107365062 & 0.176428926349378 \tabularnewline
12 & 10.3 & 10.3333419514161 & -0.0333419514161077 \tabularnewline
13 & 10.2 & 9.99795786020725 & 0.202042139792754 \tabularnewline
14 & 9.6 & 9.48583191535875 & 0.114168084641254 \tabularnewline
15 & 9.2 & 9.30349003902754 & -0.103490039027539 \tabularnewline
16 & 9.3 & 9.1447175651436 & 0.155282434856397 \tabularnewline
17 & 9.4 & 9.2938851001702 & 0.106114899829801 \tabularnewline
18 & 9.4 & 9.37078713294376 & 0.0292128670562426 \tabularnewline
19 & 9.2 & 9.16032611804207 & 0.0396738819579330 \tabularnewline
20 & 9 & 8.73515219854168 & 0.264847801458317 \tabularnewline
21 & 9 & 8.69245206289057 & 0.307547937109433 \tabularnewline
22 & 9 & 8.44376915383661 & 0.55623084616339 \tabularnewline
23 & 9.8 & 9.38820017319357 & 0.411799826806435 \tabularnewline
24 & 10 & 9.69336090194214 & 0.306639098057856 \tabularnewline
25 & 9.8 & 9.34971811475826 & 0.450281885241739 \tabularnewline
26 & 9.3 & 8.92568492697663 & 0.374315073023367 \tabularnewline
27 & 9 & 8.49558217139485 & 0.50441782860515 \tabularnewline
28 & 9 & 8.515748110303 & 0.484251889697002 \tabularnewline
29 & 9.1 & 8.78604318629654 & 0.313956813703458 \tabularnewline
30 & 9.1 & 8.6619836170113 & 0.4380163829887 \tabularnewline
31 & 9.1 & 8.51759216990976 & 0.582407830090238 \tabularnewline
32 & 9.2 & 8.1282059329678 & 1.07179406703220 \tabularnewline
33 & 8.8 & 8.02769492549155 & 0.772305074508455 \tabularnewline
34 & 8.3 & 7.94418593593797 & 0.355814064062029 \tabularnewline
35 & 8.4 & 8.80052419822806 & -0.400524198228056 \tabularnewline
36 & 8.1 & 8.98180448735135 & -0.881804487351346 \tabularnewline
37 & 7.7 & 8.73176025455101 & -1.03176025455101 \tabularnewline
38 & 7.9 & 8.47290098626977 & -0.57290098626977 \tabularnewline
39 & 7.9 & 7.81706054070413 & 0.082939459295871 \tabularnewline
40 & 8 & 7.98863590582096 & 0.0113640941790377 \tabularnewline
41 & 7.9 & 8.32500054961466 & -0.425000549614658 \tabularnewline
42 & 7.6 & 8.01649677022066 & -0.416496770220656 \tabularnewline
43 & 7.1 & 7.7950241606856 & -0.695024160685606 \tabularnewline
44 & 6.8 & 7.85986620236969 & -1.05986620236969 \tabularnewline
45 & 6.5 & 7.20326966590882 & -0.70326966590882 \tabularnewline
46 & 6.9 & 7.43359112340597 & -0.533591123405974 \tabularnewline
47 & 8.2 & 8.3202112709378 & -0.120211270937795 \tabularnewline
48 & 8.7 & 8.36935242446078 & 0.330647575539221 \tabularnewline
49 & 8.3 & 8.33678718566929 & -0.0367871856692847 \tabularnewline
50 & 7.9 & 7.83842573411248 & 0.0615742658875157 \tabularnewline
51 & 7.5 & 7.48540414096421 & 0.0145958590357862 \tabularnewline
52 & 7.8 & 7.8551882094815 & -0.0551882094815067 \tabularnewline
53 & 8.3 & 7.96581516329135 & 0.334184836708655 \tabularnewline
54 & 8.4 & 8.0427171960649 & 0.357282803935096 \tabularnewline
55 & 8.2 & 7.81849168787151 & 0.381508312128485 \tabularnewline
56 & 7.7 & 7.52820980262978 & 0.171790197370222 \tabularnewline
57 & 7.2 & 7.32584154479496 & -0.125841544794958 \tabularnewline
58 & 7.3 & 7.39374198145007 & -0.0937419814500695 \tabularnewline
59 & 8.1 & 8.16749328398996 & -0.0674932839899622 \tabularnewline
60 & 8.5 & 8.22214023482963 & 0.277859765170375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58013&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]10.9[/C][C]10.4837765848142[/C][C]0.416223415185806[/C][/ROW]
[ROW][C]2[/C][C]10[/C][C]9.97715643728237[/C][C]0.0228435627176335[/C][/ROW]
[ROW][C]3[/C][C]9.2[/C][C]9.69846310790927[/C][C]-0.498463107909269[/C][/ROW]
[ROW][C]4[/C][C]9.2[/C][C]9.79571020925093[/C][C]-0.595710209250928[/C][/ROW]
[ROW][C]5[/C][C]9.5[/C][C]9.82925600062725[/C][C]-0.329256000627255[/C][/ROW]
[ROW][C]6[/C][C]9.6[/C][C]10.0080152837594[/C][C]-0.408015283759383[/C][/ROW]
[ROW][C]7[/C][C]9.5[/C][C]9.80856586349105[/C][C]-0.30856586349105[/C][/ROW]
[ROW][C]8[/C][C]9.1[/C][C]9.54856586349105[/C][C]-0.44856586349105[/C][/ROW]
[ROW][C]9[/C][C]8.9[/C][C]9.15074180091411[/C][C]-0.250741800914110[/C][/ROW]
[ROW][C]10[/C][C]9[/C][C]9.28471180536937[/C][C]-0.284711805369375[/C][/ROW]
[ROW][C]11[/C][C]10.1[/C][C]9.92357107365062[/C][C]0.176428926349378[/C][/ROW]
[ROW][C]12[/C][C]10.3[/C][C]10.3333419514161[/C][C]-0.0333419514161077[/C][/ROW]
[ROW][C]13[/C][C]10.2[/C][C]9.99795786020725[/C][C]0.202042139792754[/C][/ROW]
[ROW][C]14[/C][C]9.6[/C][C]9.48583191535875[/C][C]0.114168084641254[/C][/ROW]
[ROW][C]15[/C][C]9.2[/C][C]9.30349003902754[/C][C]-0.103490039027539[/C][/ROW]
[ROW][C]16[/C][C]9.3[/C][C]9.1447175651436[/C][C]0.155282434856397[/C][/ROW]
[ROW][C]17[/C][C]9.4[/C][C]9.2938851001702[/C][C]0.106114899829801[/C][/ROW]
[ROW][C]18[/C][C]9.4[/C][C]9.37078713294376[/C][C]0.0292128670562426[/C][/ROW]
[ROW][C]19[/C][C]9.2[/C][C]9.16032611804207[/C][C]0.0396738819579330[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]8.73515219854168[/C][C]0.264847801458317[/C][/ROW]
[ROW][C]21[/C][C]9[/C][C]8.69245206289057[/C][C]0.307547937109433[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]8.44376915383661[/C][C]0.55623084616339[/C][/ROW]
[ROW][C]23[/C][C]9.8[/C][C]9.38820017319357[/C][C]0.411799826806435[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]9.69336090194214[/C][C]0.306639098057856[/C][/ROW]
[ROW][C]25[/C][C]9.8[/C][C]9.34971811475826[/C][C]0.450281885241739[/C][/ROW]
[ROW][C]26[/C][C]9.3[/C][C]8.92568492697663[/C][C]0.374315073023367[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]8.49558217139485[/C][C]0.50441782860515[/C][/ROW]
[ROW][C]28[/C][C]9[/C][C]8.515748110303[/C][C]0.484251889697002[/C][/ROW]
[ROW][C]29[/C][C]9.1[/C][C]8.78604318629654[/C][C]0.313956813703458[/C][/ROW]
[ROW][C]30[/C][C]9.1[/C][C]8.6619836170113[/C][C]0.4380163829887[/C][/ROW]
[ROW][C]31[/C][C]9.1[/C][C]8.51759216990976[/C][C]0.582407830090238[/C][/ROW]
[ROW][C]32[/C][C]9.2[/C][C]8.1282059329678[/C][C]1.07179406703220[/C][/ROW]
[ROW][C]33[/C][C]8.8[/C][C]8.02769492549155[/C][C]0.772305074508455[/C][/ROW]
[ROW][C]34[/C][C]8.3[/C][C]7.94418593593797[/C][C]0.355814064062029[/C][/ROW]
[ROW][C]35[/C][C]8.4[/C][C]8.80052419822806[/C][C]-0.400524198228056[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.98180448735135[/C][C]-0.881804487351346[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]8.73176025455101[/C][C]-1.03176025455101[/C][/ROW]
[ROW][C]38[/C][C]7.9[/C][C]8.47290098626977[/C][C]-0.57290098626977[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.81706054070413[/C][C]0.082939459295871[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.98863590582096[/C][C]0.0113640941790377[/C][/ROW]
[ROW][C]41[/C][C]7.9[/C][C]8.32500054961466[/C][C]-0.425000549614658[/C][/ROW]
[ROW][C]42[/C][C]7.6[/C][C]8.01649677022066[/C][C]-0.416496770220656[/C][/ROW]
[ROW][C]43[/C][C]7.1[/C][C]7.7950241606856[/C][C]-0.695024160685606[/C][/ROW]
[ROW][C]44[/C][C]6.8[/C][C]7.85986620236969[/C][C]-1.05986620236969[/C][/ROW]
[ROW][C]45[/C][C]6.5[/C][C]7.20326966590882[/C][C]-0.70326966590882[/C][/ROW]
[ROW][C]46[/C][C]6.9[/C][C]7.43359112340597[/C][C]-0.533591123405974[/C][/ROW]
[ROW][C]47[/C][C]8.2[/C][C]8.3202112709378[/C][C]-0.120211270937795[/C][/ROW]
[ROW][C]48[/C][C]8.7[/C][C]8.36935242446078[/C][C]0.330647575539221[/C][/ROW]
[ROW][C]49[/C][C]8.3[/C][C]8.33678718566929[/C][C]-0.0367871856692847[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]7.83842573411248[/C][C]0.0615742658875157[/C][/ROW]
[ROW][C]51[/C][C]7.5[/C][C]7.48540414096421[/C][C]0.0145958590357862[/C][/ROW]
[ROW][C]52[/C][C]7.8[/C][C]7.8551882094815[/C][C]-0.0551882094815067[/C][/ROW]
[ROW][C]53[/C][C]8.3[/C][C]7.96581516329135[/C][C]0.334184836708655[/C][/ROW]
[ROW][C]54[/C][C]8.4[/C][C]8.0427171960649[/C][C]0.357282803935096[/C][/ROW]
[ROW][C]55[/C][C]8.2[/C][C]7.81849168787151[/C][C]0.381508312128485[/C][/ROW]
[ROW][C]56[/C][C]7.7[/C][C]7.52820980262978[/C][C]0.171790197370222[/C][/ROW]
[ROW][C]57[/C][C]7.2[/C][C]7.32584154479496[/C][C]-0.125841544794958[/C][/ROW]
[ROW][C]58[/C][C]7.3[/C][C]7.39374198145007[/C][C]-0.0937419814500695[/C][/ROW]
[ROW][C]59[/C][C]8.1[/C][C]8.16749328398996[/C][C]-0.0674932839899622[/C][/ROW]
[ROW][C]60[/C][C]8.5[/C][C]8.22214023482963[/C][C]0.277859765170375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58013&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58013&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
110.910.48377658481420.416223415185806
2109.977156437282370.0228435627176335
39.29.69846310790927-0.498463107909269
49.29.79571020925093-0.595710209250928
59.59.82925600062725-0.329256000627255
69.610.0080152837594-0.408015283759383
79.59.80856586349105-0.30856586349105
89.19.54856586349105-0.44856586349105
98.99.15074180091411-0.250741800914110
1099.28471180536937-0.284711805369375
1110.19.923571073650620.176428926349378
1210.310.3333419514161-0.0333419514161077
1310.29.997957860207250.202042139792754
149.69.485831915358750.114168084641254
159.29.30349003902754-0.103490039027539
169.39.14471756514360.155282434856397
179.49.29388510017020.106114899829801
189.49.370787132943760.0292128670562426
199.29.160326118042070.0396738819579330
2098.735152198541680.264847801458317
2198.692452062890570.307547937109433
2298.443769153836610.55623084616339
239.89.388200173193570.411799826806435
24109.693360901942140.306639098057856
259.89.349718114758260.450281885241739
269.38.925684926976630.374315073023367
2798.495582171394850.50441782860515
2898.5157481103030.484251889697002
299.18.786043186296540.313956813703458
309.18.66198361701130.4380163829887
319.18.517592169909760.582407830090238
329.28.12820593296781.07179406703220
338.88.027694925491550.772305074508455
348.37.944185935937970.355814064062029
358.48.80052419822806-0.400524198228056
368.18.98180448735135-0.881804487351346
377.78.73176025455101-1.03176025455101
387.98.47290098626977-0.57290098626977
397.97.817060540704130.082939459295871
4087.988635905820960.0113640941790377
417.98.32500054961466-0.425000549614658
427.68.01649677022066-0.416496770220656
437.17.7950241606856-0.695024160685606
446.87.85986620236969-1.05986620236969
456.57.20326966590882-0.70326966590882
466.97.43359112340597-0.533591123405974
478.28.3202112709378-0.120211270937795
488.78.369352424460780.330647575539221
498.38.33678718566929-0.0367871856692847
507.97.838425734112480.0615742658875157
517.57.485404140964210.0145958590357862
527.87.8551882094815-0.0551882094815067
538.37.965815163291350.334184836708655
548.48.04271719606490.357282803935096
558.27.818491687871510.381508312128485
567.77.528209802629780.171790197370222
577.27.32584154479496-0.125841544794958
587.37.39374198145007-0.0937419814500695
598.18.16749328398996-0.0674932839899622
608.58.222140234829630.277859765170375







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1318216204299210.2636432408598410.868178379570079
180.05489895926049840.1097979185209970.945101040739502
190.02341691571048740.04683383142097480.976583084289513
200.007780362878725430.01556072575745090.992219637121275
210.005202777603972230.01040555520794450.994797222396028
220.001808220418592680.003616440837185370.998191779581407
230.000596307662526690.001192615325053380.999403692337473
240.0002065216533174270.0004130433066348530.999793478346683
250.0003459605172281800.0006919210344563590.999654039482772
260.0001159561396048390.0002319122792096780.999884043860395
273.83293123885556e-057.66586247771113e-050.999961670687611
281.21134342252718e-052.42268684505436e-050.999987886565775
293.34858185479907e-066.69716370959814e-060.999996651418145
301.01384278104190e-062.02768556208381e-060.99999898615722
313.44329216142565e-076.88658432285131e-070.999999655670784
321.18912711119798e-052.37825422239597e-050.999988108728888
330.0001131800314144710.0002263600628289420.999886819968586
340.005893115206703110.01178623041340620.994106884793297
350.1940239997637520.3880479995275040.805976000236248
360.6427492627644520.7145014744710970.357250737235548
370.873849453695730.252301092608540.12615054630427
380.830330914929090.3393381701418180.169669085070909
390.8111037737136880.3777924525726240.188896226286312
400.8116284314804960.3767431370390080.188371568519504
410.701148558031530.597702883936940.29885144196847
420.6005762677478250.798847464504350.399423732252175
430.6284310867124630.7431378265750740.371568913287537

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.131821620429921 & 0.263643240859841 & 0.868178379570079 \tabularnewline
18 & 0.0548989592604984 & 0.109797918520997 & 0.945101040739502 \tabularnewline
19 & 0.0234169157104874 & 0.0468338314209748 & 0.976583084289513 \tabularnewline
20 & 0.00778036287872543 & 0.0155607257574509 & 0.992219637121275 \tabularnewline
21 & 0.00520277760397223 & 0.0104055552079445 & 0.994797222396028 \tabularnewline
22 & 0.00180822041859268 & 0.00361644083718537 & 0.998191779581407 \tabularnewline
23 & 0.00059630766252669 & 0.00119261532505338 & 0.999403692337473 \tabularnewline
24 & 0.000206521653317427 & 0.000413043306634853 & 0.999793478346683 \tabularnewline
25 & 0.000345960517228180 & 0.000691921034456359 & 0.999654039482772 \tabularnewline
26 & 0.000115956139604839 & 0.000231912279209678 & 0.999884043860395 \tabularnewline
27 & 3.83293123885556e-05 & 7.66586247771113e-05 & 0.999961670687611 \tabularnewline
28 & 1.21134342252718e-05 & 2.42268684505436e-05 & 0.999987886565775 \tabularnewline
29 & 3.34858185479907e-06 & 6.69716370959814e-06 & 0.999996651418145 \tabularnewline
30 & 1.01384278104190e-06 & 2.02768556208381e-06 & 0.99999898615722 \tabularnewline
31 & 3.44329216142565e-07 & 6.88658432285131e-07 & 0.999999655670784 \tabularnewline
32 & 1.18912711119798e-05 & 2.37825422239597e-05 & 0.999988108728888 \tabularnewline
33 & 0.000113180031414471 & 0.000226360062828942 & 0.999886819968586 \tabularnewline
34 & 0.00589311520670311 & 0.0117862304134062 & 0.994106884793297 \tabularnewline
35 & 0.194023999763752 & 0.388047999527504 & 0.805976000236248 \tabularnewline
36 & 0.642749262764452 & 0.714501474471097 & 0.357250737235548 \tabularnewline
37 & 0.87384945369573 & 0.25230109260854 & 0.12615054630427 \tabularnewline
38 & 0.83033091492909 & 0.339338170141818 & 0.169669085070909 \tabularnewline
39 & 0.811103773713688 & 0.377792452572624 & 0.188896226286312 \tabularnewline
40 & 0.811628431480496 & 0.376743137039008 & 0.188371568519504 \tabularnewline
41 & 0.70114855803153 & 0.59770288393694 & 0.29885144196847 \tabularnewline
42 & 0.600576267747825 & 0.79884746450435 & 0.399423732252175 \tabularnewline
43 & 0.628431086712463 & 0.743137826575074 & 0.371568913287537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58013&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.131821620429921[/C][C]0.263643240859841[/C][C]0.868178379570079[/C][/ROW]
[ROW][C]18[/C][C]0.0548989592604984[/C][C]0.109797918520997[/C][C]0.945101040739502[/C][/ROW]
[ROW][C]19[/C][C]0.0234169157104874[/C][C]0.0468338314209748[/C][C]0.976583084289513[/C][/ROW]
[ROW][C]20[/C][C]0.00778036287872543[/C][C]0.0155607257574509[/C][C]0.992219637121275[/C][/ROW]
[ROW][C]21[/C][C]0.00520277760397223[/C][C]0.0104055552079445[/C][C]0.994797222396028[/C][/ROW]
[ROW][C]22[/C][C]0.00180822041859268[/C][C]0.00361644083718537[/C][C]0.998191779581407[/C][/ROW]
[ROW][C]23[/C][C]0.00059630766252669[/C][C]0.00119261532505338[/C][C]0.999403692337473[/C][/ROW]
[ROW][C]24[/C][C]0.000206521653317427[/C][C]0.000413043306634853[/C][C]0.999793478346683[/C][/ROW]
[ROW][C]25[/C][C]0.000345960517228180[/C][C]0.000691921034456359[/C][C]0.999654039482772[/C][/ROW]
[ROW][C]26[/C][C]0.000115956139604839[/C][C]0.000231912279209678[/C][C]0.999884043860395[/C][/ROW]
[ROW][C]27[/C][C]3.83293123885556e-05[/C][C]7.66586247771113e-05[/C][C]0.999961670687611[/C][/ROW]
[ROW][C]28[/C][C]1.21134342252718e-05[/C][C]2.42268684505436e-05[/C][C]0.999987886565775[/C][/ROW]
[ROW][C]29[/C][C]3.34858185479907e-06[/C][C]6.69716370959814e-06[/C][C]0.999996651418145[/C][/ROW]
[ROW][C]30[/C][C]1.01384278104190e-06[/C][C]2.02768556208381e-06[/C][C]0.99999898615722[/C][/ROW]
[ROW][C]31[/C][C]3.44329216142565e-07[/C][C]6.88658432285131e-07[/C][C]0.999999655670784[/C][/ROW]
[ROW][C]32[/C][C]1.18912711119798e-05[/C][C]2.37825422239597e-05[/C][C]0.999988108728888[/C][/ROW]
[ROW][C]33[/C][C]0.000113180031414471[/C][C]0.000226360062828942[/C][C]0.999886819968586[/C][/ROW]
[ROW][C]34[/C][C]0.00589311520670311[/C][C]0.0117862304134062[/C][C]0.994106884793297[/C][/ROW]
[ROW][C]35[/C][C]0.194023999763752[/C][C]0.388047999527504[/C][C]0.805976000236248[/C][/ROW]
[ROW][C]36[/C][C]0.642749262764452[/C][C]0.714501474471097[/C][C]0.357250737235548[/C][/ROW]
[ROW][C]37[/C][C]0.87384945369573[/C][C]0.25230109260854[/C][C]0.12615054630427[/C][/ROW]
[ROW][C]38[/C][C]0.83033091492909[/C][C]0.339338170141818[/C][C]0.169669085070909[/C][/ROW]
[ROW][C]39[/C][C]0.811103773713688[/C][C]0.377792452572624[/C][C]0.188896226286312[/C][/ROW]
[ROW][C]40[/C][C]0.811628431480496[/C][C]0.376743137039008[/C][C]0.188371568519504[/C][/ROW]
[ROW][C]41[/C][C]0.70114855803153[/C][C]0.59770288393694[/C][C]0.29885144196847[/C][/ROW]
[ROW][C]42[/C][C]0.600576267747825[/C][C]0.79884746450435[/C][C]0.399423732252175[/C][/ROW]
[ROW][C]43[/C][C]0.628431086712463[/C][C]0.743137826575074[/C][C]0.371568913287537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58013&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58013&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1318216204299210.2636432408598410.868178379570079
180.05489895926049840.1097979185209970.945101040739502
190.02341691571048740.04683383142097480.976583084289513
200.007780362878725430.01556072575745090.992219637121275
210.005202777603972230.01040555520794450.994797222396028
220.001808220418592680.003616440837185370.998191779581407
230.000596307662526690.001192615325053380.999403692337473
240.0002065216533174270.0004130433066348530.999793478346683
250.0003459605172281800.0006919210344563590.999654039482772
260.0001159561396048390.0002319122792096780.999884043860395
273.83293123885556e-057.66586247771113e-050.999961670687611
281.21134342252718e-052.42268684505436e-050.999987886565775
293.34858185479907e-066.69716370959814e-060.999996651418145
301.01384278104190e-062.02768556208381e-060.99999898615722
313.44329216142565e-076.88658432285131e-070.999999655670784
321.18912711119798e-052.37825422239597e-050.999988108728888
330.0001131800314144710.0002263600628289420.999886819968586
340.005893115206703110.01178623041340620.994106884793297
350.1940239997637520.3880479995275040.805976000236248
360.6427492627644520.7145014744710970.357250737235548
370.873849453695730.252301092608540.12615054630427
380.830330914929090.3393381701418180.169669085070909
390.8111037737136880.3777924525726240.188896226286312
400.8116284314804960.3767431370390080.188371568519504
410.701148558031530.597702883936940.29885144196847
420.6005762677478250.798847464504350.399423732252175
430.6284310867124630.7431378265750740.371568913287537







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level120.444444444444444NOK
5% type I error level160.592592592592593NOK
10% type I error level160.592592592592593NOK

\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 & 12 & 0.444444444444444 & NOK \tabularnewline
5% type I error level & 16 & 0.592592592592593 & NOK \tabularnewline
10% type I error level & 16 & 0.592592592592593 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58013&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]12[/C][C]0.444444444444444[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]16[/C][C]0.592592592592593[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]16[/C][C]0.592592592592593[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58013&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58013&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 level120.444444444444444NOK
5% type I error level160.592592592592593NOK
10% type I error level160.592592592592593NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}