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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 02:34:23 -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/t1258709778qv6l64snc4voiu3.htm/, Retrieved Fri, 29 Mar 2024 02:01:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57996, Retrieved Fri, 29 Mar 2024 02:01:56 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
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] [workshop 7] [2009-11-20 09:34:23] [a18540c86166a2b66550d1fef0503cc2] [Current]
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Dataseries X:
8,9	8,6
8,9	8,5
8,9	8,3
8,9	7,8
9	7,8
9	8
9	8,6
9	8,9
9	8,9
9	8,6
9	8,3
9,1	8,3
9	8,3
9,1	8,4
9,1	8,5
9	8,4
9	8,6
9	8,5
9	8,5
8,9	8,4
8,9	8,5
8,9	8,5
8,9	8,5
8,8	8,5
8,8	8,5
8,7	8,5
8,7	8,5
8,5	8,5
8,5	8,6
8,4	8,4
8,2	8,1
8,2	8
8,1	8
8,1	8
8	8
7,9	7,9
7,8	7,8
7,7	7,8
7,6	7,9
7,5	8,1
7,5	8
7,5	7,6
7,5	7,3
7,5	7
7,4	6,8
7,4	7
7,3	7,1
7,3	7,2
7,3	7,1
7,2	6,9
7,2	6,7
7,3	6,7
7,4	6,6
7,4	6,9
7,5	7,3
7,6	7,5
7,7	7,3
7,9	7,1
8	6,9
8,2	7,1




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=57996&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=57996&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57996&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] = + 6.31542137271935 + 0.362417773364777X[t] -0.263814178147375M1[t] -0.264809689297091M2[t] -0.245805200446816M3[t] -0.252304000661949M4[t] -0.195044578213561M5[t] -0.176040089363286M6[t] -0.200525733316784M7[t] -0.176017955401100M8[t] -0.149765111083529M9[t] -0.0635122667659586M10[t] -0.0300110669810927M11[t] -0.024507777915684t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  6.31542137271935 +  0.362417773364777X[t] -0.263814178147375M1[t] -0.264809689297091M2[t] -0.245805200446816M3[t] -0.252304000661949M4[t] -0.195044578213561M5[t] -0.176040089363286M6[t] -0.200525733316784M7[t] -0.176017955401100M8[t] -0.149765111083529M9[t] -0.0635122667659586M10[t] -0.0300110669810927M11[t] -0.024507777915684t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57996&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  6.31542137271935 +  0.362417773364777X[t] -0.263814178147375M1[t] -0.264809689297091M2[t] -0.245805200446816M3[t] -0.252304000661949M4[t] -0.195044578213561M5[t] -0.176040089363286M6[t] -0.200525733316784M7[t] -0.176017955401100M8[t] -0.149765111083529M9[t] -0.0635122667659586M10[t] -0.0300110669810927M11[t] -0.024507777915684t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57996&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57996&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] = + 6.31542137271935 + 0.362417773364777X[t] -0.263814178147375M1[t] -0.264809689297091M2[t] -0.245805200446816M3[t] -0.252304000661949M4[t] -0.195044578213561M5[t] -0.176040089363286M6[t] -0.200525733316784M7[t] -0.176017955401100M8[t] -0.149765111083529M9[t] -0.0635122667659586M10[t] -0.0300110669810927M11[t] -0.024507777915684t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)6.315421372719350.9693616.51500
X0.3624177733647770.1071323.38290.0014740.000737
M1-0.2638141781473750.194209-1.35840.180960.09048
M2-0.2648096892970910.193965-1.36520.1788160.089408
M3-0.2458052004468160.193753-1.26870.2109470.105474
M4-0.2523040006619490.193881-1.30130.1996240.099812
M5-0.1950445782135610.193296-1.0090.318230.159115
M6-0.1760400893632860.193169-0.91130.3668750.183437
M7-0.2005257333167840.192673-1.04080.3034290.151714
M8-0.1760179554011000.192584-0.9140.3654940.182747
M9-0.1497651110835290.192452-0.77820.4404380.220219
M10-0.06351226676595860.192396-0.33010.7428140.371407
M11-0.03001106698109270.192491-0.15590.8767870.438393
t-0.0245077779156840.004069-6.022500

\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) & 6.31542137271935 & 0.969361 & 6.515 & 0 & 0 \tabularnewline
X & 0.362417773364777 & 0.107132 & 3.3829 & 0.001474 & 0.000737 \tabularnewline
M1 & -0.263814178147375 & 0.194209 & -1.3584 & 0.18096 & 0.09048 \tabularnewline
M2 & -0.264809689297091 & 0.193965 & -1.3652 & 0.178816 & 0.089408 \tabularnewline
M3 & -0.245805200446816 & 0.193753 & -1.2687 & 0.210947 & 0.105474 \tabularnewline
M4 & -0.252304000661949 & 0.193881 & -1.3013 & 0.199624 & 0.099812 \tabularnewline
M5 & -0.195044578213561 & 0.193296 & -1.009 & 0.31823 & 0.159115 \tabularnewline
M6 & -0.176040089363286 & 0.193169 & -0.9113 & 0.366875 & 0.183437 \tabularnewline
M7 & -0.200525733316784 & 0.192673 & -1.0408 & 0.303429 & 0.151714 \tabularnewline
M8 & -0.176017955401100 & 0.192584 & -0.914 & 0.365494 & 0.182747 \tabularnewline
M9 & -0.149765111083529 & 0.192452 & -0.7782 & 0.440438 & 0.220219 \tabularnewline
M10 & -0.0635122667659586 & 0.192396 & -0.3301 & 0.742814 & 0.371407 \tabularnewline
M11 & -0.0300110669810927 & 0.192491 & -0.1559 & 0.876787 & 0.438393 \tabularnewline
t & -0.024507777915684 & 0.004069 & -6.0225 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57996&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]6.31542137271935[/C][C]0.969361[/C][C]6.515[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]0.362417773364777[/C][C]0.107132[/C][C]3.3829[/C][C]0.001474[/C][C]0.000737[/C][/ROW]
[ROW][C]M1[/C][C]-0.263814178147375[/C][C]0.194209[/C][C]-1.3584[/C][C]0.18096[/C][C]0.09048[/C][/ROW]
[ROW][C]M2[/C][C]-0.264809689297091[/C][C]0.193965[/C][C]-1.3652[/C][C]0.178816[/C][C]0.089408[/C][/ROW]
[ROW][C]M3[/C][C]-0.245805200446816[/C][C]0.193753[/C][C]-1.2687[/C][C]0.210947[/C][C]0.105474[/C][/ROW]
[ROW][C]M4[/C][C]-0.252304000661949[/C][C]0.193881[/C][C]-1.3013[/C][C]0.199624[/C][C]0.099812[/C][/ROW]
[ROW][C]M5[/C][C]-0.195044578213561[/C][C]0.193296[/C][C]-1.009[/C][C]0.31823[/C][C]0.159115[/C][/ROW]
[ROW][C]M6[/C][C]-0.176040089363286[/C][C]0.193169[/C][C]-0.9113[/C][C]0.366875[/C][C]0.183437[/C][/ROW]
[ROW][C]M7[/C][C]-0.200525733316784[/C][C]0.192673[/C][C]-1.0408[/C][C]0.303429[/C][C]0.151714[/C][/ROW]
[ROW][C]M8[/C][C]-0.176017955401100[/C][C]0.192584[/C][C]-0.914[/C][C]0.365494[/C][C]0.182747[/C][/ROW]
[ROW][C]M9[/C][C]-0.149765111083529[/C][C]0.192452[/C][C]-0.7782[/C][C]0.440438[/C][C]0.220219[/C][/ROW]
[ROW][C]M10[/C][C]-0.0635122667659586[/C][C]0.192396[/C][C]-0.3301[/C][C]0.742814[/C][C]0.371407[/C][/ROW]
[ROW][C]M11[/C][C]-0.0300110669810927[/C][C]0.192491[/C][C]-0.1559[/C][C]0.876787[/C][C]0.438393[/C][/ROW]
[ROW][C]t[/C][C]-0.024507777915684[/C][C]0.004069[/C][C]-6.0225[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57996&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57996&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)6.315421372719350.9693616.51500
X0.3624177733647770.1071323.38290.0014740.000737
M1-0.2638141781473750.194209-1.35840.180960.09048
M2-0.2648096892970910.193965-1.36520.1788160.089408
M3-0.2458052004468160.193753-1.26870.2109470.105474
M4-0.2523040006619490.193881-1.30130.1996240.099812
M5-0.1950445782135610.193296-1.0090.318230.159115
M6-0.1760400893632860.193169-0.91130.3668750.183437
M7-0.2005257333167840.192673-1.04080.3034290.151714
M8-0.1760179554011000.192584-0.9140.3654940.182747
M9-0.1497651110835290.192452-0.77820.4404380.220219
M10-0.06351226676595860.192396-0.33010.7428140.371407
M11-0.03001106698109270.192491-0.15590.8767870.438393
t-0.0245077779156840.004069-6.022500







Multiple Linear Regression - Regression Statistics
Multiple R0.919685918816145
R-squared0.845822189268697
Adjusted R-squared0.802250199279415
F-TEST (value)19.4120624161707
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.93178806284777e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.30409309579165
Sum Squared Residuals4.25374010177488

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.919685918816145 \tabularnewline
R-squared & 0.845822189268697 \tabularnewline
Adjusted R-squared & 0.802250199279415 \tabularnewline
F-TEST (value) & 19.4120624161707 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 1.93178806284777e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.30409309579165 \tabularnewline
Sum Squared Residuals & 4.25374010177488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57996&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.919685918816145[/C][/ROW]
[ROW][C]R-squared[/C][C]0.845822189268697[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.802250199279415[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]19.4120624161707[/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]1.93178806284777e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.30409309579165[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4.25374010177488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57996&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57996&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 R0.919685918816145
R-squared0.845822189268697
Adjusted R-squared0.802250199279415
F-TEST (value)19.4120624161707
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.93178806284777e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.30409309579165
Sum Squared Residuals4.25374010177488







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.99.14389226759343-0.243892267593432
28.99.0821472011915-0.182147201191508
38.99.00416035745315-0.104160357453144
48.98.791944892639940.108055107360063
598.824696537172640.175303462827358
698.891676802780190.108323197219811
799.06013404492987-0.0601340449298727
899.1688593769393-0.168859376939306
999.1706044433412-0.170604443341193
1099.12362417773365-0.123624177733646
1199.0238922675934-0.0238922675933955
129.19.02939555665880.0706044433411955
1398.741073600595750.258926399404254
149.18.751812088866820.348187911133177
159.18.78255057713790.317449422862108
1698.71530222167060.284697778329403
1798.820537420876260.179462579123744
1898.778792354474370.22120764552563
1998.729798932605190.270201067394813
208.98.693557155268710.206442844731291
218.98.731543999007070.168456000992926
228.98.793289065408960.106710934591039
238.98.802282487278140.0977175127218574
248.88.80778577634355-0.00778577634355094
258.88.51946382028050.280536179719508
268.78.49396053121510.206039468784906
278.78.488457242149680.211542757850315
288.58.457450664018870.0425493359811334
298.58.52644408588805-0.0264440858880486
308.48.44845724214968-0.0484572421496844
318.28.29073848827107-0.0907384882710694
328.28.2544967109346-0.0544967109345916
338.18.25624177733648-0.156241777336478
348.18.31798684373836-0.217986843738365
3588.32698026560755-0.326980265607547
367.98.29624177733648-0.396241777336477
377.87.97167804393694-0.171678043936941
387.77.94617475487154-0.246174754871541
397.67.97691324314261-0.37691324314261
407.58.01839021968475-0.518390219684748
417.58.01490008688097-0.514900086880975
427.57.86442968846965-0.364429688469655
437.57.70671093459104-0.206710934591039
447.57.5979856025816-0.0979856025816057
457.47.52724711431054-0.127247114310537
467.47.66147573538538-0.261475735385379
477.37.70671093459104-0.406710934591039
487.37.74845600099293-0.448456000992926
497.37.42389226759339-0.123892267593389
507.27.32590542385503-0.125905423855034
517.27.24791858011667-0.0479185801166692
527.37.216912001985850.0830879980141479
537.47.213421869182080.186578130817922
547.47.31664391212610.0833560878738974
557.57.412617599602830.0873824003971687
567.67.485101154275790.114898845724213
577.77.414362666004720.285637333995282
587.97.403624177733650.496375822266351
5987.340134044929880.659865955070124
608.27.418120888668240.78187911133176

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.9 & 9.14389226759343 & -0.243892267593432 \tabularnewline
2 & 8.9 & 9.0821472011915 & -0.182147201191508 \tabularnewline
3 & 8.9 & 9.00416035745315 & -0.104160357453144 \tabularnewline
4 & 8.9 & 8.79194489263994 & 0.108055107360063 \tabularnewline
5 & 9 & 8.82469653717264 & 0.175303462827358 \tabularnewline
6 & 9 & 8.89167680278019 & 0.108323197219811 \tabularnewline
7 & 9 & 9.06013404492987 & -0.0601340449298727 \tabularnewline
8 & 9 & 9.1688593769393 & -0.168859376939306 \tabularnewline
9 & 9 & 9.1706044433412 & -0.170604443341193 \tabularnewline
10 & 9 & 9.12362417773365 & -0.123624177733646 \tabularnewline
11 & 9 & 9.0238922675934 & -0.0238922675933955 \tabularnewline
12 & 9.1 & 9.0293955566588 & 0.0706044433411955 \tabularnewline
13 & 9 & 8.74107360059575 & 0.258926399404254 \tabularnewline
14 & 9.1 & 8.75181208886682 & 0.348187911133177 \tabularnewline
15 & 9.1 & 8.7825505771379 & 0.317449422862108 \tabularnewline
16 & 9 & 8.7153022216706 & 0.284697778329403 \tabularnewline
17 & 9 & 8.82053742087626 & 0.179462579123744 \tabularnewline
18 & 9 & 8.77879235447437 & 0.22120764552563 \tabularnewline
19 & 9 & 8.72979893260519 & 0.270201067394813 \tabularnewline
20 & 8.9 & 8.69355715526871 & 0.206442844731291 \tabularnewline
21 & 8.9 & 8.73154399900707 & 0.168456000992926 \tabularnewline
22 & 8.9 & 8.79328906540896 & 0.106710934591039 \tabularnewline
23 & 8.9 & 8.80228248727814 & 0.0977175127218574 \tabularnewline
24 & 8.8 & 8.80778577634355 & -0.00778577634355094 \tabularnewline
25 & 8.8 & 8.5194638202805 & 0.280536179719508 \tabularnewline
26 & 8.7 & 8.4939605312151 & 0.206039468784906 \tabularnewline
27 & 8.7 & 8.48845724214968 & 0.211542757850315 \tabularnewline
28 & 8.5 & 8.45745066401887 & 0.0425493359811334 \tabularnewline
29 & 8.5 & 8.52644408588805 & -0.0264440858880486 \tabularnewline
30 & 8.4 & 8.44845724214968 & -0.0484572421496844 \tabularnewline
31 & 8.2 & 8.29073848827107 & -0.0907384882710694 \tabularnewline
32 & 8.2 & 8.2544967109346 & -0.0544967109345916 \tabularnewline
33 & 8.1 & 8.25624177733648 & -0.156241777336478 \tabularnewline
34 & 8.1 & 8.31798684373836 & -0.217986843738365 \tabularnewline
35 & 8 & 8.32698026560755 & -0.326980265607547 \tabularnewline
36 & 7.9 & 8.29624177733648 & -0.396241777336477 \tabularnewline
37 & 7.8 & 7.97167804393694 & -0.171678043936941 \tabularnewline
38 & 7.7 & 7.94617475487154 & -0.246174754871541 \tabularnewline
39 & 7.6 & 7.97691324314261 & -0.37691324314261 \tabularnewline
40 & 7.5 & 8.01839021968475 & -0.518390219684748 \tabularnewline
41 & 7.5 & 8.01490008688097 & -0.514900086880975 \tabularnewline
42 & 7.5 & 7.86442968846965 & -0.364429688469655 \tabularnewline
43 & 7.5 & 7.70671093459104 & -0.206710934591039 \tabularnewline
44 & 7.5 & 7.5979856025816 & -0.0979856025816057 \tabularnewline
45 & 7.4 & 7.52724711431054 & -0.127247114310537 \tabularnewline
46 & 7.4 & 7.66147573538538 & -0.261475735385379 \tabularnewline
47 & 7.3 & 7.70671093459104 & -0.406710934591039 \tabularnewline
48 & 7.3 & 7.74845600099293 & -0.448456000992926 \tabularnewline
49 & 7.3 & 7.42389226759339 & -0.123892267593389 \tabularnewline
50 & 7.2 & 7.32590542385503 & -0.125905423855034 \tabularnewline
51 & 7.2 & 7.24791858011667 & -0.0479185801166692 \tabularnewline
52 & 7.3 & 7.21691200198585 & 0.0830879980141479 \tabularnewline
53 & 7.4 & 7.21342186918208 & 0.186578130817922 \tabularnewline
54 & 7.4 & 7.3166439121261 & 0.0833560878738974 \tabularnewline
55 & 7.5 & 7.41261759960283 & 0.0873824003971687 \tabularnewline
56 & 7.6 & 7.48510115427579 & 0.114898845724213 \tabularnewline
57 & 7.7 & 7.41436266600472 & 0.285637333995282 \tabularnewline
58 & 7.9 & 7.40362417773365 & 0.496375822266351 \tabularnewline
59 & 8 & 7.34013404492988 & 0.659865955070124 \tabularnewline
60 & 8.2 & 7.41812088866824 & 0.78187911133176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57996&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]8.9[/C][C]9.14389226759343[/C][C]-0.243892267593432[/C][/ROW]
[ROW][C]2[/C][C]8.9[/C][C]9.0821472011915[/C][C]-0.182147201191508[/C][/ROW]
[ROW][C]3[/C][C]8.9[/C][C]9.00416035745315[/C][C]-0.104160357453144[/C][/ROW]
[ROW][C]4[/C][C]8.9[/C][C]8.79194489263994[/C][C]0.108055107360063[/C][/ROW]
[ROW][C]5[/C][C]9[/C][C]8.82469653717264[/C][C]0.175303462827358[/C][/ROW]
[ROW][C]6[/C][C]9[/C][C]8.89167680278019[/C][C]0.108323197219811[/C][/ROW]
[ROW][C]7[/C][C]9[/C][C]9.06013404492987[/C][C]-0.0601340449298727[/C][/ROW]
[ROW][C]8[/C][C]9[/C][C]9.1688593769393[/C][C]-0.168859376939306[/C][/ROW]
[ROW][C]9[/C][C]9[/C][C]9.1706044433412[/C][C]-0.170604443341193[/C][/ROW]
[ROW][C]10[/C][C]9[/C][C]9.12362417773365[/C][C]-0.123624177733646[/C][/ROW]
[ROW][C]11[/C][C]9[/C][C]9.0238922675934[/C][C]-0.0238922675933955[/C][/ROW]
[ROW][C]12[/C][C]9.1[/C][C]9.0293955566588[/C][C]0.0706044433411955[/C][/ROW]
[ROW][C]13[/C][C]9[/C][C]8.74107360059575[/C][C]0.258926399404254[/C][/ROW]
[ROW][C]14[/C][C]9.1[/C][C]8.75181208886682[/C][C]0.348187911133177[/C][/ROW]
[ROW][C]15[/C][C]9.1[/C][C]8.7825505771379[/C][C]0.317449422862108[/C][/ROW]
[ROW][C]16[/C][C]9[/C][C]8.7153022216706[/C][C]0.284697778329403[/C][/ROW]
[ROW][C]17[/C][C]9[/C][C]8.82053742087626[/C][C]0.179462579123744[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]8.77879235447437[/C][C]0.22120764552563[/C][/ROW]
[ROW][C]19[/C][C]9[/C][C]8.72979893260519[/C][C]0.270201067394813[/C][/ROW]
[ROW][C]20[/C][C]8.9[/C][C]8.69355715526871[/C][C]0.206442844731291[/C][/ROW]
[ROW][C]21[/C][C]8.9[/C][C]8.73154399900707[/C][C]0.168456000992926[/C][/ROW]
[ROW][C]22[/C][C]8.9[/C][C]8.79328906540896[/C][C]0.106710934591039[/C][/ROW]
[ROW][C]23[/C][C]8.9[/C][C]8.80228248727814[/C][C]0.0977175127218574[/C][/ROW]
[ROW][C]24[/C][C]8.8[/C][C]8.80778577634355[/C][C]-0.00778577634355094[/C][/ROW]
[ROW][C]25[/C][C]8.8[/C][C]8.5194638202805[/C][C]0.280536179719508[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.4939605312151[/C][C]0.206039468784906[/C][/ROW]
[ROW][C]27[/C][C]8.7[/C][C]8.48845724214968[/C][C]0.211542757850315[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.45745066401887[/C][C]0.0425493359811334[/C][/ROW]
[ROW][C]29[/C][C]8.5[/C][C]8.52644408588805[/C][C]-0.0264440858880486[/C][/ROW]
[ROW][C]30[/C][C]8.4[/C][C]8.44845724214968[/C][C]-0.0484572421496844[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.29073848827107[/C][C]-0.0907384882710694[/C][/ROW]
[ROW][C]32[/C][C]8.2[/C][C]8.2544967109346[/C][C]-0.0544967109345916[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.25624177733648[/C][C]-0.156241777336478[/C][/ROW]
[ROW][C]34[/C][C]8.1[/C][C]8.31798684373836[/C][C]-0.217986843738365[/C][/ROW]
[ROW][C]35[/C][C]8[/C][C]8.32698026560755[/C][C]-0.326980265607547[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]8.29624177733648[/C][C]-0.396241777336477[/C][/ROW]
[ROW][C]37[/C][C]7.8[/C][C]7.97167804393694[/C][C]-0.171678043936941[/C][/ROW]
[ROW][C]38[/C][C]7.7[/C][C]7.94617475487154[/C][C]-0.246174754871541[/C][/ROW]
[ROW][C]39[/C][C]7.6[/C][C]7.97691324314261[/C][C]-0.37691324314261[/C][/ROW]
[ROW][C]40[/C][C]7.5[/C][C]8.01839021968475[/C][C]-0.518390219684748[/C][/ROW]
[ROW][C]41[/C][C]7.5[/C][C]8.01490008688097[/C][C]-0.514900086880975[/C][/ROW]
[ROW][C]42[/C][C]7.5[/C][C]7.86442968846965[/C][C]-0.364429688469655[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]7.70671093459104[/C][C]-0.206710934591039[/C][/ROW]
[ROW][C]44[/C][C]7.5[/C][C]7.5979856025816[/C][C]-0.0979856025816057[/C][/ROW]
[ROW][C]45[/C][C]7.4[/C][C]7.52724711431054[/C][C]-0.127247114310537[/C][/ROW]
[ROW][C]46[/C][C]7.4[/C][C]7.66147573538538[/C][C]-0.261475735385379[/C][/ROW]
[ROW][C]47[/C][C]7.3[/C][C]7.70671093459104[/C][C]-0.406710934591039[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]7.74845600099293[/C][C]-0.448456000992926[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.42389226759339[/C][C]-0.123892267593389[/C][/ROW]
[ROW][C]50[/C][C]7.2[/C][C]7.32590542385503[/C][C]-0.125905423855034[/C][/ROW]
[ROW][C]51[/C][C]7.2[/C][C]7.24791858011667[/C][C]-0.0479185801166692[/C][/ROW]
[ROW][C]52[/C][C]7.3[/C][C]7.21691200198585[/C][C]0.0830879980141479[/C][/ROW]
[ROW][C]53[/C][C]7.4[/C][C]7.21342186918208[/C][C]0.186578130817922[/C][/ROW]
[ROW][C]54[/C][C]7.4[/C][C]7.3166439121261[/C][C]0.0833560878738974[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7.41261759960283[/C][C]0.0873824003971687[/C][/ROW]
[ROW][C]56[/C][C]7.6[/C][C]7.48510115427579[/C][C]0.114898845724213[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]7.41436266600472[/C][C]0.285637333995282[/C][/ROW]
[ROW][C]58[/C][C]7.9[/C][C]7.40362417773365[/C][C]0.496375822266351[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]7.34013404492988[/C][C]0.659865955070124[/C][/ROW]
[ROW][C]60[/C][C]8.2[/C][C]7.41812088866824[/C][C]0.78187911133176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57996&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57996&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.99.14389226759343-0.243892267593432
28.99.0821472011915-0.182147201191508
38.99.00416035745315-0.104160357453144
48.98.791944892639940.108055107360063
598.824696537172640.175303462827358
698.891676802780190.108323197219811
799.06013404492987-0.0601340449298727
899.1688593769393-0.168859376939306
999.1706044433412-0.170604443341193
1099.12362417773365-0.123624177733646
1199.0238922675934-0.0238922675933955
129.19.02939555665880.0706044433411955
1398.741073600595750.258926399404254
149.18.751812088866820.348187911133177
159.18.78255057713790.317449422862108
1698.71530222167060.284697778329403
1798.820537420876260.179462579123744
1898.778792354474370.22120764552563
1998.729798932605190.270201067394813
208.98.693557155268710.206442844731291
218.98.731543999007070.168456000992926
228.98.793289065408960.106710934591039
238.98.802282487278140.0977175127218574
248.88.80778577634355-0.00778577634355094
258.88.51946382028050.280536179719508
268.78.49396053121510.206039468784906
278.78.488457242149680.211542757850315
288.58.457450664018870.0425493359811334
298.58.52644408588805-0.0264440858880486
308.48.44845724214968-0.0484572421496844
318.28.29073848827107-0.0907384882710694
328.28.2544967109346-0.0544967109345916
338.18.25624177733648-0.156241777336478
348.18.31798684373836-0.217986843738365
3588.32698026560755-0.326980265607547
367.98.29624177733648-0.396241777336477
377.87.97167804393694-0.171678043936941
387.77.94617475487154-0.246174754871541
397.67.97691324314261-0.37691324314261
407.58.01839021968475-0.518390219684748
417.58.01490008688097-0.514900086880975
427.57.86442968846965-0.364429688469655
437.57.70671093459104-0.206710934591039
447.57.5979856025816-0.0979856025816057
457.47.52724711431054-0.127247114310537
467.47.66147573538538-0.261475735385379
477.37.70671093459104-0.406710934591039
487.37.74845600099293-0.448456000992926
497.37.42389226759339-0.123892267593389
507.27.32590542385503-0.125905423855034
517.27.24791858011667-0.0479185801166692
527.37.216912001985850.0830879980141479
537.47.213421869182080.186578130817922
547.47.31664391212610.0833560878738974
557.57.412617599602830.0873824003971687
567.67.485101154275790.114898845724213
577.77.414362666004720.285637333995282
587.97.403624177733650.496375822266351
5987.340134044929880.659865955070124
608.27.418120888668240.78187911133176







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.005654604484966710.01130920896993340.994345395515033
180.001455920595012450.002911841190024910.998544079404988
190.0008334932312131920.001666986462426380.999166506768787
200.0009767253659422090.001953450731884420.999023274634058
210.0004400092257782580.0008800184515565150.999559990774222
220.0001857474537287550.0003714949074575110.999814252546271
238.73473722526964e-050.0001746947445053930.999912652627747
240.0002822441117157830.0005644882234315660.999717755888284
250.000189827289453810.000379654578907620.999810172710546
260.0003577568866032980.0007155137732065950.999642243113397
270.0005857363377161730.001171472675432350.999414263662284
280.00225493268052410.00450986536104820.997745067319476
290.005233853138797670.01046770627759530.994766146861202
300.01706395902967480.03412791805934950.982936040970325
310.0693305525625580.1386611051251160.930669447437442
320.1099683794961790.2199367589923580.890031620503821
330.1316919132663400.2633838265326800.86830808673366
340.1405342859823370.2810685719646740.859465714017663
350.1602772707783640.3205545415567290.839722729221636
360.1671072296799370.3342144593598730.832892770320063
370.195548574069170.391097148138340.80445142593083
380.239949849505410.479899699010820.76005015049459
390.2661128435113260.5322256870226530.733887156488674
400.2787056160483580.5574112320967160.721294383951642
410.2457225239970960.4914450479941920.754277476002904
420.5017617270229310.9964765459541380.498238272977069
430.897292959274180.2054140814516410.102707040725820

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00565460448496671 & 0.0113092089699334 & 0.994345395515033 \tabularnewline
18 & 0.00145592059501245 & 0.00291184119002491 & 0.998544079404988 \tabularnewline
19 & 0.000833493231213192 & 0.00166698646242638 & 0.999166506768787 \tabularnewline
20 & 0.000976725365942209 & 0.00195345073188442 & 0.999023274634058 \tabularnewline
21 & 0.000440009225778258 & 0.000880018451556515 & 0.999559990774222 \tabularnewline
22 & 0.000185747453728755 & 0.000371494907457511 & 0.999814252546271 \tabularnewline
23 & 8.73473722526964e-05 & 0.000174694744505393 & 0.999912652627747 \tabularnewline
24 & 0.000282244111715783 & 0.000564488223431566 & 0.999717755888284 \tabularnewline
25 & 0.00018982728945381 & 0.00037965457890762 & 0.999810172710546 \tabularnewline
26 & 0.000357756886603298 & 0.000715513773206595 & 0.999642243113397 \tabularnewline
27 & 0.000585736337716173 & 0.00117147267543235 & 0.999414263662284 \tabularnewline
28 & 0.0022549326805241 & 0.0045098653610482 & 0.997745067319476 \tabularnewline
29 & 0.00523385313879767 & 0.0104677062775953 & 0.994766146861202 \tabularnewline
30 & 0.0170639590296748 & 0.0341279180593495 & 0.982936040970325 \tabularnewline
31 & 0.069330552562558 & 0.138661105125116 & 0.930669447437442 \tabularnewline
32 & 0.109968379496179 & 0.219936758992358 & 0.890031620503821 \tabularnewline
33 & 0.131691913266340 & 0.263383826532680 & 0.86830808673366 \tabularnewline
34 & 0.140534285982337 & 0.281068571964674 & 0.859465714017663 \tabularnewline
35 & 0.160277270778364 & 0.320554541556729 & 0.839722729221636 \tabularnewline
36 & 0.167107229679937 & 0.334214459359873 & 0.832892770320063 \tabularnewline
37 & 0.19554857406917 & 0.39109714813834 & 0.80445142593083 \tabularnewline
38 & 0.23994984950541 & 0.47989969901082 & 0.76005015049459 \tabularnewline
39 & 0.266112843511326 & 0.532225687022653 & 0.733887156488674 \tabularnewline
40 & 0.278705616048358 & 0.557411232096716 & 0.721294383951642 \tabularnewline
41 & 0.245722523997096 & 0.491445047994192 & 0.754277476002904 \tabularnewline
42 & 0.501761727022931 & 0.996476545954138 & 0.498238272977069 \tabularnewline
43 & 0.89729295927418 & 0.205414081451641 & 0.102707040725820 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57996&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]0.00565460448496671[/C][C]0.0113092089699334[/C][C]0.994345395515033[/C][/ROW]
[ROW][C]18[/C][C]0.00145592059501245[/C][C]0.00291184119002491[/C][C]0.998544079404988[/C][/ROW]
[ROW][C]19[/C][C]0.000833493231213192[/C][C]0.00166698646242638[/C][C]0.999166506768787[/C][/ROW]
[ROW][C]20[/C][C]0.000976725365942209[/C][C]0.00195345073188442[/C][C]0.999023274634058[/C][/ROW]
[ROW][C]21[/C][C]0.000440009225778258[/C][C]0.000880018451556515[/C][C]0.999559990774222[/C][/ROW]
[ROW][C]22[/C][C]0.000185747453728755[/C][C]0.000371494907457511[/C][C]0.999814252546271[/C][/ROW]
[ROW][C]23[/C][C]8.73473722526964e-05[/C][C]0.000174694744505393[/C][C]0.999912652627747[/C][/ROW]
[ROW][C]24[/C][C]0.000282244111715783[/C][C]0.000564488223431566[/C][C]0.999717755888284[/C][/ROW]
[ROW][C]25[/C][C]0.00018982728945381[/C][C]0.00037965457890762[/C][C]0.999810172710546[/C][/ROW]
[ROW][C]26[/C][C]0.000357756886603298[/C][C]0.000715513773206595[/C][C]0.999642243113397[/C][/ROW]
[ROW][C]27[/C][C]0.000585736337716173[/C][C]0.00117147267543235[/C][C]0.999414263662284[/C][/ROW]
[ROW][C]28[/C][C]0.0022549326805241[/C][C]0.0045098653610482[/C][C]0.997745067319476[/C][/ROW]
[ROW][C]29[/C][C]0.00523385313879767[/C][C]0.0104677062775953[/C][C]0.994766146861202[/C][/ROW]
[ROW][C]30[/C][C]0.0170639590296748[/C][C]0.0341279180593495[/C][C]0.982936040970325[/C][/ROW]
[ROW][C]31[/C][C]0.069330552562558[/C][C]0.138661105125116[/C][C]0.930669447437442[/C][/ROW]
[ROW][C]32[/C][C]0.109968379496179[/C][C]0.219936758992358[/C][C]0.890031620503821[/C][/ROW]
[ROW][C]33[/C][C]0.131691913266340[/C][C]0.263383826532680[/C][C]0.86830808673366[/C][/ROW]
[ROW][C]34[/C][C]0.140534285982337[/C][C]0.281068571964674[/C][C]0.859465714017663[/C][/ROW]
[ROW][C]35[/C][C]0.160277270778364[/C][C]0.320554541556729[/C][C]0.839722729221636[/C][/ROW]
[ROW][C]36[/C][C]0.167107229679937[/C][C]0.334214459359873[/C][C]0.832892770320063[/C][/ROW]
[ROW][C]37[/C][C]0.19554857406917[/C][C]0.39109714813834[/C][C]0.80445142593083[/C][/ROW]
[ROW][C]38[/C][C]0.23994984950541[/C][C]0.47989969901082[/C][C]0.76005015049459[/C][/ROW]
[ROW][C]39[/C][C]0.266112843511326[/C][C]0.532225687022653[/C][C]0.733887156488674[/C][/ROW]
[ROW][C]40[/C][C]0.278705616048358[/C][C]0.557411232096716[/C][C]0.721294383951642[/C][/ROW]
[ROW][C]41[/C][C]0.245722523997096[/C][C]0.491445047994192[/C][C]0.754277476002904[/C][/ROW]
[ROW][C]42[/C][C]0.501761727022931[/C][C]0.996476545954138[/C][C]0.498238272977069[/C][/ROW]
[ROW][C]43[/C][C]0.89729295927418[/C][C]0.205414081451641[/C][C]0.102707040725820[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57996&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57996&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
170.005654604484966710.01130920896993340.994345395515033
180.001455920595012450.002911841190024910.998544079404988
190.0008334932312131920.001666986462426380.999166506768787
200.0009767253659422090.001953450731884420.999023274634058
210.0004400092257782580.0008800184515565150.999559990774222
220.0001857474537287550.0003714949074575110.999814252546271
238.73473722526964e-050.0001746947445053930.999912652627747
240.0002822441117157830.0005644882234315660.999717755888284
250.000189827289453810.000379654578907620.999810172710546
260.0003577568866032980.0007155137732065950.999642243113397
270.0005857363377161730.001171472675432350.999414263662284
280.00225493268052410.00450986536104820.997745067319476
290.005233853138797670.01046770627759530.994766146861202
300.01706395902967480.03412791805934950.982936040970325
310.0693305525625580.1386611051251160.930669447437442
320.1099683794961790.2199367589923580.890031620503821
330.1316919132663400.2633838265326800.86830808673366
340.1405342859823370.2810685719646740.859465714017663
350.1602772707783640.3205545415567290.839722729221636
360.1671072296799370.3342144593598730.832892770320063
370.195548574069170.391097148138340.80445142593083
380.239949849505410.479899699010820.76005015049459
390.2661128435113260.5322256870226530.733887156488674
400.2787056160483580.5574112320967160.721294383951642
410.2457225239970960.4914450479941920.754277476002904
420.5017617270229310.9964765459541380.498238272977069
430.897292959274180.2054140814516410.102707040725820







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level110.407407407407407NOK
5% type I error level140.518518518518518NOK
10% type I error level140.518518518518518NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 11 & 0.407407407407407 & NOK \tabularnewline
5% type I error level & 14 & 0.518518518518518 & NOK \tabularnewline
10% type I error level & 14 & 0.518518518518518 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57996&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]11[/C][C]0.407407407407407[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.518518518518518[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]14[/C][C]0.518518518518518[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57996&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57996&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 level110.407407407407407NOK
5% type I error level140.518518518518518NOK
10% type I error level140.518518518518518NOK



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')
}