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Description of Statistical Computation

Author's title

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 06:13:49 -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/t12587229029viq7pg2xvt1aew.htm/, Retrieved Thu, 18 Apr 2024 20:31:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58120, Retrieved Thu, 18 Apr 2024 20:31:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

Tree of Dependent Computations

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 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 13:13:49] [0545e25c765ce26b196961216dc11e13] [Current]
-   PD        [Multiple Regression] [] [2009-11-20 13:28:34] [2c5be225250d91402426bbbf07a5e2b3]
-   PD          [Multiple Regression] [4e multiple ] [2009-11-24 20:45:36] [ba905ddf7cdf9ecb063c35348c4dab2e]
-   P           [Multiple Regression] [workshop 7] [2009-11-26 17:56:55] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,4	2	1,7	1	1,2	1,4
2	2	2,4	1,7	1	1,2
2,1	2	2	2,4	1,7	1
2	2	2,1	2	2,4	1,7
1,8	2	2	2,1	2	2,4
2,7	2	1,8	2	2,1	2
2,3	2	2,7	1,8	2	2,1
1,9	2	2,3	2,7	1,8	2
2	2	1,9	2,3	2,7	1,8
2,3	2	2	1,9	2,3	2,7
2,8	2	2,3	2	1,9	2,3
2,4	2	2,8	2,3	2	1,9
2,3	2	2,4	2,8	2,3	2
2,7	2	2,3	2,4	2,8	2,3
2,7	2	2,7	2,3	2,4	2,8
2,9	2	2,7	2,7	2,3	2,4
3	2	2,9	2,7	2,7	2,3
2,2	2	3	2,9	2,7	2,7
2,3	2	2,2	3	2,9	2,7
2,8	2,21	2,3	2,2	3	2,9
2,8	2,25	2,8	2,3	2,2	3
2,8	2,25	2,8	2,8	2,3	2,2
2,2	2,45	2,8	2,8	2,8	2,3
2,6	2,5	2,2	2,8	2,8	2,8
2,8	2,5	2,6	2,2	2,8	2,8
2,5	2,64	2,8	2,6	2,2	2,8
2,4	2,75	2,5	2,8	2,6	2,2
2,3	2,93	2,4	2,5	2,8	2,6
1,9	3	2,3	2,4	2,5	2,8
1,7	3,17	1,9	2,3	2,4	2,5
2	3,25	1,7	1,9	2,3	2,4
2,1	3,39	2	1,7	1,9	2,3
1,7	3,5	2,1	2	1,7	1,9
1,8	3,5	1,7	2,1	2	1,7
1,8	3,65	1,8	1,7	2,1	2
1,8	3,75	1,8	1,8	1,7	2,1
1,3	3,75	1,8	1,8	1,8	1,7
1,3	3,9	1,3	1,8	1,8	1,8
1,3	4	1,3	1,3	1,8	1,8
1,2	4	1,3	1,3	1,3	1,8
1,4	4	1,2	1,3	1,3	1,3
2,2	4	1,4	1,2	1,3	1,3
2,9	4	2,2	1,4	1,2	1,3
3,1	4	2,9	2,2	1,4	1,2
3,5	4	3,1	2,9	2,2	1,4
3,6	4	3,5	3,1	2,9	2,2
4,4	4	3,6	3,5	3,1	2,9
4,1	4	4,4	3,6	3,5	3,1
5,1	4	4,1	4,4	3,6	3,5
5,8	4	5,1	4,1	4,4	3,6
5,9	4,18	5,8	5,1	4,1	4,4
5,4	4,25	5,9	5,8	5,1	4,1
5,5	4,25	5,4	5,9	5,8	5,1
4,8	3,97	5,5	5,4	5,9	5,8
3,2	3,42	4,8	5,5	5,4	5,9
2,7	2,75	3,2	4,8	5,5	5,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58120&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]3 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=58120&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58120&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.058305651363869 + 0.137027387478230X[t] + 1.10866834203965Y1[t] -0.249101268939407Y2[t] + 0.287991683589359Y3[t] -0.279080454525577Y4[t] + 0.320790312672266M1[t] + 0.116328593481165M2[t] + 0.110447908369543M3[t] -0.0673342499160004M4[t] + 0.0821570543575485M5[t] + 0.120058718766382M6[t] -0.0130182686618101M7[t] + 0.157207676289636M8[t] + 0.0393839845475236M9[t] + 0.163883815589508M10[t] + 0.218443697121927M11[t] -0.00386587778519627t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.058305651363869 +  0.137027387478230X[t] +  1.10866834203965Y1[t] -0.249101268939407Y2[t] +  0.287991683589359Y3[t] -0.279080454525577Y4[t] +  0.320790312672266M1[t] +  0.116328593481165M2[t] +  0.110447908369543M3[t] -0.0673342499160004M4[t] +  0.0821570543575485M5[t] +  0.120058718766382M6[t] -0.0130182686618101M7[t] +  0.157207676289636M8[t] +  0.0393839845475236M9[t] +  0.163883815589508M10[t] +  0.218443697121927M11[t] -0.00386587778519627t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58120&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.058305651363869 +  0.137027387478230X[t] +  1.10866834203965Y1[t] -0.249101268939407Y2[t] +  0.287991683589359Y3[t] -0.279080454525577Y4[t] +  0.320790312672266M1[t] +  0.116328593481165M2[t] +  0.110447908369543M3[t] -0.0673342499160004M4[t] +  0.0821570543575485M5[t] +  0.120058718766382M6[t] -0.0130182686618101M7[t] +  0.157207676289636M8[t] +  0.0393839845475236M9[t] +  0.163883815589508M10[t] +  0.218443697121927M11[t] -0.00386587778519627t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58120&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58120&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.058305651363869 + 0.137027387478230X[t] + 1.10866834203965Y1[t] -0.249101268939407Y2[t] + 0.287991683589359Y3[t] -0.279080454525577Y4[t] + 0.320790312672266M1[t] + 0.116328593481165M2[t] + 0.110447908369543M3[t] -0.0673342499160004M4[t] + 0.0821570543575485M5[t] + 0.120058718766382M6[t] -0.0130182686618101M7[t] + 0.157207676289636M8[t] + 0.0393839845475236M9[t] + 0.163883815589508M10[t] + 0.218443697121927M11[t] -0.00386587778519627t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.0583056513638690.637778-0.09140.9276390.46382
X0.1370273874782300.2939940.46610.6438120.321906
Y11.108668342039650.1606086.90300
Y2-0.2491012689394070.238615-1.04390.3031070.151553
Y30.2879916835893590.2395531.20220.2367230.118362
Y4-0.2790804545255770.191233-1.45940.152680.07634
M10.3207903126722660.3316690.96720.339560.16978
M20.1163285934811650.3315610.35090.7276380.363819
M30.1104479083695430.3334140.33130.7422650.371133
M4-0.06733424991600040.336104-0.20030.8422850.421142
M50.08215705435754850.3377210.24330.8091060.404553
M60.1200587187663820.3355770.35780.7224970.361248
M7-0.01301826866181010.334112-0.0390.9691230.484562
M80.1572076762896360.3392280.46340.6457010.322851
M90.03938398454752360.3508490.11230.9112130.455607
M100.1638838155895080.3505760.46750.6428330.321417
M110.2184436971219270.3488880.62610.5349830.267491
t-0.003865877785196270.017938-0.21550.8305190.415259

\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) & -0.058305651363869 & 0.637778 & -0.0914 & 0.927639 & 0.46382 \tabularnewline
X & 0.137027387478230 & 0.293994 & 0.4661 & 0.643812 & 0.321906 \tabularnewline
Y1 & 1.10866834203965 & 0.160608 & 6.903 & 0 & 0 \tabularnewline
Y2 & -0.249101268939407 & 0.238615 & -1.0439 & 0.303107 & 0.151553 \tabularnewline
Y3 & 0.287991683589359 & 0.239553 & 1.2022 & 0.236723 & 0.118362 \tabularnewline
Y4 & -0.279080454525577 & 0.191233 & -1.4594 & 0.15268 & 0.07634 \tabularnewline
M1 & 0.320790312672266 & 0.331669 & 0.9672 & 0.33956 & 0.16978 \tabularnewline
M2 & 0.116328593481165 & 0.331561 & 0.3509 & 0.727638 & 0.363819 \tabularnewline
M3 & 0.110447908369543 & 0.333414 & 0.3313 & 0.742265 & 0.371133 \tabularnewline
M4 & -0.0673342499160004 & 0.336104 & -0.2003 & 0.842285 & 0.421142 \tabularnewline
M5 & 0.0821570543575485 & 0.337721 & 0.2433 & 0.809106 & 0.404553 \tabularnewline
M6 & 0.120058718766382 & 0.335577 & 0.3578 & 0.722497 & 0.361248 \tabularnewline
M7 & -0.0130182686618101 & 0.334112 & -0.039 & 0.969123 & 0.484562 \tabularnewline
M8 & 0.157207676289636 & 0.339228 & 0.4634 & 0.645701 & 0.322851 \tabularnewline
M9 & 0.0393839845475236 & 0.350849 & 0.1123 & 0.911213 & 0.455607 \tabularnewline
M10 & 0.163883815589508 & 0.350576 & 0.4675 & 0.642833 & 0.321417 \tabularnewline
M11 & 0.218443697121927 & 0.348888 & 0.6261 & 0.534983 & 0.267491 \tabularnewline
t & -0.00386587778519627 & 0.017938 & -0.2155 & 0.830519 & 0.415259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58120&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]-0.058305651363869[/C][C]0.637778[/C][C]-0.0914[/C][C]0.927639[/C][C]0.46382[/C][/ROW]
[ROW][C]X[/C][C]0.137027387478230[/C][C]0.293994[/C][C]0.4661[/C][C]0.643812[/C][C]0.321906[/C][/ROW]
[ROW][C]Y1[/C][C]1.10866834203965[/C][C]0.160608[/C][C]6.903[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.249101268939407[/C][C]0.238615[/C][C]-1.0439[/C][C]0.303107[/C][C]0.151553[/C][/ROW]
[ROW][C]Y3[/C][C]0.287991683589359[/C][C]0.239553[/C][C]1.2022[/C][C]0.236723[/C][C]0.118362[/C][/ROW]
[ROW][C]Y4[/C][C]-0.279080454525577[/C][C]0.191233[/C][C]-1.4594[/C][C]0.15268[/C][C]0.07634[/C][/ROW]
[ROW][C]M1[/C][C]0.320790312672266[/C][C]0.331669[/C][C]0.9672[/C][C]0.33956[/C][C]0.16978[/C][/ROW]
[ROW][C]M2[/C][C]0.116328593481165[/C][C]0.331561[/C][C]0.3509[/C][C]0.727638[/C][C]0.363819[/C][/ROW]
[ROW][C]M3[/C][C]0.110447908369543[/C][C]0.333414[/C][C]0.3313[/C][C]0.742265[/C][C]0.371133[/C][/ROW]
[ROW][C]M4[/C][C]-0.0673342499160004[/C][C]0.336104[/C][C]-0.2003[/C][C]0.842285[/C][C]0.421142[/C][/ROW]
[ROW][C]M5[/C][C]0.0821570543575485[/C][C]0.337721[/C][C]0.2433[/C][C]0.809106[/C][C]0.404553[/C][/ROW]
[ROW][C]M6[/C][C]0.120058718766382[/C][C]0.335577[/C][C]0.3578[/C][C]0.722497[/C][C]0.361248[/C][/ROW]
[ROW][C]M7[/C][C]-0.0130182686618101[/C][C]0.334112[/C][C]-0.039[/C][C]0.969123[/C][C]0.484562[/C][/ROW]
[ROW][C]M8[/C][C]0.157207676289636[/C][C]0.339228[/C][C]0.4634[/C][C]0.645701[/C][C]0.322851[/C][/ROW]
[ROW][C]M9[/C][C]0.0393839845475236[/C][C]0.350849[/C][C]0.1123[/C][C]0.911213[/C][C]0.455607[/C][/ROW]
[ROW][C]M10[/C][C]0.163883815589508[/C][C]0.350576[/C][C]0.4675[/C][C]0.642833[/C][C]0.321417[/C][/ROW]
[ROW][C]M11[/C][C]0.218443697121927[/C][C]0.348888[/C][C]0.6261[/C][C]0.534983[/C][C]0.267491[/C][/ROW]
[ROW][C]t[/C][C]-0.00386587778519627[/C][C]0.017938[/C][C]-0.2155[/C][C]0.830519[/C][C]0.415259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58120&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58120&T=2

As an alternative you can also use a QR Code:  
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)-0.0583056513638690.637778-0.09140.9276390.46382
X0.1370273874782300.2939940.46610.6438120.321906
Y11.108668342039650.1606086.90300
Y2-0.2491012689394070.238615-1.04390.3031070.151553
Y30.2879916835893590.2395531.20220.2367230.118362
Y4-0.2790804545255770.191233-1.45940.152680.07634
M10.3207903126722660.3316690.96720.339560.16978
M20.1163285934811650.3315610.35090.7276380.363819
M30.1104479083695430.3334140.33130.7422650.371133
M4-0.06733424991600040.336104-0.20030.8422850.421142
M50.08215705435754850.3377210.24330.8091060.404553
M60.1200587187663820.3355770.35780.7224970.361248
M7-0.01301826866181010.334112-0.0390.9691230.484562
M80.1572076762896360.3392280.46340.6457010.322851
M90.03938398454752360.3508490.11230.9112130.455607
M100.1638838155895080.3505760.46750.6428330.321417
M110.2184436971219270.3488880.62610.5349830.267491
t-0.003865877785196270.017938-0.21550.8305190.415259






Multiple Linear Regression - Regression Statistics
Multiple R0.934763527130169
R-squared0.873782851652834
Adjusted R-squared0.817317285286997
F-TEST (value)15.4746141390249
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value3.91486842943323e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.492305597910813
Sum Squared Residuals9.20986246590427

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.934763527130169 \tabularnewline
R-squared & 0.873782851652834 \tabularnewline
Adjusted R-squared & 0.817317285286997 \tabularnewline
F-TEST (value) & 15.4746141390249 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 3.91486842943323e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.492305597910813 \tabularnewline
Sum Squared Residuals & 9.20986246590427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58120&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.934763527130169[/C][/ROW]
[ROW][C]R-squared[/C][C]0.873782851652834[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.817317285286997[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]15.4746141390249[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]3.91486842943323e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.492305597910813[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]9.20986246590427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58120&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58120&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.934763527130169
R-squared0.873782851652834
Adjusted R-squared0.817317285286997
F-TEST (value)15.4746141390249
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value3.91486842943323e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.492305597910813
Sum Squared Residuals9.20986246590427






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.42.123185854979080.276814145020917
222.51477296336021-0.514772963360206
32.12.14459844480761-0.044598444807606
422.17969561086124-0.179695610861243
51.81.87899108464804-0.078991084648042
62.71.856634679926860.843365320073144
72.32.71060636252554-0.410606362525543
81.92.17961765956515-0.279617659565151
922.02910986693328-0.0291098669332829
102.31.993882079461040.306117920538964
112.82.34870196730070.451298032699298
122.42.74642753290075-0.346427532900748
132.32.55382345612650-0.253823456126503
142.72.394541237959010.305458762040989
152.72.598435238073460.101564761926538
162.92.399979707878250.500020292121745
1732.910443521662840.0895564783371611
182.22.89389370689233-0.693893706892329
192.31.902704377871150.39729562212885
202.82.380971123217140.419028876782861
212.82.53588530099080.264114699009200
222.82.784032151757280.0159678482427183
232.22.97821942934227-0.778219429342273
242.61.958019991322480.64198000867752
252.82.86787252438906-0.0678725243890555
262.52.62802691233826-0.128026912338263
272.42.53357755181536-0.133577551815362
282.32.28642414687620.013575853123798
291.92.21347118719608-0.313471187196083
301.71.90716938776784-0.207169387767836
3121.658204429814160.34179557018584
322.12.13888045964395-0.0388804596439531
331.72.12243420135375-0.422434201353752
341.81.91690428688266-0.116904286882661
351.82.14373477253261-0.34373477253261
361.81.767113090591070.0328869094089332
371.32.22446887564730-0.924468875647303
381.31.45445317032036-0.154453170320357
391.31.58295998064106-0.282959980641065
401.21.25731610277565-0.0573161027756455
411.41.43161492232282-0.0316149223228211
422.21.712294504248330.487705495751671
432.92.383666890519850.516333109480153
443.13.21232016413276-0.112320164132756
453.53.312570630722170.187429369277835
463.63.80518148189902-0.205181481899022
474.43.729343830824420.670656169175584
484.14.4284393851857-0.328439385185703
495.14.130649288858050.969350711141945
505.85.308205716022160.491794283977837
515.95.54042878466250.359571215337495
525.45.67658443160866-0.276584431608655
535.55.165479284170220.334520715829784
544.85.23000772116465-0.43000772116465
553.24.0448179392693-0.8448179392693
562.72.6882105934410.0117894065589985

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.4 & 2.12318585497908 & 0.276814145020917 \tabularnewline
2 & 2 & 2.51477296336021 & -0.514772963360206 \tabularnewline
3 & 2.1 & 2.14459844480761 & -0.044598444807606 \tabularnewline
4 & 2 & 2.17969561086124 & -0.179695610861243 \tabularnewline
5 & 1.8 & 1.87899108464804 & -0.078991084648042 \tabularnewline
6 & 2.7 & 1.85663467992686 & 0.843365320073144 \tabularnewline
7 & 2.3 & 2.71060636252554 & -0.410606362525543 \tabularnewline
8 & 1.9 & 2.17961765956515 & -0.279617659565151 \tabularnewline
9 & 2 & 2.02910986693328 & -0.0291098669332829 \tabularnewline
10 & 2.3 & 1.99388207946104 & 0.306117920538964 \tabularnewline
11 & 2.8 & 2.3487019673007 & 0.451298032699298 \tabularnewline
12 & 2.4 & 2.74642753290075 & -0.346427532900748 \tabularnewline
13 & 2.3 & 2.55382345612650 & -0.253823456126503 \tabularnewline
14 & 2.7 & 2.39454123795901 & 0.305458762040989 \tabularnewline
15 & 2.7 & 2.59843523807346 & 0.101564761926538 \tabularnewline
16 & 2.9 & 2.39997970787825 & 0.500020292121745 \tabularnewline
17 & 3 & 2.91044352166284 & 0.0895564783371611 \tabularnewline
18 & 2.2 & 2.89389370689233 & -0.693893706892329 \tabularnewline
19 & 2.3 & 1.90270437787115 & 0.39729562212885 \tabularnewline
20 & 2.8 & 2.38097112321714 & 0.419028876782861 \tabularnewline
21 & 2.8 & 2.5358853009908 & 0.264114699009200 \tabularnewline
22 & 2.8 & 2.78403215175728 & 0.0159678482427183 \tabularnewline
23 & 2.2 & 2.97821942934227 & -0.778219429342273 \tabularnewline
24 & 2.6 & 1.95801999132248 & 0.64198000867752 \tabularnewline
25 & 2.8 & 2.86787252438906 & -0.0678725243890555 \tabularnewline
26 & 2.5 & 2.62802691233826 & -0.128026912338263 \tabularnewline
27 & 2.4 & 2.53357755181536 & -0.133577551815362 \tabularnewline
28 & 2.3 & 2.2864241468762 & 0.013575853123798 \tabularnewline
29 & 1.9 & 2.21347118719608 & -0.313471187196083 \tabularnewline
30 & 1.7 & 1.90716938776784 & -0.207169387767836 \tabularnewline
31 & 2 & 1.65820442981416 & 0.34179557018584 \tabularnewline
32 & 2.1 & 2.13888045964395 & -0.0388804596439531 \tabularnewline
33 & 1.7 & 2.12243420135375 & -0.422434201353752 \tabularnewline
34 & 1.8 & 1.91690428688266 & -0.116904286882661 \tabularnewline
35 & 1.8 & 2.14373477253261 & -0.34373477253261 \tabularnewline
36 & 1.8 & 1.76711309059107 & 0.0328869094089332 \tabularnewline
37 & 1.3 & 2.22446887564730 & -0.924468875647303 \tabularnewline
38 & 1.3 & 1.45445317032036 & -0.154453170320357 \tabularnewline
39 & 1.3 & 1.58295998064106 & -0.282959980641065 \tabularnewline
40 & 1.2 & 1.25731610277565 & -0.0573161027756455 \tabularnewline
41 & 1.4 & 1.43161492232282 & -0.0316149223228211 \tabularnewline
42 & 2.2 & 1.71229450424833 & 0.487705495751671 \tabularnewline
43 & 2.9 & 2.38366689051985 & 0.516333109480153 \tabularnewline
44 & 3.1 & 3.21232016413276 & -0.112320164132756 \tabularnewline
45 & 3.5 & 3.31257063072217 & 0.187429369277835 \tabularnewline
46 & 3.6 & 3.80518148189902 & -0.205181481899022 \tabularnewline
47 & 4.4 & 3.72934383082442 & 0.670656169175584 \tabularnewline
48 & 4.1 & 4.4284393851857 & -0.328439385185703 \tabularnewline
49 & 5.1 & 4.13064928885805 & 0.969350711141945 \tabularnewline
50 & 5.8 & 5.30820571602216 & 0.491794283977837 \tabularnewline
51 & 5.9 & 5.5404287846625 & 0.359571215337495 \tabularnewline
52 & 5.4 & 5.67658443160866 & -0.276584431608655 \tabularnewline
53 & 5.5 & 5.16547928417022 & 0.334520715829784 \tabularnewline
54 & 4.8 & 5.23000772116465 & -0.43000772116465 \tabularnewline
55 & 3.2 & 4.0448179392693 & -0.8448179392693 \tabularnewline
56 & 2.7 & 2.688210593441 & 0.0117894065589985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58120&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]2.4[/C][C]2.12318585497908[/C][C]0.276814145020917[/C][/ROW]
[ROW][C]2[/C][C]2[/C][C]2.51477296336021[/C][C]-0.514772963360206[/C][/ROW]
[ROW][C]3[/C][C]2.1[/C][C]2.14459844480761[/C][C]-0.044598444807606[/C][/ROW]
[ROW][C]4[/C][C]2[/C][C]2.17969561086124[/C][C]-0.179695610861243[/C][/ROW]
[ROW][C]5[/C][C]1.8[/C][C]1.87899108464804[/C][C]-0.078991084648042[/C][/ROW]
[ROW][C]6[/C][C]2.7[/C][C]1.85663467992686[/C][C]0.843365320073144[/C][/ROW]
[ROW][C]7[/C][C]2.3[/C][C]2.71060636252554[/C][C]-0.410606362525543[/C][/ROW]
[ROW][C]8[/C][C]1.9[/C][C]2.17961765956515[/C][C]-0.279617659565151[/C][/ROW]
[ROW][C]9[/C][C]2[/C][C]2.02910986693328[/C][C]-0.0291098669332829[/C][/ROW]
[ROW][C]10[/C][C]2.3[/C][C]1.99388207946104[/C][C]0.306117920538964[/C][/ROW]
[ROW][C]11[/C][C]2.8[/C][C]2.3487019673007[/C][C]0.451298032699298[/C][/ROW]
[ROW][C]12[/C][C]2.4[/C][C]2.74642753290075[/C][C]-0.346427532900748[/C][/ROW]
[ROW][C]13[/C][C]2.3[/C][C]2.55382345612650[/C][C]-0.253823456126503[/C][/ROW]
[ROW][C]14[/C][C]2.7[/C][C]2.39454123795901[/C][C]0.305458762040989[/C][/ROW]
[ROW][C]15[/C][C]2.7[/C][C]2.59843523807346[/C][C]0.101564761926538[/C][/ROW]
[ROW][C]16[/C][C]2.9[/C][C]2.39997970787825[/C][C]0.500020292121745[/C][/ROW]
[ROW][C]17[/C][C]3[/C][C]2.91044352166284[/C][C]0.0895564783371611[/C][/ROW]
[ROW][C]18[/C][C]2.2[/C][C]2.89389370689233[/C][C]-0.693893706892329[/C][/ROW]
[ROW][C]19[/C][C]2.3[/C][C]1.90270437787115[/C][C]0.39729562212885[/C][/ROW]
[ROW][C]20[/C][C]2.8[/C][C]2.38097112321714[/C][C]0.419028876782861[/C][/ROW]
[ROW][C]21[/C][C]2.8[/C][C]2.5358853009908[/C][C]0.264114699009200[/C][/ROW]
[ROW][C]22[/C][C]2.8[/C][C]2.78403215175728[/C][C]0.0159678482427183[/C][/ROW]
[ROW][C]23[/C][C]2.2[/C][C]2.97821942934227[/C][C]-0.778219429342273[/C][/ROW]
[ROW][C]24[/C][C]2.6[/C][C]1.95801999132248[/C][C]0.64198000867752[/C][/ROW]
[ROW][C]25[/C][C]2.8[/C][C]2.86787252438906[/C][C]-0.0678725243890555[/C][/ROW]
[ROW][C]26[/C][C]2.5[/C][C]2.62802691233826[/C][C]-0.128026912338263[/C][/ROW]
[ROW][C]27[/C][C]2.4[/C][C]2.53357755181536[/C][C]-0.133577551815362[/C][/ROW]
[ROW][C]28[/C][C]2.3[/C][C]2.2864241468762[/C][C]0.013575853123798[/C][/ROW]
[ROW][C]29[/C][C]1.9[/C][C]2.21347118719608[/C][C]-0.313471187196083[/C][/ROW]
[ROW][C]30[/C][C]1.7[/C][C]1.90716938776784[/C][C]-0.207169387767836[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]1.65820442981416[/C][C]0.34179557018584[/C][/ROW]
[ROW][C]32[/C][C]2.1[/C][C]2.13888045964395[/C][C]-0.0388804596439531[/C][/ROW]
[ROW][C]33[/C][C]1.7[/C][C]2.12243420135375[/C][C]-0.422434201353752[/C][/ROW]
[ROW][C]34[/C][C]1.8[/C][C]1.91690428688266[/C][C]-0.116904286882661[/C][/ROW]
[ROW][C]35[/C][C]1.8[/C][C]2.14373477253261[/C][C]-0.34373477253261[/C][/ROW]
[ROW][C]36[/C][C]1.8[/C][C]1.76711309059107[/C][C]0.0328869094089332[/C][/ROW]
[ROW][C]37[/C][C]1.3[/C][C]2.22446887564730[/C][C]-0.924468875647303[/C][/ROW]
[ROW][C]38[/C][C]1.3[/C][C]1.45445317032036[/C][C]-0.154453170320357[/C][/ROW]
[ROW][C]39[/C][C]1.3[/C][C]1.58295998064106[/C][C]-0.282959980641065[/C][/ROW]
[ROW][C]40[/C][C]1.2[/C][C]1.25731610277565[/C][C]-0.0573161027756455[/C][/ROW]
[ROW][C]41[/C][C]1.4[/C][C]1.43161492232282[/C][C]-0.0316149223228211[/C][/ROW]
[ROW][C]42[/C][C]2.2[/C][C]1.71229450424833[/C][C]0.487705495751671[/C][/ROW]
[ROW][C]43[/C][C]2.9[/C][C]2.38366689051985[/C][C]0.516333109480153[/C][/ROW]
[ROW][C]44[/C][C]3.1[/C][C]3.21232016413276[/C][C]-0.112320164132756[/C][/ROW]
[ROW][C]45[/C][C]3.5[/C][C]3.31257063072217[/C][C]0.187429369277835[/C][/ROW]
[ROW][C]46[/C][C]3.6[/C][C]3.80518148189902[/C][C]-0.205181481899022[/C][/ROW]
[ROW][C]47[/C][C]4.4[/C][C]3.72934383082442[/C][C]0.670656169175584[/C][/ROW]
[ROW][C]48[/C][C]4.1[/C][C]4.4284393851857[/C][C]-0.328439385185703[/C][/ROW]
[ROW][C]49[/C][C]5.1[/C][C]4.13064928885805[/C][C]0.969350711141945[/C][/ROW]
[ROW][C]50[/C][C]5.8[/C][C]5.30820571602216[/C][C]0.491794283977837[/C][/ROW]
[ROW][C]51[/C][C]5.9[/C][C]5.5404287846625[/C][C]0.359571215337495[/C][/ROW]
[ROW][C]52[/C][C]5.4[/C][C]5.67658443160866[/C][C]-0.276584431608655[/C][/ROW]
[ROW][C]53[/C][C]5.5[/C][C]5.16547928417022[/C][C]0.334520715829784[/C][/ROW]
[ROW][C]54[/C][C]4.8[/C][C]5.23000772116465[/C][C]-0.43000772116465[/C][/ROW]
[ROW][C]55[/C][C]3.2[/C][C]4.0448179392693[/C][C]-0.8448179392693[/C][/ROW]
[ROW][C]56[/C][C]2.7[/C][C]2.688210593441[/C][C]0.0117894065589985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58120&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58120&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.42.123185854979080.276814145020917
222.51477296336021-0.514772963360206
32.12.14459844480761-0.044598444807606
422.17969561086124-0.179695610861243
51.81.87899108464804-0.078991084648042
62.71.856634679926860.843365320073144
72.32.71060636252554-0.410606362525543
81.92.17961765956515-0.279617659565151
922.02910986693328-0.0291098669332829
102.31.993882079461040.306117920538964
112.82.34870196730070.451298032699298
122.42.74642753290075-0.346427532900748
132.32.55382345612650-0.253823456126503
142.72.394541237959010.305458762040989
152.72.598435238073460.101564761926538
162.92.399979707878250.500020292121745
1732.910443521662840.0895564783371611
182.22.89389370689233-0.693893706892329
192.31.902704377871150.39729562212885
202.82.380971123217140.419028876782861
212.82.53588530099080.264114699009200
222.82.784032151757280.0159678482427183
232.22.97821942934227-0.778219429342273
242.61.958019991322480.64198000867752
252.82.86787252438906-0.0678725243890555
262.52.62802691233826-0.128026912338263
272.42.53357755181536-0.133577551815362
282.32.28642414687620.013575853123798
291.92.21347118719608-0.313471187196083
301.71.90716938776784-0.207169387767836
3121.658204429814160.34179557018584
322.12.13888045964395-0.0388804596439531
331.72.12243420135375-0.422434201353752
341.81.91690428688266-0.116904286882661
351.82.14373477253261-0.34373477253261
361.81.767113090591070.0328869094089332
371.32.22446887564730-0.924468875647303
381.31.45445317032036-0.154453170320357
391.31.58295998064106-0.282959980641065
401.21.25731610277565-0.0573161027756455
411.41.43161492232282-0.0316149223228211
422.21.712294504248330.487705495751671
432.92.383666890519850.516333109480153
443.13.21232016413276-0.112320164132756
453.53.312570630722170.187429369277835
463.63.80518148189902-0.205181481899022
474.43.729343830824420.670656169175584
484.14.4284393851857-0.328439385185703
495.14.130649288858050.969350711141945
505.85.308205716022160.491794283977837
515.95.54042878466250.359571215337495
525.45.67658443160866-0.276584431608655
535.55.165479284170220.334520715829784
544.85.23000772116465-0.43000772116465
553.24.0448179392693-0.8448179392693
562.72.6882105934410.0117894065589985






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.3947262764821170.7894525529642340.605273723517883
220.2315307891103470.4630615782206950.768469210889653
230.1758459901512450.3516919803024890.824154009848755
240.1379016305303780.2758032610607570.862098369469622
250.07342904041290460.1468580808258090.926570959587095
260.03519127549605050.07038255099210090.96480872450395
270.01983849852958790.03967699705917580.980161501470412
280.01011295849160640.02022591698321290.989887041508394
290.007682600172333240.01536520034466650.992317399827667
300.005372443743157650.01074488748631530.994627556256842
310.003864073737576880.007728147475153770.996135926262423
320.002607336739320730.005214673478641470.99739266326068
330.0009718018851635830.001943603770327170.999028198114836
340.0008019827650388180.001603965530077640.99919801723496
350.0002870898530910430.0005741797061820850.999712910146909

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.394726276482117 & 0.789452552964234 & 0.605273723517883 \tabularnewline
22 & 0.231530789110347 & 0.463061578220695 & 0.768469210889653 \tabularnewline
23 & 0.175845990151245 & 0.351691980302489 & 0.824154009848755 \tabularnewline
24 & 0.137901630530378 & 0.275803261060757 & 0.862098369469622 \tabularnewline
25 & 0.0734290404129046 & 0.146858080825809 & 0.926570959587095 \tabularnewline
26 & 0.0351912754960505 & 0.0703825509921009 & 0.96480872450395 \tabularnewline
27 & 0.0198384985295879 & 0.0396769970591758 & 0.980161501470412 \tabularnewline
28 & 0.0101129584916064 & 0.0202259169832129 & 0.989887041508394 \tabularnewline
29 & 0.00768260017233324 & 0.0153652003446665 & 0.992317399827667 \tabularnewline
30 & 0.00537244374315765 & 0.0107448874863153 & 0.994627556256842 \tabularnewline
31 & 0.00386407373757688 & 0.00772814747515377 & 0.996135926262423 \tabularnewline
32 & 0.00260733673932073 & 0.00521467347864147 & 0.99739266326068 \tabularnewline
33 & 0.000971801885163583 & 0.00194360377032717 & 0.999028198114836 \tabularnewline
34 & 0.000801982765038818 & 0.00160396553007764 & 0.99919801723496 \tabularnewline
35 & 0.000287089853091043 & 0.000574179706182085 & 0.999712910146909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58120&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]21[/C][C]0.394726276482117[/C][C]0.789452552964234[/C][C]0.605273723517883[/C][/ROW]
[ROW][C]22[/C][C]0.231530789110347[/C][C]0.463061578220695[/C][C]0.768469210889653[/C][/ROW]
[ROW][C]23[/C][C]0.175845990151245[/C][C]0.351691980302489[/C][C]0.824154009848755[/C][/ROW]
[ROW][C]24[/C][C]0.137901630530378[/C][C]0.275803261060757[/C][C]0.862098369469622[/C][/ROW]
[ROW][C]25[/C][C]0.0734290404129046[/C][C]0.146858080825809[/C][C]0.926570959587095[/C][/ROW]
[ROW][C]26[/C][C]0.0351912754960505[/C][C]0.0703825509921009[/C][C]0.96480872450395[/C][/ROW]
[ROW][C]27[/C][C]0.0198384985295879[/C][C]0.0396769970591758[/C][C]0.980161501470412[/C][/ROW]
[ROW][C]28[/C][C]0.0101129584916064[/C][C]0.0202259169832129[/C][C]0.989887041508394[/C][/ROW]
[ROW][C]29[/C][C]0.00768260017233324[/C][C]0.0153652003446665[/C][C]0.992317399827667[/C][/ROW]
[ROW][C]30[/C][C]0.00537244374315765[/C][C]0.0107448874863153[/C][C]0.994627556256842[/C][/ROW]
[ROW][C]31[/C][C]0.00386407373757688[/C][C]0.00772814747515377[/C][C]0.996135926262423[/C][/ROW]
[ROW][C]32[/C][C]0.00260733673932073[/C][C]0.00521467347864147[/C][C]0.99739266326068[/C][/ROW]
[ROW][C]33[/C][C]0.000971801885163583[/C][C]0.00194360377032717[/C][C]0.999028198114836[/C][/ROW]
[ROW][C]34[/C][C]0.000801982765038818[/C][C]0.00160396553007764[/C][C]0.99919801723496[/C][/ROW]
[ROW][C]35[/C][C]0.000287089853091043[/C][C]0.000574179706182085[/C][C]0.999712910146909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58120&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58120&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.3947262764821170.7894525529642340.605273723517883
220.2315307891103470.4630615782206950.768469210889653
230.1758459901512450.3516919803024890.824154009848755
240.1379016305303780.2758032610607570.862098369469622
250.07342904041290460.1468580808258090.926570959587095
260.03519127549605050.07038255099210090.96480872450395
270.01983849852958790.03967699705917580.980161501470412
280.01011295849160640.02022591698321290.989887041508394
290.007682600172333240.01536520034466650.992317399827667
300.005372443743157650.01074488748631530.994627556256842
310.003864073737576880.007728147475153770.996135926262423
320.002607336739320730.005214673478641470.99739266326068
330.0009718018851635830.001943603770327170.999028198114836
340.0008019827650388180.001603965530077640.99919801723496
350.0002870898530910430.0005741797061820850.999712910146909






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.333333333333333NOK
5% type I error level90.6NOK
10% type I error level100.666666666666667NOK

\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 & 5 & 0.333333333333333 & NOK \tabularnewline
5% type I error level & 9 & 0.6 & NOK \tabularnewline
10% type I error level & 10 & 0.666666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58120&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]5[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]9[/C][C]0.6[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]10[/C][C]0.666666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58120&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58120&T=6

As an alternative you can also use a QR Code:  
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 level50.333333333333333NOK
5% type I error level90.6NOK
10% type I error level100.666666666666667NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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')
}