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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 07:25:51 -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/t12587272196f2rwdynalh9ul3.htm/, Retrieved Fri, 29 Mar 2024 07:54:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58206, Retrieved Fri, 29 Mar 2024 07:54:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
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] [Model 3] [2009-11-20 14:25:51] [865cd78857e928bd6e7d79509c6cdcc5] [Current]
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Dataseries X:
20,3	3016
20	2155
19,2	2172
21,8	2150
21,3	2533
21,5	2058
19,5	2160
19,5	2260
19,7	2498
18,7	2695
19,7	2799
20	2946
19,7	2930
19,2	2318
19,7	2540
22	2570
21,8	2669
22,8	2450
21	2842
25	3440
23,3	2678
25	2981
26,8	2260
25,3	2844
26,5	2546
27,8	2456
22	2295
22,3	2379
28	2479
25	2057
27,3	2280
25,8	2351
27,3	2276
23,5	2548
24,5	2311
18	2201
21,3	2725
21,8	2408
20,5	2139
22,3	1898
18,7	2537
22,3	2068
17,7	2063
19,7	2520
20,5	2434
18,5	2190
10	2794
14,2	2070
15,5	2615
16,5	2265
20,5	2139
15,7	2428
11,7	2137
7,5	1823
3,5	2063
4,5	1806
2,2	1758
5	2243
2,3	1993
6,1	1932
3,3	2465




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=58206&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=58206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58206&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 7.22953434391532 + 0.00648463349489511X[t] -1.85480014419147M1[t] + 3.16277160464226M2[t] + 3.06233004168446M3[t] + 3.48919297729325M4[t] + 1.93148382070862M5[t] + 4.08278029553563M6[t] + 0.996538751573457M7[t] + 1.00824945372864M8[t] + 1.82732939754611M9[t] + 0.221975324946219M10[t] -0.441128652098417M11[t] -0.168432673465854t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  7.22953434391532 +  0.00648463349489511X[t] -1.85480014419147M1[t] +  3.16277160464226M2[t] +  3.06233004168446M3[t] +  3.48919297729325M4[t] +  1.93148382070862M5[t] +  4.08278029553563M6[t] +  0.996538751573457M7[t] +  1.00824945372864M8[t] +  1.82732939754611M9[t] +  0.221975324946219M10[t] -0.441128652098417M11[t] -0.168432673465854t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58206&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  7.22953434391532 +  0.00648463349489511X[t] -1.85480014419147M1[t] +  3.16277160464226M2[t] +  3.06233004168446M3[t] +  3.48919297729325M4[t] +  1.93148382070862M5[t] +  4.08278029553563M6[t] +  0.996538751573457M7[t] +  1.00824945372864M8[t] +  1.82732939754611M9[t] +  0.221975324946219M10[t] -0.441128652098417M11[t] -0.168432673465854t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58206&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] = + 7.22953434391532 + 0.00648463349489511X[t] -1.85480014419147M1[t] + 3.16277160464226M2[t] + 3.06233004168446M3[t] + 3.48919297729325M4[t] + 1.93148382070862M5[t] + 4.08278029553563M6[t] + 0.996538751573457M7[t] + 1.00824945372864M8[t] + 1.82732939754611M9[t] + 0.221975324946219M10[t] -0.441128652098417M11[t] -0.168432673465854t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)7.229534343915328.5540420.84520.4023040.201152
X0.006484633494895110.0029472.20080.0327020.016351
M1-1.854800144191473.524316-0.52630.6011640.300582
M23.162771604642263.6364440.86970.3888610.194431
M33.062330041684463.657280.83730.4066480.203324
M43.489192977293253.6351220.95990.342040.17102
M51.931483820708623.5898740.5380.5930910.296545
M64.082780295535633.7418281.09110.2807830.140391
M70.9965387515734573.6157760.27560.7840570.392028
M81.008249453728643.5837420.28130.7796850.389842
M91.827329397546113.5914650.50880.6132740.306637
M100.2219753249462193.5947390.06180.9510240.475512
M11-0.4411286520984173.578791-0.12330.9024250.451213
t-0.1684326734658540.049605-3.39550.0014020.000701

\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) & 7.22953434391532 & 8.554042 & 0.8452 & 0.402304 & 0.201152 \tabularnewline
X & 0.00648463349489511 & 0.002947 & 2.2008 & 0.032702 & 0.016351 \tabularnewline
M1 & -1.85480014419147 & 3.524316 & -0.5263 & 0.601164 & 0.300582 \tabularnewline
M2 & 3.16277160464226 & 3.636444 & 0.8697 & 0.388861 & 0.194431 \tabularnewline
M3 & 3.06233004168446 & 3.65728 & 0.8373 & 0.406648 & 0.203324 \tabularnewline
M4 & 3.48919297729325 & 3.635122 & 0.9599 & 0.34204 & 0.17102 \tabularnewline
M5 & 1.93148382070862 & 3.589874 & 0.538 & 0.593091 & 0.296545 \tabularnewline
M6 & 4.08278029553563 & 3.741828 & 1.0911 & 0.280783 & 0.140391 \tabularnewline
M7 & 0.996538751573457 & 3.615776 & 0.2756 & 0.784057 & 0.392028 \tabularnewline
M8 & 1.00824945372864 & 3.583742 & 0.2813 & 0.779685 & 0.389842 \tabularnewline
M9 & 1.82732939754611 & 3.591465 & 0.5088 & 0.613274 & 0.306637 \tabularnewline
M10 & 0.221975324946219 & 3.594739 & 0.0618 & 0.951024 & 0.475512 \tabularnewline
M11 & -0.441128652098417 & 3.578791 & -0.1233 & 0.902425 & 0.451213 \tabularnewline
t & -0.168432673465854 & 0.049605 & -3.3955 & 0.001402 & 0.000701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58206&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]7.22953434391532[/C][C]8.554042[/C][C]0.8452[/C][C]0.402304[/C][C]0.201152[/C][/ROW]
[ROW][C]X[/C][C]0.00648463349489511[/C][C]0.002947[/C][C]2.2008[/C][C]0.032702[/C][C]0.016351[/C][/ROW]
[ROW][C]M1[/C][C]-1.85480014419147[/C][C]3.524316[/C][C]-0.5263[/C][C]0.601164[/C][C]0.300582[/C][/ROW]
[ROW][C]M2[/C][C]3.16277160464226[/C][C]3.636444[/C][C]0.8697[/C][C]0.388861[/C][C]0.194431[/C][/ROW]
[ROW][C]M3[/C][C]3.06233004168446[/C][C]3.65728[/C][C]0.8373[/C][C]0.406648[/C][C]0.203324[/C][/ROW]
[ROW][C]M4[/C][C]3.48919297729325[/C][C]3.635122[/C][C]0.9599[/C][C]0.34204[/C][C]0.17102[/C][/ROW]
[ROW][C]M5[/C][C]1.93148382070862[/C][C]3.589874[/C][C]0.538[/C][C]0.593091[/C][C]0.296545[/C][/ROW]
[ROW][C]M6[/C][C]4.08278029553563[/C][C]3.741828[/C][C]1.0911[/C][C]0.280783[/C][C]0.140391[/C][/ROW]
[ROW][C]M7[/C][C]0.996538751573457[/C][C]3.615776[/C][C]0.2756[/C][C]0.784057[/C][C]0.392028[/C][/ROW]
[ROW][C]M8[/C][C]1.00824945372864[/C][C]3.583742[/C][C]0.2813[/C][C]0.779685[/C][C]0.389842[/C][/ROW]
[ROW][C]M9[/C][C]1.82732939754611[/C][C]3.591465[/C][C]0.5088[/C][C]0.613274[/C][C]0.306637[/C][/ROW]
[ROW][C]M10[/C][C]0.221975324946219[/C][C]3.594739[/C][C]0.0618[/C][C]0.951024[/C][C]0.475512[/C][/ROW]
[ROW][C]M11[/C][C]-0.441128652098417[/C][C]3.578791[/C][C]-0.1233[/C][C]0.902425[/C][C]0.451213[/C][/ROW]
[ROW][C]t[/C][C]-0.168432673465854[/C][C]0.049605[/C][C]-3.3955[/C][C]0.001402[/C][C]0.000701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58206&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)7.229534343915328.5540420.84520.4023040.201152
X0.006484633494895110.0029472.20080.0327020.016351
M1-1.854800144191473.524316-0.52630.6011640.300582
M23.162771604642263.6364440.86970.3888610.194431
M33.062330041684463.657280.83730.4066480.203324
M43.489192977293253.6351220.95990.342040.17102
M51.931483820708623.5898740.5380.5930910.296545
M64.082780295535633.7418281.09110.2807830.140391
M70.9965387515734573.6157760.27560.7840570.392028
M81.008249453728643.5837420.28130.7796850.389842
M91.827329397546113.5914650.50880.6132740.306637
M100.2219753249462193.5947390.06180.9510240.475512
M11-0.4411286520984173.578791-0.12330.9024250.451213
t-0.1684326734658540.049605-3.39550.0014020.000701







Multiple Linear Regression - Regression Statistics
Multiple R0.671765465070318
R-squared0.45126884006114
Adjusted R-squared0.299492136248264
F-TEST (value)2.97324180012174
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0.00308389822045241
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.65710184469093
Sum Squared Residuals1504.13166021666

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.671765465070318 \tabularnewline
R-squared & 0.45126884006114 \tabularnewline
Adjusted R-squared & 0.299492136248264 \tabularnewline
F-TEST (value) & 2.97324180012174 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0.00308389822045241 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.65710184469093 \tabularnewline
Sum Squared Residuals & 1504.13166021666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58206&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.671765465070318[/C][/ROW]
[ROW][C]R-squared[/C][C]0.45126884006114[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.299492136248264[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.97324180012174[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]0.00308389822045241[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.65710184469093[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1504.13166021666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58206&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58206&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 R0.671765465070318
R-squared0.45126884006114
Adjusted R-squared0.299492136248264
F-TEST (value)2.97324180012174
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0.00308389822045241
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.65710184469093
Sum Squared Residuals1504.13166021666







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
120.324.7639561468617-4.46395614686168
22024.0298257831248-4.02982578312484
319.223.8711903161144-4.67119031611441
421.823.9869586413697-2.18695864136965
521.324.744431439864-3.44443143986399
621.523.6470943311500-2.14709433114998
719.521.0538527302012-1.55385273020125
819.521.5455941083801-2.04559410838008
919.723.7395841505167-4.03958415051675
1018.723.2432702029453-4.54327020294533
1119.723.0861354359039-3.38613543590394
122024.3120725382861-4.31207253828608
1319.722.1850855847104-2.48508558471044
1419.223.0656289612025-3.8656289612025
1519.724.2363433606456-4.53634336064556
162224.6893126276354-2.68931262763535
1721.823.6051495135795-1.80514951357948
1822.824.1678785795586-1.36787857955861
192123.4551806921295-2.45518069212947
202527.1762695507661-2.17626955076607
2123.322.88562609800760.414373901992383
222523.07668330089511.92331669910491
2326.817.56972590056529.23027409943477
2425.321.62944784021653.67055215978347
2526.517.67379424108058.82620575891953
2627.821.93931630190785.86068369809222
272220.6264160728061.37358392719399
2822.321.42955554852010.870444451479859
292820.35187706795927.64812293204083
302519.59822553447465.40177446552541
3127.317.78962458640829.51037541359183
3225.818.09331159323517.70668840676495
3327.318.25761135146959.04238864853047
3423.518.24764491601535.25235508398474
3524.515.87925012721468.62074987278537
361815.43863642140872.56136357859127
3721.316.81335155507644.48664844492355
3821.819.60686181256262.19313818743744
3920.517.59362116601212.90637883398787
4022.316.28925475588536.01074524411465
4118.718.7067937290728-0.00679372907283377
4222.317.64836442132824.65163557867181
4317.714.36126703642573.33873296357432
4419.717.16802257228212.53197742771792
4520.517.26099136207273.23900863792728
4618.513.90495404325264.59504595674744
471016.9901360236587-6.99013602365872
4814.212.56795735198721.63204264801278
4915.514.07884978904771.42115021095226
5016.516.6583671412023-0.158367141202320
5120.515.57242908442194.92757091557812
5215.717.7049184265895-2.00491842658951
5311.714.0917482495245-2.39174824952454
547.514.0384371334886-6.53843713348864
553.512.3400749548354-8.84007495483544
564.510.5168021753367-6.01680217533672
572.210.8561870379334-8.65618703793338
58512.2274475368918-7.22744753689176
592.39.77475251265749-7.47475251265749
606.19.65188584810145-3.55188584810145
613.311.0849626832232-7.78496268322322

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 20.3 & 24.7639561468617 & -4.46395614686168 \tabularnewline
2 & 20 & 24.0298257831248 & -4.02982578312484 \tabularnewline
3 & 19.2 & 23.8711903161144 & -4.67119031611441 \tabularnewline
4 & 21.8 & 23.9869586413697 & -2.18695864136965 \tabularnewline
5 & 21.3 & 24.744431439864 & -3.44443143986399 \tabularnewline
6 & 21.5 & 23.6470943311500 & -2.14709433114998 \tabularnewline
7 & 19.5 & 21.0538527302012 & -1.55385273020125 \tabularnewline
8 & 19.5 & 21.5455941083801 & -2.04559410838008 \tabularnewline
9 & 19.7 & 23.7395841505167 & -4.03958415051675 \tabularnewline
10 & 18.7 & 23.2432702029453 & -4.54327020294533 \tabularnewline
11 & 19.7 & 23.0861354359039 & -3.38613543590394 \tabularnewline
12 & 20 & 24.3120725382861 & -4.31207253828608 \tabularnewline
13 & 19.7 & 22.1850855847104 & -2.48508558471044 \tabularnewline
14 & 19.2 & 23.0656289612025 & -3.8656289612025 \tabularnewline
15 & 19.7 & 24.2363433606456 & -4.53634336064556 \tabularnewline
16 & 22 & 24.6893126276354 & -2.68931262763535 \tabularnewline
17 & 21.8 & 23.6051495135795 & -1.80514951357948 \tabularnewline
18 & 22.8 & 24.1678785795586 & -1.36787857955861 \tabularnewline
19 & 21 & 23.4551806921295 & -2.45518069212947 \tabularnewline
20 & 25 & 27.1762695507661 & -2.17626955076607 \tabularnewline
21 & 23.3 & 22.8856260980076 & 0.414373901992383 \tabularnewline
22 & 25 & 23.0766833008951 & 1.92331669910491 \tabularnewline
23 & 26.8 & 17.5697259005652 & 9.23027409943477 \tabularnewline
24 & 25.3 & 21.6294478402165 & 3.67055215978347 \tabularnewline
25 & 26.5 & 17.6737942410805 & 8.82620575891953 \tabularnewline
26 & 27.8 & 21.9393163019078 & 5.86068369809222 \tabularnewline
27 & 22 & 20.626416072806 & 1.37358392719399 \tabularnewline
28 & 22.3 & 21.4295555485201 & 0.870444451479859 \tabularnewline
29 & 28 & 20.3518770679592 & 7.64812293204083 \tabularnewline
30 & 25 & 19.5982255344746 & 5.40177446552541 \tabularnewline
31 & 27.3 & 17.7896245864082 & 9.51037541359183 \tabularnewline
32 & 25.8 & 18.0933115932351 & 7.70668840676495 \tabularnewline
33 & 27.3 & 18.2576113514695 & 9.04238864853047 \tabularnewline
34 & 23.5 & 18.2476449160153 & 5.25235508398474 \tabularnewline
35 & 24.5 & 15.8792501272146 & 8.62074987278537 \tabularnewline
36 & 18 & 15.4386364214087 & 2.56136357859127 \tabularnewline
37 & 21.3 & 16.8133515550764 & 4.48664844492355 \tabularnewline
38 & 21.8 & 19.6068618125626 & 2.19313818743744 \tabularnewline
39 & 20.5 & 17.5936211660121 & 2.90637883398787 \tabularnewline
40 & 22.3 & 16.2892547558853 & 6.01074524411465 \tabularnewline
41 & 18.7 & 18.7067937290728 & -0.00679372907283377 \tabularnewline
42 & 22.3 & 17.6483644213282 & 4.65163557867181 \tabularnewline
43 & 17.7 & 14.3612670364257 & 3.33873296357432 \tabularnewline
44 & 19.7 & 17.1680225722821 & 2.53197742771792 \tabularnewline
45 & 20.5 & 17.2609913620727 & 3.23900863792728 \tabularnewline
46 & 18.5 & 13.9049540432526 & 4.59504595674744 \tabularnewline
47 & 10 & 16.9901360236587 & -6.99013602365872 \tabularnewline
48 & 14.2 & 12.5679573519872 & 1.63204264801278 \tabularnewline
49 & 15.5 & 14.0788497890477 & 1.42115021095226 \tabularnewline
50 & 16.5 & 16.6583671412023 & -0.158367141202320 \tabularnewline
51 & 20.5 & 15.5724290844219 & 4.92757091557812 \tabularnewline
52 & 15.7 & 17.7049184265895 & -2.00491842658951 \tabularnewline
53 & 11.7 & 14.0917482495245 & -2.39174824952454 \tabularnewline
54 & 7.5 & 14.0384371334886 & -6.53843713348864 \tabularnewline
55 & 3.5 & 12.3400749548354 & -8.84007495483544 \tabularnewline
56 & 4.5 & 10.5168021753367 & -6.01680217533672 \tabularnewline
57 & 2.2 & 10.8561870379334 & -8.65618703793338 \tabularnewline
58 & 5 & 12.2274475368918 & -7.22744753689176 \tabularnewline
59 & 2.3 & 9.77475251265749 & -7.47475251265749 \tabularnewline
60 & 6.1 & 9.65188584810145 & -3.55188584810145 \tabularnewline
61 & 3.3 & 11.0849626832232 & -7.78496268322322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58206&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]20.3[/C][C]24.7639561468617[/C][C]-4.46395614686168[/C][/ROW]
[ROW][C]2[/C][C]20[/C][C]24.0298257831248[/C][C]-4.02982578312484[/C][/ROW]
[ROW][C]3[/C][C]19.2[/C][C]23.8711903161144[/C][C]-4.67119031611441[/C][/ROW]
[ROW][C]4[/C][C]21.8[/C][C]23.9869586413697[/C][C]-2.18695864136965[/C][/ROW]
[ROW][C]5[/C][C]21.3[/C][C]24.744431439864[/C][C]-3.44443143986399[/C][/ROW]
[ROW][C]6[/C][C]21.5[/C][C]23.6470943311500[/C][C]-2.14709433114998[/C][/ROW]
[ROW][C]7[/C][C]19.5[/C][C]21.0538527302012[/C][C]-1.55385273020125[/C][/ROW]
[ROW][C]8[/C][C]19.5[/C][C]21.5455941083801[/C][C]-2.04559410838008[/C][/ROW]
[ROW][C]9[/C][C]19.7[/C][C]23.7395841505167[/C][C]-4.03958415051675[/C][/ROW]
[ROW][C]10[/C][C]18.7[/C][C]23.2432702029453[/C][C]-4.54327020294533[/C][/ROW]
[ROW][C]11[/C][C]19.7[/C][C]23.0861354359039[/C][C]-3.38613543590394[/C][/ROW]
[ROW][C]12[/C][C]20[/C][C]24.3120725382861[/C][C]-4.31207253828608[/C][/ROW]
[ROW][C]13[/C][C]19.7[/C][C]22.1850855847104[/C][C]-2.48508558471044[/C][/ROW]
[ROW][C]14[/C][C]19.2[/C][C]23.0656289612025[/C][C]-3.8656289612025[/C][/ROW]
[ROW][C]15[/C][C]19.7[/C][C]24.2363433606456[/C][C]-4.53634336064556[/C][/ROW]
[ROW][C]16[/C][C]22[/C][C]24.6893126276354[/C][C]-2.68931262763535[/C][/ROW]
[ROW][C]17[/C][C]21.8[/C][C]23.6051495135795[/C][C]-1.80514951357948[/C][/ROW]
[ROW][C]18[/C][C]22.8[/C][C]24.1678785795586[/C][C]-1.36787857955861[/C][/ROW]
[ROW][C]19[/C][C]21[/C][C]23.4551806921295[/C][C]-2.45518069212947[/C][/ROW]
[ROW][C]20[/C][C]25[/C][C]27.1762695507661[/C][C]-2.17626955076607[/C][/ROW]
[ROW][C]21[/C][C]23.3[/C][C]22.8856260980076[/C][C]0.414373901992383[/C][/ROW]
[ROW][C]22[/C][C]25[/C][C]23.0766833008951[/C][C]1.92331669910491[/C][/ROW]
[ROW][C]23[/C][C]26.8[/C][C]17.5697259005652[/C][C]9.23027409943477[/C][/ROW]
[ROW][C]24[/C][C]25.3[/C][C]21.6294478402165[/C][C]3.67055215978347[/C][/ROW]
[ROW][C]25[/C][C]26.5[/C][C]17.6737942410805[/C][C]8.82620575891953[/C][/ROW]
[ROW][C]26[/C][C]27.8[/C][C]21.9393163019078[/C][C]5.86068369809222[/C][/ROW]
[ROW][C]27[/C][C]22[/C][C]20.626416072806[/C][C]1.37358392719399[/C][/ROW]
[ROW][C]28[/C][C]22.3[/C][C]21.4295555485201[/C][C]0.870444451479859[/C][/ROW]
[ROW][C]29[/C][C]28[/C][C]20.3518770679592[/C][C]7.64812293204083[/C][/ROW]
[ROW][C]30[/C][C]25[/C][C]19.5982255344746[/C][C]5.40177446552541[/C][/ROW]
[ROW][C]31[/C][C]27.3[/C][C]17.7896245864082[/C][C]9.51037541359183[/C][/ROW]
[ROW][C]32[/C][C]25.8[/C][C]18.0933115932351[/C][C]7.70668840676495[/C][/ROW]
[ROW][C]33[/C][C]27.3[/C][C]18.2576113514695[/C][C]9.04238864853047[/C][/ROW]
[ROW][C]34[/C][C]23.5[/C][C]18.2476449160153[/C][C]5.25235508398474[/C][/ROW]
[ROW][C]35[/C][C]24.5[/C][C]15.8792501272146[/C][C]8.62074987278537[/C][/ROW]
[ROW][C]36[/C][C]18[/C][C]15.4386364214087[/C][C]2.56136357859127[/C][/ROW]
[ROW][C]37[/C][C]21.3[/C][C]16.8133515550764[/C][C]4.48664844492355[/C][/ROW]
[ROW][C]38[/C][C]21.8[/C][C]19.6068618125626[/C][C]2.19313818743744[/C][/ROW]
[ROW][C]39[/C][C]20.5[/C][C]17.5936211660121[/C][C]2.90637883398787[/C][/ROW]
[ROW][C]40[/C][C]22.3[/C][C]16.2892547558853[/C][C]6.01074524411465[/C][/ROW]
[ROW][C]41[/C][C]18.7[/C][C]18.7067937290728[/C][C]-0.00679372907283377[/C][/ROW]
[ROW][C]42[/C][C]22.3[/C][C]17.6483644213282[/C][C]4.65163557867181[/C][/ROW]
[ROW][C]43[/C][C]17.7[/C][C]14.3612670364257[/C][C]3.33873296357432[/C][/ROW]
[ROW][C]44[/C][C]19.7[/C][C]17.1680225722821[/C][C]2.53197742771792[/C][/ROW]
[ROW][C]45[/C][C]20.5[/C][C]17.2609913620727[/C][C]3.23900863792728[/C][/ROW]
[ROW][C]46[/C][C]18.5[/C][C]13.9049540432526[/C][C]4.59504595674744[/C][/ROW]
[ROW][C]47[/C][C]10[/C][C]16.9901360236587[/C][C]-6.99013602365872[/C][/ROW]
[ROW][C]48[/C][C]14.2[/C][C]12.5679573519872[/C][C]1.63204264801278[/C][/ROW]
[ROW][C]49[/C][C]15.5[/C][C]14.0788497890477[/C][C]1.42115021095226[/C][/ROW]
[ROW][C]50[/C][C]16.5[/C][C]16.6583671412023[/C][C]-0.158367141202320[/C][/ROW]
[ROW][C]51[/C][C]20.5[/C][C]15.5724290844219[/C][C]4.92757091557812[/C][/ROW]
[ROW][C]52[/C][C]15.7[/C][C]17.7049184265895[/C][C]-2.00491842658951[/C][/ROW]
[ROW][C]53[/C][C]11.7[/C][C]14.0917482495245[/C][C]-2.39174824952454[/C][/ROW]
[ROW][C]54[/C][C]7.5[/C][C]14.0384371334886[/C][C]-6.53843713348864[/C][/ROW]
[ROW][C]55[/C][C]3.5[/C][C]12.3400749548354[/C][C]-8.84007495483544[/C][/ROW]
[ROW][C]56[/C][C]4.5[/C][C]10.5168021753367[/C][C]-6.01680217533672[/C][/ROW]
[ROW][C]57[/C][C]2.2[/C][C]10.8561870379334[/C][C]-8.65618703793338[/C][/ROW]
[ROW][C]58[/C][C]5[/C][C]12.2274475368918[/C][C]-7.22744753689176[/C][/ROW]
[ROW][C]59[/C][C]2.3[/C][C]9.77475251265749[/C][C]-7.47475251265749[/C][/ROW]
[ROW][C]60[/C][C]6.1[/C][C]9.65188584810145[/C][C]-3.55188584810145[/C][/ROW]
[ROW][C]61[/C][C]3.3[/C][C]11.0849626832232[/C][C]-7.78496268322322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58206&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58206&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
120.324.7639561468617-4.46395614686168
22024.0298257831248-4.02982578312484
319.223.8711903161144-4.67119031611441
421.823.9869586413697-2.18695864136965
521.324.744431439864-3.44443143986399
621.523.6470943311500-2.14709433114998
719.521.0538527302012-1.55385273020125
819.521.5455941083801-2.04559410838008
919.723.7395841505167-4.03958415051675
1018.723.2432702029453-4.54327020294533
1119.723.0861354359039-3.38613543590394
122024.3120725382861-4.31207253828608
1319.722.1850855847104-2.48508558471044
1419.223.0656289612025-3.8656289612025
1519.724.2363433606456-4.53634336064556
162224.6893126276354-2.68931262763535
1721.823.6051495135795-1.80514951357948
1822.824.1678785795586-1.36787857955861
192123.4551806921295-2.45518069212947
202527.1762695507661-2.17626955076607
2123.322.88562609800760.414373901992383
222523.07668330089511.92331669910491
2326.817.56972590056529.23027409943477
2425.321.62944784021653.67055215978347
2526.517.67379424108058.82620575891953
2627.821.93931630190785.86068369809222
272220.6264160728061.37358392719399
2822.321.42955554852010.870444451479859
292820.35187706795927.64812293204083
302519.59822553447465.40177446552541
3127.317.78962458640829.51037541359183
3225.818.09331159323517.70668840676495
3327.318.25761135146959.04238864853047
3423.518.24764491601535.25235508398474
3524.515.87925012721468.62074987278537
361815.43863642140872.56136357859127
3721.316.81335155507644.48664844492355
3821.819.60686181256262.19313818743744
3920.517.59362116601212.90637883398787
4022.316.28925475588536.01074524411465
4118.718.7067937290728-0.00679372907283377
4222.317.64836442132824.65163557867181
4317.714.36126703642573.33873296357432
4419.717.16802257228212.53197742771792
4520.517.26099136207273.23900863792728
4618.513.90495404325264.59504595674744
471016.9901360236587-6.99013602365872
4814.212.56795735198721.63204264801278
4915.514.07884978904771.42115021095226
5016.516.6583671412023-0.158367141202320
5120.515.57242908442194.92757091557812
5215.717.7049184265895-2.00491842658951
5311.714.0917482495245-2.39174824952454
547.514.0384371334886-6.53843713348864
553.512.3400749548354-8.84007495483544
564.510.5168021753367-6.01680217533672
572.210.8561870379334-8.65618703793338
58512.2274475368918-7.22744753689176
592.39.77475251265749-7.47475251265749
606.19.65188584810145-3.55188584810145
613.311.0849626832232-7.78496268322322







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.001082139598102820.002164279196205650.998917860401897
180.000269098448872230.000538196897744460.999730901551128
193.04499007893721e-056.08998015787441e-050.99996955009921
203.46076640413878e-056.92153280827757e-050.999965392335959
210.0006196790279157680.001239358055831540.999380320972084
220.006704507945366560.01340901589073310.993295492054633
230.02707253045804890.05414506091609780.972927469541951
240.02100556015595150.0420111203119030.978994439844048
250.01157408889513020.02314817779026030.98842591110487
260.01136695413331300.02273390826662600.988633045866687
270.02249582147007940.04499164294015870.97750417852992
280.07425570703669550.1485114140733910.925744292963305
290.0509652360590170.1019304721180340.949034763940983
300.03892794044711080.07785588089422160.96107205955289
310.02999623837681300.05999247675362590.970003761623187
320.01766691284019800.03533382568039600.982333087159802
330.01046107673959530.02092215347919060.989538923260405
340.008696267690175740.01739253538035150.991303732309824
350.01355565998778160.02711131997556320.986444340012218
360.08165914083274440.1633182816654890.918340859167255
370.0930245573363250.186049114672650.906975442663675
380.1086026382827690.2172052765655380.891397361717231
390.3477339100438910.6954678200877820.652266089956109
400.3274197484095980.6548394968191950.672580251590402
410.52881690407240.94236619185520.4711830959276
420.4334958993371970.8669917986743940.566504100662803
430.3806542312950540.7613084625901090.619345768704946
440.2971197798941530.5942395597883050.702880220105847

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00108213959810282 & 0.00216427919620565 & 0.998917860401897 \tabularnewline
18 & 0.00026909844887223 & 0.00053819689774446 & 0.999730901551128 \tabularnewline
19 & 3.04499007893721e-05 & 6.08998015787441e-05 & 0.99996955009921 \tabularnewline
20 & 3.46076640413878e-05 & 6.92153280827757e-05 & 0.999965392335959 \tabularnewline
21 & 0.000619679027915768 & 0.00123935805583154 & 0.999380320972084 \tabularnewline
22 & 0.00670450794536656 & 0.0134090158907331 & 0.993295492054633 \tabularnewline
23 & 0.0270725304580489 & 0.0541450609160978 & 0.972927469541951 \tabularnewline
24 & 0.0210055601559515 & 0.042011120311903 & 0.978994439844048 \tabularnewline
25 & 0.0115740888951302 & 0.0231481777902603 & 0.98842591110487 \tabularnewline
26 & 0.0113669541333130 & 0.0227339082666260 & 0.988633045866687 \tabularnewline
27 & 0.0224958214700794 & 0.0449916429401587 & 0.97750417852992 \tabularnewline
28 & 0.0742557070366955 & 0.148511414073391 & 0.925744292963305 \tabularnewline
29 & 0.050965236059017 & 0.101930472118034 & 0.949034763940983 \tabularnewline
30 & 0.0389279404471108 & 0.0778558808942216 & 0.96107205955289 \tabularnewline
31 & 0.0299962383768130 & 0.0599924767536259 & 0.970003761623187 \tabularnewline
32 & 0.0176669128401980 & 0.0353338256803960 & 0.982333087159802 \tabularnewline
33 & 0.0104610767395953 & 0.0209221534791906 & 0.989538923260405 \tabularnewline
34 & 0.00869626769017574 & 0.0173925353803515 & 0.991303732309824 \tabularnewline
35 & 0.0135556599877816 & 0.0271113199755632 & 0.986444340012218 \tabularnewline
36 & 0.0816591408327444 & 0.163318281665489 & 0.918340859167255 \tabularnewline
37 & 0.093024557336325 & 0.18604911467265 & 0.906975442663675 \tabularnewline
38 & 0.108602638282769 & 0.217205276565538 & 0.891397361717231 \tabularnewline
39 & 0.347733910043891 & 0.695467820087782 & 0.652266089956109 \tabularnewline
40 & 0.327419748409598 & 0.654839496819195 & 0.672580251590402 \tabularnewline
41 & 0.5288169040724 & 0.9423661918552 & 0.4711830959276 \tabularnewline
42 & 0.433495899337197 & 0.866991798674394 & 0.566504100662803 \tabularnewline
43 & 0.380654231295054 & 0.761308462590109 & 0.619345768704946 \tabularnewline
44 & 0.297119779894153 & 0.594239559788305 & 0.702880220105847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58206&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]0.00108213959810282[/C][C]0.00216427919620565[/C][C]0.998917860401897[/C][/ROW]
[ROW][C]18[/C][C]0.00026909844887223[/C][C]0.00053819689774446[/C][C]0.999730901551128[/C][/ROW]
[ROW][C]19[/C][C]3.04499007893721e-05[/C][C]6.08998015787441e-05[/C][C]0.99996955009921[/C][/ROW]
[ROW][C]20[/C][C]3.46076640413878e-05[/C][C]6.92153280827757e-05[/C][C]0.999965392335959[/C][/ROW]
[ROW][C]21[/C][C]0.000619679027915768[/C][C]0.00123935805583154[/C][C]0.999380320972084[/C][/ROW]
[ROW][C]22[/C][C]0.00670450794536656[/C][C]0.0134090158907331[/C][C]0.993295492054633[/C][/ROW]
[ROW][C]23[/C][C]0.0270725304580489[/C][C]0.0541450609160978[/C][C]0.972927469541951[/C][/ROW]
[ROW][C]24[/C][C]0.0210055601559515[/C][C]0.042011120311903[/C][C]0.978994439844048[/C][/ROW]
[ROW][C]25[/C][C]0.0115740888951302[/C][C]0.0231481777902603[/C][C]0.98842591110487[/C][/ROW]
[ROW][C]26[/C][C]0.0113669541333130[/C][C]0.0227339082666260[/C][C]0.988633045866687[/C][/ROW]
[ROW][C]27[/C][C]0.0224958214700794[/C][C]0.0449916429401587[/C][C]0.97750417852992[/C][/ROW]
[ROW][C]28[/C][C]0.0742557070366955[/C][C]0.148511414073391[/C][C]0.925744292963305[/C][/ROW]
[ROW][C]29[/C][C]0.050965236059017[/C][C]0.101930472118034[/C][C]0.949034763940983[/C][/ROW]
[ROW][C]30[/C][C]0.0389279404471108[/C][C]0.0778558808942216[/C][C]0.96107205955289[/C][/ROW]
[ROW][C]31[/C][C]0.0299962383768130[/C][C]0.0599924767536259[/C][C]0.970003761623187[/C][/ROW]
[ROW][C]32[/C][C]0.0176669128401980[/C][C]0.0353338256803960[/C][C]0.982333087159802[/C][/ROW]
[ROW][C]33[/C][C]0.0104610767395953[/C][C]0.0209221534791906[/C][C]0.989538923260405[/C][/ROW]
[ROW][C]34[/C][C]0.00869626769017574[/C][C]0.0173925353803515[/C][C]0.991303732309824[/C][/ROW]
[ROW][C]35[/C][C]0.0135556599877816[/C][C]0.0271113199755632[/C][C]0.986444340012218[/C][/ROW]
[ROW][C]36[/C][C]0.0816591408327444[/C][C]0.163318281665489[/C][C]0.918340859167255[/C][/ROW]
[ROW][C]37[/C][C]0.093024557336325[/C][C]0.18604911467265[/C][C]0.906975442663675[/C][/ROW]
[ROW][C]38[/C][C]0.108602638282769[/C][C]0.217205276565538[/C][C]0.891397361717231[/C][/ROW]
[ROW][C]39[/C][C]0.347733910043891[/C][C]0.695467820087782[/C][C]0.652266089956109[/C][/ROW]
[ROW][C]40[/C][C]0.327419748409598[/C][C]0.654839496819195[/C][C]0.672580251590402[/C][/ROW]
[ROW][C]41[/C][C]0.5288169040724[/C][C]0.9423661918552[/C][C]0.4711830959276[/C][/ROW]
[ROW][C]42[/C][C]0.433495899337197[/C][C]0.866991798674394[/C][C]0.566504100662803[/C][/ROW]
[ROW][C]43[/C][C]0.380654231295054[/C][C]0.761308462590109[/C][C]0.619345768704946[/C][/ROW]
[ROW][C]44[/C][C]0.297119779894153[/C][C]0.594239559788305[/C][C]0.702880220105847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58206&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58206&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
170.001082139598102820.002164279196205650.998917860401897
180.000269098448872230.000538196897744460.999730901551128
193.04499007893721e-056.08998015787441e-050.99996955009921
203.46076640413878e-056.92153280827757e-050.999965392335959
210.0006196790279157680.001239358055831540.999380320972084
220.006704507945366560.01340901589073310.993295492054633
230.02707253045804890.05414506091609780.972927469541951
240.02100556015595150.0420111203119030.978994439844048
250.01157408889513020.02314817779026030.98842591110487
260.01136695413331300.02273390826662600.988633045866687
270.02249582147007940.04499164294015870.97750417852992
280.07425570703669550.1485114140733910.925744292963305
290.0509652360590170.1019304721180340.949034763940983
300.03892794044711080.07785588089422160.96107205955289
310.02999623837681300.05999247675362590.970003761623187
320.01766691284019800.03533382568039600.982333087159802
330.01046107673959530.02092215347919060.989538923260405
340.008696267690175740.01739253538035150.991303732309824
350.01355565998778160.02711131997556320.986444340012218
360.08165914083274440.1633182816654890.918340859167255
370.0930245573363250.186049114672650.906975442663675
380.1086026382827690.2172052765655380.891397361717231
390.3477339100438910.6954678200877820.652266089956109
400.3274197484095980.6548394968191950.672580251590402
410.52881690407240.94236619185520.4711830959276
420.4334958993371970.8669917986743940.566504100662803
430.3806542312950540.7613084625901090.619345768704946
440.2971197798941530.5942395597883050.702880220105847







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.178571428571429NOK
5% type I error level140.5NOK
10% type I error level170.607142857142857NOK

\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 & 0.178571428571429 & NOK \tabularnewline
5% type I error level & 14 & 0.5 & NOK \tabularnewline
10% type I error level & 17 & 0.607142857142857 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58206&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]0.178571428571429[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.5[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]17[/C][C]0.607142857142857[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58206&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58206&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 level50.178571428571429NOK
5% type I error level140.5NOK
10% type I error level170.607142857142857NOK



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')
}