FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationWed, 18 Nov 2009 10:49:39 -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/18/t1258566690bw95lzphawi4wvy.htm/, Retrieved Sun, 05 May 2024 17:56:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57553, Retrieved Sun, 05 May 2024 17:56:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

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 14:14:11] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [] [2009-11-18 17:49:39] [508aab72d879399b4187e5fcd8f7c773] [Current]
-   P         [Multiple Regression] [] [2009-11-18 17:56:09] [96d96f181930b548ce74f8c3116c4873]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.2	2.4	7.5	8.3	8.9
7.4	2	7.2	7.5	8.8
8.8	2.1	7.4	7.2	8.3
9.3	2	8.8	7.4	7.5
9.3	1.8	9.3	8.8	7.2
8.7	2.7	9.3	9.3	7.4
8.2	2.3	8.7	9.3	8.8
8.3	1.9	8.2	8.7	9.3
8.5	2	8.3	8.2	9.3
8.6	2.3	8.5	8.3	8.7
8.5	2.8	8.6	8.5	8.2
8.2	2.4	8.5	8.6	8.3
8.1	2.3	8.2	8.5	8.5
7.9	2.7	8.1	8.2	8.6
8.6	2.7	7.9	8.1	8.5
8.7	2.9	8.6	7.9	8.2
8.7	3	8.7	8.6	8.1
8.5	2.2	8.7	8.7	7.9
8.4	2.3	8.5	8.7	8.6
8.5	2.8	8.4	8.5	8.7
8.7	2.8	8.5	8.4	8.7
8.7	2.8	8.7	8.5	8.5
8.6	2.2	8.7	8.7	8.4
8.5	2.6	8.6	8.7	8.5
8.3	2.8	8.5	8.6	8.7
8	2.5	8.3	8.5	8.7
8.2	2.4	8	8.3	8.6
8.1	2.3	8.2	8	8.5
8.1	1.9	8.1	8.2	8.3
8	1.7	8.1	8.1	8
7.9	2	8	8.1	8.2
7.9	2.1	7.9	8	8.1
8	1.7	7.9	7.9	8.1
8	1.8	8	7.9	8
7.9	1.8	8	8	7.9
8	1.8	7.9	8	7.9
7.7	1.3	8	7.9	8
7.2	1.3	7.7	8	8
7.5	1.3	7.2	7.7	7.9
7.3	1.2	7.5	7.2	8
7	1.4	7.3	7.5	7.7
7	2.2	7	7.3	7.2
7	2.9	7	7	7.5
7.2	3.1	7	7	7.3
7.3	3.5	7.2	7	7
7.1	3.6	7.3	7.2	7
6.8	4.4	7.1	7.3	7
6.4	4.1	6.8	7.1	7.2
6.1	5.1	6.4	6.8	7.3
6.5	5.8	6.1	6.4	7.1
7.7	5.9	6.5	6.1	6.8
7.9	5.4	7.7	6.5	6.4
7.5	5.5	7.9	7.7	6.1
6.9	4.8	7.5	7.9	6.5
6.6	3.2	6.9	7.5	7.7
6.9	2.7	6.6	6.9	7.9

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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57553&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]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57553&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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 2.27326564125142 + 0.0272063663525248`X(t)`[t] + 1.21401509190151`Y(t-1)`[t] -0.67019074567934`Y(t-2)`[t] + 0.196910902114001`Y(t-4) `[t] -0.0109050644084100t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  2.27326564125142 +  0.0272063663525248`X(t)`[t] +  1.21401509190151`Y(t-1)`[t] -0.67019074567934`Y(t-2)`[t] +  0.196910902114001`Y(t-4)
`[t] -0.0109050644084100t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57553&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  2.27326564125142 +  0.0272063663525248`X(t)`[t] +  1.21401509190151`Y(t-1)`[t] -0.67019074567934`Y(t-2)`[t] +  0.196910902114001`Y(t-4)
`[t] -0.0109050644084100t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57553&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)[t] = + 2.27326564125142 + 0.0272063663525248`X(t)`[t] + 1.21401509190151`Y(t-1)`[t] -0.67019074567934`Y(t-2)`[t] + 0.196910902114001`Y(t-4) `[t] -0.0109050644084100t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.273265641251421.0619352.14070.03720.0186
`X(t)`0.02720636635252480.0412350.65980.5124180.256209
`Y(t-1)`1.214015091901510.11385110.663200
`Y(t-2)`-0.670190745679340.11649-5.75321e-060
`Y(t-4) `0.1969109021140010.0884352.22660.0305080.015254
t-0.01090506440841000.003926-2.77740.0076930.003847

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 2.27326564125142 & 1.061935 & 2.1407 & 0.0372 & 0.0186 \tabularnewline
`X(t)` & 0.0272063663525248 & 0.041235 & 0.6598 & 0.512418 & 0.256209 \tabularnewline
`Y(t-1)` & 1.21401509190151 & 0.113851 & 10.6632 & 0 & 0 \tabularnewline
`Y(t-2)` & -0.67019074567934 & 0.11649 & -5.7532 & 1e-06 & 0 \tabularnewline
`Y(t-4)
` & 0.196910902114001 & 0.088435 & 2.2266 & 0.030508 & 0.015254 \tabularnewline
t & -0.0109050644084100 & 0.003926 & -2.7774 & 0.007693 & 0.003847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57553&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]2.27326564125142[/C][C]1.061935[/C][C]2.1407[/C][C]0.0372[/C][C]0.0186[/C][/ROW]
[ROW][C]`X(t)`[/C][C]0.0272063663525248[/C][C]0.041235[/C][C]0.6598[/C][C]0.512418[/C][C]0.256209[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]1.21401509190151[/C][C]0.113851[/C][C]10.6632[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]-0.67019074567934[/C][C]0.11649[/C][C]-5.7532[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-4)
`[/C][C]0.196910902114001[/C][C]0.088435[/C][C]2.2266[/C][C]0.030508[/C][C]0.015254[/C][/ROW]
[ROW][C]t[/C][C]-0.0109050644084100[/C][C]0.003926[/C][C]-2.7774[/C][C]0.007693[/C][C]0.003847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57553&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57553&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)2.273265641251421.0619352.14070.03720.0186
`X(t)`0.02720636635252480.0412350.65980.5124180.256209
`Y(t-1)`1.214015091901510.11385110.663200
`Y(t-2)`-0.670190745679340.11649-5.75321e-060
`Y(t-4) `0.1969109021140010.0884352.22660.0305080.015254
t-0.01090506440841000.003926-2.77740.0076930.003847






Multiple Linear Regression - Regression Statistics
Multiple R0.940926354067522
R-squared0.8853424037788
Adjusted R-squared0.87387664415668
F-TEST (value)77.2162013645198
F-TEST (DF numerator)5
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.264159428317082
Sum Squared Residuals3.48901017844037

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.940926354067522 \tabularnewline
R-squared & 0.8853424037788 \tabularnewline
Adjusted R-squared & 0.87387664415668 \tabularnewline
F-TEST (value) & 77.2162013645198 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 50 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.264159428317082 \tabularnewline
Sum Squared Residuals & 3.48901017844037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57553&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.940926354067522[/C][/ROW]
[ROW][C]R-squared[/C][C]0.8853424037788[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.87387664415668[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]77.2162013645198[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]50[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.264159428317082[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3.48901017844037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57553&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57553&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 R0.940926354067522
R-squared0.8853424037788
Adjusted R-squared0.87387664415668
F-TEST (value)77.2162013645198
F-TEST (DF numerator)5
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.264159428317082
Sum Squared Residuals3.48901017844037






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.27.62269288502648-0.422692885026483
27.47.75316225283869-0.353162252838691
38.88.090382616092630.709617383907366
49.39.48481117288402-0.184811172884023
59.39.078132066570590.221867933429413
68.78.79599953946258-0.0959995394625806
78.28.32147813633185-0.121478136331853
88.38.193252877896280.106747122103719
98.58.64156533215295-0.141565332152948
108.68.69645958019426-0.0964595801942612
118.58.5880656079594-0.0880656079593962
128.28.3975485034633-0.197548503463293
138.18.12611952983991-0.0261195298399093
147.98.22544381669756-0.325443816697561
158.68.019063718265380.580936281734617
168.78.9383753699602-0.238375369960204
178.78.562767839190260.137232160809741
188.58.42369642670910.0763035732909052
198.48.310546612035440.0894533879645642
208.58.34557246096040.154427539039594
218.78.523087980310080.176912019689919
228.78.648584679291240.0514153207087615
238.68.467626555724050.132373444275954
248.58.36589361887790.134106381122106
258.38.34542957354057-0.0454295735405719
2688.15057865541404-0.150578655414038
278.27.887095485724390.312904514275611
288.18.29763893655343-0.197638936553430
298.17.981029486855190.118970513144808
3087.972628953110010.0273710468899900
317.97.887866469840010.0121335301599935
327.97.805608517233230.094391482766768
3387.850839980851750.149160019148254
3487.944365972057340.0556340279426604
357.97.84675074286960.0532492571304045
3687.714444169271030.285555830728965
377.77.89804759565585-0.198047595655847
387.27.45591892910905-0.25591892910905
397.57.019372452242290.480627547757714
407.37.72473774182015-0.424737741820147
4177.21634043796394-0.216340437963938
4276.898578637145960.101421362854038
4377.16684852352232-0.166848523522322
447.27.122002551961620.0779974480383834
457.37.30570978184032-0.00570978184031929
467.17.28488871412144-0.184888714121445
476.86.98592664984682-0.185926649846818
486.46.77607547752087-0.376075477520865
496.16.52751905661958-0.427519056619578
506.56.400148038936420.099851961063583
517.77.019553600993470.680446399006533
527.98.10502280457327-0.205022804573272
537.57.476339229731010.0236607702689912
546.96.90550988382496-0.00550988382495796
556.66.62703495892014-0.0270349589201394
566.96.679818811595420.220181188404584

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.2 & 7.62269288502648 & -0.422692885026483 \tabularnewline
2 & 7.4 & 7.75316225283869 & -0.353162252838691 \tabularnewline
3 & 8.8 & 8.09038261609263 & 0.709617383907366 \tabularnewline
4 & 9.3 & 9.48481117288402 & -0.184811172884023 \tabularnewline
5 & 9.3 & 9.07813206657059 & 0.221867933429413 \tabularnewline
6 & 8.7 & 8.79599953946258 & -0.0959995394625806 \tabularnewline
7 & 8.2 & 8.32147813633185 & -0.121478136331853 \tabularnewline
8 & 8.3 & 8.19325287789628 & 0.106747122103719 \tabularnewline
9 & 8.5 & 8.64156533215295 & -0.141565332152948 \tabularnewline
10 & 8.6 & 8.69645958019426 & -0.0964595801942612 \tabularnewline
11 & 8.5 & 8.5880656079594 & -0.0880656079593962 \tabularnewline
12 & 8.2 & 8.3975485034633 & -0.197548503463293 \tabularnewline
13 & 8.1 & 8.12611952983991 & -0.0261195298399093 \tabularnewline
14 & 7.9 & 8.22544381669756 & -0.325443816697561 \tabularnewline
15 & 8.6 & 8.01906371826538 & 0.580936281734617 \tabularnewline
16 & 8.7 & 8.9383753699602 & -0.238375369960204 \tabularnewline
17 & 8.7 & 8.56276783919026 & 0.137232160809741 \tabularnewline
18 & 8.5 & 8.4236964267091 & 0.0763035732909052 \tabularnewline
19 & 8.4 & 8.31054661203544 & 0.0894533879645642 \tabularnewline
20 & 8.5 & 8.3455724609604 & 0.154427539039594 \tabularnewline
21 & 8.7 & 8.52308798031008 & 0.176912019689919 \tabularnewline
22 & 8.7 & 8.64858467929124 & 0.0514153207087615 \tabularnewline
23 & 8.6 & 8.46762655572405 & 0.132373444275954 \tabularnewline
24 & 8.5 & 8.3658936188779 & 0.134106381122106 \tabularnewline
25 & 8.3 & 8.34542957354057 & -0.0454295735405719 \tabularnewline
26 & 8 & 8.15057865541404 & -0.150578655414038 \tabularnewline
27 & 8.2 & 7.88709548572439 & 0.312904514275611 \tabularnewline
28 & 8.1 & 8.29763893655343 & -0.197638936553430 \tabularnewline
29 & 8.1 & 7.98102948685519 & 0.118970513144808 \tabularnewline
30 & 8 & 7.97262895311001 & 0.0273710468899900 \tabularnewline
31 & 7.9 & 7.88786646984001 & 0.0121335301599935 \tabularnewline
32 & 7.9 & 7.80560851723323 & 0.094391482766768 \tabularnewline
33 & 8 & 7.85083998085175 & 0.149160019148254 \tabularnewline
34 & 8 & 7.94436597205734 & 0.0556340279426604 \tabularnewline
35 & 7.9 & 7.8467507428696 & 0.0532492571304045 \tabularnewline
36 & 8 & 7.71444416927103 & 0.285555830728965 \tabularnewline
37 & 7.7 & 7.89804759565585 & -0.198047595655847 \tabularnewline
38 & 7.2 & 7.45591892910905 & -0.25591892910905 \tabularnewline
39 & 7.5 & 7.01937245224229 & 0.480627547757714 \tabularnewline
40 & 7.3 & 7.72473774182015 & -0.424737741820147 \tabularnewline
41 & 7 & 7.21634043796394 & -0.216340437963938 \tabularnewline
42 & 7 & 6.89857863714596 & 0.101421362854038 \tabularnewline
43 & 7 & 7.16684852352232 & -0.166848523522322 \tabularnewline
44 & 7.2 & 7.12200255196162 & 0.0779974480383834 \tabularnewline
45 & 7.3 & 7.30570978184032 & -0.00570978184031929 \tabularnewline
46 & 7.1 & 7.28488871412144 & -0.184888714121445 \tabularnewline
47 & 6.8 & 6.98592664984682 & -0.185926649846818 \tabularnewline
48 & 6.4 & 6.77607547752087 & -0.376075477520865 \tabularnewline
49 & 6.1 & 6.52751905661958 & -0.427519056619578 \tabularnewline
50 & 6.5 & 6.40014803893642 & 0.099851961063583 \tabularnewline
51 & 7.7 & 7.01955360099347 & 0.680446399006533 \tabularnewline
52 & 7.9 & 8.10502280457327 & -0.205022804573272 \tabularnewline
53 & 7.5 & 7.47633922973101 & 0.0236607702689912 \tabularnewline
54 & 6.9 & 6.90550988382496 & -0.00550988382495796 \tabularnewline
55 & 6.6 & 6.62703495892014 & -0.0270349589201394 \tabularnewline
56 & 6.9 & 6.67981881159542 & 0.220181188404584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57553&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]7.2[/C][C]7.62269288502648[/C][C]-0.422692885026483[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]7.75316225283869[/C][C]-0.353162252838691[/C][/ROW]
[ROW][C]3[/C][C]8.8[/C][C]8.09038261609263[/C][C]0.709617383907366[/C][/ROW]
[ROW][C]4[/C][C]9.3[/C][C]9.48481117288402[/C][C]-0.184811172884023[/C][/ROW]
[ROW][C]5[/C][C]9.3[/C][C]9.07813206657059[/C][C]0.221867933429413[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.79599953946258[/C][C]-0.0959995394625806[/C][/ROW]
[ROW][C]7[/C][C]8.2[/C][C]8.32147813633185[/C][C]-0.121478136331853[/C][/ROW]
[ROW][C]8[/C][C]8.3[/C][C]8.19325287789628[/C][C]0.106747122103719[/C][/ROW]
[ROW][C]9[/C][C]8.5[/C][C]8.64156533215295[/C][C]-0.141565332152948[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.69645958019426[/C][C]-0.0964595801942612[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.5880656079594[/C][C]-0.0880656079593962[/C][/ROW]
[ROW][C]12[/C][C]8.2[/C][C]8.3975485034633[/C][C]-0.197548503463293[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]8.12611952983991[/C][C]-0.0261195298399093[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.22544381669756[/C][C]-0.325443816697561[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.01906371826538[/C][C]0.580936281734617[/C][/ROW]
[ROW][C]16[/C][C]8.7[/C][C]8.9383753699602[/C][C]-0.238375369960204[/C][/ROW]
[ROW][C]17[/C][C]8.7[/C][C]8.56276783919026[/C][C]0.137232160809741[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.4236964267091[/C][C]0.0763035732909052[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.31054661203544[/C][C]0.0894533879645642[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.3455724609604[/C][C]0.154427539039594[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.52308798031008[/C][C]0.176912019689919[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]8.64858467929124[/C][C]0.0514153207087615[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.46762655572405[/C][C]0.132373444275954[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.3658936188779[/C][C]0.134106381122106[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.34542957354057[/C][C]-0.0454295735405719[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.15057865541404[/C][C]-0.150578655414038[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]7.88709548572439[/C][C]0.312904514275611[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]8.29763893655343[/C][C]-0.197638936553430[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]7.98102948685519[/C][C]0.118970513144808[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.97262895311001[/C][C]0.0273710468899900[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]7.88786646984001[/C][C]0.0121335301599935[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]7.80560851723323[/C][C]0.094391482766768[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.85083998085175[/C][C]0.149160019148254[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.94436597205734[/C][C]0.0556340279426604[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.8467507428696[/C][C]0.0532492571304045[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.71444416927103[/C][C]0.285555830728965[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]7.89804759565585[/C][C]-0.198047595655847[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.45591892910905[/C][C]-0.25591892910905[/C][/ROW]
[ROW][C]39[/C][C]7.5[/C][C]7.01937245224229[/C][C]0.480627547757714[/C][/ROW]
[ROW][C]40[/C][C]7.3[/C][C]7.72473774182015[/C][C]-0.424737741820147[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.21634043796394[/C][C]-0.216340437963938[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.89857863714596[/C][C]0.101421362854038[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]7.16684852352232[/C][C]-0.166848523522322[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.12200255196162[/C][C]0.0779974480383834[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.30570978184032[/C][C]-0.00570978184031929[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.28488871412144[/C][C]-0.184888714121445[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.98592664984682[/C][C]-0.185926649846818[/C][/ROW]
[ROW][C]48[/C][C]6.4[/C][C]6.77607547752087[/C][C]-0.376075477520865[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.52751905661958[/C][C]-0.427519056619578[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.40014803893642[/C][C]0.099851961063583[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.01955360099347[/C][C]0.680446399006533[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]8.10502280457327[/C][C]-0.205022804573272[/C][/ROW]
[ROW][C]53[/C][C]7.5[/C][C]7.47633922973101[/C][C]0.0236607702689912[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.90550988382496[/C][C]-0.00550988382495796[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.62703495892014[/C][C]-0.0270349589201394[/C][/ROW]
[ROW][C]56[/C][C]6.9[/C][C]6.67981881159542[/C][C]0.220181188404584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57553&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57553&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
17.27.62269288502648-0.422692885026483
27.47.75316225283869-0.353162252838691
38.88.090382616092630.709617383907366
49.39.48481117288402-0.184811172884023
59.39.078132066570590.221867933429413
68.78.79599953946258-0.0959995394625806
78.28.32147813633185-0.121478136331853
88.38.193252877896280.106747122103719
98.58.64156533215295-0.141565332152948
108.68.69645958019426-0.0964595801942612
118.58.5880656079594-0.0880656079593962
128.28.3975485034633-0.197548503463293
138.18.12611952983991-0.0261195298399093
147.98.22544381669756-0.325443816697561
158.68.019063718265380.580936281734617
168.78.9383753699602-0.238375369960204
178.78.562767839190260.137232160809741
188.58.42369642670910.0763035732909052
198.48.310546612035440.0894533879645642
208.58.34557246096040.154427539039594
218.78.523087980310080.176912019689919
228.78.648584679291240.0514153207087615
238.68.467626555724050.132373444275954
248.58.36589361887790.134106381122106
258.38.34542957354057-0.0454295735405719
2688.15057865541404-0.150578655414038
278.27.887095485724390.312904514275611
288.18.29763893655343-0.197638936553430
298.17.981029486855190.118970513144808
3087.972628953110010.0273710468899900
317.97.887866469840010.0121335301599935
327.97.805608517233230.094391482766768
3387.850839980851750.149160019148254
3487.944365972057340.0556340279426604
357.97.84675074286960.0532492571304045
3687.714444169271030.285555830728965
377.77.89804759565585-0.198047595655847
387.27.45591892910905-0.25591892910905
397.57.019372452242290.480627547757714
407.37.72473774182015-0.424737741820147
4177.21634043796394-0.216340437963938
4276.898578637145960.101421362854038
4377.16684852352232-0.166848523522322
447.27.122002551961620.0779974480383834
457.37.30570978184032-0.00570978184031929
467.17.28488871412144-0.184888714121445
476.86.98592664984682-0.185926649846818
486.46.77607547752087-0.376075477520865
496.16.52751905661958-0.427519056619578
506.56.400148038936420.099851961063583
517.77.019553600993470.680446399006533
527.98.10502280457327-0.205022804573272
537.57.476339229731010.0236607702689912
546.96.90550988382496-0.00550988382495796
556.66.62703495892014-0.0270349589201394
566.96.679818811595420.220181188404584






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.8384708858502430.3230582282995150.161529114149757
100.864650157821210.2706996843575790.135349842178789
110.8393258880534280.3213482238931440.160674111946572
120.902515853573710.1949682928525800.097484146426290
130.862578532056620.2748429358867620.137421467943381
140.8732644780818110.2534710438363780.126735521918189
150.9509592565292240.09808148694155270.0490407434707764
160.938805574395880.1223888512082400.0611944256041202
170.9112086540923250.1775826918153500.0887913459076752
180.9012668502811670.1974662994376650.0987331497188325
190.855233907582160.289532184835680.14476609241784
200.8062870236919560.3874259526160880.193712976308044
210.7523629157871650.495274168425670.247637084212835
220.6764482736470450.647103452705910.323551726352955
230.609291993881640.7814160122367210.390708006118361
240.5293280160288450.941343967942310.470671983971155
250.4613118622450710.9226237244901420.538688137754929
260.4766207706342170.9532415412684350.523379229365783
270.4206140413168630.8412280826337270.579385958683137
280.4706290541853450.941258108370690.529370945814655
290.3974950991473120.7949901982946230.602504900852688
300.3399449400722460.6798898801444920.660055059927754
310.2750820345455920.5501640690911840.724917965454408
320.2108122307922770.4216244615845550.789187769207723
330.1632846840547040.3265693681094090.836715315945296
340.1222975508511570.2445951017023130.877702449148843
350.09253324978921950.1850664995784390.90746675021078
360.1461596368457760.2923192736915530.853840363154224
370.1432090880501920.2864181761003850.856790911949807
380.1367624139541930.2735248279083850.863237586045807
390.6948245125188960.6103509749622070.305175487481104
400.7042882058924270.5914235882151460.295711794107573
410.6626234288492570.6747531423014850.337376571150743
420.615930669047540.768138661904920.38406933095246
430.5741109924672960.8517780150654080.425889007532704
440.5252348612748740.9495302774502520.474765138725126
450.3985627968572610.7971255937145220.601437203142739
460.2885478423929290.5770956847858580.711452157607071
470.4363850162682230.8727700325364460.563614983731777

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 & 0.838470885850243 & 0.323058228299515 & 0.161529114149757 \tabularnewline
10 & 0.86465015782121 & 0.270699684357579 & 0.135349842178789 \tabularnewline
11 & 0.839325888053428 & 0.321348223893144 & 0.160674111946572 \tabularnewline
12 & 0.90251585357371 & 0.194968292852580 & 0.097484146426290 \tabularnewline
13 & 0.86257853205662 & 0.274842935886762 & 0.137421467943381 \tabularnewline
14 & 0.873264478081811 & 0.253471043836378 & 0.126735521918189 \tabularnewline
15 & 0.950959256529224 & 0.0980814869415527 & 0.0490407434707764 \tabularnewline
16 & 0.93880557439588 & 0.122388851208240 & 0.0611944256041202 \tabularnewline
17 & 0.911208654092325 & 0.177582691815350 & 0.0887913459076752 \tabularnewline
18 & 0.901266850281167 & 0.197466299437665 & 0.0987331497188325 \tabularnewline
19 & 0.85523390758216 & 0.28953218483568 & 0.14476609241784 \tabularnewline
20 & 0.806287023691956 & 0.387425952616088 & 0.193712976308044 \tabularnewline
21 & 0.752362915787165 & 0.49527416842567 & 0.247637084212835 \tabularnewline
22 & 0.676448273647045 & 0.64710345270591 & 0.323551726352955 \tabularnewline
23 & 0.60929199388164 & 0.781416012236721 & 0.390708006118361 \tabularnewline
24 & 0.529328016028845 & 0.94134396794231 & 0.470671983971155 \tabularnewline
25 & 0.461311862245071 & 0.922623724490142 & 0.538688137754929 \tabularnewline
26 & 0.476620770634217 & 0.953241541268435 & 0.523379229365783 \tabularnewline
27 & 0.420614041316863 & 0.841228082633727 & 0.579385958683137 \tabularnewline
28 & 0.470629054185345 & 0.94125810837069 & 0.529370945814655 \tabularnewline
29 & 0.397495099147312 & 0.794990198294623 & 0.602504900852688 \tabularnewline
30 & 0.339944940072246 & 0.679889880144492 & 0.660055059927754 \tabularnewline
31 & 0.275082034545592 & 0.550164069091184 & 0.724917965454408 \tabularnewline
32 & 0.210812230792277 & 0.421624461584555 & 0.789187769207723 \tabularnewline
33 & 0.163284684054704 & 0.326569368109409 & 0.836715315945296 \tabularnewline
34 & 0.122297550851157 & 0.244595101702313 & 0.877702449148843 \tabularnewline
35 & 0.0925332497892195 & 0.185066499578439 & 0.90746675021078 \tabularnewline
36 & 0.146159636845776 & 0.292319273691553 & 0.853840363154224 \tabularnewline
37 & 0.143209088050192 & 0.286418176100385 & 0.856790911949807 \tabularnewline
38 & 0.136762413954193 & 0.273524827908385 & 0.863237586045807 \tabularnewline
39 & 0.694824512518896 & 0.610350974962207 & 0.305175487481104 \tabularnewline
40 & 0.704288205892427 & 0.591423588215146 & 0.295711794107573 \tabularnewline
41 & 0.662623428849257 & 0.674753142301485 & 0.337376571150743 \tabularnewline
42 & 0.61593066904754 & 0.76813866190492 & 0.38406933095246 \tabularnewline
43 & 0.574110992467296 & 0.851778015065408 & 0.425889007532704 \tabularnewline
44 & 0.525234861274874 & 0.949530277450252 & 0.474765138725126 \tabularnewline
45 & 0.398562796857261 & 0.797125593714522 & 0.601437203142739 \tabularnewline
46 & 0.288547842392929 & 0.577095684785858 & 0.711452157607071 \tabularnewline
47 & 0.436385016268223 & 0.872770032536446 & 0.563614983731777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57553&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]9[/C][C]0.838470885850243[/C][C]0.323058228299515[/C][C]0.161529114149757[/C][/ROW]
[ROW][C]10[/C][C]0.86465015782121[/C][C]0.270699684357579[/C][C]0.135349842178789[/C][/ROW]
[ROW][C]11[/C][C]0.839325888053428[/C][C]0.321348223893144[/C][C]0.160674111946572[/C][/ROW]
[ROW][C]12[/C][C]0.90251585357371[/C][C]0.194968292852580[/C][C]0.097484146426290[/C][/ROW]
[ROW][C]13[/C][C]0.86257853205662[/C][C]0.274842935886762[/C][C]0.137421467943381[/C][/ROW]
[ROW][C]14[/C][C]0.873264478081811[/C][C]0.253471043836378[/C][C]0.126735521918189[/C][/ROW]
[ROW][C]15[/C][C]0.950959256529224[/C][C]0.0980814869415527[/C][C]0.0490407434707764[/C][/ROW]
[ROW][C]16[/C][C]0.93880557439588[/C][C]0.122388851208240[/C][C]0.0611944256041202[/C][/ROW]
[ROW][C]17[/C][C]0.911208654092325[/C][C]0.177582691815350[/C][C]0.0887913459076752[/C][/ROW]
[ROW][C]18[/C][C]0.901266850281167[/C][C]0.197466299437665[/C][C]0.0987331497188325[/C][/ROW]
[ROW][C]19[/C][C]0.85523390758216[/C][C]0.28953218483568[/C][C]0.14476609241784[/C][/ROW]
[ROW][C]20[/C][C]0.806287023691956[/C][C]0.387425952616088[/C][C]0.193712976308044[/C][/ROW]
[ROW][C]21[/C][C]0.752362915787165[/C][C]0.49527416842567[/C][C]0.247637084212835[/C][/ROW]
[ROW][C]22[/C][C]0.676448273647045[/C][C]0.64710345270591[/C][C]0.323551726352955[/C][/ROW]
[ROW][C]23[/C][C]0.60929199388164[/C][C]0.781416012236721[/C][C]0.390708006118361[/C][/ROW]
[ROW][C]24[/C][C]0.529328016028845[/C][C]0.94134396794231[/C][C]0.470671983971155[/C][/ROW]
[ROW][C]25[/C][C]0.461311862245071[/C][C]0.922623724490142[/C][C]0.538688137754929[/C][/ROW]
[ROW][C]26[/C][C]0.476620770634217[/C][C]0.953241541268435[/C][C]0.523379229365783[/C][/ROW]
[ROW][C]27[/C][C]0.420614041316863[/C][C]0.841228082633727[/C][C]0.579385958683137[/C][/ROW]
[ROW][C]28[/C][C]0.470629054185345[/C][C]0.94125810837069[/C][C]0.529370945814655[/C][/ROW]
[ROW][C]29[/C][C]0.397495099147312[/C][C]0.794990198294623[/C][C]0.602504900852688[/C][/ROW]
[ROW][C]30[/C][C]0.339944940072246[/C][C]0.679889880144492[/C][C]0.660055059927754[/C][/ROW]
[ROW][C]31[/C][C]0.275082034545592[/C][C]0.550164069091184[/C][C]0.724917965454408[/C][/ROW]
[ROW][C]32[/C][C]0.210812230792277[/C][C]0.421624461584555[/C][C]0.789187769207723[/C][/ROW]
[ROW][C]33[/C][C]0.163284684054704[/C][C]0.326569368109409[/C][C]0.836715315945296[/C][/ROW]
[ROW][C]34[/C][C]0.122297550851157[/C][C]0.244595101702313[/C][C]0.877702449148843[/C][/ROW]
[ROW][C]35[/C][C]0.0925332497892195[/C][C]0.185066499578439[/C][C]0.90746675021078[/C][/ROW]
[ROW][C]36[/C][C]0.146159636845776[/C][C]0.292319273691553[/C][C]0.853840363154224[/C][/ROW]
[ROW][C]37[/C][C]0.143209088050192[/C][C]0.286418176100385[/C][C]0.856790911949807[/C][/ROW]
[ROW][C]38[/C][C]0.136762413954193[/C][C]0.273524827908385[/C][C]0.863237586045807[/C][/ROW]
[ROW][C]39[/C][C]0.694824512518896[/C][C]0.610350974962207[/C][C]0.305175487481104[/C][/ROW]
[ROW][C]40[/C][C]0.704288205892427[/C][C]0.591423588215146[/C][C]0.295711794107573[/C][/ROW]
[ROW][C]41[/C][C]0.662623428849257[/C][C]0.674753142301485[/C][C]0.337376571150743[/C][/ROW]
[ROW][C]42[/C][C]0.61593066904754[/C][C]0.76813866190492[/C][C]0.38406933095246[/C][/ROW]
[ROW][C]43[/C][C]0.574110992467296[/C][C]0.851778015065408[/C][C]0.425889007532704[/C][/ROW]
[ROW][C]44[/C][C]0.525234861274874[/C][C]0.949530277450252[/C][C]0.474765138725126[/C][/ROW]
[ROW][C]45[/C][C]0.398562796857261[/C][C]0.797125593714522[/C][C]0.601437203142739[/C][/ROW]
[ROW][C]46[/C][C]0.288547842392929[/C][C]0.577095684785858[/C][C]0.711452157607071[/C][/ROW]
[ROW][C]47[/C][C]0.436385016268223[/C][C]0.872770032536446[/C][C]0.563614983731777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57553&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57553&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
90.8384708858502430.3230582282995150.161529114149757
100.864650157821210.2706996843575790.135349842178789
110.8393258880534280.3213482238931440.160674111946572
120.902515853573710.1949682928525800.097484146426290
130.862578532056620.2748429358867620.137421467943381
140.8732644780818110.2534710438363780.126735521918189
150.9509592565292240.09808148694155270.0490407434707764
160.938805574395880.1223888512082400.0611944256041202
170.9112086540923250.1775826918153500.0887913459076752
180.9012668502811670.1974662994376650.0987331497188325
190.855233907582160.289532184835680.14476609241784
200.8062870236919560.3874259526160880.193712976308044
210.7523629157871650.495274168425670.247637084212835
220.6764482736470450.647103452705910.323551726352955
230.609291993881640.7814160122367210.390708006118361
240.5293280160288450.941343967942310.470671983971155
250.4613118622450710.9226237244901420.538688137754929
260.4766207706342170.9532415412684350.523379229365783
270.4206140413168630.8412280826337270.579385958683137
280.4706290541853450.941258108370690.529370945814655
290.3974950991473120.7949901982946230.602504900852688
300.3399449400722460.6798898801444920.660055059927754
310.2750820345455920.5501640690911840.724917965454408
320.2108122307922770.4216244615845550.789187769207723
330.1632846840547040.3265693681094090.836715315945296
340.1222975508511570.2445951017023130.877702449148843
350.09253324978921950.1850664995784390.90746675021078
360.1461596368457760.2923192736915530.853840363154224
370.1432090880501920.2864181761003850.856790911949807
380.1367624139541930.2735248279083850.863237586045807
390.6948245125188960.6103509749622070.305175487481104
400.7042882058924270.5914235882151460.295711794107573
410.6626234288492570.6747531423014850.337376571150743
420.615930669047540.768138661904920.38406933095246
430.5741109924672960.8517780150654080.425889007532704
440.5252348612748740.9495302774502520.474765138725126
450.3985627968572610.7971255937145220.601437203142739
460.2885478423929290.5770956847858580.711452157607071
470.4363850162682230.8727700325364460.563614983731777






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level10.0256410256410256OK

\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 & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 1 & 0.0256410256410256 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57553&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]1[/C][C]0.0256410256410256[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57553&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57553&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 level00OK
5% type I error level00OK
10% type I error level10.0256410256410256OK


Figures (Output of Computation)

Figure 1
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 2
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 3
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 4
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 5
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 6
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 7
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 8
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 9
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 10
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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')
}