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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 24 Nov 2009 01:31:24 -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/24/t1259051575mne92m0vtycv5cg.htm/, Retrieved Fri, 28 Nov 2025 18:31:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58958, Retrieved Fri, 28 Nov 2025 18:31:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact746

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [4 lag ] [2009-11-19 20:53:48] [ba905ddf7cdf9ecb063c35348c4dab2e]
-    D      [Multiple Regression] [review 7] [2009-11-23 20:50:02] [309ee52d0058ff0a6f7eec15e07b2d9f]
-   PD          [Multiple Regression] [review 7] [2009-11-24 08:31:24] [6198946fb53eb5eb18db46bb758f7fde] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,1	0	6,2	6,3
6,3	0	6,1	6,2
6,5	0	6,3	6,1
6,6	0	6,5	6,3
6,5	0	6,6	6,5
6,2	0	6,5	6,6
6,2	0	6,2	6,5
5,9	0	6,2	6,2
6,1	0	5,9	6,2
6,1	0	6,1	5,9
6,1	0	6,1	6,1
6,1	0	6,1	6,1
6,1	0	6,1	6,1
6,4	0	6,1	6,1
6,7	0	6,4	6,1
6,9	0	6,7	6,4
7	0	6,9	6,7
7	0	7	6,9
6,8	0	7	7
6,4	0	6,8	7
5,9	0	6,4	6,8
5,5	0	5,9	6,4
5,5	0	5,5	5,9
5,6	0	5,5	5,5
5,8	0	5,6	5,5
5,9	0	5,8	5,6
6,1	0	5,9	5,8
6,1	0	6,1	5,9
6	0	6,1	6,1
6	0	6	6,1
5,9	0	6	6
5,5	0	5,9	6
5,6	0	5,5	5,9
5,4	0	5,6	5,5
5,2	0	5,4	5,6
5,2	0	5,2	5,4
5,2	0	5,2	5,2
5,5	0	5,2	5,2
5,8	1	5,5	5,2
5,8	1	5,8	5,5
5,5	1	5,8	5,8
5,3	1	5,5	5,8
5,1	1	5,3	5,5
5,2	1	5,1	5,3
5,8	1	5,2	5,1
5,8	1	5,8	5,2
5,5	1	5,8	5,8
5	1	5,5	5,8
4,9	1	5	5,5
5,3	1	4,9	5
6,1	1	5,3	4,9
6,5	1	6,1	5,3
6,8	1	6,5	6,1
6,6	1	6,8	6,5
6,4	1	6,6	6,8
6,4	1	6,4	6,6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time15 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 & 15 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58958&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]15 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=58958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58958&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 time15 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
y[t] = + 0.989097746251875 + 0.00487608435585063x[t] + 1.40073692274530`y-1`[t] -0.574367374215303`y-2`[t] + 0.0852761437421179M1[t] + 0.289523775607878M2[t] + 0.286041328110218M3[t] + 0.0727959225051778M4[t] + 0.0651493773256329M5[t] + 0.0352599174579693M6[t] + 0.0815601084452934M7[t] -0.00106378547321905M8[t] + 0.297128142922298M9[t] -0.134853023618768M10[t] + 0.00937862150184482M11[t] -0.00168436928728821t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  0.989097746251875 +  0.00487608435585063x[t] +  1.40073692274530`y-1`[t] -0.574367374215303`y-2`[t] +  0.0852761437421179M1[t] +  0.289523775607878M2[t] +  0.286041328110218M3[t] +  0.0727959225051778M4[t] +  0.0651493773256329M5[t] +  0.0352599174579693M6[t] +  0.0815601084452934M7[t] -0.00106378547321905M8[t] +  0.297128142922298M9[t] -0.134853023618768M10[t] +  0.00937862150184482M11[t] -0.00168436928728821t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58958&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  0.989097746251875 +  0.00487608435585063x[t] +  1.40073692274530`y-1`[t] -0.574367374215303`y-2`[t] +  0.0852761437421179M1[t] +  0.289523775607878M2[t] +  0.286041328110218M3[t] +  0.0727959225051778M4[t] +  0.0651493773256329M5[t] +  0.0352599174579693M6[t] +  0.0815601084452934M7[t] -0.00106378547321905M8[t] +  0.297128142922298M9[t] -0.134853023618768M10[t] +  0.00937862150184482M11[t] -0.00168436928728821t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58958&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 0.989097746251875 + 0.00487608435585063x[t] + 1.40073692274530`y-1`[t] -0.574367374215303`y-2`[t] + 0.0852761437421179M1[t] + 0.289523775607878M2[t] + 0.286041328110218M3[t] + 0.0727959225051778M4[t] + 0.0651493773256329M5[t] + 0.0352599174579693M6[t] + 0.0815601084452934M7[t] -0.00106378547321905M8[t] + 0.297128142922298M9[t] -0.134853023618768M10[t] + 0.00937862150184482M11[t] -0.00168436928728821t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.9890977462518750.4613442.14390.0381690.019084
x0.004876084355850630.0926190.05260.9582760.479138
`y-1`1.400736922745300.13484510.387700
`y-2`-0.5743673742153030.141296-4.0650.0002190.000109
M10.08527614374211790.1237460.68910.4947260.247363
M20.2895237756078780.1248832.31840.0256260.012813
M30.2860413281102180.1348022.12190.0400870.020043
M40.07279592250517780.1418420.51320.6106210.30531
M50.06514937732563290.1366530.47670.6361350.318067
M60.03525991745796930.1353790.26050.795850.397925
M70.08156010844529340.1333620.61160.5442820.272141
M8-0.001063785473219050.130128-0.00820.9935180.496759
M90.2971281429222980.1320392.25030.0299980.014999
M10-0.1348530236187680.133602-1.00940.3188660.159433
M110.009378621501844820.1302780.0720.9429690.471485
t-0.001684369287288210.002882-0.58440.5622640.281132

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 0.989097746251875 & 0.461344 & 2.1439 & 0.038169 & 0.019084 \tabularnewline
x & 0.00487608435585063 & 0.092619 & 0.0526 & 0.958276 & 0.479138 \tabularnewline
`y-1` & 1.40073692274530 & 0.134845 & 10.3877 & 0 & 0 \tabularnewline
`y-2` & -0.574367374215303 & 0.141296 & -4.065 & 0.000219 & 0.000109 \tabularnewline
M1 & 0.0852761437421179 & 0.123746 & 0.6891 & 0.494726 & 0.247363 \tabularnewline
M2 & 0.289523775607878 & 0.124883 & 2.3184 & 0.025626 & 0.012813 \tabularnewline
M3 & 0.286041328110218 & 0.134802 & 2.1219 & 0.040087 & 0.020043 \tabularnewline
M4 & 0.0727959225051778 & 0.141842 & 0.5132 & 0.610621 & 0.30531 \tabularnewline
M5 & 0.0651493773256329 & 0.136653 & 0.4767 & 0.636135 & 0.318067 \tabularnewline
M6 & 0.0352599174579693 & 0.135379 & 0.2605 & 0.79585 & 0.397925 \tabularnewline
M7 & 0.0815601084452934 & 0.133362 & 0.6116 & 0.544282 & 0.272141 \tabularnewline
M8 & -0.00106378547321905 & 0.130128 & -0.0082 & 0.993518 & 0.496759 \tabularnewline
M9 & 0.297128142922298 & 0.132039 & 2.2503 & 0.029998 & 0.014999 \tabularnewline
M10 & -0.134853023618768 & 0.133602 & -1.0094 & 0.318866 & 0.159433 \tabularnewline
M11 & 0.00937862150184482 & 0.130278 & 0.072 & 0.942969 & 0.471485 \tabularnewline
t & -0.00168436928728821 & 0.002882 & -0.5844 & 0.562264 & 0.281132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58958&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]0.989097746251875[/C][C]0.461344[/C][C]2.1439[/C][C]0.038169[/C][C]0.019084[/C][/ROW]
[ROW][C]x[/C][C]0.00487608435585063[/C][C]0.092619[/C][C]0.0526[/C][C]0.958276[/C][C]0.479138[/C][/ROW]
[ROW][C]`y-1`[/C][C]1.40073692274530[/C][C]0.134845[/C][C]10.3877[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`y-2`[/C][C]-0.574367374215303[/C][C]0.141296[/C][C]-4.065[/C][C]0.000219[/C][C]0.000109[/C][/ROW]
[ROW][C]M1[/C][C]0.0852761437421179[/C][C]0.123746[/C][C]0.6891[/C][C]0.494726[/C][C]0.247363[/C][/ROW]
[ROW][C]M2[/C][C]0.289523775607878[/C][C]0.124883[/C][C]2.3184[/C][C]0.025626[/C][C]0.012813[/C][/ROW]
[ROW][C]M3[/C][C]0.286041328110218[/C][C]0.134802[/C][C]2.1219[/C][C]0.040087[/C][C]0.020043[/C][/ROW]
[ROW][C]M4[/C][C]0.0727959225051778[/C][C]0.141842[/C][C]0.5132[/C][C]0.610621[/C][C]0.30531[/C][/ROW]
[ROW][C]M5[/C][C]0.0651493773256329[/C][C]0.136653[/C][C]0.4767[/C][C]0.636135[/C][C]0.318067[/C][/ROW]
[ROW][C]M6[/C][C]0.0352599174579693[/C][C]0.135379[/C][C]0.2605[/C][C]0.79585[/C][C]0.397925[/C][/ROW]
[ROW][C]M7[/C][C]0.0815601084452934[/C][C]0.133362[/C][C]0.6116[/C][C]0.544282[/C][C]0.272141[/C][/ROW]
[ROW][C]M8[/C][C]-0.00106378547321905[/C][C]0.130128[/C][C]-0.0082[/C][C]0.993518[/C][C]0.496759[/C][/ROW]
[ROW][C]M9[/C][C]0.297128142922298[/C][C]0.132039[/C][C]2.2503[/C][C]0.029998[/C][C]0.014999[/C][/ROW]
[ROW][C]M10[/C][C]-0.134853023618768[/C][C]0.133602[/C][C]-1.0094[/C][C]0.318866[/C][C]0.159433[/C][/ROW]
[ROW][C]M11[/C][C]0.00937862150184482[/C][C]0.130278[/C][C]0.072[/C][C]0.942969[/C][C]0.471485[/C][/ROW]
[ROW][C]t[/C][C]-0.00168436928728821[/C][C]0.002882[/C][C]-0.5844[/C][C]0.562264[/C][C]0.281132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58958&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.9890977462518750.4613442.14390.0381690.019084
x0.004876084355850630.0926190.05260.9582760.479138
`y-1`1.400736922745300.13484510.387700
`y-2`-0.5743673742153030.141296-4.0650.0002190.000109
M10.08527614374211790.1237460.68910.4947260.247363
M20.2895237756078780.1248832.31840.0256260.012813
M30.2860413281102180.1348022.12190.0400870.020043
M40.07279592250517780.1418420.51320.6106210.30531
M50.06514937732563290.1366530.47670.6361350.318067
M60.03525991745796930.1353790.26050.795850.397925
M70.08156010844529340.1333620.61160.5442820.272141
M8-0.001063785473219050.130128-0.00820.9935180.496759
M90.2971281429222980.1320392.25030.0299980.014999
M10-0.1348530236187680.133602-1.00940.3188660.159433
M110.009378621501844820.1302780.0720.9429690.471485
t-0.001684369287288210.002882-0.58440.5622640.281132






Multiple Linear Regression - Regression Statistics
Multiple R0.956435186436456
R-squared0.914768265853738
Adjusted R-squared0.88280636554889
F-TEST (value)28.6205844185986
F-TEST (DF numerator)15
F-TEST (DF denominator)40
p-value1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.183690648242067
Sum Squared Residuals1.34969017006363

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.956435186436456 \tabularnewline
R-squared & 0.914768265853738 \tabularnewline
Adjusted R-squared & 0.88280636554889 \tabularnewline
F-TEST (value) & 28.6205844185986 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 40 \tabularnewline
p-value & 1.11022302462516e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.183690648242067 \tabularnewline
Sum Squared Residuals & 1.34969017006363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58958&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.956435186436456[/C][/ROW]
[ROW][C]R-squared[/C][C]0.914768265853738[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.88280636554889[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]28.6205844185986[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]40[/C][/ROW]
[ROW][C]p-value[/C][C]1.11022302462516e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.183690648242067[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.34969017006363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58958&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 R0.956435186436456
R-squared0.914768265853738
Adjusted R-squared0.88280636554889
F-TEST (value)28.6205844185986
F-TEST (DF numerator)15
F-TEST (DF denominator)40
p-value1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.183690648242067
Sum Squared Residuals1.34969017006363






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.16.13874398417115-0.0387439841711496
26.36.258670291896610.0413297081033868
36.56.59108759708225-0.0910875970822549
46.66.541431731895930.0585682681040732
56.56.55730103486056-0.0573010348605629
66.26.32821677600955-0.128216776009552
76.26.010048258307530.189951741692472
85.96.09805020736632-0.198050207366318
96.15.974336689650960.125663310349041
106.15.993128750636250.106871249363746
116.16.020802551626520.0791974483734817
126.16.009739560837390.0902604391626146
136.16.093331335292210.00666866470778512
146.46.295894597870690.104105402129314
156.76.71094885790933-0.0109488579093281
166.96.7439299475760.156070052424002
1776.842436205393630.157563794606366
1876.836062593670150.163937406329849
196.86.82324167794866-0.0232416779486567
206.46.4587860301938-0.0587860301937957
215.96.30987229504697-0.409872295046968
225.55.405585247532090.0944147524679146
235.55.275021441374940.224978558625058
245.65.493705400271930.10629459972807
255.85.717370867001290.0826291329987112
265.96.14264477670729-0.242644776707289
276.16.16267817735381-0.0626781773538121
286.16.17045904958901-0.0704590495890119
2966.04625466027912-0.0462546602791184
3065.874607138849640.125392861150363
315.95.9766596979712-0.0766596979712029
325.55.75227774249087-0.252277742490873
335.65.545927269922510.0540727300774864
345.45.48208237605481-0.0820823760548086
355.25.28704552991755-0.0870455299175448
365.25.110708629422410.0892913705775878
375.25.3091738787203-0.109173878720302
385.55.51173714129877-0.0117371412987739
395.85.93166748569327-0.131667485693266
405.85.96464857535994-0.164648575359936
415.55.78300744862851-0.283007448628513
425.35.33121254264997-0.0312125426499719
435.15.26799119206554-0.167991192065539
445.25.018409019153740.181590980846262
455.85.569863745379560.230136254620441
465.85.91920362577685-0.119203625776852
475.55.717130477081-0.217130477080995
4855.28584640946827-0.285846409468273
494.94.841379934815040.0586200651849557
505.35.191053192226640.108946807773362
516.15.803617881961340.296382118038661
526.56.479530695579130.0204693044208727
536.86.571000650838170.228999349161828
546.66.72990094882069-0.129900948820688
556.46.322059173707070.077940826292927
566.46.072477000795280.327522999204726

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.1 & 6.13874398417115 & -0.0387439841711496 \tabularnewline
2 & 6.3 & 6.25867029189661 & 0.0413297081033868 \tabularnewline
3 & 6.5 & 6.59108759708225 & -0.0910875970822549 \tabularnewline
4 & 6.6 & 6.54143173189593 & 0.0585682681040732 \tabularnewline
5 & 6.5 & 6.55730103486056 & -0.0573010348605629 \tabularnewline
6 & 6.2 & 6.32821677600955 & -0.128216776009552 \tabularnewline
7 & 6.2 & 6.01004825830753 & 0.189951741692472 \tabularnewline
8 & 5.9 & 6.09805020736632 & -0.198050207366318 \tabularnewline
9 & 6.1 & 5.97433668965096 & 0.125663310349041 \tabularnewline
10 & 6.1 & 5.99312875063625 & 0.106871249363746 \tabularnewline
11 & 6.1 & 6.02080255162652 & 0.0791974483734817 \tabularnewline
12 & 6.1 & 6.00973956083739 & 0.0902604391626146 \tabularnewline
13 & 6.1 & 6.09333133529221 & 0.00666866470778512 \tabularnewline
14 & 6.4 & 6.29589459787069 & 0.104105402129314 \tabularnewline
15 & 6.7 & 6.71094885790933 & -0.0109488579093281 \tabularnewline
16 & 6.9 & 6.743929947576 & 0.156070052424002 \tabularnewline
17 & 7 & 6.84243620539363 & 0.157563794606366 \tabularnewline
18 & 7 & 6.83606259367015 & 0.163937406329849 \tabularnewline
19 & 6.8 & 6.82324167794866 & -0.0232416779486567 \tabularnewline
20 & 6.4 & 6.4587860301938 & -0.0587860301937957 \tabularnewline
21 & 5.9 & 6.30987229504697 & -0.409872295046968 \tabularnewline
22 & 5.5 & 5.40558524753209 & 0.0944147524679146 \tabularnewline
23 & 5.5 & 5.27502144137494 & 0.224978558625058 \tabularnewline
24 & 5.6 & 5.49370540027193 & 0.10629459972807 \tabularnewline
25 & 5.8 & 5.71737086700129 & 0.0826291329987112 \tabularnewline
26 & 5.9 & 6.14264477670729 & -0.242644776707289 \tabularnewline
27 & 6.1 & 6.16267817735381 & -0.0626781773538121 \tabularnewline
28 & 6.1 & 6.17045904958901 & -0.0704590495890119 \tabularnewline
29 & 6 & 6.04625466027912 & -0.0462546602791184 \tabularnewline
30 & 6 & 5.87460713884964 & 0.125392861150363 \tabularnewline
31 & 5.9 & 5.9766596979712 & -0.0766596979712029 \tabularnewline
32 & 5.5 & 5.75227774249087 & -0.252277742490873 \tabularnewline
33 & 5.6 & 5.54592726992251 & 0.0540727300774864 \tabularnewline
34 & 5.4 & 5.48208237605481 & -0.0820823760548086 \tabularnewline
35 & 5.2 & 5.28704552991755 & -0.0870455299175448 \tabularnewline
36 & 5.2 & 5.11070862942241 & 0.0892913705775878 \tabularnewline
37 & 5.2 & 5.3091738787203 & -0.109173878720302 \tabularnewline
38 & 5.5 & 5.51173714129877 & -0.0117371412987739 \tabularnewline
39 & 5.8 & 5.93166748569327 & -0.131667485693266 \tabularnewline
40 & 5.8 & 5.96464857535994 & -0.164648575359936 \tabularnewline
41 & 5.5 & 5.78300744862851 & -0.283007448628513 \tabularnewline
42 & 5.3 & 5.33121254264997 & -0.0312125426499719 \tabularnewline
43 & 5.1 & 5.26799119206554 & -0.167991192065539 \tabularnewline
44 & 5.2 & 5.01840901915374 & 0.181590980846262 \tabularnewline
45 & 5.8 & 5.56986374537956 & 0.230136254620441 \tabularnewline
46 & 5.8 & 5.91920362577685 & -0.119203625776852 \tabularnewline
47 & 5.5 & 5.717130477081 & -0.217130477080995 \tabularnewline
48 & 5 & 5.28584640946827 & -0.285846409468273 \tabularnewline
49 & 4.9 & 4.84137993481504 & 0.0586200651849557 \tabularnewline
50 & 5.3 & 5.19105319222664 & 0.108946807773362 \tabularnewline
51 & 6.1 & 5.80361788196134 & 0.296382118038661 \tabularnewline
52 & 6.5 & 6.47953069557913 & 0.0204693044208727 \tabularnewline
53 & 6.8 & 6.57100065083817 & 0.228999349161828 \tabularnewline
54 & 6.6 & 6.72990094882069 & -0.129900948820688 \tabularnewline
55 & 6.4 & 6.32205917370707 & 0.077940826292927 \tabularnewline
56 & 6.4 & 6.07247700079528 & 0.327522999204726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58958&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]6.1[/C][C]6.13874398417115[/C][C]-0.0387439841711496[/C][/ROW]
[ROW][C]2[/C][C]6.3[/C][C]6.25867029189661[/C][C]0.0413297081033868[/C][/ROW]
[ROW][C]3[/C][C]6.5[/C][C]6.59108759708225[/C][C]-0.0910875970822549[/C][/ROW]
[ROW][C]4[/C][C]6.6[/C][C]6.54143173189593[/C][C]0.0585682681040732[/C][/ROW]
[ROW][C]5[/C][C]6.5[/C][C]6.55730103486056[/C][C]-0.0573010348605629[/C][/ROW]
[ROW][C]6[/C][C]6.2[/C][C]6.32821677600955[/C][C]-0.128216776009552[/C][/ROW]
[ROW][C]7[/C][C]6.2[/C][C]6.01004825830753[/C][C]0.189951741692472[/C][/ROW]
[ROW][C]8[/C][C]5.9[/C][C]6.09805020736632[/C][C]-0.198050207366318[/C][/ROW]
[ROW][C]9[/C][C]6.1[/C][C]5.97433668965096[/C][C]0.125663310349041[/C][/ROW]
[ROW][C]10[/C][C]6.1[/C][C]5.99312875063625[/C][C]0.106871249363746[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.02080255162652[/C][C]0.0791974483734817[/C][/ROW]
[ROW][C]12[/C][C]6.1[/C][C]6.00973956083739[/C][C]0.0902604391626146[/C][/ROW]
[ROW][C]13[/C][C]6.1[/C][C]6.09333133529221[/C][C]0.00666866470778512[/C][/ROW]
[ROW][C]14[/C][C]6.4[/C][C]6.29589459787069[/C][C]0.104105402129314[/C][/ROW]
[ROW][C]15[/C][C]6.7[/C][C]6.71094885790933[/C][C]-0.0109488579093281[/C][/ROW]
[ROW][C]16[/C][C]6.9[/C][C]6.743929947576[/C][C]0.156070052424002[/C][/ROW]
[ROW][C]17[/C][C]7[/C][C]6.84243620539363[/C][C]0.157563794606366[/C][/ROW]
[ROW][C]18[/C][C]7[/C][C]6.83606259367015[/C][C]0.163937406329849[/C][/ROW]
[ROW][C]19[/C][C]6.8[/C][C]6.82324167794866[/C][C]-0.0232416779486567[/C][/ROW]
[ROW][C]20[/C][C]6.4[/C][C]6.4587860301938[/C][C]-0.0587860301937957[/C][/ROW]
[ROW][C]21[/C][C]5.9[/C][C]6.30987229504697[/C][C]-0.409872295046968[/C][/ROW]
[ROW][C]22[/C][C]5.5[/C][C]5.40558524753209[/C][C]0.0944147524679146[/C][/ROW]
[ROW][C]23[/C][C]5.5[/C][C]5.27502144137494[/C][C]0.224978558625058[/C][/ROW]
[ROW][C]24[/C][C]5.6[/C][C]5.49370540027193[/C][C]0.10629459972807[/C][/ROW]
[ROW][C]25[/C][C]5.8[/C][C]5.71737086700129[/C][C]0.0826291329987112[/C][/ROW]
[ROW][C]26[/C][C]5.9[/C][C]6.14264477670729[/C][C]-0.242644776707289[/C][/ROW]
[ROW][C]27[/C][C]6.1[/C][C]6.16267817735381[/C][C]-0.0626781773538121[/C][/ROW]
[ROW][C]28[/C][C]6.1[/C][C]6.17045904958901[/C][C]-0.0704590495890119[/C][/ROW]
[ROW][C]29[/C][C]6[/C][C]6.04625466027912[/C][C]-0.0462546602791184[/C][/ROW]
[ROW][C]30[/C][C]6[/C][C]5.87460713884964[/C][C]0.125392861150363[/C][/ROW]
[ROW][C]31[/C][C]5.9[/C][C]5.9766596979712[/C][C]-0.0766596979712029[/C][/ROW]
[ROW][C]32[/C][C]5.5[/C][C]5.75227774249087[/C][C]-0.252277742490873[/C][/ROW]
[ROW][C]33[/C][C]5.6[/C][C]5.54592726992251[/C][C]0.0540727300774864[/C][/ROW]
[ROW][C]34[/C][C]5.4[/C][C]5.48208237605481[/C][C]-0.0820823760548086[/C][/ROW]
[ROW][C]35[/C][C]5.2[/C][C]5.28704552991755[/C][C]-0.0870455299175448[/C][/ROW]
[ROW][C]36[/C][C]5.2[/C][C]5.11070862942241[/C][C]0.0892913705775878[/C][/ROW]
[ROW][C]37[/C][C]5.2[/C][C]5.3091738787203[/C][C]-0.109173878720302[/C][/ROW]
[ROW][C]38[/C][C]5.5[/C][C]5.51173714129877[/C][C]-0.0117371412987739[/C][/ROW]
[ROW][C]39[/C][C]5.8[/C][C]5.93166748569327[/C][C]-0.131667485693266[/C][/ROW]
[ROW][C]40[/C][C]5.8[/C][C]5.96464857535994[/C][C]-0.164648575359936[/C][/ROW]
[ROW][C]41[/C][C]5.5[/C][C]5.78300744862851[/C][C]-0.283007448628513[/C][/ROW]
[ROW][C]42[/C][C]5.3[/C][C]5.33121254264997[/C][C]-0.0312125426499719[/C][/ROW]
[ROW][C]43[/C][C]5.1[/C][C]5.26799119206554[/C][C]-0.167991192065539[/C][/ROW]
[ROW][C]44[/C][C]5.2[/C][C]5.01840901915374[/C][C]0.181590980846262[/C][/ROW]
[ROW][C]45[/C][C]5.8[/C][C]5.56986374537956[/C][C]0.230136254620441[/C][/ROW]
[ROW][C]46[/C][C]5.8[/C][C]5.91920362577685[/C][C]-0.119203625776852[/C][/ROW]
[ROW][C]47[/C][C]5.5[/C][C]5.717130477081[/C][C]-0.217130477080995[/C][/ROW]
[ROW][C]48[/C][C]5[/C][C]5.28584640946827[/C][C]-0.285846409468273[/C][/ROW]
[ROW][C]49[/C][C]4.9[/C][C]4.84137993481504[/C][C]0.0586200651849557[/C][/ROW]
[ROW][C]50[/C][C]5.3[/C][C]5.19105319222664[/C][C]0.108946807773362[/C][/ROW]
[ROW][C]51[/C][C]6.1[/C][C]5.80361788196134[/C][C]0.296382118038661[/C][/ROW]
[ROW][C]52[/C][C]6.5[/C][C]6.47953069557913[/C][C]0.0204693044208727[/C][/ROW]
[ROW][C]53[/C][C]6.8[/C][C]6.57100065083817[/C][C]0.228999349161828[/C][/ROW]
[ROW][C]54[/C][C]6.6[/C][C]6.72990094882069[/C][C]-0.129900948820688[/C][/ROW]
[ROW][C]55[/C][C]6.4[/C][C]6.32205917370707[/C][C]0.077940826292927[/C][/ROW]
[ROW][C]56[/C][C]6.4[/C][C]6.07247700079528[/C][C]0.327522999204726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58958&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58958&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
16.16.13874398417115-0.0387439841711496
26.36.258670291896610.0413297081033868
36.56.59108759708225-0.0910875970822549
46.66.541431731895930.0585682681040732
56.56.55730103486056-0.0573010348605629
66.26.32821677600955-0.128216776009552
76.26.010048258307530.189951741692472
85.96.09805020736632-0.198050207366318
96.15.974336689650960.125663310349041
106.15.993128750636250.106871249363746
116.16.020802551626520.0791974483734817
126.16.009739560837390.0902604391626146
136.16.093331335292210.00666866470778512
146.46.295894597870690.104105402129314
156.76.71094885790933-0.0109488579093281
166.96.7439299475760.156070052424002
1776.842436205393630.157563794606366
1876.836062593670150.163937406329849
196.86.82324167794866-0.0232416779486567
206.46.4587860301938-0.0587860301937957
215.96.30987229504697-0.409872295046968
225.55.405585247532090.0944147524679146
235.55.275021441374940.224978558625058
245.65.493705400271930.10629459972807
255.85.717370867001290.0826291329987112
265.96.14264477670729-0.242644776707289
276.16.16267817735381-0.0626781773538121
286.16.17045904958901-0.0704590495890119
2966.04625466027912-0.0462546602791184
3065.874607138849640.125392861150363
315.95.9766596979712-0.0766596979712029
325.55.75227774249087-0.252277742490873
335.65.545927269922510.0540727300774864
345.45.48208237605481-0.0820823760548086
355.25.28704552991755-0.0870455299175448
365.25.110708629422410.0892913705775878
375.25.3091738787203-0.109173878720302
385.55.51173714129877-0.0117371412987739
395.85.93166748569327-0.131667485693266
405.85.96464857535994-0.164648575359936
415.55.78300744862851-0.283007448628513
425.35.33121254264997-0.0312125426499719
435.15.26799119206554-0.167991192065539
445.25.018409019153740.181590980846262
455.85.569863745379560.230136254620441
465.85.91920362577685-0.119203625776852
475.55.717130477081-0.217130477080995
4855.28584640946827-0.285846409468273
494.94.841379934815040.0586200651849557
505.35.191053192226640.108946807773362
516.15.803617881961340.296382118038661
526.56.479530695579130.0204693044208727
536.86.571000650838170.228999349161828
546.66.72990094882069-0.129900948820688
556.46.322059173707070.077940826292927
566.46.072477000795280.327522999204726






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2019677537419000.4039355074837990.7980322462581
200.1651741001372530.3303482002745060.834825899862747
210.5922347523288780.8155304953422430.407765247671122
220.4838012758972420.9676025517944840.516198724102758
230.5121900364391450.975619927121710.487809963560855
240.5411769119499490.9176461761001020.458823088050051
250.6164636577108980.7670726845782040.383536342289102
260.7486111196966320.5027777606067360.251388880303368
270.6522230025385050.695553994922990.347776997461495
280.6084035692282790.7831928615434430.391596430771721
290.5180152828283310.9639694343433380.481984717171669
300.6490287632741840.7019424734516320.350971236725816
310.7081139284318130.5837721431363750.291886071568188
320.6834008221639060.6331983556721870.316599177836094
330.6699549541544630.6600900916910740.330045045845537
340.6225176286404550.754964742719090.377482371359545
350.5620264567427890.8759470865144230.437973543257211
360.6148443603481840.7703112793036330.385155639651816
370.4418618095009340.8837236190018670.558138190499066

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.201967753741900 & 0.403935507483799 & 0.7980322462581 \tabularnewline
20 & 0.165174100137253 & 0.330348200274506 & 0.834825899862747 \tabularnewline
21 & 0.592234752328878 & 0.815530495342243 & 0.407765247671122 \tabularnewline
22 & 0.483801275897242 & 0.967602551794484 & 0.516198724102758 \tabularnewline
23 & 0.512190036439145 & 0.97561992712171 & 0.487809963560855 \tabularnewline
24 & 0.541176911949949 & 0.917646176100102 & 0.458823088050051 \tabularnewline
25 & 0.616463657710898 & 0.767072684578204 & 0.383536342289102 \tabularnewline
26 & 0.748611119696632 & 0.502777760606736 & 0.251388880303368 \tabularnewline
27 & 0.652223002538505 & 0.69555399492299 & 0.347776997461495 \tabularnewline
28 & 0.608403569228279 & 0.783192861543443 & 0.391596430771721 \tabularnewline
29 & 0.518015282828331 & 0.963969434343338 & 0.481984717171669 \tabularnewline
30 & 0.649028763274184 & 0.701942473451632 & 0.350971236725816 \tabularnewline
31 & 0.708113928431813 & 0.583772143136375 & 0.291886071568188 \tabularnewline
32 & 0.683400822163906 & 0.633198355672187 & 0.316599177836094 \tabularnewline
33 & 0.669954954154463 & 0.660090091691074 & 0.330045045845537 \tabularnewline
34 & 0.622517628640455 & 0.75496474271909 & 0.377482371359545 \tabularnewline
35 & 0.562026456742789 & 0.875947086514423 & 0.437973543257211 \tabularnewline
36 & 0.614844360348184 & 0.770311279303633 & 0.385155639651816 \tabularnewline
37 & 0.441861809500934 & 0.883723619001867 & 0.558138190499066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58958&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]19[/C][C]0.201967753741900[/C][C]0.403935507483799[/C][C]0.7980322462581[/C][/ROW]
[ROW][C]20[/C][C]0.165174100137253[/C][C]0.330348200274506[/C][C]0.834825899862747[/C][/ROW]
[ROW][C]21[/C][C]0.592234752328878[/C][C]0.815530495342243[/C][C]0.407765247671122[/C][/ROW]
[ROW][C]22[/C][C]0.483801275897242[/C][C]0.967602551794484[/C][C]0.516198724102758[/C][/ROW]
[ROW][C]23[/C][C]0.512190036439145[/C][C]0.97561992712171[/C][C]0.487809963560855[/C][/ROW]
[ROW][C]24[/C][C]0.541176911949949[/C][C]0.917646176100102[/C][C]0.458823088050051[/C][/ROW]
[ROW][C]25[/C][C]0.616463657710898[/C][C]0.767072684578204[/C][C]0.383536342289102[/C][/ROW]
[ROW][C]26[/C][C]0.748611119696632[/C][C]0.502777760606736[/C][C]0.251388880303368[/C][/ROW]
[ROW][C]27[/C][C]0.652223002538505[/C][C]0.69555399492299[/C][C]0.347776997461495[/C][/ROW]
[ROW][C]28[/C][C]0.608403569228279[/C][C]0.783192861543443[/C][C]0.391596430771721[/C][/ROW]
[ROW][C]29[/C][C]0.518015282828331[/C][C]0.963969434343338[/C][C]0.481984717171669[/C][/ROW]
[ROW][C]30[/C][C]0.649028763274184[/C][C]0.701942473451632[/C][C]0.350971236725816[/C][/ROW]
[ROW][C]31[/C][C]0.708113928431813[/C][C]0.583772143136375[/C][C]0.291886071568188[/C][/ROW]
[ROW][C]32[/C][C]0.683400822163906[/C][C]0.633198355672187[/C][C]0.316599177836094[/C][/ROW]
[ROW][C]33[/C][C]0.669954954154463[/C][C]0.660090091691074[/C][C]0.330045045845537[/C][/ROW]
[ROW][C]34[/C][C]0.622517628640455[/C][C]0.75496474271909[/C][C]0.377482371359545[/C][/ROW]
[ROW][C]35[/C][C]0.562026456742789[/C][C]0.875947086514423[/C][C]0.437973543257211[/C][/ROW]
[ROW][C]36[/C][C]0.614844360348184[/C][C]0.770311279303633[/C][C]0.385155639651816[/C][/ROW]
[ROW][C]37[/C][C]0.441861809500934[/C][C]0.883723619001867[/C][C]0.558138190499066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58958&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58958&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
190.2019677537419000.4039355074837990.7980322462581
200.1651741001372530.3303482002745060.834825899862747
210.5922347523288780.8155304953422430.407765247671122
220.4838012758972420.9676025517944840.516198724102758
230.5121900364391450.975619927121710.487809963560855
240.5411769119499490.9176461761001020.458823088050051
250.6164636577108980.7670726845782040.383536342289102
260.7486111196966320.5027777606067360.251388880303368
270.6522230025385050.695553994922990.347776997461495
280.6084035692282790.7831928615434430.391596430771721
290.5180152828283310.9639694343433380.481984717171669
300.6490287632741840.7019424734516320.350971236725816
310.7081139284318130.5837721431363750.291886071568188
320.6834008221639060.6331983556721870.316599177836094
330.6699549541544630.6600900916910740.330045045845537
340.6225176286404550.754964742719090.377482371359545
350.5620264567427890.8759470865144230.437973543257211
360.6148443603481840.7703112793036330.385155639651816
370.4418618095009340.8837236190018670.558138190499066






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 level00OK

\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 & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58958&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58958&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58958&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 level00OK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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