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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 computationThu, 19 Nov 2009 08:36:14 -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/19/t12586462321oraq5r0jvhjzwh.htm/, Retrieved Sat, 20 Apr 2024 05:29:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57787, Retrieved Sat, 20 Apr 2024 05:29:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148

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]
-    D      [Multiple Regression] [] [2009-11-19 15:36:14] [efd540d63f04881f500eb7fad70c8699] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.1	0	2.0	2.4
2.0	0	2.1	2.0
1.8	0	2.0	2.1
2.7	0	1.8	2.0
2.3	0	2.7	1.8
1.9	0	2.3	2.7
2.0	0	1.9	2.3
2.3	0	2.0	1.9
2.8	0	2.3	2.0
2.4	0	2.8	2.3
2.3	0	2.4	2.8
2.7	0	2.3	2.4
2.7	0	2.7	2.3
2.9	0	2.7	2.7
3.0	0	2.9	2.7
2.2	0	3.0	2.9
2.3	0	2.2	3.0
2.8	0	2.3	2.2
2.8	0	2.8	2.3
2.8	0	2.8	2.8
2.2	0	2.8	2.8
2.6	0	2.2	2.8
2.8	0	2.6	2.2
2.5	0	2.8	2.6
2.4	0	2.5	2.8
2.3	0	2.4	2.5
1.9	0	2.3	2.4
1.7	0	1.9	2.3
2.0	0	1.7	1.9
2.1	0	2.0	1.7
1.7	0	2.1	2.0
1.8	0	1.7	2.1
1.8	0	1.8	1.7
1.8	0	1.8	1.8
1.3	0	1.8	1.8
1.3	0	1.3	1.8
1.3	0	1.3	1.3
1.2	0	1.3	1.3
1.4	0	1.2	1.3
2.2	1	1.4	1.2
2.9	1	2.2	1.4
3.1	1	2.9	2.2
3.5	1	3.1	2.9
3.6	1	3.5	3.1
4.4	1	3.6	3.5
4.1	1	4.4	3.6
5.1	1	4.1	4.4
5.8	1	5.1	4.1
5.9	1	5.8	5.1
5.4	1	5.9	5.8
5.5	1	5.4	5.9
4.8	1	5.5	5.4
3.2	1	4.8	5.5
2.7	1	3.2	4.8
2.1	1	2.7	3.2
1.9	1	2.1	2.7
0.6	1	1.9	2.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57787&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57787&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57787&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.918381042450223 + 0.654697232943884X[t] + 1.08057771183516Y1[t] -0.255818518025034Y2[t] -0.201421589282912M1[t] -0.308680635057811M2[t] -0.200007912257289M3[t] -0.304535445515861M4[t] -0.48088115921706M5[t] -0.292490144066929M6[t] -0.403038896054930M7[t] -0.226210468212112M8[t] -0.422739955704922M9[t] -0.322312577454471M10[t] -0.0326139813926506M11[t] -0.0138870270198022t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.918381042450223 +  0.654697232943884X[t] +  1.08057771183516Y1[t] -0.255818518025034Y2[t] -0.201421589282912M1[t] -0.308680635057811M2[t] -0.200007912257289M3[t] -0.304535445515861M4[t] -0.48088115921706M5[t] -0.292490144066929M6[t] -0.403038896054930M7[t] -0.226210468212112M8[t] -0.422739955704922M9[t] -0.322312577454471M10[t] -0.0326139813926506M11[t] -0.0138870270198022t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57787&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.918381042450223 +  0.654697232943884X[t] +  1.08057771183516Y1[t] -0.255818518025034Y2[t] -0.201421589282912M1[t] -0.308680635057811M2[t] -0.200007912257289M3[t] -0.304535445515861M4[t] -0.48088115921706M5[t] -0.292490144066929M6[t] -0.403038896054930M7[t] -0.226210468212112M8[t] -0.422739955704922M9[t] -0.322312577454471M10[t] -0.0326139813926506M11[t] -0.0138870270198022t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57787&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57787&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] = + 0.918381042450223 + 0.654697232943884X[t] + 1.08057771183516Y1[t] -0.255818518025034Y2[t] -0.201421589282912M1[t] -0.308680635057811M2[t] -0.200007912257289M3[t] -0.304535445515861M4[t] -0.48088115921706M5[t] -0.292490144066929M6[t] -0.403038896054930M7[t] -0.226210468212112M8[t] -0.422739955704922M9[t] -0.322312577454471M10[t] -0.0326139813926506M11[t] -0.0138870270198022t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.9183810424502230.377682.43160.0194870.009743
X0.6546972329438840.3052912.14450.0379690.018985
Y11.080577711835160.1641526.582800
Y2-0.2558185180250340.155223-1.64810.1069820.053491
M1-0.2014215892829120.336739-0.59820.5530280.276514
M2-0.3086806350578110.336817-0.91650.3647830.182391
M3-0.2000079122572890.338412-0.5910.5577520.278876
M4-0.3045354455158610.343353-0.88690.3802810.190141
M5-0.480881159217060.341655-1.40750.1668140.083407
M6-0.2924901440669290.345638-0.84620.4023350.201167
M7-0.4030388960549300.34213-1.1780.2455770.122789
M8-0.2262104682121120.34373-0.65810.5141490.257075
M9-0.4227399557049220.340734-1.24070.2217780.110889
M10-0.3223125774544710.353886-0.91080.3677340.183867
M11-0.03261398139265060.35551-0.09170.9273530.463676
t-0.01388702701980220.007196-1.92970.0605830.030291

\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) & 0.918381042450223 & 0.37768 & 2.4316 & 0.019487 & 0.009743 \tabularnewline
X & 0.654697232943884 & 0.305291 & 2.1445 & 0.037969 & 0.018985 \tabularnewline
Y1 & 1.08057771183516 & 0.164152 & 6.5828 & 0 & 0 \tabularnewline
Y2 & -0.255818518025034 & 0.155223 & -1.6481 & 0.106982 & 0.053491 \tabularnewline
M1 & -0.201421589282912 & 0.336739 & -0.5982 & 0.553028 & 0.276514 \tabularnewline
M2 & -0.308680635057811 & 0.336817 & -0.9165 & 0.364783 & 0.182391 \tabularnewline
M3 & -0.200007912257289 & 0.338412 & -0.591 & 0.557752 & 0.278876 \tabularnewline
M4 & -0.304535445515861 & 0.343353 & -0.8869 & 0.380281 & 0.190141 \tabularnewline
M5 & -0.48088115921706 & 0.341655 & -1.4075 & 0.166814 & 0.083407 \tabularnewline
M6 & -0.292490144066929 & 0.345638 & -0.8462 & 0.402335 & 0.201167 \tabularnewline
M7 & -0.403038896054930 & 0.34213 & -1.178 & 0.245577 & 0.122789 \tabularnewline
M8 & -0.226210468212112 & 0.34373 & -0.6581 & 0.514149 & 0.257075 \tabularnewline
M9 & -0.422739955704922 & 0.340734 & -1.2407 & 0.221778 & 0.110889 \tabularnewline
M10 & -0.322312577454471 & 0.353886 & -0.9108 & 0.367734 & 0.183867 \tabularnewline
M11 & -0.0326139813926506 & 0.35551 & -0.0917 & 0.927353 & 0.463676 \tabularnewline
t & -0.0138870270198022 & 0.007196 & -1.9297 & 0.060583 & 0.030291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57787&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]0.918381042450223[/C][C]0.37768[/C][C]2.4316[/C][C]0.019487[/C][C]0.009743[/C][/ROW]
[ROW][C]X[/C][C]0.654697232943884[/C][C]0.305291[/C][C]2.1445[/C][C]0.037969[/C][C]0.018985[/C][/ROW]
[ROW][C]Y1[/C][C]1.08057771183516[/C][C]0.164152[/C][C]6.5828[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.255818518025034[/C][C]0.155223[/C][C]-1.6481[/C][C]0.106982[/C][C]0.053491[/C][/ROW]
[ROW][C]M1[/C][C]-0.201421589282912[/C][C]0.336739[/C][C]-0.5982[/C][C]0.553028[/C][C]0.276514[/C][/ROW]
[ROW][C]M2[/C][C]-0.308680635057811[/C][C]0.336817[/C][C]-0.9165[/C][C]0.364783[/C][C]0.182391[/C][/ROW]
[ROW][C]M3[/C][C]-0.200007912257289[/C][C]0.338412[/C][C]-0.591[/C][C]0.557752[/C][C]0.278876[/C][/ROW]
[ROW][C]M4[/C][C]-0.304535445515861[/C][C]0.343353[/C][C]-0.8869[/C][C]0.380281[/C][C]0.190141[/C][/ROW]
[ROW][C]M5[/C][C]-0.48088115921706[/C][C]0.341655[/C][C]-1.4075[/C][C]0.166814[/C][C]0.083407[/C][/ROW]
[ROW][C]M6[/C][C]-0.292490144066929[/C][C]0.345638[/C][C]-0.8462[/C][C]0.402335[/C][C]0.201167[/C][/ROW]
[ROW][C]M7[/C][C]-0.403038896054930[/C][C]0.34213[/C][C]-1.178[/C][C]0.245577[/C][C]0.122789[/C][/ROW]
[ROW][C]M8[/C][C]-0.226210468212112[/C][C]0.34373[/C][C]-0.6581[/C][C]0.514149[/C][C]0.257075[/C][/ROW]
[ROW][C]M9[/C][C]-0.422739955704922[/C][C]0.340734[/C][C]-1.2407[/C][C]0.221778[/C][C]0.110889[/C][/ROW]
[ROW][C]M10[/C][C]-0.322312577454471[/C][C]0.353886[/C][C]-0.9108[/C][C]0.367734[/C][C]0.183867[/C][/ROW]
[ROW][C]M11[/C][C]-0.0326139813926506[/C][C]0.35551[/C][C]-0.0917[/C][C]0.927353[/C][C]0.463676[/C][/ROW]
[ROW][C]t[/C][C]-0.0138870270198022[/C][C]0.007196[/C][C]-1.9297[/C][C]0.060583[/C][C]0.030291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57787&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57787&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)0.9183810424502230.377682.43160.0194870.009743
X0.6546972329438840.3052912.14450.0379690.018985
Y11.080577711835160.1641526.582800
Y2-0.2558185180250340.155223-1.64810.1069820.053491
M1-0.2014215892829120.336739-0.59820.5530280.276514
M2-0.3086806350578110.336817-0.91650.3647830.182391
M3-0.2000079122572890.338412-0.5910.5577520.278876
M4-0.3045354455158610.343353-0.88690.3802810.190141
M5-0.480881159217060.341655-1.40750.1668140.083407
M6-0.2924901440669290.345638-0.84620.4023350.201167
M7-0.4030388960549300.34213-1.1780.2455770.122789
M8-0.2262104682121120.34373-0.65810.5141490.257075
M9-0.4227399557049220.340734-1.24070.2217780.110889
M10-0.3223125774544710.353886-0.91080.3677340.183867
M11-0.03261398139265060.35551-0.09170.9273530.463676
t-0.01388702701980220.007196-1.92970.0605830.030291






Multiple Linear Regression - Regression Statistics
Multiple R0.931744212410473
R-squared0.868147277360413
Adjusted R-squared0.81990847639471
F-TEST (value)17.9968668370853
F-TEST (DF numerator)15
F-TEST (DF denominator)41
p-value2.00950367457153e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.499925504351956
Sum Squared Residuals10.2469459059638

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.931744212410473 \tabularnewline
R-squared & 0.868147277360413 \tabularnewline
Adjusted R-squared & 0.81990847639471 \tabularnewline
F-TEST (value) & 17.9968668370853 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 41 \tabularnewline
p-value & 2.00950367457153e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.499925504351956 \tabularnewline
Sum Squared Residuals & 10.2469459059638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57787&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.931744212410473[/C][/ROW]
[ROW][C]R-squared[/C][C]0.868147277360413[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.81990847639471[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]17.9968668370853[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]41[/C][/ROW]
[ROW][C]p-value[/C][C]2.00950367457153e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.499925504351956[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]10.2469459059638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57787&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57787&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 R0.931744212410473
R-squared0.868147277360413
Adjusted R-squared0.81990847639471
F-TEST (value)17.9968668370853
F-TEST (DF numerator)15
F-TEST (DF denominator)41
p-value2.00950367457153e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.499925504351956
Sum Squared Residuals10.2469459059638






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.12.25026340655775-0.150263406557748
222.33950251215658-0.339502512156579
31.82.30064858495128-0.500648584951281
42.71.991700334108380.708299665891623
52.32.82515123764403-0.525151237644028
61.92.33718747481776-0.437187474817762
721.882848018285910.117151981714092
82.32.256174597502450.0438254024975471
92.82.344349544737880.455650455262116
102.42.89443319647860-0.494433196478605
112.32.61010442177404-0.310104421774041
122.72.623101012173390.0768989878266132
132.72.86560533240724-0.165605332407241
142.92.642131852402530.257868147597473
1532.953033090550280.0469669094497221
162.22.89151259785041-0.691512597850414
172.31.811235835858780.48876416414122
182.82.298452409592650.501547590407348
192.82.688723634699930.111276365300074
202.82.723755776510420.0762442234895748
212.22.51333926199781-0.313339261997812
222.61.951532986127360.648467013872636
232.82.81306675071847-0.0130667507184674
242.52.94558184024833-0.445581840248334
252.42.354936206790060.0450637932099351
262.32.202477918219360.0975220817806422
271.92.21478769461906-0.314787694619064
281.71.689723901409130.0102760985908709
2921.385703025531110.614296974468891
302.11.935544030816990.164455969183007
311.71.84242046758520-0.142420467585196
321.81.547548931871640.252451068128356
331.81.547517595752560.252482404247439
341.81.608476095180710.191523904819294
351.31.88428766422272-0.584287664222725
361.31.36272576267799-0.0627257626779923
371.31.275326405387790.0246735946122057
381.21.154180332593090.0458196674069067
391.41.140908257190300.259091742809703
402.21.918888324025340.281111675974658
412.92.541954049167460.358045950832536
423.13.26820762116238-0.168207621162379
433.53.180814421904090.319185578095915
443.63.72482320385616-0.124823203856159
454.43.520137053317050.879862946682951
464.14.44555772221332-0.345557722213324
475.14.192541163284770.907458836715234
485.85.368591384900290.431408615099713
495.95.653868648857150.246131351142848
505.45.46170738462844-0.0617073846284438
515.54.990622372689080.50937762731092
524.85.10817484260674-0.308174842606738
533.24.13595585179862-0.93595585179862
542.72.76060846361021-0.0606084636102141
552.12.50519345752488-0.405193457524884
561.92.14769749025932-0.247697490259319
570.61.87465654419469-1.27465654419469

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.1 & 2.25026340655775 & -0.150263406557748 \tabularnewline
2 & 2 & 2.33950251215658 & -0.339502512156579 \tabularnewline
3 & 1.8 & 2.30064858495128 & -0.500648584951281 \tabularnewline
4 & 2.7 & 1.99170033410838 & 0.708299665891623 \tabularnewline
5 & 2.3 & 2.82515123764403 & -0.525151237644028 \tabularnewline
6 & 1.9 & 2.33718747481776 & -0.437187474817762 \tabularnewline
7 & 2 & 1.88284801828591 & 0.117151981714092 \tabularnewline
8 & 2.3 & 2.25617459750245 & 0.0438254024975471 \tabularnewline
9 & 2.8 & 2.34434954473788 & 0.455650455262116 \tabularnewline
10 & 2.4 & 2.89443319647860 & -0.494433196478605 \tabularnewline
11 & 2.3 & 2.61010442177404 & -0.310104421774041 \tabularnewline
12 & 2.7 & 2.62310101217339 & 0.0768989878266132 \tabularnewline
13 & 2.7 & 2.86560533240724 & -0.165605332407241 \tabularnewline
14 & 2.9 & 2.64213185240253 & 0.257868147597473 \tabularnewline
15 & 3 & 2.95303309055028 & 0.0469669094497221 \tabularnewline
16 & 2.2 & 2.89151259785041 & -0.691512597850414 \tabularnewline
17 & 2.3 & 1.81123583585878 & 0.48876416414122 \tabularnewline
18 & 2.8 & 2.29845240959265 & 0.501547590407348 \tabularnewline
19 & 2.8 & 2.68872363469993 & 0.111276365300074 \tabularnewline
20 & 2.8 & 2.72375577651042 & 0.0762442234895748 \tabularnewline
21 & 2.2 & 2.51333926199781 & -0.313339261997812 \tabularnewline
22 & 2.6 & 1.95153298612736 & 0.648467013872636 \tabularnewline
23 & 2.8 & 2.81306675071847 & -0.0130667507184674 \tabularnewline
24 & 2.5 & 2.94558184024833 & -0.445581840248334 \tabularnewline
25 & 2.4 & 2.35493620679006 & 0.0450637932099351 \tabularnewline
26 & 2.3 & 2.20247791821936 & 0.0975220817806422 \tabularnewline
27 & 1.9 & 2.21478769461906 & -0.314787694619064 \tabularnewline
28 & 1.7 & 1.68972390140913 & 0.0102760985908709 \tabularnewline
29 & 2 & 1.38570302553111 & 0.614296974468891 \tabularnewline
30 & 2.1 & 1.93554403081699 & 0.164455969183007 \tabularnewline
31 & 1.7 & 1.84242046758520 & -0.142420467585196 \tabularnewline
32 & 1.8 & 1.54754893187164 & 0.252451068128356 \tabularnewline
33 & 1.8 & 1.54751759575256 & 0.252482404247439 \tabularnewline
34 & 1.8 & 1.60847609518071 & 0.191523904819294 \tabularnewline
35 & 1.3 & 1.88428766422272 & -0.584287664222725 \tabularnewline
36 & 1.3 & 1.36272576267799 & -0.0627257626779923 \tabularnewline
37 & 1.3 & 1.27532640538779 & 0.0246735946122057 \tabularnewline
38 & 1.2 & 1.15418033259309 & 0.0458196674069067 \tabularnewline
39 & 1.4 & 1.14090825719030 & 0.259091742809703 \tabularnewline
40 & 2.2 & 1.91888832402534 & 0.281111675974658 \tabularnewline
41 & 2.9 & 2.54195404916746 & 0.358045950832536 \tabularnewline
42 & 3.1 & 3.26820762116238 & -0.168207621162379 \tabularnewline
43 & 3.5 & 3.18081442190409 & 0.319185578095915 \tabularnewline
44 & 3.6 & 3.72482320385616 & -0.124823203856159 \tabularnewline
45 & 4.4 & 3.52013705331705 & 0.879862946682951 \tabularnewline
46 & 4.1 & 4.44555772221332 & -0.345557722213324 \tabularnewline
47 & 5.1 & 4.19254116328477 & 0.907458836715234 \tabularnewline
48 & 5.8 & 5.36859138490029 & 0.431408615099713 \tabularnewline
49 & 5.9 & 5.65386864885715 & 0.246131351142848 \tabularnewline
50 & 5.4 & 5.46170738462844 & -0.0617073846284438 \tabularnewline
51 & 5.5 & 4.99062237268908 & 0.50937762731092 \tabularnewline
52 & 4.8 & 5.10817484260674 & -0.308174842606738 \tabularnewline
53 & 3.2 & 4.13595585179862 & -0.93595585179862 \tabularnewline
54 & 2.7 & 2.76060846361021 & -0.0606084636102141 \tabularnewline
55 & 2.1 & 2.50519345752488 & -0.405193457524884 \tabularnewline
56 & 1.9 & 2.14769749025932 & -0.247697490259319 \tabularnewline
57 & 0.6 & 1.87465654419469 & -1.27465654419469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57787&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]2.1[/C][C]2.25026340655775[/C][C]-0.150263406557748[/C][/ROW]
[ROW][C]2[/C][C]2[/C][C]2.33950251215658[/C][C]-0.339502512156579[/C][/ROW]
[ROW][C]3[/C][C]1.8[/C][C]2.30064858495128[/C][C]-0.500648584951281[/C][/ROW]
[ROW][C]4[/C][C]2.7[/C][C]1.99170033410838[/C][C]0.708299665891623[/C][/ROW]
[ROW][C]5[/C][C]2.3[/C][C]2.82515123764403[/C][C]-0.525151237644028[/C][/ROW]
[ROW][C]6[/C][C]1.9[/C][C]2.33718747481776[/C][C]-0.437187474817762[/C][/ROW]
[ROW][C]7[/C][C]2[/C][C]1.88284801828591[/C][C]0.117151981714092[/C][/ROW]
[ROW][C]8[/C][C]2.3[/C][C]2.25617459750245[/C][C]0.0438254024975471[/C][/ROW]
[ROW][C]9[/C][C]2.8[/C][C]2.34434954473788[/C][C]0.455650455262116[/C][/ROW]
[ROW][C]10[/C][C]2.4[/C][C]2.89443319647860[/C][C]-0.494433196478605[/C][/ROW]
[ROW][C]11[/C][C]2.3[/C][C]2.61010442177404[/C][C]-0.310104421774041[/C][/ROW]
[ROW][C]12[/C][C]2.7[/C][C]2.62310101217339[/C][C]0.0768989878266132[/C][/ROW]
[ROW][C]13[/C][C]2.7[/C][C]2.86560533240724[/C][C]-0.165605332407241[/C][/ROW]
[ROW][C]14[/C][C]2.9[/C][C]2.64213185240253[/C][C]0.257868147597473[/C][/ROW]
[ROW][C]15[/C][C]3[/C][C]2.95303309055028[/C][C]0.0469669094497221[/C][/ROW]
[ROW][C]16[/C][C]2.2[/C][C]2.89151259785041[/C][C]-0.691512597850414[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]1.81123583585878[/C][C]0.48876416414122[/C][/ROW]
[ROW][C]18[/C][C]2.8[/C][C]2.29845240959265[/C][C]0.501547590407348[/C][/ROW]
[ROW][C]19[/C][C]2.8[/C][C]2.68872363469993[/C][C]0.111276365300074[/C][/ROW]
[ROW][C]20[/C][C]2.8[/C][C]2.72375577651042[/C][C]0.0762442234895748[/C][/ROW]
[ROW][C]21[/C][C]2.2[/C][C]2.51333926199781[/C][C]-0.313339261997812[/C][/ROW]
[ROW][C]22[/C][C]2.6[/C][C]1.95153298612736[/C][C]0.648467013872636[/C][/ROW]
[ROW][C]23[/C][C]2.8[/C][C]2.81306675071847[/C][C]-0.0130667507184674[/C][/ROW]
[ROW][C]24[/C][C]2.5[/C][C]2.94558184024833[/C][C]-0.445581840248334[/C][/ROW]
[ROW][C]25[/C][C]2.4[/C][C]2.35493620679006[/C][C]0.0450637932099351[/C][/ROW]
[ROW][C]26[/C][C]2.3[/C][C]2.20247791821936[/C][C]0.0975220817806422[/C][/ROW]
[ROW][C]27[/C][C]1.9[/C][C]2.21478769461906[/C][C]-0.314787694619064[/C][/ROW]
[ROW][C]28[/C][C]1.7[/C][C]1.68972390140913[/C][C]0.0102760985908709[/C][/ROW]
[ROW][C]29[/C][C]2[/C][C]1.38570302553111[/C][C]0.614296974468891[/C][/ROW]
[ROW][C]30[/C][C]2.1[/C][C]1.93554403081699[/C][C]0.164455969183007[/C][/ROW]
[ROW][C]31[/C][C]1.7[/C][C]1.84242046758520[/C][C]-0.142420467585196[/C][/ROW]
[ROW][C]32[/C][C]1.8[/C][C]1.54754893187164[/C][C]0.252451068128356[/C][/ROW]
[ROW][C]33[/C][C]1.8[/C][C]1.54751759575256[/C][C]0.252482404247439[/C][/ROW]
[ROW][C]34[/C][C]1.8[/C][C]1.60847609518071[/C][C]0.191523904819294[/C][/ROW]
[ROW][C]35[/C][C]1.3[/C][C]1.88428766422272[/C][C]-0.584287664222725[/C][/ROW]
[ROW][C]36[/C][C]1.3[/C][C]1.36272576267799[/C][C]-0.0627257626779923[/C][/ROW]
[ROW][C]37[/C][C]1.3[/C][C]1.27532640538779[/C][C]0.0246735946122057[/C][/ROW]
[ROW][C]38[/C][C]1.2[/C][C]1.15418033259309[/C][C]0.0458196674069067[/C][/ROW]
[ROW][C]39[/C][C]1.4[/C][C]1.14090825719030[/C][C]0.259091742809703[/C][/ROW]
[ROW][C]40[/C][C]2.2[/C][C]1.91888832402534[/C][C]0.281111675974658[/C][/ROW]
[ROW][C]41[/C][C]2.9[/C][C]2.54195404916746[/C][C]0.358045950832536[/C][/ROW]
[ROW][C]42[/C][C]3.1[/C][C]3.26820762116238[/C][C]-0.168207621162379[/C][/ROW]
[ROW][C]43[/C][C]3.5[/C][C]3.18081442190409[/C][C]0.319185578095915[/C][/ROW]
[ROW][C]44[/C][C]3.6[/C][C]3.72482320385616[/C][C]-0.124823203856159[/C][/ROW]
[ROW][C]45[/C][C]4.4[/C][C]3.52013705331705[/C][C]0.879862946682951[/C][/ROW]
[ROW][C]46[/C][C]4.1[/C][C]4.44555772221332[/C][C]-0.345557722213324[/C][/ROW]
[ROW][C]47[/C][C]5.1[/C][C]4.19254116328477[/C][C]0.907458836715234[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.36859138490029[/C][C]0.431408615099713[/C][/ROW]
[ROW][C]49[/C][C]5.9[/C][C]5.65386864885715[/C][C]0.246131351142848[/C][/ROW]
[ROW][C]50[/C][C]5.4[/C][C]5.46170738462844[/C][C]-0.0617073846284438[/C][/ROW]
[ROW][C]51[/C][C]5.5[/C][C]4.99062237268908[/C][C]0.50937762731092[/C][/ROW]
[ROW][C]52[/C][C]4.8[/C][C]5.10817484260674[/C][C]-0.308174842606738[/C][/ROW]
[ROW][C]53[/C][C]3.2[/C][C]4.13595585179862[/C][C]-0.93595585179862[/C][/ROW]
[ROW][C]54[/C][C]2.7[/C][C]2.76060846361021[/C][C]-0.0606084636102141[/C][/ROW]
[ROW][C]55[/C][C]2.1[/C][C]2.50519345752488[/C][C]-0.405193457524884[/C][/ROW]
[ROW][C]56[/C][C]1.9[/C][C]2.14769749025932[/C][C]-0.247697490259319[/C][/ROW]
[ROW][C]57[/C][C]0.6[/C][C]1.87465654419469[/C][C]-1.27465654419469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57787&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57787&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.12.25026340655775-0.150263406557748
222.33950251215658-0.339502512156579
31.82.30064858495128-0.500648584951281
42.71.991700334108380.708299665891623
52.32.82515123764403-0.525151237644028
61.92.33718747481776-0.437187474817762
721.882848018285910.117151981714092
82.32.256174597502450.0438254024975471
92.82.344349544737880.455650455262116
102.42.89443319647860-0.494433196478605
112.32.61010442177404-0.310104421774041
122.72.623101012173390.0768989878266132
132.72.86560533240724-0.165605332407241
142.92.642131852402530.257868147597473
1532.953033090550280.0469669094497221
162.22.89151259785041-0.691512597850414
172.31.811235835858780.48876416414122
182.82.298452409592650.501547590407348
192.82.688723634699930.111276365300074
202.82.723755776510420.0762442234895748
212.22.51333926199781-0.313339261997812
222.61.951532986127360.648467013872636
232.82.81306675071847-0.0130667507184674
242.52.94558184024833-0.445581840248334
252.42.354936206790060.0450637932099351
262.32.202477918219360.0975220817806422
271.92.21478769461906-0.314787694619064
281.71.689723901409130.0102760985908709
2921.385703025531110.614296974468891
302.11.935544030816990.164455969183007
311.71.84242046758520-0.142420467585196
321.81.547548931871640.252451068128356
331.81.547517595752560.252482404247439
341.81.608476095180710.191523904819294
351.31.88428766422272-0.584287664222725
361.31.36272576267799-0.0627257626779923
371.31.275326405387790.0246735946122057
381.21.154180332593090.0458196674069067
391.41.140908257190300.259091742809703
402.21.918888324025340.281111675974658
412.92.541954049167460.358045950832536
423.13.26820762116238-0.168207621162379
433.53.180814421904090.319185578095915
443.63.72482320385616-0.124823203856159
454.43.520137053317050.879862946682951
464.14.44555772221332-0.345557722213324
475.14.192541163284770.907458836715234
485.85.368591384900290.431408615099713
495.95.653868648857150.246131351142848
505.45.46170738462844-0.0617073846284438
515.54.990622372689080.50937762731092
524.85.10817484260674-0.308174842606738
533.24.13595585179862-0.93595585179862
542.72.76060846361021-0.0606084636102141
552.12.50519345752488-0.405193457524884
561.92.14769749025932-0.247697490259319
570.61.87465654419469-1.27465654419469






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.5451952350925140.9096095298149730.454804764907486
200.3761822794285070.7523645588570140.623817720571493
210.4475942887416570.8951885774833140.552405711258343
220.3191086029786870.6382172059573730.680891397021313
230.2473620301002710.4947240602005430.752637969899729
240.281890395288370.563780790576740.71810960471163
250.2562305942187410.5124611884374830.743769405781259
260.2415977013030760.4831954026061520.758402298696924
270.4997362422173370.9994724844346750.500263757782663
280.5074936460683280.9850127078633440.492506353931672
290.4350172316785140.8700344633570290.564982768321486
300.3484812677222580.6969625354445150.651518732277742
310.3035939341219420.6071878682438830.696406065878058
320.2188569923194920.4377139846389840.781143007680508
330.1521772635307240.3043545270614480.847822736469276
340.1347805658464450.2695611316928890.865219434153555
350.1940347406531280.3880694813062550.805965259346872
360.1863839323507500.3727678647014990.81361606764925
370.1268158561333690.2536317122667370.873184143866631
380.0632610941600080.1265221883200160.936738905839992

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.545195235092514 & 0.909609529814973 & 0.454804764907486 \tabularnewline
20 & 0.376182279428507 & 0.752364558857014 & 0.623817720571493 \tabularnewline
21 & 0.447594288741657 & 0.895188577483314 & 0.552405711258343 \tabularnewline
22 & 0.319108602978687 & 0.638217205957373 & 0.680891397021313 \tabularnewline
23 & 0.247362030100271 & 0.494724060200543 & 0.752637969899729 \tabularnewline
24 & 0.28189039528837 & 0.56378079057674 & 0.71810960471163 \tabularnewline
25 & 0.256230594218741 & 0.512461188437483 & 0.743769405781259 \tabularnewline
26 & 0.241597701303076 & 0.483195402606152 & 0.758402298696924 \tabularnewline
27 & 0.499736242217337 & 0.999472484434675 & 0.500263757782663 \tabularnewline
28 & 0.507493646068328 & 0.985012707863344 & 0.492506353931672 \tabularnewline
29 & 0.435017231678514 & 0.870034463357029 & 0.564982768321486 \tabularnewline
30 & 0.348481267722258 & 0.696962535444515 & 0.651518732277742 \tabularnewline
31 & 0.303593934121942 & 0.607187868243883 & 0.696406065878058 \tabularnewline
32 & 0.218856992319492 & 0.437713984638984 & 0.781143007680508 \tabularnewline
33 & 0.152177263530724 & 0.304354527061448 & 0.847822736469276 \tabularnewline
34 & 0.134780565846445 & 0.269561131692889 & 0.865219434153555 \tabularnewline
35 & 0.194034740653128 & 0.388069481306255 & 0.805965259346872 \tabularnewline
36 & 0.186383932350750 & 0.372767864701499 & 0.81361606764925 \tabularnewline
37 & 0.126815856133369 & 0.253631712266737 & 0.873184143866631 \tabularnewline
38 & 0.063261094160008 & 0.126522188320016 & 0.936738905839992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57787&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]0.545195235092514[/C][C]0.909609529814973[/C][C]0.454804764907486[/C][/ROW]
[ROW][C]20[/C][C]0.376182279428507[/C][C]0.752364558857014[/C][C]0.623817720571493[/C][/ROW]
[ROW][C]21[/C][C]0.447594288741657[/C][C]0.895188577483314[/C][C]0.552405711258343[/C][/ROW]
[ROW][C]22[/C][C]0.319108602978687[/C][C]0.638217205957373[/C][C]0.680891397021313[/C][/ROW]
[ROW][C]23[/C][C]0.247362030100271[/C][C]0.494724060200543[/C][C]0.752637969899729[/C][/ROW]
[ROW][C]24[/C][C]0.28189039528837[/C][C]0.56378079057674[/C][C]0.71810960471163[/C][/ROW]
[ROW][C]25[/C][C]0.256230594218741[/C][C]0.512461188437483[/C][C]0.743769405781259[/C][/ROW]
[ROW][C]26[/C][C]0.241597701303076[/C][C]0.483195402606152[/C][C]0.758402298696924[/C][/ROW]
[ROW][C]27[/C][C]0.499736242217337[/C][C]0.999472484434675[/C][C]0.500263757782663[/C][/ROW]
[ROW][C]28[/C][C]0.507493646068328[/C][C]0.985012707863344[/C][C]0.492506353931672[/C][/ROW]
[ROW][C]29[/C][C]0.435017231678514[/C][C]0.870034463357029[/C][C]0.564982768321486[/C][/ROW]
[ROW][C]30[/C][C]0.348481267722258[/C][C]0.696962535444515[/C][C]0.651518732277742[/C][/ROW]
[ROW][C]31[/C][C]0.303593934121942[/C][C]0.607187868243883[/C][C]0.696406065878058[/C][/ROW]
[ROW][C]32[/C][C]0.218856992319492[/C][C]0.437713984638984[/C][C]0.781143007680508[/C][/ROW]
[ROW][C]33[/C][C]0.152177263530724[/C][C]0.304354527061448[/C][C]0.847822736469276[/C][/ROW]
[ROW][C]34[/C][C]0.134780565846445[/C][C]0.269561131692889[/C][C]0.865219434153555[/C][/ROW]
[ROW][C]35[/C][C]0.194034740653128[/C][C]0.388069481306255[/C][C]0.805965259346872[/C][/ROW]
[ROW][C]36[/C][C]0.186383932350750[/C][C]0.372767864701499[/C][C]0.81361606764925[/C][/ROW]
[ROW][C]37[/C][C]0.126815856133369[/C][C]0.253631712266737[/C][C]0.873184143866631[/C][/ROW]
[ROW][C]38[/C][C]0.063261094160008[/C][C]0.126522188320016[/C][C]0.936738905839992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57787&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57787&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
190.5451952350925140.9096095298149730.454804764907486
200.3761822794285070.7523645588570140.623817720571493
210.4475942887416570.8951885774833140.552405711258343
220.3191086029786870.6382172059573730.680891397021313
230.2473620301002710.4947240602005430.752637969899729
240.281890395288370.563780790576740.71810960471163
250.2562305942187410.5124611884374830.743769405781259
260.2415977013030760.4831954026061520.758402298696924
270.4997362422173370.9994724844346750.500263757782663
280.5074936460683280.9850127078633440.492506353931672
290.4350172316785140.8700344633570290.564982768321486
300.3484812677222580.6969625354445150.651518732277742
310.3035939341219420.6071878682438830.696406065878058
320.2188569923194920.4377139846389840.781143007680508
330.1521772635307240.3043545270614480.847822736469276
340.1347805658464450.2695611316928890.865219434153555
350.1940347406531280.3880694813062550.805965259346872
360.1863839323507500.3727678647014990.81361606764925
370.1268158561333690.2536317122667370.873184143866631
380.0632610941600080.1265221883200160.936738905839992






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=57787&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=57787&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57787&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')
}