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Description of Statistical Computation

Author's title

Paper: Regressie analyse (seasonal dummies, linear trend en gegevens van vo...

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 19 Dec 2009 23:08:45 -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/Dec/20/t126128965073gdx3s0vm9kmei.htm/, Retrieved Sat, 27 Apr 2024 10:26:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69788, Retrieved Sat, 27 Apr 2024 10:26:43 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Paper: Regressie ...] [2009-12-20 06:08:45] [762da55b2e2304daaed24a7cc507d14d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
79	75	74	78	84
79	79	75	74	78
82	79	79	75	74
88	82	79	79	75
81	88	82	79	79
69	81	88	82	79
62	69	81	88	82
62	62	69	81	88
68	62	62	69	81
57	68	62	62	69
67	57	68	62	62
72	67	57	68	62
75	72	67	57	68
81	75	72	67	57
80	81	75	72	67
79	80	81	75	72
81	79	80	81	75
83	81	79	80	81
84	83	81	79	80
90	84	83	81	79
84	90	84	83	81
90	84	90	84	83
92	90	84	90	84
93	92	90	84	90
85	93	92	90	84
93	85	93	92	90
94	93	85	93	92
94	94	93	85	93
102	94	94	93	85
96	102	94	94	93
96	96	102	94	94
92	96	96	102	94
90	92	96	96	102
84	90	92	96	96
86	84	90	92	96
70	86	84	90	92
67	70	86	84	90
60	67	70	86	84
62	60	67	70	86
61	62	60	67	70
54	61	62	60	67
50	54	61	62	60
45	50	54	61	62
34	45	50	54	61
37	34	45	50	54
44	37	34	45	50
34	44	37	34	45
37	34	44	37	34
31	37	34	44	37
31	31	37	34	44
28	31	31	37	34
31	28	31	31	37
33	31	28	31	31
36	33	31	28	31
39	36	33	31	28
42	39	36	33	31

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 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 & 8 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=69788&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]8 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=69788&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69788&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 time8 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] = + 6.64321270528053 + 0.872702527227202`Y(t-1)`[t] + 0.258918872405125`Y(t-2)`[t] -0.0448813312088279`Y(t-3)`[t] -0.167125823727214`Y(t-4) `[t] -0.64550965373359M1[t] + 2.56198536203161M2[t] + 2.28982093315230M3[t] + 2.77357881188303M4[t] + 0.862448902919936M5[t] -2.21338885997563M6[t] -0.527309563378737M7[t] + 0.85100122897588M8[t] + 2.81894668946818M9[t] + 1.30992470299167M10[t] + 2.642957463527M11[t] -0.0856389618791044t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  6.64321270528053 +  0.872702527227202`Y(t-1)`[t] +  0.258918872405125`Y(t-2)`[t] -0.0448813312088279`Y(t-3)`[t] -0.167125823727214`Y(t-4)

`[t] -0.64550965373359M1[t] +  2.56198536203161M2[t] +  2.28982093315230M3[t] +  2.77357881188303M4[t] +  0.862448902919936M5[t] -2.21338885997563M6[t] -0.527309563378737M7[t] +  0.85100122897588M8[t] +  2.81894668946818M9[t] +  1.30992470299167M10[t] +  2.642957463527M11[t] -0.0856389618791044t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69788&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  6.64321270528053 +  0.872702527227202`Y(t-1)`[t] +  0.258918872405125`Y(t-2)`[t] -0.0448813312088279`Y(t-3)`[t] -0.167125823727214`Y(t-4)

`[t] -0.64550965373359M1[t] +  2.56198536203161M2[t] +  2.28982093315230M3[t] +  2.77357881188303M4[t] +  0.862448902919936M5[t] -2.21338885997563M6[t] -0.527309563378737M7[t] +  0.85100122897588M8[t] +  2.81894668946818M9[t] +  1.30992470299167M10[t] +  2.642957463527M11[t] -0.0856389618791044t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69788&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69788&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] = + 6.64321270528053 + 0.872702527227202`Y(t-1)`[t] + 0.258918872405125`Y(t-2)`[t] -0.0448813312088279`Y(t-3)`[t] -0.167125823727214`Y(t-4) `[t] -0.64550965373359M1[t] + 2.56198536203161M2[t] + 2.28982093315230M3[t] + 2.77357881188303M4[t] + 0.862448902919936M5[t] -2.21338885997563M6[t] -0.527309563378737M7[t] + 0.85100122897588M8[t] + 2.81894668946818M9[t] + 1.30992470299167M10[t] + 2.642957463527M11[t] -0.0856389618791044t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)6.643212705280535.9573661.11510.2716210.135811
`Y(t-1)`0.8727025272272020.1588145.49513e-061e-06
`Y(t-2)`0.2589188724051250.209611.23520.224130.112065
`Y(t-3)`-0.04488133120882790.20937-0.21440.831380.41569
`Y(t-4) `-0.1671258237272140.161755-1.03320.3078750.153937
M1-0.645509653733594.208103-0.15340.8788760.439438
M22.561985362031614.2076230.60890.5461270.273064
M32.289820933152304.1842550.54720.5873270.293664
M42.773578811883034.1969650.66090.5125910.256296
M50.8624489029199364.1783640.20640.8375460.418773
M6-2.213388859975634.188079-0.52850.6001490.300074
M7-0.5273095633787374.230848-0.12460.9014530.450727
M80.851001228975884.2057540.20230.8407010.420351
M92.818946689468184.518710.62380.5363660.268183
M101.309924702991674.4299820.29570.7690320.384516
M112.6429574635274.4200520.59790.5533320.276666
t-0.08563896187910440.066964-1.27890.2084940.104247

\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) & 6.64321270528053 & 5.957366 & 1.1151 & 0.271621 & 0.135811 \tabularnewline
`Y(t-1)` & 0.872702527227202 & 0.158814 & 5.4951 & 3e-06 & 1e-06 \tabularnewline
`Y(t-2)` & 0.258918872405125 & 0.20961 & 1.2352 & 0.22413 & 0.112065 \tabularnewline
`Y(t-3)` & -0.0448813312088279 & 0.20937 & -0.2144 & 0.83138 & 0.41569 \tabularnewline
`Y(t-4)

` & -0.167125823727214 & 0.161755 & -1.0332 & 0.307875 & 0.153937 \tabularnewline
M1 & -0.64550965373359 & 4.208103 & -0.1534 & 0.878876 & 0.439438 \tabularnewline
M2 & 2.56198536203161 & 4.207623 & 0.6089 & 0.546127 & 0.273064 \tabularnewline
M3 & 2.28982093315230 & 4.184255 & 0.5472 & 0.587327 & 0.293664 \tabularnewline
M4 & 2.77357881188303 & 4.196965 & 0.6609 & 0.512591 & 0.256296 \tabularnewline
M5 & 0.862448902919936 & 4.178364 & 0.2064 & 0.837546 & 0.418773 \tabularnewline
M6 & -2.21338885997563 & 4.188079 & -0.5285 & 0.600149 & 0.300074 \tabularnewline
M7 & -0.527309563378737 & 4.230848 & -0.1246 & 0.901453 & 0.450727 \tabularnewline
M8 & 0.85100122897588 & 4.205754 & 0.2023 & 0.840701 & 0.420351 \tabularnewline
M9 & 2.81894668946818 & 4.51871 & 0.6238 & 0.536366 & 0.268183 \tabularnewline
M10 & 1.30992470299167 & 4.429982 & 0.2957 & 0.769032 & 0.384516 \tabularnewline
M11 & 2.642957463527 & 4.420052 & 0.5979 & 0.553332 & 0.276666 \tabularnewline
t & -0.0856389618791044 & 0.066964 & -1.2789 & 0.208494 & 0.104247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69788&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]6.64321270528053[/C][C]5.957366[/C][C]1.1151[/C][C]0.271621[/C][C]0.135811[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.872702527227202[/C][C]0.158814[/C][C]5.4951[/C][C]3e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.258918872405125[/C][C]0.20961[/C][C]1.2352[/C][C]0.22413[/C][C]0.112065[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.0448813312088279[/C][C]0.20937[/C][C]-0.2144[/C][C]0.83138[/C][C]0.41569[/C][/ROW]
[ROW][C]`Y(t-4)

`[/C][C]-0.167125823727214[/C][C]0.161755[/C][C]-1.0332[/C][C]0.307875[/C][C]0.153937[/C][/ROW]
[ROW][C]M1[/C][C]-0.64550965373359[/C][C]4.208103[/C][C]-0.1534[/C][C]0.878876[/C][C]0.439438[/C][/ROW]
[ROW][C]M2[/C][C]2.56198536203161[/C][C]4.207623[/C][C]0.6089[/C][C]0.546127[/C][C]0.273064[/C][/ROW]
[ROW][C]M3[/C][C]2.28982093315230[/C][C]4.184255[/C][C]0.5472[/C][C]0.587327[/C][C]0.293664[/C][/ROW]
[ROW][C]M4[/C][C]2.77357881188303[/C][C]4.196965[/C][C]0.6609[/C][C]0.512591[/C][C]0.256296[/C][/ROW]
[ROW][C]M5[/C][C]0.862448902919936[/C][C]4.178364[/C][C]0.2064[/C][C]0.837546[/C][C]0.418773[/C][/ROW]
[ROW][C]M6[/C][C]-2.21338885997563[/C][C]4.188079[/C][C]-0.5285[/C][C]0.600149[/C][C]0.300074[/C][/ROW]
[ROW][C]M7[/C][C]-0.527309563378737[/C][C]4.230848[/C][C]-0.1246[/C][C]0.901453[/C][C]0.450727[/C][/ROW]
[ROW][C]M8[/C][C]0.85100122897588[/C][C]4.205754[/C][C]0.2023[/C][C]0.840701[/C][C]0.420351[/C][/ROW]
[ROW][C]M9[/C][C]2.81894668946818[/C][C]4.51871[/C][C]0.6238[/C][C]0.536366[/C][C]0.268183[/C][/ROW]
[ROW][C]M10[/C][C]1.30992470299167[/C][C]4.429982[/C][C]0.2957[/C][C]0.769032[/C][C]0.384516[/C][/ROW]
[ROW][C]M11[/C][C]2.642957463527[/C][C]4.420052[/C][C]0.5979[/C][C]0.553332[/C][C]0.276666[/C][/ROW]
[ROW][C]t[/C][C]-0.0856389618791044[/C][C]0.066964[/C][C]-1.2789[/C][C]0.208494[/C][C]0.104247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69788&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69788&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)6.643212705280535.9573661.11510.2716210.135811
`Y(t-1)`0.8727025272272020.1588145.49513e-061e-06
`Y(t-2)`0.2589188724051250.209611.23520.224130.112065
`Y(t-3)`-0.04488133120882790.20937-0.21440.831380.41569
`Y(t-4) `-0.1671258237272140.161755-1.03320.3078750.153937
M1-0.645509653733594.208103-0.15340.8788760.439438
M22.561985362031614.2076230.60890.5461270.273064
M32.289820933152304.1842550.54720.5873270.293664
M42.773578811883034.1969650.66090.5125910.256296
M50.8624489029199364.1783640.20640.8375460.418773
M6-2.213388859975634.188079-0.52850.6001490.300074
M7-0.5273095633787374.230848-0.12460.9014530.450727
M80.851001228975884.2057540.20230.8407010.420351
M92.818946689468184.518710.62380.5363660.268183
M101.309924702991674.4299820.29570.7690320.384516
M112.6429574635274.4200520.59790.5533320.276666
t-0.08563896187910440.066964-1.27890.2084940.104247






Multiple Linear Regression - Regression Statistics
Multiple R0.971615849687214
R-squared0.944037359363406
Adjusted R-squared0.921078327307367
F-TEST (value)41.118343188824
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.21182366115827
Sum Squared Residuals1504.88337469570

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.971615849687214 \tabularnewline
R-squared & 0.944037359363406 \tabularnewline
Adjusted R-squared & 0.921078327307367 \tabularnewline
F-TEST (value) & 41.118343188824 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.21182366115827 \tabularnewline
Sum Squared Residuals & 1504.88337469570 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69788&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.971615849687214[/C][/ROW]
[ROW][C]R-squared[/C][C]0.944037359363406[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.921078327307367[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]41.118343188824[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/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]6.21182366115827[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1504.88337469570[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69788&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69788&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 R0.971615849687214
R-squared0.944037359363406
Adjusted R-squared0.921078327307367
F-TEST (value)41.118343188824
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.21182366115827
Sum Squared Residuals1504.88337469570






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17972.98543716231266.01456283768739
27981.0393024647114-2.03930246471138
38282.3407965272735-0.340796527273466
48885.01037187724422.98962812275582
58188.3580714920717-7.35807149207171
66980.5065463175109-11.5065463175109
76269.0514587602318-7.05145876023176
86260.43960080735391.56039919264613
96862.21793193972765.78206806027238
105768.1791653579236-11.1791653579236
116762.55022535760184.44977464239818
127265.43125862075846.56874137924159
137571.14375106626683.85624893373321
148179.56787981277121.4321201872288
158083.3273833092751-3.32738330927510
167983.4360398210677-4.43603982106772
178179.53698409215861.46301590784141
188376.90411993827876.09588006172126
198480.97981022719723.02018977280278
209083.74038549101986.25961450898025
218490.6938117155292-6.6938117155292
229085.03731585957794.96268414042212
239289.53099777618642.46900222381363
249389.36785268455513.63214731544489
258590.7607112960902-5.76071129609018
269386.06734839978296.93265160021715
279490.24068126893783.75931873106221
289493.7747785182010.225221481798963
2910293.0148844599118.98511554008894
309695.45314003192750.546859968072538
319693.72159035879582.27840964120418
329293.10169830517-1.10169830516997
339090.4254760923096-0.425476092309607
348487.0524895422424-3.05248954224237
358682.72535575756043.27464424243956
367080.9469171095045-10.9469171095045
376767.3739054377742-0.373905437774209
386064.6479442314423-4.64794423144232
396257.78831618476494.21168381523508
406160.9280652224970.0719347775030117
415459.3919783588813-5.39197835888127
425050.9427831747839-0.942783174783904
434546.9506109775114-1.9506109775114
443443.3253898244194-9.32538982441942
453735.66278025243361.33721974756643
464434.73102924025629.26897075974382
473444.1934211086514-10.1934211086514
483736.2539715851820.746028414818011
493134.7361950375562-3.7361950375562
503132.6775250912922-1.67752509129224
512832.3028227097487-4.30282270974872
523129.85074456099011.14925543900993
533330.69808159697742.30191840302261
543630.1934105374995.80658946250101
553935.29652967626383.70347032373621
564239.3929255720372.60707442796301

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 79 & 72.9854371623126 & 6.01456283768739 \tabularnewline
2 & 79 & 81.0393024647114 & -2.03930246471138 \tabularnewline
3 & 82 & 82.3407965272735 & -0.340796527273466 \tabularnewline
4 & 88 & 85.0103718772442 & 2.98962812275582 \tabularnewline
5 & 81 & 88.3580714920717 & -7.35807149207171 \tabularnewline
6 & 69 & 80.5065463175109 & -11.5065463175109 \tabularnewline
7 & 62 & 69.0514587602318 & -7.05145876023176 \tabularnewline
8 & 62 & 60.4396008073539 & 1.56039919264613 \tabularnewline
9 & 68 & 62.2179319397276 & 5.78206806027238 \tabularnewline
10 & 57 & 68.1791653579236 & -11.1791653579236 \tabularnewline
11 & 67 & 62.5502253576018 & 4.44977464239818 \tabularnewline
12 & 72 & 65.4312586207584 & 6.56874137924159 \tabularnewline
13 & 75 & 71.1437510662668 & 3.85624893373321 \tabularnewline
14 & 81 & 79.5678798127712 & 1.4321201872288 \tabularnewline
15 & 80 & 83.3273833092751 & -3.32738330927510 \tabularnewline
16 & 79 & 83.4360398210677 & -4.43603982106772 \tabularnewline
17 & 81 & 79.5369840921586 & 1.46301590784141 \tabularnewline
18 & 83 & 76.9041199382787 & 6.09588006172126 \tabularnewline
19 & 84 & 80.9798102271972 & 3.02018977280278 \tabularnewline
20 & 90 & 83.7403854910198 & 6.25961450898025 \tabularnewline
21 & 84 & 90.6938117155292 & -6.6938117155292 \tabularnewline
22 & 90 & 85.0373158595779 & 4.96268414042212 \tabularnewline
23 & 92 & 89.5309977761864 & 2.46900222381363 \tabularnewline
24 & 93 & 89.3678526845551 & 3.63214731544489 \tabularnewline
25 & 85 & 90.7607112960902 & -5.76071129609018 \tabularnewline
26 & 93 & 86.0673483997829 & 6.93265160021715 \tabularnewline
27 & 94 & 90.2406812689378 & 3.75931873106221 \tabularnewline
28 & 94 & 93.774778518201 & 0.225221481798963 \tabularnewline
29 & 102 & 93.014884459911 & 8.98511554008894 \tabularnewline
30 & 96 & 95.4531400319275 & 0.546859968072538 \tabularnewline
31 & 96 & 93.7215903587958 & 2.27840964120418 \tabularnewline
32 & 92 & 93.10169830517 & -1.10169830516997 \tabularnewline
33 & 90 & 90.4254760923096 & -0.425476092309607 \tabularnewline
34 & 84 & 87.0524895422424 & -3.05248954224237 \tabularnewline
35 & 86 & 82.7253557575604 & 3.27464424243956 \tabularnewline
36 & 70 & 80.9469171095045 & -10.9469171095045 \tabularnewline
37 & 67 & 67.3739054377742 & -0.373905437774209 \tabularnewline
38 & 60 & 64.6479442314423 & -4.64794423144232 \tabularnewline
39 & 62 & 57.7883161847649 & 4.21168381523508 \tabularnewline
40 & 61 & 60.928065222497 & 0.0719347775030117 \tabularnewline
41 & 54 & 59.3919783588813 & -5.39197835888127 \tabularnewline
42 & 50 & 50.9427831747839 & -0.942783174783904 \tabularnewline
43 & 45 & 46.9506109775114 & -1.9506109775114 \tabularnewline
44 & 34 & 43.3253898244194 & -9.32538982441942 \tabularnewline
45 & 37 & 35.6627802524336 & 1.33721974756643 \tabularnewline
46 & 44 & 34.7310292402562 & 9.26897075974382 \tabularnewline
47 & 34 & 44.1934211086514 & -10.1934211086514 \tabularnewline
48 & 37 & 36.253971585182 & 0.746028414818011 \tabularnewline
49 & 31 & 34.7361950375562 & -3.7361950375562 \tabularnewline
50 & 31 & 32.6775250912922 & -1.67752509129224 \tabularnewline
51 & 28 & 32.3028227097487 & -4.30282270974872 \tabularnewline
52 & 31 & 29.8507445609901 & 1.14925543900993 \tabularnewline
53 & 33 & 30.6980815969774 & 2.30191840302261 \tabularnewline
54 & 36 & 30.193410537499 & 5.80658946250101 \tabularnewline
55 & 39 & 35.2965296762638 & 3.70347032373621 \tabularnewline
56 & 42 & 39.392925572037 & 2.60707442796301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69788&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]79[/C][C]72.9854371623126[/C][C]6.01456283768739[/C][/ROW]
[ROW][C]2[/C][C]79[/C][C]81.0393024647114[/C][C]-2.03930246471138[/C][/ROW]
[ROW][C]3[/C][C]82[/C][C]82.3407965272735[/C][C]-0.340796527273466[/C][/ROW]
[ROW][C]4[/C][C]88[/C][C]85.0103718772442[/C][C]2.98962812275582[/C][/ROW]
[ROW][C]5[/C][C]81[/C][C]88.3580714920717[/C][C]-7.35807149207171[/C][/ROW]
[ROW][C]6[/C][C]69[/C][C]80.5065463175109[/C][C]-11.5065463175109[/C][/ROW]
[ROW][C]7[/C][C]62[/C][C]69.0514587602318[/C][C]-7.05145876023176[/C][/ROW]
[ROW][C]8[/C][C]62[/C][C]60.4396008073539[/C][C]1.56039919264613[/C][/ROW]
[ROW][C]9[/C][C]68[/C][C]62.2179319397276[/C][C]5.78206806027238[/C][/ROW]
[ROW][C]10[/C][C]57[/C][C]68.1791653579236[/C][C]-11.1791653579236[/C][/ROW]
[ROW][C]11[/C][C]67[/C][C]62.5502253576018[/C][C]4.44977464239818[/C][/ROW]
[ROW][C]12[/C][C]72[/C][C]65.4312586207584[/C][C]6.56874137924159[/C][/ROW]
[ROW][C]13[/C][C]75[/C][C]71.1437510662668[/C][C]3.85624893373321[/C][/ROW]
[ROW][C]14[/C][C]81[/C][C]79.5678798127712[/C][C]1.4321201872288[/C][/ROW]
[ROW][C]15[/C][C]80[/C][C]83.3273833092751[/C][C]-3.32738330927510[/C][/ROW]
[ROW][C]16[/C][C]79[/C][C]83.4360398210677[/C][C]-4.43603982106772[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]79.5369840921586[/C][C]1.46301590784141[/C][/ROW]
[ROW][C]18[/C][C]83[/C][C]76.9041199382787[/C][C]6.09588006172126[/C][/ROW]
[ROW][C]19[/C][C]84[/C][C]80.9798102271972[/C][C]3.02018977280278[/C][/ROW]
[ROW][C]20[/C][C]90[/C][C]83.7403854910198[/C][C]6.25961450898025[/C][/ROW]
[ROW][C]21[/C][C]84[/C][C]90.6938117155292[/C][C]-6.6938117155292[/C][/ROW]
[ROW][C]22[/C][C]90[/C][C]85.0373158595779[/C][C]4.96268414042212[/C][/ROW]
[ROW][C]23[/C][C]92[/C][C]89.5309977761864[/C][C]2.46900222381363[/C][/ROW]
[ROW][C]24[/C][C]93[/C][C]89.3678526845551[/C][C]3.63214731544489[/C][/ROW]
[ROW][C]25[/C][C]85[/C][C]90.7607112960902[/C][C]-5.76071129609018[/C][/ROW]
[ROW][C]26[/C][C]93[/C][C]86.0673483997829[/C][C]6.93265160021715[/C][/ROW]
[ROW][C]27[/C][C]94[/C][C]90.2406812689378[/C][C]3.75931873106221[/C][/ROW]
[ROW][C]28[/C][C]94[/C][C]93.774778518201[/C][C]0.225221481798963[/C][/ROW]
[ROW][C]29[/C][C]102[/C][C]93.014884459911[/C][C]8.98511554008894[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]95.4531400319275[/C][C]0.546859968072538[/C][/ROW]
[ROW][C]31[/C][C]96[/C][C]93.7215903587958[/C][C]2.27840964120418[/C][/ROW]
[ROW][C]32[/C][C]92[/C][C]93.10169830517[/C][C]-1.10169830516997[/C][/ROW]
[ROW][C]33[/C][C]90[/C][C]90.4254760923096[/C][C]-0.425476092309607[/C][/ROW]
[ROW][C]34[/C][C]84[/C][C]87.0524895422424[/C][C]-3.05248954224237[/C][/ROW]
[ROW][C]35[/C][C]86[/C][C]82.7253557575604[/C][C]3.27464424243956[/C][/ROW]
[ROW][C]36[/C][C]70[/C][C]80.9469171095045[/C][C]-10.9469171095045[/C][/ROW]
[ROW][C]37[/C][C]67[/C][C]67.3739054377742[/C][C]-0.373905437774209[/C][/ROW]
[ROW][C]38[/C][C]60[/C][C]64.6479442314423[/C][C]-4.64794423144232[/C][/ROW]
[ROW][C]39[/C][C]62[/C][C]57.7883161847649[/C][C]4.21168381523508[/C][/ROW]
[ROW][C]40[/C][C]61[/C][C]60.928065222497[/C][C]0.0719347775030117[/C][/ROW]
[ROW][C]41[/C][C]54[/C][C]59.3919783588813[/C][C]-5.39197835888127[/C][/ROW]
[ROW][C]42[/C][C]50[/C][C]50.9427831747839[/C][C]-0.942783174783904[/C][/ROW]
[ROW][C]43[/C][C]45[/C][C]46.9506109775114[/C][C]-1.9506109775114[/C][/ROW]
[ROW][C]44[/C][C]34[/C][C]43.3253898244194[/C][C]-9.32538982441942[/C][/ROW]
[ROW][C]45[/C][C]37[/C][C]35.6627802524336[/C][C]1.33721974756643[/C][/ROW]
[ROW][C]46[/C][C]44[/C][C]34.7310292402562[/C][C]9.26897075974382[/C][/ROW]
[ROW][C]47[/C][C]34[/C][C]44.1934211086514[/C][C]-10.1934211086514[/C][/ROW]
[ROW][C]48[/C][C]37[/C][C]36.253971585182[/C][C]0.746028414818011[/C][/ROW]
[ROW][C]49[/C][C]31[/C][C]34.7361950375562[/C][C]-3.7361950375562[/C][/ROW]
[ROW][C]50[/C][C]31[/C][C]32.6775250912922[/C][C]-1.67752509129224[/C][/ROW]
[ROW][C]51[/C][C]28[/C][C]32.3028227097487[/C][C]-4.30282270974872[/C][/ROW]
[ROW][C]52[/C][C]31[/C][C]29.8507445609901[/C][C]1.14925543900993[/C][/ROW]
[ROW][C]53[/C][C]33[/C][C]30.6980815969774[/C][C]2.30191840302261[/C][/ROW]
[ROW][C]54[/C][C]36[/C][C]30.193410537499[/C][C]5.80658946250101[/C][/ROW]
[ROW][C]55[/C][C]39[/C][C]35.2965296762638[/C][C]3.70347032373621[/C][/ROW]
[ROW][C]56[/C][C]42[/C][C]39.392925572037[/C][C]2.60707442796301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69788&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69788&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
17972.98543716231266.01456283768739
27981.0393024647114-2.03930246471138
38282.3407965272735-0.340796527273466
48885.01037187724422.98962812275582
58188.3580714920717-7.35807149207171
66980.5065463175109-11.5065463175109
76269.0514587602318-7.05145876023176
86260.43960080735391.56039919264613
96862.21793193972765.78206806027238
105768.1791653579236-11.1791653579236
116762.55022535760184.44977464239818
127265.43125862075846.56874137924159
137571.14375106626683.85624893373321
148179.56787981277121.4321201872288
158083.3273833092751-3.32738330927510
167983.4360398210677-4.43603982106772
178179.53698409215861.46301590784141
188376.90411993827876.09588006172126
198480.97981022719723.02018977280278
209083.74038549101986.25961450898025
218490.6938117155292-6.6938117155292
229085.03731585957794.96268414042212
239289.53099777618642.46900222381363
249389.36785268455513.63214731544489
258590.7607112960902-5.76071129609018
269386.06734839978296.93265160021715
279490.24068126893783.75931873106221
289493.7747785182010.225221481798963
2910293.0148844599118.98511554008894
309695.45314003192750.546859968072538
319693.72159035879582.27840964120418
329293.10169830517-1.10169830516997
339090.4254760923096-0.425476092309607
348487.0524895422424-3.05248954224237
358682.72535575756043.27464424243956
367080.9469171095045-10.9469171095045
376767.3739054377742-0.373905437774209
386064.6479442314423-4.64794423144232
396257.78831618476494.21168381523508
406160.9280652224970.0719347775030117
415459.3919783588813-5.39197835888127
425050.9427831747839-0.942783174783904
434546.9506109775114-1.9506109775114
443443.3253898244194-9.32538982441942
453735.66278025243361.33721974756643
464434.73102924025629.26897075974382
473444.1934211086514-10.1934211086514
483736.2539715851820.746028414818011
493134.7361950375562-3.7361950375562
503132.6775250912922-1.67752509129224
512832.3028227097487-4.30282270974872
523129.85074456099011.14925543900993
533330.69808159697742.30191840302261
543630.1934105374995.80658946250101
553935.29652967626383.70347032373621
564239.3929255720372.60707442796301






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.6783014152481940.6433971695036130.321698584751806
210.7459480321590530.5081039356818950.254051967840947
220.8693060115166040.2613879769667920.130693988483396
230.8365065503419690.3269868993160620.163493449658031
240.8379787972901950.3240424054196090.162021202709805
250.8656822671100320.2686354657799360.134317732889968
260.8031306806048410.3937386387903170.196869319395159
270.7323832238937820.5352335522124370.267616776106218
280.6414466535847630.7171066928304740.358553346415237
290.6863163314984070.6273673370031870.313683668501593
300.5970398160841480.8059203678317050.402960183915852
310.5047634208891320.9904731582217370.495236579110868
320.5670060830681840.8659878338636330.432993916931816
330.5051869967891490.9896260064217020.494813003210851
340.5766881717974990.8466236564050020.423311828202501
350.5165524957150540.9668950085698930.483447504284946
360.895410266304720.2091794673905600.104589733695280

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.678301415248194 & 0.643397169503613 & 0.321698584751806 \tabularnewline
21 & 0.745948032159053 & 0.508103935681895 & 0.254051967840947 \tabularnewline
22 & 0.869306011516604 & 0.261387976966792 & 0.130693988483396 \tabularnewline
23 & 0.836506550341969 & 0.326986899316062 & 0.163493449658031 \tabularnewline
24 & 0.837978797290195 & 0.324042405419609 & 0.162021202709805 \tabularnewline
25 & 0.865682267110032 & 0.268635465779936 & 0.134317732889968 \tabularnewline
26 & 0.803130680604841 & 0.393738638790317 & 0.196869319395159 \tabularnewline
27 & 0.732383223893782 & 0.535233552212437 & 0.267616776106218 \tabularnewline
28 & 0.641446653584763 & 0.717106692830474 & 0.358553346415237 \tabularnewline
29 & 0.686316331498407 & 0.627367337003187 & 0.313683668501593 \tabularnewline
30 & 0.597039816084148 & 0.805920367831705 & 0.402960183915852 \tabularnewline
31 & 0.504763420889132 & 0.990473158221737 & 0.495236579110868 \tabularnewline
32 & 0.567006083068184 & 0.865987833863633 & 0.432993916931816 \tabularnewline
33 & 0.505186996789149 & 0.989626006421702 & 0.494813003210851 \tabularnewline
34 & 0.576688171797499 & 0.846623656405002 & 0.423311828202501 \tabularnewline
35 & 0.516552495715054 & 0.966895008569893 & 0.483447504284946 \tabularnewline
36 & 0.89541026630472 & 0.209179467390560 & 0.104589733695280 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69788&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]20[/C][C]0.678301415248194[/C][C]0.643397169503613[/C][C]0.321698584751806[/C][/ROW]
[ROW][C]21[/C][C]0.745948032159053[/C][C]0.508103935681895[/C][C]0.254051967840947[/C][/ROW]
[ROW][C]22[/C][C]0.869306011516604[/C][C]0.261387976966792[/C][C]0.130693988483396[/C][/ROW]
[ROW][C]23[/C][C]0.836506550341969[/C][C]0.326986899316062[/C][C]0.163493449658031[/C][/ROW]
[ROW][C]24[/C][C]0.837978797290195[/C][C]0.324042405419609[/C][C]0.162021202709805[/C][/ROW]
[ROW][C]25[/C][C]0.865682267110032[/C][C]0.268635465779936[/C][C]0.134317732889968[/C][/ROW]
[ROW][C]26[/C][C]0.803130680604841[/C][C]0.393738638790317[/C][C]0.196869319395159[/C][/ROW]
[ROW][C]27[/C][C]0.732383223893782[/C][C]0.535233552212437[/C][C]0.267616776106218[/C][/ROW]
[ROW][C]28[/C][C]0.641446653584763[/C][C]0.717106692830474[/C][C]0.358553346415237[/C][/ROW]
[ROW][C]29[/C][C]0.686316331498407[/C][C]0.627367337003187[/C][C]0.313683668501593[/C][/ROW]
[ROW][C]30[/C][C]0.597039816084148[/C][C]0.805920367831705[/C][C]0.402960183915852[/C][/ROW]
[ROW][C]31[/C][C]0.504763420889132[/C][C]0.990473158221737[/C][C]0.495236579110868[/C][/ROW]
[ROW][C]32[/C][C]0.567006083068184[/C][C]0.865987833863633[/C][C]0.432993916931816[/C][/ROW]
[ROW][C]33[/C][C]0.505186996789149[/C][C]0.989626006421702[/C][C]0.494813003210851[/C][/ROW]
[ROW][C]34[/C][C]0.576688171797499[/C][C]0.846623656405002[/C][C]0.423311828202501[/C][/ROW]
[ROW][C]35[/C][C]0.516552495715054[/C][C]0.966895008569893[/C][C]0.483447504284946[/C][/ROW]
[ROW][C]36[/C][C]0.89541026630472[/C][C]0.209179467390560[/C][C]0.104589733695280[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69788&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69788&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
200.6783014152481940.6433971695036130.321698584751806
210.7459480321590530.5081039356818950.254051967840947
220.8693060115166040.2613879769667920.130693988483396
230.8365065503419690.3269868993160620.163493449658031
240.8379787972901950.3240424054196090.162021202709805
250.8656822671100320.2686354657799360.134317732889968
260.8031306806048410.3937386387903170.196869319395159
270.7323832238937820.5352335522124370.267616776106218
280.6414466535847630.7171066928304740.358553346415237
290.6863163314984070.6273673370031870.313683668501593
300.5970398160841480.8059203678317050.402960183915852
310.5047634208891320.9904731582217370.495236579110868
320.5670060830681840.8659878338636330.432993916931816
330.5051869967891490.9896260064217020.494813003210851
340.5766881717974990.8466236564050020.423311828202501
350.5165524957150540.9668950085698930.483447504284946
360.895410266304720.2091794673905600.104589733695280






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=69788&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=69788&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69788&T=6

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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)

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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')
}