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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, 17 Nov 2009 11:05:50 -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/17/t1258481279t7yyzi75yj9paza.htm/, Retrieved Thu, 19 Jun 2025 14:45:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57389, Retrieved Thu, 19 Jun 2025 14:45:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact326

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-17 18:05:50] [508aab72d879399b4187e5fcd8f7c773] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.9	1.4
8.8	1.2
8.3	1
7.5	1.7
7.2	2.4
7.4	2
8.8	2.1
9.3	2
9.3	1.8
8.7	2.7
8.2	2.3
8.3	1.9
8.5	2
8.6	2.3
8.5	2.8
8.2	2.4
8.1	2.3
7.9	2.7
8.6	2.7
8.7	2.9
8.7	3
8.5	2.2
8.4	2.3
8.5	2.8
8.7	2.8
8.7	2.8
8.6	2.2
8.5	2.6
8.3	2.8
8	2.5
8.2	2.4
8.1	2.3
8.1	1.9
8	1.7
7.9	2
7.9	2.1
8	1.7
8	1.8
7.9	1.8
8	1.8
7.7	1.3
7.2	1.3
7.5	1.3
7.3	1.2
7	1.4
7	2.2
7	2.9
7.2	3.1
7.3	3.5
7.1	3.6
6.8	4.4
6.4	4.1
6.1	5.1
6.5	5.8
7.7	5.9
7.9	5.4
7.5	5.5
6.9	4.8
6.6	3.2
6.9	2.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57389&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]4 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=57389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57389&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 8.6158773356344 -0.271381633533570X[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  8.6158773356344 -0.271381633533570X[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57389&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  8.6158773356344 -0.271381633533570X[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57389&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] = + 8.6158773356344 -0.271381633533570X[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.61587733563440.21625339.841700
X-0.2713816335335700.075663-3.58670.0006880.000344

\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) & 8.6158773356344 & 0.216253 & 39.8417 & 0 & 0 \tabularnewline
X & -0.271381633533570 & 0.075663 & -3.5867 & 0.000688 & 0.000344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57389&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]8.6158773356344[/C][C]0.216253[/C][C]39.8417[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-0.271381633533570[/C][C]0.075663[/C][C]-3.5867[/C][C]0.000688[/C][C]0.000344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57389&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57389&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)8.61587733563440.21625339.841700
X-0.2713816335335700.075663-3.58670.0006880.000344






Multiple Linear Regression - Regression Statistics
Multiple R0.426069605833812
R-squared0.18153530901538
Adjusted R-squared0.16742384882599
F-TEST (value)12.8643887010269
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.000688219457232186
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.678230028540176
Sum Squared Residuals26.6797663535893

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.426069605833812 \tabularnewline
R-squared & 0.18153530901538 \tabularnewline
Adjusted R-squared & 0.16742384882599 \tabularnewline
F-TEST (value) & 12.8643887010269 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 0.000688219457232186 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.678230028540176 \tabularnewline
Sum Squared Residuals & 26.6797663535893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57389&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.426069605833812[/C][/ROW]
[ROW][C]R-squared[/C][C]0.18153530901538[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.16742384882599[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]12.8643887010269[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]58[/C][/ROW]
[ROW][C]p-value[/C][C]0.000688219457232186[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.678230028540176[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]26.6797663535893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57389&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57389&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 R0.426069605833812
R-squared0.18153530901538
Adjusted R-squared0.16742384882599
F-TEST (value)12.8643887010269
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.000688219457232186
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.678230028540176
Sum Squared Residuals26.6797663535893






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.98.235943048687420.664056951312576
28.88.29021937539410.509780624605889
38.38.34449570210083-0.0444957021008247
47.58.15452855862733-0.654528558627327
57.27.96456141515383-0.764561415153828
67.48.07311406856726-0.673114068567255
78.88.04597590521390.754024094786102
89.38.073114068567261.22688593143274
99.38.127390395273971.17260960472603
108.77.883146925093760.816853074906242
118.27.991699578507180.208300421492814
128.38.100252231920610.199747768079388
138.58.073114068567260.426885931432744
148.67.991699578507180.608300421492815
158.57.85600876174040.6439912382596
168.27.964561415153830.235438584846171
178.17.991699578507180.108300421492815
187.97.883146925093760.0168530749062435
198.67.883146925093760.716853074906243
208.77.828870598387040.871129401612956
218.77.801732435033690.898267564966313
228.58.018837741860540.481162258139458
238.47.991699578507180.408300421492816
248.57.85600876174040.6439912382596
258.77.85600876174040.843991238259599
268.77.85600876174040.843991238259599
278.68.018837741860540.581162258139458
288.57.910285088447110.589714911552886
298.37.85600876174040.443991238259601
3087.937423251800470.0625767481995292
318.27.964561415153830.235438584846171
328.17.991699578507180.108300421492815
338.18.10025223192061-0.000252231920613064
3488.15452855862733-0.154528558627327
357.98.07311406856726-0.173114068567255
367.98.0459759052139-0.145975905213898
3788.15452855862733-0.154528558627327
3888.12739039527397-0.127390395273970
397.98.12739039527397-0.227390395273969
4088.12739039527397-0.127390395273970
417.78.26308121204075-0.563081212040754
427.28.26308121204075-1.06308121204075
437.58.26308121204075-0.763081212040755
447.38.2902193753941-0.990219375394112
4578.2359430486874-1.23594304868740
4678.01883774186054-1.01883774186054
4777.82887059838704-0.828870598387043
487.27.77459427168033-0.574594271680329
497.37.6660416182669-0.366041618266901
507.17.63890345491354-0.538903454913545
516.87.42179814808669-0.621798148086688
526.47.50321263814676-1.10321263814676
536.17.23183100461319-1.13183100461319
546.57.04186386113969-0.541863861139691
557.77.014725697786330.685274302213667
567.97.150416514553120.749583485446882
577.57.123278351199760.376721648800239
586.97.31324549467326-0.41324549467326
596.67.74745610832697-1.14745610832697
606.97.88314692509376-0.983146925093757

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.9 & 8.23594304868742 & 0.664056951312576 \tabularnewline
2 & 8.8 & 8.2902193753941 & 0.509780624605889 \tabularnewline
3 & 8.3 & 8.34449570210083 & -0.0444957021008247 \tabularnewline
4 & 7.5 & 8.15452855862733 & -0.654528558627327 \tabularnewline
5 & 7.2 & 7.96456141515383 & -0.764561415153828 \tabularnewline
6 & 7.4 & 8.07311406856726 & -0.673114068567255 \tabularnewline
7 & 8.8 & 8.0459759052139 & 0.754024094786102 \tabularnewline
8 & 9.3 & 8.07311406856726 & 1.22688593143274 \tabularnewline
9 & 9.3 & 8.12739039527397 & 1.17260960472603 \tabularnewline
10 & 8.7 & 7.88314692509376 & 0.816853074906242 \tabularnewline
11 & 8.2 & 7.99169957850718 & 0.208300421492814 \tabularnewline
12 & 8.3 & 8.10025223192061 & 0.199747768079388 \tabularnewline
13 & 8.5 & 8.07311406856726 & 0.426885931432744 \tabularnewline
14 & 8.6 & 7.99169957850718 & 0.608300421492815 \tabularnewline
15 & 8.5 & 7.8560087617404 & 0.6439912382596 \tabularnewline
16 & 8.2 & 7.96456141515383 & 0.235438584846171 \tabularnewline
17 & 8.1 & 7.99169957850718 & 0.108300421492815 \tabularnewline
18 & 7.9 & 7.88314692509376 & 0.0168530749062435 \tabularnewline
19 & 8.6 & 7.88314692509376 & 0.716853074906243 \tabularnewline
20 & 8.7 & 7.82887059838704 & 0.871129401612956 \tabularnewline
21 & 8.7 & 7.80173243503369 & 0.898267564966313 \tabularnewline
22 & 8.5 & 8.01883774186054 & 0.481162258139458 \tabularnewline
23 & 8.4 & 7.99169957850718 & 0.408300421492816 \tabularnewline
24 & 8.5 & 7.8560087617404 & 0.6439912382596 \tabularnewline
25 & 8.7 & 7.8560087617404 & 0.843991238259599 \tabularnewline
26 & 8.7 & 7.8560087617404 & 0.843991238259599 \tabularnewline
27 & 8.6 & 8.01883774186054 & 0.581162258139458 \tabularnewline
28 & 8.5 & 7.91028508844711 & 0.589714911552886 \tabularnewline
29 & 8.3 & 7.8560087617404 & 0.443991238259601 \tabularnewline
30 & 8 & 7.93742325180047 & 0.0625767481995292 \tabularnewline
31 & 8.2 & 7.96456141515383 & 0.235438584846171 \tabularnewline
32 & 8.1 & 7.99169957850718 & 0.108300421492815 \tabularnewline
33 & 8.1 & 8.10025223192061 & -0.000252231920613064 \tabularnewline
34 & 8 & 8.15452855862733 & -0.154528558627327 \tabularnewline
35 & 7.9 & 8.07311406856726 & -0.173114068567255 \tabularnewline
36 & 7.9 & 8.0459759052139 & -0.145975905213898 \tabularnewline
37 & 8 & 8.15452855862733 & -0.154528558627327 \tabularnewline
38 & 8 & 8.12739039527397 & -0.127390395273970 \tabularnewline
39 & 7.9 & 8.12739039527397 & -0.227390395273969 \tabularnewline
40 & 8 & 8.12739039527397 & -0.127390395273970 \tabularnewline
41 & 7.7 & 8.26308121204075 & -0.563081212040754 \tabularnewline
42 & 7.2 & 8.26308121204075 & -1.06308121204075 \tabularnewline
43 & 7.5 & 8.26308121204075 & -0.763081212040755 \tabularnewline
44 & 7.3 & 8.2902193753941 & -0.990219375394112 \tabularnewline
45 & 7 & 8.2359430486874 & -1.23594304868740 \tabularnewline
46 & 7 & 8.01883774186054 & -1.01883774186054 \tabularnewline
47 & 7 & 7.82887059838704 & -0.828870598387043 \tabularnewline
48 & 7.2 & 7.77459427168033 & -0.574594271680329 \tabularnewline
49 & 7.3 & 7.6660416182669 & -0.366041618266901 \tabularnewline
50 & 7.1 & 7.63890345491354 & -0.538903454913545 \tabularnewline
51 & 6.8 & 7.42179814808669 & -0.621798148086688 \tabularnewline
52 & 6.4 & 7.50321263814676 & -1.10321263814676 \tabularnewline
53 & 6.1 & 7.23183100461319 & -1.13183100461319 \tabularnewline
54 & 6.5 & 7.04186386113969 & -0.541863861139691 \tabularnewline
55 & 7.7 & 7.01472569778633 & 0.685274302213667 \tabularnewline
56 & 7.9 & 7.15041651455312 & 0.749583485446882 \tabularnewline
57 & 7.5 & 7.12327835119976 & 0.376721648800239 \tabularnewline
58 & 6.9 & 7.31324549467326 & -0.41324549467326 \tabularnewline
59 & 6.6 & 7.74745610832697 & -1.14745610832697 \tabularnewline
60 & 6.9 & 7.88314692509376 & -0.983146925093757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57389&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]8.9[/C][C]8.23594304868742[/C][C]0.664056951312576[/C][/ROW]
[ROW][C]2[/C][C]8.8[/C][C]8.2902193753941[/C][C]0.509780624605889[/C][/ROW]
[ROW][C]3[/C][C]8.3[/C][C]8.34449570210083[/C][C]-0.0444957021008247[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]8.15452855862733[/C][C]-0.654528558627327[/C][/ROW]
[ROW][C]5[/C][C]7.2[/C][C]7.96456141515383[/C][C]-0.764561415153828[/C][/ROW]
[ROW][C]6[/C][C]7.4[/C][C]8.07311406856726[/C][C]-0.673114068567255[/C][/ROW]
[ROW][C]7[/C][C]8.8[/C][C]8.0459759052139[/C][C]0.754024094786102[/C][/ROW]
[ROW][C]8[/C][C]9.3[/C][C]8.07311406856726[/C][C]1.22688593143274[/C][/ROW]
[ROW][C]9[/C][C]9.3[/C][C]8.12739039527397[/C][C]1.17260960472603[/C][/ROW]
[ROW][C]10[/C][C]8.7[/C][C]7.88314692509376[/C][C]0.816853074906242[/C][/ROW]
[ROW][C]11[/C][C]8.2[/C][C]7.99169957850718[/C][C]0.208300421492814[/C][/ROW]
[ROW][C]12[/C][C]8.3[/C][C]8.10025223192061[/C][C]0.199747768079388[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.07311406856726[/C][C]0.426885931432744[/C][/ROW]
[ROW][C]14[/C][C]8.6[/C][C]7.99169957850718[/C][C]0.608300421492815[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]7.8560087617404[/C][C]0.6439912382596[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]7.96456141515383[/C][C]0.235438584846171[/C][/ROW]
[ROW][C]17[/C][C]8.1[/C][C]7.99169957850718[/C][C]0.108300421492815[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]7.88314692509376[/C][C]0.0168530749062435[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]7.88314692509376[/C][C]0.716853074906243[/C][/ROW]
[ROW][C]20[/C][C]8.7[/C][C]7.82887059838704[/C][C]0.871129401612956[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]7.80173243503369[/C][C]0.898267564966313[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.01883774186054[/C][C]0.481162258139458[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]7.99169957850718[/C][C]0.408300421492816[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]7.8560087617404[/C][C]0.6439912382596[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]7.8560087617404[/C][C]0.843991238259599[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]7.8560087617404[/C][C]0.843991238259599[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.01883774186054[/C][C]0.581162258139458[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]7.91028508844711[/C][C]0.589714911552886[/C][/ROW]
[ROW][C]29[/C][C]8.3[/C][C]7.8560087617404[/C][C]0.443991238259601[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.93742325180047[/C][C]0.0625767481995292[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]7.96456141515383[/C][C]0.235438584846171[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]7.99169957850718[/C][C]0.108300421492815[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.10025223192061[/C][C]-0.000252231920613064[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]8.15452855862733[/C][C]-0.154528558627327[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]8.07311406856726[/C][C]-0.173114068567255[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]8.0459759052139[/C][C]-0.145975905213898[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]8.15452855862733[/C][C]-0.154528558627327[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]8.12739039527397[/C][C]-0.127390395273970[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]8.12739039527397[/C][C]-0.227390395273969[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]8.12739039527397[/C][C]-0.127390395273970[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]8.26308121204075[/C][C]-0.563081212040754[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]8.26308121204075[/C][C]-1.06308121204075[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]8.26308121204075[/C][C]-0.763081212040755[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]8.2902193753941[/C][C]-0.990219375394112[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]8.2359430486874[/C][C]-1.23594304868740[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]8.01883774186054[/C][C]-1.01883774186054[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]7.82887059838704[/C][C]-0.828870598387043[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.77459427168033[/C][C]-0.574594271680329[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.6660416182669[/C][C]-0.366041618266901[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.63890345491354[/C][C]-0.538903454913545[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]7.42179814808669[/C][C]-0.621798148086688[/C][/ROW]
[ROW][C]52[/C][C]6.4[/C][C]7.50321263814676[/C][C]-1.10321263814676[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]7.23183100461319[/C][C]-1.13183100461319[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]7.04186386113969[/C][C]-0.541863861139691[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.01472569778633[/C][C]0.685274302213667[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]7.15041651455312[/C][C]0.749583485446882[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]7.12327835119976[/C][C]0.376721648800239[/C][/ROW]
[ROW][C]58[/C][C]6.9[/C][C]7.31324549467326[/C][C]-0.41324549467326[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]7.74745610832697[/C][C]-1.14745610832697[/C][/ROW]
[ROW][C]60[/C][C]6.9[/C][C]7.88314692509376[/C][C]-0.983146925093757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57389&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57389&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
18.98.235943048687420.664056951312576
28.88.29021937539410.509780624605889
38.38.34449570210083-0.0444957021008247
47.58.15452855862733-0.654528558627327
57.27.96456141515383-0.764561415153828
67.48.07311406856726-0.673114068567255
78.88.04597590521390.754024094786102
89.38.073114068567261.22688593143274
99.38.127390395273971.17260960472603
108.77.883146925093760.816853074906242
118.27.991699578507180.208300421492814
128.38.100252231920610.199747768079388
138.58.073114068567260.426885931432744
148.67.991699578507180.608300421492815
158.57.85600876174040.6439912382596
168.27.964561415153830.235438584846171
178.17.991699578507180.108300421492815
187.97.883146925093760.0168530749062435
198.67.883146925093760.716853074906243
208.77.828870598387040.871129401612956
218.77.801732435033690.898267564966313
228.58.018837741860540.481162258139458
238.47.991699578507180.408300421492816
248.57.85600876174040.6439912382596
258.77.85600876174040.843991238259599
268.77.85600876174040.843991238259599
278.68.018837741860540.581162258139458
288.57.910285088447110.589714911552886
298.37.85600876174040.443991238259601
3087.937423251800470.0625767481995292
318.27.964561415153830.235438584846171
328.17.991699578507180.108300421492815
338.18.10025223192061-0.000252231920613064
3488.15452855862733-0.154528558627327
357.98.07311406856726-0.173114068567255
367.98.0459759052139-0.145975905213898
3788.15452855862733-0.154528558627327
3888.12739039527397-0.127390395273970
397.98.12739039527397-0.227390395273969
4088.12739039527397-0.127390395273970
417.78.26308121204075-0.563081212040754
427.28.26308121204075-1.06308121204075
437.58.26308121204075-0.763081212040755
447.38.2902193753941-0.990219375394112
4578.2359430486874-1.23594304868740
4678.01883774186054-1.01883774186054
4777.82887059838704-0.828870598387043
487.27.77459427168033-0.574594271680329
497.37.6660416182669-0.366041618266901
507.17.63890345491354-0.538903454913545
516.87.42179814808669-0.621798148086688
526.47.50321263814676-1.10321263814676
536.17.23183100461319-1.13183100461319
546.57.04186386113969-0.541863861139691
557.77.014725697786330.685274302213667
567.97.150416514553120.749583485446882
577.57.123278351199760.376721648800239
586.97.31324549467326-0.41324549467326
596.67.74745610832697-1.14745610832697
606.97.88314692509376-0.983146925093757






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.3843696392511340.7687392785022670.615630360748866
60.244266653295430.488533306590860.75573334670457
70.5503377483824270.8993245032351460.449662251617573
80.7928562553867480.4142874892265050.207143744613252
90.8603272728565240.2793454542869530.139672727143476
100.8517293546940020.2965412906119970.148270645305998
110.786920979704410.426158040591180.21307902029559
120.7111680952525030.5776638094949940.288831904747497
130.63713296272550.7257340745490.3628670372745
140.5808907924150660.8382184151698690.419109207584934
150.5242786670376570.9514426659246850.475721332962343
160.4441408885866760.8882817771733520.555859111413324
170.370408819513080.740817639026160.62959118048692
180.3073340558152040.6146681116304080.692665944184796
190.2849498457837430.5698996915674870.715050154216257
200.2890420743595820.5780841487191630.710957925640418
210.2973898478890670.5947796957781330.702610152110933
220.2592582707896340.5185165415792680.740741729210366
230.2205276605091660.4410553210183320.779472339490834
240.2060249753312340.4120499506624680.793975024668766
250.2317167236469150.4634334472938310.768283276353085
260.2738814570332090.5477629140664170.726118542966791
270.2921901237627640.5843802475255280.707809876237236
280.3191529984725680.6383059969451350.680847001527432
290.3324285192145930.6648570384291870.667571480785407
300.3214434905267220.6428869810534450.678556509473278
310.3246238823689130.6492477647378260.675376117631087
320.3229750228104840.6459500456209690.677024977189516
330.3180423187236580.6360846374473150.681957681276342
340.3071652315137060.6143304630274110.692834768486295
350.3020355671938210.6040711343876430.697964432806179
360.3019365922812980.6038731845625960.698063407718702
370.3068517879169320.6137035758338640.693148212083068
380.3287149912915370.6574299825830750.671285008708463
390.352339063497140.704678126994280.64766093650286
400.4279994040958520.8559988081917040.572000595904148
410.454909275515720.909818551031440.54509072448428
420.4683008743059010.9366017486118020.531699125694099
430.472361539655120.944723079310240.52763846034488
440.4660638349502930.9321276699005860.533936165049707
450.4644949068437320.9289898136874630.535505093156268
460.493352207392290.986704414784580.50664779260771
470.5313156822548850.937368635490230.468684317745115
480.5400269423473990.9199461153052010.459973057652601
490.5495243702808090.9009512594383820.450475629719191
500.5238077769691070.9523844460617860.476192223030893
510.4618509639784850.923701927956970.538149036021515
520.4516709489546080.9033418979092150.548329051045392
530.6716751990446870.6566496019106260.328324800955313
540.9088519930316060.1822960139367890.0911480069683943
550.805136651106940.389726697786120.19486334889306

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.384369639251134 & 0.768739278502267 & 0.615630360748866 \tabularnewline
6 & 0.24426665329543 & 0.48853330659086 & 0.75573334670457 \tabularnewline
7 & 0.550337748382427 & 0.899324503235146 & 0.449662251617573 \tabularnewline
8 & 0.792856255386748 & 0.414287489226505 & 0.207143744613252 \tabularnewline
9 & 0.860327272856524 & 0.279345454286953 & 0.139672727143476 \tabularnewline
10 & 0.851729354694002 & 0.296541290611997 & 0.148270645305998 \tabularnewline
11 & 0.78692097970441 & 0.42615804059118 & 0.21307902029559 \tabularnewline
12 & 0.711168095252503 & 0.577663809494994 & 0.288831904747497 \tabularnewline
13 & 0.6371329627255 & 0.725734074549 & 0.3628670372745 \tabularnewline
14 & 0.580890792415066 & 0.838218415169869 & 0.419109207584934 \tabularnewline
15 & 0.524278667037657 & 0.951442665924685 & 0.475721332962343 \tabularnewline
16 & 0.444140888586676 & 0.888281777173352 & 0.555859111413324 \tabularnewline
17 & 0.37040881951308 & 0.74081763902616 & 0.62959118048692 \tabularnewline
18 & 0.307334055815204 & 0.614668111630408 & 0.692665944184796 \tabularnewline
19 & 0.284949845783743 & 0.569899691567487 & 0.715050154216257 \tabularnewline
20 & 0.289042074359582 & 0.578084148719163 & 0.710957925640418 \tabularnewline
21 & 0.297389847889067 & 0.594779695778133 & 0.702610152110933 \tabularnewline
22 & 0.259258270789634 & 0.518516541579268 & 0.740741729210366 \tabularnewline
23 & 0.220527660509166 & 0.441055321018332 & 0.779472339490834 \tabularnewline
24 & 0.206024975331234 & 0.412049950662468 & 0.793975024668766 \tabularnewline
25 & 0.231716723646915 & 0.463433447293831 & 0.768283276353085 \tabularnewline
26 & 0.273881457033209 & 0.547762914066417 & 0.726118542966791 \tabularnewline
27 & 0.292190123762764 & 0.584380247525528 & 0.707809876237236 \tabularnewline
28 & 0.319152998472568 & 0.638305996945135 & 0.680847001527432 \tabularnewline
29 & 0.332428519214593 & 0.664857038429187 & 0.667571480785407 \tabularnewline
30 & 0.321443490526722 & 0.642886981053445 & 0.678556509473278 \tabularnewline
31 & 0.324623882368913 & 0.649247764737826 & 0.675376117631087 \tabularnewline
32 & 0.322975022810484 & 0.645950045620969 & 0.677024977189516 \tabularnewline
33 & 0.318042318723658 & 0.636084637447315 & 0.681957681276342 \tabularnewline
34 & 0.307165231513706 & 0.614330463027411 & 0.692834768486295 \tabularnewline
35 & 0.302035567193821 & 0.604071134387643 & 0.697964432806179 \tabularnewline
36 & 0.301936592281298 & 0.603873184562596 & 0.698063407718702 \tabularnewline
37 & 0.306851787916932 & 0.613703575833864 & 0.693148212083068 \tabularnewline
38 & 0.328714991291537 & 0.657429982583075 & 0.671285008708463 \tabularnewline
39 & 0.35233906349714 & 0.70467812699428 & 0.64766093650286 \tabularnewline
40 & 0.427999404095852 & 0.855998808191704 & 0.572000595904148 \tabularnewline
41 & 0.45490927551572 & 0.90981855103144 & 0.54509072448428 \tabularnewline
42 & 0.468300874305901 & 0.936601748611802 & 0.531699125694099 \tabularnewline
43 & 0.47236153965512 & 0.94472307931024 & 0.52763846034488 \tabularnewline
44 & 0.466063834950293 & 0.932127669900586 & 0.533936165049707 \tabularnewline
45 & 0.464494906843732 & 0.928989813687463 & 0.535505093156268 \tabularnewline
46 & 0.49335220739229 & 0.98670441478458 & 0.50664779260771 \tabularnewline
47 & 0.531315682254885 & 0.93736863549023 & 0.468684317745115 \tabularnewline
48 & 0.540026942347399 & 0.919946115305201 & 0.459973057652601 \tabularnewline
49 & 0.549524370280809 & 0.900951259438382 & 0.450475629719191 \tabularnewline
50 & 0.523807776969107 & 0.952384446061786 & 0.476192223030893 \tabularnewline
51 & 0.461850963978485 & 0.92370192795697 & 0.538149036021515 \tabularnewline
52 & 0.451670948954608 & 0.903341897909215 & 0.548329051045392 \tabularnewline
53 & 0.671675199044687 & 0.656649601910626 & 0.328324800955313 \tabularnewline
54 & 0.908851993031606 & 0.182296013936789 & 0.0911480069683943 \tabularnewline
55 & 0.80513665110694 & 0.38972669778612 & 0.19486334889306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57389&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]5[/C][C]0.384369639251134[/C][C]0.768739278502267[/C][C]0.615630360748866[/C][/ROW]
[ROW][C]6[/C][C]0.24426665329543[/C][C]0.48853330659086[/C][C]0.75573334670457[/C][/ROW]
[ROW][C]7[/C][C]0.550337748382427[/C][C]0.899324503235146[/C][C]0.449662251617573[/C][/ROW]
[ROW][C]8[/C][C]0.792856255386748[/C][C]0.414287489226505[/C][C]0.207143744613252[/C][/ROW]
[ROW][C]9[/C][C]0.860327272856524[/C][C]0.279345454286953[/C][C]0.139672727143476[/C][/ROW]
[ROW][C]10[/C][C]0.851729354694002[/C][C]0.296541290611997[/C][C]0.148270645305998[/C][/ROW]
[ROW][C]11[/C][C]0.78692097970441[/C][C]0.42615804059118[/C][C]0.21307902029559[/C][/ROW]
[ROW][C]12[/C][C]0.711168095252503[/C][C]0.577663809494994[/C][C]0.288831904747497[/C][/ROW]
[ROW][C]13[/C][C]0.6371329627255[/C][C]0.725734074549[/C][C]0.3628670372745[/C][/ROW]
[ROW][C]14[/C][C]0.580890792415066[/C][C]0.838218415169869[/C][C]0.419109207584934[/C][/ROW]
[ROW][C]15[/C][C]0.524278667037657[/C][C]0.951442665924685[/C][C]0.475721332962343[/C][/ROW]
[ROW][C]16[/C][C]0.444140888586676[/C][C]0.888281777173352[/C][C]0.555859111413324[/C][/ROW]
[ROW][C]17[/C][C]0.37040881951308[/C][C]0.74081763902616[/C][C]0.62959118048692[/C][/ROW]
[ROW][C]18[/C][C]0.307334055815204[/C][C]0.614668111630408[/C][C]0.692665944184796[/C][/ROW]
[ROW][C]19[/C][C]0.284949845783743[/C][C]0.569899691567487[/C][C]0.715050154216257[/C][/ROW]
[ROW][C]20[/C][C]0.289042074359582[/C][C]0.578084148719163[/C][C]0.710957925640418[/C][/ROW]
[ROW][C]21[/C][C]0.297389847889067[/C][C]0.594779695778133[/C][C]0.702610152110933[/C][/ROW]
[ROW][C]22[/C][C]0.259258270789634[/C][C]0.518516541579268[/C][C]0.740741729210366[/C][/ROW]
[ROW][C]23[/C][C]0.220527660509166[/C][C]0.441055321018332[/C][C]0.779472339490834[/C][/ROW]
[ROW][C]24[/C][C]0.206024975331234[/C][C]0.412049950662468[/C][C]0.793975024668766[/C][/ROW]
[ROW][C]25[/C][C]0.231716723646915[/C][C]0.463433447293831[/C][C]0.768283276353085[/C][/ROW]
[ROW][C]26[/C][C]0.273881457033209[/C][C]0.547762914066417[/C][C]0.726118542966791[/C][/ROW]
[ROW][C]27[/C][C]0.292190123762764[/C][C]0.584380247525528[/C][C]0.707809876237236[/C][/ROW]
[ROW][C]28[/C][C]0.319152998472568[/C][C]0.638305996945135[/C][C]0.680847001527432[/C][/ROW]
[ROW][C]29[/C][C]0.332428519214593[/C][C]0.664857038429187[/C][C]0.667571480785407[/C][/ROW]
[ROW][C]30[/C][C]0.321443490526722[/C][C]0.642886981053445[/C][C]0.678556509473278[/C][/ROW]
[ROW][C]31[/C][C]0.324623882368913[/C][C]0.649247764737826[/C][C]0.675376117631087[/C][/ROW]
[ROW][C]32[/C][C]0.322975022810484[/C][C]0.645950045620969[/C][C]0.677024977189516[/C][/ROW]
[ROW][C]33[/C][C]0.318042318723658[/C][C]0.636084637447315[/C][C]0.681957681276342[/C][/ROW]
[ROW][C]34[/C][C]0.307165231513706[/C][C]0.614330463027411[/C][C]0.692834768486295[/C][/ROW]
[ROW][C]35[/C][C]0.302035567193821[/C][C]0.604071134387643[/C][C]0.697964432806179[/C][/ROW]
[ROW][C]36[/C][C]0.301936592281298[/C][C]0.603873184562596[/C][C]0.698063407718702[/C][/ROW]
[ROW][C]37[/C][C]0.306851787916932[/C][C]0.613703575833864[/C][C]0.693148212083068[/C][/ROW]
[ROW][C]38[/C][C]0.328714991291537[/C][C]0.657429982583075[/C][C]0.671285008708463[/C][/ROW]
[ROW][C]39[/C][C]0.35233906349714[/C][C]0.70467812699428[/C][C]0.64766093650286[/C][/ROW]
[ROW][C]40[/C][C]0.427999404095852[/C][C]0.855998808191704[/C][C]0.572000595904148[/C][/ROW]
[ROW][C]41[/C][C]0.45490927551572[/C][C]0.90981855103144[/C][C]0.54509072448428[/C][/ROW]
[ROW][C]42[/C][C]0.468300874305901[/C][C]0.936601748611802[/C][C]0.531699125694099[/C][/ROW]
[ROW][C]43[/C][C]0.47236153965512[/C][C]0.94472307931024[/C][C]0.52763846034488[/C][/ROW]
[ROW][C]44[/C][C]0.466063834950293[/C][C]0.932127669900586[/C][C]0.533936165049707[/C][/ROW]
[ROW][C]45[/C][C]0.464494906843732[/C][C]0.928989813687463[/C][C]0.535505093156268[/C][/ROW]
[ROW][C]46[/C][C]0.49335220739229[/C][C]0.98670441478458[/C][C]0.50664779260771[/C][/ROW]
[ROW][C]47[/C][C]0.531315682254885[/C][C]0.93736863549023[/C][C]0.468684317745115[/C][/ROW]
[ROW][C]48[/C][C]0.540026942347399[/C][C]0.919946115305201[/C][C]0.459973057652601[/C][/ROW]
[ROW][C]49[/C][C]0.549524370280809[/C][C]0.900951259438382[/C][C]0.450475629719191[/C][/ROW]
[ROW][C]50[/C][C]0.523807776969107[/C][C]0.952384446061786[/C][C]0.476192223030893[/C][/ROW]
[ROW][C]51[/C][C]0.461850963978485[/C][C]0.92370192795697[/C][C]0.538149036021515[/C][/ROW]
[ROW][C]52[/C][C]0.451670948954608[/C][C]0.903341897909215[/C][C]0.548329051045392[/C][/ROW]
[ROW][C]53[/C][C]0.671675199044687[/C][C]0.656649601910626[/C][C]0.328324800955313[/C][/ROW]
[ROW][C]54[/C][C]0.908851993031606[/C][C]0.182296013936789[/C][C]0.0911480069683943[/C][/ROW]
[ROW][C]55[/C][C]0.80513665110694[/C][C]0.38972669778612[/C][C]0.19486334889306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57389&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57389&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
50.3843696392511340.7687392785022670.615630360748866
60.244266653295430.488533306590860.75573334670457
70.5503377483824270.8993245032351460.449662251617573
80.7928562553867480.4142874892265050.207143744613252
90.8603272728565240.2793454542869530.139672727143476
100.8517293546940020.2965412906119970.148270645305998
110.786920979704410.426158040591180.21307902029559
120.7111680952525030.5776638094949940.288831904747497
130.63713296272550.7257340745490.3628670372745
140.5808907924150660.8382184151698690.419109207584934
150.5242786670376570.9514426659246850.475721332962343
160.4441408885866760.8882817771733520.555859111413324
170.370408819513080.740817639026160.62959118048692
180.3073340558152040.6146681116304080.692665944184796
190.2849498457837430.5698996915674870.715050154216257
200.2890420743595820.5780841487191630.710957925640418
210.2973898478890670.5947796957781330.702610152110933
220.2592582707896340.5185165415792680.740741729210366
230.2205276605091660.4410553210183320.779472339490834
240.2060249753312340.4120499506624680.793975024668766
250.2317167236469150.4634334472938310.768283276353085
260.2738814570332090.5477629140664170.726118542966791
270.2921901237627640.5843802475255280.707809876237236
280.3191529984725680.6383059969451350.680847001527432
290.3324285192145930.6648570384291870.667571480785407
300.3214434905267220.6428869810534450.678556509473278
310.3246238823689130.6492477647378260.675376117631087
320.3229750228104840.6459500456209690.677024977189516
330.3180423187236580.6360846374473150.681957681276342
340.3071652315137060.6143304630274110.692834768486295
350.3020355671938210.6040711343876430.697964432806179
360.3019365922812980.6038731845625960.698063407718702
370.3068517879169320.6137035758338640.693148212083068
380.3287149912915370.6574299825830750.671285008708463
390.352339063497140.704678126994280.64766093650286
400.4279994040958520.8559988081917040.572000595904148
410.454909275515720.909818551031440.54509072448428
420.4683008743059010.9366017486118020.531699125694099
430.472361539655120.944723079310240.52763846034488
440.4660638349502930.9321276699005860.533936165049707
450.4644949068437320.9289898136874630.535505093156268
460.493352207392290.986704414784580.50664779260771
470.5313156822548850.937368635490230.468684317745115
480.5400269423473990.9199461153052010.459973057652601
490.5495243702808090.9009512594383820.450475629719191
500.5238077769691070.9523844460617860.476192223030893
510.4618509639784850.923701927956970.538149036021515
520.4516709489546080.9033418979092150.548329051045392
530.6716751990446870.6566496019106260.328324800955313
540.9088519930316060.1822960139367890.0911480069683943
550.805136651106940.389726697786120.19486334889306






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=57389&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=57389&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57389&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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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')
}