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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 05:47:50 -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/20/t125872130794q9ttq63pxi267.htm/, Retrieved Fri, 29 Mar 2024 01:03:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58093, Retrieved Fri, 29 Mar 2024 01:03:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [SHW WS7] [2009-11-20 12:32:24] [253127ae8da904b75450fbd69fe4eb21]
-    D        [Multiple Regression] [SHW WS7] [2009-11-20 12:47:50] [b7e46d23597387652ca7420fdeb9acca] [Current]
- R  D          [Multiple Regression] [WorkShop7 (SHW)] [2009-11-27 16:41:59] [37daf76adc256428993ec4063536c760]
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Dataseries X:
8.3	0	8.5	8.6
7.8	0	8.3	8.5
7.8	0	7.8	8.3
8	0	7.8	7.8
8.6	0	8	7.8
8.9	0	8.6	8
8.9	0	8.9	8.6
8.6	0	8.9	8.9
8.3	0	8.6	8.9
8.3	0	8.3	8.6
8.3	0	8.3	8.3
8.4	0	8.3	8.3
8.5	0	8.4	8.3
8.4	0	8.5	8.4
8.6	0	8.4	8.5
8.5	0	8.6	8.4
8.5	0	8.5	8.6
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.5	0	8.5	8.5
8.6	0	8.5	8.5
8.4	0	8.6	8.5
8.1	0	8.4	8.6
8	0	8.1	8.4
8	0	8	8.1
8	0	8	8
8	0	8	8
7.9	0	8	8
7.8	0	7.9	8
7.8	0	7.8	7.9
7.9	0	7.8	7.8
8.1	0	7.9	7.8
8	0	8.1	7.9
7.6	0	8	8.1
7.3	0	7.6	8
7	0	7.3	7.6
6.8	0	7	7.3
7	0	6.8	7
7.1	0	7	6.8
7.2	0	7.1	7
7.1	1	7.2	7.1
6.9	1	7.1	7.2
6.7	1	6.9	7.1
6.7	1	6.7	6.9
6.6	1	6.7	6.7
6.9	1	6.6	6.7
7.3	1	6.9	6.6
7.5	1	7.3	6.9
7.3	1	7.5	7.3
7.1	1	7.3	7.5
6.9	1	7.1	7.3
7.1	1	6.9	7.1




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58093&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58093&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.06927334447505 -0.0797015328416982X[t] + 1.39881716350103Y1[t] -0.633441242873896Y2[t] -0.0335768798788945M1[t] -0.0768525073841112M2[t] + 0.0358245516507144M3[t] -0.0767177553795189M4[t] + 0.078013091687698M5[t] -0.0331205954376406M6[t] -0.0843123036080516M7[t] -0.0136287700007924M8[t] -0.0542657039509433M9[t] + 0.0657425302264035M10[t] -0.0510501938447505M11[t] -0.00610933566969867t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  2.06927334447505 -0.0797015328416982X[t] +  1.39881716350103Y1[t] -0.633441242873896Y2[t] -0.0335768798788945M1[t] -0.0768525073841112M2[t] +  0.0358245516507144M3[t] -0.0767177553795189M4[t] +  0.078013091687698M5[t] -0.0331205954376406M6[t] -0.0843123036080516M7[t] -0.0136287700007924M8[t] -0.0542657039509433M9[t] +  0.0657425302264035M10[t] -0.0510501938447505M11[t] -0.00610933566969867t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58093&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  2.06927334447505 -0.0797015328416982X[t] +  1.39881716350103Y1[t] -0.633441242873896Y2[t] -0.0335768798788945M1[t] -0.0768525073841112M2[t] +  0.0358245516507144M3[t] -0.0767177553795189M4[t] +  0.078013091687698M5[t] -0.0331205954376406M6[t] -0.0843123036080516M7[t] -0.0136287700007924M8[t] -0.0542657039509433M9[t] +  0.0657425302264035M10[t] -0.0510501938447505M11[t] -0.00610933566969867t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58093&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.06927334447505 -0.0797015328416982X[t] + 1.39881716350103Y1[t] -0.633441242873896Y2[t] -0.0335768798788945M1[t] -0.0768525073841112M2[t] + 0.0358245516507144M3[t] -0.0767177553795189M4[t] + 0.078013091687698M5[t] -0.0331205954376406M6[t] -0.0843123036080516M7[t] -0.0136287700007924M8[t] -0.0542657039509433M9[t] + 0.0657425302264035M10[t] -0.0510501938447505M11[t] -0.00610933566969867t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.069273344475050.5871253.52440.001040.00052
X-0.07970153284169820.084142-0.94720.3489410.174471
Y11.398817163501030.12177511.486900
Y2-0.6334412428738960.124017-5.10777e-064e-06
M1-0.03357687987889450.113042-0.2970.7679070.383954
M2-0.07685250738411120.112984-0.68020.5001050.250053
M30.03582455165071440.1130910.31680.7529830.376491
M4-0.07671775537951890.11335-0.67680.5022310.251116
M50.0780130916876980.1129860.69050.49370.24685
M6-0.03312059543764060.113996-0.29050.7728320.386416
M7-0.08431230360805160.113241-0.74450.4606950.230348
M8-0.01362877000079240.113018-0.12060.9045910.452296
M9-0.05426570395094330.113129-0.47970.6339450.316973
M100.06574253022640350.113410.57970.5652210.282611
M11-0.05105019384475050.119009-0.4290.6701440.335072
t-0.006109335669698670.00245-2.4940.0166510.008326

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 2.06927334447505 & 0.587125 & 3.5244 & 0.00104 & 0.00052 \tabularnewline
X & -0.0797015328416982 & 0.084142 & -0.9472 & 0.348941 & 0.174471 \tabularnewline
Y1 & 1.39881716350103 & 0.121775 & 11.4869 & 0 & 0 \tabularnewline
Y2 & -0.633441242873896 & 0.124017 & -5.1077 & 7e-06 & 4e-06 \tabularnewline
M1 & -0.0335768798788945 & 0.113042 & -0.297 & 0.767907 & 0.383954 \tabularnewline
M2 & -0.0768525073841112 & 0.112984 & -0.6802 & 0.500105 & 0.250053 \tabularnewline
M3 & 0.0358245516507144 & 0.113091 & 0.3168 & 0.752983 & 0.376491 \tabularnewline
M4 & -0.0767177553795189 & 0.11335 & -0.6768 & 0.502231 & 0.251116 \tabularnewline
M5 & 0.078013091687698 & 0.112986 & 0.6905 & 0.4937 & 0.24685 \tabularnewline
M6 & -0.0331205954376406 & 0.113996 & -0.2905 & 0.772832 & 0.386416 \tabularnewline
M7 & -0.0843123036080516 & 0.113241 & -0.7445 & 0.460695 & 0.230348 \tabularnewline
M8 & -0.0136287700007924 & 0.113018 & -0.1206 & 0.904591 & 0.452296 \tabularnewline
M9 & -0.0542657039509433 & 0.113129 & -0.4797 & 0.633945 & 0.316973 \tabularnewline
M10 & 0.0657425302264035 & 0.11341 & 0.5797 & 0.565221 & 0.282611 \tabularnewline
M11 & -0.0510501938447505 & 0.119009 & -0.429 & 0.670144 & 0.335072 \tabularnewline
t & -0.00610933566969867 & 0.00245 & -2.494 & 0.016651 & 0.008326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58093&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]2.06927334447505[/C][C]0.587125[/C][C]3.5244[/C][C]0.00104[/C][C]0.00052[/C][/ROW]
[ROW][C]X[/C][C]-0.0797015328416982[/C][C]0.084142[/C][C]-0.9472[/C][C]0.348941[/C][C]0.174471[/C][/ROW]
[ROW][C]Y1[/C][C]1.39881716350103[/C][C]0.121775[/C][C]11.4869[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.633441242873896[/C][C]0.124017[/C][C]-5.1077[/C][C]7e-06[/C][C]4e-06[/C][/ROW]
[ROW][C]M1[/C][C]-0.0335768798788945[/C][C]0.113042[/C][C]-0.297[/C][C]0.767907[/C][C]0.383954[/C][/ROW]
[ROW][C]M2[/C][C]-0.0768525073841112[/C][C]0.112984[/C][C]-0.6802[/C][C]0.500105[/C][C]0.250053[/C][/ROW]
[ROW][C]M3[/C][C]0.0358245516507144[/C][C]0.113091[/C][C]0.3168[/C][C]0.752983[/C][C]0.376491[/C][/ROW]
[ROW][C]M4[/C][C]-0.0767177553795189[/C][C]0.11335[/C][C]-0.6768[/C][C]0.502231[/C][C]0.251116[/C][/ROW]
[ROW][C]M5[/C][C]0.078013091687698[/C][C]0.112986[/C][C]0.6905[/C][C]0.4937[/C][C]0.24685[/C][/ROW]
[ROW][C]M6[/C][C]-0.0331205954376406[/C][C]0.113996[/C][C]-0.2905[/C][C]0.772832[/C][C]0.386416[/C][/ROW]
[ROW][C]M7[/C][C]-0.0843123036080516[/C][C]0.113241[/C][C]-0.7445[/C][C]0.460695[/C][C]0.230348[/C][/ROW]
[ROW][C]M8[/C][C]-0.0136287700007924[/C][C]0.113018[/C][C]-0.1206[/C][C]0.904591[/C][C]0.452296[/C][/ROW]
[ROW][C]M9[/C][C]-0.0542657039509433[/C][C]0.113129[/C][C]-0.4797[/C][C]0.633945[/C][C]0.316973[/C][/ROW]
[ROW][C]M10[/C][C]0.0657425302264035[/C][C]0.11341[/C][C]0.5797[/C][C]0.565221[/C][C]0.282611[/C][/ROW]
[ROW][C]M11[/C][C]-0.0510501938447505[/C][C]0.119009[/C][C]-0.429[/C][C]0.670144[/C][C]0.335072[/C][/ROW]
[ROW][C]t[/C][C]-0.00610933566969867[/C][C]0.00245[/C][C]-2.494[/C][C]0.016651[/C][C]0.008326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58093&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58093&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.069273344475050.5871253.52440.001040.00052
X-0.07970153284169820.084142-0.94720.3489410.174471
Y11.398817163501030.12177511.486900
Y2-0.6334412428738960.124017-5.10777e-064e-06
M1-0.03357687987889450.113042-0.2970.7679070.383954
M2-0.07685250738411120.112984-0.68020.5001050.250053
M30.03582455165071440.1130910.31680.7529830.376491
M4-0.07671775537951890.11335-0.67680.5022310.251116
M50.0780130916876980.1129860.69050.49370.24685
M6-0.03312059543764060.113996-0.29050.7728320.386416
M7-0.08431230360805160.113241-0.74450.4606950.230348
M8-0.01362877000079240.113018-0.12060.9045910.452296
M9-0.05426570395094330.113129-0.47970.6339450.316973
M100.06574253022640350.113410.57970.5652210.282611
M11-0.05105019384475050.119009-0.4290.6701440.335072
t-0.006109335669698670.00245-2.4940.0166510.008326







Multiple Linear Regression - Regression Statistics
Multiple R0.975611291691286
R-squared0.95181739247554
Adjusted R-squared0.934609318359662
F-TEST (value)55.3122555183133
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.168088897767444
Sum Squared Residuals1.18666285721232

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.975611291691286 \tabularnewline
R-squared & 0.95181739247554 \tabularnewline
Adjusted R-squared & 0.934609318359662 \tabularnewline
F-TEST (value) & 55.3122555183133 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.168088897767444 \tabularnewline
Sum Squared Residuals & 1.18666285721232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58093&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.975611291691286[/C][/ROW]
[ROW][C]R-squared[/C][C]0.95181739247554[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.934609318359662[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]55.3122555183133[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.168088897767444[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.18666285721232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58093&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58093&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.975611291691286
R-squared0.95181739247554
Adjusted R-squared0.934609318359662
F-TEST (value)55.3122555183133
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.168088897767444
Sum Squared Residuals1.18666285721232







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.38.4719383299697-0.171938329969697
27.88.20613405838197-0.406134058381967
37.87.739981448571360.0600185514286436
487.938050427308370.0619495726916263
58.68.36643537140610.233564628593901
68.98.9617943981369-0.0617943981368987
78.98.94407375762276-0.0440737576227613
88.68.81861558269815-0.218615582698153
98.38.352224164028-0.0522241640279928
108.38.23651028634750.0634897136524972
118.38.30364059946882-0.00364059946881829
128.48.348581457643870.0514185423561296
138.58.448776958445380.0512230415546199
148.48.47592958733318-0.0759295873331775
158.68.379271470060810.220728529939187
168.58.60372738434848-0.103727384348475
178.58.485778930821110.0142210691788878
188.58.431880032313460.0681199676865357
198.58.374578988473350.125421011526645
208.58.439153186410910.0608468135890848
218.58.392406916791070.107593083208934
228.58.50630581529871-0.00630581529871382
238.58.383403755557860.116596244442139
248.58.428344613732910.071655386267087
258.58.388658398184320.111341601815680
268.58.33927343500940.160726564990596
278.68.445841158374530.154158841625468
288.48.4670712320247-0.0670712320247015
298.18.27258518643463-0.172585186434626
3087.862385263164060.137614736835943
3187.855234875836010.144765124163985
3287.983153198060960.0168468019390354
3387.936406928441110.063593071558885
347.98.05030582694876-0.150305826948763
357.87.78752205085780.0124779491421919
367.87.755925316970150.0440746830298544
377.97.779583225708940.120416774291058
388.17.870079978884130.229920021115869
3988.19306701066207-0.193067010662073
407.67.80784540303726-0.20784540303726
417.37.46028417332175-0.160284173321755
4277.17677249862597-0.176772498625967
436.86.88985867859772-0.089858678597718
4476.864701816697240.135298183302759
457.17.22440722835238-0.124407228352377
467.27.35149959463535-0.151499594635348
477.17.22543359411551-0.125433594115513
486.97.06714861165307-0.16714861165307
496.76.81104308769166-0.111043087691662
506.76.608582940391320.0914170596086807
516.66.84183891233123-0.241838912331226
526.96.583305553281190.31669444671881
537.37.214916338016410.0850836619835917
547.57.467167807759610.0328321922403873
557.37.43625369947015-0.136253699470151
567.17.094376216132730.0056237838672736
576.96.894554762387450.00544523761255068
587.16.855378476769670.244621523230327

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.3 & 8.4719383299697 & -0.171938329969697 \tabularnewline
2 & 7.8 & 8.20613405838197 & -0.406134058381967 \tabularnewline
3 & 7.8 & 7.73998144857136 & 0.0600185514286436 \tabularnewline
4 & 8 & 7.93805042730837 & 0.0619495726916263 \tabularnewline
5 & 8.6 & 8.3664353714061 & 0.233564628593901 \tabularnewline
6 & 8.9 & 8.9617943981369 & -0.0617943981368987 \tabularnewline
7 & 8.9 & 8.94407375762276 & -0.0440737576227613 \tabularnewline
8 & 8.6 & 8.81861558269815 & -0.218615582698153 \tabularnewline
9 & 8.3 & 8.352224164028 & -0.0522241640279928 \tabularnewline
10 & 8.3 & 8.2365102863475 & 0.0634897136524972 \tabularnewline
11 & 8.3 & 8.30364059946882 & -0.00364059946881829 \tabularnewline
12 & 8.4 & 8.34858145764387 & 0.0514185423561296 \tabularnewline
13 & 8.5 & 8.44877695844538 & 0.0512230415546199 \tabularnewline
14 & 8.4 & 8.47592958733318 & -0.0759295873331775 \tabularnewline
15 & 8.6 & 8.37927147006081 & 0.220728529939187 \tabularnewline
16 & 8.5 & 8.60372738434848 & -0.103727384348475 \tabularnewline
17 & 8.5 & 8.48577893082111 & 0.0142210691788878 \tabularnewline
18 & 8.5 & 8.43188003231346 & 0.0681199676865357 \tabularnewline
19 & 8.5 & 8.37457898847335 & 0.125421011526645 \tabularnewline
20 & 8.5 & 8.43915318641091 & 0.0608468135890848 \tabularnewline
21 & 8.5 & 8.39240691679107 & 0.107593083208934 \tabularnewline
22 & 8.5 & 8.50630581529871 & -0.00630581529871382 \tabularnewline
23 & 8.5 & 8.38340375555786 & 0.116596244442139 \tabularnewline
24 & 8.5 & 8.42834461373291 & 0.071655386267087 \tabularnewline
25 & 8.5 & 8.38865839818432 & 0.111341601815680 \tabularnewline
26 & 8.5 & 8.3392734350094 & 0.160726564990596 \tabularnewline
27 & 8.6 & 8.44584115837453 & 0.154158841625468 \tabularnewline
28 & 8.4 & 8.4670712320247 & -0.0670712320247015 \tabularnewline
29 & 8.1 & 8.27258518643463 & -0.172585186434626 \tabularnewline
30 & 8 & 7.86238526316406 & 0.137614736835943 \tabularnewline
31 & 8 & 7.85523487583601 & 0.144765124163985 \tabularnewline
32 & 8 & 7.98315319806096 & 0.0168468019390354 \tabularnewline
33 & 8 & 7.93640692844111 & 0.063593071558885 \tabularnewline
34 & 7.9 & 8.05030582694876 & -0.150305826948763 \tabularnewline
35 & 7.8 & 7.7875220508578 & 0.0124779491421919 \tabularnewline
36 & 7.8 & 7.75592531697015 & 0.0440746830298544 \tabularnewline
37 & 7.9 & 7.77958322570894 & 0.120416774291058 \tabularnewline
38 & 8.1 & 7.87007997888413 & 0.229920021115869 \tabularnewline
39 & 8 & 8.19306701066207 & -0.193067010662073 \tabularnewline
40 & 7.6 & 7.80784540303726 & -0.20784540303726 \tabularnewline
41 & 7.3 & 7.46028417332175 & -0.160284173321755 \tabularnewline
42 & 7 & 7.17677249862597 & -0.176772498625967 \tabularnewline
43 & 6.8 & 6.88985867859772 & -0.089858678597718 \tabularnewline
44 & 7 & 6.86470181669724 & 0.135298183302759 \tabularnewline
45 & 7.1 & 7.22440722835238 & -0.124407228352377 \tabularnewline
46 & 7.2 & 7.35149959463535 & -0.151499594635348 \tabularnewline
47 & 7.1 & 7.22543359411551 & -0.125433594115513 \tabularnewline
48 & 6.9 & 7.06714861165307 & -0.16714861165307 \tabularnewline
49 & 6.7 & 6.81104308769166 & -0.111043087691662 \tabularnewline
50 & 6.7 & 6.60858294039132 & 0.0914170596086807 \tabularnewline
51 & 6.6 & 6.84183891233123 & -0.241838912331226 \tabularnewline
52 & 6.9 & 6.58330555328119 & 0.31669444671881 \tabularnewline
53 & 7.3 & 7.21491633801641 & 0.0850836619835917 \tabularnewline
54 & 7.5 & 7.46716780775961 & 0.0328321922403873 \tabularnewline
55 & 7.3 & 7.43625369947015 & -0.136253699470151 \tabularnewline
56 & 7.1 & 7.09437621613273 & 0.0056237838672736 \tabularnewline
57 & 6.9 & 6.89455476238745 & 0.00544523761255068 \tabularnewline
58 & 7.1 & 6.85537847676967 & 0.244621523230327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58093&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]8.3[/C][C]8.4719383299697[/C][C]-0.171938329969697[/C][/ROW]
[ROW][C]2[/C][C]7.8[/C][C]8.20613405838197[/C][C]-0.406134058381967[/C][/ROW]
[ROW][C]3[/C][C]7.8[/C][C]7.73998144857136[/C][C]0.0600185514286436[/C][/ROW]
[ROW][C]4[/C][C]8[/C][C]7.93805042730837[/C][C]0.0619495726916263[/C][/ROW]
[ROW][C]5[/C][C]8.6[/C][C]8.3664353714061[/C][C]0.233564628593901[/C][/ROW]
[ROW][C]6[/C][C]8.9[/C][C]8.9617943981369[/C][C]-0.0617943981368987[/C][/ROW]
[ROW][C]7[/C][C]8.9[/C][C]8.94407375762276[/C][C]-0.0440737576227613[/C][/ROW]
[ROW][C]8[/C][C]8.6[/C][C]8.81861558269815[/C][C]-0.218615582698153[/C][/ROW]
[ROW][C]9[/C][C]8.3[/C][C]8.352224164028[/C][C]-0.0522241640279928[/C][/ROW]
[ROW][C]10[/C][C]8.3[/C][C]8.2365102863475[/C][C]0.0634897136524972[/C][/ROW]
[ROW][C]11[/C][C]8.3[/C][C]8.30364059946882[/C][C]-0.00364059946881829[/C][/ROW]
[ROW][C]12[/C][C]8.4[/C][C]8.34858145764387[/C][C]0.0514185423561296[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.44877695844538[/C][C]0.0512230415546199[/C][/ROW]
[ROW][C]14[/C][C]8.4[/C][C]8.47592958733318[/C][C]-0.0759295873331775[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.37927147006081[/C][C]0.220728529939187[/C][/ROW]
[ROW][C]16[/C][C]8.5[/C][C]8.60372738434848[/C][C]-0.103727384348475[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.48577893082111[/C][C]0.0142210691788878[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.43188003231346[/C][C]0.0681199676865357[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]8.37457898847335[/C][C]0.125421011526645[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.43915318641091[/C][C]0.0608468135890848[/C][/ROW]
[ROW][C]21[/C][C]8.5[/C][C]8.39240691679107[/C][C]0.107593083208934[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.50630581529871[/C][C]-0.00630581529871382[/C][/ROW]
[ROW][C]23[/C][C]8.5[/C][C]8.38340375555786[/C][C]0.116596244442139[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.42834461373291[/C][C]0.071655386267087[/C][/ROW]
[ROW][C]25[/C][C]8.5[/C][C]8.38865839818432[/C][C]0.111341601815680[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.3392734350094[/C][C]0.160726564990596[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.44584115837453[/C][C]0.154158841625468[/C][/ROW]
[ROW][C]28[/C][C]8.4[/C][C]8.4670712320247[/C][C]-0.0670712320247015[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]8.27258518643463[/C][C]-0.172585186434626[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.86238526316406[/C][C]0.137614736835943[/C][/ROW]
[ROW][C]31[/C][C]8[/C][C]7.85523487583601[/C][C]0.144765124163985[/C][/ROW]
[ROW][C]32[/C][C]8[/C][C]7.98315319806096[/C][C]0.0168468019390354[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.93640692844111[/C][C]0.063593071558885[/C][/ROW]
[ROW][C]34[/C][C]7.9[/C][C]8.05030582694876[/C][C]-0.150305826948763[/C][/ROW]
[ROW][C]35[/C][C]7.8[/C][C]7.7875220508578[/C][C]0.0124779491421919[/C][/ROW]
[ROW][C]36[/C][C]7.8[/C][C]7.75592531697015[/C][C]0.0440746830298544[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]7.77958322570894[/C][C]0.120416774291058[/C][/ROW]
[ROW][C]38[/C][C]8.1[/C][C]7.87007997888413[/C][C]0.229920021115869[/C][/ROW]
[ROW][C]39[/C][C]8[/C][C]8.19306701066207[/C][C]-0.193067010662073[/C][/ROW]
[ROW][C]40[/C][C]7.6[/C][C]7.80784540303726[/C][C]-0.20784540303726[/C][/ROW]
[ROW][C]41[/C][C]7.3[/C][C]7.46028417332175[/C][C]-0.160284173321755[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]7.17677249862597[/C][C]-0.176772498625967[/C][/ROW]
[ROW][C]43[/C][C]6.8[/C][C]6.88985867859772[/C][C]-0.089858678597718[/C][/ROW]
[ROW][C]44[/C][C]7[/C][C]6.86470181669724[/C][C]0.135298183302759[/C][/ROW]
[ROW][C]45[/C][C]7.1[/C][C]7.22440722835238[/C][C]-0.124407228352377[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]7.35149959463535[/C][C]-0.151499594635348[/C][/ROW]
[ROW][C]47[/C][C]7.1[/C][C]7.22543359411551[/C][C]-0.125433594115513[/C][/ROW]
[ROW][C]48[/C][C]6.9[/C][C]7.06714861165307[/C][C]-0.16714861165307[/C][/ROW]
[ROW][C]49[/C][C]6.7[/C][C]6.81104308769166[/C][C]-0.111043087691662[/C][/ROW]
[ROW][C]50[/C][C]6.7[/C][C]6.60858294039132[/C][C]0.0914170596086807[/C][/ROW]
[ROW][C]51[/C][C]6.6[/C][C]6.84183891233123[/C][C]-0.241838912331226[/C][/ROW]
[ROW][C]52[/C][C]6.9[/C][C]6.58330555328119[/C][C]0.31669444671881[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.21491633801641[/C][C]0.0850836619835917[/C][/ROW]
[ROW][C]54[/C][C]7.5[/C][C]7.46716780775961[/C][C]0.0328321922403873[/C][/ROW]
[ROW][C]55[/C][C]7.3[/C][C]7.43625369947015[/C][C]-0.136253699470151[/C][/ROW]
[ROW][C]56[/C][C]7.1[/C][C]7.09437621613273[/C][C]0.0056237838672736[/C][/ROW]
[ROW][C]57[/C][C]6.9[/C][C]6.89455476238745[/C][C]0.00544523761255068[/C][/ROW]
[ROW][C]58[/C][C]7.1[/C][C]6.85537847676967[/C][C]0.244621523230327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58093&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58093&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.38.4719383299697-0.171938329969697
27.88.20613405838197-0.406134058381967
37.87.739981448571360.0600185514286436
487.938050427308370.0619495726916263
58.68.36643537140610.233564628593901
68.98.9617943981369-0.0617943981368987
78.98.94407375762276-0.0440737576227613
88.68.81861558269815-0.218615582698153
98.38.352224164028-0.0522241640279928
108.38.23651028634750.0634897136524972
118.38.30364059946882-0.00364059946881829
128.48.348581457643870.0514185423561296
138.58.448776958445380.0512230415546199
148.48.47592958733318-0.0759295873331775
158.68.379271470060810.220728529939187
168.58.60372738434848-0.103727384348475
178.58.485778930821110.0142210691788878
188.58.431880032313460.0681199676865357
198.58.374578988473350.125421011526645
208.58.439153186410910.0608468135890848
218.58.392406916791070.107593083208934
228.58.50630581529871-0.00630581529871382
238.58.383403755557860.116596244442139
248.58.428344613732910.071655386267087
258.58.388658398184320.111341601815680
268.58.33927343500940.160726564990596
278.68.445841158374530.154158841625468
288.48.4670712320247-0.0670712320247015
298.18.27258518643463-0.172585186434626
3087.862385263164060.137614736835943
3187.855234875836010.144765124163985
3287.983153198060960.0168468019390354
3387.936406928441110.063593071558885
347.98.05030582694876-0.150305826948763
357.87.78752205085780.0124779491421919
367.87.755925316970150.0440746830298544
377.97.779583225708940.120416774291058
388.17.870079978884130.229920021115869
3988.19306701066207-0.193067010662073
407.67.80784540303726-0.20784540303726
417.37.46028417332175-0.160284173321755
4277.17677249862597-0.176772498625967
436.86.88985867859772-0.089858678597718
4476.864701816697240.135298183302759
457.17.22440722835238-0.124407228352377
467.27.35149959463535-0.151499594635348
477.17.22543359411551-0.125433594115513
486.97.06714861165307-0.16714861165307
496.76.81104308769166-0.111043087691662
506.76.608582940391320.0914170596086807
516.66.84183891233123-0.241838912331226
526.96.583305553281190.31669444671881
537.37.214916338016410.0850836619835917
547.57.467167807759610.0328321922403873
557.37.43625369947015-0.136253699470151
567.17.094376216132730.0056237838672736
576.96.894554762387450.00544523761255068
587.16.855378476769670.244621523230327







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2508790219104220.5017580438208440.749120978089578
200.1387788693489120.2775577386978240.861221130651088
210.1026485906343570.2052971812687140.897351409365643
220.1303751253729070.2607502507458140.869624874627093
230.07408067701647210.1481613540329440.925919322983528
240.03817957499978230.07635914999956450.961820425000218
250.01764408460808400.03528816921616790.982355915391916
260.02626796677065430.05253593354130860.973732033229346
270.03255804128270490.06511608256540970.967441958717295
280.02234774949532550.04469549899065110.977652250504675
290.08406542975278960.1681308595055790.91593457024721
300.05661652904713220.1132330580942640.943383470952868
310.07879018126801950.1575803625360390.92120981873198
320.07052607963826110.1410521592765220.92947392036174
330.08144326418037830.1628865283607570.918556735819622
340.1011210099887810.2022420199775620.898878990011219
350.08378835917980340.1675767183596070.916211640820197
360.08058352470695330.1611670494139070.919416475293047
370.0923152710541840.1846305421083680.907684728945816
380.1469246350793850.2938492701587700.853075364920615
390.7403308922655720.5193382154688550.259669107734428

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.250879021910422 & 0.501758043820844 & 0.749120978089578 \tabularnewline
20 & 0.138778869348912 & 0.277557738697824 & 0.861221130651088 \tabularnewline
21 & 0.102648590634357 & 0.205297181268714 & 0.897351409365643 \tabularnewline
22 & 0.130375125372907 & 0.260750250745814 & 0.869624874627093 \tabularnewline
23 & 0.0740806770164721 & 0.148161354032944 & 0.925919322983528 \tabularnewline
24 & 0.0381795749997823 & 0.0763591499995645 & 0.961820425000218 \tabularnewline
25 & 0.0176440846080840 & 0.0352881692161679 & 0.982355915391916 \tabularnewline
26 & 0.0262679667706543 & 0.0525359335413086 & 0.973732033229346 \tabularnewline
27 & 0.0325580412827049 & 0.0651160825654097 & 0.967441958717295 \tabularnewline
28 & 0.0223477494953255 & 0.0446954989906511 & 0.977652250504675 \tabularnewline
29 & 0.0840654297527896 & 0.168130859505579 & 0.91593457024721 \tabularnewline
30 & 0.0566165290471322 & 0.113233058094264 & 0.943383470952868 \tabularnewline
31 & 0.0787901812680195 & 0.157580362536039 & 0.92120981873198 \tabularnewline
32 & 0.0705260796382611 & 0.141052159276522 & 0.92947392036174 \tabularnewline
33 & 0.0814432641803783 & 0.162886528360757 & 0.918556735819622 \tabularnewline
34 & 0.101121009988781 & 0.202242019977562 & 0.898878990011219 \tabularnewline
35 & 0.0837883591798034 & 0.167576718359607 & 0.916211640820197 \tabularnewline
36 & 0.0805835247069533 & 0.161167049413907 & 0.919416475293047 \tabularnewline
37 & 0.092315271054184 & 0.184630542108368 & 0.907684728945816 \tabularnewline
38 & 0.146924635079385 & 0.293849270158770 & 0.853075364920615 \tabularnewline
39 & 0.740330892265572 & 0.519338215468855 & 0.259669107734428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58093&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]19[/C][C]0.250879021910422[/C][C]0.501758043820844[/C][C]0.749120978089578[/C][/ROW]
[ROW][C]20[/C][C]0.138778869348912[/C][C]0.277557738697824[/C][C]0.861221130651088[/C][/ROW]
[ROW][C]21[/C][C]0.102648590634357[/C][C]0.205297181268714[/C][C]0.897351409365643[/C][/ROW]
[ROW][C]22[/C][C]0.130375125372907[/C][C]0.260750250745814[/C][C]0.869624874627093[/C][/ROW]
[ROW][C]23[/C][C]0.0740806770164721[/C][C]0.148161354032944[/C][C]0.925919322983528[/C][/ROW]
[ROW][C]24[/C][C]0.0381795749997823[/C][C]0.0763591499995645[/C][C]0.961820425000218[/C][/ROW]
[ROW][C]25[/C][C]0.0176440846080840[/C][C]0.0352881692161679[/C][C]0.982355915391916[/C][/ROW]
[ROW][C]26[/C][C]0.0262679667706543[/C][C]0.0525359335413086[/C][C]0.973732033229346[/C][/ROW]
[ROW][C]27[/C][C]0.0325580412827049[/C][C]0.0651160825654097[/C][C]0.967441958717295[/C][/ROW]
[ROW][C]28[/C][C]0.0223477494953255[/C][C]0.0446954989906511[/C][C]0.977652250504675[/C][/ROW]
[ROW][C]29[/C][C]0.0840654297527896[/C][C]0.168130859505579[/C][C]0.91593457024721[/C][/ROW]
[ROW][C]30[/C][C]0.0566165290471322[/C][C]0.113233058094264[/C][C]0.943383470952868[/C][/ROW]
[ROW][C]31[/C][C]0.0787901812680195[/C][C]0.157580362536039[/C][C]0.92120981873198[/C][/ROW]
[ROW][C]32[/C][C]0.0705260796382611[/C][C]0.141052159276522[/C][C]0.92947392036174[/C][/ROW]
[ROW][C]33[/C][C]0.0814432641803783[/C][C]0.162886528360757[/C][C]0.918556735819622[/C][/ROW]
[ROW][C]34[/C][C]0.101121009988781[/C][C]0.202242019977562[/C][C]0.898878990011219[/C][/ROW]
[ROW][C]35[/C][C]0.0837883591798034[/C][C]0.167576718359607[/C][C]0.916211640820197[/C][/ROW]
[ROW][C]36[/C][C]0.0805835247069533[/C][C]0.161167049413907[/C][C]0.919416475293047[/C][/ROW]
[ROW][C]37[/C][C]0.092315271054184[/C][C]0.184630542108368[/C][C]0.907684728945816[/C][/ROW]
[ROW][C]38[/C][C]0.146924635079385[/C][C]0.293849270158770[/C][C]0.853075364920615[/C][/ROW]
[ROW][C]39[/C][C]0.740330892265572[/C][C]0.519338215468855[/C][C]0.259669107734428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58093&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58093&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2508790219104220.5017580438208440.749120978089578
200.1387788693489120.2775577386978240.861221130651088
210.1026485906343570.2052971812687140.897351409365643
220.1303751253729070.2607502507458140.869624874627093
230.07408067701647210.1481613540329440.925919322983528
240.03817957499978230.07635914999956450.961820425000218
250.01764408460808400.03528816921616790.982355915391916
260.02626796677065430.05253593354130860.973732033229346
270.03255804128270490.06511608256540970.967441958717295
280.02234774949532550.04469549899065110.977652250504675
290.08406542975278960.1681308595055790.91593457024721
300.05661652904713220.1132330580942640.943383470952868
310.07879018126801950.1575803625360390.92120981873198
320.07052607963826110.1410521592765220.92947392036174
330.08144326418037830.1628865283607570.918556735819622
340.1011210099887810.2022420199775620.898878990011219
350.08378835917980340.1675767183596070.916211640820197
360.08058352470695330.1611670494139070.919416475293047
370.0923152710541840.1846305421083680.907684728945816
380.1469246350793850.2938492701587700.853075364920615
390.7403308922655720.5193382154688550.259669107734428







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0952380952380952NOK
10% type I error level50.238095238095238NOK

\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 & 2 & 0.0952380952380952 & NOK \tabularnewline
10% type I error level & 5 & 0.238095238095238 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58093&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]2[/C][C]0.0952380952380952[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.238095238095238[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58093&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58093&T=6

As an alternative you can also use a 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 level20.0952380952380952NOK
10% type I error level50.238095238095238NOK



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')
}