FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationMon, 20 Dec 2010 23:51:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292888953qz52f193wih2avl.htm/, Retrieved Fri, 07 Nov 2025 02:35:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113172, Retrieved Fri, 07 Nov 2025 02:35:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact445

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
-  M D  [Classical Decomposition] [] [2010-11-26 09:51:05] [7789b9488494790f41ddb7f073cada1b]
- RMPD    [Multiple Regression] [] [2010-12-17 12:03:34] [7789b9488494790f41ddb7f073cada1b]
-   P         [Multiple Regression] [] [2010-12-20 23:51:08] [0bf4568947c4284a0258563e64d5d827] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102.86	102.38	102.37	101.76
102.87	102.86	102.38	102.37
102.92	102.87	102.86	102.38
102.95	102.92	102.87	102.86
103.02	102.95	102.92	102.87
104.08	103.02	102.95	102.92
104.16	104.08	103.02	102.95
104.24	104.16	104.08	103.02
104.33	104.24	104.16	104.08
104.73	104.33	104.24	104.16
104.86	104.73	104.33	104.24
105.03	104.86	104.73	104.33
105.62	105.03	104.86	104.73
105.63	105.62	105.03	104.86
105.63	105.63	105.62	105.03
105.94	105.63	105.63	105.62
106.61	105.94	105.63	105.63
107.69	106.61	105.94	105.63
107.78	107.69	106.61	105.94
107.93	107.78	107.69	106.61
108.48	107.93	107.78	107.69
108.14	108.48	107.93	107.78
108.48	108.14	108.48	107.93
108.48	108.48	108.14	108.48
108.89	108.48	108.48	108.14
108.93	108.89	108.48	108.48
109.21	108.93	108.89	108.48
109.47	109.21	108.93	108.89
109.80	109.47	109.21	108.93
111.73	109.80	109.47	109.21
111.85	111.73	109.80	109.47
112.12	111.85	111.73	109.80
112.15	112.12	111.85	111.73
112.17	112.15	112.12	111.85
112.67	112.17	112.15	112.12
112.80	112.67	112.17	112.15
113.44	112.80	112.67	112.17
113.53	113.44	112.80	112.67
114.53	113.53	113.44	112.80
114.51	114.53	113.53	113.44
115.05	114.51	114.53	113.53
116.67	115.05	114.51	114.53
117.07	116.67	115.05	114.51
116.92	117.07	116.67	115.05
117.00	116.92	117.07	116.67
117.02	117.00	116.92	117.07
117.35	117.02	117.00	116.92
117.36	117.35	117.02	117.00
117.82	117.36	117.35	117.02
117.88	117.82	117.36	117.35
118.24	117.88	117.82	117.36
118.50	118.24	117.88	117.82
118.80	118.50	118.24	117.88
119.76	118.80	118.50	118.24
120.09	119.76	118.80	118.50

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113172&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113172&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113172&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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
Y1[t] = + 14.2477798483089 + 0.757347311456524Y2[t] + 0.162331012991509Y3[t] -0.0605178371933855Y4[t] + 0.406078167562174M1[t] + 0.0209506478073179M2[t] + 0.198187463583214M3[t] + 0.085548437737373M4[t] + 0.238923020163978M5[t] + 1.22373482995670M6[t] + 0.319554519385561M7[t] + 0.0181348618259313M8[t] + 0.148386559720352M9[t] -0.0214456339183326M10[t] + 0.210413993094083M11[t] + 0.0490649360196856t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y1[t] =  +  14.2477798483089 +  0.757347311456524Y2[t] +  0.162331012991509Y3[t] -0.0605178371933855Y4[t] +  0.406078167562174M1[t] +  0.0209506478073179M2[t] +  0.198187463583214M3[t] +  0.085548437737373M4[t] +  0.238923020163978M5[t] +  1.22373482995670M6[t] +  0.319554519385561M7[t] +  0.0181348618259313M8[t] +  0.148386559720352M9[t] -0.0214456339183326M10[t] +  0.210413993094083M11[t] +  0.0490649360196856t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113172&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y1[t] =  +  14.2477798483089 +  0.757347311456524Y2[t] +  0.162331012991509Y3[t] -0.0605178371933855Y4[t] +  0.406078167562174M1[t] +  0.0209506478073179M2[t] +  0.198187463583214M3[t] +  0.085548437737373M4[t] +  0.238923020163978M5[t] +  1.22373482995670M6[t] +  0.319554519385561M7[t] +  0.0181348618259313M8[t] +  0.148386559720352M9[t] -0.0214456339183326M10[t] +  0.210413993094083M11[t] +  0.0490649360196856t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113172&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113172&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
Y1[t] = + 14.2477798483089 + 0.757347311456524Y2[t] + 0.162331012991509Y3[t] -0.0605178371933855Y4[t] + 0.406078167562174M1[t] + 0.0209506478073179M2[t] + 0.198187463583214M3[t] + 0.085548437737373M4[t] + 0.238923020163978M5[t] + 1.22373482995670M6[t] + 0.319554519385561M7[t] + 0.0181348618259313M8[t] + 0.148386559720352M9[t] -0.0214456339183326M10[t] + 0.210413993094083M11[t] + 0.0490649360196856t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)14.24777984830896.1746732.30750.0264240.013212
Y20.7573473114565240.1583094.7842.5e-051.2e-05
Y30.1623310129915090.2022960.80240.4271590.213579
Y4-0.06051783719338550.154901-0.39070.6981550.349077
M10.4060781675621740.1665282.43850.0194040.009702
M20.02095064780731790.1570010.13340.894530.447265
M30.1981874635832140.1745621.13530.2631610.13158
M40.0855484377373730.1534160.55760.5802870.290144
M50.2389230201639780.1625061.47020.1495180.074759
M61.223734829956700.1557927.854900
M70.3195545193855610.2285851.3980.1700230.085012
M80.01813486182593130.2708970.06690.9469680.473484
M90.1483865597203520.1688440.87880.3848710.192436
M10-0.02144563391833260.164159-0.13060.8967320.448366
M110.2104139930940830.1687371.2470.2198360.109918
t0.04906493601968560.0203152.41530.0205110.010255

\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) & 14.2477798483089 & 6.174673 & 2.3075 & 0.026424 & 0.013212 \tabularnewline
Y2 & 0.757347311456524 & 0.158309 & 4.784 & 2.5e-05 & 1.2e-05 \tabularnewline
Y3 & 0.162331012991509 & 0.202296 & 0.8024 & 0.427159 & 0.213579 \tabularnewline
Y4 & -0.0605178371933855 & 0.154901 & -0.3907 & 0.698155 & 0.349077 \tabularnewline
M1 & 0.406078167562174 & 0.166528 & 2.4385 & 0.019404 & 0.009702 \tabularnewline
M2 & 0.0209506478073179 & 0.157001 & 0.1334 & 0.89453 & 0.447265 \tabularnewline
M3 & 0.198187463583214 & 0.174562 & 1.1353 & 0.263161 & 0.13158 \tabularnewline
M4 & 0.085548437737373 & 0.153416 & 0.5576 & 0.580287 & 0.290144 \tabularnewline
M5 & 0.238923020163978 & 0.162506 & 1.4702 & 0.149518 & 0.074759 \tabularnewline
M6 & 1.22373482995670 & 0.155792 & 7.8549 & 0 & 0 \tabularnewline
M7 & 0.319554519385561 & 0.228585 & 1.398 & 0.170023 & 0.085012 \tabularnewline
M8 & 0.0181348618259313 & 0.270897 & 0.0669 & 0.946968 & 0.473484 \tabularnewline
M9 & 0.148386559720352 & 0.168844 & 0.8788 & 0.384871 & 0.192436 \tabularnewline
M10 & -0.0214456339183326 & 0.164159 & -0.1306 & 0.896732 & 0.448366 \tabularnewline
M11 & 0.210413993094083 & 0.168737 & 1.247 & 0.219836 & 0.109918 \tabularnewline
t & 0.0490649360196856 & 0.020315 & 2.4153 & 0.020511 & 0.010255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113172&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]14.2477798483089[/C][C]6.174673[/C][C]2.3075[/C][C]0.026424[/C][C]0.013212[/C][/ROW]
[ROW][C]Y2[/C][C]0.757347311456524[/C][C]0.158309[/C][C]4.784[/C][C]2.5e-05[/C][C]1.2e-05[/C][/ROW]
[ROW][C]Y3[/C][C]0.162331012991509[/C][C]0.202296[/C][C]0.8024[/C][C]0.427159[/C][C]0.213579[/C][/ROW]
[ROW][C]Y4[/C][C]-0.0605178371933855[/C][C]0.154901[/C][C]-0.3907[/C][C]0.698155[/C][C]0.349077[/C][/ROW]
[ROW][C]M1[/C][C]0.406078167562174[/C][C]0.166528[/C][C]2.4385[/C][C]0.019404[/C][C]0.009702[/C][/ROW]
[ROW][C]M2[/C][C]0.0209506478073179[/C][C]0.157001[/C][C]0.1334[/C][C]0.89453[/C][C]0.447265[/C][/ROW]
[ROW][C]M3[/C][C]0.198187463583214[/C][C]0.174562[/C][C]1.1353[/C][C]0.263161[/C][C]0.13158[/C][/ROW]
[ROW][C]M4[/C][C]0.085548437737373[/C][C]0.153416[/C][C]0.5576[/C][C]0.580287[/C][C]0.290144[/C][/ROW]
[ROW][C]M5[/C][C]0.238923020163978[/C][C]0.162506[/C][C]1.4702[/C][C]0.149518[/C][C]0.074759[/C][/ROW]
[ROW][C]M6[/C][C]1.22373482995670[/C][C]0.155792[/C][C]7.8549[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]0.319554519385561[/C][C]0.228585[/C][C]1.398[/C][C]0.170023[/C][C]0.085012[/C][/ROW]
[ROW][C]M8[/C][C]0.0181348618259313[/C][C]0.270897[/C][C]0.0669[/C][C]0.946968[/C][C]0.473484[/C][/ROW]
[ROW][C]M9[/C][C]0.148386559720352[/C][C]0.168844[/C][C]0.8788[/C][C]0.384871[/C][C]0.192436[/C][/ROW]
[ROW][C]M10[/C][C]-0.0214456339183326[/C][C]0.164159[/C][C]-0.1306[/C][C]0.896732[/C][C]0.448366[/C][/ROW]
[ROW][C]M11[/C][C]0.210413993094083[/C][C]0.168737[/C][C]1.247[/C][C]0.219836[/C][C]0.109918[/C][/ROW]
[ROW][C]t[/C][C]0.0490649360196856[/C][C]0.020315[/C][C]2.4153[/C][C]0.020511[/C][C]0.010255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113172&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113172&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)14.24777984830896.1746732.30750.0264240.013212
Y20.7573473114565240.1583094.7842.5e-051.2e-05
Y30.1623310129915090.2022960.80240.4271590.213579
Y4-0.06051783719338550.154901-0.39070.6981550.349077
M10.4060781675621740.1665282.43850.0194040.009702
M20.02095064780731790.1570010.13340.894530.447265
M30.1981874635832140.1745621.13530.2631610.13158
M40.0855484377373730.1534160.55760.5802870.290144
M50.2389230201639780.1625061.47020.1495180.074759
M61.223734829956700.1557927.854900
M70.3195545193855610.2285851.3980.1700230.085012
M80.01813486182593130.2708970.06690.9469680.473484
M90.1483865597203520.1688440.87880.3848710.192436
M10-0.02144563391833260.164159-0.13060.8967320.448366
M110.2104139930940830.1687371.2470.2198360.109918
t0.04906493601968560.0203152.41530.0205110.010255






Multiple Linear Regression - Regression Statistics
Multiple R0.999350423129952
R-squared0.998701268210013
Adjusted R-squared0.998201755983095
F-TEST (value)1999.35299756731
F-TEST (DF numerator)15
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.228410216986260
Sum Squared Residuals2.03467786172471

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.999350423129952 \tabularnewline
R-squared & 0.998701268210013 \tabularnewline
Adjusted R-squared & 0.998201755983095 \tabularnewline
F-TEST (value) & 1999.35299756731 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.228410216986260 \tabularnewline
Sum Squared Residuals & 2.03467786172471 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113172&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.999350423129952[/C][/ROW]
[ROW][C]R-squared[/C][C]0.998701268210013[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.998201755983095[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1999.35299756731[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.228410216986260[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.03467786172471[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113172&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113172&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 R0.999350423129952
R-squared0.998701268210013
Adjusted R-squared0.998201755983095
F-TEST (value)1999.35299756731
F-TEST (DF numerator)15
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.228410216986260
Sum Squared Residuals2.03467786172471






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1102.86102.6996713859510.160328614048589
2102.87102.6918429411570.178157058842567
3102.92103.003031873932-0.083031873931566
4102.95102.9498998979550.000100102044675913
5103.02103.182571208023-0.162571208022959
6104.08104.271306304167-0.191306304167390
7104.16104.228526715553-0.0685267155534605
8104.24104.2045944040970.035405595902498
9104.33104.393336396542-0.0633363965424573
10104.73104.3488754510180.381124548981608
11104.86104.942507302827-0.082507302826877
12105.03104.9390991960910.0909008039089777
13105.62105.5198872394320.100112760567971
14105.63105.650388522830-0.0203885228296365
15105.63105.969751013082-0.339751013081892
16105.94105.8720947094420.0679052905584503
17106.61106.3087067160670.301293283932571
18107.69107.900328774583-0.210328774583076
19107.78107.953149745579-0.173149745579029
20107.93107.9037268251810.0262731748185706
21108.48108.1458960828140.334103917185598
22108.14108.460572893098-0.320572893097814
23108.48108.564203751801-0.0842037518010124
24108.48108.571875425748-0.0918754257483607
25108.89109.102787138393-0.212787138393088
26108.93109.056660887709-0.126660887709332
27109.21109.379812247290-0.169812247289711
28109.47109.509976331942-0.0399763319417409
29109.8109.952358121517-0.152358121516618
30111.73111.2614205490730.468579450926687
31111.85111.905820082250-0.0558200822498856
32112.12112.0376750068850.082324993115497
33112.15112.324155710668-0.174155710667622
34112.17112.262676105437-0.0926761054368275
35112.67112.5472777290460.122722270954414
36112.8112.7660334128430.0339665871565164
37113.44113.3995868166670.0404131833334258
38113.53113.539070625356-0.00907062535577818
39114.53113.9295581646620.600441835338124
40114.51114.599209761658-0.0892097616577106
41115.05114.9433867415190.106613258481015
42116.67116.3224665780650.347533421935313
43117.07116.7831229518320.286877048167902
44116.92117.064003763837-0.144003763836566
45117117.096611809976-0.096611809975519
46117.02116.9878755504470.0321244495530341
47117.35117.3060112163270.0439887836734760
48117.36117.392991965317-0.032991965317133
49117.82117.908067419557-0.0880674195568973
50117.88117.902037022948-0.0220370229478196
51118.24118.247846701035-0.00784670103495437
52118.5118.4388192990040.0611807009963253
53118.8118.892977212874-0.0929772128740093
54119.76120.174477794112-0.414477794111534
55120.09120.0793805047860.0106194952144724

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 102.86 & 102.699671385951 & 0.160328614048589 \tabularnewline
2 & 102.87 & 102.691842941157 & 0.178157058842567 \tabularnewline
3 & 102.92 & 103.003031873932 & -0.083031873931566 \tabularnewline
4 & 102.95 & 102.949899897955 & 0.000100102044675913 \tabularnewline
5 & 103.02 & 103.182571208023 & -0.162571208022959 \tabularnewline
6 & 104.08 & 104.271306304167 & -0.191306304167390 \tabularnewline
7 & 104.16 & 104.228526715553 & -0.0685267155534605 \tabularnewline
8 & 104.24 & 104.204594404097 & 0.035405595902498 \tabularnewline
9 & 104.33 & 104.393336396542 & -0.0633363965424573 \tabularnewline
10 & 104.73 & 104.348875451018 & 0.381124548981608 \tabularnewline
11 & 104.86 & 104.942507302827 & -0.082507302826877 \tabularnewline
12 & 105.03 & 104.939099196091 & 0.0909008039089777 \tabularnewline
13 & 105.62 & 105.519887239432 & 0.100112760567971 \tabularnewline
14 & 105.63 & 105.650388522830 & -0.0203885228296365 \tabularnewline
15 & 105.63 & 105.969751013082 & -0.339751013081892 \tabularnewline
16 & 105.94 & 105.872094709442 & 0.0679052905584503 \tabularnewline
17 & 106.61 & 106.308706716067 & 0.301293283932571 \tabularnewline
18 & 107.69 & 107.900328774583 & -0.210328774583076 \tabularnewline
19 & 107.78 & 107.953149745579 & -0.173149745579029 \tabularnewline
20 & 107.93 & 107.903726825181 & 0.0262731748185706 \tabularnewline
21 & 108.48 & 108.145896082814 & 0.334103917185598 \tabularnewline
22 & 108.14 & 108.460572893098 & -0.320572893097814 \tabularnewline
23 & 108.48 & 108.564203751801 & -0.0842037518010124 \tabularnewline
24 & 108.48 & 108.571875425748 & -0.0918754257483607 \tabularnewline
25 & 108.89 & 109.102787138393 & -0.212787138393088 \tabularnewline
26 & 108.93 & 109.056660887709 & -0.126660887709332 \tabularnewline
27 & 109.21 & 109.379812247290 & -0.169812247289711 \tabularnewline
28 & 109.47 & 109.509976331942 & -0.0399763319417409 \tabularnewline
29 & 109.8 & 109.952358121517 & -0.152358121516618 \tabularnewline
30 & 111.73 & 111.261420549073 & 0.468579450926687 \tabularnewline
31 & 111.85 & 111.905820082250 & -0.0558200822498856 \tabularnewline
32 & 112.12 & 112.037675006885 & 0.082324993115497 \tabularnewline
33 & 112.15 & 112.324155710668 & -0.174155710667622 \tabularnewline
34 & 112.17 & 112.262676105437 & -0.0926761054368275 \tabularnewline
35 & 112.67 & 112.547277729046 & 0.122722270954414 \tabularnewline
36 & 112.8 & 112.766033412843 & 0.0339665871565164 \tabularnewline
37 & 113.44 & 113.399586816667 & 0.0404131833334258 \tabularnewline
38 & 113.53 & 113.539070625356 & -0.00907062535577818 \tabularnewline
39 & 114.53 & 113.929558164662 & 0.600441835338124 \tabularnewline
40 & 114.51 & 114.599209761658 & -0.0892097616577106 \tabularnewline
41 & 115.05 & 114.943386741519 & 0.106613258481015 \tabularnewline
42 & 116.67 & 116.322466578065 & 0.347533421935313 \tabularnewline
43 & 117.07 & 116.783122951832 & 0.286877048167902 \tabularnewline
44 & 116.92 & 117.064003763837 & -0.144003763836566 \tabularnewline
45 & 117 & 117.096611809976 & -0.096611809975519 \tabularnewline
46 & 117.02 & 116.987875550447 & 0.0321244495530341 \tabularnewline
47 & 117.35 & 117.306011216327 & 0.0439887836734760 \tabularnewline
48 & 117.36 & 117.392991965317 & -0.032991965317133 \tabularnewline
49 & 117.82 & 117.908067419557 & -0.0880674195568973 \tabularnewline
50 & 117.88 & 117.902037022948 & -0.0220370229478196 \tabularnewline
51 & 118.24 & 118.247846701035 & -0.00784670103495437 \tabularnewline
52 & 118.5 & 118.438819299004 & 0.0611807009963253 \tabularnewline
53 & 118.8 & 118.892977212874 & -0.0929772128740093 \tabularnewline
54 & 119.76 & 120.174477794112 & -0.414477794111534 \tabularnewline
55 & 120.09 & 120.079380504786 & 0.0106194952144724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113172&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]102.86[/C][C]102.699671385951[/C][C]0.160328614048589[/C][/ROW]
[ROW][C]2[/C][C]102.87[/C][C]102.691842941157[/C][C]0.178157058842567[/C][/ROW]
[ROW][C]3[/C][C]102.92[/C][C]103.003031873932[/C][C]-0.083031873931566[/C][/ROW]
[ROW][C]4[/C][C]102.95[/C][C]102.949899897955[/C][C]0.000100102044675913[/C][/ROW]
[ROW][C]5[/C][C]103.02[/C][C]103.182571208023[/C][C]-0.162571208022959[/C][/ROW]
[ROW][C]6[/C][C]104.08[/C][C]104.271306304167[/C][C]-0.191306304167390[/C][/ROW]
[ROW][C]7[/C][C]104.16[/C][C]104.228526715553[/C][C]-0.0685267155534605[/C][/ROW]
[ROW][C]8[/C][C]104.24[/C][C]104.204594404097[/C][C]0.035405595902498[/C][/ROW]
[ROW][C]9[/C][C]104.33[/C][C]104.393336396542[/C][C]-0.0633363965424573[/C][/ROW]
[ROW][C]10[/C][C]104.73[/C][C]104.348875451018[/C][C]0.381124548981608[/C][/ROW]
[ROW][C]11[/C][C]104.86[/C][C]104.942507302827[/C][C]-0.082507302826877[/C][/ROW]
[ROW][C]12[/C][C]105.03[/C][C]104.939099196091[/C][C]0.0909008039089777[/C][/ROW]
[ROW][C]13[/C][C]105.62[/C][C]105.519887239432[/C][C]0.100112760567971[/C][/ROW]
[ROW][C]14[/C][C]105.63[/C][C]105.650388522830[/C][C]-0.0203885228296365[/C][/ROW]
[ROW][C]15[/C][C]105.63[/C][C]105.969751013082[/C][C]-0.339751013081892[/C][/ROW]
[ROW][C]16[/C][C]105.94[/C][C]105.872094709442[/C][C]0.0679052905584503[/C][/ROW]
[ROW][C]17[/C][C]106.61[/C][C]106.308706716067[/C][C]0.301293283932571[/C][/ROW]
[ROW][C]18[/C][C]107.69[/C][C]107.900328774583[/C][C]-0.210328774583076[/C][/ROW]
[ROW][C]19[/C][C]107.78[/C][C]107.953149745579[/C][C]-0.173149745579029[/C][/ROW]
[ROW][C]20[/C][C]107.93[/C][C]107.903726825181[/C][C]0.0262731748185706[/C][/ROW]
[ROW][C]21[/C][C]108.48[/C][C]108.145896082814[/C][C]0.334103917185598[/C][/ROW]
[ROW][C]22[/C][C]108.14[/C][C]108.460572893098[/C][C]-0.320572893097814[/C][/ROW]
[ROW][C]23[/C][C]108.48[/C][C]108.564203751801[/C][C]-0.0842037518010124[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.571875425748[/C][C]-0.0918754257483607[/C][/ROW]
[ROW][C]25[/C][C]108.89[/C][C]109.102787138393[/C][C]-0.212787138393088[/C][/ROW]
[ROW][C]26[/C][C]108.93[/C][C]109.056660887709[/C][C]-0.126660887709332[/C][/ROW]
[ROW][C]27[/C][C]109.21[/C][C]109.379812247290[/C][C]-0.169812247289711[/C][/ROW]
[ROW][C]28[/C][C]109.47[/C][C]109.509976331942[/C][C]-0.0399763319417409[/C][/ROW]
[ROW][C]29[/C][C]109.8[/C][C]109.952358121517[/C][C]-0.152358121516618[/C][/ROW]
[ROW][C]30[/C][C]111.73[/C][C]111.261420549073[/C][C]0.468579450926687[/C][/ROW]
[ROW][C]31[/C][C]111.85[/C][C]111.905820082250[/C][C]-0.0558200822498856[/C][/ROW]
[ROW][C]32[/C][C]112.12[/C][C]112.037675006885[/C][C]0.082324993115497[/C][/ROW]
[ROW][C]33[/C][C]112.15[/C][C]112.324155710668[/C][C]-0.174155710667622[/C][/ROW]
[ROW][C]34[/C][C]112.17[/C][C]112.262676105437[/C][C]-0.0926761054368275[/C][/ROW]
[ROW][C]35[/C][C]112.67[/C][C]112.547277729046[/C][C]0.122722270954414[/C][/ROW]
[ROW][C]36[/C][C]112.8[/C][C]112.766033412843[/C][C]0.0339665871565164[/C][/ROW]
[ROW][C]37[/C][C]113.44[/C][C]113.399586816667[/C][C]0.0404131833334258[/C][/ROW]
[ROW][C]38[/C][C]113.53[/C][C]113.539070625356[/C][C]-0.00907062535577818[/C][/ROW]
[ROW][C]39[/C][C]114.53[/C][C]113.929558164662[/C][C]0.600441835338124[/C][/ROW]
[ROW][C]40[/C][C]114.51[/C][C]114.599209761658[/C][C]-0.0892097616577106[/C][/ROW]
[ROW][C]41[/C][C]115.05[/C][C]114.943386741519[/C][C]0.106613258481015[/C][/ROW]
[ROW][C]42[/C][C]116.67[/C][C]116.322466578065[/C][C]0.347533421935313[/C][/ROW]
[ROW][C]43[/C][C]117.07[/C][C]116.783122951832[/C][C]0.286877048167902[/C][/ROW]
[ROW][C]44[/C][C]116.92[/C][C]117.064003763837[/C][C]-0.144003763836566[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]117.096611809976[/C][C]-0.096611809975519[/C][/ROW]
[ROW][C]46[/C][C]117.02[/C][C]116.987875550447[/C][C]0.0321244495530341[/C][/ROW]
[ROW][C]47[/C][C]117.35[/C][C]117.306011216327[/C][C]0.0439887836734760[/C][/ROW]
[ROW][C]48[/C][C]117.36[/C][C]117.392991965317[/C][C]-0.032991965317133[/C][/ROW]
[ROW][C]49[/C][C]117.82[/C][C]117.908067419557[/C][C]-0.0880674195568973[/C][/ROW]
[ROW][C]50[/C][C]117.88[/C][C]117.902037022948[/C][C]-0.0220370229478196[/C][/ROW]
[ROW][C]51[/C][C]118.24[/C][C]118.247846701035[/C][C]-0.00784670103495437[/C][/ROW]
[ROW][C]52[/C][C]118.5[/C][C]118.438819299004[/C][C]0.0611807009963253[/C][/ROW]
[ROW][C]53[/C][C]118.8[/C][C]118.892977212874[/C][C]-0.0929772128740093[/C][/ROW]
[ROW][C]54[/C][C]119.76[/C][C]120.174477794112[/C][C]-0.414477794111534[/C][/ROW]
[ROW][C]55[/C][C]120.09[/C][C]120.079380504786[/C][C]0.0106194952144724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113172&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113172&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
1102.86102.6996713859510.160328614048589
2102.87102.6918429411570.178157058842567
3102.92103.003031873932-0.083031873931566
4102.95102.9498998979550.000100102044675913
5103.02103.182571208023-0.162571208022959
6104.08104.271306304167-0.191306304167390
7104.16104.228526715553-0.0685267155534605
8104.24104.2045944040970.035405595902498
9104.33104.393336396542-0.0633363965424573
10104.73104.3488754510180.381124548981608
11104.86104.942507302827-0.082507302826877
12105.03104.9390991960910.0909008039089777
13105.62105.5198872394320.100112760567971
14105.63105.650388522830-0.0203885228296365
15105.63105.969751013082-0.339751013081892
16105.94105.8720947094420.0679052905584503
17106.61106.3087067160670.301293283932571
18107.69107.900328774583-0.210328774583076
19107.78107.953149745579-0.173149745579029
20107.93107.9037268251810.0262731748185706
21108.48108.1458960828140.334103917185598
22108.14108.460572893098-0.320572893097814
23108.48108.564203751801-0.0842037518010124
24108.48108.571875425748-0.0918754257483607
25108.89109.102787138393-0.212787138393088
26108.93109.056660887709-0.126660887709332
27109.21109.379812247290-0.169812247289711
28109.47109.509976331942-0.0399763319417409
29109.8109.952358121517-0.152358121516618
30111.73111.2614205490730.468579450926687
31111.85111.905820082250-0.0558200822498856
32112.12112.0376750068850.082324993115497
33112.15112.324155710668-0.174155710667622
34112.17112.262676105437-0.0926761054368275
35112.67112.5472777290460.122722270954414
36112.8112.7660334128430.0339665871565164
37113.44113.3995868166670.0404131833334258
38113.53113.539070625356-0.00907062535577818
39114.53113.9295581646620.600441835338124
40114.51114.599209761658-0.0892097616577106
41115.05114.9433867415190.106613258481015
42116.67116.3224665780650.347533421935313
43117.07116.7831229518320.286877048167902
44116.92117.064003763837-0.144003763836566
45117117.096611809976-0.096611809975519
46117.02116.9878755504470.0321244495530341
47117.35117.3060112163270.0439887836734760
48117.36117.392991965317-0.032991965317133
49117.82117.908067419557-0.0880674195568973
50117.88117.902037022948-0.0220370229478196
51118.24118.247846701035-0.00784670103495437
52118.5118.4388192990040.0611807009963253
53118.8118.892977212874-0.0929772128740093
54119.76120.174477794112-0.414477794111534
55120.09120.0793805047860.0106194952144724






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.4754058883421190.9508117766842370.524594111657881
200.3068296240362660.6136592480725320.693170375963734
210.3046061357154420.6092122714308840.695393864284558
220.702000311522310.595999376955380.29799968847769
230.6330234032273570.7339531935452870.366976596772644
240.5177162838643920.9645674322712160.482283716135608
250.4934902938874770.9869805877749530.506509706112523
260.4063017736052890.8126035472105770.593698226394711
270.5727273791399110.8545452417201790.427272620860089
280.6459133186142880.7081733627714250.354086681385712
290.9043950738857350.1912098522285300.0956049261142649
300.968346810328770.063306379342460.03165318967123
310.960635555100260.07872888979947980.0393644448997399
320.9424104514365380.1151790971269240.0575895485634621
330.8934440894085150.213111821182970.106555910591485
340.8037778941769780.3924442116460450.196222105823022
350.7323086477319840.5353827045360320.267691352268016
360.5675183980494280.8649632039011450.432481601950572

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.475405888342119 & 0.950811776684237 & 0.524594111657881 \tabularnewline
20 & 0.306829624036266 & 0.613659248072532 & 0.693170375963734 \tabularnewline
21 & 0.304606135715442 & 0.609212271430884 & 0.695393864284558 \tabularnewline
22 & 0.70200031152231 & 0.59599937695538 & 0.29799968847769 \tabularnewline
23 & 0.633023403227357 & 0.733953193545287 & 0.366976596772644 \tabularnewline
24 & 0.517716283864392 & 0.964567432271216 & 0.482283716135608 \tabularnewline
25 & 0.493490293887477 & 0.986980587774953 & 0.506509706112523 \tabularnewline
26 & 0.406301773605289 & 0.812603547210577 & 0.593698226394711 \tabularnewline
27 & 0.572727379139911 & 0.854545241720179 & 0.427272620860089 \tabularnewline
28 & 0.645913318614288 & 0.708173362771425 & 0.354086681385712 \tabularnewline
29 & 0.904395073885735 & 0.191209852228530 & 0.0956049261142649 \tabularnewline
30 & 0.96834681032877 & 0.06330637934246 & 0.03165318967123 \tabularnewline
31 & 0.96063555510026 & 0.0787288897994798 & 0.0393644448997399 \tabularnewline
32 & 0.942410451436538 & 0.115179097126924 & 0.0575895485634621 \tabularnewline
33 & 0.893444089408515 & 0.21311182118297 & 0.106555910591485 \tabularnewline
34 & 0.803777894176978 & 0.392444211646045 & 0.196222105823022 \tabularnewline
35 & 0.732308647731984 & 0.535382704536032 & 0.267691352268016 \tabularnewline
36 & 0.567518398049428 & 0.864963203901145 & 0.432481601950572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113172&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]0.475405888342119[/C][C]0.950811776684237[/C][C]0.524594111657881[/C][/ROW]
[ROW][C]20[/C][C]0.306829624036266[/C][C]0.613659248072532[/C][C]0.693170375963734[/C][/ROW]
[ROW][C]21[/C][C]0.304606135715442[/C][C]0.609212271430884[/C][C]0.695393864284558[/C][/ROW]
[ROW][C]22[/C][C]0.70200031152231[/C][C]0.59599937695538[/C][C]0.29799968847769[/C][/ROW]
[ROW][C]23[/C][C]0.633023403227357[/C][C]0.733953193545287[/C][C]0.366976596772644[/C][/ROW]
[ROW][C]24[/C][C]0.517716283864392[/C][C]0.964567432271216[/C][C]0.482283716135608[/C][/ROW]
[ROW][C]25[/C][C]0.493490293887477[/C][C]0.986980587774953[/C][C]0.506509706112523[/C][/ROW]
[ROW][C]26[/C][C]0.406301773605289[/C][C]0.812603547210577[/C][C]0.593698226394711[/C][/ROW]
[ROW][C]27[/C][C]0.572727379139911[/C][C]0.854545241720179[/C][C]0.427272620860089[/C][/ROW]
[ROW][C]28[/C][C]0.645913318614288[/C][C]0.708173362771425[/C][C]0.354086681385712[/C][/ROW]
[ROW][C]29[/C][C]0.904395073885735[/C][C]0.191209852228530[/C][C]0.0956049261142649[/C][/ROW]
[ROW][C]30[/C][C]0.96834681032877[/C][C]0.06330637934246[/C][C]0.03165318967123[/C][/ROW]
[ROW][C]31[/C][C]0.96063555510026[/C][C]0.0787288897994798[/C][C]0.0393644448997399[/C][/ROW]
[ROW][C]32[/C][C]0.942410451436538[/C][C]0.115179097126924[/C][C]0.0575895485634621[/C][/ROW]
[ROW][C]33[/C][C]0.893444089408515[/C][C]0.21311182118297[/C][C]0.106555910591485[/C][/ROW]
[ROW][C]34[/C][C]0.803777894176978[/C][C]0.392444211646045[/C][C]0.196222105823022[/C][/ROW]
[ROW][C]35[/C][C]0.732308647731984[/C][C]0.535382704536032[/C][C]0.267691352268016[/C][/ROW]
[ROW][C]36[/C][C]0.567518398049428[/C][C]0.864963203901145[/C][C]0.432481601950572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113172&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113172&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.4754058883421190.9508117766842370.524594111657881
200.3068296240362660.6136592480725320.693170375963734
210.3046061357154420.6092122714308840.695393864284558
220.702000311522310.595999376955380.29799968847769
230.6330234032273570.7339531935452870.366976596772644
240.5177162838643920.9645674322712160.482283716135608
250.4934902938874770.9869805877749530.506509706112523
260.4063017736052890.8126035472105770.593698226394711
270.5727273791399110.8545452417201790.427272620860089
280.6459133186142880.7081733627714250.354086681385712
290.9043950738857350.1912098522285300.0956049261142649
300.968346810328770.063306379342460.03165318967123
310.960635555100260.07872888979947980.0393644448997399
320.9424104514365380.1151790971269240.0575895485634621
330.8934440894085150.213111821182970.106555910591485
340.8037778941769780.3924442116460450.196222105823022
350.7323086477319840.5353827045360320.267691352268016
360.5675183980494280.8649632039011450.432481601950572






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 level20.111111111111111NOK

\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 & 2 & 0.111111111111111 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113172&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]2[/C][C]0.111111111111111[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113172&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113172&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 level20.111111111111111NOK


Figures (Output of Computation)

Figure 1
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 2
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 3
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 4
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 5
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 6
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 7
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 8
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 9
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 10
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = no ;
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')
}