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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 17 Dec 2010 12:03:34 +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/17/t1292587286r6c07m6g7aejzun.htm/, Retrieved Thu, 26 Jun 2025 08:17:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111408, Retrieved Thu, 26 Jun 2025 08:17:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact370

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] [c05c5ae4ce2db58f67fd725429d7f25c] [Current]
-   P         [Multiple Regression] [] [2010-12-20 23:51:08] [504b6ff240ec7a3fcbc007044ae7a0bb]
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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 time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 5 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111408&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111408&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 time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Multiple Linear Regression - Estimated Regression Equation
Y1[t] = + 14.24777984831 + 0.757347311456523Y2[t] + 0.162331012991481Y3[t] -0.0605178371933684Y4[t] + 0.406078167562165M1[t] + 0.020950647807322M2[t] + 0.198187463583225M3[t] + 0.0855484377373725M4[t] + 0.238923020163983M5[t] + 1.2237348299567M6[t] + 0.319554519385565M7[t] + 0.018134861825965M8[t] + 0.148386559720362M9[t] -0.0214456339183264M10[t] + 0.210413993094089M11[t] + 0.0490649360196894t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y1[t] =  +  14.24777984831 +  0.757347311456523Y2[t] +  0.162331012991481Y3[t] -0.0605178371933684Y4[t] +  0.406078167562165M1[t] +  0.020950647807322M2[t] +  0.198187463583225M3[t] +  0.0855484377373725M4[t] +  0.238923020163983M5[t] +  1.2237348299567M6[t] +  0.319554519385565M7[t] +  0.018134861825965M8[t] +  0.148386559720362M9[t] -0.0214456339183264M10[t] +  0.210413993094089M11[t] +  0.0490649360196894t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111408&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y1[t] =  +  14.24777984831 +  0.757347311456523Y2[t] +  0.162331012991481Y3[t] -0.0605178371933684Y4[t] +  0.406078167562165M1[t] +  0.020950647807322M2[t] +  0.198187463583225M3[t] +  0.0855484377373725M4[t] +  0.238923020163983M5[t] +  1.2237348299567M6[t] +  0.319554519385565M7[t] +  0.018134861825965M8[t] +  0.148386559720362M9[t] -0.0214456339183264M10[t] +  0.210413993094089M11[t] +  0.0490649360196894t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111408&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] = + 14.24777984831 + 0.757347311456523Y2[t] + 0.162331012991481Y3[t] -0.0605178371933684Y4[t] + 0.406078167562165M1[t] + 0.020950647807322M2[t] + 0.198187463583225M3[t] + 0.0855484377373725M4[t] + 0.238923020163983M5[t] + 1.2237348299567M6[t] + 0.319554519385565M7[t] + 0.018134861825965M8[t] + 0.148386559720362M9[t] -0.0214456339183264M10[t] + 0.210413993094089M11[t] + 0.0490649360196894t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)14.247779848316.1746732.30750.0264240.013212
Y20.7573473114565230.1583094.7842.5e-051.2e-05
Y30.1623310129914810.2022960.80240.4271590.213579
Y4-0.06051783719336840.154901-0.39070.6981550.349077
M10.4060781675621650.1665282.43850.0194040.009702
M20.0209506478073220.1570010.13340.894530.447265
M30.1981874635832250.1745621.13530.2631610.13158
M40.08554843773737250.1534160.55760.5802870.290144
M50.2389230201639830.1625061.47020.1495180.074759
M61.22373482995670.1557927.854900
M70.3195545193855650.2285851.3980.1700230.085012
M80.0181348618259650.2708970.06690.9469680.473484
M90.1483865597203620.1688440.87880.3848710.192436
M10-0.02144563391832640.164159-0.13060.8967320.448366
M110.2104139930940890.1687371.2470.2198360.109918
t0.04906493601968940.0203152.41530.0205110.010255

\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) & 14.24777984831 & 6.174673 & 2.3075 & 0.026424 & 0.013212 \tabularnewline
Y2 & 0.757347311456523 & 0.158309 & 4.784 & 2.5e-05 & 1.2e-05 \tabularnewline
Y3 & 0.162331012991481 & 0.202296 & 0.8024 & 0.427159 & 0.213579 \tabularnewline
Y4 & -0.0605178371933684 & 0.154901 & -0.3907 & 0.698155 & 0.349077 \tabularnewline
M1 & 0.406078167562165 & 0.166528 & 2.4385 & 0.019404 & 0.009702 \tabularnewline
M2 & 0.020950647807322 & 0.157001 & 0.1334 & 0.89453 & 0.447265 \tabularnewline
M3 & 0.198187463583225 & 0.174562 & 1.1353 & 0.263161 & 0.13158 \tabularnewline
M4 & 0.0855484377373725 & 0.153416 & 0.5576 & 0.580287 & 0.290144 \tabularnewline
M5 & 0.238923020163983 & 0.162506 & 1.4702 & 0.149518 & 0.074759 \tabularnewline
M6 & 1.2237348299567 & 0.155792 & 7.8549 & 0 & 0 \tabularnewline
M7 & 0.319554519385565 & 0.228585 & 1.398 & 0.170023 & 0.085012 \tabularnewline
M8 & 0.018134861825965 & 0.270897 & 0.0669 & 0.946968 & 0.473484 \tabularnewline
M9 & 0.148386559720362 & 0.168844 & 0.8788 & 0.384871 & 0.192436 \tabularnewline
M10 & -0.0214456339183264 & 0.164159 & -0.1306 & 0.896732 & 0.448366 \tabularnewline
M11 & 0.210413993094089 & 0.168737 & 1.247 & 0.219836 & 0.109918 \tabularnewline
t & 0.0490649360196894 & 0.020315 & 2.4153 & 0.020511 & 0.010255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111408&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]14.24777984831[/C][C]6.174673[/C][C]2.3075[/C][C]0.026424[/C][C]0.013212[/C][/ROW]
[ROW][C]Y2[/C][C]0.757347311456523[/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]0.162331012991481[/C][C]0.202296[/C][C]0.8024[/C][C]0.427159[/C][C]0.213579[/C][/ROW]
[ROW][C]Y4[/C][C]-0.0605178371933684[/C][C]0.154901[/C][C]-0.3907[/C][C]0.698155[/C][C]0.349077[/C][/ROW]
[ROW][C]M1[/C][C]0.406078167562165[/C][C]0.166528[/C][C]2.4385[/C][C]0.019404[/C][C]0.009702[/C][/ROW]
[ROW][C]M2[/C][C]0.020950647807322[/C][C]0.157001[/C][C]0.1334[/C][C]0.89453[/C][C]0.447265[/C][/ROW]
[ROW][C]M3[/C][C]0.198187463583225[/C][C]0.174562[/C][C]1.1353[/C][C]0.263161[/C][C]0.13158[/C][/ROW]
[ROW][C]M4[/C][C]0.0855484377373725[/C][C]0.153416[/C][C]0.5576[/C][C]0.580287[/C][C]0.290144[/C][/ROW]
[ROW][C]M5[/C][C]0.238923020163983[/C][C]0.162506[/C][C]1.4702[/C][C]0.149518[/C][C]0.074759[/C][/ROW]
[ROW][C]M6[/C][C]1.2237348299567[/C][C]0.155792[/C][C]7.8549[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]0.319554519385565[/C][C]0.228585[/C][C]1.398[/C][C]0.170023[/C][C]0.085012[/C][/ROW]
[ROW][C]M8[/C][C]0.018134861825965[/C][C]0.270897[/C][C]0.0669[/C][C]0.946968[/C][C]0.473484[/C][/ROW]
[ROW][C]M9[/C][C]0.148386559720362[/C][C]0.168844[/C][C]0.8788[/C][C]0.384871[/C][C]0.192436[/C][/ROW]
[ROW][C]M10[/C][C]-0.0214456339183264[/C][C]0.164159[/C][C]-0.1306[/C][C]0.896732[/C][C]0.448366[/C][/ROW]
[ROW][C]M11[/C][C]0.210413993094089[/C][C]0.168737[/C][C]1.247[/C][C]0.219836[/C][C]0.109918[/C][/ROW]
[ROW][C]t[/C][C]0.0490649360196894[/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=111408&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111408&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)14.247779848316.1746732.30750.0264240.013212
Y20.7573473114565230.1583094.7842.5e-051.2e-05
Y30.1623310129914810.2022960.80240.4271590.213579
Y4-0.06051783719336840.154901-0.39070.6981550.349077
M10.4060781675621650.1665282.43850.0194040.009702
M20.0209506478073220.1570010.13340.894530.447265
M30.1981874635832250.1745621.13530.2631610.13158
M40.08554843773737250.1534160.55760.5802870.290144
M50.2389230201639830.1625061.47020.1495180.074759
M61.22373482995670.1557927.854900
M70.3195545193855650.2285851.3980.1700230.085012
M80.0181348618259650.2708970.06690.9469680.473484
M90.1483865597203620.1688440.87880.3848710.192436
M10-0.02144563391832640.164159-0.13060.8967320.448366
M110.2104139930940890.1687371.2470.2198360.109918
t0.04906493601968940.0203152.41530.0205110.010255






Multiple Linear Regression - Regression Statistics
Multiple R0.999350423129952
R-squared0.998701268210013
Adjusted R-squared0.998201755983095
F-TEST (value)1999.35299756734
F-TEST (DF numerator)15
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.228410216986259
Sum Squared Residuals2.03467786172468

\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) & 1999.35299756734 \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 & 0.228410216986259 \tabularnewline
Sum Squared Residuals & 2.03467786172468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111408&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]1999.35299756734[/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]0.228410216986259[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.03467786172468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111408&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111408&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)1999.35299756734
F-TEST (DF numerator)15
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.228410216986259
Sum Squared Residuals2.03467786172468






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1102.86102.6996713859510.160328614048532
2102.87102.6918429411570.178157058842593
3102.92103.003031873932-0.0830318739315512
4102.95102.9498998979550.000100102044690802
5103.02103.182571208023-0.162571208022951
6104.08104.271306304167-0.191306304167381
7104.16104.228526715553-0.0685267155534581
8104.24104.2045944040980.035405595902495
9104.33104.393336396542-0.0633363965424561
10104.73104.3488754510180.38112454898161
11104.86104.942507302827-0.0825073028268773
12105.03104.9390991960910.090900803908989
13105.62105.5198872394320.100112760567984
14105.63105.65038852283-0.0203885228296381
15105.63105.969751013082-0.339751013081891
16105.94105.8720947094420.0679052905584495
17106.61106.3087067160670.301293283932561
18107.69107.900328774583-0.210328774583075
19107.78107.953149745579-0.173149745579023
20107.93107.9037268251810.0262731748185617
21108.48108.1458960828140.334103917185593
22108.14108.460572893098-0.320572893097816
23108.48108.564203751801-0.0842037518010056
24108.48108.571875425748-0.0918754257483703
25108.89109.102787138393-0.212787138393077
26108.93109.056660887709-0.126660887709344
27109.21109.37981224729-0.169812247289722
28109.47109.509976331942-0.0399763319417501
29109.8109.952358121517-0.152358121516629
30111.73111.2614205490730.46857945092668
31111.85111.90582008225-0.0558200822498957
32112.12112.0376750068840.0823249931155014
33112.15112.324155710668-0.174155710667628
34112.17112.262676105437-0.0926761054368271
35112.67112.5472777290460.122722270954406
36112.8112.7660334128430.0339665871565115
37113.44113.3995868166670.04041318333344
38113.53113.539070625356-0.00907062535578622
39114.53113.9295581646620.600441835338121
40114.51114.599209761658-0.0892097616577136
41115.05114.9433867415190.106613258481029
42116.67116.3224665780650.34753342193531
43117.07116.7831229518320.286877048167907
44116.92117.064003763837-0.144003763836558
45117117.096611809976-0.096611809975509
46117.02116.9878755504470.0321244495530331
47117.35117.3060112163270.0439887836734767
48117.36117.392991965317-0.03299196531713
49117.82117.908067419557-0.0880674195568793
50117.88117.902037022948-0.0220370229478243
51118.24118.247846701035-0.00784670103495664
52118.5118.4388192990040.0611807009963234
53118.8118.892977212874-0.0929772128740098
54119.76120.174477794112-0.414477794111534
55120.09120.0793805047860.0106194952144697

\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 & 0.160328614048532 \tabularnewline
2 & 102.87 & 102.691842941157 & 0.178157058842593 \tabularnewline
3 & 102.92 & 103.003031873932 & -0.0830318739315512 \tabularnewline
4 & 102.95 & 102.949899897955 & 0.000100102044690802 \tabularnewline
5 & 103.02 & 103.182571208023 & -0.162571208022951 \tabularnewline
6 & 104.08 & 104.271306304167 & -0.191306304167381 \tabularnewline
7 & 104.16 & 104.228526715553 & -0.0685267155534581 \tabularnewline
8 & 104.24 & 104.204594404098 & 0.035405595902495 \tabularnewline
9 & 104.33 & 104.393336396542 & -0.0633363965424561 \tabularnewline
10 & 104.73 & 104.348875451018 & 0.38112454898161 \tabularnewline
11 & 104.86 & 104.942507302827 & -0.0825073028268773 \tabularnewline
12 & 105.03 & 104.939099196091 & 0.090900803908989 \tabularnewline
13 & 105.62 & 105.519887239432 & 0.100112760567984 \tabularnewline
14 & 105.63 & 105.65038852283 & -0.0203885228296381 \tabularnewline
15 & 105.63 & 105.969751013082 & -0.339751013081891 \tabularnewline
16 & 105.94 & 105.872094709442 & 0.0679052905584495 \tabularnewline
17 & 106.61 & 106.308706716067 & 0.301293283932561 \tabularnewline
18 & 107.69 & 107.900328774583 & -0.210328774583075 \tabularnewline
19 & 107.78 & 107.953149745579 & -0.173149745579023 \tabularnewline
20 & 107.93 & 107.903726825181 & 0.0262731748185617 \tabularnewline
21 & 108.48 & 108.145896082814 & 0.334103917185593 \tabularnewline
22 & 108.14 & 108.460572893098 & -0.320572893097816 \tabularnewline
23 & 108.48 & 108.564203751801 & -0.0842037518010056 \tabularnewline
24 & 108.48 & 108.571875425748 & -0.0918754257483703 \tabularnewline
25 & 108.89 & 109.102787138393 & -0.212787138393077 \tabularnewline
26 & 108.93 & 109.056660887709 & -0.126660887709344 \tabularnewline
27 & 109.21 & 109.37981224729 & -0.169812247289722 \tabularnewline
28 & 109.47 & 109.509976331942 & -0.0399763319417501 \tabularnewline
29 & 109.8 & 109.952358121517 & -0.152358121516629 \tabularnewline
30 & 111.73 & 111.261420549073 & 0.46857945092668 \tabularnewline
31 & 111.85 & 111.90582008225 & -0.0558200822498957 \tabularnewline
32 & 112.12 & 112.037675006884 & 0.0823249931155014 \tabularnewline
33 & 112.15 & 112.324155710668 & -0.174155710667628 \tabularnewline
34 & 112.17 & 112.262676105437 & -0.0926761054368271 \tabularnewline
35 & 112.67 & 112.547277729046 & 0.122722270954406 \tabularnewline
36 & 112.8 & 112.766033412843 & 0.0339665871565115 \tabularnewline
37 & 113.44 & 113.399586816667 & 0.04041318333344 \tabularnewline
38 & 113.53 & 113.539070625356 & -0.00907062535578622 \tabularnewline
39 & 114.53 & 113.929558164662 & 0.600441835338121 \tabularnewline
40 & 114.51 & 114.599209761658 & -0.0892097616577136 \tabularnewline
41 & 115.05 & 114.943386741519 & 0.106613258481029 \tabularnewline
42 & 116.67 & 116.322466578065 & 0.34753342193531 \tabularnewline
43 & 117.07 & 116.783122951832 & 0.286877048167907 \tabularnewline
44 & 116.92 & 117.064003763837 & -0.144003763836558 \tabularnewline
45 & 117 & 117.096611809976 & -0.096611809975509 \tabularnewline
46 & 117.02 & 116.987875550447 & 0.0321244495530331 \tabularnewline
47 & 117.35 & 117.306011216327 & 0.0439887836734767 \tabularnewline
48 & 117.36 & 117.392991965317 & -0.03299196531713 \tabularnewline
49 & 117.82 & 117.908067419557 & -0.0880674195568793 \tabularnewline
50 & 117.88 & 117.902037022948 & -0.0220370229478243 \tabularnewline
51 & 118.24 & 118.247846701035 & -0.00784670103495664 \tabularnewline
52 & 118.5 & 118.438819299004 & 0.0611807009963234 \tabularnewline
53 & 118.8 & 118.892977212874 & -0.0929772128740098 \tabularnewline
54 & 119.76 & 120.174477794112 & -0.414477794111534 \tabularnewline
55 & 120.09 & 120.079380504786 & 0.0106194952144697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111408&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]0.160328614048532[/C][/ROW]
[ROW][C]2[/C][C]102.87[/C][C]102.691842941157[/C][C]0.178157058842593[/C][/ROW]
[ROW][C]3[/C][C]102.92[/C][C]103.003031873932[/C][C]-0.0830318739315512[/C][/ROW]
[ROW][C]4[/C][C]102.95[/C][C]102.949899897955[/C][C]0.000100102044690802[/C][/ROW]
[ROW][C]5[/C][C]103.02[/C][C]103.182571208023[/C][C]-0.162571208022951[/C][/ROW]
[ROW][C]6[/C][C]104.08[/C][C]104.271306304167[/C][C]-0.191306304167381[/C][/ROW]
[ROW][C]7[/C][C]104.16[/C][C]104.228526715553[/C][C]-0.0685267155534581[/C][/ROW]
[ROW][C]8[/C][C]104.24[/C][C]104.204594404098[/C][C]0.035405595902495[/C][/ROW]
[ROW][C]9[/C][C]104.33[/C][C]104.393336396542[/C][C]-0.0633363965424561[/C][/ROW]
[ROW][C]10[/C][C]104.73[/C][C]104.348875451018[/C][C]0.38112454898161[/C][/ROW]
[ROW][C]11[/C][C]104.86[/C][C]104.942507302827[/C][C]-0.0825073028268773[/C][/ROW]
[ROW][C]12[/C][C]105.03[/C][C]104.939099196091[/C][C]0.090900803908989[/C][/ROW]
[ROW][C]13[/C][C]105.62[/C][C]105.519887239432[/C][C]0.100112760567984[/C][/ROW]
[ROW][C]14[/C][C]105.63[/C][C]105.65038852283[/C][C]-0.0203885228296381[/C][/ROW]
[ROW][C]15[/C][C]105.63[/C][C]105.969751013082[/C][C]-0.339751013081891[/C][/ROW]
[ROW][C]16[/C][C]105.94[/C][C]105.872094709442[/C][C]0.0679052905584495[/C][/ROW]
[ROW][C]17[/C][C]106.61[/C][C]106.308706716067[/C][C]0.301293283932561[/C][/ROW]
[ROW][C]18[/C][C]107.69[/C][C]107.900328774583[/C][C]-0.210328774583075[/C][/ROW]
[ROW][C]19[/C][C]107.78[/C][C]107.953149745579[/C][C]-0.173149745579023[/C][/ROW]
[ROW][C]20[/C][C]107.93[/C][C]107.903726825181[/C][C]0.0262731748185617[/C][/ROW]
[ROW][C]21[/C][C]108.48[/C][C]108.145896082814[/C][C]0.334103917185593[/C][/ROW]
[ROW][C]22[/C][C]108.14[/C][C]108.460572893098[/C][C]-0.320572893097816[/C][/ROW]
[ROW][C]23[/C][C]108.48[/C][C]108.564203751801[/C][C]-0.0842037518010056[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.571875425748[/C][C]-0.0918754257483703[/C][/ROW]
[ROW][C]25[/C][C]108.89[/C][C]109.102787138393[/C][C]-0.212787138393077[/C][/ROW]
[ROW][C]26[/C][C]108.93[/C][C]109.056660887709[/C][C]-0.126660887709344[/C][/ROW]
[ROW][C]27[/C][C]109.21[/C][C]109.37981224729[/C][C]-0.169812247289722[/C][/ROW]
[ROW][C]28[/C][C]109.47[/C][C]109.509976331942[/C][C]-0.0399763319417501[/C][/ROW]
[ROW][C]29[/C][C]109.8[/C][C]109.952358121517[/C][C]-0.152358121516629[/C][/ROW]
[ROW][C]30[/C][C]111.73[/C][C]111.261420549073[/C][C]0.46857945092668[/C][/ROW]
[ROW][C]31[/C][C]111.85[/C][C]111.90582008225[/C][C]-0.0558200822498957[/C][/ROW]
[ROW][C]32[/C][C]112.12[/C][C]112.037675006884[/C][C]0.0823249931155014[/C][/ROW]
[ROW][C]33[/C][C]112.15[/C][C]112.324155710668[/C][C]-0.174155710667628[/C][/ROW]
[ROW][C]34[/C][C]112.17[/C][C]112.262676105437[/C][C]-0.0926761054368271[/C][/ROW]
[ROW][C]35[/C][C]112.67[/C][C]112.547277729046[/C][C]0.122722270954406[/C][/ROW]
[ROW][C]36[/C][C]112.8[/C][C]112.766033412843[/C][C]0.0339665871565115[/C][/ROW]
[ROW][C]37[/C][C]113.44[/C][C]113.399586816667[/C][C]0.04041318333344[/C][/ROW]
[ROW][C]38[/C][C]113.53[/C][C]113.539070625356[/C][C]-0.00907062535578622[/C][/ROW]
[ROW][C]39[/C][C]114.53[/C][C]113.929558164662[/C][C]0.600441835338121[/C][/ROW]
[ROW][C]40[/C][C]114.51[/C][C]114.599209761658[/C][C]-0.0892097616577136[/C][/ROW]
[ROW][C]41[/C][C]115.05[/C][C]114.943386741519[/C][C]0.106613258481029[/C][/ROW]
[ROW][C]42[/C][C]116.67[/C][C]116.322466578065[/C][C]0.34753342193531[/C][/ROW]
[ROW][C]43[/C][C]117.07[/C][C]116.783122951832[/C][C]0.286877048167907[/C][/ROW]
[ROW][C]44[/C][C]116.92[/C][C]117.064003763837[/C][C]-0.144003763836558[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]117.096611809976[/C][C]-0.096611809975509[/C][/ROW]
[ROW][C]46[/C][C]117.02[/C][C]116.987875550447[/C][C]0.0321244495530331[/C][/ROW]
[ROW][C]47[/C][C]117.35[/C][C]117.306011216327[/C][C]0.0439887836734767[/C][/ROW]
[ROW][C]48[/C][C]117.36[/C][C]117.392991965317[/C][C]-0.03299196531713[/C][/ROW]
[ROW][C]49[/C][C]117.82[/C][C]117.908067419557[/C][C]-0.0880674195568793[/C][/ROW]
[ROW][C]50[/C][C]117.88[/C][C]117.902037022948[/C][C]-0.0220370229478243[/C][/ROW]
[ROW][C]51[/C][C]118.24[/C][C]118.247846701035[/C][C]-0.00784670103495664[/C][/ROW]
[ROW][C]52[/C][C]118.5[/C][C]118.438819299004[/C][C]0.0611807009963234[/C][/ROW]
[ROW][C]53[/C][C]118.8[/C][C]118.892977212874[/C][C]-0.0929772128740098[/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]0.0106194952144697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111408&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111408&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
1102.86102.6996713859510.160328614048532
2102.87102.6918429411570.178157058842593
3102.92103.003031873932-0.0830318739315512
4102.95102.9498998979550.000100102044690802
5103.02103.182571208023-0.162571208022951
6104.08104.271306304167-0.191306304167381
7104.16104.228526715553-0.0685267155534581
8104.24104.2045944040980.035405595902495
9104.33104.393336396542-0.0633363965424561
10104.73104.3488754510180.38112454898161
11104.86104.942507302827-0.0825073028268773
12105.03104.9390991960910.090900803908989
13105.62105.5198872394320.100112760567984
14105.63105.65038852283-0.0203885228296381
15105.63105.969751013082-0.339751013081891
16105.94105.8720947094420.0679052905584495
17106.61106.3087067160670.301293283932561
18107.69107.900328774583-0.210328774583075
19107.78107.953149745579-0.173149745579023
20107.93107.9037268251810.0262731748185617
21108.48108.1458960828140.334103917185593
22108.14108.460572893098-0.320572893097816
23108.48108.564203751801-0.0842037518010056
24108.48108.571875425748-0.0918754257483703
25108.89109.102787138393-0.212787138393077
26108.93109.056660887709-0.126660887709344
27109.21109.37981224729-0.169812247289722
28109.47109.509976331942-0.0399763319417501
29109.8109.952358121517-0.152358121516629
30111.73111.2614205490730.46857945092668
31111.85111.90582008225-0.0558200822498957
32112.12112.0376750068840.0823249931155014
33112.15112.324155710668-0.174155710667628
34112.17112.262676105437-0.0926761054368271
35112.67112.5472777290460.122722270954406
36112.8112.7660334128430.0339665871565115
37113.44113.3995868166670.04041318333344
38113.53113.539070625356-0.00907062535578622
39114.53113.9295581646620.600441835338121
40114.51114.599209761658-0.0892097616577136
41115.05114.9433867415190.106613258481029
42116.67116.3224665780650.34753342193531
43117.07116.7831229518320.286877048167907
44116.92117.064003763837-0.144003763836558
45117117.096611809976-0.096611809975509
46117.02116.9878755504470.0321244495530331
47117.35117.3060112163270.0439887836734767
48117.36117.392991965317-0.03299196531713
49117.82117.908067419557-0.0880674195568793
50117.88117.902037022948-0.0220370229478243
51118.24118.247846701035-0.00784670103495664
52118.5118.4388192990040.0611807009963234
53118.8118.892977212874-0.0929772128740098
54119.76120.174477794112-0.414477794111534
55120.09120.0793805047860.0106194952144697






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.4754058883421080.9508117766842170.524594111657892
200.3068296240362830.6136592480725670.693170375963717
210.3046061357153910.6092122714307820.695393864284609
220.7020003115222850.595999376955430.297999688477715
230.6330234032273380.7339531935453250.366976596772663
240.5177162838643790.9645674322712420.482283716135621
250.4934902938874980.9869805877749960.506509706112502
260.4063017736052820.8126035472105640.593698226394718
270.5727273791399010.8545452417201970.427272620860099
280.6459133186142890.7081733627714230.354086681385711
290.9043950738856830.1912098522286340.0956049261143168
300.9683468103287570.06330637934248530.0316531896712426
310.960635555100270.0787288897994590.0393644448997295
320.9424104514365320.1151790971269360.057589548563468
330.8934440894085260.2131118211829480.106555910591474
340.8037778941769960.3924442116460090.196222105823004
350.7323086477319690.5353827045360620.267691352268031
360.5675183980494620.8649632039010770.432481601950538

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.475405888342108 & 0.950811776684217 & 0.524594111657892 \tabularnewline
20 & 0.306829624036283 & 0.613659248072567 & 0.693170375963717 \tabularnewline
21 & 0.304606135715391 & 0.609212271430782 & 0.695393864284609 \tabularnewline
22 & 0.702000311522285 & 0.59599937695543 & 0.297999688477715 \tabularnewline
23 & 0.633023403227338 & 0.733953193545325 & 0.366976596772663 \tabularnewline
24 & 0.517716283864379 & 0.964567432271242 & 0.482283716135621 \tabularnewline
25 & 0.493490293887498 & 0.986980587774996 & 0.506509706112502 \tabularnewline
26 & 0.406301773605282 & 0.812603547210564 & 0.593698226394718 \tabularnewline
27 & 0.572727379139901 & 0.854545241720197 & 0.427272620860099 \tabularnewline
28 & 0.645913318614289 & 0.708173362771423 & 0.354086681385711 \tabularnewline
29 & 0.904395073885683 & 0.191209852228634 & 0.0956049261143168 \tabularnewline
30 & 0.968346810328757 & 0.0633063793424853 & 0.0316531896712426 \tabularnewline
31 & 0.96063555510027 & 0.078728889799459 & 0.0393644448997295 \tabularnewline
32 & 0.942410451436532 & 0.115179097126936 & 0.057589548563468 \tabularnewline
33 & 0.893444089408526 & 0.213111821182948 & 0.106555910591474 \tabularnewline
34 & 0.803777894176996 & 0.392444211646009 & 0.196222105823004 \tabularnewline
35 & 0.732308647731969 & 0.535382704536062 & 0.267691352268031 \tabularnewline
36 & 0.567518398049462 & 0.864963203901077 & 0.432481601950538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111408&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]0.475405888342108[/C][C]0.950811776684217[/C][C]0.524594111657892[/C][/ROW]
[ROW][C]20[/C][C]0.306829624036283[/C][C]0.613659248072567[/C][C]0.693170375963717[/C][/ROW]
[ROW][C]21[/C][C]0.304606135715391[/C][C]0.609212271430782[/C][C]0.695393864284609[/C][/ROW]
[ROW][C]22[/C][C]0.702000311522285[/C][C]0.59599937695543[/C][C]0.297999688477715[/C][/ROW]
[ROW][C]23[/C][C]0.633023403227338[/C][C]0.733953193545325[/C][C]0.366976596772663[/C][/ROW]
[ROW][C]24[/C][C]0.517716283864379[/C][C]0.964567432271242[/C][C]0.482283716135621[/C][/ROW]
[ROW][C]25[/C][C]0.493490293887498[/C][C]0.986980587774996[/C][C]0.506509706112502[/C][/ROW]
[ROW][C]26[/C][C]0.406301773605282[/C][C]0.812603547210564[/C][C]0.593698226394718[/C][/ROW]
[ROW][C]27[/C][C]0.572727379139901[/C][C]0.854545241720197[/C][C]0.427272620860099[/C][/ROW]
[ROW][C]28[/C][C]0.645913318614289[/C][C]0.708173362771423[/C][C]0.354086681385711[/C][/ROW]
[ROW][C]29[/C][C]0.904395073885683[/C][C]0.191209852228634[/C][C]0.0956049261143168[/C][/ROW]
[ROW][C]30[/C][C]0.968346810328757[/C][C]0.0633063793424853[/C][C]0.0316531896712426[/C][/ROW]
[ROW][C]31[/C][C]0.96063555510027[/C][C]0.078728889799459[/C][C]0.0393644448997295[/C][/ROW]
[ROW][C]32[/C][C]0.942410451436532[/C][C]0.115179097126936[/C][C]0.057589548563468[/C][/ROW]
[ROW][C]33[/C][C]0.893444089408526[/C][C]0.213111821182948[/C][C]0.106555910591474[/C][/ROW]
[ROW][C]34[/C][C]0.803777894176996[/C][C]0.392444211646009[/C][C]0.196222105823004[/C][/ROW]
[ROW][C]35[/C][C]0.732308647731969[/C][C]0.535382704536062[/C][C]0.267691352268031[/C][/ROW]
[ROW][C]36[/C][C]0.567518398049462[/C][C]0.864963203901077[/C][C]0.432481601950538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111408&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111408&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
190.4754058883421080.9508117766842170.524594111657892
200.3068296240362830.6136592480725670.693170375963717
210.3046061357153910.6092122714307820.695393864284609
220.7020003115222850.595999376955430.297999688477715
230.6330234032273380.7339531935453250.366976596772663
240.5177162838643790.9645674322712420.482283716135621
250.4934902938874980.9869805877749960.506509706112502
260.4063017736052820.8126035472105640.593698226394718
270.5727273791399010.8545452417201970.427272620860099
280.6459133186142890.7081733627714230.354086681385711
290.9043950738856830.1912098522286340.0956049261143168
300.9683468103287570.06330637934248530.0316531896712426
310.960635555100270.0787288897994590.0393644448997295
320.9424104514365320.1151790971269360.057589548563468
330.8934440894085260.2131118211829480.106555910591474
340.8037778941769960.3924442116460090.196222105823004
350.7323086477319690.5353827045360620.267691352268031
360.5675183980494620.8649632039010770.432481601950538






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=111408&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=111408&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111408&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
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Figure 2
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No 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')
}