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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sat, 18 Dec 2010 11:51:23 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292672975vdty6oor63pvros.htm/, Retrieved Tue, 30 Apr 2024 02:50:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111859, Retrieved Tue, 30 Apr 2024 02:50:26 +0000

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Estimated Impact

126

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Multiple Regression] [Vertragingen] [2010-12-18 11:51:23] [19046f4a6967f3fb6f5f17d42e7d38f2] [Current]

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104,7	116,7	107,5	116,1
102,8	112,5	116,7	107,5
98,1	113	112,5	116,7
113,9	126,4	113	112,5
80,9	114,1	126,4	113
95,7	112,5	114,1	126,4
113,2	112,4	112,5	114,1
105,9	113,1	112,4	112,5
108,8	116,3	113,1	112,4
102,3	111,7	116,3	113,1
99	118,8	111,7	116,3
100,7	116,5	118,8	111,7
115,5	125,1	116,5	118,8
100,7	113,1	125,1	116,5
109,9	119,6	113,1	125,1
114,6	114,4	119,6	113,1
85,4	114	114,4	119,6
100,5	117,8	114	114,4
114,8	117	117,8	114
116,5	120,9	117	117,8
112,9	115	120,9	117
102	117,3	115	120,9
106	119,4	117,3	115
105,3	114,9	119,4	117,3
118,8	125,8	114,9	119,4
106,1	117,6	125,8	114,9
109,3	117,6	117,6	125,8
117,2	114,9	117,6	117,6
92,5	121,9	114,9	117,6
104,2	117	121,9	114,9
112,5	106,4	117	121,9
122,4	110,5	106,4	117
113,3	113,6	110,5	106,4
100	114,2	113,6	110,5
110,7	125,4	114,2	113,6
112,8	124,6	125,4	114,2
109,8	120,2	124,6	125,4
117,3	120,8	120,2	124,6
109,1	111,4	120,8	120,2
115,9	124,1	111,4	120,8
96	120,2	124,1	111,4
99,8	125,5	120,2	124,1
116,8	116	125,5	120,2
115,7	117	116	125,5
99,4	105,7	117	116
94,3	102	105,7	117
91	106,4	102	105,7
93,2	96,9	106,4	102
103,1	107,6	96,9	106,4
94,1	98,8	107,6	96,9
91,8	101,1	98,8	107,6
102,7	105,7	101,1	98,8
82,6	104,6	105,7	101,1
89,1	103,2	104,6	105,7
104,5	101,6	103,2	104,6
105,1	106,7	101,6	103,2
95,1	99,5	106,7	101,6
88,7	101	99,5	106,7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 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 & 6 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111859&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111859&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111859&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 17.8886662901039 + 0.593242377727027T.I.P.[t] + 0.205154983132475`Y(t-1)`[t] + 0.115152970700046`Y(t-2)`[t] + 1.45879444891351M1[t] -2.14950402416359M2[t] -1.21608635241409M3[t] -1.28121836133137M4[t] + 10.7917317668094M5[t] + 4.87747224861314M6[t] -7.95768982198349M7[t] -4.45922797316631M8[t] -3.79312308338614M9[t] + 0.925313075396341M10[t] + 6.08788829036564M11[t] -0.089662245098952t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  17.8886662901039 +  0.593242377727027T.I.P.[t] +  0.205154983132475`Y(t-1)`[t] +  0.115152970700046`Y(t-2)`[t] +  1.45879444891351M1[t] -2.14950402416359M2[t] -1.21608635241409M3[t] -1.28121836133137M4[t] +  10.7917317668094M5[t] +  4.87747224861314M6[t] -7.95768982198349M7[t] -4.45922797316631M8[t] -3.79312308338614M9[t] +  0.925313075396341M10[t] +  6.08788829036564M11[t] -0.089662245098952t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111859&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  17.8886662901039 +  0.593242377727027T.I.P.[t] +  0.205154983132475`Y(t-1)`[t] +  0.115152970700046`Y(t-2)`[t] +  1.45879444891351M1[t] -2.14950402416359M2[t] -1.21608635241409M3[t] -1.28121836133137M4[t] +  10.7917317668094M5[t] +  4.87747224861314M6[t] -7.95768982198349M7[t] -4.45922797316631M8[t] -3.79312308338614M9[t] +  0.925313075396341M10[t] +  6.08788829036564M11[t] -0.089662245098952t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111859&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111859&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 17.8886662901039 + 0.593242377727027T.I.P.[t] + 0.205154983132475`Y(t-1)`[t] + 0.115152970700046`Y(t-2)`[t] + 1.45879444891351M1[t] -2.14950402416359M2[t] -1.21608635241409M3[t] -1.28121836133137M4[t] + 10.7917317668094M5[t] + 4.87747224861314M6[t] -7.95768982198349M7[t] -4.45922797316631M8[t] -3.79312308338614M9[t] + 0.925313075396341M10[t] + 6.08788829036564M11[t] -0.089662245098952t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	17.8886662901039	11.042792	1.6199	0.11273	0.056365
T.I.P.	0.593242377727027	0.109649	5.4104	3e-06	1e-06
`Y(t-1)`	0.205154983132475	0.117405	1.7474	0.087875	0.043937
`Y(t-2)`	0.115152970700046	0.116605	0.9875	0.329031	0.164515
M1	1.45879444891351	2.868214	0.5086	0.613689	0.306844
M2	-2.14950402416359	2.497623	-0.8606	0.394334	0.197167
M3	-1.21608635241409	2.806613	-0.4333	0.667019	0.333509
M4	-1.28121836133137	2.863701	-0.4474	0.656886	0.328443
M5	10.7917317668094	3.040126	3.5498	0.000966	0.000483
M6	4.87747224861314	2.721254	1.7924	0.08028	0.04014
M7	-7.95768982198349	2.744783	-2.8992	0.005926	0.002963
M8	-4.45922797316631	2.985327	-1.4937	0.142725	0.071363
M9	-3.79312308338614	2.56813	-1.477	0.147136	0.073568
M10	0.925313075396341	2.713631	0.341	0.734813	0.367407
M11	6.08788829036564	2.746191	2.2168	0.032102	0.016051
t	-0.089662245098952	0.033877	-2.6467	0.011394	0.005697

\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) & 17.8886662901039 & 11.042792 & 1.6199 & 0.11273 & 0.056365 \tabularnewline
T.I.P. & 0.593242377727027 & 0.109649 & 5.4104 & 3e-06 & 1e-06 \tabularnewline
`Y(t-1)` & 0.205154983132475 & 0.117405 & 1.7474 & 0.087875 & 0.043937 \tabularnewline
`Y(t-2)` & 0.115152970700046 & 0.116605 & 0.9875 & 0.329031 & 0.164515 \tabularnewline
M1 & 1.45879444891351 & 2.868214 & 0.5086 & 0.613689 & 0.306844 \tabularnewline
M2 & -2.14950402416359 & 2.497623 & -0.8606 & 0.394334 & 0.197167 \tabularnewline
M3 & -1.21608635241409 & 2.806613 & -0.4333 & 0.667019 & 0.333509 \tabularnewline
M4 & -1.28121836133137 & 2.863701 & -0.4474 & 0.656886 & 0.328443 \tabularnewline
M5 & 10.7917317668094 & 3.040126 & 3.5498 & 0.000966 & 0.000483 \tabularnewline
M6 & 4.87747224861314 & 2.721254 & 1.7924 & 0.08028 & 0.04014 \tabularnewline
M7 & -7.95768982198349 & 2.744783 & -2.8992 & 0.005926 & 0.002963 \tabularnewline
M8 & -4.45922797316631 & 2.985327 & -1.4937 & 0.142725 & 0.071363 \tabularnewline
M9 & -3.79312308338614 & 2.56813 & -1.477 & 0.147136 & 0.073568 \tabularnewline
M10 & 0.925313075396341 & 2.713631 & 0.341 & 0.734813 & 0.367407 \tabularnewline
M11 & 6.08788829036564 & 2.746191 & 2.2168 & 0.032102 & 0.016051 \tabularnewline
t & -0.089662245098952 & 0.033877 & -2.6467 & 0.011394 & 0.005697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111859&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]17.8886662901039[/C][C]11.042792[/C][C]1.6199[/C][C]0.11273[/C][C]0.056365[/C][/ROW]
[ROW][C]T.I.P.[/C][C]0.593242377727027[/C][C]0.109649[/C][C]5.4104[/C][C]3e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.205154983132475[/C][C]0.117405[/C][C]1.7474[/C][C]0.087875[/C][C]0.043937[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.115152970700046[/C][C]0.116605[/C][C]0.9875[/C][C]0.329031[/C][C]0.164515[/C][/ROW]
[ROW][C]M1[/C][C]1.45879444891351[/C][C]2.868214[/C][C]0.5086[/C][C]0.613689[/C][C]0.306844[/C][/ROW]
[ROW][C]M2[/C][C]-2.14950402416359[/C][C]2.497623[/C][C]-0.8606[/C][C]0.394334[/C][C]0.197167[/C][/ROW]
[ROW][C]M3[/C][C]-1.21608635241409[/C][C]2.806613[/C][C]-0.4333[/C][C]0.667019[/C][C]0.333509[/C][/ROW]
[ROW][C]M4[/C][C]-1.28121836133137[/C][C]2.863701[/C][C]-0.4474[/C][C]0.656886[/C][C]0.328443[/C][/ROW]
[ROW][C]M5[/C][C]10.7917317668094[/C][C]3.040126[/C][C]3.5498[/C][C]0.000966[/C][C]0.000483[/C][/ROW]
[ROW][C]M6[/C][C]4.87747224861314[/C][C]2.721254[/C][C]1.7924[/C][C]0.08028[/C][C]0.04014[/C][/ROW]
[ROW][C]M7[/C][C]-7.95768982198349[/C][C]2.744783[/C][C]-2.8992[/C][C]0.005926[/C][C]0.002963[/C][/ROW]
[ROW][C]M8[/C][C]-4.45922797316631[/C][C]2.985327[/C][C]-1.4937[/C][C]0.142725[/C][C]0.071363[/C][/ROW]
[ROW][C]M9[/C][C]-3.79312308338614[/C][C]2.56813[/C][C]-1.477[/C][C]0.147136[/C][C]0.073568[/C][/ROW]
[ROW][C]M10[/C][C]0.925313075396341[/C][C]2.713631[/C][C]0.341[/C][C]0.734813[/C][C]0.367407[/C][/ROW]
[ROW][C]M11[/C][C]6.08788829036564[/C][C]2.746191[/C][C]2.2168[/C][C]0.032102[/C][C]0.016051[/C][/ROW]
[ROW][C]t[/C][C]-0.089662245098952[/C][C]0.033877[/C][C]-2.6467[/C][C]0.011394[/C][C]0.005697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111859&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111859&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	17.8886662901039	11.042792	1.6199	0.11273	0.056365
T.I.P.	0.593242377727027	0.109649	5.4104	3e-06	1e-06
`Y(t-1)`	0.205154983132475	0.117405	1.7474	0.087875	0.043937
`Y(t-2)`	0.115152970700046	0.116605	0.9875	0.329031	0.164515
M1	1.45879444891351	2.868214	0.5086	0.613689	0.306844
M2	-2.14950402416359	2.497623	-0.8606	0.394334	0.197167
M3	-1.21608635241409	2.806613	-0.4333	0.667019	0.333509
M4	-1.28121836133137	2.863701	-0.4474	0.656886	0.328443
M5	10.7917317668094	3.040126	3.5498	0.000966	0.000483
M6	4.87747224861314	2.721254	1.7924	0.08028	0.04014
M7	-7.95768982198349	2.744783	-2.8992	0.005926	0.002963
M8	-4.45922797316631	2.985327	-1.4937	0.142725	0.071363
M9	-3.79312308338614	2.56813	-1.477	0.147136	0.073568
M10	0.925313075396341	2.713631	0.341	0.734813	0.367407
M11	6.08788829036564	2.746191	2.2168	0.032102	0.016051
t	-0.089662245098952	0.033877	-2.6467	0.011394	0.005697

Multiple Linear Regression - Regression Statistics
Multiple R	0.90677540764535
R-squared	0.82224163991039
Adjusted R-squared	0.758756511306957
F-TEST (value)	12.9517204737289
F-TEST (DF numerator)	15
F-TEST (DF denominator)	42
p-value	3.16494608298967e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.71652920335122
Sum Squared Residuals	580.128751413224

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.90677540764535 \tabularnewline
R-squared & 0.82224163991039 \tabularnewline
Adjusted R-squared & 0.758756511306957 \tabularnewline
F-TEST (value) & 12.9517204737289 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 3.16494608298967e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.71652920335122 \tabularnewline
Sum Squared Residuals & 580.128751413224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111859&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.90677540764535[/C][/ROW]
[ROW][C]R-squared[/C][C]0.82224163991039[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.758756511306957[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]12.9517204737289[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/C][/ROW]
[ROW][C]p-value[/C][C]3.16494608298967e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.71652920335122[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]580.128751413224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111859&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111859&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.90677540764535
R-squared	0.82224163991039
Adjusted R-squared	0.758756511306957
F-TEST (value)	12.9517204737289
F-TEST (DF numerator)	15
F-TEST (DF denominator)	42
p-value	3.16494608298967e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.71652920335122
Sum Squared Residuals	580.128751413224

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	116.7	116.793696026955	-0.0936960269545876
2	112.5	112.865685087896	-0.365685087895518
3	113	111.118957740513	1.88104225948694
4	126.4	119.95632806921	6.44367193079011
5	114.1	115.169270746585	-1.06927074658506
6	112.5	116.964979688501	-4.46497968850097
7	112.4	112.677267470406	-0.277267470405825
8	113.1	111.550637465283	1.54936253471654
9	116.3	113.979576196496	2.32042380350423
10	111.7	115.489377680468	-3.78937768046757
11	118.8	118.029367387669	0.770632612330495
12	116.5	113.787225609361	2.71277439063878
13	125.1	124.282074634301	0.817925365698592
14	113.1	113.303607748095	-0.203607748094534
15	119.6	118.133648800264	1.46635119973557
16	114.4	120.718765463526	-6.31876546352574
17	114	115.0610643142	-1.06106431419985
18	117.8	117.334245013689	0.46575498631052
19	117	113.626314447114	3.37368555288624
20	120.9	118.317083395122	2.58291660487787
21	115	117.465835537643	-2.46583553764267
22	117.3	114.86694971935	2.43305028064981
23	119.4	122.105286134203	-2.70528613420306
24	114.9	116.208143231518	-1.30814323151785
25	125.8	124.904671349021	0.895328650978765
26	117.6	115.390533381706	2.20946661829429
27	117.6	117.705560936027	-0.105560936026954
28	114.9	121.293127106314	-6.39312710631384
29	121.9	118.06940980504	3.83059019495954
30	117	120.131595722189	-3.13159572218863
31	106.4	111.931494519179	-5.53149451917855
32	110.5	118.47450128476	-7.9745012847599
33	113.6	113.272952233548	0.327047766452166
34	114.2	111.119710151043	3.08028984895724
35	125.4	123.020383761642	2.37961623835808
36	124.6	120.455469812908	4.14453018709216
37	120.2	121.170464168876	-0.970464168875844
38	120.8	120.92701698131	-0.127016981309569
39	111.4	116.522604829398	-5.12260482939778
40	124.1	118.5424936849	5.55750631509989
41	120.2	120.243288612376	-0.043288612376111
42	125.5	117.156026178118	8.3439738218825
43	116	114.954547108653	1.04545289134669
44	117	116.372118501824	0.627881498176457
45	105.7	106.389912151036	-0.689912151036261
46	102	105.790051599615	-3.79005159961503
47	106.4	106.844962716486	-0.444962716485515
48	96.9	102.449161346213	-5.5491613462131
49	107.6	108.249093820847	-0.649093820846925
50	98.8	100.313156800995	-1.51315680099467
51	101.1	99.2192276937978	1.88077230620222
52	105.7	104.98928567605	0.710714323949584
53	104.6	106.256966521799	-1.65696652179852
54	103.2	104.413153397503	-1.21315339750343
55	101.6	100.210376454649	1.38962354535145
56	106.7	103.485659353011	3.21434064698903
57	99.5	98.9917238812775	0.508276118722536
58	101	98.9339108495244	2.06608915047556

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 116.7 & 116.793696026955 & -0.0936960269545876 \tabularnewline
2 & 112.5 & 112.865685087896 & -0.365685087895518 \tabularnewline
3 & 113 & 111.118957740513 & 1.88104225948694 \tabularnewline
4 & 126.4 & 119.95632806921 & 6.44367193079011 \tabularnewline
5 & 114.1 & 115.169270746585 & -1.06927074658506 \tabularnewline
6 & 112.5 & 116.964979688501 & -4.46497968850097 \tabularnewline
7 & 112.4 & 112.677267470406 & -0.277267470405825 \tabularnewline
8 & 113.1 & 111.550637465283 & 1.54936253471654 \tabularnewline
9 & 116.3 & 113.979576196496 & 2.32042380350423 \tabularnewline
10 & 111.7 & 115.489377680468 & -3.78937768046757 \tabularnewline
11 & 118.8 & 118.029367387669 & 0.770632612330495 \tabularnewline
12 & 116.5 & 113.787225609361 & 2.71277439063878 \tabularnewline
13 & 125.1 & 124.282074634301 & 0.817925365698592 \tabularnewline
14 & 113.1 & 113.303607748095 & -0.203607748094534 \tabularnewline
15 & 119.6 & 118.133648800264 & 1.46635119973557 \tabularnewline
16 & 114.4 & 120.718765463526 & -6.31876546352574 \tabularnewline
17 & 114 & 115.0610643142 & -1.06106431419985 \tabularnewline
18 & 117.8 & 117.334245013689 & 0.46575498631052 \tabularnewline
19 & 117 & 113.626314447114 & 3.37368555288624 \tabularnewline
20 & 120.9 & 118.317083395122 & 2.58291660487787 \tabularnewline
21 & 115 & 117.465835537643 & -2.46583553764267 \tabularnewline
22 & 117.3 & 114.86694971935 & 2.43305028064981 \tabularnewline
23 & 119.4 & 122.105286134203 & -2.70528613420306 \tabularnewline
24 & 114.9 & 116.208143231518 & -1.30814323151785 \tabularnewline
25 & 125.8 & 124.904671349021 & 0.895328650978765 \tabularnewline
26 & 117.6 & 115.390533381706 & 2.20946661829429 \tabularnewline
27 & 117.6 & 117.705560936027 & -0.105560936026954 \tabularnewline
28 & 114.9 & 121.293127106314 & -6.39312710631384 \tabularnewline
29 & 121.9 & 118.06940980504 & 3.83059019495954 \tabularnewline
30 & 117 & 120.131595722189 & -3.13159572218863 \tabularnewline
31 & 106.4 & 111.931494519179 & -5.53149451917855 \tabularnewline
32 & 110.5 & 118.47450128476 & -7.9745012847599 \tabularnewline
33 & 113.6 & 113.272952233548 & 0.327047766452166 \tabularnewline
34 & 114.2 & 111.119710151043 & 3.08028984895724 \tabularnewline
35 & 125.4 & 123.020383761642 & 2.37961623835808 \tabularnewline
36 & 124.6 & 120.455469812908 & 4.14453018709216 \tabularnewline
37 & 120.2 & 121.170464168876 & -0.970464168875844 \tabularnewline
38 & 120.8 & 120.92701698131 & -0.127016981309569 \tabularnewline
39 & 111.4 & 116.522604829398 & -5.12260482939778 \tabularnewline
40 & 124.1 & 118.5424936849 & 5.55750631509989 \tabularnewline
41 & 120.2 & 120.243288612376 & -0.043288612376111 \tabularnewline
42 & 125.5 & 117.156026178118 & 8.3439738218825 \tabularnewline
43 & 116 & 114.954547108653 & 1.04545289134669 \tabularnewline
44 & 117 & 116.372118501824 & 0.627881498176457 \tabularnewline
45 & 105.7 & 106.389912151036 & -0.689912151036261 \tabularnewline
46 & 102 & 105.790051599615 & -3.79005159961503 \tabularnewline
47 & 106.4 & 106.844962716486 & -0.444962716485515 \tabularnewline
48 & 96.9 & 102.449161346213 & -5.5491613462131 \tabularnewline
49 & 107.6 & 108.249093820847 & -0.649093820846925 \tabularnewline
50 & 98.8 & 100.313156800995 & -1.51315680099467 \tabularnewline
51 & 101.1 & 99.2192276937978 & 1.88077230620222 \tabularnewline
52 & 105.7 & 104.98928567605 & 0.710714323949584 \tabularnewline
53 & 104.6 & 106.256966521799 & -1.65696652179852 \tabularnewline
54 & 103.2 & 104.413153397503 & -1.21315339750343 \tabularnewline
55 & 101.6 & 100.210376454649 & 1.38962354535145 \tabularnewline
56 & 106.7 & 103.485659353011 & 3.21434064698903 \tabularnewline
57 & 99.5 & 98.9917238812775 & 0.508276118722536 \tabularnewline
58 & 101 & 98.9339108495244 & 2.06608915047556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111859&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]116.7[/C][C]116.793696026955[/C][C]-0.0936960269545876[/C][/ROW]
[ROW][C]2[/C][C]112.5[/C][C]112.865685087896[/C][C]-0.365685087895518[/C][/ROW]
[ROW][C]3[/C][C]113[/C][C]111.118957740513[/C][C]1.88104225948694[/C][/ROW]
[ROW][C]4[/C][C]126.4[/C][C]119.95632806921[/C][C]6.44367193079011[/C][/ROW]
[ROW][C]5[/C][C]114.1[/C][C]115.169270746585[/C][C]-1.06927074658506[/C][/ROW]
[ROW][C]6[/C][C]112.5[/C][C]116.964979688501[/C][C]-4.46497968850097[/C][/ROW]
[ROW][C]7[/C][C]112.4[/C][C]112.677267470406[/C][C]-0.277267470405825[/C][/ROW]
[ROW][C]8[/C][C]113.1[/C][C]111.550637465283[/C][C]1.54936253471654[/C][/ROW]
[ROW][C]9[/C][C]116.3[/C][C]113.979576196496[/C][C]2.32042380350423[/C][/ROW]
[ROW][C]10[/C][C]111.7[/C][C]115.489377680468[/C][C]-3.78937768046757[/C][/ROW]
[ROW][C]11[/C][C]118.8[/C][C]118.029367387669[/C][C]0.770632612330495[/C][/ROW]
[ROW][C]12[/C][C]116.5[/C][C]113.787225609361[/C][C]2.71277439063878[/C][/ROW]
[ROW][C]13[/C][C]125.1[/C][C]124.282074634301[/C][C]0.817925365698592[/C][/ROW]
[ROW][C]14[/C][C]113.1[/C][C]113.303607748095[/C][C]-0.203607748094534[/C][/ROW]
[ROW][C]15[/C][C]119.6[/C][C]118.133648800264[/C][C]1.46635119973557[/C][/ROW]
[ROW][C]16[/C][C]114.4[/C][C]120.718765463526[/C][C]-6.31876546352574[/C][/ROW]
[ROW][C]17[/C][C]114[/C][C]115.0610643142[/C][C]-1.06106431419985[/C][/ROW]
[ROW][C]18[/C][C]117.8[/C][C]117.334245013689[/C][C]0.46575498631052[/C][/ROW]
[ROW][C]19[/C][C]117[/C][C]113.626314447114[/C][C]3.37368555288624[/C][/ROW]
[ROW][C]20[/C][C]120.9[/C][C]118.317083395122[/C][C]2.58291660487787[/C][/ROW]
[ROW][C]21[/C][C]115[/C][C]117.465835537643[/C][C]-2.46583553764267[/C][/ROW]
[ROW][C]22[/C][C]117.3[/C][C]114.86694971935[/C][C]2.43305028064981[/C][/ROW]
[ROW][C]23[/C][C]119.4[/C][C]122.105286134203[/C][C]-2.70528613420306[/C][/ROW]
[ROW][C]24[/C][C]114.9[/C][C]116.208143231518[/C][C]-1.30814323151785[/C][/ROW]
[ROW][C]25[/C][C]125.8[/C][C]124.904671349021[/C][C]0.895328650978765[/C][/ROW]
[ROW][C]26[/C][C]117.6[/C][C]115.390533381706[/C][C]2.20946661829429[/C][/ROW]
[ROW][C]27[/C][C]117.6[/C][C]117.705560936027[/C][C]-0.105560936026954[/C][/ROW]
[ROW][C]28[/C][C]114.9[/C][C]121.293127106314[/C][C]-6.39312710631384[/C][/ROW]
[ROW][C]29[/C][C]121.9[/C][C]118.06940980504[/C][C]3.83059019495954[/C][/ROW]
[ROW][C]30[/C][C]117[/C][C]120.131595722189[/C][C]-3.13159572218863[/C][/ROW]
[ROW][C]31[/C][C]106.4[/C][C]111.931494519179[/C][C]-5.53149451917855[/C][/ROW]
[ROW][C]32[/C][C]110.5[/C][C]118.47450128476[/C][C]-7.9745012847599[/C][/ROW]
[ROW][C]33[/C][C]113.6[/C][C]113.272952233548[/C][C]0.327047766452166[/C][/ROW]
[ROW][C]34[/C][C]114.2[/C][C]111.119710151043[/C][C]3.08028984895724[/C][/ROW]
[ROW][C]35[/C][C]125.4[/C][C]123.020383761642[/C][C]2.37961623835808[/C][/ROW]
[ROW][C]36[/C][C]124.6[/C][C]120.455469812908[/C][C]4.14453018709216[/C][/ROW]
[ROW][C]37[/C][C]120.2[/C][C]121.170464168876[/C][C]-0.970464168875844[/C][/ROW]
[ROW][C]38[/C][C]120.8[/C][C]120.92701698131[/C][C]-0.127016981309569[/C][/ROW]
[ROW][C]39[/C][C]111.4[/C][C]116.522604829398[/C][C]-5.12260482939778[/C][/ROW]
[ROW][C]40[/C][C]124.1[/C][C]118.5424936849[/C][C]5.55750631509989[/C][/ROW]
[ROW][C]41[/C][C]120.2[/C][C]120.243288612376[/C][C]-0.043288612376111[/C][/ROW]
[ROW][C]42[/C][C]125.5[/C][C]117.156026178118[/C][C]8.3439738218825[/C][/ROW]
[ROW][C]43[/C][C]116[/C][C]114.954547108653[/C][C]1.04545289134669[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]116.372118501824[/C][C]0.627881498176457[/C][/ROW]
[ROW][C]45[/C][C]105.7[/C][C]106.389912151036[/C][C]-0.689912151036261[/C][/ROW]
[ROW][C]46[/C][C]102[/C][C]105.790051599615[/C][C]-3.79005159961503[/C][/ROW]
[ROW][C]47[/C][C]106.4[/C][C]106.844962716486[/C][C]-0.444962716485515[/C][/ROW]
[ROW][C]48[/C][C]96.9[/C][C]102.449161346213[/C][C]-5.5491613462131[/C][/ROW]
[ROW][C]49[/C][C]107.6[/C][C]108.249093820847[/C][C]-0.649093820846925[/C][/ROW]
[ROW][C]50[/C][C]98.8[/C][C]100.313156800995[/C][C]-1.51315680099467[/C][/ROW]
[ROW][C]51[/C][C]101.1[/C][C]99.2192276937978[/C][C]1.88077230620222[/C][/ROW]
[ROW][C]52[/C][C]105.7[/C][C]104.98928567605[/C][C]0.710714323949584[/C][/ROW]
[ROW][C]53[/C][C]104.6[/C][C]106.256966521799[/C][C]-1.65696652179852[/C][/ROW]
[ROW][C]54[/C][C]103.2[/C][C]104.413153397503[/C][C]-1.21315339750343[/C][/ROW]
[ROW][C]55[/C][C]101.6[/C][C]100.210376454649[/C][C]1.38962354535145[/C][/ROW]
[ROW][C]56[/C][C]106.7[/C][C]103.485659353011[/C][C]3.21434064698903[/C][/ROW]
[ROW][C]57[/C][C]99.5[/C][C]98.9917238812775[/C][C]0.508276118722536[/C][/ROW]
[ROW][C]58[/C][C]101[/C][C]98.9339108495244[/C][C]2.06608915047556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111859&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111859&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	116.7	116.793696026955	-0.0936960269545876
2	112.5	112.865685087896	-0.365685087895518
3	113	111.118957740513	1.88104225948694
4	126.4	119.95632806921	6.44367193079011
5	114.1	115.169270746585	-1.06927074658506
6	112.5	116.964979688501	-4.46497968850097
7	112.4	112.677267470406	-0.277267470405825
8	113.1	111.550637465283	1.54936253471654
9	116.3	113.979576196496	2.32042380350423
10	111.7	115.489377680468	-3.78937768046757
11	118.8	118.029367387669	0.770632612330495
12	116.5	113.787225609361	2.71277439063878
13	125.1	124.282074634301	0.817925365698592
14	113.1	113.303607748095	-0.203607748094534
15	119.6	118.133648800264	1.46635119973557
16	114.4	120.718765463526	-6.31876546352574
17	114	115.0610643142	-1.06106431419985
18	117.8	117.334245013689	0.46575498631052
19	117	113.626314447114	3.37368555288624
20	120.9	118.317083395122	2.58291660487787
21	115	117.465835537643	-2.46583553764267
22	117.3	114.86694971935	2.43305028064981
23	119.4	122.105286134203	-2.70528613420306
24	114.9	116.208143231518	-1.30814323151785
25	125.8	124.904671349021	0.895328650978765
26	117.6	115.390533381706	2.20946661829429
27	117.6	117.705560936027	-0.105560936026954
28	114.9	121.293127106314	-6.39312710631384
29	121.9	118.06940980504	3.83059019495954
30	117	120.131595722189	-3.13159572218863
31	106.4	111.931494519179	-5.53149451917855
32	110.5	118.47450128476	-7.9745012847599
33	113.6	113.272952233548	0.327047766452166
34	114.2	111.119710151043	3.08028984895724
35	125.4	123.020383761642	2.37961623835808
36	124.6	120.455469812908	4.14453018709216
37	120.2	121.170464168876	-0.970464168875844
38	120.8	120.92701698131	-0.127016981309569
39	111.4	116.522604829398	-5.12260482939778
40	124.1	118.5424936849	5.55750631509989
41	120.2	120.243288612376	-0.043288612376111
42	125.5	117.156026178118	8.3439738218825
43	116	114.954547108653	1.04545289134669
44	117	116.372118501824	0.627881498176457
45	105.7	106.389912151036	-0.689912151036261
46	102	105.790051599615	-3.79005159961503
47	106.4	106.844962716486	-0.444962716485515
48	96.9	102.449161346213	-5.5491613462131
49	107.6	108.249093820847	-0.649093820846925
50	98.8	100.313156800995	-1.51315680099467
51	101.1	99.2192276937978	1.88077230620222
52	105.7	104.98928567605	0.710714323949584
53	104.6	106.256966521799	-1.65696652179852
54	103.2	104.413153397503	-1.21315339750343
55	101.6	100.210376454649	1.38962354535145
56	106.7	103.485659353011	3.21434064698903
57	99.5	98.9917238812775	0.508276118722536
58	101	98.9339108495244	2.06608915047556

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
19	0.805132733379345	0.389734533241309	0.194867266620655
20	0.705033605057932	0.589932789884136	0.294966394942068
21	0.587103703547356	0.825792592905289	0.412896296452644
22	0.618023772919376	0.763952454161247	0.381976227080624
23	0.514044815618347	0.971910368763306	0.485955184381653
24	0.426210961569952	0.852421923139905	0.573789038430048
25	0.324705111367581	0.649410222735163	0.675294888632419
26	0.292710787574652	0.585421575149304	0.707289212425348
27	0.216816586543326	0.433633173086653	0.783183413456674
28	0.274251341845869	0.548502683691738	0.725748658154131
29	0.336332320304831	0.672664640609662	0.663667679695169
30	0.276751170445043	0.553502340890086	0.723248829554957
31	0.224220336901902	0.448440673803804	0.775779663098098
32	0.549431459998417	0.901137080003165	0.450568540001583
33	0.455382583853671	0.910765167707341	0.54461741614633
34	0.40235009075046	0.804700181500919	0.59764990924954
35	0.305533197228286	0.611066394456573	0.694466802771714
36	0.45135271369989	0.90270542739978	0.54864728630011
37	0.344178946023517	0.688357892047033	0.655821053976483
38	0.229864827054048	0.459729654108096	0.770135172945952
39	0.309920199360235	0.61984039872047	0.690079800639765

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.805132733379345 & 0.389734533241309 & 0.194867266620655 \tabularnewline
20 & 0.705033605057932 & 0.589932789884136 & 0.294966394942068 \tabularnewline
21 & 0.587103703547356 & 0.825792592905289 & 0.412896296452644 \tabularnewline
22 & 0.618023772919376 & 0.763952454161247 & 0.381976227080624 \tabularnewline
23 & 0.514044815618347 & 0.971910368763306 & 0.485955184381653 \tabularnewline
24 & 0.426210961569952 & 0.852421923139905 & 0.573789038430048 \tabularnewline
25 & 0.324705111367581 & 0.649410222735163 & 0.675294888632419 \tabularnewline
26 & 0.292710787574652 & 0.585421575149304 & 0.707289212425348 \tabularnewline
27 & 0.216816586543326 & 0.433633173086653 & 0.783183413456674 \tabularnewline
28 & 0.274251341845869 & 0.548502683691738 & 0.725748658154131 \tabularnewline
29 & 0.336332320304831 & 0.672664640609662 & 0.663667679695169 \tabularnewline
30 & 0.276751170445043 & 0.553502340890086 & 0.723248829554957 \tabularnewline
31 & 0.224220336901902 & 0.448440673803804 & 0.775779663098098 \tabularnewline
32 & 0.549431459998417 & 0.901137080003165 & 0.450568540001583 \tabularnewline
33 & 0.455382583853671 & 0.910765167707341 & 0.54461741614633 \tabularnewline
34 & 0.40235009075046 & 0.804700181500919 & 0.59764990924954 \tabularnewline
35 & 0.305533197228286 & 0.611066394456573 & 0.694466802771714 \tabularnewline
36 & 0.45135271369989 & 0.90270542739978 & 0.54864728630011 \tabularnewline
37 & 0.344178946023517 & 0.688357892047033 & 0.655821053976483 \tabularnewline
38 & 0.229864827054048 & 0.459729654108096 & 0.770135172945952 \tabularnewline
39 & 0.309920199360235 & 0.61984039872047 & 0.690079800639765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111859&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]0.805132733379345[/C][C]0.389734533241309[/C][C]0.194867266620655[/C][/ROW]
[ROW][C]20[/C][C]0.705033605057932[/C][C]0.589932789884136[/C][C]0.294966394942068[/C][/ROW]
[ROW][C]21[/C][C]0.587103703547356[/C][C]0.825792592905289[/C][C]0.412896296452644[/C][/ROW]
[ROW][C]22[/C][C]0.618023772919376[/C][C]0.763952454161247[/C][C]0.381976227080624[/C][/ROW]
[ROW][C]23[/C][C]0.514044815618347[/C][C]0.971910368763306[/C][C]0.485955184381653[/C][/ROW]
[ROW][C]24[/C][C]0.426210961569952[/C][C]0.852421923139905[/C][C]0.573789038430048[/C][/ROW]
[ROW][C]25[/C][C]0.324705111367581[/C][C]0.649410222735163[/C][C]0.675294888632419[/C][/ROW]
[ROW][C]26[/C][C]0.292710787574652[/C][C]0.585421575149304[/C][C]0.707289212425348[/C][/ROW]
[ROW][C]27[/C][C]0.216816586543326[/C][C]0.433633173086653[/C][C]0.783183413456674[/C][/ROW]
[ROW][C]28[/C][C]0.274251341845869[/C][C]0.548502683691738[/C][C]0.725748658154131[/C][/ROW]
[ROW][C]29[/C][C]0.336332320304831[/C][C]0.672664640609662[/C][C]0.663667679695169[/C][/ROW]
[ROW][C]30[/C][C]0.276751170445043[/C][C]0.553502340890086[/C][C]0.723248829554957[/C][/ROW]
[ROW][C]31[/C][C]0.224220336901902[/C][C]0.448440673803804[/C][C]0.775779663098098[/C][/ROW]
[ROW][C]32[/C][C]0.549431459998417[/C][C]0.901137080003165[/C][C]0.450568540001583[/C][/ROW]
[ROW][C]33[/C][C]0.455382583853671[/C][C]0.910765167707341[/C][C]0.54461741614633[/C][/ROW]
[ROW][C]34[/C][C]0.40235009075046[/C][C]0.804700181500919[/C][C]0.59764990924954[/C][/ROW]
[ROW][C]35[/C][C]0.305533197228286[/C][C]0.611066394456573[/C][C]0.694466802771714[/C][/ROW]
[ROW][C]36[/C][C]0.45135271369989[/C][C]0.90270542739978[/C][C]0.54864728630011[/C][/ROW]
[ROW][C]37[/C][C]0.344178946023517[/C][C]0.688357892047033[/C][C]0.655821053976483[/C][/ROW]
[ROW][C]38[/C][C]0.229864827054048[/C][C]0.459729654108096[/C][C]0.770135172945952[/C][/ROW]
[ROW][C]39[/C][C]0.309920199360235[/C][C]0.61984039872047[/C][C]0.690079800639765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111859&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111859&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
19	0.805132733379345	0.389734533241309	0.194867266620655
20	0.705033605057932	0.589932789884136	0.294966394942068
21	0.587103703547356	0.825792592905289	0.412896296452644
22	0.618023772919376	0.763952454161247	0.381976227080624
23	0.514044815618347	0.971910368763306	0.485955184381653
24	0.426210961569952	0.852421923139905	0.573789038430048
25	0.324705111367581	0.649410222735163	0.675294888632419
26	0.292710787574652	0.585421575149304	0.707289212425348
27	0.216816586543326	0.433633173086653	0.783183413456674
28	0.274251341845869	0.548502683691738	0.725748658154131
29	0.336332320304831	0.672664640609662	0.663667679695169
30	0.276751170445043	0.553502340890086	0.723248829554957
31	0.224220336901902	0.448440673803804	0.775779663098098
32	0.549431459998417	0.901137080003165	0.450568540001583
33	0.455382583853671	0.910765167707341	0.54461741614633
34	0.40235009075046	0.804700181500919	0.59764990924954
35	0.305533197228286	0.611066394456573	0.694466802771714
36	0.45135271369989	0.90270542739978	0.54864728630011
37	0.344178946023517	0.688357892047033	0.655821053976483
38	0.229864827054048	0.459729654108096	0.770135172945952
39	0.309920199360235	0.61984039872047	0.690079800639765

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111859&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111859&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111859&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code