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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 18 Nov 2009 10:34:19 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/18/t1258565801p4289xn3wz12pg6.htm/, Retrieved Sun, 05 May 2024 16:09:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57548, Retrieved Sun, 05 May 2024 16:09:36 +0000

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Estimated Impact

169

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-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-18 17:34:19] [faa1ded5041cd5a0e2be04844f08502a] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57548&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57548&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
s[t] = + 21.3485818218273 + 0.212254119197142consv[t] -0.569446095385408M1[t] -5.12036481419157M2[t] -0.951260284566528M3[t] -0.703819760211766M4[t] -0.389420173623291M5[t] -1.17786482015882M6[t] -3.49366193821264M7[t] -1.55475411322988M8[t] + 0.00209629719801545M9[t] -0.628799173176945M10[t] -1.12665370578561M11[t] -0.241752058106757t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
s[t] =  +  21.3485818218273 +  0.212254119197142consv[t] -0.569446095385408M1[t] -5.12036481419157M2[t] -0.951260284566528M3[t] -0.703819760211766M4[t] -0.389420173623291M5[t] -1.17786482015882M6[t] -3.49366193821264M7[t] -1.55475411322988M8[t] +  0.00209629719801545M9[t] -0.628799173176945M10[t] -1.12665370578561M11[t] -0.241752058106757t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57548&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]s[t] =  +  21.3485818218273 +  0.212254119197142consv[t] -0.569446095385408M1[t] -5.12036481419157M2[t] -0.951260284566528M3[t] -0.703819760211766M4[t] -0.389420173623291M5[t] -1.17786482015882M6[t] -3.49366193821264M7[t] -1.55475411322988M8[t] +  0.00209629719801545M9[t] -0.628799173176945M10[t] -1.12665370578561M11[t] -0.241752058106757t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57548&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
s[t] = + 21.3485818218273 + 0.212254119197142consv[t] -0.569446095385408M1[t] -5.12036481419157M2[t] -0.951260284566528M3[t] -0.703819760211766M4[t] -0.389420173623291M5[t] -1.17786482015882M6[t] -3.49366193821264M7[t] -1.55475411322988M8[t] + 0.00209629719801545M9[t] -0.628799173176945M10[t] -1.12665370578561M11[t] -0.241752058106757t + 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)	21.3485818218273	2.909627	7.3372	0	0
consv	0.212254119197142	0.075131	2.8251	0.006915	0.003458
M1	-0.569446095385408	2.133534	-0.2669	0.790712	0.395356
M2	-5.12036481419157	2.254835	-2.2708	0.027781	0.01389
M3	-0.951260284566528	2.255604	-0.4217	0.675143	0.337572
M4	-0.703819760211766	2.234698	-0.315	0.754193	0.377097
M5	-0.389420173623291	2.23139	-0.1745	0.862207	0.431104
M6	-1.17786482015882	2.230011	-0.5282	0.599854	0.299927
M7	-3.49366193821264	2.228325	-1.5678	0.123627	0.061813
M8	-1.55475411322988	2.230761	-0.697	0.48926	0.24463
M9	0.00209629719801545	2.227292	9e-04	0.999253	0.499627
M10	-0.628799173176945	2.227939	-0.2822	0.779004	0.389502
M11	-1.12665370578561	2.224166	-0.5066	0.614838	0.307419
t	-0.241752058106757	0.030543	-7.915	0	0

\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) & 21.3485818218273 & 2.909627 & 7.3372 & 0 & 0 \tabularnewline
consv & 0.212254119197142 & 0.075131 & 2.8251 & 0.006915 & 0.003458 \tabularnewline
M1 & -0.569446095385408 & 2.133534 & -0.2669 & 0.790712 & 0.395356 \tabularnewline
M2 & -5.12036481419157 & 2.254835 & -2.2708 & 0.027781 & 0.01389 \tabularnewline
M3 & -0.951260284566528 & 2.255604 & -0.4217 & 0.675143 & 0.337572 \tabularnewline
M4 & -0.703819760211766 & 2.234698 & -0.315 & 0.754193 & 0.377097 \tabularnewline
M5 & -0.389420173623291 & 2.23139 & -0.1745 & 0.862207 & 0.431104 \tabularnewline
M6 & -1.17786482015882 & 2.230011 & -0.5282 & 0.599854 & 0.299927 \tabularnewline
M7 & -3.49366193821264 & 2.228325 & -1.5678 & 0.123627 & 0.061813 \tabularnewline
M8 & -1.55475411322988 & 2.230761 & -0.697 & 0.48926 & 0.24463 \tabularnewline
M9 & 0.00209629719801545 & 2.227292 & 9e-04 & 0.999253 & 0.499627 \tabularnewline
M10 & -0.628799173176945 & 2.227939 & -0.2822 & 0.779004 & 0.389502 \tabularnewline
M11 & -1.12665370578561 & 2.224166 & -0.5066 & 0.614838 & 0.307419 \tabularnewline
t & -0.241752058106757 & 0.030543 & -7.915 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57548&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]21.3485818218273[/C][C]2.909627[/C][C]7.3372[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]consv[/C][C]0.212254119197142[/C][C]0.075131[/C][C]2.8251[/C][C]0.006915[/C][C]0.003458[/C][/ROW]
[ROW][C]M1[/C][C]-0.569446095385408[/C][C]2.133534[/C][C]-0.2669[/C][C]0.790712[/C][C]0.395356[/C][/ROW]
[ROW][C]M2[/C][C]-5.12036481419157[/C][C]2.254835[/C][C]-2.2708[/C][C]0.027781[/C][C]0.01389[/C][/ROW]
[ROW][C]M3[/C][C]-0.951260284566528[/C][C]2.255604[/C][C]-0.4217[/C][C]0.675143[/C][C]0.337572[/C][/ROW]
[ROW][C]M4[/C][C]-0.703819760211766[/C][C]2.234698[/C][C]-0.315[/C][C]0.754193[/C][C]0.377097[/C][/ROW]
[ROW][C]M5[/C][C]-0.389420173623291[/C][C]2.23139[/C][C]-0.1745[/C][C]0.862207[/C][C]0.431104[/C][/ROW]
[ROW][C]M6[/C][C]-1.17786482015882[/C][C]2.230011[/C][C]-0.5282[/C][C]0.599854[/C][C]0.299927[/C][/ROW]
[ROW][C]M7[/C][C]-3.49366193821264[/C][C]2.228325[/C][C]-1.5678[/C][C]0.123627[/C][C]0.061813[/C][/ROW]
[ROW][C]M8[/C][C]-1.55475411322988[/C][C]2.230761[/C][C]-0.697[/C][C]0.48926[/C][C]0.24463[/C][/ROW]
[ROW][C]M9[/C][C]0.00209629719801545[/C][C]2.227292[/C][C]9e-04[/C][C]0.999253[/C][C]0.499627[/C][/ROW]
[ROW][C]M10[/C][C]-0.628799173176945[/C][C]2.227939[/C][C]-0.2822[/C][C]0.779004[/C][C]0.389502[/C][/ROW]
[ROW][C]M11[/C][C]-1.12665370578561[/C][C]2.224166[/C][C]-0.5066[/C][C]0.614838[/C][C]0.307419[/C][/ROW]
[ROW][C]t[/C][C]-0.241752058106757[/C][C]0.030543[/C][C]-7.915[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57548&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57548&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)	21.3485818218273	2.909627	7.3372	0	0
consv	0.212254119197142	0.075131	2.8251	0.006915	0.003458
M1	-0.569446095385408	2.133534	-0.2669	0.790712	0.395356
M2	-5.12036481419157	2.254835	-2.2708	0.027781	0.01389
M3	-0.951260284566528	2.255604	-0.4217	0.675143	0.337572
M4	-0.703819760211766	2.234698	-0.315	0.754193	0.377097
M5	-0.389420173623291	2.23139	-0.1745	0.862207	0.431104
M6	-1.17786482015882	2.230011	-0.5282	0.599854	0.299927
M7	-3.49366193821264	2.228325	-1.5678	0.123627	0.061813
M8	-1.55475411322988	2.230761	-0.697	0.48926	0.24463
M9	0.00209629719801545	2.227292	9e-04	0.999253	0.499627
M10	-0.628799173176945	2.227939	-0.2822	0.779004	0.389502
M11	-1.12665370578561	2.224166	-0.5066	0.614838	0.307419
t	-0.241752058106757	0.030543	-7.915	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.864621245324081
R-squared	0.747569897865765
Adjusted R-squared	0.677748805786083
F-TEST (value)	10.7069350478307
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	4.74262407124115e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.51640624782329
Sum Squared Residuals	581.16030628734

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.864621245324081 \tabularnewline
R-squared & 0.747569897865765 \tabularnewline
Adjusted R-squared & 0.677748805786083 \tabularnewline
F-TEST (value) & 10.7069350478307 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 4.74262407124115e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.51640624782329 \tabularnewline
Sum Squared Residuals & 581.16030628734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57548&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.864621245324081[/C][/ROW]
[ROW][C]R-squared[/C][C]0.747569897865765[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.677748805786083[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]10.7069350478307[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]4.74262407124115e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.51640624782329[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]581.16030628734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57548&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57548&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	0.864621245324081
R-squared	0.747569897865765
Adjusted R-squared	0.677748805786083
F-TEST (value)	10.7069350478307
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	4.74262407124115e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.51640624782329
Sum Squared Residuals	581.16030628734

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	24	25.6314825290665	-1.63148252906652
2	22	20.6265576329564	1.37344236704355
3	25	24.7661642236719	0.233835776328138
4	24	24.7718526899199	-0.771852689919875
5	29	25.481262575993	3.518737424007
6	26	24.6633199905479	1.33668000945214
7	26	21.4690084567959	4.53099154320413
8	21	21.892639508489	-0.892639508489017
9	23	23.2077378608102	-0.207737860810164
10	22	22.3350903323284	-0.335090332328447
11	21	21.8077378608102	-0.80773786081016
12	16	21.8436230317005	-5.84362303170045
13	19	22.3059495933911	-3.30594959339114
14	16	17.3010246972811	-1.30102469728107
15	25	22.0773936455879	2.92260635441207
16	27	22.9320985886245	4.0679014113755
17	23	22.7924919979091	0.207508002090925
18	22	21.1255329356754	0.874467064324638
19	23	18.7802378787119	4.21976212128807
20	20	20.0528854071936	-0.0528854071936464
21	24	22.2170002363034	1.78299976369664
22	23	21.3443527078216	1.65564729217836
23	20	20.6047461171062	-0.604746117106214
24	21	21.4896477647851	-0.489647764785071
25	22	21.5274660880815	0.472533911918524
26	17	16.5225411919714	0.477458808028586
27	21	18.5396065907154	2.46039340928457
28	19	20.0310738913434	-1.03107389134342
29	23	20.5282296582194	2.47177034178058
30	22	19.0735247151828	2.92647528481715
31	15	17.1527378966137	-2.1527378966137
32	23	18.8498936634897	4.1501063365103
33	21	19.9527378966137	1.0472621033863
34	18	18.6555821297377	-0.655582129737703
35	18	17.7037214198251	0.296278580174866
36	18	18.588623067504	-0.588623067503993
37	18	17.9896790332090	0.0103209667910265
38	10	11.7112294219161	-1.71122942191606
39	13	16.4875983702229	-3.48759837022292
40	10	16.0687785980766	-6.06877859807663
41	9	16.7781884841498	-7.77818848414978
42	9	15.7479917795075	-6.74799177950749
43	6	12.3414261265583	-6.34142612655835
44	11	13.6140736550401	-2.61407365504006
45	9	14.5046637689669	-5.50466376896693
46	10	13.2075080020909	-3.20750800209093
47	9	12.8924096497698	-3.89240964976978
48	16	14.2018195358429	1.79818046415708
49	10	11.6925884287736	-1.69258842877363
50	7	5.838647055875	1.16135294412500
51	7	9.12923716980186	-2.12923716980186
52	14	10.1961962320356	3.80380376796443
53	11	9.41982728372872	1.58017271627128
54	10	8.38963057908644	1.61036942091356
55	6	6.25658964132015	-0.256589641320147
56	8	8.59050776578757	-0.590507765787571
57	13	10.1178602373059	2.88213976269414
58	12	9.45746682802128	2.54253317197872
59	15	9.9913849524887	5.00861504751129
60	16	10.8762866001676	5.12371339983243
61	16	9.85283432747826	6.14716567252174

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 24 & 25.6314825290665 & -1.63148252906652 \tabularnewline
2 & 22 & 20.6265576329564 & 1.37344236704355 \tabularnewline
3 & 25 & 24.7661642236719 & 0.233835776328138 \tabularnewline
4 & 24 & 24.7718526899199 & -0.771852689919875 \tabularnewline
5 & 29 & 25.481262575993 & 3.518737424007 \tabularnewline
6 & 26 & 24.6633199905479 & 1.33668000945214 \tabularnewline
7 & 26 & 21.4690084567959 & 4.53099154320413 \tabularnewline
8 & 21 & 21.892639508489 & -0.892639508489017 \tabularnewline
9 & 23 & 23.2077378608102 & -0.207737860810164 \tabularnewline
10 & 22 & 22.3350903323284 & -0.335090332328447 \tabularnewline
11 & 21 & 21.8077378608102 & -0.80773786081016 \tabularnewline
12 & 16 & 21.8436230317005 & -5.84362303170045 \tabularnewline
13 & 19 & 22.3059495933911 & -3.30594959339114 \tabularnewline
14 & 16 & 17.3010246972811 & -1.30102469728107 \tabularnewline
15 & 25 & 22.0773936455879 & 2.92260635441207 \tabularnewline
16 & 27 & 22.9320985886245 & 4.0679014113755 \tabularnewline
17 & 23 & 22.7924919979091 & 0.207508002090925 \tabularnewline
18 & 22 & 21.1255329356754 & 0.874467064324638 \tabularnewline
19 & 23 & 18.7802378787119 & 4.21976212128807 \tabularnewline
20 & 20 & 20.0528854071936 & -0.0528854071936464 \tabularnewline
21 & 24 & 22.2170002363034 & 1.78299976369664 \tabularnewline
22 & 23 & 21.3443527078216 & 1.65564729217836 \tabularnewline
23 & 20 & 20.6047461171062 & -0.604746117106214 \tabularnewline
24 & 21 & 21.4896477647851 & -0.489647764785071 \tabularnewline
25 & 22 & 21.5274660880815 & 0.472533911918524 \tabularnewline
26 & 17 & 16.5225411919714 & 0.477458808028586 \tabularnewline
27 & 21 & 18.5396065907154 & 2.46039340928457 \tabularnewline
28 & 19 & 20.0310738913434 & -1.03107389134342 \tabularnewline
29 & 23 & 20.5282296582194 & 2.47177034178058 \tabularnewline
30 & 22 & 19.0735247151828 & 2.92647528481715 \tabularnewline
31 & 15 & 17.1527378966137 & -2.1527378966137 \tabularnewline
32 & 23 & 18.8498936634897 & 4.1501063365103 \tabularnewline
33 & 21 & 19.9527378966137 & 1.0472621033863 \tabularnewline
34 & 18 & 18.6555821297377 & -0.655582129737703 \tabularnewline
35 & 18 & 17.7037214198251 & 0.296278580174866 \tabularnewline
36 & 18 & 18.588623067504 & -0.588623067503993 \tabularnewline
37 & 18 & 17.9896790332090 & 0.0103209667910265 \tabularnewline
38 & 10 & 11.7112294219161 & -1.71122942191606 \tabularnewline
39 & 13 & 16.4875983702229 & -3.48759837022292 \tabularnewline
40 & 10 & 16.0687785980766 & -6.06877859807663 \tabularnewline
41 & 9 & 16.7781884841498 & -7.77818848414978 \tabularnewline
42 & 9 & 15.7479917795075 & -6.74799177950749 \tabularnewline
43 & 6 & 12.3414261265583 & -6.34142612655835 \tabularnewline
44 & 11 & 13.6140736550401 & -2.61407365504006 \tabularnewline
45 & 9 & 14.5046637689669 & -5.50466376896693 \tabularnewline
46 & 10 & 13.2075080020909 & -3.20750800209093 \tabularnewline
47 & 9 & 12.8924096497698 & -3.89240964976978 \tabularnewline
48 & 16 & 14.2018195358429 & 1.79818046415708 \tabularnewline
49 & 10 & 11.6925884287736 & -1.69258842877363 \tabularnewline
50 & 7 & 5.838647055875 & 1.16135294412500 \tabularnewline
51 & 7 & 9.12923716980186 & -2.12923716980186 \tabularnewline
52 & 14 & 10.1961962320356 & 3.80380376796443 \tabularnewline
53 & 11 & 9.41982728372872 & 1.58017271627128 \tabularnewline
54 & 10 & 8.38963057908644 & 1.61036942091356 \tabularnewline
55 & 6 & 6.25658964132015 & -0.256589641320147 \tabularnewline
56 & 8 & 8.59050776578757 & -0.590507765787571 \tabularnewline
57 & 13 & 10.1178602373059 & 2.88213976269414 \tabularnewline
58 & 12 & 9.45746682802128 & 2.54253317197872 \tabularnewline
59 & 15 & 9.9913849524887 & 5.00861504751129 \tabularnewline
60 & 16 & 10.8762866001676 & 5.12371339983243 \tabularnewline
61 & 16 & 9.85283432747826 & 6.14716567252174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57548&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]24[/C][C]25.6314825290665[/C][C]-1.63148252906652[/C][/ROW]
[ROW][C]2[/C][C]22[/C][C]20.6265576329564[/C][C]1.37344236704355[/C][/ROW]
[ROW][C]3[/C][C]25[/C][C]24.7661642236719[/C][C]0.233835776328138[/C][/ROW]
[ROW][C]4[/C][C]24[/C][C]24.7718526899199[/C][C]-0.771852689919875[/C][/ROW]
[ROW][C]5[/C][C]29[/C][C]25.481262575993[/C][C]3.518737424007[/C][/ROW]
[ROW][C]6[/C][C]26[/C][C]24.6633199905479[/C][C]1.33668000945214[/C][/ROW]
[ROW][C]7[/C][C]26[/C][C]21.4690084567959[/C][C]4.53099154320413[/C][/ROW]
[ROW][C]8[/C][C]21[/C][C]21.892639508489[/C][C]-0.892639508489017[/C][/ROW]
[ROW][C]9[/C][C]23[/C][C]23.2077378608102[/C][C]-0.207737860810164[/C][/ROW]
[ROW][C]10[/C][C]22[/C][C]22.3350903323284[/C][C]-0.335090332328447[/C][/ROW]
[ROW][C]11[/C][C]21[/C][C]21.8077378608102[/C][C]-0.80773786081016[/C][/ROW]
[ROW][C]12[/C][C]16[/C][C]21.8436230317005[/C][C]-5.84362303170045[/C][/ROW]
[ROW][C]13[/C][C]19[/C][C]22.3059495933911[/C][C]-3.30594959339114[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]17.3010246972811[/C][C]-1.30102469728107[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]22.0773936455879[/C][C]2.92260635441207[/C][/ROW]
[ROW][C]16[/C][C]27[/C][C]22.9320985886245[/C][C]4.0679014113755[/C][/ROW]
[ROW][C]17[/C][C]23[/C][C]22.7924919979091[/C][C]0.207508002090925[/C][/ROW]
[ROW][C]18[/C][C]22[/C][C]21.1255329356754[/C][C]0.874467064324638[/C][/ROW]
[ROW][C]19[/C][C]23[/C][C]18.7802378787119[/C][C]4.21976212128807[/C][/ROW]
[ROW][C]20[/C][C]20[/C][C]20.0528854071936[/C][C]-0.0528854071936464[/C][/ROW]
[ROW][C]21[/C][C]24[/C][C]22.2170002363034[/C][C]1.78299976369664[/C][/ROW]
[ROW][C]22[/C][C]23[/C][C]21.3443527078216[/C][C]1.65564729217836[/C][/ROW]
[ROW][C]23[/C][C]20[/C][C]20.6047461171062[/C][C]-0.604746117106214[/C][/ROW]
[ROW][C]24[/C][C]21[/C][C]21.4896477647851[/C][C]-0.489647764785071[/C][/ROW]
[ROW][C]25[/C][C]22[/C][C]21.5274660880815[/C][C]0.472533911918524[/C][/ROW]
[ROW][C]26[/C][C]17[/C][C]16.5225411919714[/C][C]0.477458808028586[/C][/ROW]
[ROW][C]27[/C][C]21[/C][C]18.5396065907154[/C][C]2.46039340928457[/C][/ROW]
[ROW][C]28[/C][C]19[/C][C]20.0310738913434[/C][C]-1.03107389134342[/C][/ROW]
[ROW][C]29[/C][C]23[/C][C]20.5282296582194[/C][C]2.47177034178058[/C][/ROW]
[ROW][C]30[/C][C]22[/C][C]19.0735247151828[/C][C]2.92647528481715[/C][/ROW]
[ROW][C]31[/C][C]15[/C][C]17.1527378966137[/C][C]-2.1527378966137[/C][/ROW]
[ROW][C]32[/C][C]23[/C][C]18.8498936634897[/C][C]4.1501063365103[/C][/ROW]
[ROW][C]33[/C][C]21[/C][C]19.9527378966137[/C][C]1.0472621033863[/C][/ROW]
[ROW][C]34[/C][C]18[/C][C]18.6555821297377[/C][C]-0.655582129737703[/C][/ROW]
[ROW][C]35[/C][C]18[/C][C]17.7037214198251[/C][C]0.296278580174866[/C][/ROW]
[ROW][C]36[/C][C]18[/C][C]18.588623067504[/C][C]-0.588623067503993[/C][/ROW]
[ROW][C]37[/C][C]18[/C][C]17.9896790332090[/C][C]0.0103209667910265[/C][/ROW]
[ROW][C]38[/C][C]10[/C][C]11.7112294219161[/C][C]-1.71122942191606[/C][/ROW]
[ROW][C]39[/C][C]13[/C][C]16.4875983702229[/C][C]-3.48759837022292[/C][/ROW]
[ROW][C]40[/C][C]10[/C][C]16.0687785980766[/C][C]-6.06877859807663[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]16.7781884841498[/C][C]-7.77818848414978[/C][/ROW]
[ROW][C]42[/C][C]9[/C][C]15.7479917795075[/C][C]-6.74799177950749[/C][/ROW]
[ROW][C]43[/C][C]6[/C][C]12.3414261265583[/C][C]-6.34142612655835[/C][/ROW]
[ROW][C]44[/C][C]11[/C][C]13.6140736550401[/C][C]-2.61407365504006[/C][/ROW]
[ROW][C]45[/C][C]9[/C][C]14.5046637689669[/C][C]-5.50466376896693[/C][/ROW]
[ROW][C]46[/C][C]10[/C][C]13.2075080020909[/C][C]-3.20750800209093[/C][/ROW]
[ROW][C]47[/C][C]9[/C][C]12.8924096497698[/C][C]-3.89240964976978[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]14.2018195358429[/C][C]1.79818046415708[/C][/ROW]
[ROW][C]49[/C][C]10[/C][C]11.6925884287736[/C][C]-1.69258842877363[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]5.838647055875[/C][C]1.16135294412500[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]9.12923716980186[/C][C]-2.12923716980186[/C][/ROW]
[ROW][C]52[/C][C]14[/C][C]10.1961962320356[/C][C]3.80380376796443[/C][/ROW]
[ROW][C]53[/C][C]11[/C][C]9.41982728372872[/C][C]1.58017271627128[/C][/ROW]
[ROW][C]54[/C][C]10[/C][C]8.38963057908644[/C][C]1.61036942091356[/C][/ROW]
[ROW][C]55[/C][C]6[/C][C]6.25658964132015[/C][C]-0.256589641320147[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]8.59050776578757[/C][C]-0.590507765787571[/C][/ROW]
[ROW][C]57[/C][C]13[/C][C]10.1178602373059[/C][C]2.88213976269414[/C][/ROW]
[ROW][C]58[/C][C]12[/C][C]9.45746682802128[/C][C]2.54253317197872[/C][/ROW]
[ROW][C]59[/C][C]15[/C][C]9.9913849524887[/C][C]5.00861504751129[/C][/ROW]
[ROW][C]60[/C][C]16[/C][C]10.8762866001676[/C][C]5.12371339983243[/C][/ROW]
[ROW][C]61[/C][C]16[/C][C]9.85283432747826[/C][C]6.14716567252174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57548&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57548&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	24	25.6314825290665	-1.63148252906652
2	22	20.6265576329564	1.37344236704355
3	25	24.7661642236719	0.233835776328138
4	24	24.7718526899199	-0.771852689919875
5	29	25.481262575993	3.518737424007
6	26	24.6633199905479	1.33668000945214
7	26	21.4690084567959	4.53099154320413
8	21	21.892639508489	-0.892639508489017
9	23	23.2077378608102	-0.207737860810164
10	22	22.3350903323284	-0.335090332328447
11	21	21.8077378608102	-0.80773786081016
12	16	21.8436230317005	-5.84362303170045
13	19	22.3059495933911	-3.30594959339114
14	16	17.3010246972811	-1.30102469728107
15	25	22.0773936455879	2.92260635441207
16	27	22.9320985886245	4.0679014113755
17	23	22.7924919979091	0.207508002090925
18	22	21.1255329356754	0.874467064324638
19	23	18.7802378787119	4.21976212128807
20	20	20.0528854071936	-0.0528854071936464
21	24	22.2170002363034	1.78299976369664
22	23	21.3443527078216	1.65564729217836
23	20	20.6047461171062	-0.604746117106214
24	21	21.4896477647851	-0.489647764785071
25	22	21.5274660880815	0.472533911918524
26	17	16.5225411919714	0.477458808028586
27	21	18.5396065907154	2.46039340928457
28	19	20.0310738913434	-1.03107389134342
29	23	20.5282296582194	2.47177034178058
30	22	19.0735247151828	2.92647528481715
31	15	17.1527378966137	-2.1527378966137
32	23	18.8498936634897	4.1501063365103
33	21	19.9527378966137	1.0472621033863
34	18	18.6555821297377	-0.655582129737703
35	18	17.7037214198251	0.296278580174866
36	18	18.588623067504	-0.588623067503993
37	18	17.9896790332090	0.0103209667910265
38	10	11.7112294219161	-1.71122942191606
39	13	16.4875983702229	-3.48759837022292
40	10	16.0687785980766	-6.06877859807663
41	9	16.7781884841498	-7.77818848414978
42	9	15.7479917795075	-6.74799177950749
43	6	12.3414261265583	-6.34142612655835
44	11	13.6140736550401	-2.61407365504006
45	9	14.5046637689669	-5.50466376896693
46	10	13.2075080020909	-3.20750800209093
47	9	12.8924096497698	-3.89240964976978
48	16	14.2018195358429	1.79818046415708
49	10	11.6925884287736	-1.69258842877363
50	7	5.838647055875	1.16135294412500
51	7	9.12923716980186	-2.12923716980186
52	14	10.1961962320356	3.80380376796443
53	11	9.41982728372872	1.58017271627128
54	10	8.38963057908644	1.61036942091356
55	6	6.25658964132015	-0.256589641320147
56	8	8.59050776578757	-0.590507765787571
57	13	10.1178602373059	2.88213976269414
58	12	9.45746682802128	2.54253317197872
59	15	9.9913849524887	5.00861504751129
60	16	10.8762866001676	5.12371339983243
61	16	9.85283432747826	6.14716567252174

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.131321011662442	0.262642023324883	0.868678988337558
18	0.0775578710148501	0.155115742029700	0.92244212898515
19	0.0385097278373563	0.0770194556747126	0.961490272162644
20	0.0207005925653359	0.0414011851306718	0.979299407434664
21	0.0108430990361390	0.0216861980722780	0.989156900963861
22	0.00458058278498988	0.00916116556997975	0.99541941721501
23	0.00233301401978601	0.00466602803957202	0.997666985980214
24	0.00110186331896363	0.00220372663792727	0.998898136681036
25	0.000366087392167951	0.000732174784335901	0.999633912607832
26	0.000207432999181084	0.000414865998362168	0.99979256700082
27	0.000206698545444532	0.000413397090889064	0.999793301454555
28	0.000205068357120666	0.000410136714241332	0.99979493164288
29	0.000147236232778612	0.000294472465557224	0.999852763767221
30	0.000202691821046355	0.000405383642092710	0.999797308178954
31	0.00796411138970885	0.0159282227794177	0.992035888610291
32	0.0269567419588238	0.0539134839176477	0.973043258041176
33	0.0464365042976975	0.092873008595395	0.953563495702302
34	0.0612827373952374	0.122565474790475	0.938717262604763
35	0.104391044040296	0.208782088080592	0.895608955959704
36	0.102317975122531	0.204635950245062	0.897682024877469
37	0.254231426618622	0.508462853237245	0.745768573381378
38	0.237096250135469	0.474192500270938	0.762903749864531
39	0.53142964504802	0.937140709903960	0.468570354951980
40	0.556322236639797	0.887355526720406	0.443677763360203
41	0.647130350559114	0.705739298881773	0.352869649440886
42	0.698132084465303	0.603735831069395	0.301867915534698
43	0.634804289279024	0.730391421441951	0.365195710720976
44	0.61136623789619	0.777267524207621	0.388633762103811

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.131321011662442 & 0.262642023324883 & 0.868678988337558 \tabularnewline
18 & 0.0775578710148501 & 0.155115742029700 & 0.92244212898515 \tabularnewline
19 & 0.0385097278373563 & 0.0770194556747126 & 0.961490272162644 \tabularnewline
20 & 0.0207005925653359 & 0.0414011851306718 & 0.979299407434664 \tabularnewline
21 & 0.0108430990361390 & 0.0216861980722780 & 0.989156900963861 \tabularnewline
22 & 0.00458058278498988 & 0.00916116556997975 & 0.99541941721501 \tabularnewline
23 & 0.00233301401978601 & 0.00466602803957202 & 0.997666985980214 \tabularnewline
24 & 0.00110186331896363 & 0.00220372663792727 & 0.998898136681036 \tabularnewline
25 & 0.000366087392167951 & 0.000732174784335901 & 0.999633912607832 \tabularnewline
26 & 0.000207432999181084 & 0.000414865998362168 & 0.99979256700082 \tabularnewline
27 & 0.000206698545444532 & 0.000413397090889064 & 0.999793301454555 \tabularnewline
28 & 0.000205068357120666 & 0.000410136714241332 & 0.99979493164288 \tabularnewline
29 & 0.000147236232778612 & 0.000294472465557224 & 0.999852763767221 \tabularnewline
30 & 0.000202691821046355 & 0.000405383642092710 & 0.999797308178954 \tabularnewline
31 & 0.00796411138970885 & 0.0159282227794177 & 0.992035888610291 \tabularnewline
32 & 0.0269567419588238 & 0.0539134839176477 & 0.973043258041176 \tabularnewline
33 & 0.0464365042976975 & 0.092873008595395 & 0.953563495702302 \tabularnewline
34 & 0.0612827373952374 & 0.122565474790475 & 0.938717262604763 \tabularnewline
35 & 0.104391044040296 & 0.208782088080592 & 0.895608955959704 \tabularnewline
36 & 0.102317975122531 & 0.204635950245062 & 0.897682024877469 \tabularnewline
37 & 0.254231426618622 & 0.508462853237245 & 0.745768573381378 \tabularnewline
38 & 0.237096250135469 & 0.474192500270938 & 0.762903749864531 \tabularnewline
39 & 0.53142964504802 & 0.937140709903960 & 0.468570354951980 \tabularnewline
40 & 0.556322236639797 & 0.887355526720406 & 0.443677763360203 \tabularnewline
41 & 0.647130350559114 & 0.705739298881773 & 0.352869649440886 \tabularnewline
42 & 0.698132084465303 & 0.603735831069395 & 0.301867915534698 \tabularnewline
43 & 0.634804289279024 & 0.730391421441951 & 0.365195710720976 \tabularnewline
44 & 0.61136623789619 & 0.777267524207621 & 0.388633762103811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57548&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]17[/C][C]0.131321011662442[/C][C]0.262642023324883[/C][C]0.868678988337558[/C][/ROW]
[ROW][C]18[/C][C]0.0775578710148501[/C][C]0.155115742029700[/C][C]0.92244212898515[/C][/ROW]
[ROW][C]19[/C][C]0.0385097278373563[/C][C]0.0770194556747126[/C][C]0.961490272162644[/C][/ROW]
[ROW][C]20[/C][C]0.0207005925653359[/C][C]0.0414011851306718[/C][C]0.979299407434664[/C][/ROW]
[ROW][C]21[/C][C]0.0108430990361390[/C][C]0.0216861980722780[/C][C]0.989156900963861[/C][/ROW]
[ROW][C]22[/C][C]0.00458058278498988[/C][C]0.00916116556997975[/C][C]0.99541941721501[/C][/ROW]
[ROW][C]23[/C][C]0.00233301401978601[/C][C]0.00466602803957202[/C][C]0.997666985980214[/C][/ROW]
[ROW][C]24[/C][C]0.00110186331896363[/C][C]0.00220372663792727[/C][C]0.998898136681036[/C][/ROW]
[ROW][C]25[/C][C]0.000366087392167951[/C][C]0.000732174784335901[/C][C]0.999633912607832[/C][/ROW]
[ROW][C]26[/C][C]0.000207432999181084[/C][C]0.000414865998362168[/C][C]0.99979256700082[/C][/ROW]
[ROW][C]27[/C][C]0.000206698545444532[/C][C]0.000413397090889064[/C][C]0.999793301454555[/C][/ROW]
[ROW][C]28[/C][C]0.000205068357120666[/C][C]0.000410136714241332[/C][C]0.99979493164288[/C][/ROW]
[ROW][C]29[/C][C]0.000147236232778612[/C][C]0.000294472465557224[/C][C]0.999852763767221[/C][/ROW]
[ROW][C]30[/C][C]0.000202691821046355[/C][C]0.000405383642092710[/C][C]0.999797308178954[/C][/ROW]
[ROW][C]31[/C][C]0.00796411138970885[/C][C]0.0159282227794177[/C][C]0.992035888610291[/C][/ROW]
[ROW][C]32[/C][C]0.0269567419588238[/C][C]0.0539134839176477[/C][C]0.973043258041176[/C][/ROW]
[ROW][C]33[/C][C]0.0464365042976975[/C][C]0.092873008595395[/C][C]0.953563495702302[/C][/ROW]
[ROW][C]34[/C][C]0.0612827373952374[/C][C]0.122565474790475[/C][C]0.938717262604763[/C][/ROW]
[ROW][C]35[/C][C]0.104391044040296[/C][C]0.208782088080592[/C][C]0.895608955959704[/C][/ROW]
[ROW][C]36[/C][C]0.102317975122531[/C][C]0.204635950245062[/C][C]0.897682024877469[/C][/ROW]
[ROW][C]37[/C][C]0.254231426618622[/C][C]0.508462853237245[/C][C]0.745768573381378[/C][/ROW]
[ROW][C]38[/C][C]0.237096250135469[/C][C]0.474192500270938[/C][C]0.762903749864531[/C][/ROW]
[ROW][C]39[/C][C]0.53142964504802[/C][C]0.937140709903960[/C][C]0.468570354951980[/C][/ROW]
[ROW][C]40[/C][C]0.556322236639797[/C][C]0.887355526720406[/C][C]0.443677763360203[/C][/ROW]
[ROW][C]41[/C][C]0.647130350559114[/C][C]0.705739298881773[/C][C]0.352869649440886[/C][/ROW]
[ROW][C]42[/C][C]0.698132084465303[/C][C]0.603735831069395[/C][C]0.301867915534698[/C][/ROW]
[ROW][C]43[/C][C]0.634804289279024[/C][C]0.730391421441951[/C][C]0.365195710720976[/C][/ROW]
[ROW][C]44[/C][C]0.61136623789619[/C][C]0.777267524207621[/C][C]0.388633762103811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57548&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57548&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
17	0.131321011662442	0.262642023324883	0.868678988337558
18	0.0775578710148501	0.155115742029700	0.92244212898515
19	0.0385097278373563	0.0770194556747126	0.961490272162644
20	0.0207005925653359	0.0414011851306718	0.979299407434664
21	0.0108430990361390	0.0216861980722780	0.989156900963861
22	0.00458058278498988	0.00916116556997975	0.99541941721501
23	0.00233301401978601	0.00466602803957202	0.997666985980214
24	0.00110186331896363	0.00220372663792727	0.998898136681036
25	0.000366087392167951	0.000732174784335901	0.999633912607832
26	0.000207432999181084	0.000414865998362168	0.99979256700082
27	0.000206698545444532	0.000413397090889064	0.999793301454555
28	0.000205068357120666	0.000410136714241332	0.99979493164288
29	0.000147236232778612	0.000294472465557224	0.999852763767221
30	0.000202691821046355	0.000405383642092710	0.999797308178954
31	0.00796411138970885	0.0159282227794177	0.992035888610291
32	0.0269567419588238	0.0539134839176477	0.973043258041176
33	0.0464365042976975	0.092873008595395	0.953563495702302
34	0.0612827373952374	0.122565474790475	0.938717262604763
35	0.104391044040296	0.208782088080592	0.895608955959704
36	0.102317975122531	0.204635950245062	0.897682024877469
37	0.254231426618622	0.508462853237245	0.745768573381378
38	0.237096250135469	0.474192500270938	0.762903749864531
39	0.53142964504802	0.937140709903960	0.468570354951980
40	0.556322236639797	0.887355526720406	0.443677763360203
41	0.647130350559114	0.705739298881773	0.352869649440886
42	0.698132084465303	0.603735831069395	0.301867915534698
43	0.634804289279024	0.730391421441951	0.365195710720976
44	0.61136623789619	0.777267524207621	0.388633762103811

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	9	0.321428571428571	NOK
5% type I error level	12	0.428571428571429	NOK
10% type I error level	15	0.535714285714286	NOK

\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 & 9 & 0.321428571428571 & NOK \tabularnewline
5% type I error level & 12 & 0.428571428571429 & NOK \tabularnewline
10% type I error level & 15 & 0.535714285714286 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57548&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]9[/C][C]0.321428571428571[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]12[/C][C]0.428571428571429[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]0.535714285714286[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57548&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57548&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	9	0.321428571428571	NOK
5% type I error level	12	0.428571428571429	NOK
10% type I error level	15	0.535714285714286	NOK

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 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code