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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 19 Nov 2009 01:41:46 -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/19/t1258620172732i9u30cbvrrgj.htm/, Retrieved Thu, 25 Apr 2024 23:29:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57653, Retrieved Thu, 25 Apr 2024 23:29:00 +0000

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Estimated Impact

195

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [model 3] [2009-11-19 08:41:46] [c60887983b0820a525cba943a935572d] [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=57653&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=57653&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57653&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
WLH[t] = + 160.480347826087 + 16.6904347826087X[t] -11.6597391304348M1[t] -19.6053913043478M2[t] -21.7510434782609M3[t] -22.6966956521739M4[t] -24.8423478260870M5[t] -28.7880000000000M6[t] -30.7336521739131M7[t] -36.2793043478261M8[t] -34.0249565217391M9[t] -1.97060869565218M10[t] + 4.88373913043478M11[t] -0.854347826086956t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WLH[t] =  +  160.480347826087 +  16.6904347826087X[t] -11.6597391304348M1[t] -19.6053913043478M2[t] -21.7510434782609M3[t] -22.6966956521739M4[t] -24.8423478260870M5[t] -28.7880000000000M6[t] -30.7336521739131M7[t] -36.2793043478261M8[t] -34.0249565217391M9[t] -1.97060869565218M10[t] +  4.88373913043478M11[t] -0.854347826086956t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57653&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WLH[t] =  +  160.480347826087 +  16.6904347826087X[t] -11.6597391304348M1[t] -19.6053913043478M2[t] -21.7510434782609M3[t] -22.6966956521739M4[t] -24.8423478260870M5[t] -28.7880000000000M6[t] -30.7336521739131M7[t] -36.2793043478261M8[t] -34.0249565217391M9[t] -1.97060869565218M10[t] +  4.88373913043478M11[t] -0.854347826086956t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57653&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57653&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
WLH[t] = + 160.480347826087 + 16.6904347826087X[t] -11.6597391304348M1[t] -19.6053913043478M2[t] -21.7510434782609M3[t] -22.6966956521739M4[t] -24.8423478260870M5[t] -28.7880000000000M6[t] -30.7336521739131M7[t] -36.2793043478261M8[t] -34.0249565217391M9[t] -1.97060869565218M10[t] + 4.88373913043478M11[t] -0.854347826086956t + 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)	160.480347826087	3.396873	47.2436	0	0
X	16.6904347826087	2.903911	5.7476	1e-06	0
M1	-11.6597391304348	4.055404	-2.8751	0.006098	0.003049
M2	-19.6053913043478	4.049985	-4.8409	1.5e-05	7e-06
M3	-21.7510434782609	4.045766	-5.3762	2e-06	1e-06
M4	-22.6966956521739	4.042749	-5.6142	1e-06	1e-06
M5	-24.8423478260870	4.040938	-6.1477	0	0
M6	-28.7880000000000	4.040334	-7.1252	0	0
M7	-30.7336521739131	4.040938	-7.6056	0	0
M8	-36.2793043478261	4.042749	-8.9739	0	0
M9	-34.0249565217391	4.045766	-8.41	0	0
M10	-1.97060869565218	4.049985	-0.4866	0.628872	0.314436
M11	4.88373913043478	4.055404	1.2043	0.234651	0.117326
t	-0.854347826086956	0.069857	-12.2299	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) & 160.480347826087 & 3.396873 & 47.2436 & 0 & 0 \tabularnewline
X & 16.6904347826087 & 2.903911 & 5.7476 & 1e-06 & 0 \tabularnewline
M1 & -11.6597391304348 & 4.055404 & -2.8751 & 0.006098 & 0.003049 \tabularnewline
M2 & -19.6053913043478 & 4.049985 & -4.8409 & 1.5e-05 & 7e-06 \tabularnewline
M3 & -21.7510434782609 & 4.045766 & -5.3762 & 2e-06 & 1e-06 \tabularnewline
M4 & -22.6966956521739 & 4.042749 & -5.6142 & 1e-06 & 1e-06 \tabularnewline
M5 & -24.8423478260870 & 4.040938 & -6.1477 & 0 & 0 \tabularnewline
M6 & -28.7880000000000 & 4.040334 & -7.1252 & 0 & 0 \tabularnewline
M7 & -30.7336521739131 & 4.040938 & -7.6056 & 0 & 0 \tabularnewline
M8 & -36.2793043478261 & 4.042749 & -8.9739 & 0 & 0 \tabularnewline
M9 & -34.0249565217391 & 4.045766 & -8.41 & 0 & 0 \tabularnewline
M10 & -1.97060869565218 & 4.049985 & -0.4866 & 0.628872 & 0.314436 \tabularnewline
M11 & 4.88373913043478 & 4.055404 & 1.2043 & 0.234651 & 0.117326 \tabularnewline
t & -0.854347826086956 & 0.069857 & -12.2299 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57653&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]160.480347826087[/C][C]3.396873[/C][C]47.2436[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]16.6904347826087[/C][C]2.903911[/C][C]5.7476[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-11.6597391304348[/C][C]4.055404[/C][C]-2.8751[/C][C]0.006098[/C][C]0.003049[/C][/ROW]
[ROW][C]M2[/C][C]-19.6053913043478[/C][C]4.049985[/C][C]-4.8409[/C][C]1.5e-05[/C][C]7e-06[/C][/ROW]
[ROW][C]M3[/C][C]-21.7510434782609[/C][C]4.045766[/C][C]-5.3762[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M4[/C][C]-22.6966956521739[/C][C]4.042749[/C][C]-5.6142[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M5[/C][C]-24.8423478260870[/C][C]4.040938[/C][C]-6.1477[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-28.7880000000000[/C][C]4.040334[/C][C]-7.1252[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]-30.7336521739131[/C][C]4.040938[/C][C]-7.6056[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-36.2793043478261[/C][C]4.042749[/C][C]-8.9739[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-34.0249565217391[/C][C]4.045766[/C][C]-8.41[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-1.97060869565218[/C][C]4.049985[/C][C]-0.4866[/C][C]0.628872[/C][C]0.314436[/C][/ROW]
[ROW][C]M11[/C][C]4.88373913043478[/C][C]4.055404[/C][C]1.2043[/C][C]0.234651[/C][C]0.117326[/C][/ROW]
[ROW][C]t[/C][C]-0.854347826086956[/C][C]0.069857[/C][C]-12.2299[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57653&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57653&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)	160.480347826087	3.396873	47.2436	0	0
X	16.6904347826087	2.903911	5.7476	1e-06	0
M1	-11.6597391304348	4.055404	-2.8751	0.006098	0.003049
M2	-19.6053913043478	4.049985	-4.8409	1.5e-05	7e-06
M3	-21.7510434782609	4.045766	-5.3762	2e-06	1e-06
M4	-22.6966956521739	4.042749	-5.6142	1e-06	1e-06
M5	-24.8423478260870	4.040938	-6.1477	0	0
M6	-28.7880000000000	4.040334	-7.1252	0	0
M7	-30.7336521739131	4.040938	-7.6056	0	0
M8	-36.2793043478261	4.042749	-8.9739	0	0
M9	-34.0249565217391	4.045766	-8.41	0	0
M10	-1.97060869565218	4.049985	-0.4866	0.628872	0.314436
M11	4.88373913043478	4.055404	1.2043	0.234651	0.117326
t	-0.854347826086956	0.069857	-12.2299	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.948465481240342
R-squared	0.899586769104474
Adjusted R-squared	0.87120911689487
F-TEST (value)	31.7005354234340
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.35662522963395
Sum Squared Residuals	1858.70747826087

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.948465481240342 \tabularnewline
R-squared & 0.899586769104474 \tabularnewline
Adjusted R-squared & 0.87120911689487 \tabularnewline
F-TEST (value) & 31.7005354234340 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.35662522963395 \tabularnewline
Sum Squared Residuals & 1858.70747826087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57653&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.948465481240342[/C][/ROW]
[ROW][C]R-squared[/C][C]0.899586769104474[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.87120911689487[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]31.7005354234340[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]6.35662522963395[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1858.70747826087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57653&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57653&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	0.948465481240342
R-squared	0.899586769104474
Adjusted R-squared	0.87120911689487
F-TEST (value)	31.7005354234340
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.35662522963395
Sum Squared Residuals	1858.70747826087

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	149	147.966260869565	1.03373913043479
2	139	139.166260869565	-0.166260869565168
3	135	136.166260869565	-1.16626086956523
4	130	134.366260869565	-4.36626086956519
5	127	131.366260869565	-4.36626086956524
6	122	126.566260869565	-4.56626086956522
7	117	123.766260869565	-6.76626086956524
8	112	117.366260869565	-5.36626086956517
9	113	118.766260869565	-5.76626086956521
10	149	149.966260869565	-0.966260869565233
11	157	155.966260869565	1.03373913043478
12	157	150.228173913043	6.7718260869565
13	147	137.714086956522	9.28591304347826
14	137	128.914086956522	8.08591304347821
15	132	125.914086956522	6.08591304347826
16	125	124.114086956522	0.885913043478253
17	123	121.114086956522	1.88591304347827
18	117	116.314086956522	0.68591304347826
19	114	113.514086956522	0.485913043478262
20	111	107.114086956522	3.88591304347825
21	112	108.514086956522	3.48591304347826
22	144	139.714086956522	4.28591304347826
23	150	145.714086956522	4.28591304347826
24	149	139.976	9.024
25	134	127.461913043478	6.53808695652174
26	123	118.661913043478	4.33808695652174
27	116	115.661913043478	0.338086956521741
28	117	113.861913043478	3.13808695652174
29	111	110.861913043478	0.138086956521751
30	105	106.061913043478	-1.06191304347826
31	102	103.261913043478	-1.26191304347826
32	95	96.8619130434783	-1.86191304347827
33	93	98.2619130434783	-5.26191304347826
34	124	129.461913043478	-5.46191304347825
35	130	135.461913043478	-5.46191304347826
36	124	129.723826086957	-5.72382608695652
37	115	117.209739130435	-2.20973913043478
38	106	108.409739130435	-2.40973913043478
39	105	105.409739130435	-0.409739130434784
40	105	103.609739130435	1.39026086956522
41	101	100.609739130435	0.390260869565224
42	95	95.8097391304348	-0.809739130434784
43	93	93.0097391304348	-0.00973913043477244
44	84	86.6097391304348	-2.60973913043479
45	87	88.0097391304348	-1.00973913043478
46	116	119.209739130435	-3.20973913043478
47	120	125.209739130435	-5.20973913043478
48	117	136.162086956522	-19.1620869565217
49	109	123.648	-14.648
50	105	114.848	-9.848
51	107	111.848	-4.848
52	109	110.048	-1.04800000000000
53	109	107.048	1.95200000000000
54	108	102.248	5.752
55	107	99.448	7.552
56	99	93.048	5.95199999999999
57	103	94.448	8.552
58	131	125.648	5.35200000000000
59	137	131.648	5.352
60	135	125.909913043478	9.09008695652174

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 149 & 147.966260869565 & 1.03373913043479 \tabularnewline
2 & 139 & 139.166260869565 & -0.166260869565168 \tabularnewline
3 & 135 & 136.166260869565 & -1.16626086956523 \tabularnewline
4 & 130 & 134.366260869565 & -4.36626086956519 \tabularnewline
5 & 127 & 131.366260869565 & -4.36626086956524 \tabularnewline
6 & 122 & 126.566260869565 & -4.56626086956522 \tabularnewline
7 & 117 & 123.766260869565 & -6.76626086956524 \tabularnewline
8 & 112 & 117.366260869565 & -5.36626086956517 \tabularnewline
9 & 113 & 118.766260869565 & -5.76626086956521 \tabularnewline
10 & 149 & 149.966260869565 & -0.966260869565233 \tabularnewline
11 & 157 & 155.966260869565 & 1.03373913043478 \tabularnewline
12 & 157 & 150.228173913043 & 6.7718260869565 \tabularnewline
13 & 147 & 137.714086956522 & 9.28591304347826 \tabularnewline
14 & 137 & 128.914086956522 & 8.08591304347821 \tabularnewline
15 & 132 & 125.914086956522 & 6.08591304347826 \tabularnewline
16 & 125 & 124.114086956522 & 0.885913043478253 \tabularnewline
17 & 123 & 121.114086956522 & 1.88591304347827 \tabularnewline
18 & 117 & 116.314086956522 & 0.68591304347826 \tabularnewline
19 & 114 & 113.514086956522 & 0.485913043478262 \tabularnewline
20 & 111 & 107.114086956522 & 3.88591304347825 \tabularnewline
21 & 112 & 108.514086956522 & 3.48591304347826 \tabularnewline
22 & 144 & 139.714086956522 & 4.28591304347826 \tabularnewline
23 & 150 & 145.714086956522 & 4.28591304347826 \tabularnewline
24 & 149 & 139.976 & 9.024 \tabularnewline
25 & 134 & 127.461913043478 & 6.53808695652174 \tabularnewline
26 & 123 & 118.661913043478 & 4.33808695652174 \tabularnewline
27 & 116 & 115.661913043478 & 0.338086956521741 \tabularnewline
28 & 117 & 113.861913043478 & 3.13808695652174 \tabularnewline
29 & 111 & 110.861913043478 & 0.138086956521751 \tabularnewline
30 & 105 & 106.061913043478 & -1.06191304347826 \tabularnewline
31 & 102 & 103.261913043478 & -1.26191304347826 \tabularnewline
32 & 95 & 96.8619130434783 & -1.86191304347827 \tabularnewline
33 & 93 & 98.2619130434783 & -5.26191304347826 \tabularnewline
34 & 124 & 129.461913043478 & -5.46191304347825 \tabularnewline
35 & 130 & 135.461913043478 & -5.46191304347826 \tabularnewline
36 & 124 & 129.723826086957 & -5.72382608695652 \tabularnewline
37 & 115 & 117.209739130435 & -2.20973913043478 \tabularnewline
38 & 106 & 108.409739130435 & -2.40973913043478 \tabularnewline
39 & 105 & 105.409739130435 & -0.409739130434784 \tabularnewline
40 & 105 & 103.609739130435 & 1.39026086956522 \tabularnewline
41 & 101 & 100.609739130435 & 0.390260869565224 \tabularnewline
42 & 95 & 95.8097391304348 & -0.809739130434784 \tabularnewline
43 & 93 & 93.0097391304348 & -0.00973913043477244 \tabularnewline
44 & 84 & 86.6097391304348 & -2.60973913043479 \tabularnewline
45 & 87 & 88.0097391304348 & -1.00973913043478 \tabularnewline
46 & 116 & 119.209739130435 & -3.20973913043478 \tabularnewline
47 & 120 & 125.209739130435 & -5.20973913043478 \tabularnewline
48 & 117 & 136.162086956522 & -19.1620869565217 \tabularnewline
49 & 109 & 123.648 & -14.648 \tabularnewline
50 & 105 & 114.848 & -9.848 \tabularnewline
51 & 107 & 111.848 & -4.848 \tabularnewline
52 & 109 & 110.048 & -1.04800000000000 \tabularnewline
53 & 109 & 107.048 & 1.95200000000000 \tabularnewline
54 & 108 & 102.248 & 5.752 \tabularnewline
55 & 107 & 99.448 & 7.552 \tabularnewline
56 & 99 & 93.048 & 5.95199999999999 \tabularnewline
57 & 103 & 94.448 & 8.552 \tabularnewline
58 & 131 & 125.648 & 5.35200000000000 \tabularnewline
59 & 137 & 131.648 & 5.352 \tabularnewline
60 & 135 & 125.909913043478 & 9.09008695652174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57653&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]149[/C][C]147.966260869565[/C][C]1.03373913043479[/C][/ROW]
[ROW][C]2[/C][C]139[/C][C]139.166260869565[/C][C]-0.166260869565168[/C][/ROW]
[ROW][C]3[/C][C]135[/C][C]136.166260869565[/C][C]-1.16626086956523[/C][/ROW]
[ROW][C]4[/C][C]130[/C][C]134.366260869565[/C][C]-4.36626086956519[/C][/ROW]
[ROW][C]5[/C][C]127[/C][C]131.366260869565[/C][C]-4.36626086956524[/C][/ROW]
[ROW][C]6[/C][C]122[/C][C]126.566260869565[/C][C]-4.56626086956522[/C][/ROW]
[ROW][C]7[/C][C]117[/C][C]123.766260869565[/C][C]-6.76626086956524[/C][/ROW]
[ROW][C]8[/C][C]112[/C][C]117.366260869565[/C][C]-5.36626086956517[/C][/ROW]
[ROW][C]9[/C][C]113[/C][C]118.766260869565[/C][C]-5.76626086956521[/C][/ROW]
[ROW][C]10[/C][C]149[/C][C]149.966260869565[/C][C]-0.966260869565233[/C][/ROW]
[ROW][C]11[/C][C]157[/C][C]155.966260869565[/C][C]1.03373913043478[/C][/ROW]
[ROW][C]12[/C][C]157[/C][C]150.228173913043[/C][C]6.7718260869565[/C][/ROW]
[ROW][C]13[/C][C]147[/C][C]137.714086956522[/C][C]9.28591304347826[/C][/ROW]
[ROW][C]14[/C][C]137[/C][C]128.914086956522[/C][C]8.08591304347821[/C][/ROW]
[ROW][C]15[/C][C]132[/C][C]125.914086956522[/C][C]6.08591304347826[/C][/ROW]
[ROW][C]16[/C][C]125[/C][C]124.114086956522[/C][C]0.885913043478253[/C][/ROW]
[ROW][C]17[/C][C]123[/C][C]121.114086956522[/C][C]1.88591304347827[/C][/ROW]
[ROW][C]18[/C][C]117[/C][C]116.314086956522[/C][C]0.68591304347826[/C][/ROW]
[ROW][C]19[/C][C]114[/C][C]113.514086956522[/C][C]0.485913043478262[/C][/ROW]
[ROW][C]20[/C][C]111[/C][C]107.114086956522[/C][C]3.88591304347825[/C][/ROW]
[ROW][C]21[/C][C]112[/C][C]108.514086956522[/C][C]3.48591304347826[/C][/ROW]
[ROW][C]22[/C][C]144[/C][C]139.714086956522[/C][C]4.28591304347826[/C][/ROW]
[ROW][C]23[/C][C]150[/C][C]145.714086956522[/C][C]4.28591304347826[/C][/ROW]
[ROW][C]24[/C][C]149[/C][C]139.976[/C][C]9.024[/C][/ROW]
[ROW][C]25[/C][C]134[/C][C]127.461913043478[/C][C]6.53808695652174[/C][/ROW]
[ROW][C]26[/C][C]123[/C][C]118.661913043478[/C][C]4.33808695652174[/C][/ROW]
[ROW][C]27[/C][C]116[/C][C]115.661913043478[/C][C]0.338086956521741[/C][/ROW]
[ROW][C]28[/C][C]117[/C][C]113.861913043478[/C][C]3.13808695652174[/C][/ROW]
[ROW][C]29[/C][C]111[/C][C]110.861913043478[/C][C]0.138086956521751[/C][/ROW]
[ROW][C]30[/C][C]105[/C][C]106.061913043478[/C][C]-1.06191304347826[/C][/ROW]
[ROW][C]31[/C][C]102[/C][C]103.261913043478[/C][C]-1.26191304347826[/C][/ROW]
[ROW][C]32[/C][C]95[/C][C]96.8619130434783[/C][C]-1.86191304347827[/C][/ROW]
[ROW][C]33[/C][C]93[/C][C]98.2619130434783[/C][C]-5.26191304347826[/C][/ROW]
[ROW][C]34[/C][C]124[/C][C]129.461913043478[/C][C]-5.46191304347825[/C][/ROW]
[ROW][C]35[/C][C]130[/C][C]135.461913043478[/C][C]-5.46191304347826[/C][/ROW]
[ROW][C]36[/C][C]124[/C][C]129.723826086957[/C][C]-5.72382608695652[/C][/ROW]
[ROW][C]37[/C][C]115[/C][C]117.209739130435[/C][C]-2.20973913043478[/C][/ROW]
[ROW][C]38[/C][C]106[/C][C]108.409739130435[/C][C]-2.40973913043478[/C][/ROW]
[ROW][C]39[/C][C]105[/C][C]105.409739130435[/C][C]-0.409739130434784[/C][/ROW]
[ROW][C]40[/C][C]105[/C][C]103.609739130435[/C][C]1.39026086956522[/C][/ROW]
[ROW][C]41[/C][C]101[/C][C]100.609739130435[/C][C]0.390260869565224[/C][/ROW]
[ROW][C]42[/C][C]95[/C][C]95.8097391304348[/C][C]-0.809739130434784[/C][/ROW]
[ROW][C]43[/C][C]93[/C][C]93.0097391304348[/C][C]-0.00973913043477244[/C][/ROW]
[ROW][C]44[/C][C]84[/C][C]86.6097391304348[/C][C]-2.60973913043479[/C][/ROW]
[ROW][C]45[/C][C]87[/C][C]88.0097391304348[/C][C]-1.00973913043478[/C][/ROW]
[ROW][C]46[/C][C]116[/C][C]119.209739130435[/C][C]-3.20973913043478[/C][/ROW]
[ROW][C]47[/C][C]120[/C][C]125.209739130435[/C][C]-5.20973913043478[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]136.162086956522[/C][C]-19.1620869565217[/C][/ROW]
[ROW][C]49[/C][C]109[/C][C]123.648[/C][C]-14.648[/C][/ROW]
[ROW][C]50[/C][C]105[/C][C]114.848[/C][C]-9.848[/C][/ROW]
[ROW][C]51[/C][C]107[/C][C]111.848[/C][C]-4.848[/C][/ROW]
[ROW][C]52[/C][C]109[/C][C]110.048[/C][C]-1.04800000000000[/C][/ROW]
[ROW][C]53[/C][C]109[/C][C]107.048[/C][C]1.95200000000000[/C][/ROW]
[ROW][C]54[/C][C]108[/C][C]102.248[/C][C]5.752[/C][/ROW]
[ROW][C]55[/C][C]107[/C][C]99.448[/C][C]7.552[/C][/ROW]
[ROW][C]56[/C][C]99[/C][C]93.048[/C][C]5.95199999999999[/C][/ROW]
[ROW][C]57[/C][C]103[/C][C]94.448[/C][C]8.552[/C][/ROW]
[ROW][C]58[/C][C]131[/C][C]125.648[/C][C]5.35200000000000[/C][/ROW]
[ROW][C]59[/C][C]137[/C][C]131.648[/C][C]5.352[/C][/ROW]
[ROW][C]60[/C][C]135[/C][C]125.909913043478[/C][C]9.09008695652174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57653&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57653&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	149	147.966260869565	1.03373913043479
2	139	139.166260869565	-0.166260869565168
3	135	136.166260869565	-1.16626086956523
4	130	134.366260869565	-4.36626086956519
5	127	131.366260869565	-4.36626086956524
6	122	126.566260869565	-4.56626086956522
7	117	123.766260869565	-6.76626086956524
8	112	117.366260869565	-5.36626086956517
9	113	118.766260869565	-5.76626086956521
10	149	149.966260869565	-0.966260869565233
11	157	155.966260869565	1.03373913043478
12	157	150.228173913043	6.7718260869565
13	147	137.714086956522	9.28591304347826
14	137	128.914086956522	8.08591304347821
15	132	125.914086956522	6.08591304347826
16	125	124.114086956522	0.885913043478253
17	123	121.114086956522	1.88591304347827
18	117	116.314086956522	0.68591304347826
19	114	113.514086956522	0.485913043478262
20	111	107.114086956522	3.88591304347825
21	112	108.514086956522	3.48591304347826
22	144	139.714086956522	4.28591304347826
23	150	145.714086956522	4.28591304347826
24	149	139.976	9.024
25	134	127.461913043478	6.53808695652174
26	123	118.661913043478	4.33808695652174
27	116	115.661913043478	0.338086956521741
28	117	113.861913043478	3.13808695652174
29	111	110.861913043478	0.138086956521751
30	105	106.061913043478	-1.06191304347826
31	102	103.261913043478	-1.26191304347826
32	95	96.8619130434783	-1.86191304347827
33	93	98.2619130434783	-5.26191304347826
34	124	129.461913043478	-5.46191304347825
35	130	135.461913043478	-5.46191304347826
36	124	129.723826086957	-5.72382608695652
37	115	117.209739130435	-2.20973913043478
38	106	108.409739130435	-2.40973913043478
39	105	105.409739130435	-0.409739130434784
40	105	103.609739130435	1.39026086956522
41	101	100.609739130435	0.390260869565224
42	95	95.8097391304348	-0.809739130434784
43	93	93.0097391304348	-0.00973913043477244
44	84	86.6097391304348	-2.60973913043479
45	87	88.0097391304348	-1.00973913043478
46	116	119.209739130435	-3.20973913043478
47	120	125.209739130435	-5.20973913043478
48	117	136.162086956522	-19.1620869565217
49	109	123.648	-14.648
50	105	114.848	-9.848
51	107	111.848	-4.848
52	109	110.048	-1.04800000000000
53	109	107.048	1.95200000000000
54	108	102.248	5.752
55	107	99.448	7.552
56	99	93.048	5.95199999999999
57	103	94.448	8.552
58	131	125.648	5.35200000000000
59	137	131.648	5.352
60	135	125.909913043478	9.09008695652174

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.00551092296990859	0.0110218459398172	0.994489077030091
18	0.00134191423656699	0.00268382847313399	0.998658085763433
19	0.000190609220848364	0.000381218441696727	0.999809390779152
20	8.1028033268132e-05	0.000162056066536264	0.999918971966732
21	2.50820466470589e-05	5.01640932941178e-05	0.999974917953353
22	7.76144018733946e-06	1.55228803746789e-05	0.999992238559813
23	9.43547055425059e-06	1.88709411085012e-05	0.999990564529446
24	2.48579265945461e-05	4.97158531890921e-05	0.999975142073405
25	0.000935191182605203	0.00187038236521041	0.999064808817395
26	0.00519170557545799	0.0103834111509160	0.994808294424542
27	0.0166989238994287	0.0333978477988573	0.983301076100571
28	0.0123683478522021	0.0247366957044042	0.987631652147798
29	0.0100526233397734	0.0201052466795469	0.989947376660227
30	0.00747330827110629	0.0149466165422126	0.992526691728894
31	0.00441210531432477	0.00882421062864955	0.995587894685675
32	0.00465933489710667	0.00931866979421335	0.995340665102893
33	0.00643011678415346	0.0128602335683069	0.993569883215847
34	0.0152545862444550	0.0305091724889101	0.984745413755545
35	0.0501333282501822	0.100266656500364	0.949866671749818
36	0.261452271178027	0.522904542356055	0.738547728821973
37	0.557976425468011	0.884047149063979	0.442023574531989
38	0.75455849178661	0.490883016426781	0.245441508213391
39	0.879175544393209	0.241648911213582	0.120824455606791
40	0.976966599943315	0.0460668001133696	0.0230334000566848
41	0.99864846040118	0.00270307919764009	0.00135153959882005
42	0.998095054833004	0.00380989033399124	0.00190494516699562
43	0.995450289409835	0.0090994211803292	0.0045497105901646

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00551092296990859 & 0.0110218459398172 & 0.994489077030091 \tabularnewline
18 & 0.00134191423656699 & 0.00268382847313399 & 0.998658085763433 \tabularnewline
19 & 0.000190609220848364 & 0.000381218441696727 & 0.999809390779152 \tabularnewline
20 & 8.1028033268132e-05 & 0.000162056066536264 & 0.999918971966732 \tabularnewline
21 & 2.50820466470589e-05 & 5.01640932941178e-05 & 0.999974917953353 \tabularnewline
22 & 7.76144018733946e-06 & 1.55228803746789e-05 & 0.999992238559813 \tabularnewline
23 & 9.43547055425059e-06 & 1.88709411085012e-05 & 0.999990564529446 \tabularnewline
24 & 2.48579265945461e-05 & 4.97158531890921e-05 & 0.999975142073405 \tabularnewline
25 & 0.000935191182605203 & 0.00187038236521041 & 0.999064808817395 \tabularnewline
26 & 0.00519170557545799 & 0.0103834111509160 & 0.994808294424542 \tabularnewline
27 & 0.0166989238994287 & 0.0333978477988573 & 0.983301076100571 \tabularnewline
28 & 0.0123683478522021 & 0.0247366957044042 & 0.987631652147798 \tabularnewline
29 & 0.0100526233397734 & 0.0201052466795469 & 0.989947376660227 \tabularnewline
30 & 0.00747330827110629 & 0.0149466165422126 & 0.992526691728894 \tabularnewline
31 & 0.00441210531432477 & 0.00882421062864955 & 0.995587894685675 \tabularnewline
32 & 0.00465933489710667 & 0.00931866979421335 & 0.995340665102893 \tabularnewline
33 & 0.00643011678415346 & 0.0128602335683069 & 0.993569883215847 \tabularnewline
34 & 0.0152545862444550 & 0.0305091724889101 & 0.984745413755545 \tabularnewline
35 & 0.0501333282501822 & 0.100266656500364 & 0.949866671749818 \tabularnewline
36 & 0.261452271178027 & 0.522904542356055 & 0.738547728821973 \tabularnewline
37 & 0.557976425468011 & 0.884047149063979 & 0.442023574531989 \tabularnewline
38 & 0.75455849178661 & 0.490883016426781 & 0.245441508213391 \tabularnewline
39 & 0.879175544393209 & 0.241648911213582 & 0.120824455606791 \tabularnewline
40 & 0.976966599943315 & 0.0460668001133696 & 0.0230334000566848 \tabularnewline
41 & 0.99864846040118 & 0.00270307919764009 & 0.00135153959882005 \tabularnewline
42 & 0.998095054833004 & 0.00380989033399124 & 0.00190494516699562 \tabularnewline
43 & 0.995450289409835 & 0.0090994211803292 & 0.0045497105901646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57653&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]0.00551092296990859[/C][C]0.0110218459398172[/C][C]0.994489077030091[/C][/ROW]
[ROW][C]18[/C][C]0.00134191423656699[/C][C]0.00268382847313399[/C][C]0.998658085763433[/C][/ROW]
[ROW][C]19[/C][C]0.000190609220848364[/C][C]0.000381218441696727[/C][C]0.999809390779152[/C][/ROW]
[ROW][C]20[/C][C]8.1028033268132e-05[/C][C]0.000162056066536264[/C][C]0.999918971966732[/C][/ROW]
[ROW][C]21[/C][C]2.50820466470589e-05[/C][C]5.01640932941178e-05[/C][C]0.999974917953353[/C][/ROW]
[ROW][C]22[/C][C]7.76144018733946e-06[/C][C]1.55228803746789e-05[/C][C]0.999992238559813[/C][/ROW]
[ROW][C]23[/C][C]9.43547055425059e-06[/C][C]1.88709411085012e-05[/C][C]0.999990564529446[/C][/ROW]
[ROW][C]24[/C][C]2.48579265945461e-05[/C][C]4.97158531890921e-05[/C][C]0.999975142073405[/C][/ROW]
[ROW][C]25[/C][C]0.000935191182605203[/C][C]0.00187038236521041[/C][C]0.999064808817395[/C][/ROW]
[ROW][C]26[/C][C]0.00519170557545799[/C][C]0.0103834111509160[/C][C]0.994808294424542[/C][/ROW]
[ROW][C]27[/C][C]0.0166989238994287[/C][C]0.0333978477988573[/C][C]0.983301076100571[/C][/ROW]
[ROW][C]28[/C][C]0.0123683478522021[/C][C]0.0247366957044042[/C][C]0.987631652147798[/C][/ROW]
[ROW][C]29[/C][C]0.0100526233397734[/C][C]0.0201052466795469[/C][C]0.989947376660227[/C][/ROW]
[ROW][C]30[/C][C]0.00747330827110629[/C][C]0.0149466165422126[/C][C]0.992526691728894[/C][/ROW]
[ROW][C]31[/C][C]0.00441210531432477[/C][C]0.00882421062864955[/C][C]0.995587894685675[/C][/ROW]
[ROW][C]32[/C][C]0.00465933489710667[/C][C]0.00931866979421335[/C][C]0.995340665102893[/C][/ROW]
[ROW][C]33[/C][C]0.00643011678415346[/C][C]0.0128602335683069[/C][C]0.993569883215847[/C][/ROW]
[ROW][C]34[/C][C]0.0152545862444550[/C][C]0.0305091724889101[/C][C]0.984745413755545[/C][/ROW]
[ROW][C]35[/C][C]0.0501333282501822[/C][C]0.100266656500364[/C][C]0.949866671749818[/C][/ROW]
[ROW][C]36[/C][C]0.261452271178027[/C][C]0.522904542356055[/C][C]0.738547728821973[/C][/ROW]
[ROW][C]37[/C][C]0.557976425468011[/C][C]0.884047149063979[/C][C]0.442023574531989[/C][/ROW]
[ROW][C]38[/C][C]0.75455849178661[/C][C]0.490883016426781[/C][C]0.245441508213391[/C][/ROW]
[ROW][C]39[/C][C]0.879175544393209[/C][C]0.241648911213582[/C][C]0.120824455606791[/C][/ROW]
[ROW][C]40[/C][C]0.976966599943315[/C][C]0.0460668001133696[/C][C]0.0230334000566848[/C][/ROW]
[ROW][C]41[/C][C]0.99864846040118[/C][C]0.00270307919764009[/C][C]0.00135153959882005[/C][/ROW]
[ROW][C]42[/C][C]0.998095054833004[/C][C]0.00380989033399124[/C][C]0.00190494516699562[/C][/ROW]
[ROW][C]43[/C][C]0.995450289409835[/C][C]0.0090994211803292[/C][C]0.0045497105901646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57653&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57653&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	0.00551092296990859	0.0110218459398172	0.994489077030091
18	0.00134191423656699	0.00268382847313399	0.998658085763433
19	0.000190609220848364	0.000381218441696727	0.999809390779152
20	8.1028033268132e-05	0.000162056066536264	0.999918971966732
21	2.50820466470589e-05	5.01640932941178e-05	0.999974917953353
22	7.76144018733946e-06	1.55228803746789e-05	0.999992238559813
23	9.43547055425059e-06	1.88709411085012e-05	0.999990564529446
24	2.48579265945461e-05	4.97158531890921e-05	0.999975142073405
25	0.000935191182605203	0.00187038236521041	0.999064808817395
26	0.00519170557545799	0.0103834111509160	0.994808294424542
27	0.0166989238994287	0.0333978477988573	0.983301076100571
28	0.0123683478522021	0.0247366957044042	0.987631652147798
29	0.0100526233397734	0.0201052466795469	0.989947376660227
30	0.00747330827110629	0.0149466165422126	0.992526691728894
31	0.00441210531432477	0.00882421062864955	0.995587894685675
32	0.00465933489710667	0.00931866979421335	0.995340665102893
33	0.00643011678415346	0.0128602335683069	0.993569883215847
34	0.0152545862444550	0.0305091724889101	0.984745413755545
35	0.0501333282501822	0.100266656500364	0.949866671749818
36	0.261452271178027	0.522904542356055	0.738547728821973
37	0.557976425468011	0.884047149063979	0.442023574531989
38	0.75455849178661	0.490883016426781	0.245441508213391
39	0.879175544393209	0.241648911213582	0.120824455606791
40	0.976966599943315	0.0460668001133696	0.0230334000566848
41	0.99864846040118	0.00270307919764009	0.00135153959882005
42	0.998095054833004	0.00380989033399124	0.00190494516699562
43	0.995450289409835	0.0090994211803292	0.0045497105901646

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	13	0.481481481481481	NOK
5% type I error level	22	0.814814814814815	NOK
10% type I error level	22	0.814814814814815	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 & 13 & 0.481481481481481 & NOK \tabularnewline
5% type I error level & 22 & 0.814814814814815 & NOK \tabularnewline
10% type I error level & 22 & 0.814814814814815 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57653&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]13[/C][C]0.481481481481481[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]22[/C][C]0.814814814814815[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]22[/C][C]0.814814814814815[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57653&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57653&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	13	0.481481481481481	NOK
5% type I error level	22	0.814814814814815	NOK
10% type I error level	22	0.814814814814815	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