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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 05:03:12 -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/20/t12587187121gsoyokw53eqvkd.htm/, Retrieved Thu, 18 Apr 2024 16:22:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58061, Retrieved Thu, 18 Apr 2024 16:22:49 +0000

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No (this computation is public)

User-defined keywords

bhschhwsw7l2

Estimated Impact

147

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 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [WS7] [2009-11-20 12:03:12] [682632737e024f9e62885141c5f654cd] [Current]
-   P         [Multiple Regression] [Workshop 7] [2009-11-27 22:03:48] [4fe1472705bb0a32f118ba3ca90ffa8e] 
-   PD        [Multiple Regression] [Workshop 7] [2009-11-27 22:09:45] [4fe1472705bb0a32f118ba3ca90ffa8e] 

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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	3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58061&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]3 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=58061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58061&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 127.5625 + 11.7475000000000X[t] -4.92000000000005M1[t] -0.244000000000000M2[t] + 4.06399999999999M3[t] + 6.16999999999999M4[t] + 2.44999999999999M5[t] -1.52399999999999M6[t] -7.496M7[t] -3.76M8[t] -1.07600000000000M9[t] + 6.594M10[t] + 2.61200000000000M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  127.5625 +  11.7475000000000X[t] -4.92000000000005M1[t] -0.244000000000000M2[t] +  4.06399999999999M3[t] +  6.16999999999999M4[t] +  2.44999999999999M5[t] -1.52399999999999M6[t] -7.496M7[t] -3.76M8[t] -1.07600000000000M9[t] +  6.594M10[t] +  2.61200000000000M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58061&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  127.5625 +  11.7475000000000X[t] -4.92000000000005M1[t] -0.244000000000000M2[t] +  4.06399999999999M3[t] +  6.16999999999999M4[t] +  2.44999999999999M5[t] -1.52399999999999M6[t] -7.496M7[t] -3.76M8[t] -1.07600000000000M9[t] +  6.594M10[t] +  2.61200000000000M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58061&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 127.5625 + 11.7475000000000X[t] -4.92000000000005M1[t] -0.244000000000000M2[t] + 4.06399999999999M3[t] + 6.16999999999999M4[t] + 2.44999999999999M5[t] -1.52399999999999M6[t] -7.496M7[t] -3.76M8[t] -1.07600000000000M9[t] + 6.594M10[t] + 2.61200000000000M11[t] + 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)	127.5625	2.981426	42.7857	0	0
X	11.7475000000000	2.12959	5.5163	1e-06	1e-06
M1	-4.92000000000005	4.173128	-1.179	0.244343	0.122172
M2	-0.244000000000000	4.173128	-0.0585	0.953623	0.476811
M3	4.06399999999999	4.173128	0.9738	0.335117	0.167558
M4	6.16999999999999	4.173128	1.4785	0.145943	0.072972
M5	2.44999999999999	4.173128	0.5871	0.559953	0.279977
M6	-1.52399999999999	4.173128	-0.3652	0.716605	0.358303
M7	-7.496	4.173128	-1.7963	0.078883	0.039442
M8	-3.76	4.173128	-0.901	0.372181	0.18609
M9	-1.07600000000000	4.173128	-0.2578	0.797656	0.398828
M10	6.594	4.173128	1.5801	0.120789	0.060394
M11	2.61200000000000	4.173128	0.6259	0.534402	0.267201

\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) & 127.5625 & 2.981426 & 42.7857 & 0 & 0 \tabularnewline
X & 11.7475000000000 & 2.12959 & 5.5163 & 1e-06 & 1e-06 \tabularnewline
M1 & -4.92000000000005 & 4.173128 & -1.179 & 0.244343 & 0.122172 \tabularnewline
M2 & -0.244000000000000 & 4.173128 & -0.0585 & 0.953623 & 0.476811 \tabularnewline
M3 & 4.06399999999999 & 4.173128 & 0.9738 & 0.335117 & 0.167558 \tabularnewline
M4 & 6.16999999999999 & 4.173128 & 1.4785 & 0.145943 & 0.072972 \tabularnewline
M5 & 2.44999999999999 & 4.173128 & 0.5871 & 0.559953 & 0.279977 \tabularnewline
M6 & -1.52399999999999 & 4.173128 & -0.3652 & 0.716605 & 0.358303 \tabularnewline
M7 & -7.496 & 4.173128 & -1.7963 & 0.078883 & 0.039442 \tabularnewline
M8 & -3.76 & 4.173128 & -0.901 & 0.372181 & 0.18609 \tabularnewline
M9 & -1.07600000000000 & 4.173128 & -0.2578 & 0.797656 & 0.398828 \tabularnewline
M10 & 6.594 & 4.173128 & 1.5801 & 0.120789 & 0.060394 \tabularnewline
M11 & 2.61200000000000 & 4.173128 & 0.6259 & 0.534402 & 0.267201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58061&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]127.5625[/C][C]2.981426[/C][C]42.7857[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]11.7475000000000[/C][C]2.12959[/C][C]5.5163[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M1[/C][C]-4.92000000000005[/C][C]4.173128[/C][C]-1.179[/C][C]0.244343[/C][C]0.122172[/C][/ROW]
[ROW][C]M2[/C][C]-0.244000000000000[/C][C]4.173128[/C][C]-0.0585[/C][C]0.953623[/C][C]0.476811[/C][/ROW]
[ROW][C]M3[/C][C]4.06399999999999[/C][C]4.173128[/C][C]0.9738[/C][C]0.335117[/C][C]0.167558[/C][/ROW]
[ROW][C]M4[/C][C]6.16999999999999[/C][C]4.173128[/C][C]1.4785[/C][C]0.145943[/C][C]0.072972[/C][/ROW]
[ROW][C]M5[/C][C]2.44999999999999[/C][C]4.173128[/C][C]0.5871[/C][C]0.559953[/C][C]0.279977[/C][/ROW]
[ROW][C]M6[/C][C]-1.52399999999999[/C][C]4.173128[/C][C]-0.3652[/C][C]0.716605[/C][C]0.358303[/C][/ROW]
[ROW][C]M7[/C][C]-7.496[/C][C]4.173128[/C][C]-1.7963[/C][C]0.078883[/C][C]0.039442[/C][/ROW]
[ROW][C]M8[/C][C]-3.76[/C][C]4.173128[/C][C]-0.901[/C][C]0.372181[/C][C]0.18609[/C][/ROW]
[ROW][C]M9[/C][C]-1.07600000000000[/C][C]4.173128[/C][C]-0.2578[/C][C]0.797656[/C][C]0.398828[/C][/ROW]
[ROW][C]M10[/C][C]6.594[/C][C]4.173128[/C][C]1.5801[/C][C]0.120789[/C][C]0.060394[/C][/ROW]
[ROW][C]M11[/C][C]2.61200000000000[/C][C]4.173128[/C][C]0.6259[/C][C]0.534402[/C][C]0.267201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58061&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)	127.5625	2.981426	42.7857	0	0
X	11.7475000000000	2.12959	5.5163	1e-06	1e-06
M1	-4.92000000000005	4.173128	-1.179	0.244343	0.122172
M2	-0.244000000000000	4.173128	-0.0585	0.953623	0.476811
M3	4.06399999999999	4.173128	0.9738	0.335117	0.167558
M4	6.16999999999999	4.173128	1.4785	0.145943	0.072972
M5	2.44999999999999	4.173128	0.5871	0.559953	0.279977
M6	-1.52399999999999	4.173128	-0.3652	0.716605	0.358303
M7	-7.496	4.173128	-1.7963	0.078883	0.039442
M8	-3.76	4.173128	-0.901	0.372181	0.18609
M9	-1.07600000000000	4.173128	-0.2578	0.797656	0.398828
M10	6.594	4.173128	1.5801	0.120789	0.060394
M11	2.61200000000000	4.173128	0.6259	0.534402	0.267201

Multiple Linear Regression - Regression Statistics
Multiple R	0.732295623763541
R-squared	0.536256880583233
Adjusted R-squared	0.41785438200874
F-TEST (value)	4.52910104972019
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	8.29031147738801e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.59829394455289
Sum Squared Residuals	2046.2617

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.732295623763541 \tabularnewline
R-squared & 0.536256880583233 \tabularnewline
Adjusted R-squared & 0.41785438200874 \tabularnewline
F-TEST (value) & 4.52910104972019 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 8.29031147738801e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.59829394455289 \tabularnewline
Sum Squared Residuals & 2046.2617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58061&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.732295623763541[/C][/ROW]
[ROW][C]R-squared[/C][C]0.536256880583233[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.41785438200874[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.52910104972019[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]8.29031147738801e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]6.59829394455289[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2046.2617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58061&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58061&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	0.732295623763541
R-squared	0.536256880583233
Adjusted R-squared	0.41785438200874
F-TEST (value)	4.52910104972019
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	8.29031147738801e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.59829394455289
Sum Squared Residuals	2046.2617

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	126.51	122.642500000000	3.86749999999979
2	131.02	127.3185	3.7015
3	136.51	131.6265	4.88349999999999
4	138.04	133.7325	4.30749999999998
5	132.92	130.0125	2.90750000000000
6	129.61	126.0385	3.57150000000002
7	122.96	120.0665	2.89350000000001
8	124.04	123.8025	0.237500000000006
9	121.29	126.4865	-5.1965
10	124.56	134.1565	-9.5965
11	118.53	130.1745	-11.6445
12	113.14	127.5625	-14.4225
13	114.15	122.6425	-8.49249999999994
14	122.17	127.3185	-5.14849999999999
15	129.23	131.6265	-2.39650000000000
16	131.19	133.7325	-2.5425
17	129.12	130.0125	-0.892499999999997
18	128.28	126.0385	2.2415
19	126.83	120.0665	6.7635
20	138.13	123.8025	14.3275
21	140.52	126.4865	14.0335
22	146.83	134.1565	12.6735000000000
23	135.14	130.1745	4.96549999999999
24	131.84	127.5625	4.2775
25	125.7	122.6425	3.05750000000005
26	128.98	127.3185	1.6615
27	133.25	131.6265	1.62350000000001
28	136.76	133.7325	3.02750000000000
29	133.24	130.0125	3.22750000000001
30	128.54	126.0385	2.50149999999999
31	121.08	120.0665	1.01350000000000
32	120.23	123.8025	-3.57250000000000
33	119.08	126.4865	-7.4065
34	125.75	134.1565	-8.4065
35	126.89	130.1745	-3.28449999999999
36	126.6	127.5625	-0.962500000000005
37	121.89	122.6425	-0.752499999999949
38	123.44	127.3185	-3.87849999999999
39	126.46	131.6265	-5.1665
40	129.49	133.7325	-4.24249999999999
41	127.78	130.0125	-2.2325
42	125.29	126.0385	-0.748499999999996
43	119.02	120.0665	-1.04650000000001
44	119.96	123.8025	-3.84250000000001
45	122.86	126.4865	-3.6265
46	131.89	134.1565	-2.26650000000001
47	132.73	130.1745	2.55549999999999
48	135.01	127.5625	7.4475
49	136.71	134.39	2.32000000000005
50	142.73	139.066	3.66399999999999
51	144.43	143.374	1.05600000000000
52	144.93	145.48	-0.549999999999997
53	138.75	141.76	-3.01000000000001
54	130.22	137.786	-7.56600000000001
55	122.19	131.814	-9.62400000000001
56	128.4	135.55	-7.15
57	140.43	138.234	2.19600000000000
58	153.5	145.904	7.596
59	149.33	141.922	7.40800000000001
60	142.97	139.31	3.65999999999999

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 126.51 & 122.642500000000 & 3.86749999999979 \tabularnewline
2 & 131.02 & 127.3185 & 3.7015 \tabularnewline
3 & 136.51 & 131.6265 & 4.88349999999999 \tabularnewline
4 & 138.04 & 133.7325 & 4.30749999999998 \tabularnewline
5 & 132.92 & 130.0125 & 2.90750000000000 \tabularnewline
6 & 129.61 & 126.0385 & 3.57150000000002 \tabularnewline
7 & 122.96 & 120.0665 & 2.89350000000001 \tabularnewline
8 & 124.04 & 123.8025 & 0.237500000000006 \tabularnewline
9 & 121.29 & 126.4865 & -5.1965 \tabularnewline
10 & 124.56 & 134.1565 & -9.5965 \tabularnewline
11 & 118.53 & 130.1745 & -11.6445 \tabularnewline
12 & 113.14 & 127.5625 & -14.4225 \tabularnewline
13 & 114.15 & 122.6425 & -8.49249999999994 \tabularnewline
14 & 122.17 & 127.3185 & -5.14849999999999 \tabularnewline
15 & 129.23 & 131.6265 & -2.39650000000000 \tabularnewline
16 & 131.19 & 133.7325 & -2.5425 \tabularnewline
17 & 129.12 & 130.0125 & -0.892499999999997 \tabularnewline
18 & 128.28 & 126.0385 & 2.2415 \tabularnewline
19 & 126.83 & 120.0665 & 6.7635 \tabularnewline
20 & 138.13 & 123.8025 & 14.3275 \tabularnewline
21 & 140.52 & 126.4865 & 14.0335 \tabularnewline
22 & 146.83 & 134.1565 & 12.6735000000000 \tabularnewline
23 & 135.14 & 130.1745 & 4.96549999999999 \tabularnewline
24 & 131.84 & 127.5625 & 4.2775 \tabularnewline
25 & 125.7 & 122.6425 & 3.05750000000005 \tabularnewline
26 & 128.98 & 127.3185 & 1.6615 \tabularnewline
27 & 133.25 & 131.6265 & 1.62350000000001 \tabularnewline
28 & 136.76 & 133.7325 & 3.02750000000000 \tabularnewline
29 & 133.24 & 130.0125 & 3.22750000000001 \tabularnewline
30 & 128.54 & 126.0385 & 2.50149999999999 \tabularnewline
31 & 121.08 & 120.0665 & 1.01350000000000 \tabularnewline
32 & 120.23 & 123.8025 & -3.57250000000000 \tabularnewline
33 & 119.08 & 126.4865 & -7.4065 \tabularnewline
34 & 125.75 & 134.1565 & -8.4065 \tabularnewline
35 & 126.89 & 130.1745 & -3.28449999999999 \tabularnewline
36 & 126.6 & 127.5625 & -0.962500000000005 \tabularnewline
37 & 121.89 & 122.6425 & -0.752499999999949 \tabularnewline
38 & 123.44 & 127.3185 & -3.87849999999999 \tabularnewline
39 & 126.46 & 131.6265 & -5.1665 \tabularnewline
40 & 129.49 & 133.7325 & -4.24249999999999 \tabularnewline
41 & 127.78 & 130.0125 & -2.2325 \tabularnewline
42 & 125.29 & 126.0385 & -0.748499999999996 \tabularnewline
43 & 119.02 & 120.0665 & -1.04650000000001 \tabularnewline
44 & 119.96 & 123.8025 & -3.84250000000001 \tabularnewline
45 & 122.86 & 126.4865 & -3.6265 \tabularnewline
46 & 131.89 & 134.1565 & -2.26650000000001 \tabularnewline
47 & 132.73 & 130.1745 & 2.55549999999999 \tabularnewline
48 & 135.01 & 127.5625 & 7.4475 \tabularnewline
49 & 136.71 & 134.39 & 2.32000000000005 \tabularnewline
50 & 142.73 & 139.066 & 3.66399999999999 \tabularnewline
51 & 144.43 & 143.374 & 1.05600000000000 \tabularnewline
52 & 144.93 & 145.48 & -0.549999999999997 \tabularnewline
53 & 138.75 & 141.76 & -3.01000000000001 \tabularnewline
54 & 130.22 & 137.786 & -7.56600000000001 \tabularnewline
55 & 122.19 & 131.814 & -9.62400000000001 \tabularnewline
56 & 128.4 & 135.55 & -7.15 \tabularnewline
57 & 140.43 & 138.234 & 2.19600000000000 \tabularnewline
58 & 153.5 & 145.904 & 7.596 \tabularnewline
59 & 149.33 & 141.922 & 7.40800000000001 \tabularnewline
60 & 142.97 & 139.31 & 3.65999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58061&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]126.51[/C][C]122.642500000000[/C][C]3.86749999999979[/C][/ROW]
[ROW][C]2[/C][C]131.02[/C][C]127.3185[/C][C]3.7015[/C][/ROW]
[ROW][C]3[/C][C]136.51[/C][C]131.6265[/C][C]4.88349999999999[/C][/ROW]
[ROW][C]4[/C][C]138.04[/C][C]133.7325[/C][C]4.30749999999998[/C][/ROW]
[ROW][C]5[/C][C]132.92[/C][C]130.0125[/C][C]2.90750000000000[/C][/ROW]
[ROW][C]6[/C][C]129.61[/C][C]126.0385[/C][C]3.57150000000002[/C][/ROW]
[ROW][C]7[/C][C]122.96[/C][C]120.0665[/C][C]2.89350000000001[/C][/ROW]
[ROW][C]8[/C][C]124.04[/C][C]123.8025[/C][C]0.237500000000006[/C][/ROW]
[ROW][C]9[/C][C]121.29[/C][C]126.4865[/C][C]-5.1965[/C][/ROW]
[ROW][C]10[/C][C]124.56[/C][C]134.1565[/C][C]-9.5965[/C][/ROW]
[ROW][C]11[/C][C]118.53[/C][C]130.1745[/C][C]-11.6445[/C][/ROW]
[ROW][C]12[/C][C]113.14[/C][C]127.5625[/C][C]-14.4225[/C][/ROW]
[ROW][C]13[/C][C]114.15[/C][C]122.6425[/C][C]-8.49249999999994[/C][/ROW]
[ROW][C]14[/C][C]122.17[/C][C]127.3185[/C][C]-5.14849999999999[/C][/ROW]
[ROW][C]15[/C][C]129.23[/C][C]131.6265[/C][C]-2.39650000000000[/C][/ROW]
[ROW][C]16[/C][C]131.19[/C][C]133.7325[/C][C]-2.5425[/C][/ROW]
[ROW][C]17[/C][C]129.12[/C][C]130.0125[/C][C]-0.892499999999997[/C][/ROW]
[ROW][C]18[/C][C]128.28[/C][C]126.0385[/C][C]2.2415[/C][/ROW]
[ROW][C]19[/C][C]126.83[/C][C]120.0665[/C][C]6.7635[/C][/ROW]
[ROW][C]20[/C][C]138.13[/C][C]123.8025[/C][C]14.3275[/C][/ROW]
[ROW][C]21[/C][C]140.52[/C][C]126.4865[/C][C]14.0335[/C][/ROW]
[ROW][C]22[/C][C]146.83[/C][C]134.1565[/C][C]12.6735000000000[/C][/ROW]
[ROW][C]23[/C][C]135.14[/C][C]130.1745[/C][C]4.96549999999999[/C][/ROW]
[ROW][C]24[/C][C]131.84[/C][C]127.5625[/C][C]4.2775[/C][/ROW]
[ROW][C]25[/C][C]125.7[/C][C]122.6425[/C][C]3.05750000000005[/C][/ROW]
[ROW][C]26[/C][C]128.98[/C][C]127.3185[/C][C]1.6615[/C][/ROW]
[ROW][C]27[/C][C]133.25[/C][C]131.6265[/C][C]1.62350000000001[/C][/ROW]
[ROW][C]28[/C][C]136.76[/C][C]133.7325[/C][C]3.02750000000000[/C][/ROW]
[ROW][C]29[/C][C]133.24[/C][C]130.0125[/C][C]3.22750000000001[/C][/ROW]
[ROW][C]30[/C][C]128.54[/C][C]126.0385[/C][C]2.50149999999999[/C][/ROW]
[ROW][C]31[/C][C]121.08[/C][C]120.0665[/C][C]1.01350000000000[/C][/ROW]
[ROW][C]32[/C][C]120.23[/C][C]123.8025[/C][C]-3.57250000000000[/C][/ROW]
[ROW][C]33[/C][C]119.08[/C][C]126.4865[/C][C]-7.4065[/C][/ROW]
[ROW][C]34[/C][C]125.75[/C][C]134.1565[/C][C]-8.4065[/C][/ROW]
[ROW][C]35[/C][C]126.89[/C][C]130.1745[/C][C]-3.28449999999999[/C][/ROW]
[ROW][C]36[/C][C]126.6[/C][C]127.5625[/C][C]-0.962500000000005[/C][/ROW]
[ROW][C]37[/C][C]121.89[/C][C]122.6425[/C][C]-0.752499999999949[/C][/ROW]
[ROW][C]38[/C][C]123.44[/C][C]127.3185[/C][C]-3.87849999999999[/C][/ROW]
[ROW][C]39[/C][C]126.46[/C][C]131.6265[/C][C]-5.1665[/C][/ROW]
[ROW][C]40[/C][C]129.49[/C][C]133.7325[/C][C]-4.24249999999999[/C][/ROW]
[ROW][C]41[/C][C]127.78[/C][C]130.0125[/C][C]-2.2325[/C][/ROW]
[ROW][C]42[/C][C]125.29[/C][C]126.0385[/C][C]-0.748499999999996[/C][/ROW]
[ROW][C]43[/C][C]119.02[/C][C]120.0665[/C][C]-1.04650000000001[/C][/ROW]
[ROW][C]44[/C][C]119.96[/C][C]123.8025[/C][C]-3.84250000000001[/C][/ROW]
[ROW][C]45[/C][C]122.86[/C][C]126.4865[/C][C]-3.6265[/C][/ROW]
[ROW][C]46[/C][C]131.89[/C][C]134.1565[/C][C]-2.26650000000001[/C][/ROW]
[ROW][C]47[/C][C]132.73[/C][C]130.1745[/C][C]2.55549999999999[/C][/ROW]
[ROW][C]48[/C][C]135.01[/C][C]127.5625[/C][C]7.4475[/C][/ROW]
[ROW][C]49[/C][C]136.71[/C][C]134.39[/C][C]2.32000000000005[/C][/ROW]
[ROW][C]50[/C][C]142.73[/C][C]139.066[/C][C]3.66399999999999[/C][/ROW]
[ROW][C]51[/C][C]144.43[/C][C]143.374[/C][C]1.05600000000000[/C][/ROW]
[ROW][C]52[/C][C]144.93[/C][C]145.48[/C][C]-0.549999999999997[/C][/ROW]
[ROW][C]53[/C][C]138.75[/C][C]141.76[/C][C]-3.01000000000001[/C][/ROW]
[ROW][C]54[/C][C]130.22[/C][C]137.786[/C][C]-7.56600000000001[/C][/ROW]
[ROW][C]55[/C][C]122.19[/C][C]131.814[/C][C]-9.62400000000001[/C][/ROW]
[ROW][C]56[/C][C]128.4[/C][C]135.55[/C][C]-7.15[/C][/ROW]
[ROW][C]57[/C][C]140.43[/C][C]138.234[/C][C]2.19600000000000[/C][/ROW]
[ROW][C]58[/C][C]153.5[/C][C]145.904[/C][C]7.596[/C][/ROW]
[ROW][C]59[/C][C]149.33[/C][C]141.922[/C][C]7.40800000000001[/C][/ROW]
[ROW][C]60[/C][C]142.97[/C][C]139.31[/C][C]3.65999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58061&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58061&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	126.51	122.642500000000	3.86749999999979
2	131.02	127.3185	3.7015
3	136.51	131.6265	4.88349999999999
4	138.04	133.7325	4.30749999999998
5	132.92	130.0125	2.90750000000000
6	129.61	126.0385	3.57150000000002
7	122.96	120.0665	2.89350000000001
8	124.04	123.8025	0.237500000000006
9	121.29	126.4865	-5.1965
10	124.56	134.1565	-9.5965
11	118.53	130.1745	-11.6445
12	113.14	127.5625	-14.4225
13	114.15	122.6425	-8.49249999999994
14	122.17	127.3185	-5.14849999999999
15	129.23	131.6265	-2.39650000000000
16	131.19	133.7325	-2.5425
17	129.12	130.0125	-0.892499999999997
18	128.28	126.0385	2.2415
19	126.83	120.0665	6.7635
20	138.13	123.8025	14.3275
21	140.52	126.4865	14.0335
22	146.83	134.1565	12.6735000000000
23	135.14	130.1745	4.96549999999999
24	131.84	127.5625	4.2775
25	125.7	122.6425	3.05750000000005
26	128.98	127.3185	1.6615
27	133.25	131.6265	1.62350000000001
28	136.76	133.7325	3.02750000000000
29	133.24	130.0125	3.22750000000001
30	128.54	126.0385	2.50149999999999
31	121.08	120.0665	1.01350000000000
32	120.23	123.8025	-3.57250000000000
33	119.08	126.4865	-7.4065
34	125.75	134.1565	-8.4065
35	126.89	130.1745	-3.28449999999999
36	126.6	127.5625	-0.962500000000005
37	121.89	122.6425	-0.752499999999949
38	123.44	127.3185	-3.87849999999999
39	126.46	131.6265	-5.1665
40	129.49	133.7325	-4.24249999999999
41	127.78	130.0125	-2.2325
42	125.29	126.0385	-0.748499999999996
43	119.02	120.0665	-1.04650000000001
44	119.96	123.8025	-3.84250000000001
45	122.86	126.4865	-3.6265
46	131.89	134.1565	-2.26650000000001
47	132.73	130.1745	2.55549999999999
48	135.01	127.5625	7.4475
49	136.71	134.39	2.32000000000005
50	142.73	139.066	3.66399999999999
51	144.43	143.374	1.05600000000000
52	144.93	145.48	-0.549999999999997
53	138.75	141.76	-3.01000000000001
54	130.22	137.786	-7.56600000000001
55	122.19	131.814	-9.62400000000001
56	128.4	135.55	-7.15
57	140.43	138.234	2.19600000000000
58	153.5	145.904	7.596
59	149.33	141.922	7.40800000000001
60	142.97	139.31	3.65999999999999

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.73589639937194	0.528207201256119	0.264103600628059
17	0.603539824719157	0.792920350561685	0.396460175280843
18	0.458752981488703	0.917505962977406	0.541247018511297
19	0.375541227317468	0.751082454634936	0.624458772682532
20	0.682367960220411	0.635264079559179	0.317632039779589
21	0.94868332322866	0.102633353542679	0.0513166767713394
22	0.996559451538348	0.0068810969233039	0.00344054846165195
23	0.997629070347254	0.00474185930549153	0.00237092965274576
24	0.99838775514341	0.00322448971317968	0.00161224485658984
25	0.997019279825688	0.00596144034862386	0.00298072017431193
26	0.99413419584067	0.0117316083186604	0.00586580415933019
27	0.989852532112003	0.0202949357759933	0.0101474678879966
28	0.98554748860594	0.0289050227881215	0.0144525113940608
29	0.981090134390577	0.0378197312188465	0.0189098656094232
30	0.978179059425586	0.0436418811488287	0.0218209405744143
31	0.976358851621372	0.0472822967572561	0.0236411483786281
32	0.971231406979726	0.0575371860405482	0.0287685930202741
33	0.970107691548494	0.0597846169030112	0.0298923084515056
34	0.982164009575174	0.0356719808496525	0.0178359904248263
35	0.980878990040457	0.0382420199190857	0.0191210099595428
36	0.975431066859627	0.0491378662807456	0.0245689331403728
37	0.953904334884833	0.0921913302303335	0.0460956651151668
38	0.941453642718261	0.117092714563478	0.0585463572817389
39	0.923791785954189	0.152416428091622	0.0762082140458112
40	0.882686447296683	0.234627105406635	0.117313552703317
41	0.802323648473791	0.395352703052418	0.197676351526209
42	0.762456024258438	0.475087951483125	0.237543975741562
43	0.821297603078206	0.357404793843588	0.178702396921794
44	0.789858940659552	0.420282118680897	0.210141059340448

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.73589639937194 & 0.528207201256119 & 0.264103600628059 \tabularnewline
17 & 0.603539824719157 & 0.792920350561685 & 0.396460175280843 \tabularnewline
18 & 0.458752981488703 & 0.917505962977406 & 0.541247018511297 \tabularnewline
19 & 0.375541227317468 & 0.751082454634936 & 0.624458772682532 \tabularnewline
20 & 0.682367960220411 & 0.635264079559179 & 0.317632039779589 \tabularnewline
21 & 0.94868332322866 & 0.102633353542679 & 0.0513166767713394 \tabularnewline
22 & 0.996559451538348 & 0.0068810969233039 & 0.00344054846165195 \tabularnewline
23 & 0.997629070347254 & 0.00474185930549153 & 0.00237092965274576 \tabularnewline
24 & 0.99838775514341 & 0.00322448971317968 & 0.00161224485658984 \tabularnewline
25 & 0.997019279825688 & 0.00596144034862386 & 0.00298072017431193 \tabularnewline
26 & 0.99413419584067 & 0.0117316083186604 & 0.00586580415933019 \tabularnewline
27 & 0.989852532112003 & 0.0202949357759933 & 0.0101474678879966 \tabularnewline
28 & 0.98554748860594 & 0.0289050227881215 & 0.0144525113940608 \tabularnewline
29 & 0.981090134390577 & 0.0378197312188465 & 0.0189098656094232 \tabularnewline
30 & 0.978179059425586 & 0.0436418811488287 & 0.0218209405744143 \tabularnewline
31 & 0.976358851621372 & 0.0472822967572561 & 0.0236411483786281 \tabularnewline
32 & 0.971231406979726 & 0.0575371860405482 & 0.0287685930202741 \tabularnewline
33 & 0.970107691548494 & 0.0597846169030112 & 0.0298923084515056 \tabularnewline
34 & 0.982164009575174 & 0.0356719808496525 & 0.0178359904248263 \tabularnewline
35 & 0.980878990040457 & 0.0382420199190857 & 0.0191210099595428 \tabularnewline
36 & 0.975431066859627 & 0.0491378662807456 & 0.0245689331403728 \tabularnewline
37 & 0.953904334884833 & 0.0921913302303335 & 0.0460956651151668 \tabularnewline
38 & 0.941453642718261 & 0.117092714563478 & 0.0585463572817389 \tabularnewline
39 & 0.923791785954189 & 0.152416428091622 & 0.0762082140458112 \tabularnewline
40 & 0.882686447296683 & 0.234627105406635 & 0.117313552703317 \tabularnewline
41 & 0.802323648473791 & 0.395352703052418 & 0.197676351526209 \tabularnewline
42 & 0.762456024258438 & 0.475087951483125 & 0.237543975741562 \tabularnewline
43 & 0.821297603078206 & 0.357404793843588 & 0.178702396921794 \tabularnewline
44 & 0.789858940659552 & 0.420282118680897 & 0.210141059340448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58061&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]16[/C][C]0.73589639937194[/C][C]0.528207201256119[/C][C]0.264103600628059[/C][/ROW]
[ROW][C]17[/C][C]0.603539824719157[/C][C]0.792920350561685[/C][C]0.396460175280843[/C][/ROW]
[ROW][C]18[/C][C]0.458752981488703[/C][C]0.917505962977406[/C][C]0.541247018511297[/C][/ROW]
[ROW][C]19[/C][C]0.375541227317468[/C][C]0.751082454634936[/C][C]0.624458772682532[/C][/ROW]
[ROW][C]20[/C][C]0.682367960220411[/C][C]0.635264079559179[/C][C]0.317632039779589[/C][/ROW]
[ROW][C]21[/C][C]0.94868332322866[/C][C]0.102633353542679[/C][C]0.0513166767713394[/C][/ROW]
[ROW][C]22[/C][C]0.996559451538348[/C][C]0.0068810969233039[/C][C]0.00344054846165195[/C][/ROW]
[ROW][C]23[/C][C]0.997629070347254[/C][C]0.00474185930549153[/C][C]0.00237092965274576[/C][/ROW]
[ROW][C]24[/C][C]0.99838775514341[/C][C]0.00322448971317968[/C][C]0.00161224485658984[/C][/ROW]
[ROW][C]25[/C][C]0.997019279825688[/C][C]0.00596144034862386[/C][C]0.00298072017431193[/C][/ROW]
[ROW][C]26[/C][C]0.99413419584067[/C][C]0.0117316083186604[/C][C]0.00586580415933019[/C][/ROW]
[ROW][C]27[/C][C]0.989852532112003[/C][C]0.0202949357759933[/C][C]0.0101474678879966[/C][/ROW]
[ROW][C]28[/C][C]0.98554748860594[/C][C]0.0289050227881215[/C][C]0.0144525113940608[/C][/ROW]
[ROW][C]29[/C][C]0.981090134390577[/C][C]0.0378197312188465[/C][C]0.0189098656094232[/C][/ROW]
[ROW][C]30[/C][C]0.978179059425586[/C][C]0.0436418811488287[/C][C]0.0218209405744143[/C][/ROW]
[ROW][C]31[/C][C]0.976358851621372[/C][C]0.0472822967572561[/C][C]0.0236411483786281[/C][/ROW]
[ROW][C]32[/C][C]0.971231406979726[/C][C]0.0575371860405482[/C][C]0.0287685930202741[/C][/ROW]
[ROW][C]33[/C][C]0.970107691548494[/C][C]0.0597846169030112[/C][C]0.0298923084515056[/C][/ROW]
[ROW][C]34[/C][C]0.982164009575174[/C][C]0.0356719808496525[/C][C]0.0178359904248263[/C][/ROW]
[ROW][C]35[/C][C]0.980878990040457[/C][C]0.0382420199190857[/C][C]0.0191210099595428[/C][/ROW]
[ROW][C]36[/C][C]0.975431066859627[/C][C]0.0491378662807456[/C][C]0.0245689331403728[/C][/ROW]
[ROW][C]37[/C][C]0.953904334884833[/C][C]0.0921913302303335[/C][C]0.0460956651151668[/C][/ROW]
[ROW][C]38[/C][C]0.941453642718261[/C][C]0.117092714563478[/C][C]0.0585463572817389[/C][/ROW]
[ROW][C]39[/C][C]0.923791785954189[/C][C]0.152416428091622[/C][C]0.0762082140458112[/C][/ROW]
[ROW][C]40[/C][C]0.882686447296683[/C][C]0.234627105406635[/C][C]0.117313552703317[/C][/ROW]
[ROW][C]41[/C][C]0.802323648473791[/C][C]0.395352703052418[/C][C]0.197676351526209[/C][/ROW]
[ROW][C]42[/C][C]0.762456024258438[/C][C]0.475087951483125[/C][C]0.237543975741562[/C][/ROW]
[ROW][C]43[/C][C]0.821297603078206[/C][C]0.357404793843588[/C][C]0.178702396921794[/C][/ROW]
[ROW][C]44[/C][C]0.789858940659552[/C][C]0.420282118680897[/C][C]0.210141059340448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58061&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58061&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
16	0.73589639937194	0.528207201256119	0.264103600628059
17	0.603539824719157	0.792920350561685	0.396460175280843
18	0.458752981488703	0.917505962977406	0.541247018511297
19	0.375541227317468	0.751082454634936	0.624458772682532
20	0.682367960220411	0.635264079559179	0.317632039779589
21	0.94868332322866	0.102633353542679	0.0513166767713394
22	0.996559451538348	0.0068810969233039	0.00344054846165195
23	0.997629070347254	0.00474185930549153	0.00237092965274576
24	0.99838775514341	0.00322448971317968	0.00161224485658984
25	0.997019279825688	0.00596144034862386	0.00298072017431193
26	0.99413419584067	0.0117316083186604	0.00586580415933019
27	0.989852532112003	0.0202949357759933	0.0101474678879966
28	0.98554748860594	0.0289050227881215	0.0144525113940608
29	0.981090134390577	0.0378197312188465	0.0189098656094232
30	0.978179059425586	0.0436418811488287	0.0218209405744143
31	0.976358851621372	0.0472822967572561	0.0236411483786281
32	0.971231406979726	0.0575371860405482	0.0287685930202741
33	0.970107691548494	0.0597846169030112	0.0298923084515056
34	0.982164009575174	0.0356719808496525	0.0178359904248263
35	0.980878990040457	0.0382420199190857	0.0191210099595428
36	0.975431066859627	0.0491378662807456	0.0245689331403728
37	0.953904334884833	0.0921913302303335	0.0460956651151668
38	0.941453642718261	0.117092714563478	0.0585463572817389
39	0.923791785954189	0.152416428091622	0.0762082140458112
40	0.882686447296683	0.234627105406635	0.117313552703317
41	0.802323648473791	0.395352703052418	0.197676351526209
42	0.762456024258438	0.475087951483125	0.237543975741562
43	0.821297603078206	0.357404793843588	0.178702396921794
44	0.789858940659552	0.420282118680897	0.210141059340448

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	4	0.137931034482759	NOK
5% type I error level	13	0.448275862068966	NOK
10% type I error level	16	0.551724137931034	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 & 4 & 0.137931034482759 & NOK \tabularnewline
5% type I error level & 13 & 0.448275862068966 & NOK \tabularnewline
10% type I error level & 16 & 0.551724137931034 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58061&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]4[/C][C]0.137931034482759[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]13[/C][C]0.448275862068966[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]16[/C][C]0.551724137931034[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58061&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58061&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	4	0.137931034482759	NOK
5% type I error level	13	0.448275862068966	NOK
10% type I error level	16	0.551724137931034	NOK

Figure 1

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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 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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