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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sat, 18 Dec 2010 17:21:06 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292692869aoct1vluv5s1faw.htm/, Retrieved Tue, 30 Apr 2024 02:42:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112114, Retrieved Tue, 30 Apr 2024 02:42:16 +0000

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159

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-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
F  MPD  [Multiple Regression] [] [2010-11-26 10:13:34] [8a9a6f7c332640af31ddca253a8ded58]
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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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112114&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112114&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation
cultuurbesteding[t] = + 100.675 -0.0901666666666308M1[t] -0.0353333333333356M2[t] -0.298500000000003M3[t] -0.109666666666670M4[t] -0.394833333333334M5[t] -0.384000000000005M6[t] -0.543166666666667M7[t] -0.488333333333337M8[t] + 0.514500000000001M9[t] + 0.391333333333330M10[t] + 0.148166666666668M11[t] + 0.327166666666666t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
cultuurbesteding[t] =  +  100.675 -0.0901666666666308M1[t] -0.0353333333333356M2[t] -0.298500000000003M3[t] -0.109666666666670M4[t] -0.394833333333334M5[t] -0.384000000000005M6[t] -0.543166666666667M7[t] -0.488333333333337M8[t] +  0.514500000000001M9[t] +  0.391333333333330M10[t] +  0.148166666666668M11[t] +  0.327166666666666t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112114&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]cultuurbesteding[t] =  +  100.675 -0.0901666666666308M1[t] -0.0353333333333356M2[t] -0.298500000000003M3[t] -0.109666666666670M4[t] -0.394833333333334M5[t] -0.384000000000005M6[t] -0.543166666666667M7[t] -0.488333333333337M8[t] +  0.514500000000001M9[t] +  0.391333333333330M10[t] +  0.148166666666668M11[t] +  0.327166666666666t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112114&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
cultuurbesteding[t] = + 100.675 -0.0901666666666308M1[t] -0.0353333333333356M2[t] -0.298500000000003M3[t] -0.109666666666670M4[t] -0.394833333333334M5[t] -0.384000000000005M6[t] -0.543166666666667M7[t] -0.488333333333337M8[t] + 0.514500000000001M9[t] + 0.391333333333330M10[t] + 0.148166666666668M11[t] + 0.327166666666666t + 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)	100.675	0.331993	303.2441	0	0
M1	-0.0901666666666308	0.404369	-0.223	0.824537	0.412269
M2	-0.0353333333333356	0.404125	-0.0874	0.930708	0.465354
M3	-0.298500000000003	0.403936	-0.739	0.463674	0.231837
M4	-0.109666666666670	0.403801	-0.2716	0.787155	0.393578
M5	-0.394833333333334	0.403719	-0.978	0.333195	0.166598
M6	-0.384000000000005	0.403692	-0.9512	0.346464	0.173232
M7	-0.543166666666667	0.403719	-1.3454	0.185089	0.092545
M8	-0.488333333333337	0.403801	-1.2093	0.23271	0.116355
M9	0.514500000000001	0.403936	1.2737	0.209162	0.104581
M10	0.391333333333330	0.404125	0.9683	0.337936	0.168968
M11	0.148166666666668	0.404369	0.3664	0.715736	0.357868
t	0.327166666666666	0.004676	69.9608	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) & 100.675 & 0.331993 & 303.2441 & 0 & 0 \tabularnewline
M1 & -0.0901666666666308 & 0.404369 & -0.223 & 0.824537 & 0.412269 \tabularnewline
M2 & -0.0353333333333356 & 0.404125 & -0.0874 & 0.930708 & 0.465354 \tabularnewline
M3 & -0.298500000000003 & 0.403936 & -0.739 & 0.463674 & 0.231837 \tabularnewline
M4 & -0.109666666666670 & 0.403801 & -0.2716 & 0.787155 & 0.393578 \tabularnewline
M5 & -0.394833333333334 & 0.403719 & -0.978 & 0.333195 & 0.166598 \tabularnewline
M6 & -0.384000000000005 & 0.403692 & -0.9512 & 0.346464 & 0.173232 \tabularnewline
M7 & -0.543166666666667 & 0.403719 & -1.3454 & 0.185089 & 0.092545 \tabularnewline
M8 & -0.488333333333337 & 0.403801 & -1.2093 & 0.23271 & 0.116355 \tabularnewline
M9 & 0.514500000000001 & 0.403936 & 1.2737 & 0.209162 & 0.104581 \tabularnewline
M10 & 0.391333333333330 & 0.404125 & 0.9683 & 0.337936 & 0.168968 \tabularnewline
M11 & 0.148166666666668 & 0.404369 & 0.3664 & 0.715736 & 0.357868 \tabularnewline
t & 0.327166666666666 & 0.004676 & 69.9608 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112114&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]100.675[/C][C]0.331993[/C][C]303.2441[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.0901666666666308[/C][C]0.404369[/C][C]-0.223[/C][C]0.824537[/C][C]0.412269[/C][/ROW]
[ROW][C]M2[/C][C]-0.0353333333333356[/C][C]0.404125[/C][C]-0.0874[/C][C]0.930708[/C][C]0.465354[/C][/ROW]
[ROW][C]M3[/C][C]-0.298500000000003[/C][C]0.403936[/C][C]-0.739[/C][C]0.463674[/C][C]0.231837[/C][/ROW]
[ROW][C]M4[/C][C]-0.109666666666670[/C][C]0.403801[/C][C]-0.2716[/C][C]0.787155[/C][C]0.393578[/C][/ROW]
[ROW][C]M5[/C][C]-0.394833333333334[/C][C]0.403719[/C][C]-0.978[/C][C]0.333195[/C][C]0.166598[/C][/ROW]
[ROW][C]M6[/C][C]-0.384000000000005[/C][C]0.403692[/C][C]-0.9512[/C][C]0.346464[/C][C]0.173232[/C][/ROW]
[ROW][C]M7[/C][C]-0.543166666666667[/C][C]0.403719[/C][C]-1.3454[/C][C]0.185089[/C][C]0.092545[/C][/ROW]
[ROW][C]M8[/C][C]-0.488333333333337[/C][C]0.403801[/C][C]-1.2093[/C][C]0.23271[/C][C]0.116355[/C][/ROW]
[ROW][C]M9[/C][C]0.514500000000001[/C][C]0.403936[/C][C]1.2737[/C][C]0.209162[/C][C]0.104581[/C][/ROW]
[ROW][C]M10[/C][C]0.391333333333330[/C][C]0.404125[/C][C]0.9683[/C][C]0.337936[/C][C]0.168968[/C][/ROW]
[ROW][C]M11[/C][C]0.148166666666668[/C][C]0.404369[/C][C]0.3664[/C][C]0.715736[/C][C]0.357868[/C][/ROW]
[ROW][C]t[/C][C]0.327166666666666[/C][C]0.004676[/C][C]69.9608[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112114&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112114&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)	100.675	0.331993	303.2441	0	0
M1	-0.0901666666666308	0.404369	-0.223	0.824537	0.412269
M2	-0.0353333333333356	0.404125	-0.0874	0.930708	0.465354
M3	-0.298500000000003	0.403936	-0.739	0.463674	0.231837
M4	-0.109666666666670	0.403801	-0.2716	0.787155	0.393578
M5	-0.394833333333334	0.403719	-0.978	0.333195	0.166598
M6	-0.384000000000005	0.403692	-0.9512	0.346464	0.173232
M7	-0.543166666666667	0.403719	-1.3454	0.185089	0.092545
M8	-0.488333333333337	0.403801	-1.2093	0.23271	0.116355
M9	0.514500000000001	0.403936	1.2737	0.209162	0.104581
M10	0.391333333333330	0.404125	0.9683	0.337936	0.168968
M11	0.148166666666668	0.404369	0.3664	0.715736	0.357868
t	0.327166666666666	0.004676	69.9608	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.99553293301821
R-squared	0.991085820723838
Adjusted R-squared	0.988760382651796
F-TEST (value)	426.193168779355
F-TEST (DF numerator)	12
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.60178899956713
Sum Squared Residuals	16.6589000000003

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99553293301821 \tabularnewline
R-squared & 0.991085820723838 \tabularnewline
Adjusted R-squared & 0.988760382651796 \tabularnewline
F-TEST (value) & 426.193168779355 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.60178899956713 \tabularnewline
Sum Squared Residuals & 16.6589000000003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112114&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99553293301821[/C][/ROW]
[ROW][C]R-squared[/C][C]0.991085820723838[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.988760382651796[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]426.193168779355[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/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]0.60178899956713[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]16.6589000000003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112114&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112114&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	0.99553293301821
R-squared	0.991085820723838
Adjusted R-squared	0.988760382651796
F-TEST (value)	426.193168779355
F-TEST (DF numerator)	12
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.60178899956713
Sum Squared Residuals	16.6589000000003

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	101.76	100.912000000000	0.848000000000147
2	102.37	101.294	1.07600000000000
3	102.38	101.358	1.02199999999999
4	102.86	101.874	0.985999999999992
5	102.87	101.916	0.954
6	102.92	102.254	0.665999999999998
7	102.95	102.422	0.527999999999995
8	103.02	102.804	0.215999999999990
9	104.08	104.134	-0.0540000000000092
10	104.16	104.338	-0.178000000000008
11	104.24	104.422	-0.182000000000011
12	104.33	104.601	-0.271000000000009
13	104.73	104.838	-0.108000000000037
14	104.86	105.22	-0.360000000000007
15	105.03	105.284	-0.254000000000003
16	105.62	105.8	-0.179999999999998
17	105.63	105.842	-0.212000000000011
18	105.63	106.18	-0.550000000000006
19	105.94	106.348	-0.408000000000007
20	106.61	106.73	-0.120000000000003
21	107.69	108.06	-0.370000000000008
22	107.78	108.264	-0.484000000000001
23	107.93	108.348	-0.417999999999998
24	108.48	108.527	-0.0469999999999995
25	108.14	108.764	-0.62400000000004
26	108.48	109.146	-0.665999999999997
27	108.48	109.21	-0.729999999999996
28	108.89	109.726	-0.836
29	108.93	109.768	-0.837999999999994
30	109.21	110.106	-0.896000000000002
31	109.47	110.274	-0.804000000000001
32	109.8	110.656	-0.856000000000001
33	111.73	111.986	-0.255999999999999
34	111.85	112.19	-0.340000000000004
35	112.12	112.274	-0.153999999999996
36	112.15	112.453	-0.302999999999994
37	112.17	112.69	-0.520000000000035
38	112.67	113.072	-0.401999999999996
39	112.8	113.136	-0.336
40	113.44	113.652	-0.211999999999997
41	113.53	113.694	-0.163999999999995
42	114.53	114.032	0.498000000000008
43	114.51	114.2	0.310000000000009
44	115.05	114.582	0.468000000000006
45	116.67	115.912	0.758000000000002
46	117.07	116.116	0.953999999999998
47	116.92	116.2	0.72
48	117	116.379	0.621000000000003
49	117.02	116.616	0.403999999999965
50	117.35	116.998	0.352000000000002
51	117.36	117.062	0.298000000000010
52	117.82	117.578	0.242000000000003
53	117.88	117.62	0.260000000000001
54	118.24	117.958	0.282000000000003
55	118.5	118.126	0.374000000000004
56	118.8	118.508	0.292000000000007
57	119.76	119.838	-0.0779999999999863
58	120.09	120.042	0.0480000000000138
59	120.16	120.126	0.034000000000004

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 101.76 & 100.912000000000 & 0.848000000000147 \tabularnewline
2 & 102.37 & 101.294 & 1.07600000000000 \tabularnewline
3 & 102.38 & 101.358 & 1.02199999999999 \tabularnewline
4 & 102.86 & 101.874 & 0.985999999999992 \tabularnewline
5 & 102.87 & 101.916 & 0.954 \tabularnewline
6 & 102.92 & 102.254 & 0.665999999999998 \tabularnewline
7 & 102.95 & 102.422 & 0.527999999999995 \tabularnewline
8 & 103.02 & 102.804 & 0.215999999999990 \tabularnewline
9 & 104.08 & 104.134 & -0.0540000000000092 \tabularnewline
10 & 104.16 & 104.338 & -0.178000000000008 \tabularnewline
11 & 104.24 & 104.422 & -0.182000000000011 \tabularnewline
12 & 104.33 & 104.601 & -0.271000000000009 \tabularnewline
13 & 104.73 & 104.838 & -0.108000000000037 \tabularnewline
14 & 104.86 & 105.22 & -0.360000000000007 \tabularnewline
15 & 105.03 & 105.284 & -0.254000000000003 \tabularnewline
16 & 105.62 & 105.8 & -0.179999999999998 \tabularnewline
17 & 105.63 & 105.842 & -0.212000000000011 \tabularnewline
18 & 105.63 & 106.18 & -0.550000000000006 \tabularnewline
19 & 105.94 & 106.348 & -0.408000000000007 \tabularnewline
20 & 106.61 & 106.73 & -0.120000000000003 \tabularnewline
21 & 107.69 & 108.06 & -0.370000000000008 \tabularnewline
22 & 107.78 & 108.264 & -0.484000000000001 \tabularnewline
23 & 107.93 & 108.348 & -0.417999999999998 \tabularnewline
24 & 108.48 & 108.527 & -0.0469999999999995 \tabularnewline
25 & 108.14 & 108.764 & -0.62400000000004 \tabularnewline
26 & 108.48 & 109.146 & -0.665999999999997 \tabularnewline
27 & 108.48 & 109.21 & -0.729999999999996 \tabularnewline
28 & 108.89 & 109.726 & -0.836 \tabularnewline
29 & 108.93 & 109.768 & -0.837999999999994 \tabularnewline
30 & 109.21 & 110.106 & -0.896000000000002 \tabularnewline
31 & 109.47 & 110.274 & -0.804000000000001 \tabularnewline
32 & 109.8 & 110.656 & -0.856000000000001 \tabularnewline
33 & 111.73 & 111.986 & -0.255999999999999 \tabularnewline
34 & 111.85 & 112.19 & -0.340000000000004 \tabularnewline
35 & 112.12 & 112.274 & -0.153999999999996 \tabularnewline
36 & 112.15 & 112.453 & -0.302999999999994 \tabularnewline
37 & 112.17 & 112.69 & -0.520000000000035 \tabularnewline
38 & 112.67 & 113.072 & -0.401999999999996 \tabularnewline
39 & 112.8 & 113.136 & -0.336 \tabularnewline
40 & 113.44 & 113.652 & -0.211999999999997 \tabularnewline
41 & 113.53 & 113.694 & -0.163999999999995 \tabularnewline
42 & 114.53 & 114.032 & 0.498000000000008 \tabularnewline
43 & 114.51 & 114.2 & 0.310000000000009 \tabularnewline
44 & 115.05 & 114.582 & 0.468000000000006 \tabularnewline
45 & 116.67 & 115.912 & 0.758000000000002 \tabularnewline
46 & 117.07 & 116.116 & 0.953999999999998 \tabularnewline
47 & 116.92 & 116.2 & 0.72 \tabularnewline
48 & 117 & 116.379 & 0.621000000000003 \tabularnewline
49 & 117.02 & 116.616 & 0.403999999999965 \tabularnewline
50 & 117.35 & 116.998 & 0.352000000000002 \tabularnewline
51 & 117.36 & 117.062 & 0.298000000000010 \tabularnewline
52 & 117.82 & 117.578 & 0.242000000000003 \tabularnewline
53 & 117.88 & 117.62 & 0.260000000000001 \tabularnewline
54 & 118.24 & 117.958 & 0.282000000000003 \tabularnewline
55 & 118.5 & 118.126 & 0.374000000000004 \tabularnewline
56 & 118.8 & 118.508 & 0.292000000000007 \tabularnewline
57 & 119.76 & 119.838 & -0.0779999999999863 \tabularnewline
58 & 120.09 & 120.042 & 0.0480000000000138 \tabularnewline
59 & 120.16 & 120.126 & 0.034000000000004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112114&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]101.76[/C][C]100.912000000000[/C][C]0.848000000000147[/C][/ROW]
[ROW][C]2[/C][C]102.37[/C][C]101.294[/C][C]1.07600000000000[/C][/ROW]
[ROW][C]3[/C][C]102.38[/C][C]101.358[/C][C]1.02199999999999[/C][/ROW]
[ROW][C]4[/C][C]102.86[/C][C]101.874[/C][C]0.985999999999992[/C][/ROW]
[ROW][C]5[/C][C]102.87[/C][C]101.916[/C][C]0.954[/C][/ROW]
[ROW][C]6[/C][C]102.92[/C][C]102.254[/C][C]0.665999999999998[/C][/ROW]
[ROW][C]7[/C][C]102.95[/C][C]102.422[/C][C]0.527999999999995[/C][/ROW]
[ROW][C]8[/C][C]103.02[/C][C]102.804[/C][C]0.215999999999990[/C][/ROW]
[ROW][C]9[/C][C]104.08[/C][C]104.134[/C][C]-0.0540000000000092[/C][/ROW]
[ROW][C]10[/C][C]104.16[/C][C]104.338[/C][C]-0.178000000000008[/C][/ROW]
[ROW][C]11[/C][C]104.24[/C][C]104.422[/C][C]-0.182000000000011[/C][/ROW]
[ROW][C]12[/C][C]104.33[/C][C]104.601[/C][C]-0.271000000000009[/C][/ROW]
[ROW][C]13[/C][C]104.73[/C][C]104.838[/C][C]-0.108000000000037[/C][/ROW]
[ROW][C]14[/C][C]104.86[/C][C]105.22[/C][C]-0.360000000000007[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]105.284[/C][C]-0.254000000000003[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.8[/C][C]-0.179999999999998[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.842[/C][C]-0.212000000000011[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]106.18[/C][C]-0.550000000000006[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]106.348[/C][C]-0.408000000000007[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.73[/C][C]-0.120000000000003[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]108.06[/C][C]-0.370000000000008[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]108.264[/C][C]-0.484000000000001[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]108.348[/C][C]-0.417999999999998[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.527[/C][C]-0.0469999999999995[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]108.764[/C][C]-0.62400000000004[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]109.146[/C][C]-0.665999999999997[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]109.21[/C][C]-0.729999999999996[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]109.726[/C][C]-0.836[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]109.768[/C][C]-0.837999999999994[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]110.106[/C][C]-0.896000000000002[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]110.274[/C][C]-0.804000000000001[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]110.656[/C][C]-0.856000000000001[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]111.986[/C][C]-0.255999999999999[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]112.19[/C][C]-0.340000000000004[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]112.274[/C][C]-0.153999999999996[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]112.453[/C][C]-0.302999999999994[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]112.69[/C][C]-0.520000000000035[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]113.072[/C][C]-0.401999999999996[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]113.136[/C][C]-0.336[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]113.652[/C][C]-0.211999999999997[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]113.694[/C][C]-0.163999999999995[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]114.032[/C][C]0.498000000000008[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.2[/C][C]0.310000000000009[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]114.582[/C][C]0.468000000000006[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]115.912[/C][C]0.758000000000002[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]116.116[/C][C]0.953999999999998[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]116.2[/C][C]0.72[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]116.379[/C][C]0.621000000000003[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]116.616[/C][C]0.403999999999965[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]116.998[/C][C]0.352000000000002[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]117.062[/C][C]0.298000000000010[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]117.578[/C][C]0.242000000000003[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]117.62[/C][C]0.260000000000001[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]117.958[/C][C]0.282000000000003[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.126[/C][C]0.374000000000004[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]118.508[/C][C]0.292000000000007[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.838[/C][C]-0.0779999999999863[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]120.042[/C][C]0.0480000000000138[/C][/ROW]
[ROW][C]59[/C][C]120.16[/C][C]120.126[/C][C]0.034000000000004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112114&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112114&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	101.76	100.912000000000	0.848000000000147
2	102.37	101.294	1.07600000000000
3	102.38	101.358	1.02199999999999
4	102.86	101.874	0.985999999999992
5	102.87	101.916	0.954
6	102.92	102.254	0.665999999999998
7	102.95	102.422	0.527999999999995
8	103.02	102.804	0.215999999999990
9	104.08	104.134	-0.0540000000000092
10	104.16	104.338	-0.178000000000008
11	104.24	104.422	-0.182000000000011
12	104.33	104.601	-0.271000000000009
13	104.73	104.838	-0.108000000000037
14	104.86	105.22	-0.360000000000007
15	105.03	105.284	-0.254000000000003
16	105.62	105.8	-0.179999999999998
17	105.63	105.842	-0.212000000000011
18	105.63	106.18	-0.550000000000006
19	105.94	106.348	-0.408000000000007
20	106.61	106.73	-0.120000000000003
21	107.69	108.06	-0.370000000000008
22	107.78	108.264	-0.484000000000001
23	107.93	108.348	-0.417999999999998
24	108.48	108.527	-0.0469999999999995
25	108.14	108.764	-0.62400000000004
26	108.48	109.146	-0.665999999999997
27	108.48	109.21	-0.729999999999996
28	108.89	109.726	-0.836
29	108.93	109.768	-0.837999999999994
30	109.21	110.106	-0.896000000000002
31	109.47	110.274	-0.804000000000001
32	109.8	110.656	-0.856000000000001
33	111.73	111.986	-0.255999999999999
34	111.85	112.19	-0.340000000000004
35	112.12	112.274	-0.153999999999996
36	112.15	112.453	-0.302999999999994
37	112.17	112.69	-0.520000000000035
38	112.67	113.072	-0.401999999999996
39	112.8	113.136	-0.336
40	113.44	113.652	-0.211999999999997
41	113.53	113.694	-0.163999999999995
42	114.53	114.032	0.498000000000008
43	114.51	114.2	0.310000000000009
44	115.05	114.582	0.468000000000006
45	116.67	115.912	0.758000000000002
46	117.07	116.116	0.953999999999998
47	116.92	116.2	0.72
48	117	116.379	0.621000000000003
49	117.02	116.616	0.403999999999965
50	117.35	116.998	0.352000000000002
51	117.36	117.062	0.298000000000010
52	117.82	117.578	0.242000000000003
53	117.88	117.62	0.260000000000001
54	118.24	117.958	0.282000000000003
55	118.5	118.126	0.374000000000004
56	118.8	118.508	0.292000000000007
57	119.76	119.838	-0.0779999999999863
58	120.09	120.042	0.0480000000000138
59	120.16	120.126	0.034000000000004

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.0547296926559853	0.109459385311971	0.945270307344015
17	0.0177728872203434	0.0355457744406867	0.982227112779657
18	0.00464095716551273	0.00928191433102546	0.995359042834487
19	0.00351427593044907	0.00702855186089814	0.99648572406955
20	0.0799763296435809	0.159952659287162	0.920023670356419
21	0.150667061567439	0.301334123134879	0.84933293843256
22	0.181333272846476	0.362666545692952	0.818666727153524
23	0.204600533398098	0.409201066796196	0.795399466601902
24	0.373371608378269	0.746743216756537	0.626628391621731
25	0.282238578186767	0.564477156373535	0.717761421813233
26	0.201369066520644	0.402738133041288	0.798630933479356
27	0.13597917911152	0.27195835822304	0.86402082088848
28	0.0912155995052147	0.182431199010429	0.908784400494785
29	0.0587392681024176	0.117478536204835	0.941260731897582
30	0.0513046301744405	0.102609260348881	0.94869536982556
31	0.0451886975235919	0.0903773950471838	0.954811302476408
32	0.0502919689068841	0.100583937813768	0.949708031093116
33	0.111110422671916	0.222220845343833	0.888889577328084
34	0.191021648544968	0.382043297089935	0.808978351455032
35	0.255702909352402	0.511405818704805	0.744297090647598
36	0.319105035321378	0.638210070642757	0.680894964678622
37	0.40091302998738	0.80182605997476	0.59908697001262
38	0.488718424464117	0.977436848928235	0.511281575535883
39	0.588117477650843	0.823765044698315	0.411882522349157
40	0.676421363415406	0.647157273169187	0.323578636584594
41	0.827958548305437	0.344082903389126	0.172041451694563
42	0.820259252819365	0.35948149436127	0.179740747180635
43	0.893445697421056	0.213108605157889	0.106554302578944

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0547296926559853 & 0.109459385311971 & 0.945270307344015 \tabularnewline
17 & 0.0177728872203434 & 0.0355457744406867 & 0.982227112779657 \tabularnewline
18 & 0.00464095716551273 & 0.00928191433102546 & 0.995359042834487 \tabularnewline
19 & 0.00351427593044907 & 0.00702855186089814 & 0.99648572406955 \tabularnewline
20 & 0.0799763296435809 & 0.159952659287162 & 0.920023670356419 \tabularnewline
21 & 0.150667061567439 & 0.301334123134879 & 0.84933293843256 \tabularnewline
22 & 0.181333272846476 & 0.362666545692952 & 0.818666727153524 \tabularnewline
23 & 0.204600533398098 & 0.409201066796196 & 0.795399466601902 \tabularnewline
24 & 0.373371608378269 & 0.746743216756537 & 0.626628391621731 \tabularnewline
25 & 0.282238578186767 & 0.564477156373535 & 0.717761421813233 \tabularnewline
26 & 0.201369066520644 & 0.402738133041288 & 0.798630933479356 \tabularnewline
27 & 0.13597917911152 & 0.27195835822304 & 0.86402082088848 \tabularnewline
28 & 0.0912155995052147 & 0.182431199010429 & 0.908784400494785 \tabularnewline
29 & 0.0587392681024176 & 0.117478536204835 & 0.941260731897582 \tabularnewline
30 & 0.0513046301744405 & 0.102609260348881 & 0.94869536982556 \tabularnewline
31 & 0.0451886975235919 & 0.0903773950471838 & 0.954811302476408 \tabularnewline
32 & 0.0502919689068841 & 0.100583937813768 & 0.949708031093116 \tabularnewline
33 & 0.111110422671916 & 0.222220845343833 & 0.888889577328084 \tabularnewline
34 & 0.191021648544968 & 0.382043297089935 & 0.808978351455032 \tabularnewline
35 & 0.255702909352402 & 0.511405818704805 & 0.744297090647598 \tabularnewline
36 & 0.319105035321378 & 0.638210070642757 & 0.680894964678622 \tabularnewline
37 & 0.40091302998738 & 0.80182605997476 & 0.59908697001262 \tabularnewline
38 & 0.488718424464117 & 0.977436848928235 & 0.511281575535883 \tabularnewline
39 & 0.588117477650843 & 0.823765044698315 & 0.411882522349157 \tabularnewline
40 & 0.676421363415406 & 0.647157273169187 & 0.323578636584594 \tabularnewline
41 & 0.827958548305437 & 0.344082903389126 & 0.172041451694563 \tabularnewline
42 & 0.820259252819365 & 0.35948149436127 & 0.179740747180635 \tabularnewline
43 & 0.893445697421056 & 0.213108605157889 & 0.106554302578944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112114&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]0.0547296926559853[/C][C]0.109459385311971[/C][C]0.945270307344015[/C][/ROW]
[ROW][C]17[/C][C]0.0177728872203434[/C][C]0.0355457744406867[/C][C]0.982227112779657[/C][/ROW]
[ROW][C]18[/C][C]0.00464095716551273[/C][C]0.00928191433102546[/C][C]0.995359042834487[/C][/ROW]
[ROW][C]19[/C][C]0.00351427593044907[/C][C]0.00702855186089814[/C][C]0.99648572406955[/C][/ROW]
[ROW][C]20[/C][C]0.0799763296435809[/C][C]0.159952659287162[/C][C]0.920023670356419[/C][/ROW]
[ROW][C]21[/C][C]0.150667061567439[/C][C]0.301334123134879[/C][C]0.84933293843256[/C][/ROW]
[ROW][C]22[/C][C]0.181333272846476[/C][C]0.362666545692952[/C][C]0.818666727153524[/C][/ROW]
[ROW][C]23[/C][C]0.204600533398098[/C][C]0.409201066796196[/C][C]0.795399466601902[/C][/ROW]
[ROW][C]24[/C][C]0.373371608378269[/C][C]0.746743216756537[/C][C]0.626628391621731[/C][/ROW]
[ROW][C]25[/C][C]0.282238578186767[/C][C]0.564477156373535[/C][C]0.717761421813233[/C][/ROW]
[ROW][C]26[/C][C]0.201369066520644[/C][C]0.402738133041288[/C][C]0.798630933479356[/C][/ROW]
[ROW][C]27[/C][C]0.13597917911152[/C][C]0.27195835822304[/C][C]0.86402082088848[/C][/ROW]
[ROW][C]28[/C][C]0.0912155995052147[/C][C]0.182431199010429[/C][C]0.908784400494785[/C][/ROW]
[ROW][C]29[/C][C]0.0587392681024176[/C][C]0.117478536204835[/C][C]0.941260731897582[/C][/ROW]
[ROW][C]30[/C][C]0.0513046301744405[/C][C]0.102609260348881[/C][C]0.94869536982556[/C][/ROW]
[ROW][C]31[/C][C]0.0451886975235919[/C][C]0.0903773950471838[/C][C]0.954811302476408[/C][/ROW]
[ROW][C]32[/C][C]0.0502919689068841[/C][C]0.100583937813768[/C][C]0.949708031093116[/C][/ROW]
[ROW][C]33[/C][C]0.111110422671916[/C][C]0.222220845343833[/C][C]0.888889577328084[/C][/ROW]
[ROW][C]34[/C][C]0.191021648544968[/C][C]0.382043297089935[/C][C]0.808978351455032[/C][/ROW]
[ROW][C]35[/C][C]0.255702909352402[/C][C]0.511405818704805[/C][C]0.744297090647598[/C][/ROW]
[ROW][C]36[/C][C]0.319105035321378[/C][C]0.638210070642757[/C][C]0.680894964678622[/C][/ROW]
[ROW][C]37[/C][C]0.40091302998738[/C][C]0.80182605997476[/C][C]0.59908697001262[/C][/ROW]
[ROW][C]38[/C][C]0.488718424464117[/C][C]0.977436848928235[/C][C]0.511281575535883[/C][/ROW]
[ROW][C]39[/C][C]0.588117477650843[/C][C]0.823765044698315[/C][C]0.411882522349157[/C][/ROW]
[ROW][C]40[/C][C]0.676421363415406[/C][C]0.647157273169187[/C][C]0.323578636584594[/C][/ROW]
[ROW][C]41[/C][C]0.827958548305437[/C][C]0.344082903389126[/C][C]0.172041451694563[/C][/ROW]
[ROW][C]42[/C][C]0.820259252819365[/C][C]0.35948149436127[/C][C]0.179740747180635[/C][/ROW]
[ROW][C]43[/C][C]0.893445697421056[/C][C]0.213108605157889[/C][C]0.106554302578944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112114&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112114&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	0.0547296926559853	0.109459385311971	0.945270307344015
17	0.0177728872203434	0.0355457744406867	0.982227112779657
18	0.00464095716551273	0.00928191433102546	0.995359042834487
19	0.00351427593044907	0.00702855186089814	0.99648572406955
20	0.0799763296435809	0.159952659287162	0.920023670356419
21	0.150667061567439	0.301334123134879	0.84933293843256
22	0.181333272846476	0.362666545692952	0.818666727153524
23	0.204600533398098	0.409201066796196	0.795399466601902
24	0.373371608378269	0.746743216756537	0.626628391621731
25	0.282238578186767	0.564477156373535	0.717761421813233
26	0.201369066520644	0.402738133041288	0.798630933479356
27	0.13597917911152	0.27195835822304	0.86402082088848
28	0.0912155995052147	0.182431199010429	0.908784400494785
29	0.0587392681024176	0.117478536204835	0.941260731897582
30	0.0513046301744405	0.102609260348881	0.94869536982556
31	0.0451886975235919	0.0903773950471838	0.954811302476408
32	0.0502919689068841	0.100583937813768	0.949708031093116
33	0.111110422671916	0.222220845343833	0.888889577328084
34	0.191021648544968	0.382043297089935	0.808978351455032
35	0.255702909352402	0.511405818704805	0.744297090647598
36	0.319105035321378	0.638210070642757	0.680894964678622
37	0.40091302998738	0.80182605997476	0.59908697001262
38	0.488718424464117	0.977436848928235	0.511281575535883
39	0.588117477650843	0.823765044698315	0.411882522349157
40	0.676421363415406	0.647157273169187	0.323578636584594
41	0.827958548305437	0.344082903389126	0.172041451694563
42	0.820259252819365	0.35948149436127	0.179740747180635
43	0.893445697421056	0.213108605157889	0.106554302578944

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	2	0.0714285714285714	NOK
5% type I error level	3	0.107142857142857	NOK
10% type I error level	4	0.142857142857143	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 & 2 & 0.0714285714285714 & NOK \tabularnewline
5% type I error level & 3 & 0.107142857142857 & NOK \tabularnewline
10% type I error level & 4 & 0.142857142857143 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112114&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]2[/C][C]0.0714285714285714[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]3[/C][C]0.107142857142857[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.142857142857143[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112114&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112114&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	2	0.0714285714285714	NOK
5% type I error level	3	0.107142857142857	NOK
10% type I error level	4	0.142857142857143	NOK

Figure 1

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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