Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 10 Dec 2017 13:37:21 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/10/t1512909691sybt6p267maym1h.htm/, Retrieved Wed, 15 May 2024 13:03:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308911, Retrieved Wed, 15 May 2024 13:03:26 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Arbeidsters

Estimated Impact

112

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

-       [Multiple Regression] [Meervoudige regre...] [2017-12-10 12:37:21] [3c3f1142cbd5b1dfc6913e0ceac18617] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

324	1200	3989	5206	1911	3983	1901	2046
400	605	1298	3861	2482	2341	1571	1759
76	87	305	1150	1030	819	110	477
25	77	264	1723	1560	765	237	892
17	63	286	1734	1240	575	308	681
13	23	141	1024	783	240	134	446
9	15	131	893	538	224	130	341
66	25	183	1083	777	507	146	348
23	70	168	774	505	398	34	350
3	17	46	342	222	125	40	141
46	300	335	1710	1428	1886	282	768
5	8	72	516	396	210	46	185
58	90	305	1003	718	440	52	458
52	113	715	2108	1475	1409	533	556
40	88	261	1425	1565	1397	260	439
5	14	103	746	784	415	245	299
0	3	27	251	221	42	20	102
0	5	46	433	401	114	74	207
57	66	254	977	952	523	167	499
16	24	89	524	347	137	135	186
10	39	72	573	581	179	34	292
4	11	46	340	363	128	6	148
3	3	20	187	120	47	20	63
27	71	400	954	1013	1058	373	313
2	6	79	364	267	112	28	112
10	32	225	651	367	160	3589	506
28	131	462	1202	585	298	121	411
8	20	108	298	195	45	181	156
6	32	260	858	540	226	93	252
5	12	151	532	307	97	314	200
2	25	230	447	455	124	147	219
7	26	173	363	360	172	32	142
167	337	1115	2449	1524	903	492	958
89	139	398	867	829	327	468	421
7	7	68	299	257	129	24	123
2	14	83	169	165	119	194	61
0	9	67	225	196	55	36	72
0	10	76	232	194	50	15	75
3	8	53	342	238	58	24	103
2	7	53	206	155	44	56	51
3	23	158	476	279	112	97	149
22	85	455	986	867	581	365	374
3	8	75	123	70	21	360	76

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	Big Analytics Cloud Computing Center
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
R Framework error message & The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

7 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [ROW]

R Framework error message[/C][C]

The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308911&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&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	7 seconds
R Server	Big Analytics Cloud Computing Center
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation
A [t] = -5.98873 -0.453393G[t] + 1.67003L[t] -0.251681LM[t] + 0.272742HM[t] + 0.234479HK[t] -0.21655`HL/U`[t] + 0.0805002O[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
A
[t] =  -5.98873 -0.453393G[t] +  1.67003L[t] -0.251681LM[t] +  0.272742HM[t] +  0.234479HK[t] -0.21655`HL/U`[t] +  0.0805002O[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]A
[t] =  -5.98873 -0.453393G[t] +  1.67003L[t] -0.251681LM[t] +  0.272742HM[t] +  0.234479HK[t] -0.21655`HL/U`[t] +  0.0805002O[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&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
A [t] = -5.98873 -0.453393G[t] + 1.67003L[t] -0.251681LM[t] + 0.272742HM[t] + 0.234479HK[t] -0.21655`HL/U`[t] + 0.0805002O[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)	-5.989	16.09	-3.7230e-01	0.7119	0.356
G	-0.4534	0.3055	-1.4840e+00	0.1468	0.07338
L	+1.67	0.2778	+6.0130e+00	7.433e-07	3.716e-07
LM	-0.2517	0.0681	-3.6960e+00	0.0007447	0.0003723
HM	+0.2727	0.05848	+4.6640e+00	4.406e-05	2.203e-05
HK	+0.2345	0.0708	+3.3120e+00	0.002159	0.00108
`HL/U`	-0.2165	0.04714	-4.5940e+00	5.434e-05	2.717e-05
O	+0.0805	0.01521	+5.2920e+00	6.624e-06	3.312e-06

\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) & -5.989 &  16.09 & -3.7230e-01 &  0.7119 &  0.356 \tabularnewline
G & -0.4534 &  0.3055 & -1.4840e+00 &  0.1468 &  0.07338 \tabularnewline
L & +1.67 &  0.2778 & +6.0130e+00 &  7.433e-07 &  3.716e-07 \tabularnewline
LM & -0.2517 &  0.0681 & -3.6960e+00 &  0.0007447 &  0.0003723 \tabularnewline
HM & +0.2727 &  0.05848 & +4.6640e+00 &  4.406e-05 &  2.203e-05 \tabularnewline
HK & +0.2345 &  0.0708 & +3.3120e+00 &  0.002159 &  0.00108 \tabularnewline
`HL/U` & -0.2165 &  0.04714 & -4.5940e+00 &  5.434e-05 &  2.717e-05 \tabularnewline
O & +0.0805 &  0.01521 & +5.2920e+00 &  6.624e-06 &  3.312e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&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]-5.989[/C][C] 16.09[/C][C]-3.7230e-01[/C][C] 0.7119[/C][C] 0.356[/C][/ROW]
[ROW][C]G[/C][C]-0.4534[/C][C] 0.3055[/C][C]-1.4840e+00[/C][C] 0.1468[/C][C] 0.07338[/C][/ROW]
[ROW][C]L[/C][C]+1.67[/C][C] 0.2778[/C][C]+6.0130e+00[/C][C] 7.433e-07[/C][C] 3.716e-07[/C][/ROW]
[ROW][C]LM[/C][C]-0.2517[/C][C] 0.0681[/C][C]-3.6960e+00[/C][C] 0.0007447[/C][C] 0.0003723[/C][/ROW]
[ROW][C]HM[/C][C]+0.2727[/C][C] 0.05848[/C][C]+4.6640e+00[/C][C] 4.406e-05[/C][C] 2.203e-05[/C][/ROW]
[ROW][C]HK[/C][C]+0.2345[/C][C] 0.0708[/C][C]+3.3120e+00[/C][C] 0.002159[/C][C] 0.00108[/C][/ROW]
[ROW][C]`HL/U`[/C][C]-0.2165[/C][C] 0.04714[/C][C]-4.5940e+00[/C][C] 5.434e-05[/C][C] 2.717e-05[/C][/ROW]
[ROW][C]O[/C][C]+0.0805[/C][C] 0.01521[/C][C]+5.2920e+00[/C][C] 6.624e-06[/C][C] 3.312e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&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)	-5.989	16.09	-3.7230e-01	0.7119	0.356
G	-0.4534	0.3055	-1.4840e+00	0.1468	0.07338
L	+1.67	0.2778	+6.0130e+00	7.433e-07	3.716e-07
LM	-0.2517	0.0681	-3.6960e+00	0.0007447	0.0003723
HM	+0.2727	0.05848	+4.6640e+00	4.406e-05	2.203e-05
HK	+0.2345	0.0708	+3.3120e+00	0.002159	0.00108
`HL/U`	-0.2165	0.04714	-4.5940e+00	5.434e-05	2.717e-05
O	+0.0805	0.01521	+5.2920e+00	6.624e-06	3.312e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.993
R-squared	0.9861
Adjusted R-squared	0.9833
F-TEST (value)	354.8
F-TEST (DF numerator)	7
F-TEST (DF denominator)	35
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	52.56
Sum Squared Residuals	9.669e+04

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.993 \tabularnewline
R-squared &  0.9861 \tabularnewline
Adjusted R-squared &  0.9833 \tabularnewline
F-TEST (value) &  354.8 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 35 \tabularnewline
p-value &  0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  52.56 \tabularnewline
Sum Squared Residuals &  9.669e+04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.993[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.9861[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.9833[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 354.8[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]35[/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] 52.56[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 9.669e+04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&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	0.993
R-squared	0.9861
Adjusted R-squared	0.9833
F-TEST (value)	354.8
F-TEST (DF numerator)	7
F-TEST (DF denominator)	35
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	52.56
Sum Squared Residuals	9.669e+04

Menu of Residual Diagnostics
Description	Link
Histogram	Compute
Central Tendency	Compute
QQ Plot	Compute
Kernel Density Plot	Compute
Skewness/Kurtosis Test	Compute
Skewness-Kurtosis Plot	Compute
Harrell-Davis Plot	Compute
Bootstrap Plot -- Central Tendency	Compute
Blocked Bootstrap Plot -- Central Tendency	Compute
(Partial) Autocorrelation Plot	Compute
Spectral Analysis	Compute
Tukey lambda PPCC Plot	Compute
Box-Cox Normality Plot	Compute
Summary Statistics	Compute

\begin{tabular}{lllllllll}
\hline
Menu of Residual Diagnostics \tabularnewline
Description & Link \tabularnewline
Histogram & Compute \tabularnewline
Central Tendency & Compute \tabularnewline
QQ Plot & Compute \tabularnewline
Kernel Density Plot & Compute \tabularnewline
Skewness/Kurtosis Test & Compute \tabularnewline
Skewness-Kurtosis Plot & Compute \tabularnewline
Harrell-Davis Plot & Compute \tabularnewline
Bootstrap Plot -- Central Tendency & Compute \tabularnewline
Blocked Bootstrap Plot -- Central Tendency & Compute \tabularnewline
(Partial) Autocorrelation Plot & Compute \tabularnewline
Spectral Analysis & Compute \tabularnewline
Tukey lambda PPCC Plot & Compute \tabularnewline
Box-Cox Normality Plot & Compute \tabularnewline
Summary Statistics & Compute \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=4

[TABLE]
[ROW][C]Menu of Residual Diagnostics[/C][/ROW]
[ROW][C]Description[/C][C]Link[/C][/ROW]
[ROW][C]Histogram[/C][C]Compute[/C][/ROW]
[ROW][C]Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]QQ Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Kernel Density Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness/Kurtosis Test[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness-Kurtosis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Harrell-Davis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]Blocked Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C](Partial) Autocorrelation Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Spectral Analysis[/C][C]Compute[/C][/ROW]
[ROW][C]Tukey lambda PPCC Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Box-Cox Normality Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Summary Statistics[/C][C]Compute[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&T=4

As an alternative you can also use a QR Code:

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

Menu of Residual Diagnostics
Description	Link
Histogram	Compute
Central Tendency	Compute
QQ Plot	Compute
Kernel Density Plot	Compute
Skewness/Kurtosis Test	Compute
Skewness-Kurtosis Plot	Compute
Harrell-Davis Plot	Compute
Bootstrap Plot -- Central Tendency	Compute
Blocked Bootstrap Plot -- Central Tendency	Compute
(Partial) Autocorrelation Plot	Compute
Spectral Analysis	Compute
Tukey lambda PPCC Plot	Compute
Box-Cox Normality Plot	Compute
Summary Statistics	Compute

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	2046	2006	40.31
2	1759	1751	8.105
3	477	414.8	62.25
4	892	734	158
5	681	683.5	-2.5
6	446	412.7	33.26
7	341	313.7	27.32
8	348	339.3	8.689
9	350	304.3	45.73
10	141	130.9	10.05
11	768	805.4	-37.36
12	185	178.8	6.201
13	458	392.1	65.93
14	556	637.8	-81.78
15	439	531.2	-92.17
16	299	306.4	-7.352
17	102	105	-3.019
18	207	184.2	22.82
19	499	404.3	94.66
20	186	209.9	-23.92
21	292	293	-0.9751
22	148	149.6	-1.603
23	63	63.2	-0.1998
24	313	298.3	14.69
25	112	123.1	-11.13
26	506	504.2	1.834
27	411	494	-83.03
28	156	128.4	27.57
29	252	298.5	-46.47
30	200	195.1	4.864
31	219	190.6	28.45
32	142	139.5	2.536
33	958	1070	-111.8
34	421	483.3	-62.34
35	123	101.2	21.78
36	61	70.23	-9.225
37	72	90.49	-18.49
38	75	90.73	-15.73
39	103	131.1	-28.13
40	51	78.96	-27.96
41	149	170.1	-21.1
42	374	387.3	-13.26
43	76	61.53	14.47

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  2046 &  2006 &  40.31 \tabularnewline
2 &  1759 &  1751 &  8.105 \tabularnewline
3 &  477 &  414.8 &  62.25 \tabularnewline
4 &  892 &  734 &  158 \tabularnewline
5 &  681 &  683.5 & -2.5 \tabularnewline
6 &  446 &  412.7 &  33.26 \tabularnewline
7 &  341 &  313.7 &  27.32 \tabularnewline
8 &  348 &  339.3 &  8.689 \tabularnewline
9 &  350 &  304.3 &  45.73 \tabularnewline
10 &  141 &  130.9 &  10.05 \tabularnewline
11 &  768 &  805.4 & -37.36 \tabularnewline
12 &  185 &  178.8 &  6.201 \tabularnewline
13 &  458 &  392.1 &  65.93 \tabularnewline
14 &  556 &  637.8 & -81.78 \tabularnewline
15 &  439 &  531.2 & -92.17 \tabularnewline
16 &  299 &  306.4 & -7.352 \tabularnewline
17 &  102 &  105 & -3.019 \tabularnewline
18 &  207 &  184.2 &  22.82 \tabularnewline
19 &  499 &  404.3 &  94.66 \tabularnewline
20 &  186 &  209.9 & -23.92 \tabularnewline
21 &  292 &  293 & -0.9751 \tabularnewline
22 &  148 &  149.6 & -1.603 \tabularnewline
23 &  63 &  63.2 & -0.1998 \tabularnewline
24 &  313 &  298.3 &  14.69 \tabularnewline
25 &  112 &  123.1 & -11.13 \tabularnewline
26 &  506 &  504.2 &  1.834 \tabularnewline
27 &  411 &  494 & -83.03 \tabularnewline
28 &  156 &  128.4 &  27.57 \tabularnewline
29 &  252 &  298.5 & -46.47 \tabularnewline
30 &  200 &  195.1 &  4.864 \tabularnewline
31 &  219 &  190.6 &  28.45 \tabularnewline
32 &  142 &  139.5 &  2.536 \tabularnewline
33 &  958 &  1070 & -111.8 \tabularnewline
34 &  421 &  483.3 & -62.34 \tabularnewline
35 &  123 &  101.2 &  21.78 \tabularnewline
36 &  61 &  70.23 & -9.225 \tabularnewline
37 &  72 &  90.49 & -18.49 \tabularnewline
38 &  75 &  90.73 & -15.73 \tabularnewline
39 &  103 &  131.1 & -28.13 \tabularnewline
40 &  51 &  78.96 & -27.96 \tabularnewline
41 &  149 &  170.1 & -21.1 \tabularnewline
42 &  374 &  387.3 & -13.26 \tabularnewline
43 &  76 &  61.53 &  14.47 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=5

[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] 2046[/C][C] 2006[/C][C] 40.31[/C][/ROW]
[ROW][C]2[/C][C] 1759[/C][C] 1751[/C][C] 8.105[/C][/ROW]
[ROW][C]3[/C][C] 477[/C][C] 414.8[/C][C] 62.25[/C][/ROW]
[ROW][C]4[/C][C] 892[/C][C] 734[/C][C] 158[/C][/ROW]
[ROW][C]5[/C][C] 681[/C][C] 683.5[/C][C]-2.5[/C][/ROW]
[ROW][C]6[/C][C] 446[/C][C] 412.7[/C][C] 33.26[/C][/ROW]
[ROW][C]7[/C][C] 341[/C][C] 313.7[/C][C] 27.32[/C][/ROW]
[ROW][C]8[/C][C] 348[/C][C] 339.3[/C][C] 8.689[/C][/ROW]
[ROW][C]9[/C][C] 350[/C][C] 304.3[/C][C] 45.73[/C][/ROW]
[ROW][C]10[/C][C] 141[/C][C] 130.9[/C][C] 10.05[/C][/ROW]
[ROW][C]11[/C][C] 768[/C][C] 805.4[/C][C]-37.36[/C][/ROW]
[ROW][C]12[/C][C] 185[/C][C] 178.8[/C][C] 6.201[/C][/ROW]
[ROW][C]13[/C][C] 458[/C][C] 392.1[/C][C] 65.93[/C][/ROW]
[ROW][C]14[/C][C] 556[/C][C] 637.8[/C][C]-81.78[/C][/ROW]
[ROW][C]15[/C][C] 439[/C][C] 531.2[/C][C]-92.17[/C][/ROW]
[ROW][C]16[/C][C] 299[/C][C] 306.4[/C][C]-7.352[/C][/ROW]
[ROW][C]17[/C][C] 102[/C][C] 105[/C][C]-3.019[/C][/ROW]
[ROW][C]18[/C][C] 207[/C][C] 184.2[/C][C] 22.82[/C][/ROW]
[ROW][C]19[/C][C] 499[/C][C] 404.3[/C][C] 94.66[/C][/ROW]
[ROW][C]20[/C][C] 186[/C][C] 209.9[/C][C]-23.92[/C][/ROW]
[ROW][C]21[/C][C] 292[/C][C] 293[/C][C]-0.9751[/C][/ROW]
[ROW][C]22[/C][C] 148[/C][C] 149.6[/C][C]-1.603[/C][/ROW]
[ROW][C]23[/C][C] 63[/C][C] 63.2[/C][C]-0.1998[/C][/ROW]
[ROW][C]24[/C][C] 313[/C][C] 298.3[/C][C] 14.69[/C][/ROW]
[ROW][C]25[/C][C] 112[/C][C] 123.1[/C][C]-11.13[/C][/ROW]
[ROW][C]26[/C][C] 506[/C][C] 504.2[/C][C] 1.834[/C][/ROW]
[ROW][C]27[/C][C] 411[/C][C] 494[/C][C]-83.03[/C][/ROW]
[ROW][C]28[/C][C] 156[/C][C] 128.4[/C][C] 27.57[/C][/ROW]
[ROW][C]29[/C][C] 252[/C][C] 298.5[/C][C]-46.47[/C][/ROW]
[ROW][C]30[/C][C] 200[/C][C] 195.1[/C][C] 4.864[/C][/ROW]
[ROW][C]31[/C][C] 219[/C][C] 190.6[/C][C] 28.45[/C][/ROW]
[ROW][C]32[/C][C] 142[/C][C] 139.5[/C][C] 2.536[/C][/ROW]
[ROW][C]33[/C][C] 958[/C][C] 1070[/C][C]-111.8[/C][/ROW]
[ROW][C]34[/C][C] 421[/C][C] 483.3[/C][C]-62.34[/C][/ROW]
[ROW][C]35[/C][C] 123[/C][C] 101.2[/C][C] 21.78[/C][/ROW]
[ROW][C]36[/C][C] 61[/C][C] 70.23[/C][C]-9.225[/C][/ROW]
[ROW][C]37[/C][C] 72[/C][C] 90.49[/C][C]-18.49[/C][/ROW]
[ROW][C]38[/C][C] 75[/C][C] 90.73[/C][C]-15.73[/C][/ROW]
[ROW][C]39[/C][C] 103[/C][C] 131.1[/C][C]-28.13[/C][/ROW]
[ROW][C]40[/C][C] 51[/C][C] 78.96[/C][C]-27.96[/C][/ROW]
[ROW][C]41[/C][C] 149[/C][C] 170.1[/C][C]-21.1[/C][/ROW]
[ROW][C]42[/C][C] 374[/C][C] 387.3[/C][C]-13.26[/C][/ROW]
[ROW][C]43[/C][C] 76[/C][C] 61.53[/C][C] 14.47[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&T=5

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	2046	2006	40.31
2	1759	1751	8.105
3	477	414.8	62.25
4	892	734	158
5	681	683.5	-2.5
6	446	412.7	33.26
7	341	313.7	27.32
8	348	339.3	8.689
9	350	304.3	45.73
10	141	130.9	10.05
11	768	805.4	-37.36
12	185	178.8	6.201
13	458	392.1	65.93
14	556	637.8	-81.78
15	439	531.2	-92.17
16	299	306.4	-7.352
17	102	105	-3.019
18	207	184.2	22.82
19	499	404.3	94.66
20	186	209.9	-23.92
21	292	293	-0.9751
22	148	149.6	-1.603
23	63	63.2	-0.1998
24	313	298.3	14.69
25	112	123.1	-11.13
26	506	504.2	1.834
27	411	494	-83.03
28	156	128.4	27.57
29	252	298.5	-46.47
30	200	195.1	4.864
31	219	190.6	28.45
32	142	139.5	2.536
33	958	1070	-111.8
34	421	483.3	-62.34
35	123	101.2	21.78
36	61	70.23	-9.225
37	72	90.49	-18.49
38	75	90.73	-15.73
39	103	131.1	-28.13
40	51	78.96	-27.96
41	149	170.1	-21.1
42	374	387.3	-13.26
43	76	61.53	14.47

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.7331	0.5339	0.2669
12	0.5909	0.8181	0.4091
13	0.6866	0.6269	0.3134
14	0.6309	0.7382	0.3691
15	0.9252	0.1496	0.07482
16	0.9154	0.1692	0.0846
17	0.8716	0.2567	0.1284
18	0.8093	0.3814	0.1907
19	0.9641	0.07189	0.03594
20	0.9446	0.1107	0.05536
21	0.9919	0.01625	0.008127
22	0.994	0.01208	0.006042
23	0.9889	0.0223	0.01115
24	0.9944	0.01128	0.005642
25	0.9876	0.02473	0.01236
26	0.9893	0.02131	0.01066
27	0.9959	0.008276	0.004138
28	0.9985	0.002904	0.001452
29	0.9995	0.0009444	0.0004722
30	0.9987	0.002618	0.001309
31	0.9969	0.006191	0.003095
32	0.9838	0.03247	0.01624

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 &  0.7331 &  0.5339 &  0.2669 \tabularnewline
12 &  0.5909 &  0.8181 &  0.4091 \tabularnewline
13 &  0.6866 &  0.6269 &  0.3134 \tabularnewline
14 &  0.6309 &  0.7382 &  0.3691 \tabularnewline
15 &  0.9252 &  0.1496 &  0.07482 \tabularnewline
16 &  0.9154 &  0.1692 &  0.0846 \tabularnewline
17 &  0.8716 &  0.2567 &  0.1284 \tabularnewline
18 &  0.8093 &  0.3814 &  0.1907 \tabularnewline
19 &  0.9641 &  0.07189 &  0.03594 \tabularnewline
20 &  0.9446 &  0.1107 &  0.05536 \tabularnewline
21 &  0.9919 &  0.01625 &  0.008127 \tabularnewline
22 &  0.994 &  0.01208 &  0.006042 \tabularnewline
23 &  0.9889 &  0.0223 &  0.01115 \tabularnewline
24 &  0.9944 &  0.01128 &  0.005642 \tabularnewline
25 &  0.9876 &  0.02473 &  0.01236 \tabularnewline
26 &  0.9893 &  0.02131 &  0.01066 \tabularnewline
27 &  0.9959 &  0.008276 &  0.004138 \tabularnewline
28 &  0.9985 &  0.002904 &  0.001452 \tabularnewline
29 &  0.9995 &  0.0009444 &  0.0004722 \tabularnewline
30 &  0.9987 &  0.002618 &  0.001309 \tabularnewline
31 &  0.9969 &  0.006191 &  0.003095 \tabularnewline
32 &  0.9838 &  0.03247 &  0.01624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=6

[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]11[/C][C] 0.7331[/C][C] 0.5339[/C][C] 0.2669[/C][/ROW]
[ROW][C]12[/C][C] 0.5909[/C][C] 0.8181[/C][C] 0.4091[/C][/ROW]
[ROW][C]13[/C][C] 0.6866[/C][C] 0.6269[/C][C] 0.3134[/C][/ROW]
[ROW][C]14[/C][C] 0.6309[/C][C] 0.7382[/C][C] 0.3691[/C][/ROW]
[ROW][C]15[/C][C] 0.9252[/C][C] 0.1496[/C][C] 0.07482[/C][/ROW]
[ROW][C]16[/C][C] 0.9154[/C][C] 0.1692[/C][C] 0.0846[/C][/ROW]
[ROW][C]17[/C][C] 0.8716[/C][C] 0.2567[/C][C] 0.1284[/C][/ROW]
[ROW][C]18[/C][C] 0.8093[/C][C] 0.3814[/C][C] 0.1907[/C][/ROW]
[ROW][C]19[/C][C] 0.9641[/C][C] 0.07189[/C][C] 0.03594[/C][/ROW]
[ROW][C]20[/C][C] 0.9446[/C][C] 0.1107[/C][C] 0.05536[/C][/ROW]
[ROW][C]21[/C][C] 0.9919[/C][C] 0.01625[/C][C] 0.008127[/C][/ROW]
[ROW][C]22[/C][C] 0.994[/C][C] 0.01208[/C][C] 0.006042[/C][/ROW]
[ROW][C]23[/C][C] 0.9889[/C][C] 0.0223[/C][C] 0.01115[/C][/ROW]
[ROW][C]24[/C][C] 0.9944[/C][C] 0.01128[/C][C] 0.005642[/C][/ROW]
[ROW][C]25[/C][C] 0.9876[/C][C] 0.02473[/C][C] 0.01236[/C][/ROW]
[ROW][C]26[/C][C] 0.9893[/C][C] 0.02131[/C][C] 0.01066[/C][/ROW]
[ROW][C]27[/C][C] 0.9959[/C][C] 0.008276[/C][C] 0.004138[/C][/ROW]
[ROW][C]28[/C][C] 0.9985[/C][C] 0.002904[/C][C] 0.001452[/C][/ROW]
[ROW][C]29[/C][C] 0.9995[/C][C] 0.0009444[/C][C] 0.0004722[/C][/ROW]
[ROW][C]30[/C][C] 0.9987[/C][C] 0.002618[/C][C] 0.001309[/C][/ROW]
[ROW][C]31[/C][C] 0.9969[/C][C] 0.006191[/C][C] 0.003095[/C][/ROW]
[ROW][C]32[/C][C] 0.9838[/C][C] 0.03247[/C][C] 0.01624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&T=6

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
11	0.7331	0.5339	0.2669
12	0.5909	0.8181	0.4091
13	0.6866	0.6269	0.3134
14	0.6309	0.7382	0.3691
15	0.9252	0.1496	0.07482
16	0.9154	0.1692	0.0846
17	0.8716	0.2567	0.1284
18	0.8093	0.3814	0.1907
19	0.9641	0.07189	0.03594
20	0.9446	0.1107	0.05536
21	0.9919	0.01625	0.008127
22	0.994	0.01208	0.006042
23	0.9889	0.0223	0.01115
24	0.9944	0.01128	0.005642
25	0.9876	0.02473	0.01236
26	0.9893	0.02131	0.01066
27	0.9959	0.008276	0.004138
28	0.9985	0.002904	0.001452
29	0.9995	0.0009444	0.0004722
30	0.9987	0.002618	0.001309
31	0.9969	0.006191	0.003095
32	0.9838	0.03247	0.01624

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	5	0.2273	NOK
5% type I error level	12	0.545455	NOK
10% type I error level	13	0.590909	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 & 5 &  0.2273 & NOK \tabularnewline
5% type I error level & 12 & 0.545455 & NOK \tabularnewline
10% type I error level & 13 & 0.590909 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=7

[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]5[/C][C] 0.2273[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]12[/C][C]0.545455[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]13[/C][C]0.590909[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=7

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&T=7

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	5	0.2273	NOK
5% type I error level	12	0.545455	NOK
10% type I error level	13	0.590909	NOK

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 5.9038, df1 = 2, df2 = 33, p-value = 0.006429
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 4.3312, df1 = 14, df2 = 21, p-value = 0.001305
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 10.076, df1 = 2, df2 = 33, p-value = 0.000384

\begin{tabular}{lllllllll}
\hline
Ramsey RESET F-Test for powers (2 and 3) of fitted values \tabularnewline
> reset_test_fitted
	RESET test
data:  mylm
RESET = 5.9038, df1 = 2, df2 = 33, p-value = 0.006429
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 4.3312, df1 = 14, df2 = 21, p-value = 0.001305
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 10.076, df1 = 2, df2 = 33, p-value = 0.000384
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=8

[TABLE]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of fitted values[/C][/ROW]
[ROW][C]> reset_test_fitted
	RESET test
data:  mylm
RESET = 5.9038, df1 = 2, df2 = 33, p-value = 0.006429
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of regressors[/C][/ROW]
[ROW][C]> reset_test_regressors
	RESET test
data:  mylm
RESET = 4.3312, df1 = 14, df2 = 21, p-value = 0.001305
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of principal components[/C][/ROW]
[ROW][C]> reset_test_principal_components
	RESET test
data:  mylm
RESET = 10.076, df1 = 2, df2 = 33, p-value = 0.000384
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=8

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&T=8

As an alternative you can also use a QR Code:

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

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 5.9038, df1 = 2, df2 = 33, p-value = 0.006429
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 4.3312, df1 = 14, df2 = 21, p-value = 0.001305
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 10.076, df1 = 2, df2 = 33, p-value = 0.000384

Variance Inflation Factors (Multicollinearity)
> vif G L LM HM HK `HL/U` O 8.970888 49.163288 27.945721 50.181672 23.300959 18.945639 1.389813

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
        G         L        LM        HM        HK    `HL/U`         O 
 8.970888 49.163288 27.945721 50.181672 23.300959 18.945639  1.389813 
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308911&T=9

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]> vif
        G         L        LM        HM        HK    `HL/U`         O 
 8.970888 49.163288 27.945721 50.181672 23.300959 18.945639  1.389813 
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308911&T=9

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308911&T=9

As an alternative you can also use a QR Code:

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

Variance Inflation Factors (Multicollinearity)
> vif G L LM HM HK `HL/U` O 8.970888 49.163288 27.945721 50.181672 23.300959 18.945639 1.389813

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Figure 8

PNG link

Postscript link

PDF link

Figure 9

PNG link

Postscript link

PDF link

Figure 10

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;

Parameters (R input):

par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;

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

par6 <- '12'
par5 <- '0'
par4 <- '0'
par3 <- 'No Linear Trend'
par2 <- 'Do not include Seasonal Dummies'
par1 <- '8'
library(lattice)
library(lmtest)
library(car)
library(MASS)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par6 <- as.numeric(par6)
if(is.na(par6)) {
par6 <- 12
mywarning = 'Warning: you did not specify the seasonality. The seasonal period was set to s = 12.'
}
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (!is.numeric(par4)) par4 <- 0
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
if (!is.numeric(par5)) par5 <- 0
x <- na.omit(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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s)'){
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
if(par5 > 0) {
x2 <- array(0, dim=c(n-par5*par6,par5), dimnames=list(1:(n-par5*par6), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*par6)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*par6-j*par6,par1]
}
}
x <- cbind(x[(par5*par6+1):n,], x2)
n <- n - par5*par6
}
if (par2 == 'Include Seasonal Dummies'){
x2 <- array(0, dim=c(n,par6-1), dimnames=list(1:n, paste('M', seq(1:(par6-1)), sep ='')))
for (i in 1:(par6-1)){
x2[seq(i,n,par6),i] <- 1
}
x <- cbind(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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
print(x)
(k <- length(x[n,]))
head(x)
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$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
sresid <- studres(mylm)
hist(sresid, freq=FALSE, main='Distribution of Studentized Residuals')
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqPlot(mylm, main='QQ Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
print(z)
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$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, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$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.row.start(a)
a<-table.element(a, mywarning)
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,'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$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
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,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
myr <- as.numeric(mysum$resid)
myr
a <-table.start()
a <- table.row.start(a)
a <- table.element(a,'Menu of Residual Diagnostics',2,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Description',1,TRUE)
a <- table.element(a,'Link',1,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Histogram',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_histogram.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_centraltendency.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'QQ Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_fitdistrnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Kernel Density Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_density.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness/Kurtosis Test',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness-Kurtosis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis_plot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Harrell-Davis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_harrell_davis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Blocked Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'(Partial) Autocorrelation Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_autocorrelation.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Spectral Analysis',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_spectrum.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Tukey lambda PPCC Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_tukeylambda.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Box-Cox Normality Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_boxcoxnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Summary Statistics',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_summary1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable7.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
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,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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')
}
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of fitted values',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_fitted <- resettest(mylm,power=2:3,type='fitted')
a<-table.element(a,paste('',RC.texteval('reset_test_fitted'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of regressors',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_regressors <- resettest(mylm,power=2:3,type='regressor')
a<-table.element(a,paste('',RC.texteval('reset_test_regressors'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of principal components',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_principal_components <- resettest(mylm,power=2:3,type='princomp')
a<-table.element(a,paste('',RC.texteval('reset_test_principal_components'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable8.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Inflation Factors (Multicollinearity)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
vif <- vif(mylm)
a<-table.element(a,paste('',RC.texteval('vif'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable9.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code