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rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 17 Dec 2010 12:34:51 +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/17/t1292589196wdsx1bsr1i6wr3b.htm/, Retrieved Mon, 06 May 2024 10:42:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111430, Retrieved Mon, 06 May 2024 10:42:47 +0000

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Estimated Impact

127

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

-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
-   PD  [Multiple Regression] [WS7 - Multiple Re...] [2010-11-20 15:02:39] [8ef49741e164ec6343c90c7935194465]
- R  D      [Multiple Regression] [Paper; Multiple R...] [2010-12-17 12:34:51] [50e0b5177c9c80b42996aa89930b928a] [Current]
-   PD        [Multiple Regression] [Paper; Multiple R...] [2010-12-21 13:36:45] [8ffb4cfa64b4677df0d2c448735a40bb] 

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108,35	98,68	100,70	104,38	97,72	15.38	31.27
109,87	99,21	99,62	103,97	98,01	15.03	35.83
111,30	99,36	99,83	103,32	97,78	15.21	37.12
115,50	100,72	100,74	105,01	98,04	15.20	36.77
116,22	102,27	100,84	104,88	98,54	14.60	35.17
116,63	102,62	100,85	104,46	98,39	13.79	37.25
116,84	102,97	99,71	104,71	98,58	14.54	33.77
116,63	102,88	100,80	106,09	98,91	14.31	30.59
117,03	102,90	100,06	106,54	98,68	13.93	33.59
117,00	103,01	100,57	104,36	98,59	14.82	37.24
117,14	103,02	99,79	105,31	99,13	14.46	34.81
116,64	103,73	99,90	105,07	98,70	14.85	34.94
117,24	104,18	100,12	105,39	99,00	14.95	34.47
117,52	103,73	100,40	105,65	98,80	14.43	30.48
117,83	103,78	100,51	108,25	98,80	14.84	30.94
119,79	103,61	100,70	107,71	99,29	14.39	30.60
120,86	103,84	100,62	108,58	99,69	15.70	28.42
120,75	103,86	99,70	108,27	100,01	15.34	25.89
120,63	104,14	99,48	107,62	99,85	13.98	26.32
120,89	104,05	99,36	108,80	99,66	14.75	27.18
120,23	104,01	99,39	109,26	101,18	14.81	25.85
121,19	104,49	99,45	108,58	101,47	14.67	26.32
120,79	104,83	99,28	107,05	101,28	15.03	23.07
120,09	104,78	99,40	109,20	101,80	14.34	20.19
120,86	104,95	99,10	109,52	102,48	12.54	18.65
121,10	105,28	99,48	111,12	102,32	11.37	17.74
121,47	105,28	99,74	108,74	102,30	12.58	17.26
122,01	105,91	100,42	110,53	102,84	13.06	16.01
123,94	106,81	100,80	110,44	102,36	12.50	17.94
125,78	106,39	100,66	111,02	102,16	11.11	15.53
125,31	107,02	101,03	111,13	102,57	12.39	14.49
125,79	106,92	101,22	110,90	102,49	12.34	15.35
126,12	107,01	101,23	111,32	104,11	11.54	14.67
125,57	106,79	100,10	109,37	104,78	10.22	12.95
125,44	107,41	99,98	110,18	104,13	8.50	8.81
126,12	107,13	99,91	110,74	104,22	9.06	9.33
126,01	107,54	99,84	111,70	104,73	9.28	9.31
126,50	108,48	99,68	111,33	104,99	7.24	9.03
126,13	108,50	99,74	110,86	104,70	7.58	10.96
126,66	108,27	99,71	109,48	104,69	7.81	14.26
126,33	109,42	99,35	108,77	104,85	8.54	14.20
126,61	110,09	99,21	109,81	104,24	9.27	13.70
126,36	109,98	99,21	109,15	104,74	10.11	17.46
126,83	109,99	99,16	109,63	104,20	9.21	18.73
125,90	109,54	99,20	111,32	105,62	10.71	20.37
126,29	108,85	99,08	109,75	106,08	10.85	18.72
126,37	106,76	98,16	110,37	105,46	11.77	21.60
125,11	107,56	98,00	108,30	105,42	11.81	22.75

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=111430&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=111430&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111430&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
Coffee[t] = -126.644403449146 + 1.11859932108523Tea[t] + 0.375159164294309Sugar[t] + 0.536573708762059Water[t] + 0.322868064613424Soda[t] + 0.115372489905679SaraLee[t] + 0.0139559697604042Starbucks[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Coffee[t] =  -126.644403449146 +  1.11859932108523Tea[t] +  0.375159164294309Sugar[t] +  0.536573708762059Water[t] +  0.322868064613424Soda[t] +  0.115372489905679SaraLee[t] +  0.0139559697604042Starbucks[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111430&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Coffee[t] =  -126.644403449146 +  1.11859932108523Tea[t] +  0.375159164294309Sugar[t] +  0.536573708762059Water[t] +  0.322868064613424Soda[t] +  0.115372489905679SaraLee[t] +  0.0139559697604042Starbucks[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111430&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111430&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
Coffee[t] = -126.644403449146 + 1.11859932108523Tea[t] + 0.375159164294309Sugar[t] + 0.536573708762059Water[t] + 0.322868064613424Soda[t] + 0.115372489905679SaraLee[t] + 0.0139559697604042Starbucks[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)	-126.644403449146	46.441652	-2.727	0.009364	0.004682
Tea	1.11859932108523	0.162903	6.8667	0	0
Sugar	0.375159164294309	0.313024	1.1985	0.237605	0.118802
Water	0.536573708762059	0.195769	2.7409	0.009036	0.004518
Soda	0.322868064613424	0.240095	1.3448	0.186098	0.093049
SaraLee	0.115372489905679	0.17171	0.6719	0.505415	0.252707
Starbucks	0.0139559697604042	0.06569	0.2125	0.832807	0.416403

\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) & -126.644403449146 & 46.441652 & -2.727 & 0.009364 & 0.004682 \tabularnewline
Tea & 1.11859932108523 & 0.162903 & 6.8667 & 0 & 0 \tabularnewline
Sugar & 0.375159164294309 & 0.313024 & 1.1985 & 0.237605 & 0.118802 \tabularnewline
Water & 0.536573708762059 & 0.195769 & 2.7409 & 0.009036 & 0.004518 \tabularnewline
Soda & 0.322868064613424 & 0.240095 & 1.3448 & 0.186098 & 0.093049 \tabularnewline
SaraLee & 0.115372489905679 & 0.17171 & 0.6719 & 0.505415 & 0.252707 \tabularnewline
Starbucks & 0.0139559697604042 & 0.06569 & 0.2125 & 0.832807 & 0.416403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111430&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]-126.644403449146[/C][C]46.441652[/C][C]-2.727[/C][C]0.009364[/C][C]0.004682[/C][/ROW]
[ROW][C]Tea[/C][C]1.11859932108523[/C][C]0.162903[/C][C]6.8667[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Sugar[/C][C]0.375159164294309[/C][C]0.313024[/C][C]1.1985[/C][C]0.237605[/C][C]0.118802[/C][/ROW]
[ROW][C]Water[/C][C]0.536573708762059[/C][C]0.195769[/C][C]2.7409[/C][C]0.009036[/C][C]0.004518[/C][/ROW]
[ROW][C]Soda[/C][C]0.322868064613424[/C][C]0.240095[/C][C]1.3448[/C][C]0.186098[/C][C]0.093049[/C][/ROW]
[ROW][C]SaraLee[/C][C]0.115372489905679[/C][C]0.17171[/C][C]0.6719[/C][C]0.505415[/C][C]0.252707[/C][/ROW]
[ROW][C]Starbucks[/C][C]0.0139559697604042[/C][C]0.06569[/C][C]0.2125[/C][C]0.832807[/C][C]0.416403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111430&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111430&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)	-126.644403449146	46.441652	-2.727	0.009364	0.004682
Tea	1.11859932108523	0.162903	6.8667	0	0
Sugar	0.375159164294309	0.313024	1.1985	0.237605	0.118802
Water	0.536573708762059	0.195769	2.7409	0.009036	0.004518
Soda	0.322868064613424	0.240095	1.3448	0.186098	0.093049
SaraLee	0.115372489905679	0.17171	0.6719	0.505415	0.252707
Starbucks	0.0139559697604042	0.06569	0.2125	0.832807	0.416403

Multiple Linear Regression - Regression Statistics
Multiple R	0.974260332908292
R-squared	0.949183196278576
Adjusted R-squared	0.941746590855928
F-TEST (value)	127.636622132450
F-TEST (DF numerator)	6
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.16191788971606
Sum Squared Residuals	55.3521804801312

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.974260332908292 \tabularnewline
R-squared & 0.949183196278576 \tabularnewline
Adjusted R-squared & 0.941746590855928 \tabularnewline
F-TEST (value) & 127.636622132450 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 41 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.16191788971606 \tabularnewline
Sum Squared Residuals & 55.3521804801312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111430&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.974260332908292[/C][/ROW]
[ROW][C]R-squared[/C][C]0.949183196278576[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.941746590855928[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]127.636622132450[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]41[/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]1.16191788971606[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]55.3521804801312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111430&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111430&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	0.974260332908292
R-squared	0.949183196278576
Adjusted R-squared	0.941746590855928
F-TEST (value)	127.636622132450
F-TEST (DF numerator)	6
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.16191788971606
Sum Squared Residuals	55.3521804801312

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	108.35	111.286568463747	-2.93656846374714
2	109.87	111.371149575270	-1.50114957527021
3	111.3	111.233460581552	0.0665394184476699
4	115.5	114.080867448028	1.41913255197175
5	116.22	115.852338716747	0.367661283252621
6	116.63	115.909385603676	0.720614396323876
7	116.84	116.106664870891	0.733335129109454
8	116.63	117.191016943971	-0.561016943971362
9	117.03	117.100996026014	-0.0709960260141837
10	117	116.370205119849	0.629794880151317
11	117.14	116.697413640241	0.442586359758654
12	116.64	117.312085255530	-0.672085255529643
13	117.24	118.171531915554	-0.931531915553823
14	117.52	117.732464324328	-0.212464324328356
15	117.83	119.278475908187	-1.44847590818745
16	119.79	118.971387163572	0.818612836428159
17	120.86	119.915332574445	0.944667425554969
18	120.75	119.452695360816	1.29730463918384
19	120.63	119.132030834267	1.49796916573295
20	120.89	119.658988790938	1.23101120906196
21	120.23	120.351443866879	-0.121443866879432
22	121.19	120.630049864838	0.559950135161718
23	120.79	120.060471064039	0.729528935960546
24	120.09	121.251284854193	-1.16128485419304
25	120.86	121.490990184969	-0.630990184968984
26	121.1	122.661861741368	-1.56186174136849
27	121.47	121.60880218324	-0.138802183239909
28	122.01	123.741377513773	-1.73137751377329
29	123.94	124.649735507669	-0.709735507669219
30	125.78	124.18003899988	1.59996100011995
31	125.31	125.348127055936	-0.0381270559364169
32	125.79	125.164539476358	0.625460523641864
33	126.12	125.915584177891	0.204415822109054
34	125.57	124.239269388141	1.33073061185877
35	125.44	124.856323932151	0.583676067848552
36	126.12	124.918260082092	1.20173991790849
37	126.01	126.055500963984	-0.0455009639843438
38	126.5	126.693104733134	-0.193104733134405
39	126.13	126.458326555763	-0.328326555763218
40	126.66	125.518683911135	1.14131608886536
41	126.33	126.424091947799	-0.0940919477993204
42	126.61	127.559362280375	-0.949362280374524
43	126.36	127.392999077399	-1.03299907739879
44	126.83	127.38252257839	-0.552522578390062
45	125.9	128.455387995298	-2.55538799529801
46	126.29	126.937758749482	-0.647758749481735
47	126.37	124.533573120258	1.83642687974182
48	125.11	124.265469075938	0.844530924062021

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 108.35 & 111.286568463747 & -2.93656846374714 \tabularnewline
2 & 109.87 & 111.371149575270 & -1.50114957527021 \tabularnewline
3 & 111.3 & 111.233460581552 & 0.0665394184476699 \tabularnewline
4 & 115.5 & 114.080867448028 & 1.41913255197175 \tabularnewline
5 & 116.22 & 115.852338716747 & 0.367661283252621 \tabularnewline
6 & 116.63 & 115.909385603676 & 0.720614396323876 \tabularnewline
7 & 116.84 & 116.106664870891 & 0.733335129109454 \tabularnewline
8 & 116.63 & 117.191016943971 & -0.561016943971362 \tabularnewline
9 & 117.03 & 117.100996026014 & -0.0709960260141837 \tabularnewline
10 & 117 & 116.370205119849 & 0.629794880151317 \tabularnewline
11 & 117.14 & 116.697413640241 & 0.442586359758654 \tabularnewline
12 & 116.64 & 117.312085255530 & -0.672085255529643 \tabularnewline
13 & 117.24 & 118.171531915554 & -0.931531915553823 \tabularnewline
14 & 117.52 & 117.732464324328 & -0.212464324328356 \tabularnewline
15 & 117.83 & 119.278475908187 & -1.44847590818745 \tabularnewline
16 & 119.79 & 118.971387163572 & 0.818612836428159 \tabularnewline
17 & 120.86 & 119.915332574445 & 0.944667425554969 \tabularnewline
18 & 120.75 & 119.452695360816 & 1.29730463918384 \tabularnewline
19 & 120.63 & 119.132030834267 & 1.49796916573295 \tabularnewline
20 & 120.89 & 119.658988790938 & 1.23101120906196 \tabularnewline
21 & 120.23 & 120.351443866879 & -0.121443866879432 \tabularnewline
22 & 121.19 & 120.630049864838 & 0.559950135161718 \tabularnewline
23 & 120.79 & 120.060471064039 & 0.729528935960546 \tabularnewline
24 & 120.09 & 121.251284854193 & -1.16128485419304 \tabularnewline
25 & 120.86 & 121.490990184969 & -0.630990184968984 \tabularnewline
26 & 121.1 & 122.661861741368 & -1.56186174136849 \tabularnewline
27 & 121.47 & 121.60880218324 & -0.138802183239909 \tabularnewline
28 & 122.01 & 123.741377513773 & -1.73137751377329 \tabularnewline
29 & 123.94 & 124.649735507669 & -0.709735507669219 \tabularnewline
30 & 125.78 & 124.18003899988 & 1.59996100011995 \tabularnewline
31 & 125.31 & 125.348127055936 & -0.0381270559364169 \tabularnewline
32 & 125.79 & 125.164539476358 & 0.625460523641864 \tabularnewline
33 & 126.12 & 125.915584177891 & 0.204415822109054 \tabularnewline
34 & 125.57 & 124.239269388141 & 1.33073061185877 \tabularnewline
35 & 125.44 & 124.856323932151 & 0.583676067848552 \tabularnewline
36 & 126.12 & 124.918260082092 & 1.20173991790849 \tabularnewline
37 & 126.01 & 126.055500963984 & -0.0455009639843438 \tabularnewline
38 & 126.5 & 126.693104733134 & -0.193104733134405 \tabularnewline
39 & 126.13 & 126.458326555763 & -0.328326555763218 \tabularnewline
40 & 126.66 & 125.518683911135 & 1.14131608886536 \tabularnewline
41 & 126.33 & 126.424091947799 & -0.0940919477993204 \tabularnewline
42 & 126.61 & 127.559362280375 & -0.949362280374524 \tabularnewline
43 & 126.36 & 127.392999077399 & -1.03299907739879 \tabularnewline
44 & 126.83 & 127.38252257839 & -0.552522578390062 \tabularnewline
45 & 125.9 & 128.455387995298 & -2.55538799529801 \tabularnewline
46 & 126.29 & 126.937758749482 & -0.647758749481735 \tabularnewline
47 & 126.37 & 124.533573120258 & 1.83642687974182 \tabularnewline
48 & 125.11 & 124.265469075938 & 0.844530924062021 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111430&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]108.35[/C][C]111.286568463747[/C][C]-2.93656846374714[/C][/ROW]
[ROW][C]2[/C][C]109.87[/C][C]111.371149575270[/C][C]-1.50114957527021[/C][/ROW]
[ROW][C]3[/C][C]111.3[/C][C]111.233460581552[/C][C]0.0665394184476699[/C][/ROW]
[ROW][C]4[/C][C]115.5[/C][C]114.080867448028[/C][C]1.41913255197175[/C][/ROW]
[ROW][C]5[/C][C]116.22[/C][C]115.852338716747[/C][C]0.367661283252621[/C][/ROW]
[ROW][C]6[/C][C]116.63[/C][C]115.909385603676[/C][C]0.720614396323876[/C][/ROW]
[ROW][C]7[/C][C]116.84[/C][C]116.106664870891[/C][C]0.733335129109454[/C][/ROW]
[ROW][C]8[/C][C]116.63[/C][C]117.191016943971[/C][C]-0.561016943971362[/C][/ROW]
[ROW][C]9[/C][C]117.03[/C][C]117.100996026014[/C][C]-0.0709960260141837[/C][/ROW]
[ROW][C]10[/C][C]117[/C][C]116.370205119849[/C][C]0.629794880151317[/C][/ROW]
[ROW][C]11[/C][C]117.14[/C][C]116.697413640241[/C][C]0.442586359758654[/C][/ROW]
[ROW][C]12[/C][C]116.64[/C][C]117.312085255530[/C][C]-0.672085255529643[/C][/ROW]
[ROW][C]13[/C][C]117.24[/C][C]118.171531915554[/C][C]-0.931531915553823[/C][/ROW]
[ROW][C]14[/C][C]117.52[/C][C]117.732464324328[/C][C]-0.212464324328356[/C][/ROW]
[ROW][C]15[/C][C]117.83[/C][C]119.278475908187[/C][C]-1.44847590818745[/C][/ROW]
[ROW][C]16[/C][C]119.79[/C][C]118.971387163572[/C][C]0.818612836428159[/C][/ROW]
[ROW][C]17[/C][C]120.86[/C][C]119.915332574445[/C][C]0.944667425554969[/C][/ROW]
[ROW][C]18[/C][C]120.75[/C][C]119.452695360816[/C][C]1.29730463918384[/C][/ROW]
[ROW][C]19[/C][C]120.63[/C][C]119.132030834267[/C][C]1.49796916573295[/C][/ROW]
[ROW][C]20[/C][C]120.89[/C][C]119.658988790938[/C][C]1.23101120906196[/C][/ROW]
[ROW][C]21[/C][C]120.23[/C][C]120.351443866879[/C][C]-0.121443866879432[/C][/ROW]
[ROW][C]22[/C][C]121.19[/C][C]120.630049864838[/C][C]0.559950135161718[/C][/ROW]
[ROW][C]23[/C][C]120.79[/C][C]120.060471064039[/C][C]0.729528935960546[/C][/ROW]
[ROW][C]24[/C][C]120.09[/C][C]121.251284854193[/C][C]-1.16128485419304[/C][/ROW]
[ROW][C]25[/C][C]120.86[/C][C]121.490990184969[/C][C]-0.630990184968984[/C][/ROW]
[ROW][C]26[/C][C]121.1[/C][C]122.661861741368[/C][C]-1.56186174136849[/C][/ROW]
[ROW][C]27[/C][C]121.47[/C][C]121.60880218324[/C][C]-0.138802183239909[/C][/ROW]
[ROW][C]28[/C][C]122.01[/C][C]123.741377513773[/C][C]-1.73137751377329[/C][/ROW]
[ROW][C]29[/C][C]123.94[/C][C]124.649735507669[/C][C]-0.709735507669219[/C][/ROW]
[ROW][C]30[/C][C]125.78[/C][C]124.18003899988[/C][C]1.59996100011995[/C][/ROW]
[ROW][C]31[/C][C]125.31[/C][C]125.348127055936[/C][C]-0.0381270559364169[/C][/ROW]
[ROW][C]32[/C][C]125.79[/C][C]125.164539476358[/C][C]0.625460523641864[/C][/ROW]
[ROW][C]33[/C][C]126.12[/C][C]125.915584177891[/C][C]0.204415822109054[/C][/ROW]
[ROW][C]34[/C][C]125.57[/C][C]124.239269388141[/C][C]1.33073061185877[/C][/ROW]
[ROW][C]35[/C][C]125.44[/C][C]124.856323932151[/C][C]0.583676067848552[/C][/ROW]
[ROW][C]36[/C][C]126.12[/C][C]124.918260082092[/C][C]1.20173991790849[/C][/ROW]
[ROW][C]37[/C][C]126.01[/C][C]126.055500963984[/C][C]-0.0455009639843438[/C][/ROW]
[ROW][C]38[/C][C]126.5[/C][C]126.693104733134[/C][C]-0.193104733134405[/C][/ROW]
[ROW][C]39[/C][C]126.13[/C][C]126.458326555763[/C][C]-0.328326555763218[/C][/ROW]
[ROW][C]40[/C][C]126.66[/C][C]125.518683911135[/C][C]1.14131608886536[/C][/ROW]
[ROW][C]41[/C][C]126.33[/C][C]126.424091947799[/C][C]-0.0940919477993204[/C][/ROW]
[ROW][C]42[/C][C]126.61[/C][C]127.559362280375[/C][C]-0.949362280374524[/C][/ROW]
[ROW][C]43[/C][C]126.36[/C][C]127.392999077399[/C][C]-1.03299907739879[/C][/ROW]
[ROW][C]44[/C][C]126.83[/C][C]127.38252257839[/C][C]-0.552522578390062[/C][/ROW]
[ROW][C]45[/C][C]125.9[/C][C]128.455387995298[/C][C]-2.55538799529801[/C][/ROW]
[ROW][C]46[/C][C]126.29[/C][C]126.937758749482[/C][C]-0.647758749481735[/C][/ROW]
[ROW][C]47[/C][C]126.37[/C][C]124.533573120258[/C][C]1.83642687974182[/C][/ROW]
[ROW][C]48[/C][C]125.11[/C][C]124.265469075938[/C][C]0.844530924062021[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111430&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111430&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	108.35	111.286568463747	-2.93656846374714
2	109.87	111.371149575270	-1.50114957527021
3	111.3	111.233460581552	0.0665394184476699
4	115.5	114.080867448028	1.41913255197175
5	116.22	115.852338716747	0.367661283252621
6	116.63	115.909385603676	0.720614396323876
7	116.84	116.106664870891	0.733335129109454
8	116.63	117.191016943971	-0.561016943971362
9	117.03	117.100996026014	-0.0709960260141837
10	117	116.370205119849	0.629794880151317
11	117.14	116.697413640241	0.442586359758654
12	116.64	117.312085255530	-0.672085255529643
13	117.24	118.171531915554	-0.931531915553823
14	117.52	117.732464324328	-0.212464324328356
15	117.83	119.278475908187	-1.44847590818745
16	119.79	118.971387163572	0.818612836428159
17	120.86	119.915332574445	0.944667425554969
18	120.75	119.452695360816	1.29730463918384
19	120.63	119.132030834267	1.49796916573295
20	120.89	119.658988790938	1.23101120906196
21	120.23	120.351443866879	-0.121443866879432
22	121.19	120.630049864838	0.559950135161718
23	120.79	120.060471064039	0.729528935960546
24	120.09	121.251284854193	-1.16128485419304
25	120.86	121.490990184969	-0.630990184968984
26	121.1	122.661861741368	-1.56186174136849
27	121.47	121.60880218324	-0.138802183239909
28	122.01	123.741377513773	-1.73137751377329
29	123.94	124.649735507669	-0.709735507669219
30	125.78	124.18003899988	1.59996100011995
31	125.31	125.348127055936	-0.0381270559364169
32	125.79	125.164539476358	0.625460523641864
33	126.12	125.915584177891	0.204415822109054
34	125.57	124.239269388141	1.33073061185877
35	125.44	124.856323932151	0.583676067848552
36	126.12	124.918260082092	1.20173991790849
37	126.01	126.055500963984	-0.0455009639843438
38	126.5	126.693104733134	-0.193104733134405
39	126.13	126.458326555763	-0.328326555763218
40	126.66	125.518683911135	1.14131608886536
41	126.33	126.424091947799	-0.0940919477993204
42	126.61	127.559362280375	-0.949362280374524
43	126.36	127.392999077399	-1.03299907739879
44	126.83	127.38252257839	-0.552522578390062
45	125.9	128.455387995298	-2.55538799529801
46	126.29	126.937758749482	-0.647758749481735
47	126.37	124.533573120258	1.83642687974182
48	125.11	124.265469075938	0.844530924062021

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.451120733095265	0.902241466190531	0.548879266904735
11	0.290688745267803	0.581377490535606	0.709311254732197
12	0.49145875544314	0.98291751088628	0.50854124455686
13	0.525244824117871	0.949510351764257	0.474755175882129
14	0.514807435554273	0.970385128891454	0.485192564445727
15	0.549949654899034	0.900100690201931	0.450050345100966
16	0.616089990717905	0.76782001856419	0.383910009282095
17	0.609444427769704	0.781111144460591	0.390555572230296
18	0.611066084945323	0.777867830109354	0.388933915054677
19	0.562397397854417	0.875205204291166	0.437602602145583
20	0.570320056756084	0.859359886487832	0.429679943243916
21	0.754254727571139	0.491490544857723	0.245745272428862
22	0.68668729451542	0.62662541096916	0.31331270548458
23	0.621057154033502	0.757885691932997	0.378942845966498
24	0.627720939368242	0.744558121263517	0.372279060631758
25	0.565239563338128	0.869520873323745	0.434760436661872
26	0.701502044449329	0.596995911101343	0.298497955550671
27	0.78556890881833	0.42886218236334	0.21443109118167
28	0.988219925665133	0.0235601486697343	0.0117800743348672
29	0.999208643256787	0.00158271348642592	0.000791356743212961
30	0.999264406155596	0.00147118768880873	0.000735593844404367
31	0.998610340980862	0.00277931803827606	0.00138965901913803
32	0.996683464348246	0.00663307130350878	0.00331653565175439
33	0.992148166731964	0.0157036665360726	0.00785183326803628
34	0.98375867991465	0.0324826401707016	0.0162413200853508
35	0.979392827319527	0.0412143453609454	0.0206071726804727
36	0.95062059568004	0.0987588086399194	0.0493794043199597
37	0.910283580291431	0.179432839417138	0.0897164197085688
38	0.820380125767573	0.359239748464854	0.179619874232427

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 & 0.451120733095265 & 0.902241466190531 & 0.548879266904735 \tabularnewline
11 & 0.290688745267803 & 0.581377490535606 & 0.709311254732197 \tabularnewline
12 & 0.49145875544314 & 0.98291751088628 & 0.50854124455686 \tabularnewline
13 & 0.525244824117871 & 0.949510351764257 & 0.474755175882129 \tabularnewline
14 & 0.514807435554273 & 0.970385128891454 & 0.485192564445727 \tabularnewline
15 & 0.549949654899034 & 0.900100690201931 & 0.450050345100966 \tabularnewline
16 & 0.616089990717905 & 0.76782001856419 & 0.383910009282095 \tabularnewline
17 & 0.609444427769704 & 0.781111144460591 & 0.390555572230296 \tabularnewline
18 & 0.611066084945323 & 0.777867830109354 & 0.388933915054677 \tabularnewline
19 & 0.562397397854417 & 0.875205204291166 & 0.437602602145583 \tabularnewline
20 & 0.570320056756084 & 0.859359886487832 & 0.429679943243916 \tabularnewline
21 & 0.754254727571139 & 0.491490544857723 & 0.245745272428862 \tabularnewline
22 & 0.68668729451542 & 0.62662541096916 & 0.31331270548458 \tabularnewline
23 & 0.621057154033502 & 0.757885691932997 & 0.378942845966498 \tabularnewline
24 & 0.627720939368242 & 0.744558121263517 & 0.372279060631758 \tabularnewline
25 & 0.565239563338128 & 0.869520873323745 & 0.434760436661872 \tabularnewline
26 & 0.701502044449329 & 0.596995911101343 & 0.298497955550671 \tabularnewline
27 & 0.78556890881833 & 0.42886218236334 & 0.21443109118167 \tabularnewline
28 & 0.988219925665133 & 0.0235601486697343 & 0.0117800743348672 \tabularnewline
29 & 0.999208643256787 & 0.00158271348642592 & 0.000791356743212961 \tabularnewline
30 & 0.999264406155596 & 0.00147118768880873 & 0.000735593844404367 \tabularnewline
31 & 0.998610340980862 & 0.00277931803827606 & 0.00138965901913803 \tabularnewline
32 & 0.996683464348246 & 0.00663307130350878 & 0.00331653565175439 \tabularnewline
33 & 0.992148166731964 & 0.0157036665360726 & 0.00785183326803628 \tabularnewline
34 & 0.98375867991465 & 0.0324826401707016 & 0.0162413200853508 \tabularnewline
35 & 0.979392827319527 & 0.0412143453609454 & 0.0206071726804727 \tabularnewline
36 & 0.95062059568004 & 0.0987588086399194 & 0.0493794043199597 \tabularnewline
37 & 0.910283580291431 & 0.179432839417138 & 0.0897164197085688 \tabularnewline
38 & 0.820380125767573 & 0.359239748464854 & 0.179619874232427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111430&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]10[/C][C]0.451120733095265[/C][C]0.902241466190531[/C][C]0.548879266904735[/C][/ROW]
[ROW][C]11[/C][C]0.290688745267803[/C][C]0.581377490535606[/C][C]0.709311254732197[/C][/ROW]
[ROW][C]12[/C][C]0.49145875544314[/C][C]0.98291751088628[/C][C]0.50854124455686[/C][/ROW]
[ROW][C]13[/C][C]0.525244824117871[/C][C]0.949510351764257[/C][C]0.474755175882129[/C][/ROW]
[ROW][C]14[/C][C]0.514807435554273[/C][C]0.970385128891454[/C][C]0.485192564445727[/C][/ROW]
[ROW][C]15[/C][C]0.549949654899034[/C][C]0.900100690201931[/C][C]0.450050345100966[/C][/ROW]
[ROW][C]16[/C][C]0.616089990717905[/C][C]0.76782001856419[/C][C]0.383910009282095[/C][/ROW]
[ROW][C]17[/C][C]0.609444427769704[/C][C]0.781111144460591[/C][C]0.390555572230296[/C][/ROW]
[ROW][C]18[/C][C]0.611066084945323[/C][C]0.777867830109354[/C][C]0.388933915054677[/C][/ROW]
[ROW][C]19[/C][C]0.562397397854417[/C][C]0.875205204291166[/C][C]0.437602602145583[/C][/ROW]
[ROW][C]20[/C][C]0.570320056756084[/C][C]0.859359886487832[/C][C]0.429679943243916[/C][/ROW]
[ROW][C]21[/C][C]0.754254727571139[/C][C]0.491490544857723[/C][C]0.245745272428862[/C][/ROW]
[ROW][C]22[/C][C]0.68668729451542[/C][C]0.62662541096916[/C][C]0.31331270548458[/C][/ROW]
[ROW][C]23[/C][C]0.621057154033502[/C][C]0.757885691932997[/C][C]0.378942845966498[/C][/ROW]
[ROW][C]24[/C][C]0.627720939368242[/C][C]0.744558121263517[/C][C]0.372279060631758[/C][/ROW]
[ROW][C]25[/C][C]0.565239563338128[/C][C]0.869520873323745[/C][C]0.434760436661872[/C][/ROW]
[ROW][C]26[/C][C]0.701502044449329[/C][C]0.596995911101343[/C][C]0.298497955550671[/C][/ROW]
[ROW][C]27[/C][C]0.78556890881833[/C][C]0.42886218236334[/C][C]0.21443109118167[/C][/ROW]
[ROW][C]28[/C][C]0.988219925665133[/C][C]0.0235601486697343[/C][C]0.0117800743348672[/C][/ROW]
[ROW][C]29[/C][C]0.999208643256787[/C][C]0.00158271348642592[/C][C]0.000791356743212961[/C][/ROW]
[ROW][C]30[/C][C]0.999264406155596[/C][C]0.00147118768880873[/C][C]0.000735593844404367[/C][/ROW]
[ROW][C]31[/C][C]0.998610340980862[/C][C]0.00277931803827606[/C][C]0.00138965901913803[/C][/ROW]
[ROW][C]32[/C][C]0.996683464348246[/C][C]0.00663307130350878[/C][C]0.00331653565175439[/C][/ROW]
[ROW][C]33[/C][C]0.992148166731964[/C][C]0.0157036665360726[/C][C]0.00785183326803628[/C][/ROW]
[ROW][C]34[/C][C]0.98375867991465[/C][C]0.0324826401707016[/C][C]0.0162413200853508[/C][/ROW]
[ROW][C]35[/C][C]0.979392827319527[/C][C]0.0412143453609454[/C][C]0.0206071726804727[/C][/ROW]
[ROW][C]36[/C][C]0.95062059568004[/C][C]0.0987588086399194[/C][C]0.0493794043199597[/C][/ROW]
[ROW][C]37[/C][C]0.910283580291431[/C][C]0.179432839417138[/C][C]0.0897164197085688[/C][/ROW]
[ROW][C]38[/C][C]0.820380125767573[/C][C]0.359239748464854[/C][C]0.179619874232427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111430&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111430&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
10	0.451120733095265	0.902241466190531	0.548879266904735
11	0.290688745267803	0.581377490535606	0.709311254732197
12	0.49145875544314	0.98291751088628	0.50854124455686
13	0.525244824117871	0.949510351764257	0.474755175882129
14	0.514807435554273	0.970385128891454	0.485192564445727
15	0.549949654899034	0.900100690201931	0.450050345100966
16	0.616089990717905	0.76782001856419	0.383910009282095
17	0.609444427769704	0.781111144460591	0.390555572230296
18	0.611066084945323	0.777867830109354	0.388933915054677
19	0.562397397854417	0.875205204291166	0.437602602145583
20	0.570320056756084	0.859359886487832	0.429679943243916
21	0.754254727571139	0.491490544857723	0.245745272428862
22	0.68668729451542	0.62662541096916	0.31331270548458
23	0.621057154033502	0.757885691932997	0.378942845966498
24	0.627720939368242	0.744558121263517	0.372279060631758
25	0.565239563338128	0.869520873323745	0.434760436661872
26	0.701502044449329	0.596995911101343	0.298497955550671
27	0.78556890881833	0.42886218236334	0.21443109118167
28	0.988219925665133	0.0235601486697343	0.0117800743348672
29	0.999208643256787	0.00158271348642592	0.000791356743212961
30	0.999264406155596	0.00147118768880873	0.000735593844404367
31	0.998610340980862	0.00277931803827606	0.00138965901913803
32	0.996683464348246	0.00663307130350878	0.00331653565175439
33	0.992148166731964	0.0157036665360726	0.00785183326803628
34	0.98375867991465	0.0324826401707016	0.0162413200853508
35	0.979392827319527	0.0412143453609454	0.0206071726804727
36	0.95062059568004	0.0987588086399194	0.0493794043199597
37	0.910283580291431	0.179432839417138	0.0897164197085688
38	0.820380125767573	0.359239748464854	0.179619874232427

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	4	0.137931034482759	NOK
5% type I error level	8	0.275862068965517	NOK
10% type I error level	9	0.310344827586207	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 4 & 0.137931034482759 & NOK \tabularnewline
5% type I error level & 8 & 0.275862068965517 & NOK \tabularnewline
10% type I error level & 9 & 0.310344827586207 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111430&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]4[/C][C]0.137931034482759[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]8[/C][C]0.275862068965517[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]9[/C][C]0.310344827586207[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111430&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111430&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	4	0.137931034482759	NOK
5% type I error level	8	0.275862068965517	NOK
10% type I error level	9	0.310344827586207	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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code