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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 20 Dec 2011 12:24:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t132440192652jgp62u0n54inb.htm/, Retrieved Fri, 07 Nov 2025 04:04:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158085, Retrieved Fri, 07 Nov 2025 04:04:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact429

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [WS 7 4] [2009-11-14 13:58:56] [6e4e01d7eb22a9f33d58ebb35753a195]
-   PD      [Multiple Regression] [ws7 4] [2009-11-18 20:49:31] [6e4e01d7eb22a9f33d58ebb35753a195]
-    D        [Multiple Regression] [WS 75] [2009-11-18 20:57:24] [6e4e01d7eb22a9f33d58ebb35753a195]
-    D          [Multiple Regression] [Paper hypothese t...] [2010-12-19 12:54:13] [a9e130f95bad0a0597234e75c6380c5a]
-    D              [Multiple Regression] [] [2011-12-20 17:24:43] [3b32143baae8ca4a077b118800e50af3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104,17	89.00	103.88	103.77
104,18	86.40	103.91	103.88
104,2	84.50	103.91	103.91
104,5	82.70	103.92	103.91
104,78	80.80	104.05	103.92
104,88	81.80	104.23	104.05
104,89	81.80	104.30	104.23
104,9	82.90	104.31	104.30
104,95	83.80	104.31	104.31
105,24	86.20	104.34	104.31
105,35	86.10	104.55	104.34
105,44	86.20	104.65	104.55
105,46	88.80	104.73	104.65
105,47	89.60	104.75	104.73
105,48	87.80	104.75	104.75
105,75	88.30	104.76	104.75
106,1	88.60	104.94	104.76
106,19	91.00	105.29	104.94
106,23	91.50	105.38	105.29
106,24	95.40	105.43	105.38
106,25	98.70	105.43	105.43
106,35	99.90	105.42	105.43
106,48	98.60	105.52	105.42
106,52	100.30	105.69	105.52
106,55	100.20	105.72	105.69
106,55	100.40	105.74	105.72
106,56	101.40	105.74	105.74
106,89	103.00	105.74	105.74
107,09	109.10	105.95	105.74
107,24	111.40	106.17	105.95
107,28	114.10	106.34	106.17
107,3	121.80	106.37	106.34
107,31	127.60	106.37	106.37
107,47	129.90	106.36	106.37
107,35	128.00	106.44	106.36
107,31	123.50	106.29	106.44
107,32	124.00	106.23	106.29
107,32	127.40	106.23	106.23
107,34	127.60	106.23	106.23
107,53	128.40	106.23	106.23
107,72	131.40	106.34	106.23
107,75	135.10	106.44	106.34
107,79	134.00	106.44	106.44
107,81	144.50	106.48	106.44
107,9	147.30	106.50	106.48
107,8	150.90	106.57	106.50
107,86	148.70	106.40	106.57
107,8	141.40	106.37	106.40
107,74	138.90	106.25	106.37
107,75	139.80	106.21	106.25
107,83	145.60	106.21	106.21
107,8	147.90	106.24	106.21
107,81	148.50	106.19	106.24
107,86	151.10	106.08	106.19
107,83	157.50	106.13	106.08

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158085&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158085&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158085&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Multiple Linear Regression - Estimated Regression Equation
X[t] = + 25.7267919840376 -0.00823946509526631Y[t] + 1.23002986579692Y1[t] -0.467759327195805Y2[t] + 0.0460425932424228t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X[t] =  +  25.7267919840376 -0.00823946509526631Y[t] +  1.23002986579692Y1[t] -0.467759327195805Y2[t] +  0.0460425932424228t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158085&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X[t] =  +  25.7267919840376 -0.00823946509526631Y[t] +  1.23002986579692Y1[t] -0.467759327195805Y2[t] +  0.0460425932424228t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158085&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158085&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
X[t] = + 25.7267919840376 -0.00823946509526631Y[t] + 1.23002986579692Y1[t] -0.467759327195805Y2[t] + 0.0460425932424228t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)25.72679198403764.2553046.045800
Y-0.008239465095266310.002317-3.55680.0008320.000416
Y11.230029865796920.1574147.81400
Y2-0.4677593271958050.163279-2.86480.0060870.003043
t0.04604259324242280.00437610.520600

\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) & 25.7267919840376 & 4.255304 & 6.0458 & 0 & 0 \tabularnewline
Y & -0.00823946509526631 & 0.002317 & -3.5568 & 0.000832 & 0.000416 \tabularnewline
Y1 & 1.23002986579692 & 0.157414 & 7.814 & 0 & 0 \tabularnewline
Y2 & -0.467759327195805 & 0.163279 & -2.8648 & 0.006087 & 0.003043 \tabularnewline
t & 0.0460425932424228 & 0.004376 & 10.5206 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158085&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]25.7267919840376[/C][C]4.255304[/C][C]6.0458[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y[/C][C]-0.00823946509526631[/C][C]0.002317[/C][C]-3.5568[/C][C]0.000832[/C][C]0.000416[/C][/ROW]
[ROW][C]Y1[/C][C]1.23002986579692[/C][C]0.157414[/C][C]7.814[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.467759327195805[/C][C]0.163279[/C][C]-2.8648[/C][C]0.006087[/C][C]0.003043[/C][/ROW]
[ROW][C]t[/C][C]0.0460425932424228[/C][C]0.004376[/C][C]10.5206[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158085&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158085&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)25.72679198403764.2553046.045800
Y-0.008239465095266310.002317-3.55680.0008320.000416
Y11.230029865796920.1574147.81400
Y2-0.4677593271958050.163279-2.86480.0060870.003043
t0.04604259324242280.00437610.520600






Multiple Linear Regression - Regression Statistics
Multiple R0.996714490043566
R-squared0.993439774662806
Adjusted R-squared0.99291495663583
F-TEST (value)1892.9223532734
F-TEST (DF numerator)4
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0992785185599964
Sum Squared Residuals0.492811212373378

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996714490043566 \tabularnewline
R-squared & 0.993439774662806 \tabularnewline
Adjusted R-squared & 0.99291495663583 \tabularnewline
F-TEST (value) & 1892.9223532734 \tabularnewline
F-TEST (DF numerator) & 4 \tabularnewline
F-TEST (DF denominator) & 50 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0992785185599964 \tabularnewline
Sum Squared Residuals & 0.492811212373378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158085&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996714490043566[/C][/ROW]
[ROW][C]R-squared[/C][C]0.993439774662806[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.99291495663583[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1892.9223532734[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]4[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]50[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0992785185599964[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.492811212373378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158085&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158085&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.996714490043566
R-squared0.993439774662806
Adjusted R-squared0.99291495663583
F-TEST (value)1892.9223532734
F-TEST (DF numerator)4
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0992785185599964
Sum Squared Residuals0.492811212373378






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1104.17104.275639259676-0.105639259676094
2104.18104.328551832149-0.148551832148692
3104.2104.376216629256-0.176216629256249
4104.5104.4493905583280.0506094416718705
5104.78104.6663144245330.11368557546681
6104.88104.8647142159880.0152857840116471
7104.89104.912662220941-0.0226622209412982
8104.9104.929198548333-0.0291985483331952
9104.95104.963148029718-0.0131480297179208
10105.24105.0263168027060.213683197294379
11105.35105.3174568344590.0325431655409587
12105.44105.3874490090610.0525509909394802
13105.46105.463695449599-0.00369544959942088
14105.47105.490326321906-0.0203263219058953
15105.48105.541844765776-0.0618447657758781
16105.75105.5960679251290.153932074871353
17106.1105.8563664614140.243633538586029
18106.19106.228948112561-0.0389481125614406
19106.23106.2178578966590.0121421033406027
20106.24106.251169729873-0.0111697298725329
21106.25106.2466341219410.00336587805922372
22106.35106.2704890584110.0795109415890903
23106.48106.4549235361290.025076463871186
24106.52106.649288183175-0.129288183175192
25106.55106.653536533278-0.103536533277762
26106.55106.708499051001-0.15849905100119
27106.56106.736946992604-0.176946992604427
28106.89106.7698064416940.120193558305575
29107.09107.0238945696730.0661054303269172
30107.24107.2233635049610.0166364950394013
31107.28107.353357567648-0.0733575676481975
32107.3107.2933380900080.00666190999230533
33107.31107.2775590058820.0324409941183069
34107.47107.2923505307470.177649469252969
35107.35107.457128090206-0.107128090206176
36107.31107.318323050332-0.00832305033209918
37107.32107.356608018158-0.0366080181584469
38107.32107.402701989709-0.0827019897087135
39107.34107.447096689932-0.107096689932073
40107.53107.4865477110980.0434522889017152
41107.72107.6431751942930.076824805707429
42107.75107.7302812272710.0197187727293465
43107.79107.7386112993980.051388700601715
44107.81107.7473407037720.0626592962277002
45107.9107.7762030189760.123796981023928
46107.8107.869330441937-0.0693304419374058
47107.86107.69165162830.168348371699751
48107.8107.840460506387-0.0404605063874901
49107.74107.773530958288-0.0335309582883204
50107.75107.819087957577-0.0690879575766127
51107.83107.836052026354-0.00605202635432783
52107.8107.900044745852-0.100044745851548
53107.81107.865609386931-0.055609386931089
54107.86107.7783140520480.0816859479520487
55107.83107.884579087962-0.0545790879620511

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 104.17 & 104.275639259676 & -0.105639259676094 \tabularnewline
2 & 104.18 & 104.328551832149 & -0.148551832148692 \tabularnewline
3 & 104.2 & 104.376216629256 & -0.176216629256249 \tabularnewline
4 & 104.5 & 104.449390558328 & 0.0506094416718705 \tabularnewline
5 & 104.78 & 104.666314424533 & 0.11368557546681 \tabularnewline
6 & 104.88 & 104.864714215988 & 0.0152857840116471 \tabularnewline
7 & 104.89 & 104.912662220941 & -0.0226622209412982 \tabularnewline
8 & 104.9 & 104.929198548333 & -0.0291985483331952 \tabularnewline
9 & 104.95 & 104.963148029718 & -0.0131480297179208 \tabularnewline
10 & 105.24 & 105.026316802706 & 0.213683197294379 \tabularnewline
11 & 105.35 & 105.317456834459 & 0.0325431655409587 \tabularnewline
12 & 105.44 & 105.387449009061 & 0.0525509909394802 \tabularnewline
13 & 105.46 & 105.463695449599 & -0.00369544959942088 \tabularnewline
14 & 105.47 & 105.490326321906 & -0.0203263219058953 \tabularnewline
15 & 105.48 & 105.541844765776 & -0.0618447657758781 \tabularnewline
16 & 105.75 & 105.596067925129 & 0.153932074871353 \tabularnewline
17 & 106.1 & 105.856366461414 & 0.243633538586029 \tabularnewline
18 & 106.19 & 106.228948112561 & -0.0389481125614406 \tabularnewline
19 & 106.23 & 106.217857896659 & 0.0121421033406027 \tabularnewline
20 & 106.24 & 106.251169729873 & -0.0111697298725329 \tabularnewline
21 & 106.25 & 106.246634121941 & 0.00336587805922372 \tabularnewline
22 & 106.35 & 106.270489058411 & 0.0795109415890903 \tabularnewline
23 & 106.48 & 106.454923536129 & 0.025076463871186 \tabularnewline
24 & 106.52 & 106.649288183175 & -0.129288183175192 \tabularnewline
25 & 106.55 & 106.653536533278 & -0.103536533277762 \tabularnewline
26 & 106.55 & 106.708499051001 & -0.15849905100119 \tabularnewline
27 & 106.56 & 106.736946992604 & -0.176946992604427 \tabularnewline
28 & 106.89 & 106.769806441694 & 0.120193558305575 \tabularnewline
29 & 107.09 & 107.023894569673 & 0.0661054303269172 \tabularnewline
30 & 107.24 & 107.223363504961 & 0.0166364950394013 \tabularnewline
31 & 107.28 & 107.353357567648 & -0.0733575676481975 \tabularnewline
32 & 107.3 & 107.293338090008 & 0.00666190999230533 \tabularnewline
33 & 107.31 & 107.277559005882 & 0.0324409941183069 \tabularnewline
34 & 107.47 & 107.292350530747 & 0.177649469252969 \tabularnewline
35 & 107.35 & 107.457128090206 & -0.107128090206176 \tabularnewline
36 & 107.31 & 107.318323050332 & -0.00832305033209918 \tabularnewline
37 & 107.32 & 107.356608018158 & -0.0366080181584469 \tabularnewline
38 & 107.32 & 107.402701989709 & -0.0827019897087135 \tabularnewline
39 & 107.34 & 107.447096689932 & -0.107096689932073 \tabularnewline
40 & 107.53 & 107.486547711098 & 0.0434522889017152 \tabularnewline
41 & 107.72 & 107.643175194293 & 0.076824805707429 \tabularnewline
42 & 107.75 & 107.730281227271 & 0.0197187727293465 \tabularnewline
43 & 107.79 & 107.738611299398 & 0.051388700601715 \tabularnewline
44 & 107.81 & 107.747340703772 & 0.0626592962277002 \tabularnewline
45 & 107.9 & 107.776203018976 & 0.123796981023928 \tabularnewline
46 & 107.8 & 107.869330441937 & -0.0693304419374058 \tabularnewline
47 & 107.86 & 107.6916516283 & 0.168348371699751 \tabularnewline
48 & 107.8 & 107.840460506387 & -0.0404605063874901 \tabularnewline
49 & 107.74 & 107.773530958288 & -0.0335309582883204 \tabularnewline
50 & 107.75 & 107.819087957577 & -0.0690879575766127 \tabularnewline
51 & 107.83 & 107.836052026354 & -0.00605202635432783 \tabularnewline
52 & 107.8 & 107.900044745852 & -0.100044745851548 \tabularnewline
53 & 107.81 & 107.865609386931 & -0.055609386931089 \tabularnewline
54 & 107.86 & 107.778314052048 & 0.0816859479520487 \tabularnewline
55 & 107.83 & 107.884579087962 & -0.0545790879620511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158085&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]104.17[/C][C]104.275639259676[/C][C]-0.105639259676094[/C][/ROW]
[ROW][C]2[/C][C]104.18[/C][C]104.328551832149[/C][C]-0.148551832148692[/C][/ROW]
[ROW][C]3[/C][C]104.2[/C][C]104.376216629256[/C][C]-0.176216629256249[/C][/ROW]
[ROW][C]4[/C][C]104.5[/C][C]104.449390558328[/C][C]0.0506094416718705[/C][/ROW]
[ROW][C]5[/C][C]104.78[/C][C]104.666314424533[/C][C]0.11368557546681[/C][/ROW]
[ROW][C]6[/C][C]104.88[/C][C]104.864714215988[/C][C]0.0152857840116471[/C][/ROW]
[ROW][C]7[/C][C]104.89[/C][C]104.912662220941[/C][C]-0.0226622209412982[/C][/ROW]
[ROW][C]8[/C][C]104.9[/C][C]104.929198548333[/C][C]-0.0291985483331952[/C][/ROW]
[ROW][C]9[/C][C]104.95[/C][C]104.963148029718[/C][C]-0.0131480297179208[/C][/ROW]
[ROW][C]10[/C][C]105.24[/C][C]105.026316802706[/C][C]0.213683197294379[/C][/ROW]
[ROW][C]11[/C][C]105.35[/C][C]105.317456834459[/C][C]0.0325431655409587[/C][/ROW]
[ROW][C]12[/C][C]105.44[/C][C]105.387449009061[/C][C]0.0525509909394802[/C][/ROW]
[ROW][C]13[/C][C]105.46[/C][C]105.463695449599[/C][C]-0.00369544959942088[/C][/ROW]
[ROW][C]14[/C][C]105.47[/C][C]105.490326321906[/C][C]-0.0203263219058953[/C][/ROW]
[ROW][C]15[/C][C]105.48[/C][C]105.541844765776[/C][C]-0.0618447657758781[/C][/ROW]
[ROW][C]16[/C][C]105.75[/C][C]105.596067925129[/C][C]0.153932074871353[/C][/ROW]
[ROW][C]17[/C][C]106.1[/C][C]105.856366461414[/C][C]0.243633538586029[/C][/ROW]
[ROW][C]18[/C][C]106.19[/C][C]106.228948112561[/C][C]-0.0389481125614406[/C][/ROW]
[ROW][C]19[/C][C]106.23[/C][C]106.217857896659[/C][C]0.0121421033406027[/C][/ROW]
[ROW][C]20[/C][C]106.24[/C][C]106.251169729873[/C][C]-0.0111697298725329[/C][/ROW]
[ROW][C]21[/C][C]106.25[/C][C]106.246634121941[/C][C]0.00336587805922372[/C][/ROW]
[ROW][C]22[/C][C]106.35[/C][C]106.270489058411[/C][C]0.0795109415890903[/C][/ROW]
[ROW][C]23[/C][C]106.48[/C][C]106.454923536129[/C][C]0.025076463871186[/C][/ROW]
[ROW][C]24[/C][C]106.52[/C][C]106.649288183175[/C][C]-0.129288183175192[/C][/ROW]
[ROW][C]25[/C][C]106.55[/C][C]106.653536533278[/C][C]-0.103536533277762[/C][/ROW]
[ROW][C]26[/C][C]106.55[/C][C]106.708499051001[/C][C]-0.15849905100119[/C][/ROW]
[ROW][C]27[/C][C]106.56[/C][C]106.736946992604[/C][C]-0.176946992604427[/C][/ROW]
[ROW][C]28[/C][C]106.89[/C][C]106.769806441694[/C][C]0.120193558305575[/C][/ROW]
[ROW][C]29[/C][C]107.09[/C][C]107.023894569673[/C][C]0.0661054303269172[/C][/ROW]
[ROW][C]30[/C][C]107.24[/C][C]107.223363504961[/C][C]0.0166364950394013[/C][/ROW]
[ROW][C]31[/C][C]107.28[/C][C]107.353357567648[/C][C]-0.0733575676481975[/C][/ROW]
[ROW][C]32[/C][C]107.3[/C][C]107.293338090008[/C][C]0.00666190999230533[/C][/ROW]
[ROW][C]33[/C][C]107.31[/C][C]107.277559005882[/C][C]0.0324409941183069[/C][/ROW]
[ROW][C]34[/C][C]107.47[/C][C]107.292350530747[/C][C]0.177649469252969[/C][/ROW]
[ROW][C]35[/C][C]107.35[/C][C]107.457128090206[/C][C]-0.107128090206176[/C][/ROW]
[ROW][C]36[/C][C]107.31[/C][C]107.318323050332[/C][C]-0.00832305033209918[/C][/ROW]
[ROW][C]37[/C][C]107.32[/C][C]107.356608018158[/C][C]-0.0366080181584469[/C][/ROW]
[ROW][C]38[/C][C]107.32[/C][C]107.402701989709[/C][C]-0.0827019897087135[/C][/ROW]
[ROW][C]39[/C][C]107.34[/C][C]107.447096689932[/C][C]-0.107096689932073[/C][/ROW]
[ROW][C]40[/C][C]107.53[/C][C]107.486547711098[/C][C]0.0434522889017152[/C][/ROW]
[ROW][C]41[/C][C]107.72[/C][C]107.643175194293[/C][C]0.076824805707429[/C][/ROW]
[ROW][C]42[/C][C]107.75[/C][C]107.730281227271[/C][C]0.0197187727293465[/C][/ROW]
[ROW][C]43[/C][C]107.79[/C][C]107.738611299398[/C][C]0.051388700601715[/C][/ROW]
[ROW][C]44[/C][C]107.81[/C][C]107.747340703772[/C][C]0.0626592962277002[/C][/ROW]
[ROW][C]45[/C][C]107.9[/C][C]107.776203018976[/C][C]0.123796981023928[/C][/ROW]
[ROW][C]46[/C][C]107.8[/C][C]107.869330441937[/C][C]-0.0693304419374058[/C][/ROW]
[ROW][C]47[/C][C]107.86[/C][C]107.6916516283[/C][C]0.168348371699751[/C][/ROW]
[ROW][C]48[/C][C]107.8[/C][C]107.840460506387[/C][C]-0.0404605063874901[/C][/ROW]
[ROW][C]49[/C][C]107.74[/C][C]107.773530958288[/C][C]-0.0335309582883204[/C][/ROW]
[ROW][C]50[/C][C]107.75[/C][C]107.819087957577[/C][C]-0.0690879575766127[/C][/ROW]
[ROW][C]51[/C][C]107.83[/C][C]107.836052026354[/C][C]-0.00605202635432783[/C][/ROW]
[ROW][C]52[/C][C]107.8[/C][C]107.900044745852[/C][C]-0.100044745851548[/C][/ROW]
[ROW][C]53[/C][C]107.81[/C][C]107.865609386931[/C][C]-0.055609386931089[/C][/ROW]
[ROW][C]54[/C][C]107.86[/C][C]107.778314052048[/C][C]0.0816859479520487[/C][/ROW]
[ROW][C]55[/C][C]107.83[/C][C]107.884579087962[/C][C]-0.0545790879620511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158085&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158085&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1104.17104.275639259676-0.105639259676094
2104.18104.328551832149-0.148551832148692
3104.2104.376216629256-0.176216629256249
4104.5104.4493905583280.0506094416718705
5104.78104.6663144245330.11368557546681
6104.88104.8647142159880.0152857840116471
7104.89104.912662220941-0.0226622209412982
8104.9104.929198548333-0.0291985483331952
9104.95104.963148029718-0.0131480297179208
10105.24105.0263168027060.213683197294379
11105.35105.3174568344590.0325431655409587
12105.44105.3874490090610.0525509909394802
13105.46105.463695449599-0.00369544959942088
14105.47105.490326321906-0.0203263219058953
15105.48105.541844765776-0.0618447657758781
16105.75105.5960679251290.153932074871353
17106.1105.8563664614140.243633538586029
18106.19106.228948112561-0.0389481125614406
19106.23106.2178578966590.0121421033406027
20106.24106.251169729873-0.0111697298725329
21106.25106.2466341219410.00336587805922372
22106.35106.2704890584110.0795109415890903
23106.48106.4549235361290.025076463871186
24106.52106.649288183175-0.129288183175192
25106.55106.653536533278-0.103536533277762
26106.55106.708499051001-0.15849905100119
27106.56106.736946992604-0.176946992604427
28106.89106.7698064416940.120193558305575
29107.09107.0238945696730.0661054303269172
30107.24107.2233635049610.0166364950394013
31107.28107.353357567648-0.0733575676481975
32107.3107.2933380900080.00666190999230533
33107.31107.2775590058820.0324409941183069
34107.47107.2923505307470.177649469252969
35107.35107.457128090206-0.107128090206176
36107.31107.318323050332-0.00832305033209918
37107.32107.356608018158-0.0366080181584469
38107.32107.402701989709-0.0827019897087135
39107.34107.447096689932-0.107096689932073
40107.53107.4865477110980.0434522889017152
41107.72107.6431751942930.076824805707429
42107.75107.7302812272710.0197187727293465
43107.79107.7386112993980.051388700601715
44107.81107.7473407037720.0626592962277002
45107.9107.7762030189760.123796981023928
46107.8107.869330441937-0.0693304419374058
47107.86107.69165162830.168348371699751
48107.8107.840460506387-0.0404605063874901
49107.74107.773530958288-0.0335309582883204
50107.75107.819087957577-0.0690879575766127
51107.83107.836052026354-0.00605202635432783
52107.8107.900044745852-0.100044745851548
53107.81107.865609386931-0.055609386931089
54107.86107.7783140520480.0816859479520487
55107.83107.884579087962-0.0545790879620511






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.2984298582985080.5968597165970150.701570141701492
90.2199854277848690.4399708555697380.780014572215131
100.1991852901550820.3983705803101650.800814709844918
110.3966517146776780.7933034293553550.603348285322322
120.3026605597618170.6053211195236350.697339440238183
130.2142646231066710.4285292462133420.785735376893329
140.1657172164323830.3314344328647650.834282783567618
150.3105588002166520.6211176004333050.689441199783348
160.234887939154420.469775878308840.76511206084558
170.2997816126722980.5995632253445960.700218387327702
180.2597343003481090.5194686006962190.740265699651891
190.4651470297298990.9302940594597980.534852970270101
200.4268899653578670.8537799307157350.573110034642133
210.3563780670024970.7127561340049950.643621932997503
220.3053059486724380.6106118973448760.694694051327562
230.2752778232884120.5505556465768240.724722176711588
240.3741362478821520.7482724957643040.625863752117848
250.3690494595947230.7380989191894450.630950540405277
260.5353384259126860.9293231481746290.464661574087314
270.8240450028214660.3519099943570670.175954997178534
280.8156847833863590.3686304332272830.184315216613641
290.8099917598387030.3800164803225940.190008240161297
300.8295663467813120.3408673064373760.170433653218688
310.7777203636633190.4445592726733620.222279636336681
320.778675961644270.4426480767114610.22132403835573
330.7348457723681490.5303084552637030.265154227631851
340.8205496782070080.3589006435859850.179450321792992
350.8819558216161070.2360883567677860.118044178383893
360.8560906105745060.2878187788509880.143909389425494
370.8527491435265370.2945017129469260.147250856473463
380.897646077146410.2047078457071810.10235392285359
390.9925876348484580.01482473030308450.00741236515154226
400.9996514336171080.0006971327657845260.000348566382892263
410.999199145577710.001601708844579770.000800854422289883
420.998351620100410.003296759799180610.00164837989959031
430.9951248870626920.009750225874616780.00487511293730839
440.99257434936090.01485130127820070.00742565063910034
450.9926238853383470.01475222932330670.00737611466165335
460.9821128483443950.03577430331121070.0178871516556053
470.9450219150796310.1099561698407380.0549780849203692

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
8 & 0.298429858298508 & 0.596859716597015 & 0.701570141701492 \tabularnewline
9 & 0.219985427784869 & 0.439970855569738 & 0.780014572215131 \tabularnewline
10 & 0.199185290155082 & 0.398370580310165 & 0.800814709844918 \tabularnewline
11 & 0.396651714677678 & 0.793303429355355 & 0.603348285322322 \tabularnewline
12 & 0.302660559761817 & 0.605321119523635 & 0.697339440238183 \tabularnewline
13 & 0.214264623106671 & 0.428529246213342 & 0.785735376893329 \tabularnewline
14 & 0.165717216432383 & 0.331434432864765 & 0.834282783567618 \tabularnewline
15 & 0.310558800216652 & 0.621117600433305 & 0.689441199783348 \tabularnewline
16 & 0.23488793915442 & 0.46977587830884 & 0.76511206084558 \tabularnewline
17 & 0.299781612672298 & 0.599563225344596 & 0.700218387327702 \tabularnewline
18 & 0.259734300348109 & 0.519468600696219 & 0.740265699651891 \tabularnewline
19 & 0.465147029729899 & 0.930294059459798 & 0.534852970270101 \tabularnewline
20 & 0.426889965357867 & 0.853779930715735 & 0.573110034642133 \tabularnewline
21 & 0.356378067002497 & 0.712756134004995 & 0.643621932997503 \tabularnewline
22 & 0.305305948672438 & 0.610611897344876 & 0.694694051327562 \tabularnewline
23 & 0.275277823288412 & 0.550555646576824 & 0.724722176711588 \tabularnewline
24 & 0.374136247882152 & 0.748272495764304 & 0.625863752117848 \tabularnewline
25 & 0.369049459594723 & 0.738098919189445 & 0.630950540405277 \tabularnewline
26 & 0.535338425912686 & 0.929323148174629 & 0.464661574087314 \tabularnewline
27 & 0.824045002821466 & 0.351909994357067 & 0.175954997178534 \tabularnewline
28 & 0.815684783386359 & 0.368630433227283 & 0.184315216613641 \tabularnewline
29 & 0.809991759838703 & 0.380016480322594 & 0.190008240161297 \tabularnewline
30 & 0.829566346781312 & 0.340867306437376 & 0.170433653218688 \tabularnewline
31 & 0.777720363663319 & 0.444559272673362 & 0.222279636336681 \tabularnewline
32 & 0.77867596164427 & 0.442648076711461 & 0.22132403835573 \tabularnewline
33 & 0.734845772368149 & 0.530308455263703 & 0.265154227631851 \tabularnewline
34 & 0.820549678207008 & 0.358900643585985 & 0.179450321792992 \tabularnewline
35 & 0.881955821616107 & 0.236088356767786 & 0.118044178383893 \tabularnewline
36 & 0.856090610574506 & 0.287818778850988 & 0.143909389425494 \tabularnewline
37 & 0.852749143526537 & 0.294501712946926 & 0.147250856473463 \tabularnewline
38 & 0.89764607714641 & 0.204707845707181 & 0.10235392285359 \tabularnewline
39 & 0.992587634848458 & 0.0148247303030845 & 0.00741236515154226 \tabularnewline
40 & 0.999651433617108 & 0.000697132765784526 & 0.000348566382892263 \tabularnewline
41 & 0.99919914557771 & 0.00160170884457977 & 0.000800854422289883 \tabularnewline
42 & 0.99835162010041 & 0.00329675979918061 & 0.00164837989959031 \tabularnewline
43 & 0.995124887062692 & 0.00975022587461678 & 0.00487511293730839 \tabularnewline
44 & 0.9925743493609 & 0.0148513012782007 & 0.00742565063910034 \tabularnewline
45 & 0.992623885338347 & 0.0147522293233067 & 0.00737611466165335 \tabularnewline
46 & 0.982112848344395 & 0.0357743033112107 & 0.0178871516556053 \tabularnewline
47 & 0.945021915079631 & 0.109956169840738 & 0.0549780849203692 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158085&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]8[/C][C]0.298429858298508[/C][C]0.596859716597015[/C][C]0.701570141701492[/C][/ROW]
[ROW][C]9[/C][C]0.219985427784869[/C][C]0.439970855569738[/C][C]0.780014572215131[/C][/ROW]
[ROW][C]10[/C][C]0.199185290155082[/C][C]0.398370580310165[/C][C]0.800814709844918[/C][/ROW]
[ROW][C]11[/C][C]0.396651714677678[/C][C]0.793303429355355[/C][C]0.603348285322322[/C][/ROW]
[ROW][C]12[/C][C]0.302660559761817[/C][C]0.605321119523635[/C][C]0.697339440238183[/C][/ROW]
[ROW][C]13[/C][C]0.214264623106671[/C][C]0.428529246213342[/C][C]0.785735376893329[/C][/ROW]
[ROW][C]14[/C][C]0.165717216432383[/C][C]0.331434432864765[/C][C]0.834282783567618[/C][/ROW]
[ROW][C]15[/C][C]0.310558800216652[/C][C]0.621117600433305[/C][C]0.689441199783348[/C][/ROW]
[ROW][C]16[/C][C]0.23488793915442[/C][C]0.46977587830884[/C][C]0.76511206084558[/C][/ROW]
[ROW][C]17[/C][C]0.299781612672298[/C][C]0.599563225344596[/C][C]0.700218387327702[/C][/ROW]
[ROW][C]18[/C][C]0.259734300348109[/C][C]0.519468600696219[/C][C]0.740265699651891[/C][/ROW]
[ROW][C]19[/C][C]0.465147029729899[/C][C]0.930294059459798[/C][C]0.534852970270101[/C][/ROW]
[ROW][C]20[/C][C]0.426889965357867[/C][C]0.853779930715735[/C][C]0.573110034642133[/C][/ROW]
[ROW][C]21[/C][C]0.356378067002497[/C][C]0.712756134004995[/C][C]0.643621932997503[/C][/ROW]
[ROW][C]22[/C][C]0.305305948672438[/C][C]0.610611897344876[/C][C]0.694694051327562[/C][/ROW]
[ROW][C]23[/C][C]0.275277823288412[/C][C]0.550555646576824[/C][C]0.724722176711588[/C][/ROW]
[ROW][C]24[/C][C]0.374136247882152[/C][C]0.748272495764304[/C][C]0.625863752117848[/C][/ROW]
[ROW][C]25[/C][C]0.369049459594723[/C][C]0.738098919189445[/C][C]0.630950540405277[/C][/ROW]
[ROW][C]26[/C][C]0.535338425912686[/C][C]0.929323148174629[/C][C]0.464661574087314[/C][/ROW]
[ROW][C]27[/C][C]0.824045002821466[/C][C]0.351909994357067[/C][C]0.175954997178534[/C][/ROW]
[ROW][C]28[/C][C]0.815684783386359[/C][C]0.368630433227283[/C][C]0.184315216613641[/C][/ROW]
[ROW][C]29[/C][C]0.809991759838703[/C][C]0.380016480322594[/C][C]0.190008240161297[/C][/ROW]
[ROW][C]30[/C][C]0.829566346781312[/C][C]0.340867306437376[/C][C]0.170433653218688[/C][/ROW]
[ROW][C]31[/C][C]0.777720363663319[/C][C]0.444559272673362[/C][C]0.222279636336681[/C][/ROW]
[ROW][C]32[/C][C]0.77867596164427[/C][C]0.442648076711461[/C][C]0.22132403835573[/C][/ROW]
[ROW][C]33[/C][C]0.734845772368149[/C][C]0.530308455263703[/C][C]0.265154227631851[/C][/ROW]
[ROW][C]34[/C][C]0.820549678207008[/C][C]0.358900643585985[/C][C]0.179450321792992[/C][/ROW]
[ROW][C]35[/C][C]0.881955821616107[/C][C]0.236088356767786[/C][C]0.118044178383893[/C][/ROW]
[ROW][C]36[/C][C]0.856090610574506[/C][C]0.287818778850988[/C][C]0.143909389425494[/C][/ROW]
[ROW][C]37[/C][C]0.852749143526537[/C][C]0.294501712946926[/C][C]0.147250856473463[/C][/ROW]
[ROW][C]38[/C][C]0.89764607714641[/C][C]0.204707845707181[/C][C]0.10235392285359[/C][/ROW]
[ROW][C]39[/C][C]0.992587634848458[/C][C]0.0148247303030845[/C][C]0.00741236515154226[/C][/ROW]
[ROW][C]40[/C][C]0.999651433617108[/C][C]0.000697132765784526[/C][C]0.000348566382892263[/C][/ROW]
[ROW][C]41[/C][C]0.99919914557771[/C][C]0.00160170884457977[/C][C]0.000800854422289883[/C][/ROW]
[ROW][C]42[/C][C]0.99835162010041[/C][C]0.00329675979918061[/C][C]0.00164837989959031[/C][/ROW]
[ROW][C]43[/C][C]0.995124887062692[/C][C]0.00975022587461678[/C][C]0.00487511293730839[/C][/ROW]
[ROW][C]44[/C][C]0.9925743493609[/C][C]0.0148513012782007[/C][C]0.00742565063910034[/C][/ROW]
[ROW][C]45[/C][C]0.992623885338347[/C][C]0.0147522293233067[/C][C]0.00737611466165335[/C][/ROW]
[ROW][C]46[/C][C]0.982112848344395[/C][C]0.0357743033112107[/C][C]0.0178871516556053[/C][/ROW]
[ROW][C]47[/C][C]0.945021915079631[/C][C]0.109956169840738[/C][C]0.0549780849203692[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158085&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158085&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.2984298582985080.5968597165970150.701570141701492
90.2199854277848690.4399708555697380.780014572215131
100.1991852901550820.3983705803101650.800814709844918
110.3966517146776780.7933034293553550.603348285322322
120.3026605597618170.6053211195236350.697339440238183
130.2142646231066710.4285292462133420.785735376893329
140.1657172164323830.3314344328647650.834282783567618
150.3105588002166520.6211176004333050.689441199783348
160.234887939154420.469775878308840.76511206084558
170.2997816126722980.5995632253445960.700218387327702
180.2597343003481090.5194686006962190.740265699651891
190.4651470297298990.9302940594597980.534852970270101
200.4268899653578670.8537799307157350.573110034642133
210.3563780670024970.7127561340049950.643621932997503
220.3053059486724380.6106118973448760.694694051327562
230.2752778232884120.5505556465768240.724722176711588
240.3741362478821520.7482724957643040.625863752117848
250.3690494595947230.7380989191894450.630950540405277
260.5353384259126860.9293231481746290.464661574087314
270.8240450028214660.3519099943570670.175954997178534
280.8156847833863590.3686304332272830.184315216613641
290.8099917598387030.3800164803225940.190008240161297
300.8295663467813120.3408673064373760.170433653218688
310.7777203636633190.4445592726733620.222279636336681
320.778675961644270.4426480767114610.22132403835573
330.7348457723681490.5303084552637030.265154227631851
340.8205496782070080.3589006435859850.179450321792992
350.8819558216161070.2360883567677860.118044178383893
360.8560906105745060.2878187788509880.143909389425494
370.8527491435265370.2945017129469260.147250856473463
380.897646077146410.2047078457071810.10235392285359
390.9925876348484580.01482473030308450.00741236515154226
400.9996514336171080.0006971327657845260.000348566382892263
410.999199145577710.001601708844579770.000800854422289883
420.998351620100410.003296759799180610.00164837989959031
430.9951248870626920.009750225874616780.00487511293730839
440.99257434936090.01485130127820070.00742565063910034
450.9926238853383470.01475222932330670.00737611466165335
460.9821128483443950.03577430331121070.0178871516556053
470.9450219150796310.1099561698407380.0549780849203692






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.1NOK
5% type I error level80.2NOK
10% type I error level80.2NOK

\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 & 0.1 & NOK \tabularnewline
5% type I error level & 8 & 0.2 & NOK \tabularnewline
10% type I error level & 8 & 0.2 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158085&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]0.1[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]8[/C][C]0.2[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.2[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158085&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158085&T=6

As an alternative you can also use a QR Code:  
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 testsOK/NOK
1% type I error level40.1NOK
5% type I error level80.2NOK
10% type I error level80.2NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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