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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 19 Nov 2009 13:05:09 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t125866122187ga0zsyst1232l.htm/, Retrieved Tue, 23 Apr 2024 15:21:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57927, Retrieved Tue, 23 Apr 2024 15:21:16 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

131

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]
-   PD    [Multiple Regression] [] [2009-11-19 19:58:46] [5edbdb7a459c4059b6c3b063ba86821c]
-    D        [Multiple Regression] [] [2009-11-19 20:05:09] [24029b2c7217429de6ff94b5379eb52c] [Current]

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Dataseries X:

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Histogram

Boxplots

100.4	120.2	17	74	79.9	72.9	72.9
103	122.1	16	76	74	79.9	72.9
99	119.3	20	69.6	76	74	79.9
104.8	121.7	24	77.3	69.6	76	74
104.5	113.5	23	75.2	77.3	69.6	76
104.8	123.7	20	75.8	75.2	77.3	69.6
103.8	123.4	21	77.6	75.8	75.2	77.3
106.3	126.4	19	76.7	77.6	75.8	75.2
105.2	124.1	23	77	76.7	77.6	75.8
108.2	125.6	23	77.9	77	76.7	77.6
106.2	124.8	23	76.7	77.9	77	76.7
103.9	123	23	71.9	76.7	77.9	77
104.9	126.9	27	73.4	71.9	76.7	77.9
106.2	127.3	26	72.5	73.4	71.9	76.7
107.9	129	17	73.7	72.5	73.4	71.9
106.9	126.2	24	69.5	73.7	72.5	73.4
110.3	125.4	26	74.7	69.5	73.7	72.5
109.8	126.3	24	72.5	74.7	69.5	73.7
108.3	126.3	27	72.1	72.5	74.7	69.5
110.9	128.4	27	70.7	72.1	72.5	74.7
109.8	127.2	26	71.4	70.7	72.1	72.5
109.3	128.5	24	69.5	71.4	70.7	72.1
109	129	23	73.5	69.5	71.4	70.7
107.9	128.9	23	72.4	73.5	69.5	71.4
108.4	128.3	24	74.5	72.4	73.5	69.5
107.2	124.6	17	72.2	74.5	72.4	73.5
109.5	126.2	21	73	72.2	74.5	72.4
109.9	129.1	19	73.3	73	72.2	74.5
108	127.3	22	71.3	73.3	73	72.2
114.7	129.2	22	73.6	71.3	73.3	73
115.6	130.4	18	71.3	73.6	71.3	73.3
107.6	125.9	16	71.2	71.3	73.6	71.3
115.9	135.8	14	81.4	71.2	71.3	73.6
111.8	126.4	12	76.1	81.4	71.2	71.3
110	129.5	14	71.1	76.1	81.4	71.2
109.2	128.4	16	75.7	71.1	76.1	81.4
108	125.6	8	70	75.7	71.1	76.1
105.6	127.7	3	68.5	70	75.7	71.1
103	126.4	0	56.7	68.5	70	75.7
99.6	124.2	5	57.9	56.7	68.5	70
97.9	126.4	1	58.8	57.9	56.7	68.5
97.6	123.7	1	59.3	58.8	57.9	56.7
96.2	121.8	3	61.3	59.3	58.8	57.9
97.9	124	6	62.9	61.3	59.3	58.8
94.5	122.7	7	61.4	62.9	61.3	59.3
95.4	122.9	8	64.5	61.4	62.9	61.3
94.4	121	14	63.8	64.5	61.4	62.9
96.3	122.8	14	61.6	63.8	64.5	61.4
95.1	122.9	13	64.7	61.6	63.8	64.5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57927&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57927&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 20.2513189201664 + 0.425341901487542totid[t] -0.0455449630743466ndzcg[t] + 0.0436802973309247indc[t] + 0.188344373020551y1[t] + 0.163567515100477y2[t] -0.130967620439291`y3 `[t] + 0.296514116202145M1[t] -0.835837579481557M2[t] -3.76745489042413M3[t] -2.08061356471506M4[t] -1.12030986429559M5[t] -1.97031879592753M6[t] -1.21767349589456M7[t] -1.11620771659602M8[t] + 1.25633708049614M9[t] + 0.269097496660407M10[t] -0.08551092511179M11[t] -0.166442807258652t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  20.2513189201664 +  0.425341901487542totid[t] -0.0455449630743466ndzcg[t] +  0.0436802973309247indc[t] +  0.188344373020551y1[t] +  0.163567515100477y2[t] -0.130967620439291`y3
`[t] +  0.296514116202145M1[t] -0.835837579481557M2[t] -3.76745489042413M3[t] -2.08061356471506M4[t] -1.12030986429559M5[t] -1.97031879592753M6[t] -1.21767349589456M7[t] -1.11620771659602M8[t] +  1.25633708049614M9[t] +  0.269097496660407M10[t] -0.08551092511179M11[t] -0.166442807258652t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57927&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  20.2513189201664 +  0.425341901487542totid[t] -0.0455449630743466ndzcg[t] +  0.0436802973309247indc[t] +  0.188344373020551y1[t] +  0.163567515100477y2[t] -0.130967620439291`y3
`[t] +  0.296514116202145M1[t] -0.835837579481557M2[t] -3.76745489042413M3[t] -2.08061356471506M4[t] -1.12030986429559M5[t] -1.97031879592753M6[t] -1.21767349589456M7[t] -1.11620771659602M8[t] +  1.25633708049614M9[t] +  0.269097496660407M10[t] -0.08551092511179M11[t] -0.166442807258652t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57927&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 20.2513189201664 + 0.425341901487542totid[t] -0.0455449630743466ndzcg[t] + 0.0436802973309247indc[t] + 0.188344373020551y1[t] + 0.163567515100477y2[t] -0.130967620439291`y3 `[t] + 0.296514116202145M1[t] -0.835837579481557M2[t] -3.76745489042413M3[t] -2.08061356471506M4[t] -1.12030986429559M5[t] -1.97031879592753M6[t] -1.21767349589456M7[t] -1.11620771659602M8[t] + 1.25633708049614M9[t] + 0.269097496660407M10[t] -0.08551092511179M11[t] -0.166442807258652t + 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)	20.2513189201664	23.268082	0.8703	0.391022	0.195511
totid	0.425341901487542	0.244499	1.7396	0.092173	0.046086
ndzcg	-0.0455449630743466	0.268582	-0.1696	0.866482	0.433241
indc	0.0436802973309247	0.104583	0.4177	0.67917	0.339585
y1	0.188344373020551	0.189551	0.9936	0.328348	0.164174
y2	0.163567515100477	0.16883	0.9688	0.340378	0.170189
`y3 `	-0.130967620439291	0.163436	-0.8013	0.429237	0.214619
M1	0.296514116202145	2.127164	0.1394	0.89007	0.445035
M2	-0.835837579481557	2.415932	-0.346	0.731781	0.36589
M3	-3.76745489042413	2.405121	-1.5664	0.127737	0.063868
M4	-2.08061356471506	2.526785	-0.8234	0.416765	0.208383
M5	-1.12030986429559	2.680751	-0.4179	0.67899	0.339495
M6	-1.97031879592753	2.718052	-0.7249	0.474129	0.237065
M7	-1.21767349589456	2.517465	-0.4837	0.632118	0.316059
M8	-1.11620771659602	2.409731	-0.4632	0.646558	0.323279
M9	1.25633708049614	2.385667	0.5266	0.602331	0.301165
M10	0.269097496660407	2.362987	0.1139	0.910091	0.455046
M11	-0.08551092511179	2.259958	-0.0378	0.970068	0.485034
t	-0.166442807258652	0.077479	-2.1482	0.039892	0.019946

\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) & 20.2513189201664 & 23.268082 & 0.8703 & 0.391022 & 0.195511 \tabularnewline
totid & 0.425341901487542 & 0.244499 & 1.7396 & 0.092173 & 0.046086 \tabularnewline
ndzcg & -0.0455449630743466 & 0.268582 & -0.1696 & 0.866482 & 0.433241 \tabularnewline
indc & 0.0436802973309247 & 0.104583 & 0.4177 & 0.67917 & 0.339585 \tabularnewline
y1 & 0.188344373020551 & 0.189551 & 0.9936 & 0.328348 & 0.164174 \tabularnewline
y2 & 0.163567515100477 & 0.16883 & 0.9688 & 0.340378 & 0.170189 \tabularnewline
`y3
` & -0.130967620439291 & 0.163436 & -0.8013 & 0.429237 & 0.214619 \tabularnewline
M1 & 0.296514116202145 & 2.127164 & 0.1394 & 0.89007 & 0.445035 \tabularnewline
M2 & -0.835837579481557 & 2.415932 & -0.346 & 0.731781 & 0.36589 \tabularnewline
M3 & -3.76745489042413 & 2.405121 & -1.5664 & 0.127737 & 0.063868 \tabularnewline
M4 & -2.08061356471506 & 2.526785 & -0.8234 & 0.416765 & 0.208383 \tabularnewline
M5 & -1.12030986429559 & 2.680751 & -0.4179 & 0.67899 & 0.339495 \tabularnewline
M6 & -1.97031879592753 & 2.718052 & -0.7249 & 0.474129 & 0.237065 \tabularnewline
M7 & -1.21767349589456 & 2.517465 & -0.4837 & 0.632118 & 0.316059 \tabularnewline
M8 & -1.11620771659602 & 2.409731 & -0.4632 & 0.646558 & 0.323279 \tabularnewline
M9 & 1.25633708049614 & 2.385667 & 0.5266 & 0.602331 & 0.301165 \tabularnewline
M10 & 0.269097496660407 & 2.362987 & 0.1139 & 0.910091 & 0.455046 \tabularnewline
M11 & -0.08551092511179 & 2.259958 & -0.0378 & 0.970068 & 0.485034 \tabularnewline
t & -0.166442807258652 & 0.077479 & -2.1482 & 0.039892 & 0.019946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57927&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]20.2513189201664[/C][C]23.268082[/C][C]0.8703[/C][C]0.391022[/C][C]0.195511[/C][/ROW]
[ROW][C]totid[/C][C]0.425341901487542[/C][C]0.244499[/C][C]1.7396[/C][C]0.092173[/C][C]0.046086[/C][/ROW]
[ROW][C]ndzcg[/C][C]-0.0455449630743466[/C][C]0.268582[/C][C]-0.1696[/C][C]0.866482[/C][C]0.433241[/C][/ROW]
[ROW][C]indc[/C][C]0.0436802973309247[/C][C]0.104583[/C][C]0.4177[/C][C]0.67917[/C][C]0.339585[/C][/ROW]
[ROW][C]y1[/C][C]0.188344373020551[/C][C]0.189551[/C][C]0.9936[/C][C]0.328348[/C][C]0.164174[/C][/ROW]
[ROW][C]y2[/C][C]0.163567515100477[/C][C]0.16883[/C][C]0.9688[/C][C]0.340378[/C][C]0.170189[/C][/ROW]
[ROW][C]`y3
`[/C][C]-0.130967620439291[/C][C]0.163436[/C][C]-0.8013[/C][C]0.429237[/C][C]0.214619[/C][/ROW]
[ROW][C]M1[/C][C]0.296514116202145[/C][C]2.127164[/C][C]0.1394[/C][C]0.89007[/C][C]0.445035[/C][/ROW]
[ROW][C]M2[/C][C]-0.835837579481557[/C][C]2.415932[/C][C]-0.346[/C][C]0.731781[/C][C]0.36589[/C][/ROW]
[ROW][C]M3[/C][C]-3.76745489042413[/C][C]2.405121[/C][C]-1.5664[/C][C]0.127737[/C][C]0.063868[/C][/ROW]
[ROW][C]M4[/C][C]-2.08061356471506[/C][C]2.526785[/C][C]-0.8234[/C][C]0.416765[/C][C]0.208383[/C][/ROW]
[ROW][C]M5[/C][C]-1.12030986429559[/C][C]2.680751[/C][C]-0.4179[/C][C]0.67899[/C][C]0.339495[/C][/ROW]
[ROW][C]M6[/C][C]-1.97031879592753[/C][C]2.718052[/C][C]-0.7249[/C][C]0.474129[/C][C]0.237065[/C][/ROW]
[ROW][C]M7[/C][C]-1.21767349589456[/C][C]2.517465[/C][C]-0.4837[/C][C]0.632118[/C][C]0.316059[/C][/ROW]
[ROW][C]M8[/C][C]-1.11620771659602[/C][C]2.409731[/C][C]-0.4632[/C][C]0.646558[/C][C]0.323279[/C][/ROW]
[ROW][C]M9[/C][C]1.25633708049614[/C][C]2.385667[/C][C]0.5266[/C][C]0.602331[/C][C]0.301165[/C][/ROW]
[ROW][C]M10[/C][C]0.269097496660407[/C][C]2.362987[/C][C]0.1139[/C][C]0.910091[/C][C]0.455046[/C][/ROW]
[ROW][C]M11[/C][C]-0.08551092511179[/C][C]2.259958[/C][C]-0.0378[/C][C]0.970068[/C][C]0.485034[/C][/ROW]
[ROW][C]t[/C][C]-0.166442807258652[/C][C]0.077479[/C][C]-2.1482[/C][C]0.039892[/C][C]0.019946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57927&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)	20.2513189201664	23.268082	0.8703	0.391022	0.195511
totid	0.425341901487542	0.244499	1.7396	0.092173	0.046086
ndzcg	-0.0455449630743466	0.268582	-0.1696	0.866482	0.433241
indc	0.0436802973309247	0.104583	0.4177	0.67917	0.339585
y1	0.188344373020551	0.189551	0.9936	0.328348	0.164174
y2	0.163567515100477	0.16883	0.9688	0.340378	0.170189
`y3 `	-0.130967620439291	0.163436	-0.8013	0.429237	0.214619
M1	0.296514116202145	2.127164	0.1394	0.89007	0.445035
M2	-0.835837579481557	2.415932	-0.346	0.731781	0.36589
M3	-3.76745489042413	2.405121	-1.5664	0.127737	0.063868
M4	-2.08061356471506	2.526785	-0.8234	0.416765	0.208383
M5	-1.12030986429559	2.680751	-0.4179	0.67899	0.339495
M6	-1.97031879592753	2.718052	-0.7249	0.474129	0.237065
M7	-1.21767349589456	2.517465	-0.4837	0.632118	0.316059
M8	-1.11620771659602	2.409731	-0.4632	0.646558	0.323279
M9	1.25633708049614	2.385667	0.5266	0.602331	0.301165
M10	0.269097496660407	2.362987	0.1139	0.910091	0.455046
M11	-0.08551092511179	2.259958	-0.0378	0.970068	0.485034
t	-0.166442807258652	0.077479	-2.1482	0.039892	0.019946

Multiple Linear Regression - Regression Statistics
Multiple R	0.90975669067051
R-squared	0.827657236219756
Adjusted R-squared	0.72425157795161
F-TEST (value)	8.00398401868412
F-TEST (DF numerator)	18
F-TEST (DF denominator)	30
p-value	4.22611395878292e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.10793514765004
Sum Squared Residuals	289.777826459955

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.90975669067051 \tabularnewline
R-squared & 0.827657236219756 \tabularnewline
Adjusted R-squared & 0.72425157795161 \tabularnewline
F-TEST (value) & 8.00398401868412 \tabularnewline
F-TEST (DF numerator) & 18 \tabularnewline
F-TEST (DF denominator) & 30 \tabularnewline
p-value & 4.22611395878292e-07 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.10793514765004 \tabularnewline
Sum Squared Residuals & 289.777826459955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57927&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.90975669067051[/C][/ROW]
[ROW][C]R-squared[/C][C]0.827657236219756[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.72425157795161[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8.00398401868412[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]18[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]30[/C][/ROW]
[ROW][C]p-value[/C][C]4.22611395878292e-07[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.10793514765004[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]289.777826459955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57927&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57927&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	0.90975669067051
R-squared	0.827657236219756
Adjusted R-squared	0.72425157795161
F-TEST (value)	8.00398401868412
F-TEST (DF numerator)	18
F-TEST (DF denominator)	30
p-value	4.22611395878292e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.10793514765004
Sum Squared Residuals	289.777826459955

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	74	75.7790253566907	-1.7790253566907
2	76	75.489644875326	0.510355124674
3	69.6	69.4873313009797	0.112668699020267
4	77.3	73.4345661294644	3.8654338705356
5	75.2	74.5720971867943	0.627902813205723
6	75.8	74.7897879567408	1.01021204325918
7	77.6	73.7690564989996	3.83094350100039
8	76.7	75.2556311242933	1.44436887570675
9	77	77.319662646084	-0.319662646083947
10	77.9	77.0472393463657	0.852760653634317
11	76.7	76.0483913334632	0.651608666536769
12	71.9	74.9530612412628	-3.05306124126283
13	73.4	74.287365418013	-0.887365418013026
14	72.5	73.1341707360195	-0.634170736019501
15	73.7	70.9931286521832	2.70687134781680
16	69.5	72.403824300446	-2.90382430044602
17	74.7	74.2907497336154	0.409250266384581
18	72.5	73.06852201431	-0.568522014310007
19	72.1	74.134010010568	-2.03401001056808
20	70.7	73.9630595953059	-3.26305959530586
21	71.4	75.6712787885589	-4.27127878855884
22	69.5	74.1135899882116	-4.61358998821163
23	73.5	73.3384810303127	0.161518969687286
24	72.4	73.1451494319208	-0.745149431920782
25	74.5	74.2548286956975	0.245171304302463
26	72.2	72.0001066280042	0.199893371995791
27	73	70.036546237876	2.96345376212398
28	73.3	71.0070787401068	2.29292125989316
29	71.3	71.6943946969648	-0.394394696964843
30	73.6	73.0088056803371	0.591194319662869
31	71.3	73.8152074810518	-2.51520748105184
32	71.2	70.6700354480265	0.529964551973485
33	81.4	75.1719542420652	6.22804575793478
34	76.1	74.8211134934189	1.27888650658112
35	71.1	74.1638782899017	-3.0638782899017
36	75.7	70.7356335169924	4.96436648300763
37	70	70.876052990832	-0.876052990831986
38	68.5	68.5760777606503	-0.0760777606502896
39	56.7	62.482993808961	-5.78299380896104
40	57.9	61.1545308299827	-3.25453082998274
41	58.8	59.4427583826255	-0.64275838262546
42	59.3	60.332884348612	-1.03288434861204
43	61.3	60.5817260093805	0.718273990619535
44	62.9	61.6112738323744	1.28872616762563
45	61.4	63.037104323292	-1.63710432329199
46	64.5	62.0180571720038	2.48194282799619
47	63.8	61.5492493463223	2.25075065367765
48	61.6	62.766155809824	-1.16615580982402
49	64.7	61.4027275387668	3.29727246123325

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 74 & 75.7790253566907 & -1.7790253566907 \tabularnewline
2 & 76 & 75.489644875326 & 0.510355124674 \tabularnewline
3 & 69.6 & 69.4873313009797 & 0.112668699020267 \tabularnewline
4 & 77.3 & 73.4345661294644 & 3.8654338705356 \tabularnewline
5 & 75.2 & 74.5720971867943 & 0.627902813205723 \tabularnewline
6 & 75.8 & 74.7897879567408 & 1.01021204325918 \tabularnewline
7 & 77.6 & 73.7690564989996 & 3.83094350100039 \tabularnewline
8 & 76.7 & 75.2556311242933 & 1.44436887570675 \tabularnewline
9 & 77 & 77.319662646084 & -0.319662646083947 \tabularnewline
10 & 77.9 & 77.0472393463657 & 0.852760653634317 \tabularnewline
11 & 76.7 & 76.0483913334632 & 0.651608666536769 \tabularnewline
12 & 71.9 & 74.9530612412628 & -3.05306124126283 \tabularnewline
13 & 73.4 & 74.287365418013 & -0.887365418013026 \tabularnewline
14 & 72.5 & 73.1341707360195 & -0.634170736019501 \tabularnewline
15 & 73.7 & 70.9931286521832 & 2.70687134781680 \tabularnewline
16 & 69.5 & 72.403824300446 & -2.90382430044602 \tabularnewline
17 & 74.7 & 74.2907497336154 & 0.409250266384581 \tabularnewline
18 & 72.5 & 73.06852201431 & -0.568522014310007 \tabularnewline
19 & 72.1 & 74.134010010568 & -2.03401001056808 \tabularnewline
20 & 70.7 & 73.9630595953059 & -3.26305959530586 \tabularnewline
21 & 71.4 & 75.6712787885589 & -4.27127878855884 \tabularnewline
22 & 69.5 & 74.1135899882116 & -4.61358998821163 \tabularnewline
23 & 73.5 & 73.3384810303127 & 0.161518969687286 \tabularnewline
24 & 72.4 & 73.1451494319208 & -0.745149431920782 \tabularnewline
25 & 74.5 & 74.2548286956975 & 0.245171304302463 \tabularnewline
26 & 72.2 & 72.0001066280042 & 0.199893371995791 \tabularnewline
27 & 73 & 70.036546237876 & 2.96345376212398 \tabularnewline
28 & 73.3 & 71.0070787401068 & 2.29292125989316 \tabularnewline
29 & 71.3 & 71.6943946969648 & -0.394394696964843 \tabularnewline
30 & 73.6 & 73.0088056803371 & 0.591194319662869 \tabularnewline
31 & 71.3 & 73.8152074810518 & -2.51520748105184 \tabularnewline
32 & 71.2 & 70.6700354480265 & 0.529964551973485 \tabularnewline
33 & 81.4 & 75.1719542420652 & 6.22804575793478 \tabularnewline
34 & 76.1 & 74.8211134934189 & 1.27888650658112 \tabularnewline
35 & 71.1 & 74.1638782899017 & -3.0638782899017 \tabularnewline
36 & 75.7 & 70.7356335169924 & 4.96436648300763 \tabularnewline
37 & 70 & 70.876052990832 & -0.876052990831986 \tabularnewline
38 & 68.5 & 68.5760777606503 & -0.0760777606502896 \tabularnewline
39 & 56.7 & 62.482993808961 & -5.78299380896104 \tabularnewline
40 & 57.9 & 61.1545308299827 & -3.25453082998274 \tabularnewline
41 & 58.8 & 59.4427583826255 & -0.64275838262546 \tabularnewline
42 & 59.3 & 60.332884348612 & -1.03288434861204 \tabularnewline
43 & 61.3 & 60.5817260093805 & 0.718273990619535 \tabularnewline
44 & 62.9 & 61.6112738323744 & 1.28872616762563 \tabularnewline
45 & 61.4 & 63.037104323292 & -1.63710432329199 \tabularnewline
46 & 64.5 & 62.0180571720038 & 2.48194282799619 \tabularnewline
47 & 63.8 & 61.5492493463223 & 2.25075065367765 \tabularnewline
48 & 61.6 & 62.766155809824 & -1.16615580982402 \tabularnewline
49 & 64.7 & 61.4027275387668 & 3.29727246123325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57927&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]74[/C][C]75.7790253566907[/C][C]-1.7790253566907[/C][/ROW]
[ROW][C]2[/C][C]76[/C][C]75.489644875326[/C][C]0.510355124674[/C][/ROW]
[ROW][C]3[/C][C]69.6[/C][C]69.4873313009797[/C][C]0.112668699020267[/C][/ROW]
[ROW][C]4[/C][C]77.3[/C][C]73.4345661294644[/C][C]3.8654338705356[/C][/ROW]
[ROW][C]5[/C][C]75.2[/C][C]74.5720971867943[/C][C]0.627902813205723[/C][/ROW]
[ROW][C]6[/C][C]75.8[/C][C]74.7897879567408[/C][C]1.01021204325918[/C][/ROW]
[ROW][C]7[/C][C]77.6[/C][C]73.7690564989996[/C][C]3.83094350100039[/C][/ROW]
[ROW][C]8[/C][C]76.7[/C][C]75.2556311242933[/C][C]1.44436887570675[/C][/ROW]
[ROW][C]9[/C][C]77[/C][C]77.319662646084[/C][C]-0.319662646083947[/C][/ROW]
[ROW][C]10[/C][C]77.9[/C][C]77.0472393463657[/C][C]0.852760653634317[/C][/ROW]
[ROW][C]11[/C][C]76.7[/C][C]76.0483913334632[/C][C]0.651608666536769[/C][/ROW]
[ROW][C]12[/C][C]71.9[/C][C]74.9530612412628[/C][C]-3.05306124126283[/C][/ROW]
[ROW][C]13[/C][C]73.4[/C][C]74.287365418013[/C][C]-0.887365418013026[/C][/ROW]
[ROW][C]14[/C][C]72.5[/C][C]73.1341707360195[/C][C]-0.634170736019501[/C][/ROW]
[ROW][C]15[/C][C]73.7[/C][C]70.9931286521832[/C][C]2.70687134781680[/C][/ROW]
[ROW][C]16[/C][C]69.5[/C][C]72.403824300446[/C][C]-2.90382430044602[/C][/ROW]
[ROW][C]17[/C][C]74.7[/C][C]74.2907497336154[/C][C]0.409250266384581[/C][/ROW]
[ROW][C]18[/C][C]72.5[/C][C]73.06852201431[/C][C]-0.568522014310007[/C][/ROW]
[ROW][C]19[/C][C]72.1[/C][C]74.134010010568[/C][C]-2.03401001056808[/C][/ROW]
[ROW][C]20[/C][C]70.7[/C][C]73.9630595953059[/C][C]-3.26305959530586[/C][/ROW]
[ROW][C]21[/C][C]71.4[/C][C]75.6712787885589[/C][C]-4.27127878855884[/C][/ROW]
[ROW][C]22[/C][C]69.5[/C][C]74.1135899882116[/C][C]-4.61358998821163[/C][/ROW]
[ROW][C]23[/C][C]73.5[/C][C]73.3384810303127[/C][C]0.161518969687286[/C][/ROW]
[ROW][C]24[/C][C]72.4[/C][C]73.1451494319208[/C][C]-0.745149431920782[/C][/ROW]
[ROW][C]25[/C][C]74.5[/C][C]74.2548286956975[/C][C]0.245171304302463[/C][/ROW]
[ROW][C]26[/C][C]72.2[/C][C]72.0001066280042[/C][C]0.199893371995791[/C][/ROW]
[ROW][C]27[/C][C]73[/C][C]70.036546237876[/C][C]2.96345376212398[/C][/ROW]
[ROW][C]28[/C][C]73.3[/C][C]71.0070787401068[/C][C]2.29292125989316[/C][/ROW]
[ROW][C]29[/C][C]71.3[/C][C]71.6943946969648[/C][C]-0.394394696964843[/C][/ROW]
[ROW][C]30[/C][C]73.6[/C][C]73.0088056803371[/C][C]0.591194319662869[/C][/ROW]
[ROW][C]31[/C][C]71.3[/C][C]73.8152074810518[/C][C]-2.51520748105184[/C][/ROW]
[ROW][C]32[/C][C]71.2[/C][C]70.6700354480265[/C][C]0.529964551973485[/C][/ROW]
[ROW][C]33[/C][C]81.4[/C][C]75.1719542420652[/C][C]6.22804575793478[/C][/ROW]
[ROW][C]34[/C][C]76.1[/C][C]74.8211134934189[/C][C]1.27888650658112[/C][/ROW]
[ROW][C]35[/C][C]71.1[/C][C]74.1638782899017[/C][C]-3.0638782899017[/C][/ROW]
[ROW][C]36[/C][C]75.7[/C][C]70.7356335169924[/C][C]4.96436648300763[/C][/ROW]
[ROW][C]37[/C][C]70[/C][C]70.876052990832[/C][C]-0.876052990831986[/C][/ROW]
[ROW][C]38[/C][C]68.5[/C][C]68.5760777606503[/C][C]-0.0760777606502896[/C][/ROW]
[ROW][C]39[/C][C]56.7[/C][C]62.482993808961[/C][C]-5.78299380896104[/C][/ROW]
[ROW][C]40[/C][C]57.9[/C][C]61.1545308299827[/C][C]-3.25453082998274[/C][/ROW]
[ROW][C]41[/C][C]58.8[/C][C]59.4427583826255[/C][C]-0.64275838262546[/C][/ROW]
[ROW][C]42[/C][C]59.3[/C][C]60.332884348612[/C][C]-1.03288434861204[/C][/ROW]
[ROW][C]43[/C][C]61.3[/C][C]60.5817260093805[/C][C]0.718273990619535[/C][/ROW]
[ROW][C]44[/C][C]62.9[/C][C]61.6112738323744[/C][C]1.28872616762563[/C][/ROW]
[ROW][C]45[/C][C]61.4[/C][C]63.037104323292[/C][C]-1.63710432329199[/C][/ROW]
[ROW][C]46[/C][C]64.5[/C][C]62.0180571720038[/C][C]2.48194282799619[/C][/ROW]
[ROW][C]47[/C][C]63.8[/C][C]61.5492493463223[/C][C]2.25075065367765[/C][/ROW]
[ROW][C]48[/C][C]61.6[/C][C]62.766155809824[/C][C]-1.16615580982402[/C][/ROW]
[ROW][C]49[/C][C]64.7[/C][C]61.4027275387668[/C][C]3.29727246123325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57927&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57927&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	74	75.7790253566907	-1.7790253566907
2	76	75.489644875326	0.510355124674
3	69.6	69.4873313009797	0.112668699020267
4	77.3	73.4345661294644	3.8654338705356
5	75.2	74.5720971867943	0.627902813205723
6	75.8	74.7897879567408	1.01021204325918
7	77.6	73.7690564989996	3.83094350100039
8	76.7	75.2556311242933	1.44436887570675
9	77	77.319662646084	-0.319662646083947
10	77.9	77.0472393463657	0.852760653634317
11	76.7	76.0483913334632	0.651608666536769
12	71.9	74.9530612412628	-3.05306124126283
13	73.4	74.287365418013	-0.887365418013026
14	72.5	73.1341707360195	-0.634170736019501
15	73.7	70.9931286521832	2.70687134781680
16	69.5	72.403824300446	-2.90382430044602
17	74.7	74.2907497336154	0.409250266384581
18	72.5	73.06852201431	-0.568522014310007
19	72.1	74.134010010568	-2.03401001056808
20	70.7	73.9630595953059	-3.26305959530586
21	71.4	75.6712787885589	-4.27127878855884
22	69.5	74.1135899882116	-4.61358998821163
23	73.5	73.3384810303127	0.161518969687286
24	72.4	73.1451494319208	-0.745149431920782
25	74.5	74.2548286956975	0.245171304302463
26	72.2	72.0001066280042	0.199893371995791
27	73	70.036546237876	2.96345376212398
28	73.3	71.0070787401068	2.29292125989316
29	71.3	71.6943946969648	-0.394394696964843
30	73.6	73.0088056803371	0.591194319662869
31	71.3	73.8152074810518	-2.51520748105184
32	71.2	70.6700354480265	0.529964551973485
33	81.4	75.1719542420652	6.22804575793478
34	76.1	74.8211134934189	1.27888650658112
35	71.1	74.1638782899017	-3.0638782899017
36	75.7	70.7356335169924	4.96436648300763
37	70	70.876052990832	-0.876052990831986
38	68.5	68.5760777606503	-0.0760777606502896
39	56.7	62.482993808961	-5.78299380896104
40	57.9	61.1545308299827	-3.25453082998274
41	58.8	59.4427583826255	-0.64275838262546
42	59.3	60.332884348612	-1.03288434861204
43	61.3	60.5817260093805	0.718273990619535
44	62.9	61.6112738323744	1.28872616762563
45	61.4	63.037104323292	-1.63710432329199
46	64.5	62.0180571720038	2.48194282799619
47	63.8	61.5492493463223	2.25075065367765
48	61.6	62.766155809824	-1.16615580982402
49	64.7	61.4027275387668	3.29727246123325

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
22	0.0716374951492726	0.143274990298545	0.928362504850727
23	0.0489277650497474	0.0978555300994948	0.951072234950253
24	0.0409123541930088	0.0818247083860176	0.959087645806991
25	0.276858783762207	0.553717567524414	0.723141216237793
26	0.41717679278587	0.83435358557174	0.58282320721413
27	0.306602647819216	0.613205295638432	0.693397352180784

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
22 & 0.0716374951492726 & 0.143274990298545 & 0.928362504850727 \tabularnewline
23 & 0.0489277650497474 & 0.0978555300994948 & 0.951072234950253 \tabularnewline
24 & 0.0409123541930088 & 0.0818247083860176 & 0.959087645806991 \tabularnewline
25 & 0.276858783762207 & 0.553717567524414 & 0.723141216237793 \tabularnewline
26 & 0.41717679278587 & 0.83435358557174 & 0.58282320721413 \tabularnewline
27 & 0.306602647819216 & 0.613205295638432 & 0.693397352180784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57927&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]22[/C][C]0.0716374951492726[/C][C]0.143274990298545[/C][C]0.928362504850727[/C][/ROW]
[ROW][C]23[/C][C]0.0489277650497474[/C][C]0.0978555300994948[/C][C]0.951072234950253[/C][/ROW]
[ROW][C]24[/C][C]0.0409123541930088[/C][C]0.0818247083860176[/C][C]0.959087645806991[/C][/ROW]
[ROW][C]25[/C][C]0.276858783762207[/C][C]0.553717567524414[/C][C]0.723141216237793[/C][/ROW]
[ROW][C]26[/C][C]0.41717679278587[/C][C]0.83435358557174[/C][C]0.58282320721413[/C][/ROW]
[ROW][C]27[/C][C]0.306602647819216[/C][C]0.613205295638432[/C][C]0.693397352180784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57927&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57927&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
22	0.0716374951492726	0.143274990298545	0.928362504850727
23	0.0489277650497474	0.0978555300994948	0.951072234950253
24	0.0409123541930088	0.0818247083860176	0.959087645806991
25	0.276858783762207	0.553717567524414	0.723141216237793
26	0.41717679278587	0.83435358557174	0.58282320721413
27	0.306602647819216	0.613205295638432	0.693397352180784

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	2	0.333333333333333	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 & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 2 & 0.333333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57927&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]2[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57927&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57927&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	0	0	OK
5% type I error level	0	0	OK
10% type I error level	2	0.333333333333333	NOK

Figure 1

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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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 = 4 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code