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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 18 Dec 2010 12:25:58 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292675056dbbjaxypxzovu4z.htm/, Retrieved Mon, 29 Apr 2024 14:29:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111886, Retrieved Mon, 29 Apr 2024 14:29:48 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

194

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

-     [Multiple Regression] [] [2009-11-24 11:34:57] [f57b281e621ed7dff28b90886f5aa97c]
-   PD  [Multiple Regression] [] [2009-11-24 12:09:41] [f57b281e621ed7dff28b90886f5aa97c]
-    D    [Multiple Regression] [] [2009-11-24 12:16:30] [f57b281e621ed7dff28b90886f5aa97c]
-    D        [Multiple Regression] [2 vertragingen] [2010-12-18 12:25:58] [19046f4a6967f3fb6f5f17d42e7d38f2] [Current]

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Dataseries X:

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Histogram

Boxplots

102.8	112.5	116.7	116.1
98.1	113	112.5	107.5
113.9	126.4	113	116.7
80.9	114.1	126.4	112.5
95.7	112.5	114.1	113
113.2	112.4	112.5	126.4
105.9	113.1	112.4	114.1
108.8	116.3	113.1	112.5
102.3	111.7	116.3	112.4
99	118.8	111.7	113.1
100.7	116.5	118.8	116.3
115.5	125.1	116.5	111.7
100.7	113.1	125.1	118.8
109.9	119.6	113.1	116.5
114.6	114.4	119.6	125.1
85.4	114	114.4	113.1
100.5	117.8	114	119.6
114.8	117	117.8	114.4
116.5	120.9	117	114
112.9	115	120.9	117.8
102	117.3	115	117
106	119.4	117.3	120.9
105.3	114.9	119.4	115
118.8	125.8	114.9	117.3
106.1	117.6	125.8	119.4
109.3	117.6	117.6	114.9
117.2	114.9	117.6	125.8
92.5	121.9	114.9	117.6
104.2	117	121.9	117.6
112.5	106.4	117	114.9
122.4	110.5	106.4	121.9
113.3	113.6	110.5	117
100	114.2	113.6	106.4
110.7	125.4	114.2	110.5
112.8	124.6	125.4	113.6
109.8	120.2	124.6	114.2
117.3	120.8	120.2	125.4
109.1	111.4	120.8	124.6
115.9	124.1	111.4	120.2
96	120.2	124.1	120.8
99.8	125.5	120.2	111.4
116.8	116	125.5	124.1
115.7	117	116	120.2
99.4	105.7	117	125.5
94.3	102	105.7	116
91	106.4	102	117
93.2	96.9	106.4	105.7
103.1	107.6	96.9	102
94.1	98.8	107.6	106.4
91.8	101.1	98.8	96.9
102.7	105.7	101.1	107.6
82.6	104.6	105.7	98.8
89.1	103.2	104.6	101.1
104.5	101.6	103.2	105.7
105.1	106.7	101.6	104.6
95.1	99.5	106.7	103.2
88.7	101	99.5	101.6

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	'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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111886&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111886&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 27.5646541936156 + 0.719237622037051T.I.P.[t] + 0.351615816868488`Y(t-1)`[t] -0.225481858966781`Y(t-3)`[t] -2.87531712508168M1[t] -1.25845267587132M2[t] -1.64388521197177M3[t] + 11.4973887999212M4[t] + 5.12018350407216M5[t] -8.78441952464868M6[t] -5.16373479336386M7[t] -4.47697332405873M8[t] + 1.16759647044438M9[t] + 6.50191392593397M10[t] -1.4199990435579M11[t] -0.100533009976323t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  27.5646541936156 +  0.719237622037051T.I.P.[t] +  0.351615816868488`Y(t-1)`[t] -0.225481858966781`Y(t-3)`[t] -2.87531712508168M1[t] -1.25845267587132M2[t] -1.64388521197177M3[t] +  11.4973887999212M4[t] +  5.12018350407216M5[t] -8.78441952464868M6[t] -5.16373479336386M7[t] -4.47697332405873M8[t] +  1.16759647044438M9[t] +  6.50191392593397M10[t] -1.4199990435579M11[t] -0.100533009976323t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111886&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  27.5646541936156 +  0.719237622037051T.I.P.[t] +  0.351615816868488`Y(t-1)`[t] -0.225481858966781`Y(t-3)`[t] -2.87531712508168M1[t] -1.25845267587132M2[t] -1.64388521197177M3[t] +  11.4973887999212M4[t] +  5.12018350407216M5[t] -8.78441952464868M6[t] -5.16373479336386M7[t] -4.47697332405873M8[t] +  1.16759647044438M9[t] +  6.50191392593397M10[t] -1.4199990435579M11[t] -0.100533009976323t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111886&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)[t] = + 27.5646541936156 + 0.719237622037051T.I.P.[t] + 0.351615816868488`Y(t-1)`[t] -0.225481858966781`Y(t-3)`[t] -2.87531712508168M1[t] -1.25845267587132M2[t] -1.64388521197177M3[t] + 11.4973887999212M4[t] + 5.12018350407216M5[t] -8.78441952464868M6[t] -5.16373479336386M7[t] -4.47697332405873M8[t] + 1.16759647044438M9[t] + 6.50191392593397M10[t] -1.4199990435579M11[t] -0.100533009976323t + 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)	27.5646541936156	11.154238	2.4712	0.01771	0.008855
T.I.P.	0.719237622037051	0.110576	6.5044	0	0
`Y(t-1)`	0.351615816868488	0.111572	3.1515	0.003033	0.001516
`Y(t-3)`	-0.225481858966781	0.111906	-2.0149	0.050501	0.025251
M1	-2.87531712508168	2.810467	-1.0231	0.312271	0.156136
M2	-1.25845267587132	2.606872	-0.4827	0.631845	0.315922
M3	-1.64388521197177	2.585307	-0.6359	0.528403	0.264202
M4	11.4973887999212	3.793259	3.031	0.00421	0.002105
M5	5.12018350407216	2.950822	1.7352	0.090223	0.045111
M6	-8.78441952464868	2.498781	-3.5155	0.001087	0.000543
M7	-5.16373479336386	2.503896	-2.0623	0.045556	0.022778
M8	-4.47697332405873	2.606334	-1.7177	0.093392	0.046696
M9	1.16759647044438	2.841313	0.4109	0.68326	0.34163
M10	6.50191392593397	2.902503	2.2401	0.030567	0.015283
M11	-1.4199990435579	2.854385	-0.4975	0.621508	0.310754
t	-0.100533009976323	0.034392	-2.9231	0.005618	0.002809

\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) & 27.5646541936156 & 11.154238 & 2.4712 & 0.01771 & 0.008855 \tabularnewline
T.I.P. & 0.719237622037051 & 0.110576 & 6.5044 & 0 & 0 \tabularnewline
`Y(t-1)` & 0.351615816868488 & 0.111572 & 3.1515 & 0.003033 & 0.001516 \tabularnewline
`Y(t-3)` & -0.225481858966781 & 0.111906 & -2.0149 & 0.050501 & 0.025251 \tabularnewline
M1 & -2.87531712508168 & 2.810467 & -1.0231 & 0.312271 & 0.156136 \tabularnewline
M2 & -1.25845267587132 & 2.606872 & -0.4827 & 0.631845 & 0.315922 \tabularnewline
M3 & -1.64388521197177 & 2.585307 & -0.6359 & 0.528403 & 0.264202 \tabularnewline
M4 & 11.4973887999212 & 3.793259 & 3.031 & 0.00421 & 0.002105 \tabularnewline
M5 & 5.12018350407216 & 2.950822 & 1.7352 & 0.090223 & 0.045111 \tabularnewline
M6 & -8.78441952464868 & 2.498781 & -3.5155 & 0.001087 & 0.000543 \tabularnewline
M7 & -5.16373479336386 & 2.503896 & -2.0623 & 0.045556 & 0.022778 \tabularnewline
M8 & -4.47697332405873 & 2.606334 & -1.7177 & 0.093392 & 0.046696 \tabularnewline
M9 & 1.16759647044438 & 2.841313 & 0.4109 & 0.68326 & 0.34163 \tabularnewline
M10 & 6.50191392593397 & 2.902503 & 2.2401 & 0.030567 & 0.015283 \tabularnewline
M11 & -1.4199990435579 & 2.854385 & -0.4975 & 0.621508 & 0.310754 \tabularnewline
t & -0.100533009976323 & 0.034392 & -2.9231 & 0.005618 & 0.002809 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111886&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]27.5646541936156[/C][C]11.154238[/C][C]2.4712[/C][C]0.01771[/C][C]0.008855[/C][/ROW]
[ROW][C]T.I.P.[/C][C]0.719237622037051[/C][C]0.110576[/C][C]6.5044[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.351615816868488[/C][C]0.111572[/C][C]3.1515[/C][C]0.003033[/C][C]0.001516[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.225481858966781[/C][C]0.111906[/C][C]-2.0149[/C][C]0.050501[/C][C]0.025251[/C][/ROW]
[ROW][C]M1[/C][C]-2.87531712508168[/C][C]2.810467[/C][C]-1.0231[/C][C]0.312271[/C][C]0.156136[/C][/ROW]
[ROW][C]M2[/C][C]-1.25845267587132[/C][C]2.606872[/C][C]-0.4827[/C][C]0.631845[/C][C]0.315922[/C][/ROW]
[ROW][C]M3[/C][C]-1.64388521197177[/C][C]2.585307[/C][C]-0.6359[/C][C]0.528403[/C][C]0.264202[/C][/ROW]
[ROW][C]M4[/C][C]11.4973887999212[/C][C]3.793259[/C][C]3.031[/C][C]0.00421[/C][C]0.002105[/C][/ROW]
[ROW][C]M5[/C][C]5.12018350407216[/C][C]2.950822[/C][C]1.7352[/C][C]0.090223[/C][C]0.045111[/C][/ROW]
[ROW][C]M6[/C][C]-8.78441952464868[/C][C]2.498781[/C][C]-3.5155[/C][C]0.001087[/C][C]0.000543[/C][/ROW]
[ROW][C]M7[/C][C]-5.16373479336386[/C][C]2.503896[/C][C]-2.0623[/C][C]0.045556[/C][C]0.022778[/C][/ROW]
[ROW][C]M8[/C][C]-4.47697332405873[/C][C]2.606334[/C][C]-1.7177[/C][C]0.093392[/C][C]0.046696[/C][/ROW]
[ROW][C]M9[/C][C]1.16759647044438[/C][C]2.841313[/C][C]0.4109[/C][C]0.68326[/C][C]0.34163[/C][/ROW]
[ROW][C]M10[/C][C]6.50191392593397[/C][C]2.902503[/C][C]2.2401[/C][C]0.030567[/C][C]0.015283[/C][/ROW]
[ROW][C]M11[/C][C]-1.4199990435579[/C][C]2.854385[/C][C]-0.4975[/C][C]0.621508[/C][C]0.310754[/C][/ROW]
[ROW][C]t[/C][C]-0.100533009976323[/C][C]0.034392[/C][C]-2.9231[/C][C]0.005618[/C][C]0.002809[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111886&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111886&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)	27.5646541936156	11.154238	2.4712	0.01771	0.008855
T.I.P.	0.719237622037051	0.110576	6.5044	0	0
`Y(t-1)`	0.351615816868488	0.111572	3.1515	0.003033	0.001516
`Y(t-3)`	-0.225481858966781	0.111906	-2.0149	0.050501	0.025251
M1	-2.87531712508168	2.810467	-1.0231	0.312271	0.156136
M2	-1.25845267587132	2.606872	-0.4827	0.631845	0.315922
M3	-1.64388521197177	2.585307	-0.6359	0.528403	0.264202
M4	11.4973887999212	3.793259	3.031	0.00421	0.002105
M5	5.12018350407216	2.950822	1.7352	0.090223	0.045111
M6	-8.78441952464868	2.498781	-3.5155	0.001087	0.000543
M7	-5.16373479336386	2.503896	-2.0623	0.045556	0.022778
M8	-4.47697332405873	2.606334	-1.7177	0.093392	0.046696
M9	1.16759647044438	2.841313	0.4109	0.68326	0.34163
M10	6.50191392593397	2.902503	2.2401	0.030567	0.015283
M11	-1.4199990435579	2.854385	-0.4975	0.621508	0.310754
t	-0.100533009976323	0.034392	-2.9231	0.005618	0.002809

Multiple Linear Regression - Regression Statistics
Multiple R	0.913268637606618
R-squared	0.834059604435848
Adjusted R-squared	0.773349703619695
F-TEST (value)	13.7384445242568
F-TEST (DF numerator)	15
F-TEST (DF denominator)	41
p-value	1.75230940868687e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.62948298030304
Sum Squared Residuals	540.099014876688

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.913268637606618 \tabularnewline
R-squared & 0.834059604435848 \tabularnewline
Adjusted R-squared & 0.773349703619695 \tabularnewline
F-TEST (value) & 13.7384445242568 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 41 \tabularnewline
p-value & 1.75230940868687e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.62948298030304 \tabularnewline
Sum Squared Residuals & 540.099014876688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111886&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.913268637606618[/C][/ROW]
[ROW][C]R-squared[/C][C]0.834059604435848[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.773349703619695[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]13.7384445242568[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]41[/C][/ROW]
[ROW][C]p-value[/C][C]1.75230940868687e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.62948298030304[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]540.099014876688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111886&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111886&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	0.913268637606618
R-squared	0.834059604435848
Adjusted R-squared	0.773349703619695
F-TEST (value)	13.7384445242568
F-TEST (DF numerator)	15
F-TEST (DF denominator)	41
p-value	1.75230940868687e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.62948298030304
Sum Squared Residuals	540.099014876688

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	112.5	113.381553606476	-0.881553606475701
2	113	111.979825778402	1.02017422159778
3	126.4	120.959189466451	5.44081053354928
4	114.1	115.923764694843	-1.82376469484289
5	112.5	115.6531277182	-3.15312771820009
6	112.4	110.650607848007	1.74939215199312
7	113.1	111.658590212049	1.44140978795053
8	116.3	114.937509821441	1.36249017855949
9	111.7	116.954220862602	-5.2542208626023
10	118.8	118.039251096522	0.760748903478475
11	116.5	113.014439425589	3.48556057441113
12	125.1	125.207122437768	-0.107122437768481
13	113.1	113.009530322967	0.0904696770330307
14	119.6	117.442066358144	2.15793364185637
15	114.4	120.682876458172	-6.28287645817183
16	114	113.599258956492	0.40074104350817
17	117.8	116.375730333394	1.42426966660554
18	117	115.164338060555	1.83566193944535
19	120.9	119.716093829418	1.18390617058195
20	115	118.227537471127	-3.22753747112682
21	117.3	114.037736343099	3.26226365690091
22	119.4	122.077808405588	-2.67780840558763
23	114.9	115.620632274021	-0.720632274021336
24	125.8	124.548926753571	1.25107324642868
25	117.6	115.797859318679	1.80214068132096
26	117.6	117.747169815461	-0.147169815460565
27	114.9	120.485429220739	-5.58542922073857
28	121.9	116.660589496323	5.23941050367726
29	117	121.059242086410	-4.0592420864103
30	106.4	111.909661827175	-5.50966182717538
31	110.5	117.244765335077	-6.74476533507725
32	113.6	113.832417391967	-0.232417391966923
33	114.2	113.290710540741	0.909289459258885
34	125.4	125.506831410408	-0.106831410408123
35	124.6	122.233887823348	2.36611217665222
36	120.2	120.979059221943	-0.779059221943333
37	120.8	119.324984837514	1.47501516248608
38	111.4	115.334922753339	-3.93492275333866
39	124.1	117.426704538004	6.67329546199609
40	120.2	120.484848620233	-0.284848620232935
41	125.5	117.488441066649	8.01155893335099
42	116	114.710288823107	1.28971117689341
43	117	114.978308149894	2.02169185010586
44	105.7	102.997525334364	2.70247466563643
45	102	103.042269176072	-1.04226917607191
46	106.4	104.376109087483	2.02389091251728
47	96.9	102.031040477042	-5.13104047704201
48	107.6	107.964891586717	-0.364891586716859
49	98.8	101.286071914364	-2.48607191436437
50	101.1	100.196015294655	0.903984705345068
51	105.7	105.945800316635	-0.245800316634972
52	104.6	108.131538232110	-3.5315382321096
53	103.2	105.423458795346	-2.22345879534613
54	101.6	100.965103441157	0.634896558843497
55	106.7	104.602242473561	2.09775752643891
56	99.5	100.105009981102	-0.605009981102175
57	101	98.8750630774856	2.12493692251442

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 112.5 & 113.381553606476 & -0.881553606475701 \tabularnewline
2 & 113 & 111.979825778402 & 1.02017422159778 \tabularnewline
3 & 126.4 & 120.959189466451 & 5.44081053354928 \tabularnewline
4 & 114.1 & 115.923764694843 & -1.82376469484289 \tabularnewline
5 & 112.5 & 115.6531277182 & -3.15312771820009 \tabularnewline
6 & 112.4 & 110.650607848007 & 1.74939215199312 \tabularnewline
7 & 113.1 & 111.658590212049 & 1.44140978795053 \tabularnewline
8 & 116.3 & 114.937509821441 & 1.36249017855949 \tabularnewline
9 & 111.7 & 116.954220862602 & -5.2542208626023 \tabularnewline
10 & 118.8 & 118.039251096522 & 0.760748903478475 \tabularnewline
11 & 116.5 & 113.014439425589 & 3.48556057441113 \tabularnewline
12 & 125.1 & 125.207122437768 & -0.107122437768481 \tabularnewline
13 & 113.1 & 113.009530322967 & 0.0904696770330307 \tabularnewline
14 & 119.6 & 117.442066358144 & 2.15793364185637 \tabularnewline
15 & 114.4 & 120.682876458172 & -6.28287645817183 \tabularnewline
16 & 114 & 113.599258956492 & 0.40074104350817 \tabularnewline
17 & 117.8 & 116.375730333394 & 1.42426966660554 \tabularnewline
18 & 117 & 115.164338060555 & 1.83566193944535 \tabularnewline
19 & 120.9 & 119.716093829418 & 1.18390617058195 \tabularnewline
20 & 115 & 118.227537471127 & -3.22753747112682 \tabularnewline
21 & 117.3 & 114.037736343099 & 3.26226365690091 \tabularnewline
22 & 119.4 & 122.077808405588 & -2.67780840558763 \tabularnewline
23 & 114.9 & 115.620632274021 & -0.720632274021336 \tabularnewline
24 & 125.8 & 124.548926753571 & 1.25107324642868 \tabularnewline
25 & 117.6 & 115.797859318679 & 1.80214068132096 \tabularnewline
26 & 117.6 & 117.747169815461 & -0.147169815460565 \tabularnewline
27 & 114.9 & 120.485429220739 & -5.58542922073857 \tabularnewline
28 & 121.9 & 116.660589496323 & 5.23941050367726 \tabularnewline
29 & 117 & 121.059242086410 & -4.0592420864103 \tabularnewline
30 & 106.4 & 111.909661827175 & -5.50966182717538 \tabularnewline
31 & 110.5 & 117.244765335077 & -6.74476533507725 \tabularnewline
32 & 113.6 & 113.832417391967 & -0.232417391966923 \tabularnewline
33 & 114.2 & 113.290710540741 & 0.909289459258885 \tabularnewline
34 & 125.4 & 125.506831410408 & -0.106831410408123 \tabularnewline
35 & 124.6 & 122.233887823348 & 2.36611217665222 \tabularnewline
36 & 120.2 & 120.979059221943 & -0.779059221943333 \tabularnewline
37 & 120.8 & 119.324984837514 & 1.47501516248608 \tabularnewline
38 & 111.4 & 115.334922753339 & -3.93492275333866 \tabularnewline
39 & 124.1 & 117.426704538004 & 6.67329546199609 \tabularnewline
40 & 120.2 & 120.484848620233 & -0.284848620232935 \tabularnewline
41 & 125.5 & 117.488441066649 & 8.01155893335099 \tabularnewline
42 & 116 & 114.710288823107 & 1.28971117689341 \tabularnewline
43 & 117 & 114.978308149894 & 2.02169185010586 \tabularnewline
44 & 105.7 & 102.997525334364 & 2.70247466563643 \tabularnewline
45 & 102 & 103.042269176072 & -1.04226917607191 \tabularnewline
46 & 106.4 & 104.376109087483 & 2.02389091251728 \tabularnewline
47 & 96.9 & 102.031040477042 & -5.13104047704201 \tabularnewline
48 & 107.6 & 107.964891586717 & -0.364891586716859 \tabularnewline
49 & 98.8 & 101.286071914364 & -2.48607191436437 \tabularnewline
50 & 101.1 & 100.196015294655 & 0.903984705345068 \tabularnewline
51 & 105.7 & 105.945800316635 & -0.245800316634972 \tabularnewline
52 & 104.6 & 108.131538232110 & -3.5315382321096 \tabularnewline
53 & 103.2 & 105.423458795346 & -2.22345879534613 \tabularnewline
54 & 101.6 & 100.965103441157 & 0.634896558843497 \tabularnewline
55 & 106.7 & 104.602242473561 & 2.09775752643891 \tabularnewline
56 & 99.5 & 100.105009981102 & -0.605009981102175 \tabularnewline
57 & 101 & 98.8750630774856 & 2.12493692251442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111886&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]112.5[/C][C]113.381553606476[/C][C]-0.881553606475701[/C][/ROW]
[ROW][C]2[/C][C]113[/C][C]111.979825778402[/C][C]1.02017422159778[/C][/ROW]
[ROW][C]3[/C][C]126.4[/C][C]120.959189466451[/C][C]5.44081053354928[/C][/ROW]
[ROW][C]4[/C][C]114.1[/C][C]115.923764694843[/C][C]-1.82376469484289[/C][/ROW]
[ROW][C]5[/C][C]112.5[/C][C]115.6531277182[/C][C]-3.15312771820009[/C][/ROW]
[ROW][C]6[/C][C]112.4[/C][C]110.650607848007[/C][C]1.74939215199312[/C][/ROW]
[ROW][C]7[/C][C]113.1[/C][C]111.658590212049[/C][C]1.44140978795053[/C][/ROW]
[ROW][C]8[/C][C]116.3[/C][C]114.937509821441[/C][C]1.36249017855949[/C][/ROW]
[ROW][C]9[/C][C]111.7[/C][C]116.954220862602[/C][C]-5.2542208626023[/C][/ROW]
[ROW][C]10[/C][C]118.8[/C][C]118.039251096522[/C][C]0.760748903478475[/C][/ROW]
[ROW][C]11[/C][C]116.5[/C][C]113.014439425589[/C][C]3.48556057441113[/C][/ROW]
[ROW][C]12[/C][C]125.1[/C][C]125.207122437768[/C][C]-0.107122437768481[/C][/ROW]
[ROW][C]13[/C][C]113.1[/C][C]113.009530322967[/C][C]0.0904696770330307[/C][/ROW]
[ROW][C]14[/C][C]119.6[/C][C]117.442066358144[/C][C]2.15793364185637[/C][/ROW]
[ROW][C]15[/C][C]114.4[/C][C]120.682876458172[/C][C]-6.28287645817183[/C][/ROW]
[ROW][C]16[/C][C]114[/C][C]113.599258956492[/C][C]0.40074104350817[/C][/ROW]
[ROW][C]17[/C][C]117.8[/C][C]116.375730333394[/C][C]1.42426966660554[/C][/ROW]
[ROW][C]18[/C][C]117[/C][C]115.164338060555[/C][C]1.83566193944535[/C][/ROW]
[ROW][C]19[/C][C]120.9[/C][C]119.716093829418[/C][C]1.18390617058195[/C][/ROW]
[ROW][C]20[/C][C]115[/C][C]118.227537471127[/C][C]-3.22753747112682[/C][/ROW]
[ROW][C]21[/C][C]117.3[/C][C]114.037736343099[/C][C]3.26226365690091[/C][/ROW]
[ROW][C]22[/C][C]119.4[/C][C]122.077808405588[/C][C]-2.67780840558763[/C][/ROW]
[ROW][C]23[/C][C]114.9[/C][C]115.620632274021[/C][C]-0.720632274021336[/C][/ROW]
[ROW][C]24[/C][C]125.8[/C][C]124.548926753571[/C][C]1.25107324642868[/C][/ROW]
[ROW][C]25[/C][C]117.6[/C][C]115.797859318679[/C][C]1.80214068132096[/C][/ROW]
[ROW][C]26[/C][C]117.6[/C][C]117.747169815461[/C][C]-0.147169815460565[/C][/ROW]
[ROW][C]27[/C][C]114.9[/C][C]120.485429220739[/C][C]-5.58542922073857[/C][/ROW]
[ROW][C]28[/C][C]121.9[/C][C]116.660589496323[/C][C]5.23941050367726[/C][/ROW]
[ROW][C]29[/C][C]117[/C][C]121.059242086410[/C][C]-4.0592420864103[/C][/ROW]
[ROW][C]30[/C][C]106.4[/C][C]111.909661827175[/C][C]-5.50966182717538[/C][/ROW]
[ROW][C]31[/C][C]110.5[/C][C]117.244765335077[/C][C]-6.74476533507725[/C][/ROW]
[ROW][C]32[/C][C]113.6[/C][C]113.832417391967[/C][C]-0.232417391966923[/C][/ROW]
[ROW][C]33[/C][C]114.2[/C][C]113.290710540741[/C][C]0.909289459258885[/C][/ROW]
[ROW][C]34[/C][C]125.4[/C][C]125.506831410408[/C][C]-0.106831410408123[/C][/ROW]
[ROW][C]35[/C][C]124.6[/C][C]122.233887823348[/C][C]2.36611217665222[/C][/ROW]
[ROW][C]36[/C][C]120.2[/C][C]120.979059221943[/C][C]-0.779059221943333[/C][/ROW]
[ROW][C]37[/C][C]120.8[/C][C]119.324984837514[/C][C]1.47501516248608[/C][/ROW]
[ROW][C]38[/C][C]111.4[/C][C]115.334922753339[/C][C]-3.93492275333866[/C][/ROW]
[ROW][C]39[/C][C]124.1[/C][C]117.426704538004[/C][C]6.67329546199609[/C][/ROW]
[ROW][C]40[/C][C]120.2[/C][C]120.484848620233[/C][C]-0.284848620232935[/C][/ROW]
[ROW][C]41[/C][C]125.5[/C][C]117.488441066649[/C][C]8.01155893335099[/C][/ROW]
[ROW][C]42[/C][C]116[/C][C]114.710288823107[/C][C]1.28971117689341[/C][/ROW]
[ROW][C]43[/C][C]117[/C][C]114.978308149894[/C][C]2.02169185010586[/C][/ROW]
[ROW][C]44[/C][C]105.7[/C][C]102.997525334364[/C][C]2.70247466563643[/C][/ROW]
[ROW][C]45[/C][C]102[/C][C]103.042269176072[/C][C]-1.04226917607191[/C][/ROW]
[ROW][C]46[/C][C]106.4[/C][C]104.376109087483[/C][C]2.02389091251728[/C][/ROW]
[ROW][C]47[/C][C]96.9[/C][C]102.031040477042[/C][C]-5.13104047704201[/C][/ROW]
[ROW][C]48[/C][C]107.6[/C][C]107.964891586717[/C][C]-0.364891586716859[/C][/ROW]
[ROW][C]49[/C][C]98.8[/C][C]101.286071914364[/C][C]-2.48607191436437[/C][/ROW]
[ROW][C]50[/C][C]101.1[/C][C]100.196015294655[/C][C]0.903984705345068[/C][/ROW]
[ROW][C]51[/C][C]105.7[/C][C]105.945800316635[/C][C]-0.245800316634972[/C][/ROW]
[ROW][C]52[/C][C]104.6[/C][C]108.131538232110[/C][C]-3.5315382321096[/C][/ROW]
[ROW][C]53[/C][C]103.2[/C][C]105.423458795346[/C][C]-2.22345879534613[/C][/ROW]
[ROW][C]54[/C][C]101.6[/C][C]100.965103441157[/C][C]0.634896558843497[/C][/ROW]
[ROW][C]55[/C][C]106.7[/C][C]104.602242473561[/C][C]2.09775752643891[/C][/ROW]
[ROW][C]56[/C][C]99.5[/C][C]100.105009981102[/C][C]-0.605009981102175[/C][/ROW]
[ROW][C]57[/C][C]101[/C][C]98.8750630774856[/C][C]2.12493692251442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111886&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111886&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	112.5	113.381553606476	-0.881553606475701
2	113	111.979825778402	1.02017422159778
3	126.4	120.959189466451	5.44081053354928
4	114.1	115.923764694843	-1.82376469484289
5	112.5	115.6531277182	-3.15312771820009
6	112.4	110.650607848007	1.74939215199312
7	113.1	111.658590212049	1.44140978795053
8	116.3	114.937509821441	1.36249017855949
9	111.7	116.954220862602	-5.2542208626023
10	118.8	118.039251096522	0.760748903478475
11	116.5	113.014439425589	3.48556057441113
12	125.1	125.207122437768	-0.107122437768481
13	113.1	113.009530322967	0.0904696770330307
14	119.6	117.442066358144	2.15793364185637
15	114.4	120.682876458172	-6.28287645817183
16	114	113.599258956492	0.40074104350817
17	117.8	116.375730333394	1.42426966660554
18	117	115.164338060555	1.83566193944535
19	120.9	119.716093829418	1.18390617058195
20	115	118.227537471127	-3.22753747112682
21	117.3	114.037736343099	3.26226365690091
22	119.4	122.077808405588	-2.67780840558763
23	114.9	115.620632274021	-0.720632274021336
24	125.8	124.548926753571	1.25107324642868
25	117.6	115.797859318679	1.80214068132096
26	117.6	117.747169815461	-0.147169815460565
27	114.9	120.485429220739	-5.58542922073857
28	121.9	116.660589496323	5.23941050367726
29	117	121.059242086410	-4.0592420864103
30	106.4	111.909661827175	-5.50966182717538
31	110.5	117.244765335077	-6.74476533507725
32	113.6	113.832417391967	-0.232417391966923
33	114.2	113.290710540741	0.909289459258885
34	125.4	125.506831410408	-0.106831410408123
35	124.6	122.233887823348	2.36611217665222
36	120.2	120.979059221943	-0.779059221943333
37	120.8	119.324984837514	1.47501516248608
38	111.4	115.334922753339	-3.93492275333866
39	124.1	117.426704538004	6.67329546199609
40	120.2	120.484848620233	-0.284848620232935
41	125.5	117.488441066649	8.01155893335099
42	116	114.710288823107	1.28971117689341
43	117	114.978308149894	2.02169185010586
44	105.7	102.997525334364	2.70247466563643
45	102	103.042269176072	-1.04226917607191
46	106.4	104.376109087483	2.02389091251728
47	96.9	102.031040477042	-5.13104047704201
48	107.6	107.964891586717	-0.364891586716859
49	98.8	101.286071914364	-2.48607191436437
50	101.1	100.196015294655	0.903984705345068
51	105.7	105.945800316635	-0.245800316634972
52	104.6	108.131538232110	-3.5315382321096
53	103.2	105.423458795346	-2.22345879534613
54	101.6	100.965103441157	0.634896558843497
55	106.7	104.602242473561	2.09775752643891
56	99.5	100.105009981102	-0.605009981102175
57	101	98.8750630774856	2.12493692251442

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
19	0.681613208712021	0.636773582575958	0.318386791287979
20	0.531004287850866	0.937991424298268	0.468995712149134
21	0.628429159765247	0.743141680469507	0.371570840234753
22	0.499038584422185	0.99807716884437	0.500961415577815
23	0.44766625500748	0.89533251001496	0.55233374499252
24	0.336500613659002	0.673001227318004	0.663499386340998
25	0.2707139146065	0.541427829213	0.7292860853935
26	0.191891597872708	0.383783195745415	0.808108402127293
27	0.245754418030207	0.491508836060413	0.754245581969793
28	0.42253002280863	0.84506004561726	0.57746997719137
29	0.366610788456309	0.733221576912618	0.633389211543691
30	0.3847917742107	0.7695835484214	0.6152082257893
31	0.660769453956495	0.678461092087009	0.339230546043505
32	0.575409217872904	0.849181564254192	0.424590782127096
33	0.481018204225057	0.962036408450114	0.518981795774943
34	0.715753949059422	0.568492101881156	0.284246050940578
35	0.596869411093025	0.806261177813951	0.403130588906975
36	0.51531562556361	0.96936874887278	0.48468437443639
37	0.3810355730472	0.7620711460944	0.6189644269528
38	0.287416526121309	0.574833052242618	0.71258347387869

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.681613208712021 & 0.636773582575958 & 0.318386791287979 \tabularnewline
20 & 0.531004287850866 & 0.937991424298268 & 0.468995712149134 \tabularnewline
21 & 0.628429159765247 & 0.743141680469507 & 0.371570840234753 \tabularnewline
22 & 0.499038584422185 & 0.99807716884437 & 0.500961415577815 \tabularnewline
23 & 0.44766625500748 & 0.89533251001496 & 0.55233374499252 \tabularnewline
24 & 0.336500613659002 & 0.673001227318004 & 0.663499386340998 \tabularnewline
25 & 0.2707139146065 & 0.541427829213 & 0.7292860853935 \tabularnewline
26 & 0.191891597872708 & 0.383783195745415 & 0.808108402127293 \tabularnewline
27 & 0.245754418030207 & 0.491508836060413 & 0.754245581969793 \tabularnewline
28 & 0.42253002280863 & 0.84506004561726 & 0.57746997719137 \tabularnewline
29 & 0.366610788456309 & 0.733221576912618 & 0.633389211543691 \tabularnewline
30 & 0.3847917742107 & 0.7695835484214 & 0.6152082257893 \tabularnewline
31 & 0.660769453956495 & 0.678461092087009 & 0.339230546043505 \tabularnewline
32 & 0.575409217872904 & 0.849181564254192 & 0.424590782127096 \tabularnewline
33 & 0.481018204225057 & 0.962036408450114 & 0.518981795774943 \tabularnewline
34 & 0.715753949059422 & 0.568492101881156 & 0.284246050940578 \tabularnewline
35 & 0.596869411093025 & 0.806261177813951 & 0.403130588906975 \tabularnewline
36 & 0.51531562556361 & 0.96936874887278 & 0.48468437443639 \tabularnewline
37 & 0.3810355730472 & 0.7620711460944 & 0.6189644269528 \tabularnewline
38 & 0.287416526121309 & 0.574833052242618 & 0.71258347387869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111886&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]19[/C][C]0.681613208712021[/C][C]0.636773582575958[/C][C]0.318386791287979[/C][/ROW]
[ROW][C]20[/C][C]0.531004287850866[/C][C]0.937991424298268[/C][C]0.468995712149134[/C][/ROW]
[ROW][C]21[/C][C]0.628429159765247[/C][C]0.743141680469507[/C][C]0.371570840234753[/C][/ROW]
[ROW][C]22[/C][C]0.499038584422185[/C][C]0.99807716884437[/C][C]0.500961415577815[/C][/ROW]
[ROW][C]23[/C][C]0.44766625500748[/C][C]0.89533251001496[/C][C]0.55233374499252[/C][/ROW]
[ROW][C]24[/C][C]0.336500613659002[/C][C]0.673001227318004[/C][C]0.663499386340998[/C][/ROW]
[ROW][C]25[/C][C]0.2707139146065[/C][C]0.541427829213[/C][C]0.7292860853935[/C][/ROW]
[ROW][C]26[/C][C]0.191891597872708[/C][C]0.383783195745415[/C][C]0.808108402127293[/C][/ROW]
[ROW][C]27[/C][C]0.245754418030207[/C][C]0.491508836060413[/C][C]0.754245581969793[/C][/ROW]
[ROW][C]28[/C][C]0.42253002280863[/C][C]0.84506004561726[/C][C]0.57746997719137[/C][/ROW]
[ROW][C]29[/C][C]0.366610788456309[/C][C]0.733221576912618[/C][C]0.633389211543691[/C][/ROW]
[ROW][C]30[/C][C]0.3847917742107[/C][C]0.7695835484214[/C][C]0.6152082257893[/C][/ROW]
[ROW][C]31[/C][C]0.660769453956495[/C][C]0.678461092087009[/C][C]0.339230546043505[/C][/ROW]
[ROW][C]32[/C][C]0.575409217872904[/C][C]0.849181564254192[/C][C]0.424590782127096[/C][/ROW]
[ROW][C]33[/C][C]0.481018204225057[/C][C]0.962036408450114[/C][C]0.518981795774943[/C][/ROW]
[ROW][C]34[/C][C]0.715753949059422[/C][C]0.568492101881156[/C][C]0.284246050940578[/C][/ROW]
[ROW][C]35[/C][C]0.596869411093025[/C][C]0.806261177813951[/C][C]0.403130588906975[/C][/ROW]
[ROW][C]36[/C][C]0.51531562556361[/C][C]0.96936874887278[/C][C]0.48468437443639[/C][/ROW]
[ROW][C]37[/C][C]0.3810355730472[/C][C]0.7620711460944[/C][C]0.6189644269528[/C][/ROW]
[ROW][C]38[/C][C]0.287416526121309[/C][C]0.574833052242618[/C][C]0.71258347387869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111886&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111886&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
19	0.681613208712021	0.636773582575958	0.318386791287979
20	0.531004287850866	0.937991424298268	0.468995712149134
21	0.628429159765247	0.743141680469507	0.371570840234753
22	0.499038584422185	0.99807716884437	0.500961415577815
23	0.44766625500748	0.89533251001496	0.55233374499252
24	0.336500613659002	0.673001227318004	0.663499386340998
25	0.2707139146065	0.541427829213	0.7292860853935
26	0.191891597872708	0.383783195745415	0.808108402127293
27	0.245754418030207	0.491508836060413	0.754245581969793
28	0.42253002280863	0.84506004561726	0.57746997719137
29	0.366610788456309	0.733221576912618	0.633389211543691
30	0.3847917742107	0.7695835484214	0.6152082257893
31	0.660769453956495	0.678461092087009	0.339230546043505
32	0.575409217872904	0.849181564254192	0.424590782127096
33	0.481018204225057	0.962036408450114	0.518981795774943
34	0.715753949059422	0.568492101881156	0.284246050940578
35	0.596869411093025	0.806261177813951	0.403130588906975
36	0.51531562556361	0.96936874887278	0.48468437443639
37	0.3810355730472	0.7620711460944	0.6189644269528
38	0.287416526121309	0.574833052242618	0.71258347387869

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	0	0	OK

\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 & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111886&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111886&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111886&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	0	0	OK

Figure 1

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Figure 2

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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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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