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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 computationWed, 18 Nov 2009 08:02:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/18/t1258556589w0g39c5ypnbpjyn.htm/, Retrieved Wed, 19 Nov 2025 23:29:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57468, Retrieved Wed, 19 Nov 2025 23:29:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact507

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] [] [2009-11-18 15:02:28] [873be88d67c17ca20f1ec7e5d8eb10d1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.2	97.78	7.5	8.3	8.8	8.9
7.4	97.69	7.2	7.5	8.3	8.8
8.8	96.67	7.4	7.2	7.5	8.3
9.3	98.29	8.8	7.4	7.2	7.5
9.3	98.2	9.3	8.8	7.4	7.2
8.7	98.71	9.3	9.3	8.8	7.4
8.2	98.54	8.7	9.3	9.3	8.8
8.3	98.2	8.2	8.7	9.3	9.3
8.5	96.92	8.3	8.2	8.7	9.3
8.6	99.06	8.5	8.3	8.2	8.7
8.5	99.65	8.6	8.5	8.3	8.2
8.2	99.82	8.5	8.6	8.5	8.3
8.1	99.99	8.2	8.5	8.6	8.5
7.9	100.33	8.1	8.2	8.5	8.6
8.6	99.31	7.9	8.1	8.2	8.5
8.7	101.1	8.6	7.9	8.1	8.2
8.7	101.1	8.7	8.6	7.9	8.1
8.5	100.93	8.7	8.7	8.6	7.9
8.4	100.85	8.5	8.7	8.7	8.6
8.5	100.93	8.4	8.5	8.7	8.7
8.7	99.6	8.5	8.4	8.5	8.7
8.7	101.88	8.7	8.5	8.4	8.5
8.6	101.81	8.7	8.7	8.5	8.4
8.5	102.38	8.6	8.7	8.7	8.5
8.3	102.74	8.5	8.6	8.7	8.7
8	102.82	8.3	8.5	8.6	8.7
8.2	101.72	8	8.3	8.5	8.6
8.1	103.47	8.2	8	8.3	8.5
8.1	102.98	8.1	8.2	8	8.3
8	102.68	8.1	8.1	8.2	8
7.9	102.9	8	8.1	8.1	8.2
7.9	103.03	7.9	8	8.1	8.1
8	101.29	7.9	7.9	8	8.1
8	103.69	8	7.9	7.9	8
7.9	103.68	8	8	7.9	7.9
8	104.2	7.9	8	8	7.9
7.7	104.08	8	7.9	8	8
7.2	104.16	7.7	8	7.9	8
7.5	103.05	7.2	7.7	8	7.9
7.3	104.66	7.5	7.2	7.7	8
7	104.46	7.3	7.5	7.2	7.7
7	104.95	7	7.3	7.5	7.2
7	105.85	7	7	7.3	7.5
7.2	106.23	7	7	7	7.3
7.3	104.86	7.2	7	7	7
7.1	107.44	7.3	7.2	7	7
6.8	108.23	7.1	7.3	7.2	7
6.4	108.45	6.8	7.1	7.3	7.2
6.1	109.39	6.4	6.8	7.1	7.3
6.5	110.15	6.1	6.4	6.8	7.1
7.7	109.13	6.5	6.1	6.4	6.8
7.9	110.28	7.7	6.5	6.1	6.4
7.5	110.17	7.9	7.7	6.5	6.1
6.9	109.99	7.5	7.9	7.7	6.5
6.6	109.26	6.9	7.5	7.9	7.7
6.9	109.11	6.6	6.9	7.5	7.9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57468&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57468&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57468&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = -4.2624270514545 + 0.0544200722822084X[t] + 1.46532978957155Y1[t] -0.781224197342366Y2[t] -0.145033370420391Y3[t] + 0.348490784025746Y4[t] -0.148355004747847M1[t] -0.124115508443071M2[t] + 0.67376339796129M3[t] -0.401217733032853M4[t] + 0.0053311824447823M5[t] + 0.140524604956648M6[t] + 0.0365083464145630M7[t] + 0.196594506474901M8[t] + 0.134986853801317M9[t] -0.0889181651253318M10[t] -0.0096689769740506M11[t] -0.0176296130558109t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -4.2624270514545 +  0.0544200722822084X[t] +  1.46532978957155Y1[t] -0.781224197342366Y2[t] -0.145033370420391Y3[t] +  0.348490784025746Y4[t] -0.148355004747847M1[t] -0.124115508443071M2[t] +  0.67376339796129M3[t] -0.401217733032853M4[t] +  0.0053311824447823M5[t] +  0.140524604956648M6[t] +  0.0365083464145630M7[t] +  0.196594506474901M8[t] +  0.134986853801317M9[t] -0.0889181651253318M10[t] -0.0096689769740506M11[t] -0.0176296130558109t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57468&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -4.2624270514545 +  0.0544200722822084X[t] +  1.46532978957155Y1[t] -0.781224197342366Y2[t] -0.145033370420391Y3[t] +  0.348490784025746Y4[t] -0.148355004747847M1[t] -0.124115508443071M2[t] +  0.67376339796129M3[t] -0.401217733032853M4[t] +  0.0053311824447823M5[t] +  0.140524604956648M6[t] +  0.0365083464145630M7[t] +  0.196594506474901M8[t] +  0.134986853801317M9[t] -0.0889181651253318M10[t] -0.0096689769740506M11[t] -0.0176296130558109t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57468&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57468&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
Y[t] = -4.2624270514545 + 0.0544200722822084X[t] + 1.46532978957155Y1[t] -0.781224197342366Y2[t] -0.145033370420391Y3[t] + 0.348490784025746Y4[t] -0.148355004747847M1[t] -0.124115508443071M2[t] + 0.67376339796129M3[t] -0.401217733032853M4[t] + 0.0053311824447823M5[t] + 0.140524604956648M6[t] + 0.0365083464145630M7[t] + 0.196594506474901M8[t] + 0.134986853801317M9[t] -0.0889181651253318M10[t] -0.0096689769740506M11[t] -0.0176296130558109t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-4.26242705145453.264481-1.30570.1995050.099753
X0.05442007228220840.0302721.79770.080170.040085
Y11.465329789571550.13649210.735600
Y2-0.7812241973423660.261591-2.98640.004920.00246
Y3-0.1450333704203910.262515-0.55250.5838570.291928
Y40.3484907840257460.1433982.43020.0199210.00996
M1-0.1483550047478470.102582-1.44620.1563150.078158
M2-0.1241155084430710.105851-1.17250.2482770.124139
M30.673763397961290.1113116.05300
M4-0.4012177330328530.139823-2.86950.006680.00334
M50.00533118244478230.1539720.03460.9725610.48628
M60.1405246049566480.1252571.12190.2689490.134475
M70.03650834641456300.10030.3640.7178820.358941
M80.1965945064749010.1031551.90580.0642590.032129
M90.1349868538013170.1280211.05440.2983520.149176
M10-0.08891816512533180.112482-0.79050.4341370.217069
M11-0.00966897697405060.106662-0.09070.9282460.464123
t-0.01762961305581090.006378-2.7640.0087580.004379

\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) & -4.2624270514545 & 3.264481 & -1.3057 & 0.199505 & 0.099753 \tabularnewline
X & 0.0544200722822084 & 0.030272 & 1.7977 & 0.08017 & 0.040085 \tabularnewline
Y1 & 1.46532978957155 & 0.136492 & 10.7356 & 0 & 0 \tabularnewline
Y2 & -0.781224197342366 & 0.261591 & -2.9864 & 0.00492 & 0.00246 \tabularnewline
Y3 & -0.145033370420391 & 0.262515 & -0.5525 & 0.583857 & 0.291928 \tabularnewline
Y4 & 0.348490784025746 & 0.143398 & 2.4302 & 0.019921 & 0.00996 \tabularnewline
M1 & -0.148355004747847 & 0.102582 & -1.4462 & 0.156315 & 0.078158 \tabularnewline
M2 & -0.124115508443071 & 0.105851 & -1.1725 & 0.248277 & 0.124139 \tabularnewline
M3 & 0.67376339796129 & 0.111311 & 6.053 & 0 & 0 \tabularnewline
M4 & -0.401217733032853 & 0.139823 & -2.8695 & 0.00668 & 0.00334 \tabularnewline
M5 & 0.0053311824447823 & 0.153972 & 0.0346 & 0.972561 & 0.48628 \tabularnewline
M6 & 0.140524604956648 & 0.125257 & 1.1219 & 0.268949 & 0.134475 \tabularnewline
M7 & 0.0365083464145630 & 0.1003 & 0.364 & 0.717882 & 0.358941 \tabularnewline
M8 & 0.196594506474901 & 0.103155 & 1.9058 & 0.064259 & 0.032129 \tabularnewline
M9 & 0.134986853801317 & 0.128021 & 1.0544 & 0.298352 & 0.149176 \tabularnewline
M10 & -0.0889181651253318 & 0.112482 & -0.7905 & 0.434137 & 0.217069 \tabularnewline
M11 & -0.0096689769740506 & 0.106662 & -0.0907 & 0.928246 & 0.464123 \tabularnewline
t & -0.0176296130558109 & 0.006378 & -2.764 & 0.008758 & 0.004379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57468&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]-4.2624270514545[/C][C]3.264481[/C][C]-1.3057[/C][C]0.199505[/C][C]0.099753[/C][/ROW]
[ROW][C]X[/C][C]0.0544200722822084[/C][C]0.030272[/C][C]1.7977[/C][C]0.08017[/C][C]0.040085[/C][/ROW]
[ROW][C]Y1[/C][C]1.46532978957155[/C][C]0.136492[/C][C]10.7356[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.781224197342366[/C][C]0.261591[/C][C]-2.9864[/C][C]0.00492[/C][C]0.00246[/C][/ROW]
[ROW][C]Y3[/C][C]-0.145033370420391[/C][C]0.262515[/C][C]-0.5525[/C][C]0.583857[/C][C]0.291928[/C][/ROW]
[ROW][C]Y4[/C][C]0.348490784025746[/C][C]0.143398[/C][C]2.4302[/C][C]0.019921[/C][C]0.00996[/C][/ROW]
[ROW][C]M1[/C][C]-0.148355004747847[/C][C]0.102582[/C][C]-1.4462[/C][C]0.156315[/C][C]0.078158[/C][/ROW]
[ROW][C]M2[/C][C]-0.124115508443071[/C][C]0.105851[/C][C]-1.1725[/C][C]0.248277[/C][C]0.124139[/C][/ROW]
[ROW][C]M3[/C][C]0.67376339796129[/C][C]0.111311[/C][C]6.053[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-0.401217733032853[/C][C]0.139823[/C][C]-2.8695[/C][C]0.00668[/C][C]0.00334[/C][/ROW]
[ROW][C]M5[/C][C]0.0053311824447823[/C][C]0.153972[/C][C]0.0346[/C][C]0.972561[/C][C]0.48628[/C][/ROW]
[ROW][C]M6[/C][C]0.140524604956648[/C][C]0.125257[/C][C]1.1219[/C][C]0.268949[/C][C]0.134475[/C][/ROW]
[ROW][C]M7[/C][C]0.0365083464145630[/C][C]0.1003[/C][C]0.364[/C][C]0.717882[/C][C]0.358941[/C][/ROW]
[ROW][C]M8[/C][C]0.196594506474901[/C][C]0.103155[/C][C]1.9058[/C][C]0.064259[/C][C]0.032129[/C][/ROW]
[ROW][C]M9[/C][C]0.134986853801317[/C][C]0.128021[/C][C]1.0544[/C][C]0.298352[/C][C]0.149176[/C][/ROW]
[ROW][C]M10[/C][C]-0.0889181651253318[/C][C]0.112482[/C][C]-0.7905[/C][C]0.434137[/C][C]0.217069[/C][/ROW]
[ROW][C]M11[/C][C]-0.0096689769740506[/C][C]0.106662[/C][C]-0.0907[/C][C]0.928246[/C][C]0.464123[/C][/ROW]
[ROW][C]t[/C][C]-0.0176296130558109[/C][C]0.006378[/C][C]-2.764[/C][C]0.008758[/C][C]0.004379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57468&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57468&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)-4.26242705145453.264481-1.30570.1995050.099753
X0.05442007228220840.0302721.79770.080170.040085
Y11.465329789571550.13649210.735600
Y2-0.7812241973423660.261591-2.98640.004920.00246
Y3-0.1450333704203910.262515-0.55250.5838570.291928
Y40.3484907840257460.1433982.43020.0199210.00996
M1-0.1483550047478470.102582-1.44620.1563150.078158
M2-0.1241155084430710.105851-1.17250.2482770.124139
M30.673763397961290.1113116.05300
M4-0.4012177330328530.139823-2.86950.006680.00334
M50.00533118244478230.1539720.03460.9725610.48628
M60.1405246049566480.1252571.12190.2689490.134475
M70.03650834641456300.10030.3640.7178820.358941
M80.1965945064749010.1031551.90580.0642590.032129
M90.1349868538013170.1280211.05440.2983520.149176
M10-0.08891816512533180.112482-0.79050.4341370.217069
M11-0.00966897697405060.106662-0.09070.9282460.464123
t-0.01762961305581090.006378-2.7640.0087580.004379






Multiple Linear Regression - Regression Statistics
Multiple R0.986303646694806
R-squared0.972794883483472
Adjusted R-squared0.96062417346292
F-TEST (value)79.9291809467797
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.147598926463559
Sum Squared Residuals0.827846837541415

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.986303646694806 \tabularnewline
R-squared & 0.972794883483472 \tabularnewline
Adjusted R-squared & 0.96062417346292 \tabularnewline
F-TEST (value) & 79.9291809467797 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.147598926463559 \tabularnewline
Sum Squared Residuals & 0.827846837541415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57468&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.986303646694806[/C][/ROW]
[ROW][C]R-squared[/C][C]0.972794883483472[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.96062417346292[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]79.9291809467797[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/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]0.147598926463559[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.827846837541415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57468&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57468&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 R0.986303646694806
R-squared0.972794883483472
Adjusted R-squared0.96062417346292
F-TEST (value)79.9291809467797
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.147598926463559
Sum Squared Residuals0.827846837541415






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.27.22386990047083-0.0238699004708295
27.47.44863000502446-0.048630005024465
38.88.642585346085620.157414653914379
49.39.298069368970060.00193063102993888
59.39.187487974101150.112512025898855
68.78.80884535996655-0.108845359966547
78.28.2141206147636-0.0141206147635935
88.38.248389352824690.051610647175313
98.58.72365949445464-0.223659494454642
108.68.67694957013093-0.0769495701309264
118.58.57221639830667-0.072216398306669
128.28.35469418013999-0.154694180139990
138.17.891679277250190.208320722749811
147.98.05397868076527-0.153978680765273
158.68.572436894929440.0275631050705577
168.78.669169874267510.030830125732488
178.78.651922813188340.0480771868116619
188.58.51089127452276-0.0108912745227593
198.48.321266051003960.0787339489960404
208.58.51263714270496-0.0126371427049567
218.78.61468325361570.0853167463843062
228.78.656975104853630.0430248951463683
238.68.509188019976260.0908119800237387
248.58.39155625045670.108443749543299
258.38.246450456256870.0535495437431318
2688.05697374415038-0.0569737441503771
278.28.47366111922497-0.273661119224971
288.17.99787631446740.102123685532596
298.18.031163817366290.0688361826337123
3088.07697011558011-0.0769701155801146
317.97.90496517477434-0.0049651747743374
327.97.95123669355006-0.0512366935500586
3387.86993425882590.130065741174103
3487.885195037917360.114804962082644
357.97.83329891415320.0667010858468063
3687.692600399658990.307399600341011
377.77.77958985027543-0.0795898502754307
387.27.28733531974331-0.0873353197433102
397.57.459528281830930.0404717181690688
407.37.36310397922667-0.0631039792266722
4177.18167550007751-0.181675500077507
4276.824795644409860.175204355590137
4377.12004900636047-0.120049006360466
447.27.2569970351532-0.0569970351532001
457.37.291722993103770.00827700689623347
467.17.18088028709809-0.0808802870980856
476.86.88529666756388-0.085296667563876
486.46.66114916974432-0.261149169744320
496.16.25841051574668-0.158410515746683
506.56.153082250316570.346917749683426
517.77.651788357929030.0482116420709653
527.97.97178046306835-0.071780463068351
537.57.54774989526672-0.0477498952667225
546.96.878497605520720.0215023944792845
556.66.539599153097640.0604008469023566
566.96.83073977576710.0692602242329024

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.2 & 7.22386990047083 & -0.0238699004708295 \tabularnewline
2 & 7.4 & 7.44863000502446 & -0.048630005024465 \tabularnewline
3 & 8.8 & 8.64258534608562 & 0.157414653914379 \tabularnewline
4 & 9.3 & 9.29806936897006 & 0.00193063102993888 \tabularnewline
5 & 9.3 & 9.18748797410115 & 0.112512025898855 \tabularnewline
6 & 8.7 & 8.80884535996655 & -0.108845359966547 \tabularnewline
7 & 8.2 & 8.2141206147636 & -0.0141206147635935 \tabularnewline
8 & 8.3 & 8.24838935282469 & 0.051610647175313 \tabularnewline
9 & 8.5 & 8.72365949445464 & -0.223659494454642 \tabularnewline
10 & 8.6 & 8.67694957013093 & -0.0769495701309264 \tabularnewline
11 & 8.5 & 8.57221639830667 & -0.072216398306669 \tabularnewline
12 & 8.2 & 8.35469418013999 & -0.154694180139990 \tabularnewline
13 & 8.1 & 7.89167927725019 & 0.208320722749811 \tabularnewline
14 & 7.9 & 8.05397868076527 & -0.153978680765273 \tabularnewline
15 & 8.6 & 8.57243689492944 & 0.0275631050705577 \tabularnewline
16 & 8.7 & 8.66916987426751 & 0.030830125732488 \tabularnewline
17 & 8.7 & 8.65192281318834 & 0.0480771868116619 \tabularnewline
18 & 8.5 & 8.51089127452276 & -0.0108912745227593 \tabularnewline
19 & 8.4 & 8.32126605100396 & 0.0787339489960404 \tabularnewline
20 & 8.5 & 8.51263714270496 & -0.0126371427049567 \tabularnewline
21 & 8.7 & 8.6146832536157 & 0.0853167463843062 \tabularnewline
22 & 8.7 & 8.65697510485363 & 0.0430248951463683 \tabularnewline
23 & 8.6 & 8.50918801997626 & 0.0908119800237387 \tabularnewline
24 & 8.5 & 8.3915562504567 & 0.108443749543299 \tabularnewline
25 & 8.3 & 8.24645045625687 & 0.0535495437431318 \tabularnewline
26 & 8 & 8.05697374415038 & -0.0569737441503771 \tabularnewline
27 & 8.2 & 8.47366111922497 & -0.273661119224971 \tabularnewline
28 & 8.1 & 7.9978763144674 & 0.102123685532596 \tabularnewline
29 & 8.1 & 8.03116381736629 & 0.0688361826337123 \tabularnewline
30 & 8 & 8.07697011558011 & -0.0769701155801146 \tabularnewline
31 & 7.9 & 7.90496517477434 & -0.0049651747743374 \tabularnewline
32 & 7.9 & 7.95123669355006 & -0.0512366935500586 \tabularnewline
33 & 8 & 7.8699342588259 & 0.130065741174103 \tabularnewline
34 & 8 & 7.88519503791736 & 0.114804962082644 \tabularnewline
35 & 7.9 & 7.8332989141532 & 0.0667010858468063 \tabularnewline
36 & 8 & 7.69260039965899 & 0.307399600341011 \tabularnewline
37 & 7.7 & 7.77958985027543 & -0.0795898502754307 \tabularnewline
38 & 7.2 & 7.28733531974331 & -0.0873353197433102 \tabularnewline
39 & 7.5 & 7.45952828183093 & 0.0404717181690688 \tabularnewline
40 & 7.3 & 7.36310397922667 & -0.0631039792266722 \tabularnewline
41 & 7 & 7.18167550007751 & -0.181675500077507 \tabularnewline
42 & 7 & 6.82479564440986 & 0.175204355590137 \tabularnewline
43 & 7 & 7.12004900636047 & -0.120049006360466 \tabularnewline
44 & 7.2 & 7.2569970351532 & -0.0569970351532001 \tabularnewline
45 & 7.3 & 7.29172299310377 & 0.00827700689623347 \tabularnewline
46 & 7.1 & 7.18088028709809 & -0.0808802870980856 \tabularnewline
47 & 6.8 & 6.88529666756388 & -0.085296667563876 \tabularnewline
48 & 6.4 & 6.66114916974432 & -0.261149169744320 \tabularnewline
49 & 6.1 & 6.25841051574668 & -0.158410515746683 \tabularnewline
50 & 6.5 & 6.15308225031657 & 0.346917749683426 \tabularnewline
51 & 7.7 & 7.65178835792903 & 0.0482116420709653 \tabularnewline
52 & 7.9 & 7.97178046306835 & -0.071780463068351 \tabularnewline
53 & 7.5 & 7.54774989526672 & -0.0477498952667225 \tabularnewline
54 & 6.9 & 6.87849760552072 & 0.0215023944792845 \tabularnewline
55 & 6.6 & 6.53959915309764 & 0.0604008469023566 \tabularnewline
56 & 6.9 & 6.8307397757671 & 0.0692602242329024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57468&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]7.2[/C][C]7.22386990047083[/C][C]-0.0238699004708295[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]7.44863000502446[/C][C]-0.048630005024465[/C][/ROW]
[ROW][C]3[/C][C]8.8[/C][C]8.64258534608562[/C][C]0.157414653914379[/C][/ROW]
[ROW][C]4[/C][C]9.3[/C][C]9.29806936897006[/C][C]0.00193063102993888[/C][/ROW]
[ROW][C]5[/C][C]9.3[/C][C]9.18748797410115[/C][C]0.112512025898855[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.80884535996655[/C][C]-0.108845359966547[/C][/ROW]
[ROW][C]7[/C][C]8.2[/C][C]8.2141206147636[/C][C]-0.0141206147635935[/C][/ROW]
[ROW][C]8[/C][C]8.3[/C][C]8.24838935282469[/C][C]0.051610647175313[/C][/ROW]
[ROW][C]9[/C][C]8.5[/C][C]8.72365949445464[/C][C]-0.223659494454642[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.67694957013093[/C][C]-0.0769495701309264[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.57221639830667[/C][C]-0.072216398306669[/C][/ROW]
[ROW][C]12[/C][C]8.2[/C][C]8.35469418013999[/C][C]-0.154694180139990[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]7.89167927725019[/C][C]0.208320722749811[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.05397868076527[/C][C]-0.153978680765273[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.57243689492944[/C][C]0.0275631050705577[/C][/ROW]
[ROW][C]16[/C][C]8.7[/C][C]8.66916987426751[/C][C]0.030830125732488[/C][/ROW]
[ROW][C]17[/C][C]8.7[/C][C]8.65192281318834[/C][C]0.0480771868116619[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.51089127452276[/C][C]-0.0108912745227593[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.32126605100396[/C][C]0.0787339489960404[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.51263714270496[/C][C]-0.0126371427049567[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.6146832536157[/C][C]0.0853167463843062[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]8.65697510485363[/C][C]0.0430248951463683[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.50918801997626[/C][C]0.0908119800237387[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.3915562504567[/C][C]0.108443749543299[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.24645045625687[/C][C]0.0535495437431318[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.05697374415038[/C][C]-0.0569737441503771[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.47366111922497[/C][C]-0.273661119224971[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]7.9978763144674[/C][C]0.102123685532596[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]8.03116381736629[/C][C]0.0688361826337123[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.07697011558011[/C][C]-0.0769701155801146[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]7.90496517477434[/C][C]-0.0049651747743374[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]7.95123669355006[/C][C]-0.0512366935500586[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.8699342588259[/C][C]0.130065741174103[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.88519503791736[/C][C]0.114804962082644[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.8332989141532[/C][C]0.0667010858468063[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.69260039965899[/C][C]0.307399600341011[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]7.77958985027543[/C][C]-0.0795898502754307[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.28733531974331[/C][C]-0.0873353197433102[/C][/ROW]
[ROW][C]39[/C][C]7.5[/C][C]7.45952828183093[/C][C]0.0404717181690688[/C][/ROW]
[ROW][C]40[/C][C]7.3[/C][C]7.36310397922667[/C][C]-0.0631039792266722[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.18167550007751[/C][C]-0.181675500077507[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.82479564440986[/C][C]0.175204355590137[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]7.12004900636047[/C][C]-0.120049006360466[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.2569970351532[/C][C]-0.0569970351532001[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.29172299310377[/C][C]0.00827700689623347[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.18088028709809[/C][C]-0.0808802870980856[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.88529666756388[/C][C]-0.085296667563876[/C][/ROW]
[ROW][C]48[/C][C]6.4[/C][C]6.66114916974432[/C][C]-0.261149169744320[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.25841051574668[/C][C]-0.158410515746683[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.15308225031657[/C][C]0.346917749683426[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.65178835792903[/C][C]0.0482116420709653[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.97178046306835[/C][C]-0.071780463068351[/C][/ROW]
[ROW][C]53[/C][C]7.5[/C][C]7.54774989526672[/C][C]-0.0477498952667225[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.87849760552072[/C][C]0.0215023944792845[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.53959915309764[/C][C]0.0604008469023566[/C][/ROW]
[ROW][C]56[/C][C]6.9[/C][C]6.8307397757671[/C][C]0.0692602242329024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57468&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57468&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
17.27.22386990047083-0.0238699004708295
27.47.44863000502446-0.048630005024465
38.88.642585346085620.157414653914379
49.39.298069368970060.00193063102993888
59.39.187487974101150.112512025898855
68.78.80884535996655-0.108845359966547
78.28.2141206147636-0.0141206147635935
88.38.248389352824690.051610647175313
98.58.72365949445464-0.223659494454642
108.68.67694957013093-0.0769495701309264
118.58.57221639830667-0.072216398306669
128.28.35469418013999-0.154694180139990
138.17.891679277250190.208320722749811
147.98.05397868076527-0.153978680765273
158.68.572436894929440.0275631050705577
168.78.669169874267510.030830125732488
178.78.651922813188340.0480771868116619
188.58.51089127452276-0.0108912745227593
198.48.321266051003960.0787339489960404
208.58.51263714270496-0.0126371427049567
218.78.61468325361570.0853167463843062
228.78.656975104853630.0430248951463683
238.68.509188019976260.0908119800237387
248.58.39155625045670.108443749543299
258.38.246450456256870.0535495437431318
2688.05697374415038-0.0569737441503771
278.28.47366111922497-0.273661119224971
288.17.99787631446740.102123685532596
298.18.031163817366290.0688361826337123
3088.07697011558011-0.0769701155801146
317.97.90496517477434-0.0049651747743374
327.97.95123669355006-0.0512366935500586
3387.86993425882590.130065741174103
3487.885195037917360.114804962082644
357.97.83329891415320.0667010858468063
3687.692600399658990.307399600341011
377.77.77958985027543-0.0795898502754307
387.27.28733531974331-0.0873353197433102
397.57.459528281830930.0404717181690688
407.37.36310397922667-0.0631039792266722
4177.18167550007751-0.181675500077507
4276.824795644409860.175204355590137
4377.12004900636047-0.120049006360466
447.27.2569970351532-0.0569970351532001
457.37.291722993103770.00827700689623347
467.17.18088028709809-0.0808802870980856
476.86.88529666756388-0.085296667563876
486.46.66114916974432-0.261149169744320
496.16.25841051574668-0.158410515746683
506.56.153082250316570.346917749683426
517.77.651788357929030.0482116420709653
527.97.97178046306835-0.071780463068351
537.57.54774989526672-0.0477498952667225
546.96.878497605520720.0215023944792845
556.66.539599153097640.0604008469023566
566.96.83073977576710.0692602242329024






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.1084308147751040.2168616295502090.891569185224896
220.0656230324397340.1312460648794680.934376967560266
230.02434723254511670.04869446509023330.975652767454883
240.03730260207051650.0746052041410330.962697397929484
250.01630484715466060.03260969430932130.98369515284534
260.01464048537858980.02928097075717950.98535951462141
270.3051884657982170.6103769315964350.694811534201783
280.2062294759827990.4124589519655990.7937705240172
290.1350598045630430.2701196091260860.864940195436957
300.1599697899224140.3199395798448280.840030210077586
310.1175820813180260.2351641626360530.882417918681974
320.1003946842130450.200789368426090.899605315786955
330.0748223665642320.1496447331284640.925177633435768
340.0482004452454420.0964008904908840.951799554754558
350.02168771170247280.04337542340494570.978312288297527

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.108430814775104 & 0.216861629550209 & 0.891569185224896 \tabularnewline
22 & 0.065623032439734 & 0.131246064879468 & 0.934376967560266 \tabularnewline
23 & 0.0243472325451167 & 0.0486944650902333 & 0.975652767454883 \tabularnewline
24 & 0.0373026020705165 & 0.074605204141033 & 0.962697397929484 \tabularnewline
25 & 0.0163048471546606 & 0.0326096943093213 & 0.98369515284534 \tabularnewline
26 & 0.0146404853785898 & 0.0292809707571795 & 0.98535951462141 \tabularnewline
27 & 0.305188465798217 & 0.610376931596435 & 0.694811534201783 \tabularnewline
28 & 0.206229475982799 & 0.412458951965599 & 0.7937705240172 \tabularnewline
29 & 0.135059804563043 & 0.270119609126086 & 0.864940195436957 \tabularnewline
30 & 0.159969789922414 & 0.319939579844828 & 0.840030210077586 \tabularnewline
31 & 0.117582081318026 & 0.235164162636053 & 0.882417918681974 \tabularnewline
32 & 0.100394684213045 & 0.20078936842609 & 0.899605315786955 \tabularnewline
33 & 0.074822366564232 & 0.149644733128464 & 0.925177633435768 \tabularnewline
34 & 0.048200445245442 & 0.096400890490884 & 0.951799554754558 \tabularnewline
35 & 0.0216877117024728 & 0.0433754234049457 & 0.978312288297527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57468&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]21[/C][C]0.108430814775104[/C][C]0.216861629550209[/C][C]0.891569185224896[/C][/ROW]
[ROW][C]22[/C][C]0.065623032439734[/C][C]0.131246064879468[/C][C]0.934376967560266[/C][/ROW]
[ROW][C]23[/C][C]0.0243472325451167[/C][C]0.0486944650902333[/C][C]0.975652767454883[/C][/ROW]
[ROW][C]24[/C][C]0.0373026020705165[/C][C]0.074605204141033[/C][C]0.962697397929484[/C][/ROW]
[ROW][C]25[/C][C]0.0163048471546606[/C][C]0.0326096943093213[/C][C]0.98369515284534[/C][/ROW]
[ROW][C]26[/C][C]0.0146404853785898[/C][C]0.0292809707571795[/C][C]0.98535951462141[/C][/ROW]
[ROW][C]27[/C][C]0.305188465798217[/C][C]0.610376931596435[/C][C]0.694811534201783[/C][/ROW]
[ROW][C]28[/C][C]0.206229475982799[/C][C]0.412458951965599[/C][C]0.7937705240172[/C][/ROW]
[ROW][C]29[/C][C]0.135059804563043[/C][C]0.270119609126086[/C][C]0.864940195436957[/C][/ROW]
[ROW][C]30[/C][C]0.159969789922414[/C][C]0.319939579844828[/C][C]0.840030210077586[/C][/ROW]
[ROW][C]31[/C][C]0.117582081318026[/C][C]0.235164162636053[/C][C]0.882417918681974[/C][/ROW]
[ROW][C]32[/C][C]0.100394684213045[/C][C]0.20078936842609[/C][C]0.899605315786955[/C][/ROW]
[ROW][C]33[/C][C]0.074822366564232[/C][C]0.149644733128464[/C][C]0.925177633435768[/C][/ROW]
[ROW][C]34[/C][C]0.048200445245442[/C][C]0.096400890490884[/C][C]0.951799554754558[/C][/ROW]
[ROW][C]35[/C][C]0.0216877117024728[/C][C]0.0433754234049457[/C][C]0.978312288297527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57468&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57468&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
210.1084308147751040.2168616295502090.891569185224896
220.0656230324397340.1312460648794680.934376967560266
230.02434723254511670.04869446509023330.975652767454883
240.03730260207051650.0746052041410330.962697397929484
250.01630484715466060.03260969430932130.98369515284534
260.01464048537858980.02928097075717950.98535951462141
270.3051884657982170.6103769315964350.694811534201783
280.2062294759827990.4124589519655990.7937705240172
290.1350598045630430.2701196091260860.864940195436957
300.1599697899224140.3199395798448280.840030210077586
310.1175820813180260.2351641626360530.882417918681974
320.1003946842130450.200789368426090.899605315786955
330.0748223665642320.1496447331284640.925177633435768
340.0482004452454420.0964008904908840.951799554754558
350.02168771170247280.04337542340494570.978312288297527






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.266666666666667NOK
10% type I error level60.4NOK

\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 & 4 & 0.266666666666667 & NOK \tabularnewline
10% type I error level & 6 & 0.4 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57468&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]4[/C][C]0.266666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]6[/C][C]0.4[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57468&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57468&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 level00OK
5% type I error level40.266666666666667NOK
10% type I error level60.4NOK


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 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; 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')
}