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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 30 Nov 2018 16:22:19 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Nov/30/t1543591453avxaimyinl5g57r.htm/, Retrieved Fri, 03 May 2024 05:31:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315734, Retrieved Fri, 03 May 2024 05:31:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Otto

Estimated Impact

124

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

-       [Multiple Regression] [Les 1] [2018-11-30 15:22:19] [22d4a11ea5ee287e32af9f8f184ec355] [Current]

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Dataseries X:

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Histogram

Boxplots

0.2 0.02 0 0.24 0.79
0.21 0.29 0.07 0.55 2.21
0.27 0.03 0.01 0.24 2.12
1.42 0.64 0.26 0.2 0.93
NA NA NA NA 5.38
1.86 0.66 1.67 2.64 3.14
0.26 0.1 0.02 0.44 2.23
NA NA NA NA 11.88
5.81 2.01 3.19 5.42 9.31
0.16 2.04 0 0.71 6.06
0.2 0.11 0.02 0.46 2.31
0 1.18 8.27 0.05 6.84
0 0 0.46 0.01 7.49
0 0 0.05 0.25 0.72
0 0.02 0.04 0.08 4.48
0.3 1.71 0.02 1.52 5.09
0.03 0.28 0.04 0.56 7.44
0.04 0.34 0.02 0.44 1.41
NA NA NA NA 5.77
0.34 4.38 0.01 0.28 4.84
2.18 13.86 0.05 0.59 2.96
0.19 1.13 0 0.3 3.12
2.49 0.63 0.27 0.06 3.83
1 6.82 0.17 1 3.11
NA NA NA NA 2.86
0.01 1.57 1.24 0.02 4.06
0.08 1.2 0.12 1.33 3.32
0.17 0.25 0 0.5 1.21
0.07 0.01 0.01 0.2 0.8
NA NA NA NA 2.52
NA NA NA NA 1.21
0.1 0.92 0.08 0.55 1.17
0.29 9.12 3.41 3.11 8.17
0.02 0.19 0.11 0 5.65
0.57 6.98 0 0.29 1.24
1.15 0.41 0.07 0.35 1.46
0.45 2.19 0.38 0.47 4.36
0.1 0.22 0.04 0.46 3.38
1.13 2.09 0.07 0.22 1.87
0.01 0.02 0.07 0.23 1.03
3.06 7.33 0.35 0.13 1.29
0.32 2.52 0.05 0.13 0.82
0.3 0.63 0.12 0.38 2.84
0.3 0.48 0.04 0.88 1.27
0.19 1.55 0.33 0.68 3.92
0.09 0.23 0.16 0.26 1.95
0 0.06 0.06 0.18 4.21
0.07 1.31 0 0.94 5.19
0.01 0.34 1.8 2.38 5.51
NA NA NA NA 2.19
0.01 0.52 0.1 0.4 2.57
0.11 0.16 0.02 0.22 1.53
0.3 1.41 0.11 0.32 2.17
0 0 0.02 0.38 2.15
0.15 0.04 0.11 0.27 2.07
0.15 3.1 1.01 0.13 3.97
0.18 0.09 0.93 0.07 0.42
NA NA NA NA 6.86
0.12 0.05 0.04 0.31 1.02
0.09 1.3 0.65 0.28 2.9
NA NA NA NA 5.87
0.16 0.96 0.11 1.67 5.14
0.06 95.16 16.07 0.07 2.34
0.03 0.73 0.42 0.19 4.73
3.6 19.5 2.93 0.25 2.02
0.04 0.2 0.32 0.23 1.03
0.36 0.61 0.05 0.12 1.58
0.06 0.68 0.07 1.23 5.3
0.26 0.29 0.06 0.67 1.97
0.14 0.23 0.17 1.01 4.38
NA NA NA NA 2.98
0.03 0.13 0.18 0.11 3.23
0.15 0.34 0.05 0.38 1.89
0.75 0.64 0.3 0.35 1.41
0.36 0.34 1.79 0.48 1.53
1.51 59.19 5.12 0.69 3.07
0.03 0.01 0.01 0.18 0.61
0.26 0.89 0.23 0.33 1.68
0.06 0.69 0 1.28 2.92
0 0.02 0.03 0.35 1.16
0.06 0.3 0.38 0.46 1.58
0.07 0.06 0.19 0.48 2.79
0.02 0.05 0 0.18 1.88
0.76 0.5 1.49 0.84 5.57
0.01 0.03 0.02 0.22 6.22
0.04 0.33 0.06 0.58 4.61
0 0.1 0.11 0.16 1.89
0 0.35 0.1 0.16 5.02
0.02 0.03 0 0.09 2.1
1.93 0.24 0.06 1.14 5.55
0.24 0.02 0.02 0.2 1.03
0 0.21 0.09 0.24 1.17
0 0.09 0.4 0.13 5.69
0.01 0 0.37 0.02 8.13
0.63 0.06 0.05 0.47 1.91
0.13 0.78 0.03 0.57 1.22
0.31 4.08 1.93 3.1 6.29
0.04 0.06 0.01 0.16 3.84
0.74 0 0 0.04 1.66
0.61 1.45 0.32 0.15 1.21
0.23 0.02 0.25 0.17 3.69
0.11 2.09 0.3 3.03 5.83
0.08 0.89 0 0.57 15.82
0.17 0.92 0.02 0.38 3.26
1.3 0.8 0.21 0.26 0.99
0.07 0.02 0.06 0.45 0.81
0.01 0.73 0.84 0.75 3.71
0.71 0.25 0.05 0.51 1.53
0.02 0.1 0.09 0.13 2.08
2.91 0.05 1.38 0.1 2.54
0 0.01 0.56 0.14 3.46
0.24 0.47 0.14 0.37 2.89
0.07 0.1 0.01 0.59 1.78
8.23 7.03 0.14 0.21 6.08
0.22 2.63 0.24 0.14 3.78
NA NA NA NA 7.78
0.17 0.1 0.07 0.34 1.68
0.96 0.61 0.17 0.28 0.87
0 0.56 0.28 0.88 1.43
1.6 0.36 4.76 0.14 2.48
NA NA NA NA 2.94
0.05 0.06 0.01 0.37 0.98
0.04 0.08 0.43 0.45 5.28
0.31 1.94 5.35 0.07 3.58
2.7 5.95 0.86 0.51 5.6
0.58 0.74 0.49 0.4 1.39
0.51 0.05 0 0.65 1.56
0.12 0.02 0.02 0.5 1.16
NA NA NA NA 4.98
0.04 0 1.61 0.07 7.52
0 0.01 0.04 0.26 0.79
0.43 1.74 0.6 0.14 2.79
0.04 2.66 0.73 0.36 1.91
2.28 5.54 0.05 2.51 4.16
0.51 2.82 0.2 0.36 2.28
0.02 0.09 0.07 0.32 1.1
0.07 0.77 0.11 1.05 4.44
0.06 0.85 0.07 0.47 3.88
0 0 1.17 0.01 10.8
0.01 0.04 0 0.14 3.65
0.11 1.14 0.08 0.87 2.71
0.34 4.38 1.19 0.85 5.69
0.05 0.01 0.01 0.42 0.87
0.01 0.17 0.38 0.06 4.94
0 0.1 0.14 0.1 2.45
NA NA NA NA 3.11
0.01 1.17 0.06 0.69 2.77
0 0.22 0.4 0.25 1.49
0.12 0.07 0.18 0.09 5.61
0.17 0.46 0.17 0.21 1.21
0.02 0.46 0 0.73 2.7
0.35 0.19 0.22 0.42 1.24
0 0 0.01 0 7.97
0.06 1.85 0 0.71 4.06
0.07 1.87 0 0.37 5.81
0.01 2.28 1.19 0.66 1.29
0.56 0.22 0.33 0.09 1.24
0.58 0.02 0.17 0.35 3.31
0.1 0.34 0.06 0.72 3.67
0.02 0.04 0.07 0.26 1.32
0.03 81.52 7.39 0.3 4.25
0.51 0.05 0 0.25 2.01
0.22 6.66 2.19 1.31 7.25
0.12 0.74 0.01 0.32 5.79
0.1 0.04 0 0.41 1.51
0.14 0.01 0.01 0.29 0.91
0.34 0.17 0.06 0.46 1.32
0.01 0.2 0.19 0.77 2.66
0.06 0.52 0.94 0.21 0.48
0.12 0.03 0.02 0.34 1.13
0.02 0.11 0.52 0.83 2.7
0.01 0.15 1.37 0.04 7.92
0.08 0.05 0.24 0.53 2.34
0.09 0.6 0.04 0.75 3.33
1.96 0.02 0.13 0.6 5.47
0.15 0.01 0.04 0.35 1.24
0.12 0.43 0.15 1.5 2.84
0.12 0.12 0.3 0.6 4.94
0 0.07 0.47 0.02 7.93
0.28 1.57 0.33 1.49 8.22
4.86 1.22 2.18 1.89 2.91
0.2 0.06 0.03 0.56 2.32
0.57 1.79 0.24 0.14 3.57
0.01 0.17 0.16 0.55 1.65
NA NA NA NA 2.07
0.12 0.04 0.2 0.09 1.03
0.94 0.99 0.02 0.24 0.99
0.32 0.12 0.01 0.15 1.37

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	14 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time14 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

14 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=315734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&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	14 seconds
R Server	Big Analytics Cloud Computing Center

Multiple Linear Regression - Estimated Regression Equation
Total_Ecological_Footprint[t] = + 2.58433 -0.00563894Grazing_Land[t] -0.0375181Forest_Land[t] + 0.351754Fishing_Water[t] + 0.960884Cropland[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Total_Ecological_Footprint[t] =  +  2.58433 -0.00563894Grazing_Land[t] -0.0375181Forest_Land[t] +  0.351754Fishing_Water[t] +  0.960884Cropland[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Total_Ecological_Footprint[t] =  +  2.58433 -0.00563894Grazing_Land[t] -0.0375181Forest_Land[t] +  0.351754Fishing_Water[t] +  0.960884Cropland[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&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
Total_Ecological_Footprint[t] = + 2.58433 -0.00563894Grazing_Land[t] -0.0375181Forest_Land[t] + 0.351754Fishing_Water[t] + 0.960884Cropland[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+2.584	0.2207	+1.1710e+01	1.554e-23	7.769e-24
Grazing_Land	-0.005639	0.1737	-3.2470e-02	0.9741	0.4871
Forest_Land	-0.03752	0.02547	-1.4730e+00	0.1426	0.07128
Fishing_Water	+0.3518	0.1629	+2.1590e+00	0.03224	0.01612
Cropland	+0.9609	0.2632	+3.6510e+00	0.0003486	0.0001743

\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) & +2.584 &  0.2207 & +1.1710e+01 &  1.554e-23 &  7.769e-24 \tabularnewline
Grazing_Land & -0.005639 &  0.1737 & -3.2470e-02 &  0.9741 &  0.4871 \tabularnewline
Forest_Land & -0.03752 &  0.02547 & -1.4730e+00 &  0.1426 &  0.07128 \tabularnewline
Fishing_Water & +0.3518 &  0.1629 & +2.1590e+00 &  0.03224 &  0.01612 \tabularnewline
Cropland & +0.9609 &  0.2632 & +3.6510e+00 &  0.0003486 &  0.0001743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&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]+2.584[/C][C] 0.2207[/C][C]+1.1710e+01[/C][C] 1.554e-23[/C][C] 7.769e-24[/C][/ROW]
[ROW][C]Grazing_Land[/C][C]-0.005639[/C][C] 0.1737[/C][C]-3.2470e-02[/C][C] 0.9741[/C][C] 0.4871[/C][/ROW]
[ROW][C]Forest_Land[/C][C]-0.03752[/C][C] 0.02547[/C][C]-1.4730e+00[/C][C] 0.1426[/C][C] 0.07128[/C][/ROW]
[ROW][C]Fishing_Water[/C][C]+0.3518[/C][C] 0.1629[/C][C]+2.1590e+00[/C][C] 0.03224[/C][C] 0.01612[/C][/ROW]
[ROW][C]Cropland[/C][C]+0.9609[/C][C] 0.2632[/C][C]+3.6510e+00[/C][C] 0.0003486[/C][C] 0.0001743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&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)	+2.584	0.2207	+1.1710e+01	1.554e-23	7.769e-24
Grazing_Land	-0.005639	0.1737	-3.2470e-02	0.9741	0.4871
Forest_Land	-0.03752	0.02547	-1.4730e+00	0.1426	0.07128
Fishing_Water	+0.3518	0.1629	+2.1590e+00	0.03224	0.01612
Cropland	+0.9609	0.2632	+3.6510e+00	0.0003486	0.0001743

Multiple Linear Regression - Regression Statistics
Multiple R	0.3416
R-squared	0.1167
Adjusted R-squared	0.09563
F-TEST (value)	5.547
F-TEST (DF numerator)	4
F-TEST (DF denominator)	168
p-value	0.0003221
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.194
Sum Squared Residuals	808.6

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.3416 \tabularnewline
R-squared &  0.1167 \tabularnewline
Adjusted R-squared &  0.09563 \tabularnewline
F-TEST (value) &  5.547 \tabularnewline
F-TEST (DF numerator) & 4 \tabularnewline
F-TEST (DF denominator) & 168 \tabularnewline
p-value &  0.0003221 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  2.194 \tabularnewline
Sum Squared Residuals &  808.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.3416[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.1167[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.09563[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 5.547[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]4[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]168[/C][/ROW]
[ROW][C]p-value[/C][C] 0.0003221[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 2.194[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 808.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&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	0.3416
R-squared	0.1167
Adjusted R-squared	0.09563
F-TEST (value)	5.547
F-TEST (DF numerator)	4
F-TEST (DF denominator)	168
p-value	0.0003221
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.194
Sum Squared Residuals	808.6

Menu of Residual Diagnostics
Description	Link
Histogram	Compute
Central Tendency	Compute
QQ Plot	Compute
Kernel Density Plot	Compute
Skewness/Kurtosis Test	Compute
Skewness-Kurtosis Plot	Compute
Harrell-Davis Plot	Compute
Bootstrap Plot -- Central Tendency	Compute
Blocked Bootstrap Plot -- Central Tendency	Compute
(Partial) Autocorrelation Plot	Compute
Spectral Analysis	Compute
Tukey lambda PPCC Plot	Compute
Box-Cox Normality Plot	Compute
Summary Statistics	Compute

\begin{tabular}{lllllllll}
\hline
Menu of Residual Diagnostics \tabularnewline
Description & Link \tabularnewline
Histogram & Compute \tabularnewline
Central Tendency & Compute \tabularnewline
QQ Plot & Compute \tabularnewline
Kernel Density Plot & Compute \tabularnewline
Skewness/Kurtosis Test & Compute \tabularnewline
Skewness-Kurtosis Plot & Compute \tabularnewline
Harrell-Davis Plot & Compute \tabularnewline
Bootstrap Plot -- Central Tendency & Compute \tabularnewline
Blocked Bootstrap Plot -- Central Tendency & Compute \tabularnewline
(Partial) Autocorrelation Plot & Compute \tabularnewline
Spectral Analysis & Compute \tabularnewline
Tukey lambda PPCC Plot & Compute \tabularnewline
Box-Cox Normality Plot & Compute \tabularnewline
Summary Statistics & Compute \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=4

[TABLE]
[ROW][C]Menu of Residual Diagnostics[/C][/ROW]
[ROW][C]Description[/C][C]Link[/C][/ROW]
[ROW][C]Histogram[/C][C]Compute[/C][/ROW]
[ROW][C]Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]QQ Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Kernel Density Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness/Kurtosis Test[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness-Kurtosis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Harrell-Davis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]Blocked Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C](Partial) Autocorrelation Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Spectral Analysis[/C][C]Compute[/C][/ROW]
[ROW][C]Tukey lambda PPCC Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Box-Cox Normality Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Summary Statistics[/C][C]Compute[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&T=4

As an alternative you can also use a QR Code:

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

Menu of Residual Diagnostics
Description	Link
Histogram	Compute
Central Tendency	Compute
QQ Plot	Compute
Kernel Density Plot	Compute
Skewness/Kurtosis Test	Compute
Skewness-Kurtosis Plot	Compute
Harrell-Davis Plot	Compute
Bootstrap Plot -- Central Tendency	Compute
Blocked Bootstrap Plot -- Central Tendency	Compute
(Partial) Autocorrelation Plot	Compute
Spectral Analysis	Compute
Tukey lambda PPCC Plot	Compute
Box-Cox Normality Plot	Compute
Summary Statistics	Compute

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	0.79	2.813	-2.023
2	2.21	3.125	-0.9154
3	2.12	2.816	-0.6958
4	0.93	2.836	-1.906
5	3.14	5.673	-2.533
6	2.23	3.009	-0.7789
7	9.31	8.806	0.5038
8	6.06	3.189	2.871
9	2.31	3.028	-0.7181
10	6.84	5.497	1.343
11	7.49	2.756	4.734
12	0.72	2.842	-2.122
13	4.48	2.675	1.805
14	5.09	3.986	1.104
15	7.44	3.126	4.314
16	1.41	3.001	-1.591
17	4.84	2.691	2.149
18	2.96	2.637	0.3235
19	3.12	2.829	0.2909
20	3.83	2.699	1.131
21	3.11	3.344	-0.2335
22	4.06	2.981	1.079
23	3.32	3.859	-0.539
24	1.21	3.054	-1.844
25	0.8	2.779	-1.979
26	1.17	3.106	-1.936
27	8.17	6.428	1.742
28	5.65	2.616	3.034
29	1.24	2.598	-1.358
30	1.46	2.923	-1.463
31	4.36	3.085	1.275
32	3.38	3.032	0.3484
33	1.87	2.736	-0.8656
34	1.03	2.829	-1.799
35	1.29	2.54	-1.25
36	0.82	2.63	-1.81
37	2.84	2.966	-0.1264
38	1.27	3.424	-2.154
39	3.92	3.295	0.6254
40	1.95	2.881	-0.9313
41	4.21	2.776	1.434
42	5.19	3.438	1.752
43	5.51	5.492	0.01842
44	2.57	2.984	-0.4143
45	1.53	2.796	-1.266
46	2.17	2.876	-0.7059
47	2.15	2.957	-0.8065
48	2.07	2.88	-0.8101
49	3.97	2.947	1.023
50	0.42	2.974	-2.554
51	1.02	2.894	-1.874
52	2.9	3.033	-0.1327
53	5.14	4.191	0.9492
54	2.34	4.734	-2.394
55	4.73	2.887	1.843
56	2.02	3.103	-1.083
57	1.03	2.91	-1.88
58	1.58	2.692	-1.112
59	5.3	3.765	1.535
60	1.97	3.237	-1.267
61	4.38	3.605	0.7748
62	3.23	2.748	0.4817
63	1.89	2.953	-1.063
64	1.41	2.998	-1.588
65	1.53	3.66	-2.13
66	3.07	2.819	0.2509
67	0.61	2.76	-2.15
68	1.68	2.947	-1.267
69	2.92	3.788	-0.868
70	1.16	2.93	-1.77
71	1.58	3.148	-1.568
72	2.79	3.11	-0.3197
73	1.88	2.755	-0.8753
74	5.57	3.893	1.677
75	6.22	2.802	3.418
76	4.61	3.15	1.46
77	1.89	2.773	-0.883
78	5.02	2.76	2.26
79	2.1	2.67	-0.5696
80	5.55	3.681	1.869
81	1.03	2.781	-1.751
82	1.17	2.839	-1.669
83	5.69	2.847	2.843
84	8.13	2.734	5.396
85	1.91	3.048	-1.138
86	1.22	3.113	-1.893
87	6.29	6.087	0.2029
88	3.84	2.739	1.101
89	1.66	2.619	-0.9586
90	1.21	2.783	-1.573
91	3.69	2.834	0.8564
92	5.83	5.522	0.3077
93	15.82	3.098	12.72
94	3.26	2.921	0.339
95	0.99	2.871	-1.881
96	0.81	3.037	-2.227
97	3.71	3.573	0.137
98	1.53	3.079	-1.549
99	2.08	2.737	-0.657
100	2.54	3.148	-0.6076
101	3.46	2.915	0.5445
102	2.89	2.97	-0.08012
103	1.78	3.151	-1.371
104	6.08	2.525	3.555
105	3.78	2.703	1.077
106	1.68	2.931	-1.251
107	0.87	2.885	-2.015
108	1.43	3.507	-2.077
109	2.48	4.371	-1.891
110	0.98	2.941	-1.961
111	5.28	3.165	2.115
112	3.58	4.459	-0.8789
113	5.6	3.138	2.462
114	1.39	3.11	-1.72
115	1.56	3.204	-1.644
116	1.16	3.07	-1.91
117	7.52	3.218	4.302
118	0.79	2.848	-2.058
119	2.79	2.862	-0.0722
120	1.91	3.087	-1.177
121	4.16	4.793	-0.633
122	2.28	2.892	-0.6119
123	1.1	2.913	-1.813
124	4.44	3.603	0.8373
125	3.88	3.028	0.8517
126	10.8	3.005	7.795
127	3.65	2.717	0.9327
128	2.71	3.405	-0.6951
129	5.69	3.653	2.037
130	0.87	2.991	-2.121
131	4.94	2.769	2.171
132	2.45	2.726	-0.2759
133	2.77	3.224	-0.4545
134	1.49	2.957	-1.467
135	5.61	2.731	2.879
136	1.21	2.828	-1.618
137	2.7	3.268	-0.5684
138	1.24	3.056	-1.816
139	7.97	2.588	5.382
140	4.06	3.197	0.8632
141	5.81	2.869	2.941
142	1.29	3.552	-2.262
143	1.24	2.775	-1.535
144	3.31	2.976	0.3336
145	3.67	3.284	0.386
146	1.32	2.857	-1.537
147	4.25	2.413	1.837
148	2.01	2.82	-0.8098
149	7.25	4.362	2.888
150	5.79	2.867	2.923
151	1.51	2.976	-1.466
152	0.91	2.865	-1.955
153	1.32	3.039	-1.719
154	2.66	3.383	-0.7235
155	0.48	3.097	-2.617
156	1.13	2.916	-1.786
157	2.7	3.561	-0.8605
158	7.92	3.099	4.821
159	2.34	3.176	-0.8357
160	3.33	3.296	0.03395
161	5.47	3.195	2.275
162	1.24	2.933	-1.693
163	2.84	4.062	-1.222
164	4.94	3.261	1.679
165	7.93	2.766	5.164
166	8.22	4.072	4.148
167	2.91	5.094	-2.184
168	2.32	3.13	-0.8096
169	3.57	2.733	0.8371
170	1.65	3.163	-1.513
171	1.03	2.739	-1.709
172	0.99	2.78	-1.79
173	1.37	2.726	-1.356

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  0.79 &  2.813 & -2.023 \tabularnewline
2 &  2.21 &  3.125 & -0.9154 \tabularnewline
3 &  2.12 &  2.816 & -0.6958 \tabularnewline
4 &  0.93 &  2.836 & -1.906 \tabularnewline
5 &  3.14 &  5.673 & -2.533 \tabularnewline
6 &  2.23 &  3.009 & -0.7789 \tabularnewline
7 &  9.31 &  8.806 &  0.5038 \tabularnewline
8 &  6.06 &  3.189 &  2.871 \tabularnewline
9 &  2.31 &  3.028 & -0.7181 \tabularnewline
10 &  6.84 &  5.497 &  1.343 \tabularnewline
11 &  7.49 &  2.756 &  4.734 \tabularnewline
12 &  0.72 &  2.842 & -2.122 \tabularnewline
13 &  4.48 &  2.675 &  1.805 \tabularnewline
14 &  5.09 &  3.986 &  1.104 \tabularnewline
15 &  7.44 &  3.126 &  4.314 \tabularnewline
16 &  1.41 &  3.001 & -1.591 \tabularnewline
17 &  4.84 &  2.691 &  2.149 \tabularnewline
18 &  2.96 &  2.637 &  0.3235 \tabularnewline
19 &  3.12 &  2.829 &  0.2909 \tabularnewline
20 &  3.83 &  2.699 &  1.131 \tabularnewline
21 &  3.11 &  3.344 & -0.2335 \tabularnewline
22 &  4.06 &  2.981 &  1.079 \tabularnewline
23 &  3.32 &  3.859 & -0.539 \tabularnewline
24 &  1.21 &  3.054 & -1.844 \tabularnewline
25 &  0.8 &  2.779 & -1.979 \tabularnewline
26 &  1.17 &  3.106 & -1.936 \tabularnewline
27 &  8.17 &  6.428 &  1.742 \tabularnewline
28 &  5.65 &  2.616 &  3.034 \tabularnewline
29 &  1.24 &  2.598 & -1.358 \tabularnewline
30 &  1.46 &  2.923 & -1.463 \tabularnewline
31 &  4.36 &  3.085 &  1.275 \tabularnewline
32 &  3.38 &  3.032 &  0.3484 \tabularnewline
33 &  1.87 &  2.736 & -0.8656 \tabularnewline
34 &  1.03 &  2.829 & -1.799 \tabularnewline
35 &  1.29 &  2.54 & -1.25 \tabularnewline
36 &  0.82 &  2.63 & -1.81 \tabularnewline
37 &  2.84 &  2.966 & -0.1264 \tabularnewline
38 &  1.27 &  3.424 & -2.154 \tabularnewline
39 &  3.92 &  3.295 &  0.6254 \tabularnewline
40 &  1.95 &  2.881 & -0.9313 \tabularnewline
41 &  4.21 &  2.776 &  1.434 \tabularnewline
42 &  5.19 &  3.438 &  1.752 \tabularnewline
43 &  5.51 &  5.492 &  0.01842 \tabularnewline
44 &  2.57 &  2.984 & -0.4143 \tabularnewline
45 &  1.53 &  2.796 & -1.266 \tabularnewline
46 &  2.17 &  2.876 & -0.7059 \tabularnewline
47 &  2.15 &  2.957 & -0.8065 \tabularnewline
48 &  2.07 &  2.88 & -0.8101 \tabularnewline
49 &  3.97 &  2.947 &  1.023 \tabularnewline
50 &  0.42 &  2.974 & -2.554 \tabularnewline
51 &  1.02 &  2.894 & -1.874 \tabularnewline
52 &  2.9 &  3.033 & -0.1327 \tabularnewline
53 &  5.14 &  4.191 &  0.9492 \tabularnewline
54 &  2.34 &  4.734 & -2.394 \tabularnewline
55 &  4.73 &  2.887 &  1.843 \tabularnewline
56 &  2.02 &  3.103 & -1.083 \tabularnewline
57 &  1.03 &  2.91 & -1.88 \tabularnewline
58 &  1.58 &  2.692 & -1.112 \tabularnewline
59 &  5.3 &  3.765 &  1.535 \tabularnewline
60 &  1.97 &  3.237 & -1.267 \tabularnewline
61 &  4.38 &  3.605 &  0.7748 \tabularnewline
62 &  3.23 &  2.748 &  0.4817 \tabularnewline
63 &  1.89 &  2.953 & -1.063 \tabularnewline
64 &  1.41 &  2.998 & -1.588 \tabularnewline
65 &  1.53 &  3.66 & -2.13 \tabularnewline
66 &  3.07 &  2.819 &  0.2509 \tabularnewline
67 &  0.61 &  2.76 & -2.15 \tabularnewline
68 &  1.68 &  2.947 & -1.267 \tabularnewline
69 &  2.92 &  3.788 & -0.868 \tabularnewline
70 &  1.16 &  2.93 & -1.77 \tabularnewline
71 &  1.58 &  3.148 & -1.568 \tabularnewline
72 &  2.79 &  3.11 & -0.3197 \tabularnewline
73 &  1.88 &  2.755 & -0.8753 \tabularnewline
74 &  5.57 &  3.893 &  1.677 \tabularnewline
75 &  6.22 &  2.802 &  3.418 \tabularnewline
76 &  4.61 &  3.15 &  1.46 \tabularnewline
77 &  1.89 &  2.773 & -0.883 \tabularnewline
78 &  5.02 &  2.76 &  2.26 \tabularnewline
79 &  2.1 &  2.67 & -0.5696 \tabularnewline
80 &  5.55 &  3.681 &  1.869 \tabularnewline
81 &  1.03 &  2.781 & -1.751 \tabularnewline
82 &  1.17 &  2.839 & -1.669 \tabularnewline
83 &  5.69 &  2.847 &  2.843 \tabularnewline
84 &  8.13 &  2.734 &  5.396 \tabularnewline
85 &  1.91 &  3.048 & -1.138 \tabularnewline
86 &  1.22 &  3.113 & -1.893 \tabularnewline
87 &  6.29 &  6.087 &  0.2029 \tabularnewline
88 &  3.84 &  2.739 &  1.101 \tabularnewline
89 &  1.66 &  2.619 & -0.9586 \tabularnewline
90 &  1.21 &  2.783 & -1.573 \tabularnewline
91 &  3.69 &  2.834 &  0.8564 \tabularnewline
92 &  5.83 &  5.522 &  0.3077 \tabularnewline
93 &  15.82 &  3.098 &  12.72 \tabularnewline
94 &  3.26 &  2.921 &  0.339 \tabularnewline
95 &  0.99 &  2.871 & -1.881 \tabularnewline
96 &  0.81 &  3.037 & -2.227 \tabularnewline
97 &  3.71 &  3.573 &  0.137 \tabularnewline
98 &  1.53 &  3.079 & -1.549 \tabularnewline
99 &  2.08 &  2.737 & -0.657 \tabularnewline
100 &  2.54 &  3.148 & -0.6076 \tabularnewline
101 &  3.46 &  2.915 &  0.5445 \tabularnewline
102 &  2.89 &  2.97 & -0.08012 \tabularnewline
103 &  1.78 &  3.151 & -1.371 \tabularnewline
104 &  6.08 &  2.525 &  3.555 \tabularnewline
105 &  3.78 &  2.703 &  1.077 \tabularnewline
106 &  1.68 &  2.931 & -1.251 \tabularnewline
107 &  0.87 &  2.885 & -2.015 \tabularnewline
108 &  1.43 &  3.507 & -2.077 \tabularnewline
109 &  2.48 &  4.371 & -1.891 \tabularnewline
110 &  0.98 &  2.941 & -1.961 \tabularnewline
111 &  5.28 &  3.165 &  2.115 \tabularnewline
112 &  3.58 &  4.459 & -0.8789 \tabularnewline
113 &  5.6 &  3.138 &  2.462 \tabularnewline
114 &  1.39 &  3.11 & -1.72 \tabularnewline
115 &  1.56 &  3.204 & -1.644 \tabularnewline
116 &  1.16 &  3.07 & -1.91 \tabularnewline
117 &  7.52 &  3.218 &  4.302 \tabularnewline
118 &  0.79 &  2.848 & -2.058 \tabularnewline
119 &  2.79 &  2.862 & -0.0722 \tabularnewline
120 &  1.91 &  3.087 & -1.177 \tabularnewline
121 &  4.16 &  4.793 & -0.633 \tabularnewline
122 &  2.28 &  2.892 & -0.6119 \tabularnewline
123 &  1.1 &  2.913 & -1.813 \tabularnewline
124 &  4.44 &  3.603 &  0.8373 \tabularnewline
125 &  3.88 &  3.028 &  0.8517 \tabularnewline
126 &  10.8 &  3.005 &  7.795 \tabularnewline
127 &  3.65 &  2.717 &  0.9327 \tabularnewline
128 &  2.71 &  3.405 & -0.6951 \tabularnewline
129 &  5.69 &  3.653 &  2.037 \tabularnewline
130 &  0.87 &  2.991 & -2.121 \tabularnewline
131 &  4.94 &  2.769 &  2.171 \tabularnewline
132 &  2.45 &  2.726 & -0.2759 \tabularnewline
133 &  2.77 &  3.224 & -0.4545 \tabularnewline
134 &  1.49 &  2.957 & -1.467 \tabularnewline
135 &  5.61 &  2.731 &  2.879 \tabularnewline
136 &  1.21 &  2.828 & -1.618 \tabularnewline
137 &  2.7 &  3.268 & -0.5684 \tabularnewline
138 &  1.24 &  3.056 & -1.816 \tabularnewline
139 &  7.97 &  2.588 &  5.382 \tabularnewline
140 &  4.06 &  3.197 &  0.8632 \tabularnewline
141 &  5.81 &  2.869 &  2.941 \tabularnewline
142 &  1.29 &  3.552 & -2.262 \tabularnewline
143 &  1.24 &  2.775 & -1.535 \tabularnewline
144 &  3.31 &  2.976 &  0.3336 \tabularnewline
145 &  3.67 &  3.284 &  0.386 \tabularnewline
146 &  1.32 &  2.857 & -1.537 \tabularnewline
147 &  4.25 &  2.413 &  1.837 \tabularnewline
148 &  2.01 &  2.82 & -0.8098 \tabularnewline
149 &  7.25 &  4.362 &  2.888 \tabularnewline
150 &  5.79 &  2.867 &  2.923 \tabularnewline
151 &  1.51 &  2.976 & -1.466 \tabularnewline
152 &  0.91 &  2.865 & -1.955 \tabularnewline
153 &  1.32 &  3.039 & -1.719 \tabularnewline
154 &  2.66 &  3.383 & -0.7235 \tabularnewline
155 &  0.48 &  3.097 & -2.617 \tabularnewline
156 &  1.13 &  2.916 & -1.786 \tabularnewline
157 &  2.7 &  3.561 & -0.8605 \tabularnewline
158 &  7.92 &  3.099 &  4.821 \tabularnewline
159 &  2.34 &  3.176 & -0.8357 \tabularnewline
160 &  3.33 &  3.296 &  0.03395 \tabularnewline
161 &  5.47 &  3.195 &  2.275 \tabularnewline
162 &  1.24 &  2.933 & -1.693 \tabularnewline
163 &  2.84 &  4.062 & -1.222 \tabularnewline
164 &  4.94 &  3.261 &  1.679 \tabularnewline
165 &  7.93 &  2.766 &  5.164 \tabularnewline
166 &  8.22 &  4.072 &  4.148 \tabularnewline
167 &  2.91 &  5.094 & -2.184 \tabularnewline
168 &  2.32 &  3.13 & -0.8096 \tabularnewline
169 &  3.57 &  2.733 &  0.8371 \tabularnewline
170 &  1.65 &  3.163 & -1.513 \tabularnewline
171 &  1.03 &  2.739 & -1.709 \tabularnewline
172 &  0.99 &  2.78 & -1.79 \tabularnewline
173 &  1.37 &  2.726 & -1.356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=5

[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] 0.79[/C][C] 2.813[/C][C]-2.023[/C][/ROW]
[ROW][C]2[/C][C] 2.21[/C][C] 3.125[/C][C]-0.9154[/C][/ROW]
[ROW][C]3[/C][C] 2.12[/C][C] 2.816[/C][C]-0.6958[/C][/ROW]
[ROW][C]4[/C][C] 0.93[/C][C] 2.836[/C][C]-1.906[/C][/ROW]
[ROW][C]5[/C][C] 3.14[/C][C] 5.673[/C][C]-2.533[/C][/ROW]
[ROW][C]6[/C][C] 2.23[/C][C] 3.009[/C][C]-0.7789[/C][/ROW]
[ROW][C]7[/C][C] 9.31[/C][C] 8.806[/C][C] 0.5038[/C][/ROW]
[ROW][C]8[/C][C] 6.06[/C][C] 3.189[/C][C] 2.871[/C][/ROW]
[ROW][C]9[/C][C] 2.31[/C][C] 3.028[/C][C]-0.7181[/C][/ROW]
[ROW][C]10[/C][C] 6.84[/C][C] 5.497[/C][C] 1.343[/C][/ROW]
[ROW][C]11[/C][C] 7.49[/C][C] 2.756[/C][C] 4.734[/C][/ROW]
[ROW][C]12[/C][C] 0.72[/C][C] 2.842[/C][C]-2.122[/C][/ROW]
[ROW][C]13[/C][C] 4.48[/C][C] 2.675[/C][C] 1.805[/C][/ROW]
[ROW][C]14[/C][C] 5.09[/C][C] 3.986[/C][C] 1.104[/C][/ROW]
[ROW][C]15[/C][C] 7.44[/C][C] 3.126[/C][C] 4.314[/C][/ROW]
[ROW][C]16[/C][C] 1.41[/C][C] 3.001[/C][C]-1.591[/C][/ROW]
[ROW][C]17[/C][C] 4.84[/C][C] 2.691[/C][C] 2.149[/C][/ROW]
[ROW][C]18[/C][C] 2.96[/C][C] 2.637[/C][C] 0.3235[/C][/ROW]
[ROW][C]19[/C][C] 3.12[/C][C] 2.829[/C][C] 0.2909[/C][/ROW]
[ROW][C]20[/C][C] 3.83[/C][C] 2.699[/C][C] 1.131[/C][/ROW]
[ROW][C]21[/C][C] 3.11[/C][C] 3.344[/C][C]-0.2335[/C][/ROW]
[ROW][C]22[/C][C] 4.06[/C][C] 2.981[/C][C] 1.079[/C][/ROW]
[ROW][C]23[/C][C] 3.32[/C][C] 3.859[/C][C]-0.539[/C][/ROW]
[ROW][C]24[/C][C] 1.21[/C][C] 3.054[/C][C]-1.844[/C][/ROW]
[ROW][C]25[/C][C] 0.8[/C][C] 2.779[/C][C]-1.979[/C][/ROW]
[ROW][C]26[/C][C] 1.17[/C][C] 3.106[/C][C]-1.936[/C][/ROW]
[ROW][C]27[/C][C] 8.17[/C][C] 6.428[/C][C] 1.742[/C][/ROW]
[ROW][C]28[/C][C] 5.65[/C][C] 2.616[/C][C] 3.034[/C][/ROW]
[ROW][C]29[/C][C] 1.24[/C][C] 2.598[/C][C]-1.358[/C][/ROW]
[ROW][C]30[/C][C] 1.46[/C][C] 2.923[/C][C]-1.463[/C][/ROW]
[ROW][C]31[/C][C] 4.36[/C][C] 3.085[/C][C] 1.275[/C][/ROW]
[ROW][C]32[/C][C] 3.38[/C][C] 3.032[/C][C] 0.3484[/C][/ROW]
[ROW][C]33[/C][C] 1.87[/C][C] 2.736[/C][C]-0.8656[/C][/ROW]
[ROW][C]34[/C][C] 1.03[/C][C] 2.829[/C][C]-1.799[/C][/ROW]
[ROW][C]35[/C][C] 1.29[/C][C] 2.54[/C][C]-1.25[/C][/ROW]
[ROW][C]36[/C][C] 0.82[/C][C] 2.63[/C][C]-1.81[/C][/ROW]
[ROW][C]37[/C][C] 2.84[/C][C] 2.966[/C][C]-0.1264[/C][/ROW]
[ROW][C]38[/C][C] 1.27[/C][C] 3.424[/C][C]-2.154[/C][/ROW]
[ROW][C]39[/C][C] 3.92[/C][C] 3.295[/C][C] 0.6254[/C][/ROW]
[ROW][C]40[/C][C] 1.95[/C][C] 2.881[/C][C]-0.9313[/C][/ROW]
[ROW][C]41[/C][C] 4.21[/C][C] 2.776[/C][C] 1.434[/C][/ROW]
[ROW][C]42[/C][C] 5.19[/C][C] 3.438[/C][C] 1.752[/C][/ROW]
[ROW][C]43[/C][C] 5.51[/C][C] 5.492[/C][C] 0.01842[/C][/ROW]
[ROW][C]44[/C][C] 2.57[/C][C] 2.984[/C][C]-0.4143[/C][/ROW]
[ROW][C]45[/C][C] 1.53[/C][C] 2.796[/C][C]-1.266[/C][/ROW]
[ROW][C]46[/C][C] 2.17[/C][C] 2.876[/C][C]-0.7059[/C][/ROW]
[ROW][C]47[/C][C] 2.15[/C][C] 2.957[/C][C]-0.8065[/C][/ROW]
[ROW][C]48[/C][C] 2.07[/C][C] 2.88[/C][C]-0.8101[/C][/ROW]
[ROW][C]49[/C][C] 3.97[/C][C] 2.947[/C][C] 1.023[/C][/ROW]
[ROW][C]50[/C][C] 0.42[/C][C] 2.974[/C][C]-2.554[/C][/ROW]
[ROW][C]51[/C][C] 1.02[/C][C] 2.894[/C][C]-1.874[/C][/ROW]
[ROW][C]52[/C][C] 2.9[/C][C] 3.033[/C][C]-0.1327[/C][/ROW]
[ROW][C]53[/C][C] 5.14[/C][C] 4.191[/C][C] 0.9492[/C][/ROW]
[ROW][C]54[/C][C] 2.34[/C][C] 4.734[/C][C]-2.394[/C][/ROW]
[ROW][C]55[/C][C] 4.73[/C][C] 2.887[/C][C] 1.843[/C][/ROW]
[ROW][C]56[/C][C] 2.02[/C][C] 3.103[/C][C]-1.083[/C][/ROW]
[ROW][C]57[/C][C] 1.03[/C][C] 2.91[/C][C]-1.88[/C][/ROW]
[ROW][C]58[/C][C] 1.58[/C][C] 2.692[/C][C]-1.112[/C][/ROW]
[ROW][C]59[/C][C] 5.3[/C][C] 3.765[/C][C] 1.535[/C][/ROW]
[ROW][C]60[/C][C] 1.97[/C][C] 3.237[/C][C]-1.267[/C][/ROW]
[ROW][C]61[/C][C] 4.38[/C][C] 3.605[/C][C] 0.7748[/C][/ROW]
[ROW][C]62[/C][C] 3.23[/C][C] 2.748[/C][C] 0.4817[/C][/ROW]
[ROW][C]63[/C][C] 1.89[/C][C] 2.953[/C][C]-1.063[/C][/ROW]
[ROW][C]64[/C][C] 1.41[/C][C] 2.998[/C][C]-1.588[/C][/ROW]
[ROW][C]65[/C][C] 1.53[/C][C] 3.66[/C][C]-2.13[/C][/ROW]
[ROW][C]66[/C][C] 3.07[/C][C] 2.819[/C][C] 0.2509[/C][/ROW]
[ROW][C]67[/C][C] 0.61[/C][C] 2.76[/C][C]-2.15[/C][/ROW]
[ROW][C]68[/C][C] 1.68[/C][C] 2.947[/C][C]-1.267[/C][/ROW]
[ROW][C]69[/C][C] 2.92[/C][C] 3.788[/C][C]-0.868[/C][/ROW]
[ROW][C]70[/C][C] 1.16[/C][C] 2.93[/C][C]-1.77[/C][/ROW]
[ROW][C]71[/C][C] 1.58[/C][C] 3.148[/C][C]-1.568[/C][/ROW]
[ROW][C]72[/C][C] 2.79[/C][C] 3.11[/C][C]-0.3197[/C][/ROW]
[ROW][C]73[/C][C] 1.88[/C][C] 2.755[/C][C]-0.8753[/C][/ROW]
[ROW][C]74[/C][C] 5.57[/C][C] 3.893[/C][C] 1.677[/C][/ROW]
[ROW][C]75[/C][C] 6.22[/C][C] 2.802[/C][C] 3.418[/C][/ROW]
[ROW][C]76[/C][C] 4.61[/C][C] 3.15[/C][C] 1.46[/C][/ROW]
[ROW][C]77[/C][C] 1.89[/C][C] 2.773[/C][C]-0.883[/C][/ROW]
[ROW][C]78[/C][C] 5.02[/C][C] 2.76[/C][C] 2.26[/C][/ROW]
[ROW][C]79[/C][C] 2.1[/C][C] 2.67[/C][C]-0.5696[/C][/ROW]
[ROW][C]80[/C][C] 5.55[/C][C] 3.681[/C][C] 1.869[/C][/ROW]
[ROW][C]81[/C][C] 1.03[/C][C] 2.781[/C][C]-1.751[/C][/ROW]
[ROW][C]82[/C][C] 1.17[/C][C] 2.839[/C][C]-1.669[/C][/ROW]
[ROW][C]83[/C][C] 5.69[/C][C] 2.847[/C][C] 2.843[/C][/ROW]
[ROW][C]84[/C][C] 8.13[/C][C] 2.734[/C][C] 5.396[/C][/ROW]
[ROW][C]85[/C][C] 1.91[/C][C] 3.048[/C][C]-1.138[/C][/ROW]
[ROW][C]86[/C][C] 1.22[/C][C] 3.113[/C][C]-1.893[/C][/ROW]
[ROW][C]87[/C][C] 6.29[/C][C] 6.087[/C][C] 0.2029[/C][/ROW]
[ROW][C]88[/C][C] 3.84[/C][C] 2.739[/C][C] 1.101[/C][/ROW]
[ROW][C]89[/C][C] 1.66[/C][C] 2.619[/C][C]-0.9586[/C][/ROW]
[ROW][C]90[/C][C] 1.21[/C][C] 2.783[/C][C]-1.573[/C][/ROW]
[ROW][C]91[/C][C] 3.69[/C][C] 2.834[/C][C] 0.8564[/C][/ROW]
[ROW][C]92[/C][C] 5.83[/C][C] 5.522[/C][C] 0.3077[/C][/ROW]
[ROW][C]93[/C][C] 15.82[/C][C] 3.098[/C][C] 12.72[/C][/ROW]
[ROW][C]94[/C][C] 3.26[/C][C] 2.921[/C][C] 0.339[/C][/ROW]
[ROW][C]95[/C][C] 0.99[/C][C] 2.871[/C][C]-1.881[/C][/ROW]
[ROW][C]96[/C][C] 0.81[/C][C] 3.037[/C][C]-2.227[/C][/ROW]
[ROW][C]97[/C][C] 3.71[/C][C] 3.573[/C][C] 0.137[/C][/ROW]
[ROW][C]98[/C][C] 1.53[/C][C] 3.079[/C][C]-1.549[/C][/ROW]
[ROW][C]99[/C][C] 2.08[/C][C] 2.737[/C][C]-0.657[/C][/ROW]
[ROW][C]100[/C][C] 2.54[/C][C] 3.148[/C][C]-0.6076[/C][/ROW]
[ROW][C]101[/C][C] 3.46[/C][C] 2.915[/C][C] 0.5445[/C][/ROW]
[ROW][C]102[/C][C] 2.89[/C][C] 2.97[/C][C]-0.08012[/C][/ROW]
[ROW][C]103[/C][C] 1.78[/C][C] 3.151[/C][C]-1.371[/C][/ROW]
[ROW][C]104[/C][C] 6.08[/C][C] 2.525[/C][C] 3.555[/C][/ROW]
[ROW][C]105[/C][C] 3.78[/C][C] 2.703[/C][C] 1.077[/C][/ROW]
[ROW][C]106[/C][C] 1.68[/C][C] 2.931[/C][C]-1.251[/C][/ROW]
[ROW][C]107[/C][C] 0.87[/C][C] 2.885[/C][C]-2.015[/C][/ROW]
[ROW][C]108[/C][C] 1.43[/C][C] 3.507[/C][C]-2.077[/C][/ROW]
[ROW][C]109[/C][C] 2.48[/C][C] 4.371[/C][C]-1.891[/C][/ROW]
[ROW][C]110[/C][C] 0.98[/C][C] 2.941[/C][C]-1.961[/C][/ROW]
[ROW][C]111[/C][C] 5.28[/C][C] 3.165[/C][C] 2.115[/C][/ROW]
[ROW][C]112[/C][C] 3.58[/C][C] 4.459[/C][C]-0.8789[/C][/ROW]
[ROW][C]113[/C][C] 5.6[/C][C] 3.138[/C][C] 2.462[/C][/ROW]
[ROW][C]114[/C][C] 1.39[/C][C] 3.11[/C][C]-1.72[/C][/ROW]
[ROW][C]115[/C][C] 1.56[/C][C] 3.204[/C][C]-1.644[/C][/ROW]
[ROW][C]116[/C][C] 1.16[/C][C] 3.07[/C][C]-1.91[/C][/ROW]
[ROW][C]117[/C][C] 7.52[/C][C] 3.218[/C][C] 4.302[/C][/ROW]
[ROW][C]118[/C][C] 0.79[/C][C] 2.848[/C][C]-2.058[/C][/ROW]
[ROW][C]119[/C][C] 2.79[/C][C] 2.862[/C][C]-0.0722[/C][/ROW]
[ROW][C]120[/C][C] 1.91[/C][C] 3.087[/C][C]-1.177[/C][/ROW]
[ROW][C]121[/C][C] 4.16[/C][C] 4.793[/C][C]-0.633[/C][/ROW]
[ROW][C]122[/C][C] 2.28[/C][C] 2.892[/C][C]-0.6119[/C][/ROW]
[ROW][C]123[/C][C] 1.1[/C][C] 2.913[/C][C]-1.813[/C][/ROW]
[ROW][C]124[/C][C] 4.44[/C][C] 3.603[/C][C] 0.8373[/C][/ROW]
[ROW][C]125[/C][C] 3.88[/C][C] 3.028[/C][C] 0.8517[/C][/ROW]
[ROW][C]126[/C][C] 10.8[/C][C] 3.005[/C][C] 7.795[/C][/ROW]
[ROW][C]127[/C][C] 3.65[/C][C] 2.717[/C][C] 0.9327[/C][/ROW]
[ROW][C]128[/C][C] 2.71[/C][C] 3.405[/C][C]-0.6951[/C][/ROW]
[ROW][C]129[/C][C] 5.69[/C][C] 3.653[/C][C] 2.037[/C][/ROW]
[ROW][C]130[/C][C] 0.87[/C][C] 2.991[/C][C]-2.121[/C][/ROW]
[ROW][C]131[/C][C] 4.94[/C][C] 2.769[/C][C] 2.171[/C][/ROW]
[ROW][C]132[/C][C] 2.45[/C][C] 2.726[/C][C]-0.2759[/C][/ROW]
[ROW][C]133[/C][C] 2.77[/C][C] 3.224[/C][C]-0.4545[/C][/ROW]
[ROW][C]134[/C][C] 1.49[/C][C] 2.957[/C][C]-1.467[/C][/ROW]
[ROW][C]135[/C][C] 5.61[/C][C] 2.731[/C][C] 2.879[/C][/ROW]
[ROW][C]136[/C][C] 1.21[/C][C] 2.828[/C][C]-1.618[/C][/ROW]
[ROW][C]137[/C][C] 2.7[/C][C] 3.268[/C][C]-0.5684[/C][/ROW]
[ROW][C]138[/C][C] 1.24[/C][C] 3.056[/C][C]-1.816[/C][/ROW]
[ROW][C]139[/C][C] 7.97[/C][C] 2.588[/C][C] 5.382[/C][/ROW]
[ROW][C]140[/C][C] 4.06[/C][C] 3.197[/C][C] 0.8632[/C][/ROW]
[ROW][C]141[/C][C] 5.81[/C][C] 2.869[/C][C] 2.941[/C][/ROW]
[ROW][C]142[/C][C] 1.29[/C][C] 3.552[/C][C]-2.262[/C][/ROW]
[ROW][C]143[/C][C] 1.24[/C][C] 2.775[/C][C]-1.535[/C][/ROW]
[ROW][C]144[/C][C] 3.31[/C][C] 2.976[/C][C] 0.3336[/C][/ROW]
[ROW][C]145[/C][C] 3.67[/C][C] 3.284[/C][C] 0.386[/C][/ROW]
[ROW][C]146[/C][C] 1.32[/C][C] 2.857[/C][C]-1.537[/C][/ROW]
[ROW][C]147[/C][C] 4.25[/C][C] 2.413[/C][C] 1.837[/C][/ROW]
[ROW][C]148[/C][C] 2.01[/C][C] 2.82[/C][C]-0.8098[/C][/ROW]
[ROW][C]149[/C][C] 7.25[/C][C] 4.362[/C][C] 2.888[/C][/ROW]
[ROW][C]150[/C][C] 5.79[/C][C] 2.867[/C][C] 2.923[/C][/ROW]
[ROW][C]151[/C][C] 1.51[/C][C] 2.976[/C][C]-1.466[/C][/ROW]
[ROW][C]152[/C][C] 0.91[/C][C] 2.865[/C][C]-1.955[/C][/ROW]
[ROW][C]153[/C][C] 1.32[/C][C] 3.039[/C][C]-1.719[/C][/ROW]
[ROW][C]154[/C][C] 2.66[/C][C] 3.383[/C][C]-0.7235[/C][/ROW]
[ROW][C]155[/C][C] 0.48[/C][C] 3.097[/C][C]-2.617[/C][/ROW]
[ROW][C]156[/C][C] 1.13[/C][C] 2.916[/C][C]-1.786[/C][/ROW]
[ROW][C]157[/C][C] 2.7[/C][C] 3.561[/C][C]-0.8605[/C][/ROW]
[ROW][C]158[/C][C] 7.92[/C][C] 3.099[/C][C] 4.821[/C][/ROW]
[ROW][C]159[/C][C] 2.34[/C][C] 3.176[/C][C]-0.8357[/C][/ROW]
[ROW][C]160[/C][C] 3.33[/C][C] 3.296[/C][C] 0.03395[/C][/ROW]
[ROW][C]161[/C][C] 5.47[/C][C] 3.195[/C][C] 2.275[/C][/ROW]
[ROW][C]162[/C][C] 1.24[/C][C] 2.933[/C][C]-1.693[/C][/ROW]
[ROW][C]163[/C][C] 2.84[/C][C] 4.062[/C][C]-1.222[/C][/ROW]
[ROW][C]164[/C][C] 4.94[/C][C] 3.261[/C][C] 1.679[/C][/ROW]
[ROW][C]165[/C][C] 7.93[/C][C] 2.766[/C][C] 5.164[/C][/ROW]
[ROW][C]166[/C][C] 8.22[/C][C] 4.072[/C][C] 4.148[/C][/ROW]
[ROW][C]167[/C][C] 2.91[/C][C] 5.094[/C][C]-2.184[/C][/ROW]
[ROW][C]168[/C][C] 2.32[/C][C] 3.13[/C][C]-0.8096[/C][/ROW]
[ROW][C]169[/C][C] 3.57[/C][C] 2.733[/C][C] 0.8371[/C][/ROW]
[ROW][C]170[/C][C] 1.65[/C][C] 3.163[/C][C]-1.513[/C][/ROW]
[ROW][C]171[/C][C] 1.03[/C][C] 2.739[/C][C]-1.709[/C][/ROW]
[ROW][C]172[/C][C] 0.99[/C][C] 2.78[/C][C]-1.79[/C][/ROW]
[ROW][C]173[/C][C] 1.37[/C][C] 2.726[/C][C]-1.356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&T=5

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	0.79	2.813	-2.023
2	2.21	3.125	-0.9154
3	2.12	2.816	-0.6958
4	0.93	2.836	-1.906
5	3.14	5.673	-2.533
6	2.23	3.009	-0.7789
7	9.31	8.806	0.5038
8	6.06	3.189	2.871
9	2.31	3.028	-0.7181
10	6.84	5.497	1.343
11	7.49	2.756	4.734
12	0.72	2.842	-2.122
13	4.48	2.675	1.805
14	5.09	3.986	1.104
15	7.44	3.126	4.314
16	1.41	3.001	-1.591
17	4.84	2.691	2.149
18	2.96	2.637	0.3235
19	3.12	2.829	0.2909
20	3.83	2.699	1.131
21	3.11	3.344	-0.2335
22	4.06	2.981	1.079
23	3.32	3.859	-0.539
24	1.21	3.054	-1.844
25	0.8	2.779	-1.979
26	1.17	3.106	-1.936
27	8.17	6.428	1.742
28	5.65	2.616	3.034
29	1.24	2.598	-1.358
30	1.46	2.923	-1.463
31	4.36	3.085	1.275
32	3.38	3.032	0.3484
33	1.87	2.736	-0.8656
34	1.03	2.829	-1.799
35	1.29	2.54	-1.25
36	0.82	2.63	-1.81
37	2.84	2.966	-0.1264
38	1.27	3.424	-2.154
39	3.92	3.295	0.6254
40	1.95	2.881	-0.9313
41	4.21	2.776	1.434
42	5.19	3.438	1.752
43	5.51	5.492	0.01842
44	2.57	2.984	-0.4143
45	1.53	2.796	-1.266
46	2.17	2.876	-0.7059
47	2.15	2.957	-0.8065
48	2.07	2.88	-0.8101
49	3.97	2.947	1.023
50	0.42	2.974	-2.554
51	1.02	2.894	-1.874
52	2.9	3.033	-0.1327
53	5.14	4.191	0.9492
54	2.34	4.734	-2.394
55	4.73	2.887	1.843
56	2.02	3.103	-1.083
57	1.03	2.91	-1.88
58	1.58	2.692	-1.112
59	5.3	3.765	1.535
60	1.97	3.237	-1.267
61	4.38	3.605	0.7748
62	3.23	2.748	0.4817
63	1.89	2.953	-1.063
64	1.41	2.998	-1.588
65	1.53	3.66	-2.13
66	3.07	2.819	0.2509
67	0.61	2.76	-2.15
68	1.68	2.947	-1.267
69	2.92	3.788	-0.868
70	1.16	2.93	-1.77
71	1.58	3.148	-1.568
72	2.79	3.11	-0.3197
73	1.88	2.755	-0.8753
74	5.57	3.893	1.677
75	6.22	2.802	3.418
76	4.61	3.15	1.46
77	1.89	2.773	-0.883
78	5.02	2.76	2.26
79	2.1	2.67	-0.5696
80	5.55	3.681	1.869
81	1.03	2.781	-1.751
82	1.17	2.839	-1.669
83	5.69	2.847	2.843
84	8.13	2.734	5.396
85	1.91	3.048	-1.138
86	1.22	3.113	-1.893
87	6.29	6.087	0.2029
88	3.84	2.739	1.101
89	1.66	2.619	-0.9586
90	1.21	2.783	-1.573
91	3.69	2.834	0.8564
92	5.83	5.522	0.3077
93	15.82	3.098	12.72
94	3.26	2.921	0.339
95	0.99	2.871	-1.881
96	0.81	3.037	-2.227
97	3.71	3.573	0.137
98	1.53	3.079	-1.549
99	2.08	2.737	-0.657
100	2.54	3.148	-0.6076
101	3.46	2.915	0.5445
102	2.89	2.97	-0.08012
103	1.78	3.151	-1.371
104	6.08	2.525	3.555
105	3.78	2.703	1.077
106	1.68	2.931	-1.251
107	0.87	2.885	-2.015
108	1.43	3.507	-2.077
109	2.48	4.371	-1.891
110	0.98	2.941	-1.961
111	5.28	3.165	2.115
112	3.58	4.459	-0.8789
113	5.6	3.138	2.462
114	1.39	3.11	-1.72
115	1.56	3.204	-1.644
116	1.16	3.07	-1.91
117	7.52	3.218	4.302
118	0.79	2.848	-2.058
119	2.79	2.862	-0.0722
120	1.91	3.087	-1.177
121	4.16	4.793	-0.633
122	2.28	2.892	-0.6119
123	1.1	2.913	-1.813
124	4.44	3.603	0.8373
125	3.88	3.028	0.8517
126	10.8	3.005	7.795
127	3.65	2.717	0.9327
128	2.71	3.405	-0.6951
129	5.69	3.653	2.037
130	0.87	2.991	-2.121
131	4.94	2.769	2.171
132	2.45	2.726	-0.2759
133	2.77	3.224	-0.4545
134	1.49	2.957	-1.467
135	5.61	2.731	2.879
136	1.21	2.828	-1.618
137	2.7	3.268	-0.5684
138	1.24	3.056	-1.816
139	7.97	2.588	5.382
140	4.06	3.197	0.8632
141	5.81	2.869	2.941
142	1.29	3.552	-2.262
143	1.24	2.775	-1.535
144	3.31	2.976	0.3336
145	3.67	3.284	0.386
146	1.32	2.857	-1.537
147	4.25	2.413	1.837
148	2.01	2.82	-0.8098
149	7.25	4.362	2.888
150	5.79	2.867	2.923
151	1.51	2.976	-1.466
152	0.91	2.865	-1.955
153	1.32	3.039	-1.719
154	2.66	3.383	-0.7235
155	0.48	3.097	-2.617
156	1.13	2.916	-1.786
157	2.7	3.561	-0.8605
158	7.92	3.099	4.821
159	2.34	3.176	-0.8357
160	3.33	3.296	0.03395
161	5.47	3.195	2.275
162	1.24	2.933	-1.693
163	2.84	4.062	-1.222
164	4.94	3.261	1.679
165	7.93	2.766	5.164
166	8.22	4.072	4.148
167	2.91	5.094	-2.184
168	2.32	3.13	-0.8096
169	3.57	2.733	0.8371
170	1.65	3.163	-1.513
171	1.03	2.739	-1.709
172	0.99	2.78	-1.79
173	1.37	2.726	-1.356

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.02608	0.05215	0.9739
9	0.005763	0.01153	0.9942
10	0.05045	0.1009	0.9496
11	0.7467	0.5065	0.2533
12	0.6893	0.6215	0.3107
13	0.6865	0.6269	0.3135
14	0.5967	0.8067	0.4033
15	0.7854	0.4292	0.2146
16	0.7598	0.4803	0.2402
17	0.7144	0.5712	0.2856
18	0.7096	0.5807	0.2904
19	0.6373	0.7253	0.3627
20	0.6239	0.7522	0.3761
21	0.5609	0.8783	0.4391
22	0.4915	0.9831	0.5085
23	0.4284	0.8568	0.5716
24	0.4171	0.8342	0.5829
25	0.4095	0.8189	0.5905
26	0.3962	0.7925	0.6038
27	0.3416	0.6833	0.6584
28	0.3956	0.7913	0.6044
29	0.3791	0.7581	0.6209
30	0.3419	0.6838	0.6581
31	0.3011	0.6023	0.6989
32	0.2504	0.5008	0.7496
33	0.2108	0.4215	0.7892
34	0.1988	0.3976	0.8012
35	0.1687	0.3374	0.8313
36	0.1596	0.3191	0.8404
37	0.1266	0.2532	0.8734
38	0.1254	0.2508	0.8746
39	0.1004	0.2008	0.8996
40	0.0809	0.1618	0.9191
41	0.07177	0.1435	0.9282
42	0.06581	0.1316	0.9342
43	0.05074	0.1015	0.9493
44	0.03839	0.07677	0.9616
45	0.03133	0.06266	0.9687
46	0.02365	0.04731	0.9763
47	0.01778	0.03556	0.9822
48	0.01318	0.02635	0.9868
49	0.009855	0.01971	0.9901
50	0.01181	0.02361	0.9882
51	0.01057	0.02114	0.9894
52	0.007449	0.0149	0.9926
53	0.005627	0.01125	0.9944
54	0.007368	0.01474	0.9926
55	0.007017	0.01404	0.993
56	0.005173	0.01035	0.9948
57	0.004873	0.009745	0.9951
58	0.003671	0.007343	0.9963
59	0.0031	0.0062	0.9969
60	0.002433	0.004867	0.9976
61	0.001741	0.003482	0.9983
62	0.001204	0.002408	0.9988
63	0.0008836	0.001767	0.9991
64	0.0007182	0.001436	0.9993
65	0.0007658	0.001532	0.9992
66	0.0006429	0.001286	0.9994
67	0.0006456	0.001291	0.9994
68	0.0004834	0.0009668	0.9995
69	0.0003436	0.0006872	0.9997
70	0.0002972	0.0005944	0.9997
71	0.0002403	0.0004805	0.9998
72	0.0001546	0.0003092	0.9998
73	0.0001038	0.0002076	0.9999
74	9.567e-05	0.0001913	0.9999
75	0.0002465	0.0004931	0.9998
76	0.0002036	0.0004072	0.9998
77	0.0001397	0.0002795	0.9999
78	0.0001629	0.0003258	0.9998
79	0.0001069	0.0002139	0.9999
80	0.0001085	0.000217	0.9999
81	9.249e-05	0.000185	0.9999
82	7.713e-05	0.0001543	0.9999
83	0.000122	0.000244	0.9999
84	0.001271	0.002542	0.9987
85	0.0009607	0.001921	0.999
86	0.0008834	0.001767	0.9991
87	0.0006116	0.001223	0.9994
88	0.0004603	0.0009205	0.9995
89	0.00033	0.0006599	0.9997
90	0.00027	0.00054	0.9997
91	0.0001911	0.0003823	0.9998
92	0.0001319	0.0002639	0.9999
93	0.5174	0.9651	0.4826
94	0.474	0.948	0.526
95	0.4623	0.9246	0.5377
96	0.4626	0.9252	0.5374
97	0.4193	0.8386	0.5807
98	0.3958	0.7917	0.6042
99	0.3581	0.7161	0.6419
100	0.3262	0.6525	0.6738
101	0.2883	0.5766	0.7117
102	0.2511	0.5022	0.7489
103	0.2286	0.4571	0.7714
104	0.282	0.5639	0.718
105	0.2526	0.5052	0.7474
106	0.2284	0.4568	0.7716
107	0.2211	0.4423	0.7789
108	0.2152	0.4304	0.7848
109	0.2254	0.4508	0.7746
110	0.218	0.436	0.782
111	0.2124	0.4248	0.7876
112	0.3091	0.6181	0.6909
113	0.3511	0.7023	0.6489
114	0.3389	0.6779	0.6611
115	0.3121	0.6241	0.6879
116	0.2983	0.5966	0.7017
117	0.3344	0.6687	0.6656
118	0.3292	0.6583	0.6708
119	0.2886	0.5772	0.7114
120	0.2729	0.5459	0.7271
121	0.2728	0.5457	0.7272
122	0.2346	0.4692	0.7654
123	0.2252	0.4504	0.7748
124	0.1998	0.3997	0.8002
125	0.1728	0.3455	0.8272
126	0.4984	0.9968	0.5016
127	0.4559	0.9117	0.5441
128	0.408	0.8159	0.592
129	0.3861	0.7722	0.6139
130	0.3799	0.7599	0.6201
131	0.3649	0.7298	0.6351
132	0.3179	0.6358	0.6821
133	0.2731	0.5463	0.7269
134	0.2563	0.5127	0.7437
135	0.2775	0.555	0.7225
136	0.2566	0.5132	0.7434
137	0.2161	0.4322	0.7839
138	0.2022	0.4044	0.7978
139	0.4335	0.867	0.5665
140	0.3885	0.777	0.6115
141	0.455	0.9099	0.545
142	0.5251	0.9498	0.4749
143	0.4867	0.9735	0.5133
144	0.431	0.862	0.569
145	0.3743	0.7486	0.6257
146	0.338	0.676	0.662
147	0.324	0.6479	0.676
148	0.2685	0.5369	0.7315
149	0.2767	0.5534	0.7233
150	0.3077	0.6154	0.6923
151	0.2566	0.5133	0.7434
152	0.2215	0.4431	0.7785
153	0.1843	0.3686	0.8157
154	0.1413	0.2826	0.8587
155	0.2866	0.5732	0.7134
156	0.2478	0.4956	0.7522
157	0.2212	0.4424	0.7788
158	0.2045	0.409	0.7955
159	0.1562	0.3123	0.8438
160	0.1064	0.2129	0.8936
161	0.7753	0.4494	0.2247
162	0.674	0.6521	0.326
163	0.6036	0.7929	0.3964
164	0.4644	0.9287	0.5356
165	0.9361	0.1278	0.0639

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
8 &  0.02608 &  0.05215 &  0.9739 \tabularnewline
9 &  0.005763 &  0.01153 &  0.9942 \tabularnewline
10 &  0.05045 &  0.1009 &  0.9496 \tabularnewline
11 &  0.7467 &  0.5065 &  0.2533 \tabularnewline
12 &  0.6893 &  0.6215 &  0.3107 \tabularnewline
13 &  0.6865 &  0.6269 &  0.3135 \tabularnewline
14 &  0.5967 &  0.8067 &  0.4033 \tabularnewline
15 &  0.7854 &  0.4292 &  0.2146 \tabularnewline
16 &  0.7598 &  0.4803 &  0.2402 \tabularnewline
17 &  0.7144 &  0.5712 &  0.2856 \tabularnewline
18 &  0.7096 &  0.5807 &  0.2904 \tabularnewline
19 &  0.6373 &  0.7253 &  0.3627 \tabularnewline
20 &  0.6239 &  0.7522 &  0.3761 \tabularnewline
21 &  0.5609 &  0.8783 &  0.4391 \tabularnewline
22 &  0.4915 &  0.9831 &  0.5085 \tabularnewline
23 &  0.4284 &  0.8568 &  0.5716 \tabularnewline
24 &  0.4171 &  0.8342 &  0.5829 \tabularnewline
25 &  0.4095 &  0.8189 &  0.5905 \tabularnewline
26 &  0.3962 &  0.7925 &  0.6038 \tabularnewline
27 &  0.3416 &  0.6833 &  0.6584 \tabularnewline
28 &  0.3956 &  0.7913 &  0.6044 \tabularnewline
29 &  0.3791 &  0.7581 &  0.6209 \tabularnewline
30 &  0.3419 &  0.6838 &  0.6581 \tabularnewline
31 &  0.3011 &  0.6023 &  0.6989 \tabularnewline
32 &  0.2504 &  0.5008 &  0.7496 \tabularnewline
33 &  0.2108 &  0.4215 &  0.7892 \tabularnewline
34 &  0.1988 &  0.3976 &  0.8012 \tabularnewline
35 &  0.1687 &  0.3374 &  0.8313 \tabularnewline
36 &  0.1596 &  0.3191 &  0.8404 \tabularnewline
37 &  0.1266 &  0.2532 &  0.8734 \tabularnewline
38 &  0.1254 &  0.2508 &  0.8746 \tabularnewline
39 &  0.1004 &  0.2008 &  0.8996 \tabularnewline
40 &  0.0809 &  0.1618 &  0.9191 \tabularnewline
41 &  0.07177 &  0.1435 &  0.9282 \tabularnewline
42 &  0.06581 &  0.1316 &  0.9342 \tabularnewline
43 &  0.05074 &  0.1015 &  0.9493 \tabularnewline
44 &  0.03839 &  0.07677 &  0.9616 \tabularnewline
45 &  0.03133 &  0.06266 &  0.9687 \tabularnewline
46 &  0.02365 &  0.04731 &  0.9763 \tabularnewline
47 &  0.01778 &  0.03556 &  0.9822 \tabularnewline
48 &  0.01318 &  0.02635 &  0.9868 \tabularnewline
49 &  0.009855 &  0.01971 &  0.9901 \tabularnewline
50 &  0.01181 &  0.02361 &  0.9882 \tabularnewline
51 &  0.01057 &  0.02114 &  0.9894 \tabularnewline
52 &  0.007449 &  0.0149 &  0.9926 \tabularnewline
53 &  0.005627 &  0.01125 &  0.9944 \tabularnewline
54 &  0.007368 &  0.01474 &  0.9926 \tabularnewline
55 &  0.007017 &  0.01404 &  0.993 \tabularnewline
56 &  0.005173 &  0.01035 &  0.9948 \tabularnewline
57 &  0.004873 &  0.009745 &  0.9951 \tabularnewline
58 &  0.003671 &  0.007343 &  0.9963 \tabularnewline
59 &  0.0031 &  0.0062 &  0.9969 \tabularnewline
60 &  0.002433 &  0.004867 &  0.9976 \tabularnewline
61 &  0.001741 &  0.003482 &  0.9983 \tabularnewline
62 &  0.001204 &  0.002408 &  0.9988 \tabularnewline
63 &  0.0008836 &  0.001767 &  0.9991 \tabularnewline
64 &  0.0007182 &  0.001436 &  0.9993 \tabularnewline
65 &  0.0007658 &  0.001532 &  0.9992 \tabularnewline
66 &  0.0006429 &  0.001286 &  0.9994 \tabularnewline
67 &  0.0006456 &  0.001291 &  0.9994 \tabularnewline
68 &  0.0004834 &  0.0009668 &  0.9995 \tabularnewline
69 &  0.0003436 &  0.0006872 &  0.9997 \tabularnewline
70 &  0.0002972 &  0.0005944 &  0.9997 \tabularnewline
71 &  0.0002403 &  0.0004805 &  0.9998 \tabularnewline
72 &  0.0001546 &  0.0003092 &  0.9998 \tabularnewline
73 &  0.0001038 &  0.0002076 &  0.9999 \tabularnewline
74 &  9.567e-05 &  0.0001913 &  0.9999 \tabularnewline
75 &  0.0002465 &  0.0004931 &  0.9998 \tabularnewline
76 &  0.0002036 &  0.0004072 &  0.9998 \tabularnewline
77 &  0.0001397 &  0.0002795 &  0.9999 \tabularnewline
78 &  0.0001629 &  0.0003258 &  0.9998 \tabularnewline
79 &  0.0001069 &  0.0002139 &  0.9999 \tabularnewline
80 &  0.0001085 &  0.000217 &  0.9999 \tabularnewline
81 &  9.249e-05 &  0.000185 &  0.9999 \tabularnewline
82 &  7.713e-05 &  0.0001543 &  0.9999 \tabularnewline
83 &  0.000122 &  0.000244 &  0.9999 \tabularnewline
84 &  0.001271 &  0.002542 &  0.9987 \tabularnewline
85 &  0.0009607 &  0.001921 &  0.999 \tabularnewline
86 &  0.0008834 &  0.001767 &  0.9991 \tabularnewline
87 &  0.0006116 &  0.001223 &  0.9994 \tabularnewline
88 &  0.0004603 &  0.0009205 &  0.9995 \tabularnewline
89 &  0.00033 &  0.0006599 &  0.9997 \tabularnewline
90 &  0.00027 &  0.00054 &  0.9997 \tabularnewline
91 &  0.0001911 &  0.0003823 &  0.9998 \tabularnewline
92 &  0.0001319 &  0.0002639 &  0.9999 \tabularnewline
93 &  0.5174 &  0.9651 &  0.4826 \tabularnewline
94 &  0.474 &  0.948 &  0.526 \tabularnewline
95 &  0.4623 &  0.9246 &  0.5377 \tabularnewline
96 &  0.4626 &  0.9252 &  0.5374 \tabularnewline
97 &  0.4193 &  0.8386 &  0.5807 \tabularnewline
98 &  0.3958 &  0.7917 &  0.6042 \tabularnewline
99 &  0.3581 &  0.7161 &  0.6419 \tabularnewline
100 &  0.3262 &  0.6525 &  0.6738 \tabularnewline
101 &  0.2883 &  0.5766 &  0.7117 \tabularnewline
102 &  0.2511 &  0.5022 &  0.7489 \tabularnewline
103 &  0.2286 &  0.4571 &  0.7714 \tabularnewline
104 &  0.282 &  0.5639 &  0.718 \tabularnewline
105 &  0.2526 &  0.5052 &  0.7474 \tabularnewline
106 &  0.2284 &  0.4568 &  0.7716 \tabularnewline
107 &  0.2211 &  0.4423 &  0.7789 \tabularnewline
108 &  0.2152 &  0.4304 &  0.7848 \tabularnewline
109 &  0.2254 &  0.4508 &  0.7746 \tabularnewline
110 &  0.218 &  0.436 &  0.782 \tabularnewline
111 &  0.2124 &  0.4248 &  0.7876 \tabularnewline
112 &  0.3091 &  0.6181 &  0.6909 \tabularnewline
113 &  0.3511 &  0.7023 &  0.6489 \tabularnewline
114 &  0.3389 &  0.6779 &  0.6611 \tabularnewline
115 &  0.3121 &  0.6241 &  0.6879 \tabularnewline
116 &  0.2983 &  0.5966 &  0.7017 \tabularnewline
117 &  0.3344 &  0.6687 &  0.6656 \tabularnewline
118 &  0.3292 &  0.6583 &  0.6708 \tabularnewline
119 &  0.2886 &  0.5772 &  0.7114 \tabularnewline
120 &  0.2729 &  0.5459 &  0.7271 \tabularnewline
121 &  0.2728 &  0.5457 &  0.7272 \tabularnewline
122 &  0.2346 &  0.4692 &  0.7654 \tabularnewline
123 &  0.2252 &  0.4504 &  0.7748 \tabularnewline
124 &  0.1998 &  0.3997 &  0.8002 \tabularnewline
125 &  0.1728 &  0.3455 &  0.8272 \tabularnewline
126 &  0.4984 &  0.9968 &  0.5016 \tabularnewline
127 &  0.4559 &  0.9117 &  0.5441 \tabularnewline
128 &  0.408 &  0.8159 &  0.592 \tabularnewline
129 &  0.3861 &  0.7722 &  0.6139 \tabularnewline
130 &  0.3799 &  0.7599 &  0.6201 \tabularnewline
131 &  0.3649 &  0.7298 &  0.6351 \tabularnewline
132 &  0.3179 &  0.6358 &  0.6821 \tabularnewline
133 &  0.2731 &  0.5463 &  0.7269 \tabularnewline
134 &  0.2563 &  0.5127 &  0.7437 \tabularnewline
135 &  0.2775 &  0.555 &  0.7225 \tabularnewline
136 &  0.2566 &  0.5132 &  0.7434 \tabularnewline
137 &  0.2161 &  0.4322 &  0.7839 \tabularnewline
138 &  0.2022 &  0.4044 &  0.7978 \tabularnewline
139 &  0.4335 &  0.867 &  0.5665 \tabularnewline
140 &  0.3885 &  0.777 &  0.6115 \tabularnewline
141 &  0.455 &  0.9099 &  0.545 \tabularnewline
142 &  0.5251 &  0.9498 &  0.4749 \tabularnewline
143 &  0.4867 &  0.9735 &  0.5133 \tabularnewline
144 &  0.431 &  0.862 &  0.569 \tabularnewline
145 &  0.3743 &  0.7486 &  0.6257 \tabularnewline
146 &  0.338 &  0.676 &  0.662 \tabularnewline
147 &  0.324 &  0.6479 &  0.676 \tabularnewline
148 &  0.2685 &  0.5369 &  0.7315 \tabularnewline
149 &  0.2767 &  0.5534 &  0.7233 \tabularnewline
150 &  0.3077 &  0.6154 &  0.6923 \tabularnewline
151 &  0.2566 &  0.5133 &  0.7434 \tabularnewline
152 &  0.2215 &  0.4431 &  0.7785 \tabularnewline
153 &  0.1843 &  0.3686 &  0.8157 \tabularnewline
154 &  0.1413 &  0.2826 &  0.8587 \tabularnewline
155 &  0.2866 &  0.5732 &  0.7134 \tabularnewline
156 &  0.2478 &  0.4956 &  0.7522 \tabularnewline
157 &  0.2212 &  0.4424 &  0.7788 \tabularnewline
158 &  0.2045 &  0.409 &  0.7955 \tabularnewline
159 &  0.1562 &  0.3123 &  0.8438 \tabularnewline
160 &  0.1064 &  0.2129 &  0.8936 \tabularnewline
161 &  0.7753 &  0.4494 &  0.2247 \tabularnewline
162 &  0.674 &  0.6521 &  0.326 \tabularnewline
163 &  0.6036 &  0.7929 &  0.3964 \tabularnewline
164 &  0.4644 &  0.9287 &  0.5356 \tabularnewline
165 &  0.9361 &  0.1278 &  0.0639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=6

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]8[/C][C] 0.02608[/C][C] 0.05215[/C][C] 0.9739[/C][/ROW]
[ROW][C]9[/C][C] 0.005763[/C][C] 0.01153[/C][C] 0.9942[/C][/ROW]
[ROW][C]10[/C][C] 0.05045[/C][C] 0.1009[/C][C] 0.9496[/C][/ROW]
[ROW][C]11[/C][C] 0.7467[/C][C] 0.5065[/C][C] 0.2533[/C][/ROW]
[ROW][C]12[/C][C] 0.6893[/C][C] 0.6215[/C][C] 0.3107[/C][/ROW]
[ROW][C]13[/C][C] 0.6865[/C][C] 0.6269[/C][C] 0.3135[/C][/ROW]
[ROW][C]14[/C][C] 0.5967[/C][C] 0.8067[/C][C] 0.4033[/C][/ROW]
[ROW][C]15[/C][C] 0.7854[/C][C] 0.4292[/C][C] 0.2146[/C][/ROW]
[ROW][C]16[/C][C] 0.7598[/C][C] 0.4803[/C][C] 0.2402[/C][/ROW]
[ROW][C]17[/C][C] 0.7144[/C][C] 0.5712[/C][C] 0.2856[/C][/ROW]
[ROW][C]18[/C][C] 0.7096[/C][C] 0.5807[/C][C] 0.2904[/C][/ROW]
[ROW][C]19[/C][C] 0.6373[/C][C] 0.7253[/C][C] 0.3627[/C][/ROW]
[ROW][C]20[/C][C] 0.6239[/C][C] 0.7522[/C][C] 0.3761[/C][/ROW]
[ROW][C]21[/C][C] 0.5609[/C][C] 0.8783[/C][C] 0.4391[/C][/ROW]
[ROW][C]22[/C][C] 0.4915[/C][C] 0.9831[/C][C] 0.5085[/C][/ROW]
[ROW][C]23[/C][C] 0.4284[/C][C] 0.8568[/C][C] 0.5716[/C][/ROW]
[ROW][C]24[/C][C] 0.4171[/C][C] 0.8342[/C][C] 0.5829[/C][/ROW]
[ROW][C]25[/C][C] 0.4095[/C][C] 0.8189[/C][C] 0.5905[/C][/ROW]
[ROW][C]26[/C][C] 0.3962[/C][C] 0.7925[/C][C] 0.6038[/C][/ROW]
[ROW][C]27[/C][C] 0.3416[/C][C] 0.6833[/C][C] 0.6584[/C][/ROW]
[ROW][C]28[/C][C] 0.3956[/C][C] 0.7913[/C][C] 0.6044[/C][/ROW]
[ROW][C]29[/C][C] 0.3791[/C][C] 0.7581[/C][C] 0.6209[/C][/ROW]
[ROW][C]30[/C][C] 0.3419[/C][C] 0.6838[/C][C] 0.6581[/C][/ROW]
[ROW][C]31[/C][C] 0.3011[/C][C] 0.6023[/C][C] 0.6989[/C][/ROW]
[ROW][C]32[/C][C] 0.2504[/C][C] 0.5008[/C][C] 0.7496[/C][/ROW]
[ROW][C]33[/C][C] 0.2108[/C][C] 0.4215[/C][C] 0.7892[/C][/ROW]
[ROW][C]34[/C][C] 0.1988[/C][C] 0.3976[/C][C] 0.8012[/C][/ROW]
[ROW][C]35[/C][C] 0.1687[/C][C] 0.3374[/C][C] 0.8313[/C][/ROW]
[ROW][C]36[/C][C] 0.1596[/C][C] 0.3191[/C][C] 0.8404[/C][/ROW]
[ROW][C]37[/C][C] 0.1266[/C][C] 0.2532[/C][C] 0.8734[/C][/ROW]
[ROW][C]38[/C][C] 0.1254[/C][C] 0.2508[/C][C] 0.8746[/C][/ROW]
[ROW][C]39[/C][C] 0.1004[/C][C] 0.2008[/C][C] 0.8996[/C][/ROW]
[ROW][C]40[/C][C] 0.0809[/C][C] 0.1618[/C][C] 0.9191[/C][/ROW]
[ROW][C]41[/C][C] 0.07177[/C][C] 0.1435[/C][C] 0.9282[/C][/ROW]
[ROW][C]42[/C][C] 0.06581[/C][C] 0.1316[/C][C] 0.9342[/C][/ROW]
[ROW][C]43[/C][C] 0.05074[/C][C] 0.1015[/C][C] 0.9493[/C][/ROW]
[ROW][C]44[/C][C] 0.03839[/C][C] 0.07677[/C][C] 0.9616[/C][/ROW]
[ROW][C]45[/C][C] 0.03133[/C][C] 0.06266[/C][C] 0.9687[/C][/ROW]
[ROW][C]46[/C][C] 0.02365[/C][C] 0.04731[/C][C] 0.9763[/C][/ROW]
[ROW][C]47[/C][C] 0.01778[/C][C] 0.03556[/C][C] 0.9822[/C][/ROW]
[ROW][C]48[/C][C] 0.01318[/C][C] 0.02635[/C][C] 0.9868[/C][/ROW]
[ROW][C]49[/C][C] 0.009855[/C][C] 0.01971[/C][C] 0.9901[/C][/ROW]
[ROW][C]50[/C][C] 0.01181[/C][C] 0.02361[/C][C] 0.9882[/C][/ROW]
[ROW][C]51[/C][C] 0.01057[/C][C] 0.02114[/C][C] 0.9894[/C][/ROW]
[ROW][C]52[/C][C] 0.007449[/C][C] 0.0149[/C][C] 0.9926[/C][/ROW]
[ROW][C]53[/C][C] 0.005627[/C][C] 0.01125[/C][C] 0.9944[/C][/ROW]
[ROW][C]54[/C][C] 0.007368[/C][C] 0.01474[/C][C] 0.9926[/C][/ROW]
[ROW][C]55[/C][C] 0.007017[/C][C] 0.01404[/C][C] 0.993[/C][/ROW]
[ROW][C]56[/C][C] 0.005173[/C][C] 0.01035[/C][C] 0.9948[/C][/ROW]
[ROW][C]57[/C][C] 0.004873[/C][C] 0.009745[/C][C] 0.9951[/C][/ROW]
[ROW][C]58[/C][C] 0.003671[/C][C] 0.007343[/C][C] 0.9963[/C][/ROW]
[ROW][C]59[/C][C] 0.0031[/C][C] 0.0062[/C][C] 0.9969[/C][/ROW]
[ROW][C]60[/C][C] 0.002433[/C][C] 0.004867[/C][C] 0.9976[/C][/ROW]
[ROW][C]61[/C][C] 0.001741[/C][C] 0.003482[/C][C] 0.9983[/C][/ROW]
[ROW][C]62[/C][C] 0.001204[/C][C] 0.002408[/C][C] 0.9988[/C][/ROW]
[ROW][C]63[/C][C] 0.0008836[/C][C] 0.001767[/C][C] 0.9991[/C][/ROW]
[ROW][C]64[/C][C] 0.0007182[/C][C] 0.001436[/C][C] 0.9993[/C][/ROW]
[ROW][C]65[/C][C] 0.0007658[/C][C] 0.001532[/C][C] 0.9992[/C][/ROW]
[ROW][C]66[/C][C] 0.0006429[/C][C] 0.001286[/C][C] 0.9994[/C][/ROW]
[ROW][C]67[/C][C] 0.0006456[/C][C] 0.001291[/C][C] 0.9994[/C][/ROW]
[ROW][C]68[/C][C] 0.0004834[/C][C] 0.0009668[/C][C] 0.9995[/C][/ROW]
[ROW][C]69[/C][C] 0.0003436[/C][C] 0.0006872[/C][C] 0.9997[/C][/ROW]
[ROW][C]70[/C][C] 0.0002972[/C][C] 0.0005944[/C][C] 0.9997[/C][/ROW]
[ROW][C]71[/C][C] 0.0002403[/C][C] 0.0004805[/C][C] 0.9998[/C][/ROW]
[ROW][C]72[/C][C] 0.0001546[/C][C] 0.0003092[/C][C] 0.9998[/C][/ROW]
[ROW][C]73[/C][C] 0.0001038[/C][C] 0.0002076[/C][C] 0.9999[/C][/ROW]
[ROW][C]74[/C][C] 9.567e-05[/C][C] 0.0001913[/C][C] 0.9999[/C][/ROW]
[ROW][C]75[/C][C] 0.0002465[/C][C] 0.0004931[/C][C] 0.9998[/C][/ROW]
[ROW][C]76[/C][C] 0.0002036[/C][C] 0.0004072[/C][C] 0.9998[/C][/ROW]
[ROW][C]77[/C][C] 0.0001397[/C][C] 0.0002795[/C][C] 0.9999[/C][/ROW]
[ROW][C]78[/C][C] 0.0001629[/C][C] 0.0003258[/C][C] 0.9998[/C][/ROW]
[ROW][C]79[/C][C] 0.0001069[/C][C] 0.0002139[/C][C] 0.9999[/C][/ROW]
[ROW][C]80[/C][C] 0.0001085[/C][C] 0.000217[/C][C] 0.9999[/C][/ROW]
[ROW][C]81[/C][C] 9.249e-05[/C][C] 0.000185[/C][C] 0.9999[/C][/ROW]
[ROW][C]82[/C][C] 7.713e-05[/C][C] 0.0001543[/C][C] 0.9999[/C][/ROW]
[ROW][C]83[/C][C] 0.000122[/C][C] 0.000244[/C][C] 0.9999[/C][/ROW]
[ROW][C]84[/C][C] 0.001271[/C][C] 0.002542[/C][C] 0.9987[/C][/ROW]
[ROW][C]85[/C][C] 0.0009607[/C][C] 0.001921[/C][C] 0.999[/C][/ROW]
[ROW][C]86[/C][C] 0.0008834[/C][C] 0.001767[/C][C] 0.9991[/C][/ROW]
[ROW][C]87[/C][C] 0.0006116[/C][C] 0.001223[/C][C] 0.9994[/C][/ROW]
[ROW][C]88[/C][C] 0.0004603[/C][C] 0.0009205[/C][C] 0.9995[/C][/ROW]
[ROW][C]89[/C][C] 0.00033[/C][C] 0.0006599[/C][C] 0.9997[/C][/ROW]
[ROW][C]90[/C][C] 0.00027[/C][C] 0.00054[/C][C] 0.9997[/C][/ROW]
[ROW][C]91[/C][C] 0.0001911[/C][C] 0.0003823[/C][C] 0.9998[/C][/ROW]
[ROW][C]92[/C][C] 0.0001319[/C][C] 0.0002639[/C][C] 0.9999[/C][/ROW]
[ROW][C]93[/C][C] 0.5174[/C][C] 0.9651[/C][C] 0.4826[/C][/ROW]
[ROW][C]94[/C][C] 0.474[/C][C] 0.948[/C][C] 0.526[/C][/ROW]
[ROW][C]95[/C][C] 0.4623[/C][C] 0.9246[/C][C] 0.5377[/C][/ROW]
[ROW][C]96[/C][C] 0.4626[/C][C] 0.9252[/C][C] 0.5374[/C][/ROW]
[ROW][C]97[/C][C] 0.4193[/C][C] 0.8386[/C][C] 0.5807[/C][/ROW]
[ROW][C]98[/C][C] 0.3958[/C][C] 0.7917[/C][C] 0.6042[/C][/ROW]
[ROW][C]99[/C][C] 0.3581[/C][C] 0.7161[/C][C] 0.6419[/C][/ROW]
[ROW][C]100[/C][C] 0.3262[/C][C] 0.6525[/C][C] 0.6738[/C][/ROW]
[ROW][C]101[/C][C] 0.2883[/C][C] 0.5766[/C][C] 0.7117[/C][/ROW]
[ROW][C]102[/C][C] 0.2511[/C][C] 0.5022[/C][C] 0.7489[/C][/ROW]
[ROW][C]103[/C][C] 0.2286[/C][C] 0.4571[/C][C] 0.7714[/C][/ROW]
[ROW][C]104[/C][C] 0.282[/C][C] 0.5639[/C][C] 0.718[/C][/ROW]
[ROW][C]105[/C][C] 0.2526[/C][C] 0.5052[/C][C] 0.7474[/C][/ROW]
[ROW][C]106[/C][C] 0.2284[/C][C] 0.4568[/C][C] 0.7716[/C][/ROW]
[ROW][C]107[/C][C] 0.2211[/C][C] 0.4423[/C][C] 0.7789[/C][/ROW]
[ROW][C]108[/C][C] 0.2152[/C][C] 0.4304[/C][C] 0.7848[/C][/ROW]
[ROW][C]109[/C][C] 0.2254[/C][C] 0.4508[/C][C] 0.7746[/C][/ROW]
[ROW][C]110[/C][C] 0.218[/C][C] 0.436[/C][C] 0.782[/C][/ROW]
[ROW][C]111[/C][C] 0.2124[/C][C] 0.4248[/C][C] 0.7876[/C][/ROW]
[ROW][C]112[/C][C] 0.3091[/C][C] 0.6181[/C][C] 0.6909[/C][/ROW]
[ROW][C]113[/C][C] 0.3511[/C][C] 0.7023[/C][C] 0.6489[/C][/ROW]
[ROW][C]114[/C][C] 0.3389[/C][C] 0.6779[/C][C] 0.6611[/C][/ROW]
[ROW][C]115[/C][C] 0.3121[/C][C] 0.6241[/C][C] 0.6879[/C][/ROW]
[ROW][C]116[/C][C] 0.2983[/C][C] 0.5966[/C][C] 0.7017[/C][/ROW]
[ROW][C]117[/C][C] 0.3344[/C][C] 0.6687[/C][C] 0.6656[/C][/ROW]
[ROW][C]118[/C][C] 0.3292[/C][C] 0.6583[/C][C] 0.6708[/C][/ROW]
[ROW][C]119[/C][C] 0.2886[/C][C] 0.5772[/C][C] 0.7114[/C][/ROW]
[ROW][C]120[/C][C] 0.2729[/C][C] 0.5459[/C][C] 0.7271[/C][/ROW]
[ROW][C]121[/C][C] 0.2728[/C][C] 0.5457[/C][C] 0.7272[/C][/ROW]
[ROW][C]122[/C][C] 0.2346[/C][C] 0.4692[/C][C] 0.7654[/C][/ROW]
[ROW][C]123[/C][C] 0.2252[/C][C] 0.4504[/C][C] 0.7748[/C][/ROW]
[ROW][C]124[/C][C] 0.1998[/C][C] 0.3997[/C][C] 0.8002[/C][/ROW]
[ROW][C]125[/C][C] 0.1728[/C][C] 0.3455[/C][C] 0.8272[/C][/ROW]
[ROW][C]126[/C][C] 0.4984[/C][C] 0.9968[/C][C] 0.5016[/C][/ROW]
[ROW][C]127[/C][C] 0.4559[/C][C] 0.9117[/C][C] 0.5441[/C][/ROW]
[ROW][C]128[/C][C] 0.408[/C][C] 0.8159[/C][C] 0.592[/C][/ROW]
[ROW][C]129[/C][C] 0.3861[/C][C] 0.7722[/C][C] 0.6139[/C][/ROW]
[ROW][C]130[/C][C] 0.3799[/C][C] 0.7599[/C][C] 0.6201[/C][/ROW]
[ROW][C]131[/C][C] 0.3649[/C][C] 0.7298[/C][C] 0.6351[/C][/ROW]
[ROW][C]132[/C][C] 0.3179[/C][C] 0.6358[/C][C] 0.6821[/C][/ROW]
[ROW][C]133[/C][C] 0.2731[/C][C] 0.5463[/C][C] 0.7269[/C][/ROW]
[ROW][C]134[/C][C] 0.2563[/C][C] 0.5127[/C][C] 0.7437[/C][/ROW]
[ROW][C]135[/C][C] 0.2775[/C][C] 0.555[/C][C] 0.7225[/C][/ROW]
[ROW][C]136[/C][C] 0.2566[/C][C] 0.5132[/C][C] 0.7434[/C][/ROW]
[ROW][C]137[/C][C] 0.2161[/C][C] 0.4322[/C][C] 0.7839[/C][/ROW]
[ROW][C]138[/C][C] 0.2022[/C][C] 0.4044[/C][C] 0.7978[/C][/ROW]
[ROW][C]139[/C][C] 0.4335[/C][C] 0.867[/C][C] 0.5665[/C][/ROW]
[ROW][C]140[/C][C] 0.3885[/C][C] 0.777[/C][C] 0.6115[/C][/ROW]
[ROW][C]141[/C][C] 0.455[/C][C] 0.9099[/C][C] 0.545[/C][/ROW]
[ROW][C]142[/C][C] 0.5251[/C][C] 0.9498[/C][C] 0.4749[/C][/ROW]
[ROW][C]143[/C][C] 0.4867[/C][C] 0.9735[/C][C] 0.5133[/C][/ROW]
[ROW][C]144[/C][C] 0.431[/C][C] 0.862[/C][C] 0.569[/C][/ROW]
[ROW][C]145[/C][C] 0.3743[/C][C] 0.7486[/C][C] 0.6257[/C][/ROW]
[ROW][C]146[/C][C] 0.338[/C][C] 0.676[/C][C] 0.662[/C][/ROW]
[ROW][C]147[/C][C] 0.324[/C][C] 0.6479[/C][C] 0.676[/C][/ROW]
[ROW][C]148[/C][C] 0.2685[/C][C] 0.5369[/C][C] 0.7315[/C][/ROW]
[ROW][C]149[/C][C] 0.2767[/C][C] 0.5534[/C][C] 0.7233[/C][/ROW]
[ROW][C]150[/C][C] 0.3077[/C][C] 0.6154[/C][C] 0.6923[/C][/ROW]
[ROW][C]151[/C][C] 0.2566[/C][C] 0.5133[/C][C] 0.7434[/C][/ROW]
[ROW][C]152[/C][C] 0.2215[/C][C] 0.4431[/C][C] 0.7785[/C][/ROW]
[ROW][C]153[/C][C] 0.1843[/C][C] 0.3686[/C][C] 0.8157[/C][/ROW]
[ROW][C]154[/C][C] 0.1413[/C][C] 0.2826[/C][C] 0.8587[/C][/ROW]
[ROW][C]155[/C][C] 0.2866[/C][C] 0.5732[/C][C] 0.7134[/C][/ROW]
[ROW][C]156[/C][C] 0.2478[/C][C] 0.4956[/C][C] 0.7522[/C][/ROW]
[ROW][C]157[/C][C] 0.2212[/C][C] 0.4424[/C][C] 0.7788[/C][/ROW]
[ROW][C]158[/C][C] 0.2045[/C][C] 0.409[/C][C] 0.7955[/C][/ROW]
[ROW][C]159[/C][C] 0.1562[/C][C] 0.3123[/C][C] 0.8438[/C][/ROW]
[ROW][C]160[/C][C] 0.1064[/C][C] 0.2129[/C][C] 0.8936[/C][/ROW]
[ROW][C]161[/C][C] 0.7753[/C][C] 0.4494[/C][C] 0.2247[/C][/ROW]
[ROW][C]162[/C][C] 0.674[/C][C] 0.6521[/C][C] 0.326[/C][/ROW]
[ROW][C]163[/C][C] 0.6036[/C][C] 0.7929[/C][C] 0.3964[/C][/ROW]
[ROW][C]164[/C][C] 0.4644[/C][C] 0.9287[/C][C] 0.5356[/C][/ROW]
[ROW][C]165[/C][C] 0.9361[/C][C] 0.1278[/C][C] 0.0639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&T=6

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
8	0.02608	0.05215	0.9739
9	0.005763	0.01153	0.9942
10	0.05045	0.1009	0.9496
11	0.7467	0.5065	0.2533
12	0.6893	0.6215	0.3107
13	0.6865	0.6269	0.3135
14	0.5967	0.8067	0.4033
15	0.7854	0.4292	0.2146
16	0.7598	0.4803	0.2402
17	0.7144	0.5712	0.2856
18	0.7096	0.5807	0.2904
19	0.6373	0.7253	0.3627
20	0.6239	0.7522	0.3761
21	0.5609	0.8783	0.4391
22	0.4915	0.9831	0.5085
23	0.4284	0.8568	0.5716
24	0.4171	0.8342	0.5829
25	0.4095	0.8189	0.5905
26	0.3962	0.7925	0.6038
27	0.3416	0.6833	0.6584
28	0.3956	0.7913	0.6044
29	0.3791	0.7581	0.6209
30	0.3419	0.6838	0.6581
31	0.3011	0.6023	0.6989
32	0.2504	0.5008	0.7496
33	0.2108	0.4215	0.7892
34	0.1988	0.3976	0.8012
35	0.1687	0.3374	0.8313
36	0.1596	0.3191	0.8404
37	0.1266	0.2532	0.8734
38	0.1254	0.2508	0.8746
39	0.1004	0.2008	0.8996
40	0.0809	0.1618	0.9191
41	0.07177	0.1435	0.9282
42	0.06581	0.1316	0.9342
43	0.05074	0.1015	0.9493
44	0.03839	0.07677	0.9616
45	0.03133	0.06266	0.9687
46	0.02365	0.04731	0.9763
47	0.01778	0.03556	0.9822
48	0.01318	0.02635	0.9868
49	0.009855	0.01971	0.9901
50	0.01181	0.02361	0.9882
51	0.01057	0.02114	0.9894
52	0.007449	0.0149	0.9926
53	0.005627	0.01125	0.9944
54	0.007368	0.01474	0.9926
55	0.007017	0.01404	0.993
56	0.005173	0.01035	0.9948
57	0.004873	0.009745	0.9951
58	0.003671	0.007343	0.9963
59	0.0031	0.0062	0.9969
60	0.002433	0.004867	0.9976
61	0.001741	0.003482	0.9983
62	0.001204	0.002408	0.9988
63	0.0008836	0.001767	0.9991
64	0.0007182	0.001436	0.9993
65	0.0007658	0.001532	0.9992
66	0.0006429	0.001286	0.9994
67	0.0006456	0.001291	0.9994
68	0.0004834	0.0009668	0.9995
69	0.0003436	0.0006872	0.9997
70	0.0002972	0.0005944	0.9997
71	0.0002403	0.0004805	0.9998
72	0.0001546	0.0003092	0.9998
73	0.0001038	0.0002076	0.9999
74	9.567e-05	0.0001913	0.9999
75	0.0002465	0.0004931	0.9998
76	0.0002036	0.0004072	0.9998
77	0.0001397	0.0002795	0.9999
78	0.0001629	0.0003258	0.9998
79	0.0001069	0.0002139	0.9999
80	0.0001085	0.000217	0.9999
81	9.249e-05	0.000185	0.9999
82	7.713e-05	0.0001543	0.9999
83	0.000122	0.000244	0.9999
84	0.001271	0.002542	0.9987
85	0.0009607	0.001921	0.999
86	0.0008834	0.001767	0.9991
87	0.0006116	0.001223	0.9994
88	0.0004603	0.0009205	0.9995
89	0.00033	0.0006599	0.9997
90	0.00027	0.00054	0.9997
91	0.0001911	0.0003823	0.9998
92	0.0001319	0.0002639	0.9999
93	0.5174	0.9651	0.4826
94	0.474	0.948	0.526
95	0.4623	0.9246	0.5377
96	0.4626	0.9252	0.5374
97	0.4193	0.8386	0.5807
98	0.3958	0.7917	0.6042
99	0.3581	0.7161	0.6419
100	0.3262	0.6525	0.6738
101	0.2883	0.5766	0.7117
102	0.2511	0.5022	0.7489
103	0.2286	0.4571	0.7714
104	0.282	0.5639	0.718
105	0.2526	0.5052	0.7474
106	0.2284	0.4568	0.7716
107	0.2211	0.4423	0.7789
108	0.2152	0.4304	0.7848
109	0.2254	0.4508	0.7746
110	0.218	0.436	0.782
111	0.2124	0.4248	0.7876
112	0.3091	0.6181	0.6909
113	0.3511	0.7023	0.6489
114	0.3389	0.6779	0.6611
115	0.3121	0.6241	0.6879
116	0.2983	0.5966	0.7017
117	0.3344	0.6687	0.6656
118	0.3292	0.6583	0.6708
119	0.2886	0.5772	0.7114
120	0.2729	0.5459	0.7271
121	0.2728	0.5457	0.7272
122	0.2346	0.4692	0.7654
123	0.2252	0.4504	0.7748
124	0.1998	0.3997	0.8002
125	0.1728	0.3455	0.8272
126	0.4984	0.9968	0.5016
127	0.4559	0.9117	0.5441
128	0.408	0.8159	0.592
129	0.3861	0.7722	0.6139
130	0.3799	0.7599	0.6201
131	0.3649	0.7298	0.6351
132	0.3179	0.6358	0.6821
133	0.2731	0.5463	0.7269
134	0.2563	0.5127	0.7437
135	0.2775	0.555	0.7225
136	0.2566	0.5132	0.7434
137	0.2161	0.4322	0.7839
138	0.2022	0.4044	0.7978
139	0.4335	0.867	0.5665
140	0.3885	0.777	0.6115
141	0.455	0.9099	0.545
142	0.5251	0.9498	0.4749
143	0.4867	0.9735	0.5133
144	0.431	0.862	0.569
145	0.3743	0.7486	0.6257
146	0.338	0.676	0.662
147	0.324	0.6479	0.676
148	0.2685	0.5369	0.7315
149	0.2767	0.5534	0.7233
150	0.3077	0.6154	0.6923
151	0.2566	0.5133	0.7434
152	0.2215	0.4431	0.7785
153	0.1843	0.3686	0.8157
154	0.1413	0.2826	0.8587
155	0.2866	0.5732	0.7134
156	0.2478	0.4956	0.7522
157	0.2212	0.4424	0.7788
158	0.2045	0.409	0.7955
159	0.1562	0.3123	0.8438
160	0.1064	0.2129	0.8936
161	0.7753	0.4494	0.2247
162	0.674	0.6521	0.326
163	0.6036	0.7929	0.3964
164	0.4644	0.9287	0.5356
165	0.9361	0.1278	0.0639

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	36	0.2278	NOK
5% type I error level	48	0.303797	NOK
10% type I error level	51	0.322785	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 36 &  0.2278 & NOK \tabularnewline
5% type I error level & 48 & 0.303797 & NOK \tabularnewline
10% type I error level & 51 & 0.322785 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=7

[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]36[/C][C] 0.2278[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]48[/C][C]0.303797[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]51[/C][C]0.322785[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=7

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&T=7

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	36	0.2278	NOK
5% type I error level	48	0.303797	NOK
10% type I error level	51	0.322785	NOK

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 0.23611, df1 = 2, df2 = 166, p-value = 0.79
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 2.0188, df1 = 8, df2 = 160, p-value = 0.04734
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 1.3197, df1 = 2, df2 = 166, p-value = 0.27

\begin{tabular}{lllllllll}
\hline
Ramsey RESET F-Test for powers (2 and 3) of fitted values \tabularnewline
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.23611, df1 = 2, df2 = 166, p-value = 0.79
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 2.0188, df1 = 8, df2 = 160, p-value = 0.04734
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.3197, df1 = 2, df2 = 166, p-value = 0.27
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=8

[TABLE]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of fitted values[/C][/ROW]
[ROW][C]> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.23611, df1 = 2, df2 = 166, p-value = 0.79
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of regressors[/C][/ROW]
[ROW][C]> reset_test_regressors
	RESET test
data:  mylm
RESET = 2.0188, df1 = 8, df2 = 160, p-value = 0.04734
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of principal components[/C][/ROW]
[ROW][C]> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.3197, df1 = 2, df2 = 166, p-value = 0.27
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=8

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&T=8

As an alternative you can also use a QR Code:

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

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 0.23611, df1 = 2, df2 = 166, p-value = 0.79
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 2.0188, df1 = 8, df2 = 160, p-value = 0.04734
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 1.3197, df1 = 2, df2 = 166, p-value = 0.27

Variance Inflation Factors (Multicollinearity)
> vif Grazing_Land Forest_Land Fishing_Water Cropland 1.110049 2.600970 2.618816 1.119633

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
 Grazing_Land   Forest_Land Fishing_Water      Cropland 
     1.110049      2.600970      2.618816      1.119633 
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315734&T=9

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]> vif
 Grazing_Land   Forest_Land Fishing_Water      Cropland 
     1.110049      2.600970      2.618816      1.119633 
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315734&T=9

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315734&T=9

As an alternative you can also use a QR Code:

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

Variance Inflation Factors (Multicollinearity)
> vif Grazing_Land Forest_Land Fishing_Water Cropland 1.110049 2.600970 2.618816 1.119633

Figure 1

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;

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

library(lattice)
library(lmtest)
library(car)
library(MASS)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par6 <- as.numeric(par6)
if(is.na(par6)) {
par6 <- 12
mywarning = 'Warning: you did not specify the seasonality. The seasonal period was set to s = 12.'
}
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (!is.numeric(par4)) par4 <- 0
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
if (!is.numeric(par5)) par5 <- 0
x <- na.omit(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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s)'){
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
if(par5 > 0) {
x2 <- array(0, dim=c(n-par5*par6,par5), dimnames=list(1:(n-par5*par6), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*par6)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*par6-j*par6,par1]
}
}
x <- cbind(x[(par5*par6+1):n,], x2)
n <- n - par5*par6
}
if (par2 == 'Include Seasonal Dummies'){
x2 <- array(0, dim=c(n,par6-1), dimnames=list(1:n, paste('M', seq(1:(par6-1)), sep ='')))
for (i in 1:(par6-1)){
x2[seq(i,n,par6),i] <- 1
}
x <- cbind(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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
print(x)
(k <- length(x[n,]))
head(x)
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$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
sresid <- studres(mylm)
hist(sresid, freq=FALSE, main='Distribution of Studentized Residuals')
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqPlot(mylm, main='QQ Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
print(z)
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$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, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$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.row.start(a)
a<-table.element(a, mywarning)
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,'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$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
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,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
myr <- as.numeric(mysum$resid)
myr
a <-table.start()
a <- table.row.start(a)
a <- table.element(a,'Menu of Residual Diagnostics',2,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Description',1,TRUE)
a <- table.element(a,'Link',1,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Histogram',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_histogram.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_centraltendency.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'QQ Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_fitdistrnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Kernel Density Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_density.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness/Kurtosis Test',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness-Kurtosis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis_plot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Harrell-Davis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_harrell_davis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Blocked Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'(Partial) Autocorrelation Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_autocorrelation.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Spectral Analysis',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_spectrum.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Tukey lambda PPCC Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_tukeylambda.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Box-Cox Normality Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_boxcoxnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Summary Statistics',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_summary1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable7.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
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,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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')
}
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of fitted values',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_fitted <- resettest(mylm,power=2:3,type='fitted')
a<-table.element(a,paste('',RC.texteval('reset_test_fitted'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of regressors',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_regressors <- resettest(mylm,power=2:3,type='regressor')
a<-table.element(a,paste('',RC.texteval('reset_test_regressors'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of principal components',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_principal_components <- resettest(mylm,power=2:3,type='princomp')
a<-table.element(a,paste('',RC.texteval('reset_test_principal_components'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable8.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Inflation Factors (Multicollinearity)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
vif <- vif(mylm)
a<-table.element(a,paste('',RC.texteval('vif'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable9.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code