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ResInsight/plot-window/regressionanalysis/index.html
Magne Sjaastad 0b37bb91a0 Updates for 2023.06
2023-06-19 14:44:59 +02:00

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<title>Regression Analysis :: ResInsight</title>
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Getting Started
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Linux Installation
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Build Instructions Ubuntu
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Testimonials
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3D Main Window
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3D Views
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Cell Results
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Result Color Legend
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Result Info
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Color Legends
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Comparison View
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Contour Maps
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Flow Results
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Streamlines
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Tensor Results
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Result Inspection
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Filters
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Intersections
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Seismic Sections
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Surfaces
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Allan Diagram
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Faults
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Zonations/Formations
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<li data-nav-id="/3d-main-window/depthplot/" title="Depth Plot" class="dd-item ">
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Depth Plot
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Grid Statistics Dialog
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Grid Case Groups and Statistics
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Linked Views
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Measurement
</a>
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<li data-nav-id="/3d-main-window/annotations/" title="Annotations" class="dd-item ">
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Annotations
</a>
</li>
</ul>
</li>
<li data-nav-id="/plot-window/" title="Plot Main Window" class="dd-item
parent
">
<a href="/plot-window/">
Plot Main Window
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<ul>
<li data-nav-id="/plot-window/summaryplots/" title="Summary Plots" class="dd-item ">
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Summary Plots
</a>
</li>
<li data-nav-id="/plot-window/summaryplotdatasources/" title="Data Sources" class="dd-item ">
<a href="/plot-window/summaryplotdatasources/">
Data Sources
</a>
</li>
<li data-nav-id="/plot-window/summaryplotmanager/" title="Summary Plot Manager" class="dd-item ">
<a href="/plot-window/summaryplotmanager/">
Summary Plot Manager
</a>
</li>
<li data-nav-id="/plot-window/summarysourcestepping/" title="Summary Plot Source Stepping" class="dd-item ">
<a href="/plot-window/summarysourcestepping/">
Summary Plot Source Stepping
</a>
</li>
<li data-nav-id="/plot-window/summaryploteditor/" title="Summary Plot Editor" class="dd-item ">
<a href="/plot-window/summaryploteditor/">
Summary Plot Editor
</a>
</li>
<li data-nav-id="/plot-window/summarycrossplots/" title="Summary Cross Plot" class="dd-item ">
<a href="/plot-window/summarycrossplots/">
Summary Cross Plot
</a>
</li>
<li data-nav-id="/plot-window/summaryplottemplate/" title="Summary Plot Template" class="dd-item ">
<a href="/plot-window/summaryplottemplate/">
Summary Plot Template
</a>
</li>
<li data-nav-id="/plot-window/summarytables/" title="Summary Tables" class="dd-item ">
<a href="/plot-window/summarytables/">
Summary Tables
</a>
</li>
<li data-nav-id="/plot-window/multiplots/" title="Multi Plots" class="dd-item ">
<a href="/plot-window/multiplots/">
Multi Plots
</a>
</li>
<li data-nav-id="/plot-window/ensembleplotting/" title="Ensemble Plotting" class="dd-item ">
<a href="/plot-window/ensembleplotting/">
Ensemble Plotting
</a>
</li>
<li data-nav-id="/plot-window/objectivefunctions/" title="Objective Functions" class="dd-item ">
<a href="/plot-window/objectivefunctions/">
Objective Functions
</a>
</li>
<li data-nav-id="/plot-window/analysisplots/" title="Analysis Plots" class="dd-item ">
<a href="/plot-window/analysisplots/">
Analysis Plots
</a>
</li>
<li data-nav-id="/plot-window/gridstatisticsplots/" title="Grid Statistics Plots" class="dd-item ">
<a href="/plot-window/gridstatisticsplots/">
Grid Statistics Plots
</a>
</li>
<li data-nav-id="/plot-window/correlationplots/" title="Correlation Plots" class="dd-item ">
<a href="/plot-window/correlationplots/">
Correlation Plots
</a>
</li>
<li data-nav-id="/plot-window/welllogsandplots/" title="Well Log Plots" class="dd-item ">
<a href="/plot-window/welllogsandplots/">
Well Log Plots
</a>
</li>
<li data-nav-id="/plot-window/declinecurveanalysis/" title="Decline Curve Analysis" class="dd-item ">
<a href="/plot-window/declinecurveanalysis/">
Decline Curve Analysis
</a>
</li>
<li data-nav-id="/plot-window/regressionanalysis/" title="Regression Analysis" class="dd-item active">
<a href="/plot-window/regressionanalysis/">
Regression Analysis
</a>
</li>
<li data-nav-id="/plot-window/wellborestabilityplots/" title="Well Bore Stability Plots" class="dd-item ">
<a href="/plot-window/wellborestabilityplots/">
Well Bore Stability Plots
</a>
</li>
<li data-nav-id="/plot-window/rftplot/" title="RFT Plot" class="dd-item ">
<a href="/plot-window/rftplot/">
RFT Plot
</a>
</li>
<li data-nav-id="/plot-window/rftsegmentplot/" title="RFT Segment Plot" class="dd-item ">
<a href="/plot-window/rftsegmentplot/">
RFT Segment Plot
</a>
</li>
<li data-nav-id="/plot-window/ensemblerftplot/" title="Ensemble RFT Plot" class="dd-item ">
<a href="/plot-window/ensemblerftplot/">
Ensemble RFT Plot
</a>
</li>
<li data-nav-id="/plot-window/pltplot/" title="PLT Plot" class="dd-item ">
<a href="/plot-window/pltplot/">
PLT Plot
</a>
</li>
<li data-nav-id="/plot-window/vfpplot/" title="VFP Plot" class="dd-item ">
<a href="/plot-window/vfpplot/">
VFP Plot
</a>
</li>
<li data-nav-id="/plot-window/flow-diagnostics-plots/" title="Flow Diagnostics Plots" class="dd-item
">
<a href="/plot-window/flow-diagnostics-plots/">
Flow Diagnostics Plots
</a>
<ul>
<li data-nav-id="/plot-window/flow-diagnostics-plots/producerinjectorconnectivitytable/" title="Producer/Injector Connectivity Tables" class="dd-item ">
<a href="/plot-window/flow-diagnostics-plots/producerinjectorconnectivitytable/">
Producer/Injector Connectivity Tables
</a>
</li>
<li data-nav-id="/plot-window/flow-diagnostics-plots/wellallocationovertimeplot/" title="Well Allocation Over Time Plot" class="dd-item ">
<a href="/plot-window/flow-diagnostics-plots/wellallocationovertimeplot/">
Well Allocation Over Time Plot
</a>
</li>
</ul>
</li>
<li data-nav-id="/plot-window/gridcrossplots/" title="Grid Cross Plots" class="dd-item ">
<a href="/plot-window/gridcrossplots/">
Grid Cross Plots
</a>
</li>
<li data-nav-id="/plot-window/saturationpressureplots/" title="Saturation Pressure Plots" class="dd-item ">
<a href="/plot-window/saturationpressureplots/">
Saturation Pressure Plots
</a>
</li>
</ul>
</li>
<li data-nav-id="/workflows/" title="Workflows" class="dd-item
">
<a href="/workflows/">
Workflows
</a>
<ul>
<li data-nav-id="/workflows/biotcoefficient/" title="Biot Coefficient" class="dd-item ">
<a href="/workflows/biotcoefficient/">
Biot Coefficient
</a>
</li>
<li data-nav-id="/workflows/ensemblesurface/" title="Ensemble Surface" class="dd-item ">
<a href="/workflows/ensemblesurface/">
Ensemble Surface
</a>
</li>
<li data-nav-id="/workflows/ensemblewelllog/" title="Ensemble Well Log" class="dd-item ">
<a href="/workflows/ensemblewelllog/">
Ensemble Well Log
</a>
</li>
</ul>
</li>
<li data-nav-id="/wells-and-completions/" title="Wells and Completions" class="dd-item
">
<a href="/wells-and-completions/">
Wells and Completions
</a>
<ul>
<li data-nav-id="/wells-and-completions/simulationwells/" title="Simulation Wells" class="dd-item ">
<a href="/wells-and-completions/simulationwells/">
Simulation Wells
</a>
</li>
<li data-nav-id="/wells-and-completions/wellpaths/" title="Well Paths" class="dd-item ">
<a href="/wells-and-completions/wellpaths/">
Well Paths
</a>
</li>
<li data-nav-id="/wells-and-completions/createnewwellpaths/" title="Create Well Paths" class="dd-item ">
<a href="/wells-and-completions/createnewwellpaths/">
Create Well Paths
</a>
</li>
<li data-nav-id="/wells-and-completions/createmultilateralwellpaths/" title="Create Multilaterals Well Paths" class="dd-item ">
<a href="/wells-and-completions/createmultilateralwellpaths/">
Create Multilaterals Well Paths
</a>
</li>
<li data-nav-id="/wells-and-completions/3dwelllogcurves/" title="3D Well Log Plots" class="dd-item ">
<a href="/wells-and-completions/3dwelllogcurves/">
3D Well Log Plots
</a>
</li>
<li data-nav-id="/wells-and-completions/completions/" title="Completions" class="dd-item ">
<a href="/wells-and-completions/completions/">
Completions
</a>
</li>
<li data-nav-id="/wells-and-completions/ensemblefracturestatistics/" title="Ensemble Fracture Statistics" class="dd-item ">
<a href="/wells-and-completions/ensemblefracturestatistics/">
Ensemble Fracture Statistics
</a>
</li>
<li data-nav-id="/wells-and-completions/completionslgr/" title="Completions LGR" class="dd-item ">
<a href="/wells-and-completions/completionslgr/">
Completions LGR
</a>
</li>
<li data-nav-id="/wells-and-completions/wellmeasurements/" title="Well Measurements" class="dd-item ">
<a href="/wells-and-completions/wellmeasurements/">
Well Measurements
</a>
</li>
</ul>
</li>
<li data-nav-id="/import/" title="Import" class="dd-item
">
<a href="/import/">
Import
</a>
<ul>
<li data-nav-id="/import/eclipsecases/" title="Eclipse Cases" class="dd-item ">
<a href="/import/eclipsecases/">
Eclipse Cases
</a>
</li>
<li data-nav-id="/import/eclipsesummarydata/" title="Eclipse Summary Data" class="dd-item ">
<a href="/import/eclipsesummarydata/">
Eclipse Summary Data
</a>
</li>
<li data-nav-id="/import/ensemblefiledialog/" title="Ensemble File Dialog" class="dd-item ">
<a href="/import/ensemblefiledialog/">
Ensemble File Dialog
</a>
</li>
<li data-nav-id="/import/roffgridmodels/" title="ROFF Grid Models" class="dd-item ">
<a href="/import/roffgridmodels/">
ROFF Grid Models
</a>
</li>
<li data-nav-id="/import/seismicdata/" title="Seismic Data" class="dd-item ">
<a href="/import/seismicdata/">
Seismic Data
</a>
</li>
<li data-nav-id="/import/lasfile/" title="Log ASCII Standard File" class="dd-item ">
<a href="/import/lasfile/">
Log ASCII Standard File
</a>
</li>
<li data-nav-id="/import/geomechanicaldata/" title="Geomechanical Data" class="dd-item ">
<a href="/import/geomechanicaldata/">
Geomechanical Data
</a>
</li>
<li data-nav-id="/import/soursimrlresults/" title="SourSimRL Results" class="dd-item ">
<a href="/import/soursimrlresults/">
SourSimRL Results
</a>
</li>
<li data-nav-id="/import/elementpropertytable/" title="Element Property Table" class="dd-item ">
<a href="/import/elementpropertytable/">
Element Property Table
</a>
</li>
<li data-nav-id="/import/observeddata/" title="Observed Time History Data" class="dd-item ">
<a href="/import/observeddata/">
Observed Time History Data
</a>
</li>
<li data-nav-id="/import/pressuredata/" title="Pressure/Depth Data" class="dd-item ">
<a href="/import/pressuredata/">
Pressure/Depth Data
</a>
</li>
<li data-nav-id="/import/appendingadditionalproperties/" title="Appending Additional Properties" class="dd-item ">
<a href="/import/appendingadditionalproperties/">
Appending Additional Properties
</a>
</li>
<li data-nav-id="/import/pasteexceltimedata/" title="Paste Excel Time History Data" class="dd-item ">
<a href="/import/pasteexceltimedata/">
Paste Excel Time History Data
</a>
</li>
</ul>
</li>
<li data-nav-id="/export/" title="Export" class="dd-item
">
<a href="/export/">
Export
</a>
<ul>
<li data-nav-id="/export/snapshots/" title="Snapshots" class="dd-item ">
<a href="/export/snapshots/">
Snapshots
</a>
</li>
<li data-nav-id="/export/eclipseproperties/" title="Eclipse Properties" class="dd-item ">
<a href="/export/eclipseproperties/">
Eclipse Properties
</a>
</li>
<li data-nav-id="/export/fluxnummultnum/" title="FLUXNUM/MULTNUM" class="dd-item ">
<a href="/export/fluxnummultnum/">
FLUXNUM/MULTNUM
</a>
</li>
<li data-nav-id="/export/completionexport/" title="Completions" class="dd-item ">
<a href="/export/completionexport/">
Completions
</a>
</li>
<li data-nav-id="/export/exportwellpaths/" title="Well Paths" class="dd-item ">
<a href="/export/exportwellpaths/">
Well Paths
</a>
</li>
<li data-nav-id="/export/sectormodel/" title="Sector Model" class="dd-item ">
<a href="/export/sectormodel/">
Sector Model
</a>
</li>
<li data-nav-id="/export/contourmapexport/" title="Contour Map Export" class="dd-item ">
<a href="/export/contourmapexport/">
Contour Map Export
</a>
</li>
</ul>
</li>
<li data-nav-id="/scripting/" title="Scripting" class="dd-item
">
<a href="/scripting/">
Scripting
</a>
<ul>
<li data-nav-id="/scripting/pythoninterface/" title="Python interface" class="dd-item ">
<a href="/scripting/pythoninterface/">
Python interface
</a>
</li>
<li data-nav-id="/scripting/commandlineinterface/" title="Command Line Interface" class="dd-item ">
<a href="/scripting/commandlineinterface/">
Command Line Interface
</a>
</li>
<li data-nav-id="/scripting/commandfile/" title="Command File" class="dd-item ">
<a href="/scripting/commandfile/">
Command File
</a>
</li>
<li data-nav-id="/scripting/octaveinterface/" title="Octave Interface" class="dd-item ">
<a href="/scripting/octaveinterface/">
Octave Interface
</a>
</li>
<li data-nav-id="/scripting/octaveinterfacereference/" title="Octave Interface Reference" class="dd-item ">
<a href="/scripting/octaveinterfacereference/">
Octave Interface Reference
</a>
</li>
</ul>
</li>
<li data-nav-id="/misc/" title="Miscellaneous" class="dd-item
">
<a href="/misc/">
Miscellaneous
</a>
<ul>
<li data-nav-id="/misc/preferences/" title="Preferences" class="dd-item ">
<a href="/misc/preferences/">
Preferences
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<li><a href="#create-regression-analysis">Create Regression Analysis</a></li>
<li><a href="#regression-types">Regression Types</a>
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<li><a href="#polynomial-regression">Polynomial Regression</a></li>
<li><a href="#power-fit-regression">Power Fit Regression</a></li>
<li><a href="#exponential-regression">Exponential Regression</a></li>
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<h1>
Regression Analysis
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<p><img src="/images/plot-window/RegressionAnalysis.png" alt=""></p>
<h2 id="create-regression-analysis">Create Regression Analysis</h2>
<p>Regression analysis curves can be created from the right-click menu for a curve in the <strong>Plot Project Tree</strong>.</p>
<p><img src="/images/plot-window/RegressionAnalysis_create.png" alt=""></p>
<h2 id="regression-types">Regression Types</h2>
<h3 id="linear-regression">Linear Regression</h3>
<p>The linear regression (i.e. straight line fit) is calculated by choosing the line that minimizes the sum of the squared differences between the observed dependent variable values and the values predicted by the linear equation. The straight line equation can be written as:</p>
<p>$$ y = a + bx $$</p>
<p>where:</p>
<ul>
<li>$y$ is the dependent variable,</li>
<li>$x$ is the independent variable,</li>
<li>$a$ is the intercept,</li>
<li>$b$ is the slope.</li>
</ul>
<h3 id="polynomial-regression">Polynomial Regression</h3>
<p>Polynomial regression is a form of linear regression where the relationship between the independent variable(s) and the dependent variable is modeled as an nth-degree polynomial. It allows for more complex relationships between the variables by introducing polynomial terms into the regression equation.</p>
<p>A polynomial in a single indeterminate x can always be written (or rewritten) in the form</p>
<p>$$ y = a_{n}x^n + a_{n-1}x^{n-1} + \dots + a_{2}x^{2}+a_{1}x+a_{0} $$</p>
<p>where:</p>
<ul>
<li>$a_0 , \ldots, a_n$ are constants that are called the coefficients of the polynomial,</li>
<li>$x$ is the indeterminate.</li>
<li>$n$ is the degree of the polynomial.</li>
</ul>
<p>To determine the degree of the polynomial, one needs to consider the complexity of the relationship between the variables and the nature of the data. A higher degree polynomial can capture more intricate relationships but may also lead to overfitting if the model becomes too flexible.</p>
<p>Polynomial regression can be beneficial when the relationship between the variables is curvilinear or nonlinear. By introducing polynomial terms, it can capture the curvature in the data and provide a better fit compared to simple linear regression.</p>
<h3 id="power-fit-regression">Power Fit Regression</h3>
<p>The Power Fit regression is described by the following equation:</p>
<p>$$ y = ax^b $$</p>
<p>where:</p>
<ul>
<li>$y$ is the dependent variable,</li>
<li>$x$ is the independent variable,</li>
<li>$a$ is the coefficient,</li>
<li>$b$ is the exponent.</li>
</ul>
<p>In power fit regression, the goal is to estimate the values of $a$ and $b$ that best describe the relationship between the variables. This is done by minimizing the sum of the squared differences between the observed dependent variable values and the values predicted by the power-law equation.</p>
<h3 id="exponential-regression">Exponential Regression</h3>
<p>Exponential regression is a type of nonlinear regression used to model relationships where the dependent variable changes exponentially with the independent variable. It is suitable when the data exhibits exponential growth or decay patterns.</p>
<p>The equation for exponential regression can be written as:</p>
<p>$$ y = ae^{bx} $$</p>
<p>where:</p>
<ul>
<li>$y$ is the dependent variable,</li>
<li>$x$ is the independent variable,</li>
<li>$a$ is the coefficient,</li>
<li>$b$ is the rate of growth or decay,</li>
<li>$e$ is the base of the natural logarithm (approximately 2.71828).</li>
</ul>
<p>Exponential models are commonly used in biological applications, for example, for exponential growth of bacteria. Spotfire uses a nonlinear regression method for this calculation. This will result in better accuracy of the calculation compared to using linear regression on transformed values only.</p>
<h3 id="logarithmic-regression">Logarithmic Regression</h3>
<p>The logarithmic fit calculates the least squares fit through points by using the following equation:</p>
<p>$$ y = a + b \ln( x ) $$</p>
<ul>
<li>$y$ is the dependent variable,</li>
<li>$x$ is the independent variable,</li>
<li>$a$ and $b$ are coefficients.</li>
</ul>
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