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Residual Plots

Residual Plots

A residual plot is a statistical representation of data used to analyze correlation and regression results. It helps verify the requirements for drawing specific conclusions about correlation and regression. To obtain the residual plot, first, the residual for each data value is calculated, which is simply the vertical distance between the observed and the predicted value obtained from the regression equation.
When the residual values are plotted against the variable x, it is called a residual...

Residuals and Least-Squares Property

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...

Density

Density

Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...

Density and Archimedes' Principle

Density and Archimedes' Principle

When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same holds true for steel ships. The average density of an object majorly determines if the object will float. If an object's average density is less than that of the surrounding fluid, it will float. The reason...

The Principle of Superposition and the Gravitational Field

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The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...

Residual Stresses

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Related Experiment Video

Updated: Jul 5, 2026

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

Foundations of residual-density analysis.

Kathrin Meindl¹, Julian Henn

¹Georg-August Universität Göttingen, Tammannstrasse 4, 37077 Göttingen, Germany.

Acta Crystallographica. Section A, Foundations of Crystallography

|April 19, 2008

Summary

New descriptors for residual density, including gross residual electrons and fractal dimension, quantify noise and model errors. Minimizing these metrics enhances data quality and identifies systematic errors in experimental analysis.

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Area of Science:

Crystallography
Data Analysis
Scientific Computing

Background:

Residual density analysis is crucial for evaluating crystallographic models.
Existing methods may not adequately capture noise and systematic errors.
Quantifying the distribution of residual density is essential for refinement quality.

Purpose of the Study:

Introduce novel descriptors for residual density: gross residual electrons, net residual electrons, and fractal dimension distribution.
Establish these descriptors as quality criteria for refinement and indicators of systematic errors.
Assess the utility of these measures in analyzing various data imperfections.

Main Methods:

Development of new mathematical descriptors for residual density.
Application of these descriptors to simulated and experimental crystallographic data.
Analysis of the impact of noise, model inadequacies, and resolution truncation.

Main Results:

Gross residual electrons serve as a quality criterion, with minimization indicating better refinement.
Fractal dimension distribution reveals deviations from Gaussian noise, signaling systematic errors.
The new measures effectively characterize noise, model deficiencies, and resolution effects.

Conclusions:

The proposed descriptors offer a comprehensive assessment of residual density.
These measures are broadly applicable to various dimensions and types of residual densities.
Enhanced analysis of residual density improves crystallographic model quality and error detection.