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Related Concept Videos

Linearization and Approximation01:26

Linearization and Approximation

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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
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Linear Approximation in Frequency Domain01:26

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Residuals and Least-Squares Property01:11

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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
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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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Related Experiment Video

Updated: Mar 5, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

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Underestimation in linear function learning: Anchoring to zero or x-y similarity?

Mark A Brown1, Guy Lacroix1

  • 1Department of Psychology, Carleton University.

Canadian Journal of Experimental Psychology = Revue Canadienne De Psychologie Experimentale
|March 24, 2017
PubMed
Summary
This summary is machine-generated.

People underestimate positive linear functions when extrapolating below the training range. This study suggests anchoring at the y-intercept, not zero, explains this function learning bias.

Related Experiment Videos

Last Updated: Mar 5, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

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Area of Science:

  • Cognitive Psychology
  • Human Learning
  • Mathematical Cognition

Background:

  • Research indicates a tendency to underestimate positive linear functions during extrapolation below the training range.
  • Existing theories propose anchoring at zero or bias towards the presented X-value as explanations for this underestimation.

Purpose of the Study:

  • To differentiate between anchoring at zero and X-value similarity as explanations for underestimation in function extrapolation.
  • To investigate the role of the y-intercept in modulating extrapolation biases.

Main Methods:

  • 135 participants were tasked with extrapolating positive linear functions.
  • Functions varied in their y-intercept (positive or negative).
  • Extrapolation performance was analyzed in the lower extrapolation region.

Main Results:

  • Participants underestimated positive linear functions with a positive y-intercept.
  • Participants overestimated positive linear functions with a negative y-intercept.
  • Results support the anchoring hypothesis over the X-value similarity hypothesis.

Conclusions:

  • The y-intercept significantly influences extrapolation biases in function learning.
  • Findings align with the extrapolation association model (EXAM), suggesting interpolation towards the y-intercept.
  • This research refines our understanding of cognitive biases in mathematical extrapolation.