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Related Concept Videos

Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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Related Experiment Video

Updated: Jun 24, 2026

Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street
14:55

Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street

Published on: January 20, 2023

Urban daytime traffic noise prediction models.

Elaine Carvalho da Paz1, Paulo Henrique Trombetta Zannin

  • 1Laboratory of Environmental and Industrial Acoustics and Acoustic Comfort - LAAICA, UFPR - Federal University of Paraná, Jardim das Américas, 55-81531-990, Curitiba, Parana, Brazil. epaz@bol.com.br

Environmental Monitoring and Assessment
|April 9, 2009
PubMed
Summary

New mathematical models accurately predict urban highway noise levels. These models utilize linearity and class intervals for improved assessment of traffic noise, offering a valuable tool for urban planning and environmental studies.

Related Experiment Videos

Last Updated: Jun 24, 2026

Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street
14:55

Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street

Published on: January 20, 2023

Area of Science:

  • Environmental Science
  • Acoustics
  • Urban Planning

Background:

  • Urban highways generate significant acoustic environments.
  • Accurate assessment of traffic noise is crucial for urban planning and public health.

Purpose of the Study:

  • To develop and validate mathematical models for predicting key sound levels from urban highways.
  • To assess the accuracy and characteristics of the new models compared to existing literature.

Main Methods:

  • In situ measurements of the acoustic environment.
  • Development of mathematical models for sound levels (L (eq), L (10), L (50), L (90)).
  • Statistical validation of generated models using traffic variables and sound level correlations.

Main Results:

  • Four groups of statistically validated mathematical models for daytime sound levels were generated.
  • The new models demonstrate accuracy comparable to existing traffic noise prediction models.
  • Key differentiating characteristics include model linearity and the application of class intervals.

Conclusions:

  • The developed mathematical models provide an accurate and effective method for assessing and predicting daytime traffic noise.
  • The linearity and class interval application offer distinct advantages over current models in the literature.
  • These findings support improved urban noise management strategies.