Mathematical modelling is a tool to uncover relationships about observable quantities in the real-world. Consider a model for bacterial growth rate given by the linear equation y = mx + b where x is the population size in cells and y is the growth rate. m and b are the slope and intercept respectively. Often in real life, data has noise and may not follow theoretical relationships exactly. For a given data point (xi, y₁) we define the error between the data and the linear model as e₁ = yi (mxi + b), noting that if the data matches the line perfectly then the error is zero. If we can't find an exact linear relationship then our objective is to find the best line we can. One method for doing this is called the method of least squares which minimizes the total square error, n f=Σe² i=1 рор- where n is the number of data points. Consider a series of measurements of the bacterial ulation given by (1,4.7), (2,7.5), (3,9.8),(4,13.2), (5,15.4), (6,19.6), (7,21.2), (8,24.3), (9,27.4), and (10,28.9).
Mathematical modelling is a tool to uncover relationships about observable quantities in the real-world. Consider a model for bacterial growth rate given by the linear equation y = mx + b where x is the population size in cells and y is the growth rate. m and b are the slope and intercept respectively. Often in real life, data has noise and may not follow theoretical relationships exactly. For a given data point (xi, y₁) we define the error between the data and the linear model as e₁ = yi (mxi + b), noting that if the data matches the line perfectly then the error is zero. If we can't find an exact linear relationship then our objective is to find the best line we can. One method for doing this is called the method of least squares which minimizes the total square error, n f=Σe² i=1 рор- where n is the number of data points. Consider a series of measurements of the bacterial ulation given by (1,4.7), (2,7.5), (3,9.8),(4,13.2), (5,15.4), (6,19.6), (7,21.2), (8,24.3), (9,27.4), and (10,28.9).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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