1. The problem of finding a line that best "fits" a set of data can be solved using the method of least squares. Consider the simple set of data below, where we have the heat capacity, Cy, of a material at different temperatures, T, and pressures, P. T P 5 10 2 10 25 3 20 4 10 40 10 We can use the method of least squares to fit a model of the form, c, = Bo + B1T + B2P, where and a and b are parameters of the linear fit. The following equations can be used to derive the parameters: 1 5 1 2 10 A =|1 3 1 4 10 1 5 10/ 10 B =| 25 20 \40, AT A B1) = AT B

1. The problem of finding a line that best "fits" a set of data can be solved using the method of least squares. Consider the simple set of data below, where we have the heat capacity, Cy, of a material at different temperatures, T, and pressures, P. T P 5 10 2 10 25 3 20 4 10 40 10 We can use the method of least squares to fit a model of the form, c, = Bo + B1T + B2P, where and a and b are parameters of the linear fit. The following equations can be used to derive the parameters: 1 5 1 2 10 A =|1 3 1 4 10 1 5 10/ 10 B =| 25 20 \40, AT A B1) = AT B

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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