Suppose you have n data points (x 1 ; y 1 ), (x 2 ; y2 ),

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Suppose you have n data points (x1; y1 ), (x2; y2 ), . . . , (xn; yn ) and you wish to fit a line through the origin (y = ax) to these data using the method of least squares. Derive Equation A.1-6 (Appendix A.1) for the slope of the line by writing the expression for the vertical distance di from the ith data point (xi ; yi ) to the line, then writing the expression for ϕ = Σd2i , and finding by differentiation the value of a that minimizes this function.


Equation A.1-6

a = Sy - Exy; Σ (The intercept equals 0.0.) Sxx

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Elementary Principles of Chemical Processes

ISBN: 978-1119498759

4th edition

Authors: Richard M. Felder, ‎ Ronald W. Rousseau, ‎ Lisa G. Bullard

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