Suppose you have n data points (x₁; y₁ ), (x₂; y2 ), . . . , (x_n; y_n ) 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 (x_i ; y_i ) to the line, then writing the expression for ϕ = Σd²_i , and finding by differentiation the value of a that minimizes this function.

Equation A.1-6

Transcribed Image Text:

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