Mathematics

Mathematics

Problem

Graph showing a scatter plot of data points P1, P2, P3, P4, ..., Pn. A line of best fit is drawn through the origin O(0,0). For each point Pi, a vertical dashed line is drawn to the line of best fit at point Mi. The points Pi and Mi are connected by a dashed line segment. P1(a1,b1),P2(a2,b2),P3(a3,b3),…,Pn(an,bn)P_1(a_1, b_1), P_2(a_2, b_2), P_3(a_3, b_3), \dots, P_n(a_n, b_n) are a set of data points which are approximately linear through the origin O(0,0)O(0, 0) . To find the equation of the “line of best fit” through the origin, we minimise (P1M1)2+(P2M2)2+(P3M3)2+⋯+(PnMn)2(P_1M_1)^2 + (P_2M_2)^2 + (P_3M_3)^2 + \dots + (P_nM_n)^2 where MiM_i lies on the line and has xx -coordinate aia_i . Find the gradient mm of the “line of best fit” in terms of aia_i and bib_i , i=1,2,3,4,…,ni = 1, 2, 3, 4, \dots, n .

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