Deep Dives 1. Least Squares (#differentiation, #theoreticaltools) Adapted from Stewart's "Cal- culus" Suppose that a scientist has reason to believe that two quantities z and y are related linearly, that is y = mz+b, at least approximately, for some values of m and b. The scientist performs an experiment and collects data in the form of points (21,31). (72.32), (n.), and then plots these points. The points don't lie exactly on a straight line, so the scientist wants to find constants m and b so that the line y=mx+b "fits" the points as well as possible. *** Let dy- (mz, + b) be the vertical deviation of the point (z,y) from the line. The method of least squares determines m and b so as to minimize of the sum of the squares of these vertical deviations. Show that, according to this method, the line of best fit is obtained when m and b satisfy the following system of equations: z₁+ bn => mΣ²²+ b[x₁=[zy inl

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