deep dives 1 least squares differentiation theoreticaltools adapted fr
1. Least Squares (#differentiation, #theoreticaltools) Adapted from Stewart's "Cal-
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 =>
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