The following data were obtained in connection with the values of a certain fictitious material…

The
following data were obtained in connection with the values of a certain
fictitious material property:

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It was then
hypothesized that the underlying material property is a piecewise constant
function with one break point (i.e., two constant pieces).

(a) Plot the
data points and decide where (approximately) the break point should be.

(b) Find the
piecewise constant function which best fits the data by least squares, and plot
it, too.