(a) Suppose you are given the following (x, y) data pairs:

Show that the least-squares equation for these data is Å· = 0.143 + 1.071x (rounded to three digits after the decimal).
(b) Now suppose you are given these (x, y) data pairs:

Show that the least-squares equation for these data is Å· = 1.595 + 0.357x (rounded to three digits after the decimal).
(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?
(d) Solve Å· = 0.143 + 1.071x for x. Do you get the least-squares equation of part (b) with the symbols x and y exchanged?
(e) In general, suppose we have the least-squares equation Å· = a + bx for a set of data pairs (x, y). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (y, x) (with x and y exchanged)? Explain using parts (a) through (d).

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