(a) Suppose you are given the following (x,y) data pairs.x 2 1 5 y 4 3 6

Find the least-squares equation for these data (rounded to four digits after the decimal).

=+x

(b) Now suppose you are given these (x,y) data pairs.x436y215Find the least-squares equation for these data (rounded to four digits after the decimal).

=+x

(c) In the data for parts (a) and (b), did we simply exchange thexandyvalues of each data pair?

Yes

No

(d) Solve your answer from part (a) forx(rounded to four digits after the decimal).

x=+y

Do you get the least-squares equation of part (b) with the symbolsxandyexchanged?

Yes

No

(e) In general, suppose we have the least-squares equationy=a+bxfor a set of data pairs (x,y). If we solve this equation forx, will wenecessarilyget the least-squares equation for the set of data pairs(y,x),(withxandyexchanged)? Explain using parts (a) through (d).

In general, switchingxandyvalues produces a different least-squares equation.

Switchingxandyvalues sometimes produces the same least-squares equation and sometimes it is different.

In general, switchingxandyvalues produces the same least-squares equation.