# Suppose you are given the following (x, y) data pairs. x 1 2 6 y 4 3 9 Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ =  +  x(b) Now suppose you are given these (x, y) data pairs. x 4 3 9 y 1 2 6 Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ =  +  x (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? YesNo     (d) Solve your answer from part (a) for x (rounded to three digits after the decimal).x =  +  y Do you get the least-squares equation of part (b) with the symbols x and yexchanged? YesNo     (e) In general, suppose we have the least-squares equation y = 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). In general, switching x and y values produces the same least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.    In general, switching x and y values produces a different least-squares equation.

Question

Suppose you are given the following (xy) data pairs.

 x 1 2 6 y 4 3 9

Find the least-squares equation for these data (rounded to three digits after the decimal).
ŷ =  +  x

(b) Now suppose you are given these (xy) data pairs.

 x 4 3 9 y 1 2 6

Find the least-squares equation for these data (rounded to three digits after the decimal).
ŷ =  +  x

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

YesNo

(d) Solve your answer from part (a) for x (rounded to three digits after the decimal).
x =  +  y

Do you get the least-squares equation of part (b) with the symbols x and yexchanged?

YesNo

(e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (xy). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (yx), (with x and y exchanged)? Explain using parts (a) through (d).

In general, switching x and y values produces the same least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.    In general, switching x and y values produces a different least-squares equation.