Question

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

x	2	3	6
y	4	3	7

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	7
y	2	3	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 y exchanged?

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 a different least-squares equation.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.

Answer 1

a)

b)

c) yes,

d)

x = - 0.462 + 0.885 y

yes

e)

In general, switching x and y values produces a different least-squares equation