Question

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

x	1	2	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	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?

Yes No    

(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?

Yes No    

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

Answer 1

a)

a) least square line: y= 2.524+0.714x

b) least square line: y= -2.385+1.154x

c)

Yes

d) exchanging symbol x and y:      x=-3.535+1.401y      which is not same as that of part a)

No

e)

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