(a) Suppose you are given the following ( x , y ) data pairs. Find the least-squ

Question

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

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

(b) Now suppose you are given these (x, y) data pairs.

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

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

Yes or 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 or 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).

a) Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.

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

C) In general, switching x and y values produces the same least-squares equation.

Explanation / Answer

a)

y= 2.308+0.885*x

b)

y = -1.462+0.885*x

c)

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

No

d) x = -1.462+0.885*y

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

Yes

e)   

C) In general, switching x and y values produces the same least-squares equation.

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