(a) Suppose you are given the following (x, y) data pairs. 2 3 4 3 6 A USE SALT Find the least-squares equation for these data (rounded to four digits after the decimal). (b) Now suppose you are given these (x, y) data pairs. 4 3 Find the least-squares equation for these data (rounded to four digits after the decimal). (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? O Yes O No

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

(a) Suppose you are given the following (x, y) data pairs.
y
4
3
6
n USE SALT
Find the least-squares equation for these data (rounded to four digits after the decimal).
(b) Now suppose you are given these (x, y) data pairs.
4
3
6
у |
3
5
Find the least-squares equation for these data (rounded to four digits after the decimal).
(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?
O Yes
O No
(d) Solve your answer from part (a) for x (rounded to four digits after the decimal).
x =
Do you get the least-squares equation of part (b) with the symbols x and y exchanged?
O Yes
O 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).
O In general, switching x and y values produces the same least-squares equation.
O In general, switching x and y values produces a different least-squares equation.
O switching x and y values sometimes produces the same least-squares equation and sometimes it is different.
Transcribed Image Text:(a) Suppose you are given the following (x, y) data pairs. y 4 3 6 n USE SALT Find the least-squares equation for these data (rounded to four digits after the decimal). (b) Now suppose you are given these (x, y) data pairs. 4 3 6 у | 3 5 Find the least-squares equation for these data (rounded to four digits after the decimal). (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? O Yes O No (d) Solve your answer from part (a) for x (rounded to four digits after the decimal). x = Do you get the least-squares equation of part (b) with the symbols x and y exchanged? O Yes O 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). O In general, switching x and y values produces the same least-squares equation. O In general, switching x and y values produces a different least-squares equation. O switching x and y values sometimes produces the same least-squares equation and sometimes it is different.
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