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(a) Suppose you are given the following (x, y) data pairs. 1 6 y 4 3 9 n USE SALT Find the least-squares equation for these data (rounded to four digits after the decimal). 1.9048 1.1429 (b) Now suppose you are given these (x, y) data pairs. 4 3 9. y 1 2 Find the least-squares equation for these data (rounded to four digits after the decimal). -1.9290 0.7442 (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes O No (d) Solve your answer from part (a) for x (rounded to four digits after the decimal). -1.129 0.7742 X Y %3D Do you get the least-squares equation of part (b) with the symbols x and y exchanged? O 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). O In general, switching x and y values produces the same least-squares equation.

(a) Suppose you are given the following (x, y) data pairs. 1 6 y 4 3 9 n USE SALT Find the least-squares equation for these data (rounded to four digits after the decimal). 1.9048 1.1429 (b) Now suppose you are given these (x, y) data pairs. 4 3 9. y 1 2 Find the least-squares equation for these data (rounded to four digits after the decimal). -1.9290 0.7442 (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes O No (d) Solve your answer from part (a) for x (rounded to four digits after the decimal). -1.129 0.7742 X Y %3D Do you get the least-squares equation of part (b) with the symbols x and y exchanged? O 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). O In general, switching x and y values produces the same least-squares equation.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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(a) Suppose you are given the following (x, y) data pairs. 1 2 6 y 4 3 n USE SALT Find the least-squares equation for these data (rounded to four digits after the decimal). ý = 1.9048 1.1429 (b) Now suppose you are given these (x, y) data pairs. 4 3 9 y 1 2 6 Find the least-squares equation for these data (rounded to four digits after the decimal). ý = -1.9290 0.7442 X X (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes O No (d) Solve your answer from part (a) for x (rounded to four digits after the decimal). X = -1.12g 0.7742 X Y Do you get the least-squares equation of part (b) with the symbols x and y exchanged? O 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). O 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.
Transcribed Image Text:(a) Suppose you are given the following (x, y) data pairs. 1 2 6 y 4 3 n USE SALT Find the least-squares equation for these data (rounded to four digits after the decimal). ý = 1.9048 1.1429 (b) Now suppose you are given these (x, y) data pairs. 4 3 9 y 1 2 6 Find the least-squares equation for these data (rounded to four digits after the decimal). ý = -1.9290 0.7442 X X (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes O No (d) Solve your answer from part (a) for x (rounded to four digits after the decimal). X = -1.12g 0.7742 X Y Do you get the least-squares equation of part (b) with the symbols x and y exchanged? O 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). O 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.
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