12. Question Details BBBasicStat7 4.2.021. Ask Your Teacher My Notes Question Pa

Question

12. Question Details BBBasicStat7 4.2.021. Ask Your Teacher My Notes Question Part Submissions Used (a) Suppose you are given the following (x, y) data pairs. x 1 3 6 y 2 1 7 Find the least-squares equation for these data (rounded to three digits after the decimal). y = + x (b) Now suppose you are given these (x, y) data pairs. x 2 1 7 y 1 3 6 Find the least-squares equation for these data (rounded to three digits after the decimal). y = + 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). Switching x and y values sometimes produces the same least-squares equation and sometimes it is different. 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.

Explanation / Answer

a) slope = [nxy - xy]/[nx^2 - (x)^2]
intercept = [y - bx]/n

slope = [3*47 - 10*10]/[3*46 - 100] = 1.079
intercept = [10 - 1.079*10]/3 = -0.263

y = 1.079x - 0.263

b)

slope = [3*47 - 10*10]/[3*54 - 100] = 0.661
intercept = [10 - 0.661*10]/3 = 1.13

y = 0.661x + 1.13

c) Yes

d) y = 1.079x - 0.263, x = (0.263 + y)/1.079 = 0.244 + 0.927y
No

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

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