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ProbabilityQ&A LibrarySuppose you are given the following (x, y) data pairs. x 1 2 6 y 4 3 9 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 9 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? YesNo (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 yexchanged? YesNo (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.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.Question

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

x |
1 | 2 | 6 |

y |
4 | 3 | 9 |

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 | 9 |

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?

YesNo

(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?

YesNo

(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.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.

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