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#35

Let *x* be per capita income in thousands of dollars. Let *y* be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about *x* and *y*.

x | 8.2 | 9.7 | 9.9 | 8.0 | 8.3 | 8.7 |

y | 10.0 | 18.7 | 20.2 | 10.2 | 11.4 | 13.1 |

Complete parts (a) through (e), given Σ*x* = 52.8, Σ*y* = 83.6, Σ*x*^{2} = 467.92, Σ*y*^{2} = 1263.34, Σ*xy* = 753.56, and *r* ≈ 0.995.

(c) Find x, and y. Then find the equation of the least-squares line = *a* + *bx*. (Round your answers for x and y to two decimal places. Round your answers for *a* and *b* to three decimal places.)

x | = | |

y | = | |

= | + x |

(e) Find the value of the coefficient of determination *r*^{2}. What percentage of the variation in *y* can be *explained* by the corresponding variation in *x* and the least-squares line? What percentage is *unexplained*? (Round your answer for *r*^{2}to three decimal places. Round your answers for the percentages to one decimal place.)

r^{2} = | |

explained | % |

unexplained | % |

(f) Suppose a small city in Oregon has a per capita income of 9.5 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.)

M.D.s per 10,000 residents

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