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Q.12.8

Expert-verifiedFound in: Page 694

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

For a given line of best fit, you compute that $r=0.5204$ using $n=9$ data points, and the critical value is 0.666. Can the line be used for prediction? Why or why not?

The critical value associated with degrees of freedom $7$ is $0.666$.Therefore,$r$ is insignificant.

$r=0.5204$

$n=9$$criticalvalue=0.666$.

The degrees of freedom can be computed as shown below:

$df=n-2$

$=9-2$$=7$The critical value associated with degrees of freedom $7$ is $0.666$. If $r$ is less than negative critical value or $r$ is greater than positive critical value then $r$ is significant. Here, $r(0.5204)$ is less than positive critical value $(0.666)$. Therefore, $r$ is insignificant.

75. The following table consists of one student athlete's time (in minutes) to swim 2000 yards and the student's heart rate (beats per minute) after swimming on a random sample of 10 days:

Swim Time | Heart Rate |

34.12 | 144 |

35.72 | 152 |

34.72 | 124 |

34.05 | 140 |

34.13 | 152 |

35.73 | 146 |

36.17 | 128 |

35.57 | 136 |

35.37 | 144 |

35.57 | 148 |

a. Enter the data into your calculator and make a scatter plot.b. Use your calculator's regression function to find the equation of the least-squares regression line. Add this to your scatter plot from part a.c. Explain in words what the slope and y-intercept of the regression line tell us.d. How well does the regression line fit the data? Explain your response.e. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.

Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where $x$ is the number of endorsements the player has and $y$ is the amount of money made (in millions of dollars).

x | y | x | y |

0 | 2 | 5 | 12 |

3 | 8 | 4 | 9 |

2 | 7 | 3 | 9 |

1 | 3 | 0 | 3 |

5 | 13 | 4 | 10 |

What is the slope of the line of best fit? What does it represent?

Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where $x$ is the number of endorsements the player has and $y$is the amount of money made (in millions of dollars)

x | y | x | y |

0 | 2 | 5 | 12 |

3 | 8 | 4 | 9 |

2 | 7 | 3 | 9 |

1 | 3 | 0 | 3 |

5 | 13 | $4$ | $10$ |

When $n=100$and $r=-0.89$, is there a significant correlation? Explain.

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