# Lesson 7

The Correlation Coefficient

- Let’s see how good a linear model is for some data.

### Problem 1

Select **all** the values for \(r\) that indicate a positive slope for the line of best fit.

1

-1

0.5

-0.5

0

0.8

-0.8

### Problem 2

The correlation coefficient, \(r\), is given for several different data sets. Which value for \(r\) indicates the strongest correlation?

0.01

-0.34

-0.82

-0.95

### Problem 3

Which of the values is the best estimate of the correlation coefficient for the line of best fit shown in the scatter plot?

-0.9

-0.4

0.4

0.9

### Problem 4

*Technology required. *

A study investigated the relationship between the amount of daily food waste measured in pounds and the number of people in a household. The data in the table displays the results of the study.

number of people in household, \( x\) | food waste (pounds), \(y\) |
---|---|

2 | 3.4 |

3 | 2.5 |

4 | 8.9 |

4 | 4.7 |

4 | 3.5 |

4 | 4 |

5 | 5.3 |

5 | 4.6 |

5 | 7.8 |

6 | 3.2 |

8 | 12 |

Use graphing technology to create the line of best fit for the data in the table.

- What is the equation of the line of best fit for this data? Round numbers to two decimal places.
- What is the slope of the line of best fit? What does it mean in this situation? Is this realistic?
- What is the \(y\)-intercept of the line of best fit? What does it mean in this situation? Is this realistic?

### Problem 5

A table of values and the plot of the residuals for the line of best fit are shown.

\(x\) | \(y\) |
---|---|

1 | 10 |

2 | 8 |

2.5 | 9.5 |

4 | 8 |

5 | 8 |

6 | 7.5 |

7.2 | 7 |

8.5 | 6 |

- Which point does the line estimate the best?
- Which point does the line estimate the worst?

### Problem 6

Tyler creates a scatter plot that displays the relationship between the grams of food a hamster eats, \(x\), and the total number of rotations that the hamster’s wheel makes, \(y\). Tyler creates a line of best fit and finds that the residual for the point \((1.4, 1250)\) is -132. The point \((1.2, 1364)\) has a residual of 117. Interpret the meaning of 117 in the context of the problem.