# Lesson 9

Causal Relationships

- Let’s get a closer look at related variables.

### Problem 1

Priya creates a scatter plot showing the relationship between the number of steps she takes and her heart rate. The correlation coefficient of the line of best fit is 0.88.

- Are they correlated? Explain your reasoning.
- Do either of the variables cause the other to change? Explain your reasoning.

### Problem 2

Kiran creates a scatter plot showing the relationship between the number of students attending drama club and the number of students attending poetry club each week. The correlation coefficient for the line of best fit is -0.36.

- Are they correlated? Explain your reasoning.
- Do either of the variables cause the other to change? Explain your reasoning.

### Problem 3

A news website shows a scatter plot with a negative relationship between the amount of sugar eaten and happiness levels. The headline reads, “Eating sugar causes happiness to decrease!”

- What is wrong with this claim?
- What is a better headline for this information?

### Problem 4

A group of 125 college students are surveyed about their note taking and study habits. Some results are represented in the table.

prefer writing notes by hand | prefer typing notes | don't take notes | |
---|---|---|---|

study for less than 1 hour | 22 | 8 | |

study for 1 hour or more | 38 | 28 | 3 |

How many students prefer typing notes and study for less than 1 hour?

### Problem 5

The number of miles driven, \(x\), and the number of gallons remaining in the gas tank, \(y\), have a strong negative relationship.

Explain what it means to have a strong negative relationship in this context.

### Problem 6

*Technology required. Use a graphing calculator to answer the questions.*

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

10.2 | 31 |

10.4 | 27 |

10.5 | 29 |

10.5 | 30 |

10.5 | 31 |

10.6 | 26 |

10.8 | 25 |

10.8 | 26 |

10.9 | 27 |

11 | 24 |

11.2 | 22 |

- What is an equation of the line of best fit?
- What is the value of the correlation coefficient?