# 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 for the data 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 data 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?