# Lesson 10

Putting It All Together

- Let’s interpret data

### 10.1: Which One Doesn’t Belong: Data Correlations

Which one doesn’t belong?

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

3 | 6 |

3.75 | 8.50 |

7.25 | 7.50 |

5.50 | 11 |

6 | 9 |

8 | 10.25 |

### 10.2: Electric Power

Here are Elena’s representations of the data set.

energy (kwh) | electric bill price (dollars) |
---|---|

500 | 50 |

560 | 57.60 |

610 | 65.10 |

675 | 70.25 |

700 | 74.80 |

755 | 90.66 |

790 | 92.34 |

836 | 105 |

892 | 150 |

940 | 173 |

932 | 182 |

energy (kwh) | electric bill price (dollars) |
---|---|

967 | 170 |

999 | 198 |

1,005 | 201.22 |

1,039 | 215.35 |

1,057 | 217 |

1,100 | 233 |

1,191 | 284.62 |

1,150 | 256.98 |

1,200 | 289.60 |

1,270 | 292 |

After analyzing the data, Elena concludes:

- An estimate for the correlation coefficient for the line of best fit is \(r = \text-0.98\).
- Energy consumption and the price of electric bills have a positive relationship.
- Energy consumption and the price of electric bills have a weak relationship.
- Using the linear model, the electric bill is $260 when 1,200 kWh are consumed.

What parts of Elena’s interpretation of the data do you agree with and what parts do you disagree with? Explain your reasoning.

### 10.3: Confident Players

Before Diego’s game, his coach asked each of his players, “On a scale of 1–10, how confident are you in the team winning the game?” Here is the data he collected from the team.

players | confidence in winning (1–10) | number of points scored in a game |
---|---|---|

Player A | 3 | 2 |

Diego | 6 | 10 |

Player B | 10 | 2 |

Player C | 4 | 10 |

Player D | 7 | 13 |

Player E | 5 | 6 |

Player F | 8 | 15 |

Player G | 4 | 3 |

Player H | 9 | 15 |

Player I | 7 | 12 |

Player J | 1 | 0 |

Player K | 9 | 14 |

Player L | 8 | 13 |

Player M | 5 | 8 |

- Use technology to create a scatter plot, a line of best fit, and the correlation coefficient.
- Is there a relationship between players’ level of confidence in winning and the amount of points they score in a game? Explain your reasoning.
- How many points does the linear model predict a player will score when his or her confidence is at a 4?
- Which players performed worse than the model predicted?
- Did Diego score better or worse than the linear model predicts?