# Lesson 5

Fitting Lines

- Let’s find the best linear model for some data.

### Problem 1

*Technology required.*

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

83 | 102 |

87 | 115 |

91 | 107 |

93 | 122 |

97 | 125 |

97 | 127 |

101 | 120 |

104 | 127 |

- Use graphing technology to create a scatter plot and find the best fit line.
- What does the best fit line estimate for the \(y\) value when \(x\) is 100?

### Problem 2

*Technology required.*

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

2.3 | 6.2 |

2.8 | 5.7 |

3.1 | 4.7 |

3 | 3.2 |

3.5 | 3 |

3.8 | 2.8 |

- What is the equation of the line of best fit? Round numbers to 2 decimal places.
- What does the equation estimate for \(y\) when \(x\) is 2.3? Round to 3 decimal places.
- How does the estimated value compare to the actual value from the table when \(x\) is 2.3?
- How does the estimated value compare to the actual value from the table when \(x\) is 3?

### Problem 3

Which of these scatter plots are best fit by the shown linear model?

### Problem 4

A seed is planted in a glass pot and its height is measured in centimeters every day.

The best fit line is given by the equation \(y = 0.404x-5.18\), where \(y\) represents the height of the plant above ground level, and \(x\) represents the number of days since it was planted.

- What is the slope of the best fit line? What does the slope of the line mean in this situation? Is it reasonable?
- What is the \(y\)-intercept of the best fit line? What does the \(y\)-intercept of the line mean in this situation? Is it reasonable?

### Problem 5

At a restaurant, the total bill and the percentage of the bill left as a tip is represented in the scatter plot.

The best fit line is represented by the equation \(y = \text{-}0.632x + 27.1\), where \(x\) represents the total bill in dollars, and \(y\) represents the percentage of the bill left as a tip.

- What does the best fit line estimate for the percentage of the bill left as a tip when the bill is $15? Is this reasonable?
- What does the best fit line predict for the percentage of the bill left as a tip when the bill is $50? Is this reasonable?

### Problem 6

A recent study investigated the amount of battery life remaining in alkaline batteries of different ages. The scatter-plot shows this relationship between the different alkaline batteries tested.

The scatter plot includes a point at \((7, 15)\). Describe the meaning of this point in this situation.