### Scatterplots

A **scatterplot** is a data display consisting of the graph of a set of ordered pairs. A scatterplot shows data for two variables and helps to indicate whether there is a relationship between those variables. The data points of a scatterplot, unlike those of a line graph, are not connected by line segments.

A scatterplot can be used in the real world to analyze data to make informed decisions about a situation. For example, a forester might use a scatterplot to determine how fast maple trees in a reforested area are growing based on their age. Before plotting the data on a scatterplot, a table can be created to organize the data, which represent ordered pairs. Plotting the data on to a scatterplot can then reveal the relationship between the $x$- and $y$-values of the data set.

### Maple Tree Age and Height

Age (years) | Height (meters) |
---|---|

2 | 1.5 |

2 | 1.6 |

3 | 1.75 |

3 | 2.1 |

4 | 1.55 |

4 | 1.75 |

4 | 1.95 |

5 | 2 |

5 | 2.15 |

5 | 2.4 |

5 | 2.7 |

6 | 2.25 |

6 | 3.1 |

7 | 2.6 |

8 | 2.5 |

8 | 2.75 |

8 | 3.05 |

9 | 3.2 |

#### Scatterplot of Maple Tree Age and Height

### Trends in Data

**line of best fit**, or regression line, minimizes the sum of the squared distances to all the points in a scatterplot. When the line of best fit for a data set is graphed on a scatterplot, about half the data points will be above the line and about half will be below the line. Any line that is far away from the data points and does not follow the general direction of the data points are not lines of best fit.

#### Scatterplot with a Positive Trend

*negative*refers only to the direction of the trend, not its strength.