# How to Interpret a Scatterplot

Scatterplots are useful for interpreting trends in statistical data. Each observation (or point) in a scatterplot has two coordinates; the first corresponds to the first piece of data in the pair (that’s the* X *coordinate; the amount that you go left or right). The second coordinate corresponds to the second piece of data in the pair (that’s the *Y*-coordinate; the amount that you go up or down). The point representing that observation is placed at the intersection of the two coordinates.

The above figure shows a scatterplot for the temperature and cricket chirps data listed in the following table.

Temperature Data and Cricket Chirps (Excerpt) | |

Temperature (Fahrenheit) | Number of Chirps (in 15 Seconds) |
---|---|

57 | 18 |

60 | 20 |

64 | 21 |

65 | 23 |

68 | 27 |

71 | 30 |

74 | 34 |

77 | 39 |

Because the data are ordered according to their *X*-values, the points on the scatterplot correspond from left to right to the observations given in the table, in the order listed.

You interpret a scatterplot by looking for trends in the data as you go from left to right:

If the data show an uphill pattern as you move from left to right, this indicates a

*positive relationship between X and Y.*As the*X-*values increase (move right), the*Y*-values tend to increase (move up).If the data show a downhill pattern as you move from left to right, this indicates a

*negative relationship between X and Y.*As the*X*-values*Y*-values tend to decrease (move down).If the data don’t seem to resemble any kind of pattern (even a vague one), then no relationship exists between

*X*and*Y*.

One pattern of special interest is a *linear *pattern, where the data has a general look of a line going uphill or downhill. Looking at the preceding figure, you can see that a positive linear relationship does appear between the temperature and the number of cricket chirps. That is, as the temperature increases, the number of cricket chirps increases as well. Note that the scatterplot only suggests a linear relationship between the two sets of values. It does __not__ suggest that an increase in the temperature *causes* the number of cricket chirps to increase.

A *linear relationship between X and Y *exists when the pattern of *X*- and *Y*-values resembles a line, either uphill (with a positive slope) or downhill (with a negative slope).

Scatterplots show possible associations or relationships between two variables. However, just because your graph or chart shows something is going on, it doesn’t mean that a cause-and-effect relationship exists.

For example, a doctor observes that people who take vitamin C each day seem to have fewer colds. Does this mean vitamin C prevents colds? Not necessarily. It could be that people who are more health conscious take vitamin C each day, but they also eat healthier, are not overweight, exercise every day, and wash their hands more often. If this doctor really wants to know if it’s the vitamin C that’s doing it, she needs a well-designed experiment that rules out these other factors.