## Finding the Line of Best Fit

### Drawing and Interpreting Scatter Plots

A scatter plot is a graph of plotted points that may show a relationship between two sets of data. If the relationship is from a linear model, or a model that is nearly linear, the professor can draw conclusions using his knowledge of linear functions. Figure 1 shows a sample scatter plot.

**Figure 1** A scatter plot of age and final exam score variables

Notice this scatter plot does not indicate a linear relationship. The points do not appear to follow a trend. In other words, there does not appear to be a relationship between the age of the student and the score on the final exam.

#### EXAMPLE 1

##### Using a Scatter Plot to Investigate Cricket Chirps

Table 1 shows the number of cricket chirps in 15 seconds, for several different air temperatures, in degrees Fahrenheit. Plot this data, and determine whether the data appears to be linearly related.

Chirps |
44 | 35 | 20.4 | 33 | 31 | 35 | 18.5 | 37 | 26 |

Temperature |
80.5 | 70.5 | 57 | 66 | 68 | 72 | 52 | 73.5 | 53 |

**Table **1 Cricket Chirps vs Air Temperature

##### Solution

Plotting this data, as depicted in Figure 2 suggests that there may be a trend. We can see from the trend in the data that the number of chirps increases as the temperature increases. The trend appears to be roughly linear, though certainly not perfectly so.

**Figure 2**