We are asked to explain why we estimate the line of best fit for a scatter plot. To do that, consider the following situation.
Example
The student council holds weekly meetings to discuss burning issues in the college community. Each week the turnout of people to the meetings are different.
Let's take a look at the weekly turnout in the following scatter plot. The number of students are on the y-axis and the number of weeks on the x-axis.
The council wants to estimate the number of students that will come to the fifth meeting. This way they can have the right number of chairs ready. For that, we can use the line of best fit. Let's add it onto the plot.
First, the line has a positive slope. This means that the student council should expect a greater turnout than the week before. Now, we can use the line to estimate the number of students that will come to the fifth meeting. To do so, we should find the y-value that corresponds to x=5.
The y-value is 46. This means that the expected turnout at the fifth meeting is 46 students.
Summary
We use line of best fit for scatter plots to make conjectures and estimate future data points. What is more, line of best fit also displays the trends in data.
