Exercise 2 Page 191

Several tools exist in the world to assist you with statistical analysis, a really fancy phrase that describes interpreting and understanding data. You can use a computer or graphing calculator that is capable of doing linear regression to find the line of best fit.

What is a Line of Best Fit?

A line of best fit is exactly what it sounds like. It is the BEST line of fit! It has been optimized to have a perfectly balanced number of positive and negative residuals and is as centered as possible. Thanks to those features, it has as strong a correlation coefficient as possible for the given data.

How can we find one?

Using some handy dandy technology and a process called Linear Regression, we can have this line of best fit calculated for us! First, we enter our data into a spreadsheet on a computer or into the lists on our graphing calculator. Then, we use the linear regression function to populate a list that can look something like below.

Having entered the lists, we get output. An example of this is shown below.

The $y=ax+b$ is the statistics version of slope-intercept form. That makes $a$ your slope and $b$ your $y\text{-}$intercept. The variable $r$ is your correlation coefficient. Using that output, you know the equation for the line of best fit as well as how strongly the correlation of your data is and how well the line fits with the data.