How can you use a graph to learn about your residuals? What about a calculator?
We can graph the residuals to make sure they are centered about the x-axis or we can calculate the correlation coefficient with our calculator.
Practice makes perfect
There are two ways to use residuals to check the appropriateness of our line of fit.
By graphing
With a calculator
Graphing
Because residuals are the difference between the y-coordinate of the data point and the y-coordinate produced by the line of fit, a scatter plot of residuals should be centered around the x-axis if the line is a good line of fit. Positive residuals will be above the x-axis and negative residuals will be below the x-axis.
If the line of fit is a bad fit, we will have too many positive or negative residuals and not enough of the other.
The above residual graph shows a line of fit that lies below most of the data points rather than being centrally placed — there are 8 positive residuals and only 3 negative residuals. If the line of fit is a good fit, the scatter plot will be evenly divided by the x-axis like the one below.
Calculator
If we have many data points, we may want to use a graphing calculator to calculate the line of fit. Enter all of the data points and use the linear regression function to find the r value, also known the correlation coefficient. The values for r will always fall between 1 and - 1.
-1≤ r≤1
When r is close to -1, it is a strong negative correlation and the line is a good fit. When r is close to 1, it is a strong positive correlation and the line is a good fit. When r is close to 0, it is a weak correlation, the line is a bad fit or the data just has no correlation to it.
