How can you use a graph to learn about your residuals? What about a calculator?
You can graph the residuals to make sure they are centered about the x-axis or you can calculate the correlation coefficient with your calculator.
Practice makes perfect
There are two ways to use residuals to check the goodness of your 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,
data point'sy-line of fit'sy=residual,
the scatter plot of residuals should be centered around the x-axis if its 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, you 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 you have many data points, you may want to use a graphing calculator to calculate the goodness of fit. You can enter all of your data points and use the linear regression functions to find an r value, also known the correlation coefficient. The values for r will always be within the range:
-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.
