Linear regression is a mathematical process that replaces information provided by a scatter plot by a line that has the same general properties, assuming that the relationship that connects the two variables involved is linear.
- The line found in this way is a line of regression. The line of regression also allows us to interpolate or extrapolate new results that have the same properties as the scatter plot obtained experimentally.
- The line of regression is a theoretical line that represents the correlation between two statistical characters considered from one population.
- We say “regression” because it consists of reducing a set of one-time observations to a single continuous model that allows us to obtain new results.
Example
This scatter plot represents the data obtained on two statistical characteristics from the same population. The line is the graphic representation obtained here by a method of calculation that is called the method of least squares.
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Educational Note
To draw a line of regression freehand, we can apply these rules:
- Orient the line in the same direction as the one suggested by the scatter plot;
- Draw the line so that there are as many points above it as below it.