# Linear Regression

## Linear Regression

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.

### 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.