Linear regression of bivariate data

A form of statistical analysis that uses bivariate data (where both are numerical variables) to examine how knowledge of one of the variables (the explanatory variable) provides information about the values of the other variable (the response variable). The roles of the explanatory and response variables are therefore different.

When the bivariate numerical data are displayed on a scatter plot, the relationship between the two variables becomes visible. Linear regression fits a straight line to the data that is added to the scatter plot. The fitted line helps to show whether or not a linear regression model is a good fit to the data.

If a linear regression model is appropriate then the fitted line (regression line) is used to predict a value of the response variable for a given value of the explanatory variable and to describe how the values of the response variable change, on average, as the values of the explanatory variable change.

An appropriately fitted linear regression model estimates the true, but unknown, linear relationship between the two variables and the underlying system the data was taken from is regarded as having two components: trend (the general linear tendency) and scatter (variation from the trend).

Note: Linear regression can be used when there is more than one explanatory variable, but at level 8 only one explanatory variable is used. When there is one explanatory variable, the method is called simple linear regression.

Curriculum achievement objectives reference

Statistical investigation: Level 8

The quality of the images on this page may vary depending on the device you are using.