An association is linear when there is no strong curvature present in the scatterplot.

The correlation is close to [r = 0], when the pattern slopes does not slope upwards nor downwards.

More precisely, an association that is linear with a correlation coefficient close to 0 needs to have a pattern that is (nearly) horizontal in the scatterplot.

For example, the following graph then has a correlation close to [r = 0] while also being linear.

The correlation is close to [r = 0], when the pattern slopes does not slope upwards nor downwards.

More precisely, an association that is linear with a correlation coefficient close to 0 needs to have a pattern that is (nearly) horizontal in the scatterplot.

For example, the following graph then has a correlation close to [r = 0] while also being linear.