Example of Covariance

An engineer at an aluminum castings plant assesses the relationship between the hydrogen content and the porosity of aluminum alloy castings. The engineer collects a random sample of 14 castings and measures the following properties of each casting: hydrogen content, porosity, and strength.

The engineer uses the covariance to examine the linear relationship between each pair of variables.
  1. Open the sample data, AluminumProperties.MTW.
  2. Choose Stat > Basic Statistics > Covariance.
  3. In Variables, enter hydrogen Porosity Strength.
  4. Click OK.

Interpret the results

The covariance between hydrogen and porosity is 0.00357582, which suggests, that as hydrogen content increases, porosity also increases. The covariance between hydrogen and strength is −0.00704865 and the covariance between porosity and strength is −0.03710245. Both of these covariances are negative, which indicates that as either hydrogen or porosity increase, strength tends to decrease.

Covariances: hydrogen, Porosity, Strength