Statistics for CSAI 2

by Albert Major

CORRELATION AND WHY IT MATTERS

• You study correlation to understand how two variables move together.
• You need this for regression, which is the next major topic in the course.
• Correlation, covariance, partial correlation, and non-parametric correlation are tools you will use in data analysis, modeling, and your thesis.

COVARIANCE RECAP

• Covariance measures how two variables vary together.

• Formula structure

  • For each observation, take the difference from each mean.

  • Multiply the two differences.

  • Sum everything.

  • Divide by n minus 1.

• A positive covariance means they increase together.

• A negative covariance means one goes up while the other goes down.

• Problem

  • Covariance is in raw units, so you cannot interpret it directly.

  • If income is in euros and years of education is in years, the covariance mixes both scales.

STANDARDIZING TO GET THE PEARSON CORRELATION

• Correlation removes units. It becomes scale free.

• Formula

  • r equals covariance divided by the product of the two standard deviations.

• Meaning

  • r always lies between minus 1 and plus 1.

  • This makes it easy to compare across studies and tasks.

• Example from lecture

  • Covariance is 500.

  • Standard deviations are 10000 and 2.

  • Product equals 20000.

  • r equals 500 divided by 20000 equals 0.025.

  • This is almost zero, so the relationship is weak.

INTERPRETING r

• r equals 0 means no linear relationship.