Covariance and Correlation:

1
Covariance and Correlation
Covariance and correlation measure linear
association between two variables, say X and Y.
Covariance
Population Parameter
The population parameter describes linear
association between X and Y for the population.
Estimator/Sample Statistic
The sample statistic or estimator is used with
sample data to estimate the linear association
between X and Y for the population.
2
Covariance

• Create deviations for Y and deviations for X for
  each observation.
• Form the products of these deviations.
• The graph that follows illustrates these
  deviations.
• In Quadrant 1, the products of deviations are
  positive.
• In Quadrant 2, the products of deviations are
  negative.
• Covariance on average, what are the products of
  deviations? Are the positive or negative?
• Covariance is not widely used, because the units
  are often confusing. We do need it for Portfolio
  Analysis where all units are .

3
Quadrant II
Quadrant I
Quadrant IV
Quadrant III
4
Correlation
Correlation measures the degree of linear
association between two variables, say X and Y.
There are no units dividing covariance by the
standard deviations eliminates units. Correlation
is a pure number. The range is from -1 to 1. If
the correlation coefficient is -1, it means
perfect negative linear association 1 means
perfect positive linear association.
Population Parameter
Estimator/Sample Statistic
The sample statistic or estimator is used with
sample data to estimate the linear association
between X and Y for the population.