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Covariance and Correlation:

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Estimator/Sample Statistic: Population Parameter: ... The sample statistic or estimator is used with sample data to estimate the ... Estimator/Sample Statistic: ... – PowerPoint PPT presentation

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Title: 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.
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