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

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Covariance 1.Create deviations for Y and deviations for X for each observation. 2.Form the products of these deviations. 3.The graph that follows illustrates these deviations. 4.In Quadrant 1, the products of deviations are positive. 5.In Quadrant 2, the products of deviations are negative. 6.Covariance – on average, what are the products of deviations? Are the positive or negative? 7.Covariance is not widely used, because the units are often confusing. We do need it for Portfolio Analysis – where all units are $.

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Quadrant II Quadrant I Quadrant III Quadrant IV

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Correlation: Population Parameter: Estimator/Sample Statistic: 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. 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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