Covariance(Numeric Data Covariance is similar to correlation ∑=1(a-A)(b-B) OU (A,B)=E(4-A)(B-B)= Cou(A, B) Correlation coefficient: TA, B- 0AOB where n is the number of tuples, A and b are the respective mean or expected values of a and b, oa and oB are the respective standard deviation of a and B Positive covariance: If cova>0, then a and b both tend to be larger than their expected values Negative covariance: If CovA B <0 then if a is larger than its expected value, B is likely to be smaller than its expected value Independence: CovAB =0 but the converse is not true Some pairs of random variables may have a covariance of o but are not independent. Only under some additional assumptions(e.g, the data follow multivariate normal distributions) does a covariance of 0 imply independence 同济大学软件学院 ool of Software Engineering. Tongpi Unversity 2020 Covariance (Numeric Data) ◼ Covariance is similar to correlation where n is the number of tuples, and are the respective mean or expected values of A and B, σA and σB are the respective standard deviation of A and B. ◼ Positive covariance: If CovA,B > 0, then A and B both tend to be larger than their expected values. ◼ Negative covariance: If CovA,B < 0 then if A is larger than its expected value, B is likely to be smaller than its expected value. ◼ Independence: CovA,B = 0 but the converse is not true: ◆ Some pairs of random variables may have a covariance of 0 but are not independent. Only under some additional assumptions (e.g., the data follow multivariate normal distributions) does a covariance of 0 imply independence A B Correlation coefficient: