# 2 the correlation coecient denitions examples

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Unformatted text preview: is an unstandardized index of how two variables linearly relate to each other. Culpepper, SA STAT 400: Statistics and Probability I (12) 4.1: Distributions of two random variables 4.2: The Correlation Coeﬃcient Deﬁnitions Examples Predictions, Best Fit Line Deﬁnition of Pearson Correlation One limitation of the covariance is that it is dependent upon the scale (i.e., variances) of the two variables. Instead, Pearson’s correlation, ρX ,Y , standardizes the covariance by dividing by the standard deviations of X and Y , ρX ,Y = σX ,Y σX σY (13) Some properties of correlations follow: Correlations fall between ±1. ρX ,Y = 0 if two random variables are independent, however, the converse is not necessarily true. Larger values of ρX ,Y imply a stronger linear association. Pearson’s correlation is sensitive to outliers and nonlinearity, in addition to other factors. Culpepper, SA STAT 400: Statistics and Probability I 4.1: Distributions of two random variables 4.2: The Correlation Coe...
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