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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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