+1 : perfectly positive linear relationship.-1 : perfectly negative linear relationship.The sign of the correlation coefficient indicates the direction of the relationship, while the magnitude of the correlation (how close it is to -1 or +1) indicates the strength of the relationship. Where cov( x, y) is the sample covariance of x and y var( x) is the sample variance of x and var( y) is the sample variance of y.Ĭorrelation can take on any value in the range. The sample correlation coefficient between two variables x and y is denoted r or r xy, and can be computed as: $$ r_ $$ Random sample of data from the population.Linearity can be assessed visually using a scatterplot of the data. This assumption ensures that the variables are linearly related violations of this assumption may indicate that non-linear relationships among variables exist.Each pair of variables is bivariately normally distributed at all levels of the other variable(s).Each pair of variables is bivariately normally distributed.The biviariate Pearson correlation coefficient and corresponding significance test are not robust when independence is violated.no case can influence another case on any variable.for any case, the value for any variable cannot influence the value of any variable for other cases.
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