stats[describe,linearcorrelation]  Coefficient of linear correlation between two data lists

Calling Sequence


stats[describe, linearcorrelation](data1, data2)
describe[linearcorrelation](data1, data2)


Parameters


data1



first statistical list

data2



second statistical list





Description


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The function linearcorrelation of the subpackage stats[describe, ...] computes the coefficient of linear correlation between two statistical lists.

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The linear correlation measures how well a linear function (a straight line) explains the relationship between two data lists. If a straight line is an excellent explanation of the relationship, then the linear correlation coefficient will have a high magnitude. The correlation is positive if an increase in one variable corresponds to an increase in the other, and negative when an increase in one corresponds to a decrease in the other. The range of this function is 1 (high negative correlation) to 0 (no linear correlation) to 1 (high positive linear correlation).

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The two data lists must have the same number of observations, with the same weights for each corresponding element.

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The coefficient of linear correlation is computed by dividing the covariance by the square root of the product of the variance of the two data lists.

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Classes are assumed to be represented by the class mark, for example 10..12 has the value 11.

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See stats[describe, covariance] and stats[describe, variance] for the treatment of missing data.

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There are other measures of correlation besides the linear correlation. A low value for the coefficient of linear correlation does not imply that the data is not correlated. For example, if the pairs of data describe a circle, the correlation is high with respect to the circle, but low with respect to a straight line.

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The command with(stats[describe],linearcorrelation) allows the use of the abbreviated form of this command.



Examples


Important: The stats package has been deprecated. Use the superseding package Statistics instead.
>


These two sets of data are on an increasing straight line
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 (1) 
>


 (2) 
>


 (3) 
These are on a decreasing straight line
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 (4) 
>


 (5) 
>


 (6) 
These have low correlation
>


 (7) 
>


 (8) 
>


 (9) 


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