Question

Suppose the correlation between two variables (x, y) in a data set is determined to be r = 0.63, what must be true about the slope, b, of the least-squares line estimated for the same set of data?

Answer 1

Since the correlation is positive, the slope b must be positive.

Answer 2

The slope, b of the regression line will be positive.

The correlation Coefficient, r , between (x, y) = 0.63

Hence, r = 0.63

A property of the slope which can be deduced from the correlation Coefficient is the sign, that is : if the slope is positive or negative.

• A negative, r value will mean that the slope of the regression line will be negative.
• A positive r value means that the slope of the regression line will be positive.

Hence, since the r value of (x, y) = 0.63 ( positive) ; then the slope of (x, y) will be positive.

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