It tells us just how strong of a linear relationship exists between the two quantitative variables we are using. A correlation near 0 indicates that there is not a strong linear relationship; a value near (-1) indicates the relationship is strong and the association is a negative one; a value near (+1) indicates a strong positive linear relationship. Note: It is possible to have a strong nonlinear relationship for which the value of r is close to 0.

• converting all of the heights to inches and recalculating the correlation?
• adding to the data one more observation that lay well off of the regression line?

• The change in units would have no effect on the value of r. The new r would be exactly the same as the old one.
• The new observation would make the relationship less strongly linear, and we would expect the value of r to move away from 1 (move closer to 0).
  

  Note: We assumed above that the relationship was already strongly linear before the extra data point was added. It is possible that, by adding an outlier, we can make a semi-strong linear relationship even stronger. This is illustrated in Problem 2.4 (and Figure 2.9, p. 119).

A likely formula is

x = y - 3        or, equivalently,       y = x + 3.

This is an equation of a line (slope is 1, y-intercept is 3).