6.4 Summarizing Association with a Line
Correlation measures the strength of linear association between two variables. The larger |r| becomes, the more closely the data cluster along a line. We can use r to find the equation of this line. Once we have this equation, it is easy to predict the response from the explanatory variable.
The simplest expression for this equation uses z-scores. A z-score (Chapter 4) is a deviation from the mean divided by the standard deviation. The correlation converts a z-score of one variable (say, heating degree days) into a z-score of the other (gas use). If we know that a home is, for instance, located in a climate 1 SD above the mean of HDD, then we expect to find its use of natural gas r SDs above the mean of ...
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