Question: Consider the formula b = r(sy/sx) that expresses the slope in terms of the correlation. Suppose the data are equally spread out for each variable.

Consider the formula b = r(sy/sx) that expresses the slope in terms of the correlation. Suppose the data are equally spread out for each variable. That is, suppose the data satisfy sx = sy. Show that the correlation and the slope are the same. (In practice, the standard deviations are not usually identical. However, this provides an interpretation for the correlation as representing what we would get for the slope of the regression line if the two variables were equally spread out.)

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