EXAMPLE 2.8 Forecasting Earnings

Stock analysts regularly forecast the earnings per share (EPS) of companies they follow. EPS is calculated by dividing a company’s net income for a given time period by the number of common stock shares outstanding. We have two analysts’ EPS forecasts for a computer manufacturer for the next six quarters. How well do the two forecasts agree? The correlation between them is r = 0.9, but the mean of the first analyst’s forecasts is $3 per share lower than the second analyst’s mean.

These facts do not contradict each other. They are simply different kinds of information. The means show that the first analyst predicts lower EPS than the second. But because the first analyst’s EPS predictions are about $3 per share lower than the second analyst’s for every quarter, the correlation remains high. Adding or subtracting the same number to all values of either x or y does not change the correlation. The two analysts agree on which quarters will see higher EPS values. The high r shows this agreement, despite the fact that the actual predicted values differ by $3 per share.