Estimation lines (the so-called “regression” lines)

In the preceding chapter, the correlation coefficient has been treated as a tool for detecting the existence of a straight-line statistical relationship between two variates and for measuring the intensity of such a relationship. In this chapter, the presence of a straight-line relationship will be taken advantage of for estimating the value of one of the two variates, called the predicted variate, from that of the other, called the predictor variate. For instance, the relationship between the latitude X and the mean length Y in mm reached at the age of four years by the small-mouth black bass Micropterus dolomieui is illustrated in figure Figure 20.1.1. The analysis was done originally by Gérard Pageau (1967), an ichthyologist who kindly made these interesting data available. Since the lower left and upper right corners of this scatter diagram are empty, the mean length reached at the age of four years by the various local populations appears to decrease when the latitude increases. This phenomenon seems easy enough to interpret since the increase of latitude entails a decrease of the mean water temperature and a shortening of the annual growth season for this poikilothermal fish (of which the body temperature follows that of the environment).