A model for y — f X

Reaction yield as a function of temperature, in the 40-60°C range, with catalyst A 

To determine the values of Po and Pi we should fit Eq. (5.1a) to the five pairs of values (yi, Ti) in Table 5.1. That is, we should solve a system of five equations, 

Matrix Eq. (5.1b) has the important advantage of remaining valid in general, for any number of observations or model parameters. All that needs to be done, as the model changes, is to augment the matrices correspondingly, as we will see later. 

In practical terms, to pass closest to means to minimize the distance of the points to the line, that is, minimize the total length of the vertical segments in Fig. 5.3. The traditional way of doing this is to locate the line in such a way that the sum of the squares of the residuals — the vertical distances — is minimal. For this reason, the method is called a 

Since the yi values are known before making the regression, the residuals wiU depend only on the values we choose for bo and b. For the least-squares fit, these values are the ones that make e small as possible. 

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