A First Course in Statistics, 12th Edition

9.2 Fitting the Model: The Least Squares Approach

After the straight-line model has been hypothesized to relate the mean E(y) to the independent variable x, the next step is to collect data and to estimate the (unknown) population parameters, the y-intercept ${\beta }_0$ and the slope ${\beta }_1.$

Consider the experiment described in Example 9.1 (p. 503), where we want to determine the relationship between the percentage (x) of a certain drug in the bloodstream and the length of time (y) it takes to react to a stimulus. Data were collected for five subjects, and the results are shown in Table 9.1. (The number of measurements and the measurements themselves are unrealistically simple in order to avoid arithmetic confusion in this introductory example.) This set ...