LINEAR REGRESSION AND CORRELATION
Simple linear regression analysis is a statistical technique that defines the functional relationship between two variables, X and Y, by the ‘‘best-fitting’’ straight line. A straight line is described by the equation, Y A BX, where Y is the dependent variable (ordinate), X is the independent variable (abscissa), and A and B are the Y intercept and slope of the line, respectively (see Fig. 7.1).* Applications of regression analysis in pharmaceutical experimentation are numerous. This procedure is commonly used:
1. To describe the relationship between variables where the functional relationship is known to be linear, such as in Beer’s law plots, where optical density is plotted against drug concentration
2. When the functional form of a response is unknown, but where we wish to represent a trend or rate as characterized by the slope (e.g., as may occur when following a pharmacological response over time)
3. When we wish to describe a process by a relatively simple equation that will relate the response, Y, to a fixed value of X, such as in stability prediction (concentration of drug versus time).