Changes

* ''b'' = y-intercept in an (x, y) coordinate system

* ''b'' = y-intercept in an (x, y) coordinate system

One feature of this line is that it always passes through the centroid of the data (x, y) defined by the two arithmetic averages. The formulas for the parameters a and b are

One feature of this line is that it always passes through the centroid of the data (<math> \bar{x}, \bar{y}</math>) defined by the two arithmetic averages. The formulas for the parameters a and b are

:<math>\mathbf{Equation}</math>

:<math>a = \frac{\displaystyle \sum_{i} (x_{i}-\bar{x})(y_{i}-\bar{y})}{\displaystyle \sum_i (x_{i}-\bar{x})^2}</math>, and <math>b = \bar{y} - a\bar{x}</math>

There are two primary statistical applications for the regression line. It can be used as a sample-based estimate of an underlying linear functional relationship among the quantities of interest, or it can be employed as a predictive tool. To use the regression line for prediction, which is the most common usage in geology, simply substitute various values of x into the equation y = ax + b and solve for the corresponding predicted values of y.

There are two primary statistical applications for the regression line. It can be used as a sample-based estimate of an underlying linear functional relationship among the quantities of interest, or it can be employed as a predictive tool. To use the regression line for prediction, which is the most common usage in geology, simply substitute various values of x into the equation y = ax + b and solve for the corresponding predicted values of y.