Linear Regression Regression is an analytic technique for modeling the relationship between a dependent wvariable and an independent variable. Linear regression is used when the two variables have a linear association (i.e. changes in one variable tend to be proportional to changes in the other). Using linear regression, we are able to create an equation for the regression line or line of best fit (LOBF), rather than simply estimating it by drawing it through a series of points. A. Using the Least Squares Method to Find the LOBF Drawing in a line of best fit usually involves some compromise: we move the line closer to some points while increasing its distance from other points; we strive to have a similar number of points above the line as below the line; and we take into consideration the relative distances from each point to the line. The least squares method formalizes this and gives us a precise method for determining the line. A residual is * Residuals are positive * Residuals are negative For the LOBF in the Least Squares Method: - For the LOBF in the Least S5guares Method: - y=mx+b where m= When we have the equation of the regression line, we can estimate values and make predictions by: Interpolating Extrapolating