Other Concerns In Applying Linear Regression Just like ANOVA, linear regression has assumptions concerning the origin and structure of the dependent variable. Linear regression results are only meaningful if these assumptions have been met. Linear regression assumes that the residuals follow a normal distribution with constant standard deviation, as outlined below. Residuals The coefficients and significance values that result from regression analysis are calculated under the assumption that a straight line is a good model for the relationship. How well a line serves as a model for the relationship can be checked by looking at how the actual observations sit in relation to the predicted values along the line. This is measured by the vertical distance from the prediction to the actual observation and is called the residual (illustrated with the dashed lines in Figure 7.9). Regression coefficients are calculated so that the resulting line has the lowest possible accumulation of residuals, minimizing the overall distance between the observations and the predictions.
