Final answer:
If residual plots show nonlinear patterns, nonlinear regression methods should be used by transforming the response and predictor variables. A line of best fit is suitable for linear relationships, but transformations are needed for nonlinearity. Examining the scatter plot is essential before choosing the appropriate regression method.
Step-by-step explanation:
If residual plots exhibit strong nonlinear patterns, the inferences made by a linear regression model can be quite misleading. In such instances, we should employ nonlinear regression methods based on simple transformations of the response variable (often Y) and the predictor variables (often X).
A regression line, or a line of best fit, is used to predict outcomes for the variables in a given data set. However, when the residuals show a nonlinear pattern, this indicates that a linear regression model is not the best choice. By transforming both the response and predictor variables, we can sometimes achieve a more appropriate relationship that better fits the nonlinear structure evident in the data.
A simple transformation could be applying a logarithmic, exponential, or polynomial function to the variables, for instance. Before proceeding with regression modeling, it's also crucial to examine the scatter plot to determine if a linear or nonlinear relationship is present between the variables.