The general idea of regression

All models define the outcome (Y) as a function of one or more parameters and an independent variable (X) [or several independent variables].

The goal of is to adjust the values of the model's parameters to find the line or curve that comes closest to your data. For example, with linear regression, the goal is to find the best-fit values of the slope and intercept that makes the line come close to the data. With nonlinear regression of a normalized dose-response curve, the goal is to adjust the values of the EC50 (the concentration that provokes a response halfway between the minimum and maximum responses) and the slope of the curve.

More precisely, the goal of regression is to find the values of the parameters that are most likely to be correct. To do this requires making an assumption about the scatter of data around the curve.

The goals of regression

Scientists use regression with one of three distinct goals:

•To fit a model to your data in order to obtain best-fit values of the parameters, or to compare the fits of alternative models. If this is your goal, you must pick a model (or two alternative models) carefully, and pay attention all the results. The whole point is to obtain best-fit values for the parameters, so you need to understand what those parameters mean scientifically.

•To fit a smooth curve in order to interpolate values from the curve, or perhaps to draw a graph with a smooth curve. If this is your goal, you can assess it purely by looking at the graph of data and curve. There is no need to learn much theory.

•To make predictions.