Linear regression assumes the existence of a linear relationship between the input variables and the observed output. In general, a successful model must satisfy several requirements to be considered acceptable as a predictive tool :
- sufficiently high \(R^2\) (typically, at least 0.7) - this will confirm that a large proportion of variation in the dependent variable can be explained by the variation in the independent variable(s);
- reasonably good visual fit between the straight line predicted by the model and the actual functional relationship between the dependent and independent variables;
- sufficiently random residuals (at least no noticeable trend)
Once these requirements have been satisfied, the model can be deemed sufficiently accurate for our needs.