We are often interested in understanding the relationship among several variables. Scatterplots and scatterplot matrices can be used to explore potential relationships between pairs of variables. Correlation provides a measure of the linear association between pairs of variables, but it doesn’t tell us about more complex relationships. For example, if the relationship is curvilinear, the correlation might be near zero. Four Scatterplots
You can use regression to develop a more formal understanding of relationships between variables. In regression, and in statistical modeling in general, we want to model the relationship between an output variable, or a response, and one or more input variables, or factors.
Depending on the context, output variables might also be referred to as dependent variables, outcomes, or simply Y variables, and input variables might be referred to as explanatory variables, effects, predictors or X variables.
We can use regression, and the results of regression modeling, to determine which variables have an effect on the response or help explain the response. This is known as explanatory modeling.
We can also use regression to predict the values of a response variable based on the values of the important predictors. This is generally referred to as predictive modeling. Or, we can use regression models for optimization, to determine settings of factors to optimize a response. Our optimization goal might be to find settings that lead to a maximum response or to a minimum response. Or the goal might be to hit a target within an acceptable window.
For example, let’s say we’re trying to improve process yield.
- We might use regression to determine which variables contribute to high yields,
- We might be interested in predicting process yield for future production, given values of our predictors, or
- We might want to identify factor settings that lead to optimal yields.
We might also use the knowledge gained through regression modeling to design an experiment that will refine our process knowledge and drive further improvement.