The motivation behind multivariate models

If you would like to measure the strength of association between a response and a predictor, you can choose a simple two-way association measure, such as correlation or the odds ratio, depending on the nature of your data. But, if your aim is to model a complex mechanism by taking into account other predictors as well, you will need regression models.

As Ben Goldacre, the evidence-based columnist for The Guardian, tells in his brilliant TED talk that the strong association between olive oil consumption and young looking skin does not imply that olive oil is beneficial to our skin. When modeling a complex association structure, we should also control for other predictors, such as smoking status or physical activity, because those who consume more olive oil are more likely to live a healthy life in general, so it may not be the olive oil itself that prevents skin wrinkles. In short, it seems that the kind of lifestyle is likely to confound the relationship...