Introduction

“All models are wrong, but some are useful.”

— George E. P. Box

After reading this chapter you will be able to:

• Understand the concept of a model.
• Describe two ways in which regression coefficients are derived.
• Estimate and visualize a regression model using R.
• Interpret regression coefficients and statistics in the context of real-world problems.
• Use a regression model to make predictions.

Why fit statistical (regression) models?

You have some data $X_1,\dots ,X_p,Y$: the variables $X_1,\dots ,X_p$ are called predictors, and $Y$ is called a response. You’re interested in the relationship that governs them.

So you posit that $Y|X_1,\dots ,X_p\sim P_{\theta }$, where $\theta$ represents some unknown parameters. This is called regression model for $Y$ given $X_1,\dots ,X_p$. Goal is to estimate parameters. Why?

• To assess model validity, predictor importance (inference)
• To predict future $Y$’s from future $X_1,\dots ,X_p$’s (prediction)

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