Here we want to predict some \(y\) variable-maybe the price of a house or the number of flu cases we expect to see next week-using information from a set of predictors ( \(x\) variables). What’s driving our outcome of interest? Is one variable a stronger predictor than the other? Could we attribute what we’re seeing to causation? Our goal is to tell a story: what are we seeing in the data and why? Here we want to understand and explain the relationships in the data. Most applications of regression will fall into one of two use cases:Įxplanation. In this lesson, we learn about multiple regression models, which incorporate arbitrary combinations of categorical and numerical variables as predictors. In the last lesson, we had only categorical variables as predictors, which we learned to encode using dummies. In this lesson, we continue our discussion of the theme we introduced in the last lesson: building models that incorporate the effect of multiple explanatory variables (x) on a single response (y). Application: modeling long-term asset returns.When is the normal distribution an appropriate model?.17.3 The normal distribution, revisited.One possible solution: stepwise selection.Example: predicting the price of a house.15.6 “What variables should I include?”.Statistical vs. practical significance, revisited.15.2 Interactions of numerical and grouping variables.Example 1: causal confusion in house prices.15.1 Numerical and grouping variables together.14.3 Models with multiple dummy variables.12.5 Example: labor market discrimination.The basic recipe of large-sample inference.10.2 The four steps of hypothesis testing.10.1 Example 1: did the Patriots cheat?.9.5 Bootstrapping usually, but not always, works.Bootstrap standard errors and confidence intervals.9.1 The bootstrap sampling distribution.8.3 The truth about statistical uncertainty.What the sampling distribution tells us.7.3 Using and interpreting regression models.2.6 Importing data from the command line.Data Science in R: A Gentle Introduction.
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