9.2 New terms

Response variable: \(Y\)

Predictor variables: \(X_{1}, X_{2}, ..., X_{p}\)

• When we want to analyze a quantitative response : Regression

• When we want to analyze a categorical response: Classification

In this chapter we will focus on the Normal regression model.

Our toy example will come from a bike sharing service. We will try to understand the demand for it service.

Source: Washington Business Journal

We want a model of the number of rides/day.

• Poisson model is not valid here because we do not have an equal mean and variance.
• Instead we are going to go with a normal model:

\[\begin{array}{rcl} Y_{i}|\mu, \sigma & \overset{ind}{\sim} & N(\mu, \sigma^2) \\ \mu & \sim & N(\theta, \tau^2) \\ \sigma & \sim & \text{[some other prior model]} \\ \end{array}\]

Here the predictor variable will be the temperature in Fahrenheit.