Practical Applications of Bayesian Reliability

9Regression Models

This chapter introduces how to use Bayesian methods to build linear regression and binary logistic regression models. Examples and R scripts are provided. We also show how to use a Bayesian regression model to make predictions.

9.1 Linear Regression

Linear regression builds a relationship between a continuous response variable (also called a dependent variable) and one or more predictors (also called independent variables) by fitting a linear equation to observed data.

A simple linear regression model builds a relationship between a continuous response variable and one predictor, and the relationship is a straight line, i.e.

9.1

where

• y is the response (or dependent variable, or predicted variable)
• x is the predictor (or independent variable, or regressor variable)
• β₀ and β₁ are unknown regression coefficients
• β₀ is the intercept, which is the mean of the distribution of y when x equals to zero
• β₁ is the slope coefficient, which indicates the change of the mean of the distribution of y when x changes by a unit
• ε is the error term, which is assumed to follow a normal distribution with a mean of 0 and unknown variance σ².

Thus, at each given value of x, the distribution of y has a mean of β₀ + β₁x and variance σ². This makes a simple linear regression model easy to use in various fields.

For example, a linear regression equation can be used to establish the ...