Chapter 5 · Section 2 practice

Bayesian Regression and Predictive Checks

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These questions review the examples in the companion slides. Choose an answer, then check the explanation.

Question 1

In the Bayesian regression, which quantities get a prior?

• \(x\) and \(y\)
• \(y\) only
• \(\beta_0\), \(\beta_1\) and \(\sigma\)
• The residuals \(\varepsilon_i\)

Question 2

Draw 100 lines with \(\beta_0, \beta_1 \sim N(0, 10)\). At \(x = 10\), what range covers 95 % of them?

• About ±3
• About ±10
• About ±30
• About ±200

Question 3

yrep has shape (1000, 200). What is yrep[7]?

• 1000 predictions for observation 7
• One simulated data set of 200 points, from posterior draw 7
• The 7th observed value repeated
• The posterior mean line