Lectures and Labs

Stat 151A: Linear Models

• Linear algebra review materials

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Weeks 1–2

• Course philosophy
• Sample means
  • Final exam grades
• Inference in the Ames housing data

Weeks 3–4

• Multilinear Regression as loss minimization
• Familiar examples in matrix form
• Multilinear Regression as projection

Weeks 5–6

• Data transformations of the regressors
• Data transformations of the response
• Influence and outliers

Weeks 7–8

• The FWL theorem
• Multivariate random variables
• Stochastic modeling of the residual
• Regression to the mean

Weeks 9–10

• Confidence intervals and hypothesis testing
• Test statistics under the assumption of normality
• Test statistics under homoskedastic and heteroskedastic assumptions

Weeks 10–12

• Variable selection with the F–statistic
• Bias–variance tradeoff in prediction
  • Bias–variance example notebook
  • Using glmnet example notebook
• Ridge for variable selection
• Lasso for variable selection