Advanced Linear Models for Data Science 2: Statistical Linear Models

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  • Introduction and expected values
    • In this module, we cover the basics of the course as well as the prerequisites. We then cover the basics of expected values for multivariate vectors. We conclude with the moment properties of the ordinary least squares estimates.
  • The multivariate normal distribution
    • In this module, we build up the multivariate and singular normal distribution by starting with iid normals.
  • Distributional results
    • In this module, we build the basic distributional results that we see in multivariable regression.
  • Residuals
    • In this module we will revisit residuals and consider their distributional results. We also consider the so-called PRESS residuals and show how they can be calculated without re-fitting the model.