Online class on Tuesday, March 16, from 14h30 to 17h00

[Slides 116-155] The Linear Model (in the regression context): the additional assumptions, the vector notation. Tools for random vectors: the  expected vector and its properties; the (co-)variance matrix and its properties; the MultiNormal distribution and its properties. The Linear Model in vector notation. The consequences of the Linear Model for the observations of the response vector Y (Normal distribution, independence). The vector of parameter estimators Beta-hat: definition; its probability distribution under the Linear Model and its interpretation. The final hurdle to using the distribution of each beta-hat_j for inference: the unknown variance of random errors, sigma^2. Estimating sigma^2 with the Residual Mean Square (QMRE). The effect of replacing sigma^2 with QMRE on the distribution: the appropriate Student's-t distribution. A confidence interval for any parameter beta_j: deduction and interpretation. Hypothesis tests for any beta_j.