Further features of the hat matrix; y=Hy, X=HX, e=(I-H)y  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Regression vodcast 3.3

Properties of (I-H); symmetric, idempotent, trace = n-p  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Regression vodcast 3.2

This video shows that the Binomial belongs to the Exponential Family.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Exponential.Family_the.Binomial

In this video Bayes' theorem is applied to the Binomial density, choosing an appropriate conjugate prior.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Binomial.Conjugate.Analysis

Brief slide explaining how to estimate phi in a GLM  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

GLMs - estimating phi

The Normal density written in (Canonical) form of the Exponential Family format suitable for GLMs  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Normal Density (Canonical) Exponential Family Format

Brief outline of the canonical form of the exponential family, illustrated with the Poisson distribution.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Exponential family (canonical form)

This briefly and roughly introduces the standard uniform distribution  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Introduction to Standard Uniform Distribution

Here we set out the simplest statistical model we could perhaps suggest for the regression situation, and see what beta_2 is in terms of moments  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Regression: one possible model

Maximum likelihood for the Normal distribution  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Maximum_likelihood_mu_js

Our Applied Statistics courses give you the opportunity to use professional software and real data. Statistics research aims to develop novel statistical methodology motivated by applications including medicine, environmental and official statistics.

A brief introduction to the hat matrix, and some ideas around leverage  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Hat matrix

This attempts to sketch out regression as a problem for vec(y), vec(x1), vec(x2) etc.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Regression as a projection problem

Assumes we've done this in a previous course (linear algebra/calculus or even statistics)  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Revision of single variable least squares

We briefly outline the kind of work we intend to develop by examining a simple regression model fitted to the Zagat data on New York Restaurants.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Regression-application to New York Restaurant Prices

A description of the Moment Generating Function for the Poisson distribution, and one example of its use.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Poisson MGF

Brief explanation of the Poisson probability mass function (no explanation of where the formula comes from, but there is a check that it is a valid probability function and we find E[X])  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

The Poisson PMF

Description of the Binomial(n,p) distribution, find the first moment, state Var(X)  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Binomial

Some properties and derivation of the Geometric distribution, including check on validity and finding E[X]  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Geometric Distribution

Finds the maximum likelihood estimator for the exponential distribution  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Exponential MLE

A brief description of how we obtain the Binomial m.l.e.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Binomial MLE

Statistics

This gives the variance of a Random variable in terms of its expectation  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Variance of a random variable

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