Polynomial regression is a considered a special case of linear regression where higher order powers (x2, x3, etc.) of an independent variable are included. It's appropriate where your data may best be fitted to some sort of curve rather than a simple straight line. The polynomial module of numpy is easily used to explore fitting the best... Continue Reading →

# Co-variance, Correlation & Linear Regression

Typically we have 2 sets of values and we want to find out if these 2 sets of values are related, and if so how, and by how much? Could height be indicative of weight? Could hours of practice be related to how many errors are made in a mathematical test paper? Co-variance is a... Continue Reading →

# Linear algebra – check!

It's been a quiet few weeks on this blog as I spent nearly every spare moment wrestling with the challenges of linear algebra - and I'm in a celebratory mood this afternoon having passed everything within time! I must say that, having some tentative foundational skills, I'm left with 2 main feelings: A tremendous sense of... Continue Reading →

# A gem of a book :)

I've just bought this delightfully titled book: No bullshit guide to linear algebra by Ivan Savov. It's not necessarily easy learning everything you need to know about linear algebra for machine learning in 5 weeks (is that just me???) - so when I hit a bit of a brick wall in week 4 I went looking... Continue Reading →

# Conditional probability refresher

Probability is always... A number between 1 (certain) and 0 (impossible): 1 ≤ P ≥ 0 The probability experiment A process that can be repeated & in which the outcome will be uncertain rolling a dice, tossing a coin, selecting a card The sample space A list of all possible outcomes of a probability experiment,... Continue Reading →

# T testing – a worked example

A simple one-sample T-test This variant on hypothesis testing is used when you have limitations, specifically: The population standard deviation (σ) is unknown and your sample size (n) is <30 The fundamentals The formula is a variant of what we've seen thus far, where x̄ = your sample mean, μ = a hypothesized population mean,... Continue Reading →

# Proportion testing

Using everything we've learned so far about the central limit theorem, the z-score, and hypothesis testing, we can now also perform proportion testing! There are just a few new concepts to add into the mix: The preliminary terrors - notation & terminology p = the proportion of items that falls into H0 q = the... Continue Reading →

# Hypothesis testing basics

A simple example of hypothesis testing is where we know what "normal" is, and we want to evaluate whether some sample conforms to our understanding of "normal", or is so unusual that it's indicative of an actual shift in behaviour or pattern. Make your hypothesis statement If I…(do this to an independent variable)….then (this will... Continue Reading →

# Preliminary terrors of statistics

The "preliminary terrors", of course, being the notation as Silvanus P. Thompson so aptly described them :). Pronunciation μ sounds like "mew" σ sounds like "sigma" x̄ sounds like "x-bar" The population So we can think of this as the complete set of "things", whatever the "things" are that are under consideration - for example... Continue Reading →