Statistics is easily my favourite branch of mathematics. It has a way of telling a story with numbers and applying it to everyday situations that never fails to amuse me.
In essence, statistics consists of collecting, organizing, displaying, analyzing, and interpreting data. It is then applied to scientific, industrial, and social problems.
Statistics at its core helps us understand data in a way that allows us to come up with solutions to real-life problems.
Statistics is more than math; it is a combination of art and science.
In this article, we will dive headfirst into the world of statistics, exploring five of the most interesting concepts.
Regression
Regression is the relationship between one dependent variable and an independent variable. It helps us find the perfect combination between two things — like how cookie consumption relates to your level of happiness.
The basic concept of regression would help you estimate how many cookies you would need to feel happy. Furthermore, it can also interpret whether you're having too many cookies or not enough.
Residual Sum of Squares (RSS)
The Residual Sum of Squares is a measure in statistics that adds up the squared differences between predicted values. It’s a lot like measuring the leftover mess after trying to fit a puzzle perfectly together.
RSS, in essence, calculates the total squared difference between where each puzzle piece ended up and where it should have been. It’s a way to quantify how much error or discrepancy remains between your model’s predictions and the actual observed data.
Bayesian Statistics
This part of inferential statistics is based on Bayes' theorem, or in other words, it involves a concept called “influence of prior beliefs.” This uses sequential analysis techniques to include the outcome of earlier experiments in the design of the next. It’s like a super flexible brain that adds new information to its prior set of data.
Imagine you start with an idea of how likely something is based on a past experience — like determining how good a restaurant is over time as you keep going and trying more items from the menu. As you try more items, you gain more data, and as a result, your predictions become smarter and more accurate over time.
Markov Chains
This concept of statistics contradicts Bayes' theorem in a way because now you draw conclusions solely based on the present state, with no consideration of the events that preceded it or might happen.
It’s like playing a board game with no memory of what happened in the past and how you got there. Markov chains use this idea to model sequences where the future solely depends on the present state.
Multivariate Normal Distribution
Lastly, this is a beautiful concept in the world of statistics. The entire concept can be personified where each note plays its own melody but ultimately comes together to create a harmonious piece of music.
Think of it like having random variables such as height, weight, and age of a group of people — each following a normal distribution. The multivariate normal distribution describes how they vary together and influence one another.
From this, data analysts can draw several conclusions — like insights about how each factor influences and interacts with each other. Just like a symphony conductor in a choir conducting diverse instruments into a cohesive sound producing music, the multivariate normal distribution harmonizes multiple variables into a unified probabilistic model.
Statistics offers us a beautiful way to understand numbers better — almost painting a picture with numbers. In a world with a growing demand for data scientists and analysts, it is important to see the beauty of statistics and the ways numbers can tell stories. We learn from it by listening to those stories.