Introduction to Statistics
Statistics is the science of collecting, analyzing, interpreting, and presenting data. While probability theory provides the mathematical tools to describe theoretical randomness, statistics gives us the tools to infer properties of the underlying probability distributions from real-world, empirical data.
Core Concepts
- Descriptive Statistics: Summarizing and organizing data so it can be easily understood. Includes measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation, range).
- Inferential Statistics: Using a random sample of data taken from a population to describe and make inferences about the population.
- Hypothesis Testing: A formal procedure for investigating our ideas about the world using statistics. It involves a null hypothesis (the default position) and an alternative hypothesis.
- Estimators: Rules for calculating an estimate of a given quantity based on observed data. A good estimator is unbiased and has low variance.
- Regression Analysis: A set of statistical processes for estimating the relationships among variables. Linear regression is widely used in finance to model the relationship between an asset's return and market risk factors.