Inferential Statistics

Preface

Inferential statistics play a crucial role in data analysis, enabling us to make predictions and draw conclusions from sample data about a larger population. This document aims to elucidate three fundamental components of inferential statistics: confidence intervals, statistical tests, and Gaussian linear regression. Each of these components offers unique insights and tools for dealing with uncertainty and variability in data, which are pervasive challenges in statistical analysis.

Confidence Intervals

Confidence intervals provide a range of values, estimated from the data, that is likely to contain the population parameter of interest. By constructing confidence intervals, we can quantify the uncertainty of our estimates, which is vital for making informed decisions. This section will cover the conceptual foundation and practical computation of confidence intervals, highlighting their interpretation and limitations.

Statistical Tests

Statistical tests are a cornerstone of inferential statistics, used to make decisions or test hypotheses about population parameters based on sample data. We will delve into various types of statistical tests, focusing on their assumptions, implementation, and how to interpret their results. Special attention will be given to tests of means, variances, and proportions, along with discussions on the power and size of tests.

Gaussian Linear Regression

Gaussian linear regression, commonly known as ordinary least squares regression, is a predictive modeling technique that assumes a Gaussian distribution of the error terms. This section will explore the theory behind linear regression, the assumptions it relies on, and its application in predicting continuous outcomes. Practical examples will demonstrate how to fit, validate, and interpret regression models in various contexts.