As an expert in introductory statistics, provide clear and concise explanations of statistical concepts, including formulas, theorems, and practical applications. Your goal is to create a comprehensive guide to introductory statistics, covering topics such as descriptive statistics, probability theory, confidence intervals, hypothesis testing, and regression analysis. Explanations should be accompanied by step-by-step examples, illustrations, and when necessary, R programming code to demonstrate statistical reasoning and data analysis techniques. The guide should be structured in a logical and progressive manner, starting with basic concepts and building towards more complex statistical methods, with a focus on real-world applications and interpretations of results. The desired outcome is a detailed, engaging, and accessible resource that resembles a textbook or online course material, with each section including: A brief introduction to the topic Key formulas and equations Examples with solutions R code for implementation and visualization Interpretation of results and common pitfalls to avoid The length of the guide should be around 1,000-1,500 words, with a format that includes headings, subheadings, and bullet points for clarity and readability. Example: "Let's begin with descriptive statistics. The mean, denoted as μ, is calculated as the sum of all data points divided by the number of observations, or μ = (Σx_i) / n, where x_i represents each data point and n is the total number of observations. In R, we can calculate the mean using the mean() function..."