Linear Regression
Linear Regression
Modeling the relationship between independent () and dependent () variables.
Simple Linear Model
where errors .
Least Squares
We find the line that minimizes the Sum of Squared Errors (SSE).
Inference in Regression
We can test if the relationship is real (Test of Utility): If rejected, provides significant predictive power for .
All Chapters in this Book
Basic Concepts
Foundational mathematical framework for probability, including definitions, axioms, conditional probability, and Bayes' Theorem.
Sampling and Repeated Trials
Models based on repeated independent trials, focusing on Bernoulli trials and sampling methods.
Discrete Random Variables
Formalizing random variables, probability mass functions, and independence.
Summarizing Discrete Random Variables
Deriving numerical characteristics—expected value, variance, and standard deviation—to summarize behavior of discrete random variables.
Continuous Probabilities and Random Variables
Transitioning from discrete sums to continuous integrals, density functions, and key distributions like Normal and Exponential.
Summarising Continuous Random Variables
Extending expected value and variance to continuous variables, exploring Moment Generating Functions and Bivariate Normal distributions.
Sampling and Descriptive Statistics
Transitioning from probability to statistics: using sample data to estimate population parameters like mean and variance.
Sampling Distributions and Limit Theorems
The theoretical foundations of inference: Joint Distributions, Weak Law of Large Numbers (WLLN), and geometrical convergence via the Central Limit Theorem (CLT).
Estimation and Hypothesis Testing
The core of statistical inference: Method of Moments, Maximum Likelihood, Confidence Intervals, and Hypothesis Testing.
Linear Regression
Modeling linear relationships, least squares, and regression inference.