This unit introduces statistical inference for single‑predictor linear regression. Building on the examples from last week, we will learn about estimators and their properties, such as standard errors and confidence intervals. We will then derive unbiased estimators of the paramaters in a linear regression model. We will learn about coefficient of determination and correlations – two key quantities we use to access the relationship between variables in a linear regression model. Regression to the mean will also be covered.
Material:
Estimators, bias and consistency, Linear regression (single predictor) model and assumptions, Covariance, correlation and their relationship to regression slope. Regression to the mean. Least squares interpretation of covariance formula. Hypothesis testing for regression models.