Just three points

Linear regression by OLS on a minimal dataset

This is a medium-difficulty statistics question that tests whether you can correctly apply ordinary least squares (OLS) regression to a small, concrete dataset. It rewards accuracy in both setup and algebra, and is commonly used to verify that candidates understand the mechanics of linear regression rather than relying on black-box libraries.

Solving it requires you to compute the OLS estimators from first principles: either by setting up and solving the normal equations, or by deriving the closed-form expressions for the intercept and slope using covariance and variance. With only three points, arithmetic is manageable but requires careful bookkeeping. The question probes whether you can confidently navigate the difference between sample statistics and estimated parameters, and handle the presence of an intercept term.

• Normal equations and their matrix form
• Covariance and variance calculations on finite samples
• Role of the intercept in regression
• Interpreting OLS estimates geometrically