# Evaluate Linear Regression Assumptions and Fit Three Points Discuss the assumptions behind ordinary least squares, how multicollinearity affects a fitted model, and practical ways to address multicollinearity and overfitting. Then fit a simple linear regression with an intercept to the three observations `(0, 0)`, `(0, 1)`, and `(1, 1)`. Report the fitted line and its residual sum of squares. ### Constraints & Assumptions - Use ordinary least squares with one predictor and an intercept. - Treat residual sum of squares as the requested least-squares error. - Distinguish assumptions needed for coefficient interpretation or classical inference from concerns that mainly affect prediction quality. ### Clarifying Questions to Ask - Is the goal causal interpretation, statistical inference, or prediction? - Should “error” mean residual sum of squares, mean squared error, or another normalized quantity? Use residual sum of squares here. ```hint Separate the two goals Organize the discussion by what makes coefficients meaningful and what makes uncertainty estimates reliable before doing the three-point arithmetic. ``` ### Part 1 — Assumptions and Remedies Explain the linear conditional-mean assumption, exogeneity, error dependence, error variance, multicollinearity, and the role of normality. Describe diagnostics and remedies for multicollinearity and overfitting without treating every assumption as interchangeable. #### What This Part Should Cover - Which violations bias coefficients, which inflate uncertainty, and which invalidate common standard errors. - Feature removal or combination, additional data, regularization, and validation-based model selection. ### Part 2 — Fit the Three Observations Derive the slope and intercept for the specified points, list all three fitted values and residuals, and calculate the residual sum of squares. #### What This Part Should Cover - A reproducible least-squares calculation and an exact final error. - A check that the intercept and slope satisfy the normal equations. ### What a Strong Answer Covers - Correct separation of modeling assumptions, diagnostics, remedies, and exact arithmetic for the fitted line. ### Follow-up Questions - What line results if the intercept is forced to zero? - How does ridge regression change the treatment of correlated predictors?