# Use a Fitted Line to Predict a Future Data Point You receive observed points `(x_i, y_i)` and need to predict `y` for a future input `x_future`. Assume a provided helper fits ordinary least squares and returns a slope `m` and intercept `b`; you do not need to implement the fitting routine. Explain how you would use the returned parameters, validate that the result is meaningful, and handle cases where a straight-line extrapolation is unsafe. Include how you would evaluate predictions without leaking future information. ### Constraints & Assumptions - Inputs and fitted parameters are finite numeric values. - `x_future` may lie outside the observed range. - The points may be ordered in time, but time dependence is not guaranteed; clarify it. - The helper's fitting behavior for degenerate inputs must be defined or checked. ### Clarifying Questions to Ask - Is `x` time, and are observations equally spaced? - Is the goal one-step prediction, long-horizon extrapolation, or both? - Are there trends, seasonality, outliers, or regime changes? - What error metric and uncertainty information does the consumer need? ### What a Strong Answer Covers - The prediction formula and unit interpretation - Residual checks and a time-appropriate evaluation split - Extrapolation risk and degenerate data - Uncertainty and communication of model limitations - A decision rule for when a richer model is justified ### Follow-up Questions - What if every observed `x` value is identical? - Why is a random train-test split risky for time-ordered data? - How would one extreme point affect the fitted line? - What evidence would support adding seasonal or nonlinear terms?