Module · More than one thing✅Knowledge checkCheck: can you choose a model honestly?5 questions · Pass at 60%1. Fitted on its own, newspaper's coefficient is clearly positive. Fitted alongside TV and radio, it is zero. What happened?The larger model is less accurate, so its coefficients are less trustworthyNewspaper and radio budgets travel together — fitted alone, newspaper was taking credit for radio's workAdding columns always shrinks the earlier coefficientsNewspaper's effect is real but too small to measure with 200 markets2. You add a column of random numbers to a regression. What happens to R²?It falls, because the column is uselessIt stays exactly the sameIt rises — R² can never fall when a column is addedIt rises or falls depending on the random numbers3. What question is adjusted R² really asking about a new column?Is this column statistically significant?Did this column do more for the model than a column of random numbers would have?Does this column correlate with the target?Is this column independent of the others?4. Which of these comparisons carries no information at all?AIC between two models fitted on the same marketsAdjusted R² between a two-column and a three-column model on the same marketsAIC between a model fitted on all markets and one fitted only on markets with no missing valuesCross-validated RMSE between two models over the same folds5. A model scores far better on the markets it was fitted to than on markets it has never seen. What is that, and what would reveal it?Overfitting — and only a held-out score reveals it, because the training score cannotBias — and a residual plot reveals itExtrapolation — and checking the range of the data reveals itNothing unusual; training scores are always betterCheck answers← Back to Regression I — predicting a numberNext topic →
