To select the best model among linear, quadratic, and exponential regressions that fit a given set of data points, additional pieces of information that could be useful include:

1. R-squared values for each model, which measure how well each regression fits the data. A higher R-squared value indicates a model that better explains the variance in the data.
2. Mean Squared Error (MSE) or Root Mean Squared Error (RMSE) for each model. These metrics provide insight into how close the predicted values are to the actual data points on average. Lower values indicate a better fit.
3. Examination of residuals to understand if there’s a pattern left unexplained by any of the models. Ideally, residuals should be randomly distributed without patterns. If a particular model shows systematic deviations in residuals, it may not be the best fit.
4. Cross-validation performance, especially if more data points are available outside the initial five. Cross-validation can help assess how well each model generalizes to unseen data, which can be critical if the model will be applied beyond these points.
5. Domain knowledge or theoretical justification for the choice of model type. For instance, if the data points represent population growth, the exponential model may be more suitable due to typical growth patterns in such contexts.

Would you like to explore any of these factors in more depth, or do you have a specific question about selecting the best regression model?

Here are some related questions to consider:

1. How does R-squared differ between linear, quadratic, and exponential models?
2. What role does MSE play in model selection, and why is it important?
3. How can examining residuals help in determining the appropriateness of a model?
4. Why is cross-validation useful in model selection?
5. When might domain knowledge overrule purely statistical metrics in model selection?

Tip: When comparing models, always ensure to balance statistical fit with practical interpretability. A complex model may fit well but might not generalize or interpret easily.