Final answer:
The best model can be determined by using least-squares regression to minimize the SSE, while balancing bias and variance through methods like cross-validation. Weighted pooled variance is used for different sample sizes, with random sampling essential to minimize bias.
Step-by-step explanation:
To determine the best model among the available options while accounting for error terms, one should use a method that balances bias and variance to avoid overfitting or underfitting the data. We minimize the sum of squared errors (SSE), typically by using the least-squares regression line, which aims to reduce the sum of the squared vertical distances between the actual data points and the predicted points on the regression line.
Moreover, when the sample sizes are different, we should use a weighted pooled variance. Variance represents the unexplained variation within the model due to errors. This unexplained variance is fixed once we select the model. To remedy bias, a well-designed random sample is important to ensure the data aren't systematically off from the true population values. By carefully selecting a model that balances the bias and variance components, we can minimize the expected value of the error term and find the most appropriate model. In practice, a popular approach to evaluate the balance between bias and variance is cross-validation, which helps to estimate the model's predictive performance on an independent dataset.