Final answer:
The untrue statement is that we can always get a perfect prediction with more effort. While stronger correlations and smaller relative errors imply better models, perfect prediction is unachievable due to inherent randomness and variability.
Step-by-step explanation:
The statement that is NOT true from the options provided is: 'We can always get a perfect prediction if we try harder.' The essence of prediction models, particularly in linear regression, is that they summarize the general patterns in data. However, they do not account for the random components or unique variations present in real-world data. Our predictive models improve with higher correlation coefficients and smaller relative errors, but there's a limitation due to intrinsic randomness that can never be completely eliminated, precluding the possibility of always making a perfect prediction.
Relative errors are important in assessing the model's accuracy. A smaller relative error means the prediction is closer to the actual value. Yet, precision and accuracy in predictions are subject to the limitations imposed by the data and the natural variability in the relationships between variables. Correlation between X and Y can indicate a strong linear relationship but does not guarantee perfect prediction.
The size of the errors indeed indicates how good the line is as a model, and higher correlations generally produce smaller relative errors, providing a better model fit. However, even with small errors and a high correlation, the predictive capability is never perfect due to the aforementioned reasons.