Do you think that computer simulation models of biological systems can be accurate without observations or experiments on actual living organisms or tissues? Explain why both observational and experimental investigations are useful in science.
This problem is common to observational inference, proximal goals, and extrapolation. There are three approaches to solving this: (1) using raw priors; (2) using correlation across units (surrogacy); (3) using correlation across experiments (meta-analysis).
Extrapolation is the tool for forecasting: predicting what hasnt happened yet. The further you extrapolate from observed data, the more uncertainty accumulates. A trend that holds perfectly within your data range may bend, flatten, or reverse just beyond it.
In sum, experimental studies are very useful to infer causal conclusions, but extrapolation of the results to the target population can be problematic. In what follows, two theories will be discussed that address the problem of extrapolation: one by Steel (2008) and one by Guala (2003, 2005).
Researchers measured the number of colonies of grown bacteria for various concentrations of urine (ml/plate). The scope of the model that is, the range of the x values was 0 to 5.80 ml/plate. The researchers obtained the following estimated regression equation:
