Final answer:
The best definition of extrapolation is the extension of a trend or pattern beyond known data. It is utilized in statistical modeling, such as regression analysis, to predict future data points. Outliers, which are more than two standard deviations from the regression line, should be carefully considered in extrapolation.
Step-by-step explanation:
The best definition of extrapolation among the options provided is: 1) Extending a trend or pattern beyond the known data. Extrapolation involves applying mathematical methods to predict future trends or values for a dataset based on its existing pattern. It is commonly used in various forms of statistical analyses and modeling, including regression analysis.
In terms of identifying outliers, a rule of thumb for evaluating if a given value in a data set is an outlier is to check if the point lies more than two standard deviations away from the predicted value on a least squares regression line. Outliers can significantly affect the results of an extrapolation because they might not follow the same trend as the rest of the data.
Extrapolation is a form of inference used to forecast specific results from general principles or laws and is essential in fields like climate change studies. For instance, scientists can extrapolate to predict changes in plant and animal distribution due to a warmer climate.