What are the differences between prediction, extrapolation, and interpolation?

The former belongs to the realm of explanatory models, the latter to the realm of predictive analytics. Explanatory models, often involving linear regression, are concerned with explaining a given phenomenon and finding causal relationships between an output (dependent) variable, and a host, often very few, input (independent) variables. The objective is to find a good regression model that fits the data very well which meets the underlying assumption of linear regression. The emphasis here is on hypothesis testing, p-values, confidence intervals,…Once a good model is found, one can use it for estimating the value of the output variable for given values of the input variables. It is OK to estimate an output value based on interpolation, but one must use extreme caution in estimating output values based on extrapolation because the regression model is an explanatory model, not a predictive one.