| When attempting to predict a single observation resulting from a new regressor variable case, it is evident that the farther from the center of the historical data base the prediction is made, the larger the uncertainty of the results coming from the regression model. This uncertainty can be expressed in terms of prediction bounds, which, in the case of a single regressor variable, appears to form hyperbolas above and below the graph of the regression line, widening as the regressor variable values move away from the center of the data base. Explicit formulas for the prediction bounds are known only when the modeling relationship has been derived using classical linear regression (i.e., "Ordinary Least Squares" or OLS), and these formulas are known to describe hyperbolas. When working with relationships derived by non-OLS regression, no explicit formulas currently exist. Bootstrap random sampling has been suggested as a method for deriving an approximation of the hyperbolic prediction bounds. It has been hypothesized that approximate algebraic formulas for these prediction bounds can be derived by fitting a rotated and translated general-form hyperbola to the bootstrap results. In addition to examining the prediction bounds, inferences about the regression parameters are made to determine their statistical significance. Thus a similar investigation into utilizing bootstrap sampling to approximate confidence bounds on the parameters is done for the non-OLS situation, as explicit formulas for these confidence bounds are already known in OLS. |
