Scenic beauty of pines. Arti?cial Intelligence (AI) Applications (January 1993) discussed the use of computer-based technologies in building explana- tion systems for regression models. As an example, the authors presented a model for predicting the scenic beauty (y) of southeastern pine stands (mea- sured on a numeric scale) as a function of age (x1) of the dominant stand, stems per acre (x2) in trees, and basal area (x3) per acre in hardwoods. A user of the AI system simply inputs the values of x1, x2, and x3, and the system uses the least squares equation to predict the scenic beauty (y) value.

(a) The AI system generates information on how each independent variable can be manipulated to effect changes in the dependent variable. For example, ‘‘If all else were held constant in the stand, allowing the age (x1) of the dominant trees in the stand to mature by 1 year will increase scenic beauty (y).'' From what portion of the regression analysis would the AI system extract this type of information?

(b) The AI system is designed to check the values of the input variables (x1, x2, and x3) with the sample data ranges. If the input data value is ‘‘out-of-range,'' a warning is issued about the potential inaccuracy of the predicted y-value. Explain the reasoning behind this warning.