Feature recognition from surface models of complicated parts is becoming increasingly im...

Feature recognition from surface models of complicated parts is becoming increasingly important in the development of efficient computer-aided design (CAD) systems. The article “A Computationally Efficient Approach to Feature Abstraction in Design-Manufacturing Integration” (J. of Engr. for Industry, 1995: 16–27) contained a graph of log₁₀(total recognition time), with time in sec, versus log₁₀(number of edges of a part), from which the following representative values were read:

a. Does a scatter plot of log(time) versus log(edges) suggest an approximate linear relationship between these two variables?

b. What probabilistic model for relating y = recognition time to x = number of edges is implied by the simple linear regression relationship between the transformed variables?

c. Summary quantities calculated from the data are

Calculate estimates of the parameters for the model in part (b), and then obtain a point prediction of time when the number of edges is 300.