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:

Log(edges) 1.1 1.5 1.7 1.9 2.0 2.1 Log(time) .30 .50 .55 .52 .85 .98 Log(edges) 2.2 2.3 2.7 2.8 3.0 3.3 Log(time) 1.10 1.00 1.18 1.45 1.65 1.84 Log(edges) 3.5 3.8 4.2 4.3 Log(time) 2.05 2.46 2.50 2.76

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

n 5 20 SSE 5 30.1033 SST 5 102.3922 VO2max 5 3.15 bˆ

1 5 .6566 bˆ

3 5 2.0996 2.0996x 3 2 .0080x 4 y 5 3.5959 1 .6566x 1 1 .0096x 2 x x 3 5 1-mile walk time (min) 4 5 x x male 5 1), 2 5 weight (lb), 1 5 gender (female 5 0, y 5 VO2max

b. What probabilistic model for relating time to 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.