Chapter 13, Problem 68SE

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

1. a. Does a scatterplot of log(time) versus log(edges) suggest an approximate linear relationship between these two variables?
2. 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?
3. c. Summary quantities calculated from the data are

n = 16 ${\displaystyle \sum {x^{\prime }}_i}$ = 42.4 ${\displaystyle \sum {y^{\prime }}_i}$  = 21.69 ${{\displaystyle \sum \left({x^{\prime }}_i\right)}}^2$ = 126.34 ${{\displaystyle \sum \left({y^{\prime }}_i\right)}}^2$ = 38.5305 ${\displaystyle \sum {x^{\prime }}_i}{y^{\prime }}_i$ = 68.640

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.