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
scatterplot 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
n = 16
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.
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