51. Plasma etching is essential to the ne-line pattern transfer in current semiconductor processes. The article Ion Beam-Assisted Etching of Aluminum with Chlorine (J. Electrochem. Soc., 1985: 2010—

2012) gives the accompanying data (read from a graph) on chlorine ow (x, in SCCM) through a nozzle used in the etching mechanism and etch rate (y, in 100 A/min).

x 1.5 1.5 2.0 2.5 2.5 3.0 3.5 3.5 4.0 y 23.0 24.5 25.0 30.0 33.5 40.0 40.5 47.0 49.0 The summary statistics are xi  24.0, yi 

312.5, , xiyi  902.25, 

11,626.75,  6.448718,  10.602564.

a. Does the simple linear regression model specify a useful relationship between chlorine ow and etch rate?

b. Estimate the true average change in etch rate associated with a 1-SCCM increase in ow rate using a 95% con dence interval, and interpret the interval.

c. Calculate a 95% CI for mY##3.0, the true average etch rate when ow  3.0. Has this average been precisely estimated?

d. Calculate a 95% PI for a single future observation on etch rate to be made when ow  3.0. Is the prediction likely to be accurate?

e. Would the 95% CI and PI when ow  2.5 be wider or narrower than the corresponding intervals of parts

(c) and (d)? Answer without actually computing the intervals.

f. Would you recommend calculating a 95% PI for a ow of 6.0? Explain.

g. Calculate simultaneous CI s for true average etch rate when chlorine ow is 2.0, 2.5, and 3.0, respectively.

Your simultaneous con dence level should be at least 97%.