52. Plasma etching is essential to the fine-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 flow (x, in SCCM) through a nozzle used in the etching mechanism and etch rate (y, in 100 A/min).

The summary statistics are
xi
24.0,
yi
312.5,
x 2 i

70.50,
xi yi
902.25,
y2 i
11,626.75,
ˆ

0
6.448718,

ˆ

1
10.602564.

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

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

c. Calculate a 95% CI for Y
3.0, the true average etch rate when flow
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 flow
3.0. Is the prediction likely to be accurate?

e. Would the 95% CI and PI when flow
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 flow of 6.0? Explain.