Plasma etching is essential to the fine-line pattern transfer in semiconductor processes. The article "Ion Beam- Assisted Etching of Aluminum with Chlorine" (J. of the 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, (x2i = 70.50, (xiyi = 902.25, (y2i = 11,626.75, 0 = 6.448718, 0 = 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 µY.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.

x 1.5 .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