Chapter 12.4, Problem 52E

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).

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 Σx_i = 24.0, Σy_i = 312.5, $\sum x_i^2=70.50,\sum x_i{y}_i=902.25,\sum y_i^2=11,626.75,{\hat{\beta }}_0=6.448718,{\hat{\beta }}_1=10.602564$.

1. a. Does the simple linear regression model specify a useful relationship between chlorine flow and etch rate?
2. 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.
3. c. Calculate a 95% Cl for μ_Y·3.0, the true average etch rate when flow = 3.0. Has this average been precisely estimated?
4. 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?
5. 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.
6. f. Would you recommend calculating a 95% PI for a flow of 6.0? Explain.