(c) Calculate a 95% CI for Y · 3.0 , the true average etch rate when flow = 3.0.

Question

(c) Calculate a 95% CI for Y · 3.0, the true average etch rate when flow = 3.0. (Round your answers to three decimal places.)

( , ) 100 A/min

(d) Calculate a 95% PI for a single future observation on etch rate to be made when flow = 3.0. (Round your answers to three decimal places.)

( , ) 100 A/min

Plasma etching is essential to the fine-line pattern transfer in current semiconductor processes. An article 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 23.5 24.5 25.5 29.5 33.5 39.0 40.5 46.5 49.0 The summary statistics are Ex,-24.0,2y,311.5, Ex? = 70.50, = 898.00, -11,519.75,-6.987 179, .-10.358974.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 6.9871795 + 10.358974 x
Sample size: 9
R (correlation coefficient) = 0.97192076
R-sq = 0.94462997
Estimate of error standard deviation: 2.4167456

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

c) 95% CI for Y = 3.0:

(36.018, 40.110) 100 A/ min

d) 95% PI for Y = 3.0:

(31.994, 44.134) 100 A/ min

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 6.9871795 2.653063 0 7 2.6336274 0.0337 Slope 10.358974 0.94792562 0 7 10.928046 <0.0001

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