An article in Optical Engineering (“Operating Curve Extraction of a Correlator’s Filter,” Vol. 43, 2004, pp.

2775–2779) reported the use of an optical correlator to perform an experiment by varying brightness and contrast. The resulting modulation is characterized by the useful range of gray levels. The data are shown here:

Brightness (%): 54 61 65 100 100 100 50 57 54 Contrast (%): 56 80 70 50 65 80 25 35 26 Useful range (ng): 96 50 50 112 96 80 155 144 255

(a) Fit a multiple linear regression model to these data.

(b) Estimate and the standard errors of the regression coefficients.

(c) Test for significance of and

(d) Predict the useful range when and

. Construct a 95% PI.

(e) Compute the mean response of the useful range when and Compute a 95% CI.

(f) Interpret parts

(d) and

(e) and comment on the comparison between the 95% PI and 95% CI.