An article in Optical Engineering [Operating Curve Extraction of a Correlators Filter (2004, Vol. 43, pp. 27752779)] reported on the use of an optical correlator

An article in Optical Engineering [€œOperating Curve Extraction of a Correlator€™s Filter€ (2004, Vol. 43, pp. 2775€“2779)] reported on 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 follow:

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

(b) Estimate σ².

(c) Compute the standard errors of the regression coefficients.

(d) Predict the useful range when brightness = 80 and contrast = 75.

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