Consider the regression model fit to the gray range modulation data in Exercise 12-19. Use the useful range as the response.

(a) Test for significance of regression using α = 0.05. What is the P-value for this test?

(b) Construct a t-test on each regression coefficient. What conclusions can you draw about the variables in this model? Use α = 0.05.

Exercise 12-19

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:

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