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

(a) Calculate 99% confidence intervals on each regression coefficient.

(b) Calculate a 99% confidence interval on mean useful range when brightness = 70 and contrast = 80.

(c) Calculate a prediction interval on useful range for the same values of the regressors used in part (b).

(d) Calculate a 99% confidence interval and a 99% a prediction interval on useful range when brightness = 50 and contrast = 25. Compare the widths of these intervals to those calculated in parts (b) and (c). Explain any differences in widths.

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