Consider the stack loss data in Exercise 12-20.

(a) Calculate 95% confidence intervals on each regression coefficient.

(b) Calculate a 95% confidence interval on mean stack loss when x₁ = 80, x₂ = 25 and x₃ = 90.

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

(d) Calculate a 95% confidence interval and a 95% prediction interval on stack loss when x₁ = 80, x₂ = 19, and x₃ = 93. Compare the widths of these intervals to those calculated in parts (b) and (c). Explain any differences in widths.

Exercise 12-20

An article in Technometrics (1974, Vol. 16, pp. 523€“531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow x₁, temperature x₂, and acid concentration x₃.

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y = 42, 37, 37, 28, 18, 18, 19, 20, 15, 14, 14, 13, 11, 12, 8, 7, 8, 8, 9, 15, 15 x, = 80, 80, 75, 62, 62, 62, 62, 62, 58, 58, 58, 58, 58, 58, 50, 50, 50, 50, 50, 56, 70 x, = 27, 27, 25, 24, 22, 23, 24, 24, 23, 18, 18, 17, 18, 19, 18, 18, 19, 19, 20, 20, 20 x, = 89, 88, 90, 87, 87, 87, 93, 93, 87, 80, 89, 88, 82, 93, 89, 86, 72, 79, 80, 82, 91