An article in Technometrics (1974, Vol. 16, pp. 523–531) considered the following stack-loss data from a plant oxidizing

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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.
y = 42, 37, 37, 28, 18, 18, 19, 20, 15, 14, 14, 13, 11, 12, 8, 7, 8, 8, 9, 15, 15
x1 = 80, 80, 75, 62, 62, 62, 62, 62, 58, 58, 58, 58, 58, 58, 50, 50, 50, 50, 50, 56, 70
x2 = 27, 27, 25, 24, 22, 23, 24, 24, 23, 18, 18, 17, 18, 19, 18, 18, 19, 19, 20, 20, 20
x3 = 89, 88, 90, 87, 87, 87, 93, 93, 87, 80, 89, 88, 82, 93, 89, 86, 72, 79, 80, 82, 91
(a) Fit a linear regression model relating the results of the stack loss to the three regressor variables.
(b) Estimate σ2.
(c) Find the standard error se(βj).
(d) Use the model in part (a) to predict stack loss when x1 = 60, x2 = 26, and x3 = 85.