A chemical reaction was run 48 times. In each run, different values were chosen for the temperature in degrees Celsius

(x1), the concentration of the primary reactant (x2), and the number of hours the reaction was allowed to run (x3). The outcome variable (y)

is the amount of product.

a. Construct the multiple regression equation ̂y = b0 + b1x1 + b2x2 + b3x3.

b. A reaction is run at a temperature of 50 degrees Celsius, with the concentration of the primary reactant set to 30, and the reaction is allowed to run for 6 hours. Predict the amount of product produced.

c. Refer to part (b). Construct a 95% confidence interval for the amount produced.

d. Refer to part (b). Construct a 95% prediction interval for the amount produced.

e. What percentage of the variation in the amount of product is explained by the model?

f. Is the model useful for prediction? Why or why not? Use the α = 0.05 level.
g. Test H0: β1 = 0 versus H1: β1 ≠ 0 at the α = 0.05 level. Can you reject H0? Repeat for β2 and β3.

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y x1 x2 x3 y x1 x2 x3 x1 x2 x3 y x1 x2 x3 31.3 50 19 4.0 37.4 60 30 5.0 24.0 60 24 4.0 51.0 80 34 7.5 56.9 90 38 8.0 43.3 60 26 7.0 36.2 50 21 7.0 34.3 60 22 2.5 43.1 70 28 6.5 36.3 70 25 7.5 26.5 50 17 2.0 31.5 60 24 5.0 41.5 70 25 5.5 38.4 70 31 5.5 47.1 80 34 8.5 33.2 60 23 4.0 39.0 60 26 6.5 41.5 60 27 7.5 38.1 70 27 5.5 39.2 60 29 6.5 40.9 70 29 5.0 36.1 60 23 6.0 33.5 60 24 2.5 46.7 70 27 7.5 35.9 60 23 5.5 38.5 60 23 6.0 43.6 70 27 10.0 30.4 70 32 4.0 43.5 70 28 5.5 42.4 60 24 9.0 41.0 80 32 6.5 43.2 60 25 5.5 47.9 80 34 6.5 46.5 70 31 5.5 50.2 50 26 9.0 30.6 60 26 3.5 33.8 70 26 4.5 43.1 80 32 6.0 34.4 50 22 41.1 38.7 70 70 26 8.0 50.8 26 8.0 44.2 88 60 26 10.0 47.9 70 28 4.5 46.2 50 21 50 4.0 43.3 70 28 7.5 80 34. 6.5 10.0 88 32.4 60 22 5.5 35.5 60 22 4.5 22