1. A solid-fuel rocket propellant loses weight after it is produced. The following data are available:

Months since Production, x; Weight Loss, y (kg)

0.25 ; 1.42

0.50 ; 1.39

0.75 ; 1.55

1.00 ; 1.89

1.25 ; 2.43

1.50 ; 3.15

1.75 ; 4.05

2.00 ; 5.15

2.25 ; 6.43

2.50 ; 7.89

a. Fit a second-order polynomial that expresses weight loss as a function of the number of months since production.

b. Test for significance of regression.

c. Test the hypothesis H0: b2 = 0. Comment on the need for the quadratic term in this model.

d. Are there any potential hazards in extrapolating with this model?