A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond y is thought to be a linear function of the age of the propellant x when the motor is cast. Twenty observations are shown in the table that follows.

(a) Draw a scatter diagram of the data. Does the straight-line regression model seem to be plausible?

(b) Find the least squares estimates of the slope and intercept in the simple linear regression model.

(c) Estimate the mean shear strength of a motor made from propellant that is 20 weeks old.

(d) Obtain the fitted values that correspond to each observed value yi. Plot versus yi, and comment on what this plot would look like if the linear relationship between shear strength and age were perfectly deterministic (no error).
Does this plot indicate that age is a reasonable choice of regressor variable in this model?

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Observation Strength y Age.x Number (psi) (weeks) 1 2158.70 15.50 2 1678.15 23.75 3 2316.00 8.00 4 2061.30 17.00 5 2207.50 5.00 6 1708.30 19.00 7 1784.70 24.00 8 2575.00 2.50 9 2357.90 7.50 10 2277.70 11.00 11 2165.20 13.00 12 2399.55 3.75 13 1779.80 25.00 14 2336.75 9.75 15 1765.30 22.00 16 2053.50 18.00 17 2414.40 6.00 18 2200.50 12.50 19 2654.20 2.00 20 1753.70 21.50