11-13. 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. Table E11-4 provides 20 observations. (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 inter- cept in the simple linear regression model. Find an estimate of o (c) Estimate the mean shear strength of a motor made from propellant that is 20 weeks old. (d) Obtain the fitted values y, that correspond to each observed value y. Plot , versus y, 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? 11-57. Refer to the data in Exercise 11-13 on rocket motor shear strength y and propellant age x. Find a 95% confi- dence interval on each of the following: (a) Slope B, (b) Intercept Bo (c) Mean shear strength when age x = 20 weeks (d) Find a 95% prediction interval on shear strength when age x = 20 weeks. TABLE E11-4 Propellant Data Observation Strength y (psi) Age x (weeks) Number 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 2575.00 2.50 2357.90 7.50 2277.70 11.00 2165.20 13.00 2399.55 3.75 1779.80 25.00 2336.75 9.75 1765.30 22.00 2053.50 18.00 2414.40 6.00 2200.50 12.50 2654.20 2.00 1753.70 21.50 8 9 10 11 12 13 14 15 16 17 18 19 20