Tools › Statistics › Regression and Modelling › Regression and Curve Fitting › Example

Montgomery, Peck and Vining Examples 2.1–2.8: shear strength of rocket propellant against propellant age

ToolRegression and Curve Fitting
SourceMontgomery, D. C., Peck, E. A., and Vining, G. G. (2012). Introduction to Linear Regression Analysis, 5th ed. Wiley, Hoboken, NJ. Table 2.1 and Examples 2.1, 2.3, 2.4, 2.7 and 2.8.
LevelUndergraduate

Problem

Twenty rocket motors were tested for the shear strength (psi) of the bond between propellant and liner against the age of the sustainer propellant (weeks). Fit the straight line, test the slope, report R², give the 95 % confidence interval of the mean strength at the mean age 13.3625 weeks and the 95 % prediction interval of a new motor aged 10 weeks.

Inputs to Enter

  • Age x (weeks): 15.50 23.75 8.00 17.00 5.50 19.00 24.00 2.50 7.50 11.00 13.00 3.75 25.00 9.75 22.00 18.00 6.00 12.50 2.00 21.50
  • Strength y (psi): 2158.70 1678.15 2316.00 2061.30 2207.50 1708.30 1784.70 2575.00 2357.90 2256.70 2165.20 2399.55 1779.80 2336.75 1765.30 2053.50 2414.40 2200.50 2654.20 1753.70
  • Model linear with intercept, confidence 95 %, predict at x₀ = 13.3625 (then 10)
Open the Regression and Curve Fitting tool

Answers

  • Example 2.1: ŷ = 2627.82 − 37.15 x; SS_Res = 166,402.65, MS_Res = 9,244.59 (book, with b1 rounded to −37.15; full precision 166,254.86)
  • Example 2.3: t₀ for the slope = −12.85; Example 2.4: R² = 0.9018
  • Example 2.7: 95 % CI of the mean response at x = 13.3625: 2,086.23 to 2,176.57 psi
  • Example 2.8: ŷ(10) = 2,256.32 psi, 95 % prediction interval 2,048.32 to 2,464.32 psi

Notes

Paste the twenty pairs (x first). The book carries the rounded slope into SS_Res and the intervals, so the tool agrees with the printed values to 0.1 % (test_regression.php); the data sums (Σy 42,627.15, S_xx 1,106.56, S_xy −41,112.65, SST 1,693,737.60) agree exactly.

More Examples for This Tool