15. Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data (read from a graph in the article “Effects of Aggregates and Microfillers on the Flexural Properties of Concrete,” Magazine of Concrete Research, 1997: 81–98):

a. Construct a stem-and-leaf display of the MOE values, and comment on any interesting features.

b. Is the value of strength completely and uniquely determined by the value of MOE? Explain.

c. Use the accompanying MINITAB output to obtain the equation of the least squares line for predicting strength from modulus of elasticity, and then predict strength for a beam whose modulus of elasticity is 40. Would you feel comfortable using the least squares line to predict strength when modulus of elasticity is 100? Explain.

Predictor Coef Stdev t-ratio p Constant 3.2925 0.6008 5.48 0.000 mod elas 0.10748 0.01280 8.40 0.000 s
0.8657 Rsq
73.8% Rsq (adj)
72.8%

Analysis of Variance SOURCE DF SS MS F p Regression 1 52.870 52.870 70.55 0.000 Error 25 18.736 0.749 Total 26 71.605

d. What are the values of SSE, SST, and the coefficient of determination? Do these values suggest that the simple linear regression model effectively describes the relationship between the two variables? Explain.