Solved: Values of modulus of elasticity (MOE, the ratio of stress,i.e., force per unit

Chapter 12, Problem 15

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Values of modulus of elasticity (MOE, the ratio of stress,i.e., force per unit area, to strain, i.e., deformation per unitlength, in GPa) and flexural strength (a measure of the abilityto resist failure in bending, in MPa) were determined fora sample of concrete beams of a certain type, resulting in thefollowing data (read from a graph in the article Effects ofAggregates and Microfillers on the Flexural Properties ofConcrete, Magazine of Concrete Research, 1997: 8198):MOE 29.8 33.2 33.7 35.3 35.5 36.1 36.2Strength 5.9 7.2 7.3 6.3 8.1 6.8 7.0MOE 36.3 37.5 37.7 38.7 38.8 39.6 41.0Strength 7.6 6.8 6.5 7.0 6.3 7.9 9.0MOE 42.8 42.8 43.5 45.6 46.0 46.9 48.0Strength 8.2 8.7 7.8 9.7 7.4 7.7 9.7MOE 49.3 51.7 62.6 69.8 79.5 80.0Strength 7.8 7.7 11.6 11.3 11.8 10.7a. 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 determinedby the value of MOE? Explain.c. Use the accompanying Minitab output to obtain theequation of the least squares line for predictingstrength from modulus of elasticity, and then predictstrength for a beam whose modulus of elasticity is 40.Would you feel comfortable using the least squaresline to predict strength when modulus of elasticity is100? Explain.d. What are the values of SSE, SST, and the coefficient ofdetermination? Do these values suggest that the simplelinear regression model effectively describes the relationshipbetween the two variables? Explain.

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