Exercise 15 of Section 12.2 included Minitab output for a regression of flexural strengt...

Exercise 15 of Section 12.2 included Minitab output for a regression of flexural strength of concrete beams on modulus of elasticity.

a. Use the output to calculate a confidence interval with a confidence level of 95% for the slope β₁ of the population regression line, and interpret the resulting interval.

b. Suppose it had previously been believed that when modulus of elasticity increased by 1 GPa, the associated true average change in flexural strength would be at most .1 MPa. Does the sample data contradict this belief? State and test the relevant hypotheses.

Reference exercise 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.

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.