In a discussion of the article “Tensile Behavior of Slurry Infiltrated Mat Concrete (SIMCON)” (ACI Materials J., 1998: 77–79), the discussant presented data on y toughness (psi) and aspect ratio. He stated that “a (simple linear) regression analysis clearly shows that the aspect ratio is not a reliable variable that can be used to predict toughness.” The following observations were read from a graph in the article:
a. Why is the relationship between these two variables clearly not deterministic?
b. Fit the simple linear regression model, and state whether you agree with the discussant’s assessment.
c. Even if the y values had been much closer together, so that the model could be judged useful, would there be any way to check model adequacy to decide whether a quadratic regression model would be more appropriate? Explain your reasoning.