A. Evaluate the residuals from the analysis of covariance you performed in Problem 11.9. Do they meet the assumption of a linear relationship between the response, F, and the covariate, L? If not, reformulate the problem to conduct an analysis of covariance, while accounting for a nonlinearity. B. Test the assumption of parallel relationships between F and L (line or curve, depending on the result of part A of this problem). Are the lines (or curves) parallel? If not, how do you interpret the analysis of these data?
Problem 11.9
There are many forms of heart disease, most of which eventually lead to heart failure, a condition in which the heart does not pump strongly enough to serve the needs of the body. Presumably, the dysfunction of the heart has its roots in the dysfunction of the cardiac muscle cells that make up the heart. Vahl and colleagues* studied cardiac muscle cells isolated from both normal human hearts and human hearts that were in failure due to dilated cardiomyopathy (DCM). One hypothesis they studied was that the inability of the failing heart to respond to increased return of blood to the heart, by a property known as the Frank–Starling mechanism (after the early cardiovascular scientists who first described this property), had its origin in a depression of the force-length relation of the cardiac muscle. Thus, they studied how force, F, related to muscle length (normalized to the length that produced maximum force, Lmax , by computing L/Lmax ), L, in cells isolated from two groups of hearts, G: those from normal hearts and those from DCM hearts. Is there evidence of reduced force production in DCM hearts, compared to normal, when accounting for length, L, as a covariate?