83 Detecting quantitative traits in genes. In gene therapy, it is important to know the location of a gene for a disease on the genome (genetic map). Although many genes yield a specific trait (e.g., disease or not), others cannot be categorized, since they are quantitative in nature (e.g., extent of disease). Researchers at the University of North Carolina at Wilmington developed statistical models that link quantitative genetic traits to locations on the genome

( Chance , Summer 2006). The extent of a certain disease is determined by the absence (A) or presence (B) of a gene marker at each of two locations, L1 and L2, on the genome.
For example, AA represents absence of the marker at both locations, while AB represents absence at location L1, but presence at location L2.

a. How many different gene marker combinations are possible at the two locations?

b. Using dummy variables, write a model for extent of the disease, y , as a function of gene marker combination.

c. Interpret the b -values in the model you wrote in part b.

d. Give the null hypothesis for testing whether the overall model from part b is statistically useful for predicting extent of the disease, y .