165 Genetics of a brain disease. Spinocerebellar ataxia type 1 (SCA1) is an inherited neurodegenerative disorder characterized by dysfunction of the brain. From a deoxyribonucleic acid (DNA) analysis of SCA1 chromosomes, researchers discovered the presence of repeat gene sequences ( Cell Biology , Feb. 1995). In general, the more repeat sequences observed, the earlier was the onset of the disease (in years of the person’s age). The scatterplot (next column) shows this relationship for data collected on 113 individuals diagnosed with SCA1.

a. Suppose you want to model the age y of onset of the disease as a function of number x of repeat gene sequences in SCA1 chromosomes. Propose a quadratic model for y .

b. Will the sign of b2 in the model you proposed in part a be positive or negative? Base your decision on the results shown in the scatterplot.

c. The researchers reported a correlation of r = -.815 between age and number of repeats.

Since r 2 = (-.815)2 = .664, they concluded that about “66% of the variability in the age of onset can be accounted for by the number of repeats.”

Does this statement apply to the quadratic model E(y) = b0 + b1 x + b2 x2? If not, give the equation of the model for which it does apply.

Transcribed Image Text:

Scatterplot for Exercise 165 Age of onset 80 60 4 40 20 0 40 50 60 70 80 90 Number of repeats