Study of tree frogs. Refer to the Experimen- tal Zoology study of the optomotor responses of tree frogs, Exercise 5.9 (p. 271). Recall that the researchers modeled the light intensity at which optomotor response was ?rst observed (y) as a function of spectral wavelength (x). In the solution to the exercise you hypothesized the third-order model, E(y) = β0 + β1x + β2x2 + β3x3. Suppose data on n = 10 tree frogs were collected, with spectral wavelength (measured in microns) set at x = 1 for the ?rst frog, x = 2 for the second, x = 3 for the third,... , and x = 10 for the 10th frog.
(a) Demonstrate the potential for round-off errors in the parameter estimates by ?nding the cor- relation between x and x2,x and x3, and x2 and x3.
(b) Provide a formula for the coded independent variable u that will reduce level of multi- collinearity in the independent variables.
(c) Refer to part b. Find the correlation between u and u2, u and u3, and u2 and u3. What do you observe? Is the level of correlation reduced for all three pairs?