Relation of eye and head movements. How do eye and head movements relate to body movements when a person reacts to a visual stimulus? Scientists at the California Institute of LO9 

Technology designed an experiment to answer this question and reported their results in Nature (Aug. 1998). Adult male rhesus monkeys were exposed to a visual stimulus (i.e., a panel of light-emitting diodes), and their eye, head, and body movements were electronically recorded. In one variation of the experiment, two variables were measured: active head movement (x, percent per degree) and body- plus-head rotation (y, percent per degree). The data for n = 39 trials were subjected to a simple linear regression analysis, with the following results: b n 1 = .88, sbn 1

= .14

a. Conduct a test to determine whether the two variables, active head movement x and body-plus-head rotation y, are positively linearly related. Use a = .05.

b. Construct and interpret a 90% confidence interval for b1.

c. The scientists want to know whether the true slope of the line differs significantly from 1. On the basis of your answer to part

b, make the appropriate inference.

tit occupancy x (i.e., the percentage of nest boxes occupied by tits) at each plot. Consider the simple linear regression model E1y2 = b0 + b1x.
Plot Number of Flycatchers Killed y Nest Box Tit Occupancy x (%)
1 0 24 2 0 33 3 0 34 4 0 43 5 0 50 6 1 35 7 1 35 8 1 38 9 1 40 10 2 31 11 2 43 12 3 55 13 4 57 14 5 64 Based on Merila, J., and Wiggins, D. A. “Interspecific competition for nest holes causes adult mortality in the collard flycatcher.” The Condor, Vol.
97, No. 2, May 1995, p. 449 (Figure 2), Cooper Ornithological Society.

a. Plot the data in a scatterplot. Does the frequency of flycatcher casualties per plot appear to increase linearly with increasing proportion of nest boxes occupied by tits?

b. Use the method of least squares to find the estimates of b0 and b1. Interpret their values.

c. Test the utility of the model, using a = .05.

d. Find r and r2 and interpret their values.

e. Find s and interpret the result.

f. Do you recommend using the model to predict the number of flycatchers killed? Explain.