Refer to the Brain and Behavior Evolution (Apr. 2000) study of the feeding behavior of black-bream fish, presented in Exercise 2.162 (p. 96). Recall that the zoologists recorded the number of aggressive strikes of two black-bream fish feeding at the bottom of an aquarium in the 10-minute period following the addition of food. The table listing the weekly number of strikes and the age of the fish (in days) is reproduced below.
Week__________ Number of Strikes __________ Age of Fish (days)
1 ........................... 85........................... 120
2........................... 63 ........................... 136
3...........................34 ........................... 150
4 ...........................39 ...........................155
5 ...........................58 ...........................162
6 ...........................35 ...........................169
7 ...........................57 ...........................178
8 ...........................12 ...........................184
9 ...........................15 ...........................190
a. Write the equation of a straight-line model relating number of strikes (y) to age of fish (x).
b. Fit the model to the data by the method of least squares and give the least squares prediction equation.
c. Give a practical interpretation of the value of β0 if possible.
d. Give a practical interpretation of the value of β1 if possible.
e. Test H0: β1 = 0 versus Ha: β1 < 0, using α = .10. Interpret the result.