Feeding habits of fish. Refer to the Brain and Behavior Evolution (Apr. 2000) study of the...

Feeding habits of fish. Refer to the Brain and Behavior Evolution (Apr. 2000) study of the feeding behavior of black-bream fish, presented in Exercise.

Feeding behavior of fish. Zoologists at the University of Western Australia conducted a study of the feeding behavior of black bream (a type of fish) spawned in aquariums. ( Brain, Behavior and Evolution , April 2000). In one experiment, the zoologists recorded the number of aggressive strikes of two black bream feeding at the bottom of the aquarium in the 10-minute period following the addition of food. The number of strikes and age of the fish (in days) were recorded approximately each week for nineweeks, as shown in the table above. The data are saved in the BLACKBREAM file.

a. Construct a scatterplot of the data, with number of strikes on the y -axis and age of the fish on the x -axis.

---

b. Examine the scatterplot of part a. Do you detect a trend?

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 in the next column. These data are saved in the BLACKBREAM file.

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 b n 0 if possible.

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

Based on Shand, J., et al. “Variability in the location of the retinal ganglion cell area centralis is correlated with ontogenetic changes in feeding behavior in the Blackbream, Acanthopagrus ‘butcher’.” Brain and Behavior , Vol. 55, No. 4, Apr. 2000.

---

d. Give a practical interpretation of the value of  if possible.

---

e. Test H0: β1 = 0 versus H0: β1 < 0, using α =.10. Interpret the result.

[Note: Starred (*) exercises are from the optional section in this chapter.] f. Find Spearman’s rank correlation coefficient relating number of strikes (y) to age (x).

[Note: Starred (*) exercises are from the optional section in this chapter.] g. Test whether number of strikes (y) and age (x) are negatively rank correlated. Use α =.01.