Question 5 Regression (20 Marks)

In recent years, fishermen have suffered financial hardship because of shortened fishing seasons, reduced catches and lower market prices. Moreover, fishermen have complained about price fluctuations and have called for a system of minimum prices. One suggestion was that the size of the catch had an immediate impact on prices and that this relationship should be clarified before potential solutions were discussed.

In an investigation of this issue, a random 12-week-period was selected to study the price of fish ($ per kg.) versus average daily catch (in 100 kgs). The data collected were analysed, and the following results were obtained:

Variable	Coefficient	Standard deviation	p
Constant	2.6344	0.3883	0.000
Catch (in 100 kgs)	-0.0321	0.0009	0.004

R² = 0.42

(a) What is the estimated regression equation/line? (4 marks)

(b) Interpret the estimated catch coefficient in terms of size, direction and significance (4 marks)

(c) Interpret the R² value and implications for future research. (4 marks)

(d) Would you conclude that the size of the catch is significantly related to the price of fish? Why/Why not? (4 marks)

(e) What is the predicted level of the price if the daily catch is 7,500 kg. (4 marks)