8.21 SIMPLE LINEAR REGRESSION - ESTIMATION OF THE PARAMETERS OF THE W-L RELATION AND GROWTH PARAMETERS (FORD-WALFORD, GULLAND AND HOLT AND STAMATOPOULOS AND CADDY)

(7.2)

GROUP I

Consider the following 10 pairs of values of x and y:

1. Estimate the constants A and B of the straight line.

2. Estimate the values of Y corresponding to the given values of x.

3. Calculate the determination coefficient r².

4. Draw a graph with the observed values and with the estimated line. Observe the adjustment and say if you consider the linear model adequate.

GROUP II

The data presented on the following table represent the individual weights by length class of European anglerfish, Lophius budegassa samples from the Iberic coast in 1994.

1. Using the simple linear regression model, estimate the parameters of the weight-length relation for this stock, considering that W_central = W_mean. (Notice that the ln W_central is linear to the ln L_central).

GROUP III

The data presented in the following table represent the mean length (cm) of the individuals at the beginning of the age (years), obtained from direct age reading of the individuals of the stock of European anglerfish, Lophius budegassa, (ICES Div. VIIIc and IXa), Section 8.7

From this data and using the simple linear regression model, estimate the growth parameters K and L_∞ with the expressions:

1. Ford-Walford (1933-1946)

2. Gulland and Holt (1959)

3. Stamatopoulos and Caddy (1989). (The expressions for 1), 2) and 3), were studied in the Chapter concerning Individual Growth).

4. Comment on the results obtained in the previous questions with the values of the parameters given in Section 8.7.