# 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:

 xi 2 6 7 8 11 15 16 18 19 21 yi 13 40 52 56 78 105 111 130 132 149

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.

 Li (cm) Li (cm) 20- 129 50- 1685 22- 163 52- 1896 24- 219 54- 2107 26- 265 56- 2345 28- 320 58- 2569 30- 397 60- 2848 32- 486 62- 3126 34- 545 64- 3407 36- 664 66- 3700 38- 773 68- 4056 40- 890 70- 4411 42- 1027 72- 4764 44- 1122 74- 5203 46- 1334 76- 5587 48- 1503 78- 5982

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

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

 T Lt t Lt 1 9.2 7 44.4 2 16.5 8 49.0 3 22.9 9 52.3 4 28.8 10 55.0 5 34.7 11 60.8 6 38.6 12 63.4

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.