(7.2)
GROUP I
Consider the following 10 pairs of values of x and y:
x_{i} 
2 
6 
7 
8 
11 
15 
16 
18 
19 
21 
y_{i} 
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 r^{2}.
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.
L_{i} (cm) 

L_{i} (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 weightlength 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
T 
L_{t} 
t 
L_{t} 
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. FordWalford (19331946)
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.