50 -i 



40 



<fc 



5 



§ 30 



ki 



1 



Z 



200 -i 



234.31- 20.1 U+0.43X 



= -12.28 + I.IIX 

 = 0.47 



15.0 20.0 25.0 



WATER TEMPERATURE CO 



30.0 



Figure 1. — Mean number of Arenaeua cribrarius per collection ver- 

 sus mean water temperature for surf collections (by months). 



Simple correlation coefficients of monthly averages of 

 environmental variables and monthly average number of 

 specimens per collection in the surf are given in Table 11. 

 Water temperature and its square correlated significant- 

 ly with number of specimens for all species. Height of sea 

 was significantly correlated with occurrence for A. 

 mltchilli and M. littoralis. A significant negative correla- 

 tion existed between salinity and number of specimens 

 for M. menidia. No other correlations were significant. 



Stepwise regression was then undertaken for each 

 species. The list of variables and notation used is con- 

 tained in Table 12. In addition to the stepwise procedure, 

 all independent variables were forced to enter the equa- 

 tion (forward selection) to assess the percentage reduc- 

 tion of the sum of squares of deviations of Y from its 

 mean attributed to regression. 



An examination of residuals (e, = Y ; — Y, ) was con- 

 ducted using the methods of Draper and Smith (1966). In 

 conducting the regression analyses, assumptions were 

 made about e, : errors were independent, had zero mean 

 and a constant variance, and followed a normal distribu- 

 tion. Residuals were examined to see if these assump- 

 tions were violated and to suggest possible transfor- 

 mations of the variables (e.g., squares and cross products 

 of the independent variables). Residuals for the final 

 equations selected for each species were plotted overall, 

 in time sequence, against the fitted values Y- , and 

 against the independent variables X jt , for; = 1, 2, . . . , 

 k. Our assumptions apparently were not violated, with 

 one exception. There appeared to be a time sequence 

 effect for some species when the residuals were ordered 



5.0 10.0 15.0 20.0 25.0 



WATER TEMPERATURE (°C) 



30.0 



Figure 2. — Mean number of Menidia menidia per collection versus 

 mean water temperature for surf collections (by months). 



Table 12.— List of variables and notation for stepwise multiple 

 regression. 



Response variables 







Monthly average number of 





Independent variables 



specimens per collection 





Monthly average 



in the surf 





in the surf 



Y x Arenaeus cribrarius 



x, 



duration of effort (min) 



Y 2 Anchoa mitchilli 



X, 



water temperature (°C) 



V 3 Menidia menidia 



x. 



salinity (%o) 



Y 4 Trachinotus carolinus 



x< 



height of sea (m) 



V 5 Menticirrhus littoralis 



x s 



visibility of Secchi disc (m) 





X, 



square of water temperature 



by month, i.e., long runs of positive residuals followed by 

 runs of negative residuals. A one-sample runs test was 

 used to examine this time sequence effect. Results were 

 not significant. It was concluded that our final equations 

 did not violate the assumptions and no other transfor- 

 mations seemed relevant. 



The summary statistics for the forward selection of six 

 independent variables are given in Tables 13 through 17 

 along with the final equation selected by the stepwise 

 procedure. 



Water temperature (or the square of water 

 temperature) was more highly correlated with occurrence 

 than any of the other independent variables (Table 11). 

 The stepwise procedure was modified to enter water 

 temperature before its square. This modification had lit- 

 tle effect on the results because the correlation between 

 water temperature and its square was high (r = 0.992). 



Table 11.— Simple correlation coefficients of monthly averages (N - 24) of environmental variables 

 and monthly average number of specimens per collection in the surf for five selected species. ('Sig- 

 nificant correlation, P< 0.05; "highly significant correlation, P< 0.01.) 







Water 







Visibility 



Square of 







temper- 





Height 



of 



water 





Duration 



ature 



Salinity 



of sea 



Secchi disc 



temperature 



Species 



(min) 



(°C) 



(%o) 



(m) 



(m) 



i°cy 



Arenaeus cribrarius 



0.080 



0.683** 



0.275 



0.296 



0.082 



0.706** 



Anchoa mitchilli 



-0.104 



0.405* 



0.242 



0.402* 



-0.329 



0.405* 



Menidia menidia 



-0.232 



-0.711** 



-0.495* 



-0.167 



0.056 



-0.667** 



Trachinotus carolinus 



0.237 



0.657** 



0.370 



0.002 



0.149 



0.674** 



Menticirrhus littoralis 



-0.219 



0.497* 



0.208 



0.464* 



-0.113 



0.506* 



13 



