correlation-coefficient matrix for all pairs of variables in table A. 

 Inasmuch as r±^ is the same as rjj_ the matrix is symmetrical and only 

 half of it need be examined. The diagonal in table D carries the value 

 1.0 for all entries, and merely means that any variable correlated with 

 itself always has r = 1. The top row of the table has the correlation 

 coefficients of Y with each X in turn, and the relation between the values 

 in table B and the corresponding r's in table D is that the 63.1'^ listed 



opposite mean grain size in table B is the same as 100 rYj^j_'^ 



(-.795)2 = 



100 



%, which agrees within rounding error. 



Table D. -Correlation Matrix For All Pairs of Variables In Table A. 



-ij 



Slope Mean 

 Grain 

 Size 



Wave 

 Period 



Wave 

 Height 



Angle 

 of Wave 

 Approach 



Still- 

 Water 

 Depth 





1.00 -.795 



.10i+ 



-.^87 



-.238 



.228 



Slope 



1.000 



.062 



.205 



Ul9 



-.060 



Mean Grain Size 





1.000 



-.0^9 



-.035 



-.356 



Wave Period 







1.000 



-.217 



-.305 



Wave Height 









1.000 



-.222 



Angle Wave App. 



Note: Attention is called to 

 correlation between 



negative 







1.000 



Still-Water Depth 



and S g wtiich l> exp 



lained on p. 45 











The most interesting parts of table D are the linear relations 

 among the Xs in this subset of data. For example, ^xiXQ^ between grain 

 size and angle of wave approach, is + 0.^+19, the largest r in any row 

 other than the first. This correlation with at least one of the process 

 elements is perhaps to be expected, considering that mean grain size is 

 itself in general dependent in part on shore process elements. For a set 

 of data having only l8 observations, any r less than about O.to is of 

 doubtful significance. 



The lack of strong correlations among the variables (except for 

 mean grain size and slope) merely means that the linear relations among 

 the variables are "^eak, and neither the correlation table nor the re- 

 gression results gives any direct information on non-linear relations 

 that may occur. The problem of non-linearity is always present in linear 

 analysis, and it will be examined in the next section of this paper, where 

 an extension of the linear model is described that permits examination 



17 



